diff --git a/examples/doc.txt b/examples/doc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..086b1828157a019a06e91ef3600b526d098d08b0
--- /dev/null
+++ b/examples/doc.txt
@@ -0,0 +1,19 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser
+ * General Public License v2.1. See the file LICENSE in the top level
+ * directory for more details.
+ */
+
+/**
+ * @defgroup examples EXAMPLES
+ *
+ * @brief Examples of the RcdMathLib
+ *
+ * @details Includes examples of all RcdMathLib's modules.
+ *
+ * @author Zakaria Kasmi
+ *
+ */
diff --git a/examples/example_results/distance_based_test.txt b/examples/example_results/distance_based_test.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3936f35795224267103ccc8e8ad539f8629b03ae
--- /dev/null
+++ b/examples/example_results/distance_based_test.txt
@@ -0,0 +1,4 @@
+**************** Testing the MicroPosMath-Lib!! 03/11/20 12:07:34 ****************
+***************** Distance-based system example *****************
+true position = {1.0000, 3.0000, 0.0000}
+estimated position = {0.9759567, 2.9980380, -0.0421651}
diff --git a/examples/example_results/fsolve_test.txt b/examples/example_results/fsolve_test.txt
new file mode 100644
index 0000000000000000000000000000000000000000..df6a2932bab59e84e6bb11191d83839e39593790
--- /dev/null
+++ b/examples/example_results/fsolve_test.txt
@@ -0,0 +1,35 @@
+**************** Testing the MicroPosMath-Lib!! 03/12/20 12:28:57 ****************
+############ Test Solve Non-linear Algebra Module ############
+
+******************************* f1 ******************************
+iter_num = 7
+x1 = {1.000, 0.000}
+f1(x1) = {0.000, 0.000}
+Damped Newton
+iter_num = 6
+x1 = {1.000, 0.000}
+f1(x1) = {0.000, 0.000}/
+******************************** f2 ******************************/
+iter_num = 8
+x2 = {0.500000000, -0.000000000, -0.523598776}
+f2(x2) = {-0.000, -0.000, 0.000}
+
+Damped Newton
+iter_num = 7
+x2 = {0.500000000, 0.000000000, -0.523598776}
+f2(x2) = {0.000, -0.000, 0.000}/
+******************************** f3 ******************************/
+The minimum rank-value of a matrix is one
+The minimum rank-value of a matrix is one
+The minimum rank-value of a matrix is one
+iter_num = 13
+x2 = {1.000000000, 2.000000000, 4.000000000}
+f3(x3) = {0.000, 0.000, 0.000}
+
+Damped Newton
+The minimum rank-value of a matrix is one
+The minimum rank-value of a matrix is one
+The minimum rank-value of a matrix is one
+iter_num = 13
+x3 = {1.000000000, 2.000000000, 4.000000000}
+f3(x3) = {0.000, 0.000, 0.000}
diff --git a/examples/example_results/givens_test.txt b/examples/example_results/givens_test.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5ffd41c2920b2b6d4768c2876a441a5ad00a083a
--- /dev/null
+++ b/examples/example_results/givens_test.txt
@@ -0,0 +1,94 @@
+**************** Testing the MicroPosMath-Lib!! 03/11/20 15:41:17 ****************
+c = 0.6097
+s = 0.7926
+t = 1.3000
+r = 164.0122
+************ MATRIX A ************
++++++++ Reduced QR-form +++++++
+red_Q = {
+ { 0.3655, -0.4666, 0.2411, -0.1772, 0.0735},
+ { 0.4064, 0.1403, -0.4483, -0.0432, 0.1830},
+ { 0.0570, 0.7001, 0.3279, 0.1421, -0.1997},
+ { 0.4098, -0.2673, 0.3313, 0.6320, -0.3003},
+ { 0.2837, 0.1996, 0.1277, 0.3120, 0.7745},
+ { 0.0437, 0.0461, 0.4879, -0.3315, -0.1537},
+ { 0.1249, 0.1454, 0.3595, -0.2337, 0.1175},
+ { 0.2454, 0.3579, -0.0908, -0.1353, -0.1637},
+ { 0.4296, -0.0454, 0.0366, -0.5136, 0.0494},
+ { 0.4329, 0.0878, -0.3611, 0.0560, -0.4056}
+ };
+
+red_R = {
+ { 2.2290, 1.9717, 1.4557, 0.9569, 1.6050},
+ { 0.0000, 1.2068, 0.4480, 0.0883, 0.5623},
+ { 0.0000, 0.0000, 1.3800, 0.9196, 0.5670},
+ { 0.0000, 0.0000, 0.0000, -0.9920, -0.1006},
+ { 0.0000, 0.0000, 0.0000, 0.0000, -0.5446}
+ };
++++++++ Full QR-form +++++++
+full_Q = {
+ { 0.3655, -0.4666, 0.2411, -0.1772, 0.0735, -0.5842, -0.2468, -0.0226, -0.3884, 0.0134},
+ { 0.4064, 0.1403, -0.4483, -0.0432, 0.1830, 0.2307, 0.0058, -0.5093, -0.3444, -0.3841},
+ { 0.0570, 0.7001, 0.3279, 0.1421, -0.1997, -0.4205, -0.2010, -0.3276, 0.0900, -0.0797},
+ { 0.4098, -0.2673, 0.3313, 0.6320, -0.3003, 0.2179, 0.1553, 0.0152, 0.1305, -0.2690},
+ { 0.2837, 0.1996, 0.1277, 0.3120, 0.7745, 0.0980, -0.1750, 0.1995, 0.0728, 0.2844},
+ { 0.0437, 0.0461, 0.4879, -0.3315, -0.1537, 0.6096, -0.4048, -0.0924, -0.2382, 0.1537},
+ { 0.1249, 0.1454, 0.3595, -0.2337, 0.1175, 0.0000, 0.8246, -0.0890, -0.2180, 0.1738},
+ { 0.2454, 0.3579, -0.0908, -0.1353, -0.1637, 0.0000, 0.0000, 0.7591, -0.2801, -0.3220},
+ { 0.4296, -0.0454, 0.0366, -0.5136, 0.0494, 0.0000, 0.0000, 0.0000, 0.7194, -0.1685},
+ { 0.4329, 0.0878, -0.3611, 0.0560, -0.4056, 0.0000, 0.0000, 0.0000, 0.0000, 0.7119}
+ };
+
+full_R = {
+ { 2.2290, 1.9717, 1.4557, 0.9569, 1.6050},
+ { 0.0000, 1.2068, 0.4480, 0.0883, 0.5623},
+ { 0.0000, 0.0000, 1.3800, 0.9196, 0.5670},
+ { 0.0000, 0.0000, 0.0000, -0.9920, -0.1006},
+ { 0.0000, 0.0000, 0.0000, 0.0000, -0.5446},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000}
+ };
+************ MATRIX B ************
++++++++ Reduced QR-form +++++++
+red_Q = {
+ { 0.4850, -0.1030, 0.1615, -0.7383, -0.3664, 0.1868, -0.1174},
+ { 0.5392, 0.1218, -0.7120, 0.0999, 0.3028, 0.2911, 0.0310},
+ { 0.0756, 0.5787, -0.0892, 0.3233, -0.7370, 0.0520, 0.0317},
+ { 0.5438, -0.4235, 0.4087, 0.5775, -0.0739, 0.0615, -0.1232},
+ { 0.3765, 0.2893, 0.0412, -0.0728, 0.1655, -0.8579, -0.0650},
+ { 0.0580, 0.5906, 0.4531, -0.0053, 0.4217, 0.3564, -0.3709},
+ { 0.1658, 0.1666, 0.2913, -0.0392, 0.1419, 0.1047, 0.9095}
+ };
+
+red_R = {
+ { 1.6798, 1.4417, 1.4571, 1.3083, 0.6039, 1.4164, 1.4034},
+ { 0.0000, 1.4789, 0.6963, 1.0763, 0.4720, 0.1135, 0.5475},
+ { 0.0000, 0.0000, 1.0233, 0.0774, -0.0054, 0.3097, 0.2588},
+ { 0.0000, 0.0000, 0.0000, 0.6779, -0.2445, 0.0929, -0.2062},
+ { 0.0000, 0.0000, 0.0000, 0.0000, -0.6319, -0.1504, 0.2334},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.5978, 0.3366},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.2569}
+ };
++++++++ Full QR-form +++++++
+full_Q = {
+ { 0.4850, -0.1030, 0.1615, -0.7383, -0.3664, 0.1868, -0.1174},
+ { 0.5392, 0.1218, -0.7120, 0.0999, 0.3028, 0.2911, 0.0310},
+ { 0.0756, 0.5787, -0.0892, 0.3233, -0.7370, 0.0520, 0.0317},
+ { 0.5438, -0.4235, 0.4087, 0.5775, -0.0739, 0.0615, -0.1232},
+ { 0.3765, 0.2893, 0.0412, -0.0728, 0.1655, -0.8579, -0.0650},
+ { 0.0580, 0.5906, 0.4531, -0.0053, 0.4217, 0.3564, -0.3709},
+ { 0.1658, 0.1666, 0.2913, -0.0392, 0.1419, 0.1047, 0.9095}
+ };
+
+full_R = {
+ { 1.6798, 1.4417, 1.4571, 1.3083, 0.6039, 1.4164, 1.4034},
+ { 0.0000, 1.4789, 0.6963, 1.0763, 0.4720, 0.1135, 0.5475},
+ { 0.0000, 0.0000, 1.0233, 0.0774, -0.0054, 0.3097, 0.2588},
+ { 0.0000, 0.0000, 0.0000, 0.6779, -0.2445, 0.0929, -0.2062},
+ { 0.0000, 0.0000, 0.0000, 0.0000, -0.6319, -0.1504, 0.2334},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.5978, 0.3366},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.2569}
+ };
diff --git a/examples/example_results/householder_test.txt b/examples/example_results/householder_test.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4ffb28a2f6d42b08d9448ab283cdaed40ba24f09
--- /dev/null
+++ b/examples/example_results/householder_test.txt
@@ -0,0 +1,56 @@
+**************** Testing the MicroPosMath-Lib!! 03/10/20 11:01:14 ****************
+Q_red = {
+ {-0.3655, 0.4666, -0.2411, 0.1772, -0.0735},
+ {-0.4064, -0.1403, 0.4483, 0.0432, -0.1830},
+ {-0.0570, -0.7001, -0.3279, -0.1421, 0.1997},
+ {-0.4098, 0.2673, -0.3313, -0.6320, 0.3003},
+ {-0.2837, -0.1996, -0.1277, -0.3120, -0.7745},
+ {-0.0437, -0.0461, -0.4879, 0.3315, 0.1537},
+ {-0.1249, -0.1454, -0.3595, 0.2337, -0.1175},
+ {-0.2454, -0.3579, 0.0908, 0.1353, 0.1637},
+ {-0.4296, 0.0454, -0.0366, 0.5136, -0.0494},
+ {-0.4329, -0.0878, 0.3611, -0.0560, 0.4056}
+ };
+R_red = {
+ {-2.2290, -1.9717, -1.4557, -0.9569, -1.6050},
+ { 0.0000, -1.2068, -0.4480, -0.0883, -0.5623},
+ { 0.0000, 0.0000, -1.3800, -0.9196, -0.5670},
+ { 0.0000, 0.0000, 0.0000, 0.9920, 0.1006},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.5446}
+ };
+Q = {
+ {-0.3655, 0.4666, -0.2411, 0.1772, -0.0735, -0.3790, -0.2908, -0.0056, -0.5685, -0.0482},
+ {-0.4064, -0.1403, 0.4483, 0.0432, -0.1830, 0.2779, 0.0922, -0.3942, -0.1889, -0.5495},
+ {-0.0570, -0.7001, -0.3279, -0.1421, 0.1997, -0.3499, -0.3030, -0.3348, -0.0700, -0.0879},
+ {-0.4098, 0.2673, -0.3313, -0.6320, 0.3003, 0.1042, 0.1405, 0.0537, 0.2658, -0.2389},
+ {-0.2837, -0.1996, -0.1277, -0.3120, -0.7745, 0.1399, -0.1301, 0.1420, 0.0195, 0.3304},
+ {-0.0437, -0.0461, -0.4879, 0.3315, 0.1537, 0.7502, -0.1807, -0.0791, -0.1324, 0.0722},
+ {-0.1249, -0.1454, -0.3595, 0.2337, -0.1175, -0.1611, 0.8455, -0.0760, -0.1273, 0.0524},
+ {-0.2454, -0.3579, 0.0908, 0.1353, 0.1637, 0.0118, -0.0050, 0.8258, -0.1471, -0.2337},
+ {-0.4296, 0.0454, -0.0366, 0.5136, -0.0494, -0.1836, -0.1552, -0.0496, 0.6968, 0.0102},
+ {-0.4329, -0.0878, 0.3611, -0.0560, 0.4056, 0.0609, 0.0822, -0.1140, -0.1558, 0.6776}
+ };
+R = {
+ {-2.2290, -1.9717, -1.4557, -0.9569, -1.6050},
+ { 0.0000, -1.2068, -0.4480, -0.0883, -0.5623},
+ { 0.0000, 0.0000, -1.3800, -0.9196, -0.5670},
+ { 0.0000, 0.0000, 0.0000, 0.9920, 0.1006},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.5446},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000}
+ };
+Q1 = {
+ {-0.9487, 0.1945, -0.0872, 0.2336},
+ {-0.3162, -0.5834, 0.2617, -0.7009},
+ { 0.0000, -0.7778, -0.0581, 0.6258},
+ { 0.0000, -0.1296, -0.9594, -0.2503}
+ };
+R1 = {
+ {-6.3246, -1.5811, 0.0000, -6.9570},
+ { 0.0000, -7.7136, -2.2039, -4.1485},
+ { 0.0000, 0.0000, -4.9135, -4.4484},
+ { 0.0000, 0.0000, 0.0000, -0.7759}
+ };
diff --git a/examples/example_results/lu_decomp_test.txt b/examples/example_results/lu_decomp_test.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fe573bbf810bde8dd315d3ee6fe9eb9e4add9575
--- /dev/null
+++ b/examples/example_results/lu_decomp_test.txt
@@ -0,0 +1,61 @@
+**************** Testing the MicroPosMath-Lib!! 03/09/20 17:01:26 ****************
+L = {
+ { 1.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.1390, 1.0000, 0.0000, 0.0000, 0.0000},
+ { 0.9917, 0.5499, 1.0000, 0.0000, 0.0000},
+ { 0.8919, -0.3095, -0.0352, 1.0000, 0.0000},
+ { 0.6924, 0.5218, 0.2669, -0.0439, 1.0000}
+ };
+U = {
+ { 0.9134, 0.4854, 0.9340, 0.0462, 0.7952},
+ { 0.0000, 0.8897, 0.7192, 0.2705, 0.6549},
+ { 0.0000, 0.0000, -1.2860, -0.1627, -0.7671},
+ { 0.0000, 0.0000, 0.0000, 0.7428, -0.0949},
+ { 0.0000, 0.0000, 0.0000, 0.0000, -0.5048}
+ };
+P = {
+ { 0.0000, 0.0000, 0.0000, 1.0000, 0.0000},
+ { 0.0000, 0.0000, 1.0000, 0.0000, 0.0000},
+ { 0.0000, 1.0000, 0.0000, 0.0000, 0.0000},
+ { 1.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 1.0000}
+ };
+L1 = {
+ { 1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.6159, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.3471, 0.2412, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.8921, 0.1327, 0.0761, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.4799, 0.6746, 0.9211, 0.2980, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.5604, 0.3088, -0.4210, 0.6453, -0.0384, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.9491, 0.7202, -0.5596, 0.4357, -0.6471, 0.0494, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.2350, 0.5307, 0.9514, -0.7156, 0.9016, 0.3235, -0.6718, 1.0000, 0.0000, 0.0000, 0.0000},
+ { 0.9627, 0.0542, -0.0136, 0.2470, -0.1254, 0.4751, -0.0350, -0.0844, 1.0000, 0.0000, 0.0000},
+ { 0.8128, 0.5512, -0.4622, 0.1538, 0.4184, 0.7202, 0.3070, 0.7490, 0.8327, 1.0000, 0.0000},
+ { 0.5517, 0.6927, 0.4913, -0.6861, 0.0423, 0.0900, -0.4523, 0.9282, -0.2907, -0.1129, 1.0000}
+ };
+U1 = {
+ { 0.7952, 0.1190, 0.9593, 0.1966, 0.7537, 0.0119, 0.7482, 0.1067, 0.9106, 0.3510, 0.9448},
+ { 0.0000, 0.8864, -0.4523, 0.4949, 0.1036, 0.1549, -0.3771, -0.0611, -0.2971, 0.1856, -0.0926},
+ { 0.0000, 0.0000, 0.5904, 0.3621, 0.6474, 0.5605, 0.3696, 0.3775, 0.3055, 0.0734, 0.4747},
+ { 0.0000, 0.0000, 0.0000, 0.5622, -0.2046, 0.4547, -0.4932, 0.7529, 0.0731, -0.2200, -0.4975},
+ { 0.0000, 0.0000, 0.0000, 0.0000, -0.6812, -0.1932, 0.3560, -0.5039, 0.2603, 0.5573, -0.6302},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.6750, 0.4137, 0.3877, -0.1816, 0.0163, 0.3335},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 1.0188, -0.4348, 0.2460, 0.2139, -0.6606},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 1.1856, -0.1236, -0.2591, -0.4732},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, -0.3259, 0.3772, -0.1730},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, -0.5105, 1.2040},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, -0.3916}
+ };
+P1 = {
+ { 0.0000, 0.0000, 0.0000, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 1.0000},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 1.0000, 0.0000, 0.0000},
+ { 0.0000, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 1.0000, 0.0000},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.0000, 0.0000, 1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 1.0000, 0.0000, 0.0000, 0.0000},
+ { 1.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000}
+ };
diff --git a/examples/example_results/magnetic_based_test.txt b/examples/example_results/magnetic_based_test.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3ee80efaf44cbc0ac39c267dd11dd41da0b9606c
--- /dev/null
+++ b/examples/example_results/magnetic_based_test.txt
@@ -0,0 +1,4 @@
+**************** Testing the MicroPosMath-Lib!! 03/11/20 12:20:12 ****************
+***************** Magnetic-based system example *****************
+true position = {102.0000, 18.0000, 2.3080}
+estimated position = {101.7997638, 17.9822461, 3.0978578}
diff --git a/examples/example_results/multipath_algo_own_norm_distr_test.txt b/examples/example_results/multipath_algo_own_norm_distr_test.txt
new file mode 100644
index 0000000000000000000000000000000000000000..18cb6326b4fa487d8339acd6b63c8a1d16b866bb
--- /dev/null
+++ b/examples/example_results/multipath_algo_own_norm_distr_test.txt
@@ -0,0 +1,7018 @@
+**************** Testing the MicroPosMath-Lib!! 03/12/20 12:39:28 ****************
+################ START ################
+seed = 3
+------------------------------------------------------------
+PDOP = 4.643744 | it = 0
+r_noised_vec = {1.6358559, 16.8843724, 25.5868968, 19.2976565, 19.1902460, 25.3133719, 31.8908002, 26.7822731}
+anchors_optimal = {6, 7, 2, 0}
+exact point = {3, 1, 1}
+x_sol = {2.6122898, 1.2294664, 0.9648987}
+seed = 7
+------------------------------------------------------------
+PDOP = 2.951334 | it = 0
+r_noised_vec = {4.3892176, 15.0386434, 23.2273716, 19.4184104, 19.3442298, 24.1502338, 30.7765600, 27.1295001}
+anchors_optimal = {7, 2, 1, 0}
+exact point = {5, 1, 1}
+x_sol = {5.0553799, 2.2539475, -0.1156460}
+seed = 9
+------------------------------------------------------------
+PDOP = 2.954220 | it = 0
+r_noised_vec = {6.1765858, 13.0463261, 29.0417719, 20.0259916, 19.7472290, 22.9642996, 29.8041250, 27.5449235}
+anchors_optimal = {2, 7, 5, 0}
+exact point = {7, 1, 1}
+x_sol = {2.9485454, -3.1399745, 5.1775377}
+seed = 11
+------------------------------------------------------------
+PDOP = 4.967539 | it = 0
+r_noised_vec = {7.5911756, 11.1465951, 22.5169907, 20.5031277, 20.5913503, 21.9149360, 28.8898216, 28.0834514}
+anchors_optimal = {6, 5, 4, 3}
+exact point = {9, 1, 1}
+x_sol = {9.0194549, 1.1748060, 1.0793991}
+seed = 13
+------------------------------------------------------------
+PDOP = 3.959556 | it = 0
+r_noised_vec = {9.8933413, 9.0607135, 24.7963856, 21.5160656, 21.5063808, 21.0240549, 28.2742470, 28.7349194}
+anchors_optimal = {7, 3, 4, 1}
+exact point = {11, 1, 1}
+x_sol = {10.9650887, 0.9428638, 0.9538286}
+seed = 15
+------------------------------------------------------------
+PDOP = 5.343255 | it = 0
+r_noised_vec = {12.4193628, 7.1077871, 22.8077485, 22.5063411, 22.6531186, 20.2677808, 27.6438883, 29.4904647}
+anchors_optimal = {7, 6, 4, 3}
+exact point = {13, 1, 1}
+x_sol = {13.2763934, 1.1177966, 0.9433653}
+seed = 17
+------------------------------------------------------------
+PDOP = 3.286921 | it = 0
+r_noised_vec = {14.0367395, 5.0168920, 20.4018364, 23.5361715, 23.6852549, 19.7020637, 27.1580398, 30.3422154}
+anchors_optimal = {4, 2, 5, 1}
+exact point = {15, 1, 1}
+x_sol = {15.0478944, 0.2087967, 0.9473129}
+seed = 19
+------------------------------------------------------------
+PDOP = 2.273887 | it = 0
+r_noised_vec = {15.5801581, 2.9680990, 26.8959955, 24.8775353, 24.8420330, 19.3428241, 26.9989193, 31.5378787}
+anchors_optimal = {6, 3, 4, 1}
+exact point = {17, 1, 1}
+x_sol = {17.0561462, 1.0013528, 1.0478044}
+seed = 21
+------------------------------------------------------------
+PDOP = 2.874589 | it = 0
+r_noised_vec = {18.0322134, 0.9639380, 14.8611888, 26.1719019, 26.0599001, 19.2287337, 26.8696933, 32.4879447}
+anchors_optimal = {6, 3, 0, 1}
+exact point = {19, 1, 1}
+x_sol = {19.0324090, 1.0313755, 0.9935918}
+seed = 23
+------------------------------------------------------------
+PDOP = 104.568903 | it = 2
+r_noised_vec = {2.4100070, 18.9721971, 36.4289661, 16.8312172, 19.0078322, 27.0037711, 31.8547807, 25.5650955}
+anchors_optimal = {3, 5, 7, 1}
+exact point = {1, 3, 1}
+start_optimal = {1.180628, 3.170879, 0.782648}
+x_sol = {1.1812812, 3.1715325, 0.7556781}
+seed = 25
+------------------------------------------------------------
+PDOP = 2.068468 | it = 0
+r_noised_vec = {2.7295703, 17.0700772, 19.5666611, 17.3006533, 19.1967090, 25.6761207, 30.6901919, 25.5803713}
+anchors_optimal = {7, 3, 1, 0}
+exact point = {3, 3, 1}
+x_sol = {3.0279742, 2.8194197, 1.1567686}
+seed = 27
+------------------------------------------------------------
+PDOP = 4.239785 | it = 0
+r_noised_vec = {4.0821109, 15.0322036, 31.1187518, 17.3868949, 19.5314577, 24.4322545, 29.6981360, 25.7661192}
+anchors_optimal = {6, 7, 5, 3}
+exact point = {5, 3, 1}
+x_sol = {4.7608848, 2.9988363, 0.9845057}
+seed = 29
+------------------------------------------------------------
+PDOP = 4.090281 | it = 0
+r_noised_vec = {6.4862923, 13.1395085, 20.6287675, 17.9730234, 20.0914173, 23.2978248, 28.8336858, 26.1212540}
+anchors_optimal = {6, 7, 5, 3}
+exact point = {7, 3, 1}
+x_sol = {6.5773283, 2.9054528, 1.0449910}
+seed = 31
+------------------------------------------------------------
+PDOP = 4.779745 | it = 0
+r_noised_vec = {8.6065996, 11.2063856, 24.1952301, 18.9082811, 20.9479883, 22.0843890, 27.8335857, 26.6403070}
+anchors_optimal = {6, 5, 4, 3}
+exact point = {9, 3, 1}
+x_sol = {9.2131047, 2.9476775, 0.8083321}
+seed = 33
+------------------------------------------------------------
+PDOP = 3.274694 | it = 0
+r_noised_vec = {9.9786250, 9.2437162, 22.6084243, 19.6339430, 21.6381311, 21.1769594, 27.1201983, 27.3133677}
+anchors_optimal = {7, 4, 5, 1}
+exact point = {11, 3, 1}
+x_sol = {11.0196080, 3.1891753, 0.9469126}
+seed = 35
+------------------------------------------------------------
+PDOP = 3.983531 | it = 0
+r_noised_vec = {11.8436569, 7.4002391, 18.8172272, 20.8146713, 22.5451406, 20.4031940, 26.4939558, 28.1270926}
+anchors_optimal = {7, 6, 3, 1}
+exact point = {13, 3, 1}
+x_sol = {12.8474643, 2.8872800, 1.0820317}
+seed = 37
+------------------------------------------------------------
+PDOP = 3.205751 | it = 0
+r_noised_vec = {14.4126733, 5.4141524, 23.2485967, 22.0798664, 23.5119857, 19.7843833, 25.9668015, 29.0689616}
+anchors_optimal = {7, 6, 5, 1}
+exact point = {15, 3, 1}
+x_sol = {14.9928882, 3.0565011, 0.9708217}
+seed = 39
+------------------------------------------------------------
+PDOP = 3.045250 | it = 0
+r_noised_vec = {16.3999944, 3.6991035, 16.7812084, 23.2858272, 24.8060107, 19.3377249, 25.5934055, 29.9788728}
+anchors_optimal = {4, 3, 5, 1}
+exact point = {17, 3, 1}
+x_sol = {16.8523832, 2.9432679, 1.0193621}
+seed = 41
+------------------------------------------------------------
+PDOP = 4.141205 | it = 0
+r_noised_vec = {17.7968685, 2.2428670, 22.1167596, 24.7780752, 26.2238617, 19.1081647, 25.3141828, 31.1723603}
+anchors_optimal = {7, 4, 3, 1}
+exact point = {19, 3, 1}
+x_sol = {19.0499325, 3.0256547, 1.0851834}
+seed = 43
+------------------------------------------------------------
+PDOP = 51.526862 | it = 2
+r_noised_vec = {3.7775549, 19.3955803, 25.1987556, 15.0992598, 19.4796934, 27.1054664, 30.6945700, 24.2337817}
+anchors_optimal = {1, 5, 7, 3}
+exact point = {1, 5, 1}
+start_optimal = {0.996109, 4.875849, 1.045039}
+x_sol = {0.9956401, 4.8753805, 1.0653218}
+seed = 45
+------------------------------------------------------------
+PDOP = 2.085988 | it = 0
+r_noised_vec = {4.8206217, 17.2403232, 26.1166812, 14.9353036, 19.6177683, 25.6914405, 29.4521031, 24.3593778}
+anchors_optimal = {5, 1, 3, 0}
+exact point = {3, 5, 1}
+x_sol = {3.2897276, 5.2414500, 0.9520693}
+seed = 47
+------------------------------------------------------------
+PDOP = 3.883820 | it = 0
+r_noised_vec = {5.8210192, 15.4159240, 20.8859463, 15.6710673, 19.8595343, 24.3035231, 28.3078347, 24.6274267}
+anchors_optimal = {6, 7, 5, 3}
+exact point = {5, 5, 1}
+x_sol = {5.3730695, 4.9559928, 1.0019001}
+seed = 49
+------------------------------------------------------------
+PDOP = 119.754604 | it = 2
+r_noised_vec = {6.8376150, 13.3330108, 21.2326387, 16.1416016, 20.3712828, 23.3014392, 27.4491848, 25.0339374}
+anchors_optimal = {5, 6, 7, 4}
+exact point = {7, 5, 1}
+start_optimal = {7.164218, 4.928714, 0.921587}
+x_sol = {7.1642177, 4.9605084, 0.9601961}
+seed = 51
+------------------------------------------------------------
+PDOP = 2.546804 | it = 0
+r_noised_vec = {8.8421005, 11.6181172, 25.4627876, 16.9024527, 20.9544723, 22.2081990, 26.6009884, 25.5746885}
+anchors_optimal = {7, 5, 1, 0}
+exact point = {9, 5, 1}
+x_sol = {9.0053182, 4.7721449, 1.0730670}
+seed = 53
+------------------------------------------------------------
+PDOP = 4.276357 | it = 0
+r_noised_vec = {11.1586774, 9.7600831, 14.0990055, 18.1456733, 21.5066257, 21.2536226, 25.9512478, 26.2455345}
+anchors_optimal = {7, 6, 4, 1}
+exact point = {11, 5, 1}
+x_sol = {10.9042321, 4.5449175, 1.2390815}
+seed = 55
+------------------------------------------------------------
+PDOP = 3.014235 | it = 0
+r_noised_vec = {12.6872011, 8.0786403, 25.5788195, 19.1554461, 22.7058630, 20.4411780, 25.2675638, 27.0419429}
+anchors_optimal = {4, 5, 3, 1}
+exact point = {13, 5, 1}
+x_sol = {13.0714331, 5.1328361, 1.2216493}
+seed = 57
+------------------------------------------------------------
+PDOP = 2.340742 | it = 0
+r_noised_vec = {14.1674531, 6.5468779, 12.2640356, 20.4887720, 23.9234819, 20.0068464, 24.8579716, 28.0509815}
+anchors_optimal = {6, 5, 0, 1}
+exact point = {15, 5, 1}
+x_sol = {14.6540820, 4.7725040, 1.0944133}
+seed = 59
+------------------------------------------------------------
+PDOP = 4.131492 | it = 0
+r_noised_vec = {16.5188247, 5.0968510, 22.5440139, 21.9990782, 25.2956480, 19.5878951, 24.6531122, 29.0144283}
+anchors_optimal = {7, 4, 3, 5}
+exact point = {17, 5, 1}
+x_sol = {17.2416887, 5.1850726, 1.0821682}
+seed = 61
+------------------------------------------------------------
+PDOP = 3.299981 | it = 0
+r_noised_vec = {18.8258015, 4.3394415, 14.3849919, 23.3860056, 26.6043907, 19.3875168, 24.2949837, 30.1042475}
+anchors_optimal = {7, 4, 0, 1}
+exact point = {19, 5, 1}
+x_sol = {19.3310539, 5.2770496, 1.2004526}
+seed = 63
+------------------------------------------------------------
+PDOP = 4.395128 | it = 0
+r_noised_vec = {5.9103746, 20.0043005, 27.2452838, 13.0031451, 19.9757579, 27.4997861, 29.9128563, 22.9242282}
+anchors_optimal = {6, 2, 7, 1}
+exact point = {1, 7, 1}
+x_sol = {0.7826649, 1.4964882, 6.4875398}
+seed = 65
+------------------------------------------------------------
+PDOP = 3.639905 | it = 0
+r_noised_vec = {5.9541318, 18.1071605, 24.6405659, 13.3204529, 20.0311039, 26.1945370, 28.6233961, 22.9978675}
+anchors_optimal = {6, 7, 1, 3}
+exact point = {3, 7, 1}
+x_sol = {2.8579764, 6.8167869, 1.2508567}
+seed = 67
+------------------------------------------------------------
+PDOP = 2.618792 | it = 0
+r_noised_vec = {7.3610401, 16.1430881, 20.6297836, 13.4083479, 20.2403900, 24.9667643, 27.4413504, 23.2627936}
+anchors_optimal = {6, 7, 3, 0}
+exact point = {5, 7, 1}
+x_sol = {4.9244698, 7.1947663, 0.9901639}
+seed = 69
+------------------------------------------------------------
+PDOP = 2.763239 | it = 0
+r_noised_vec = {8.8296825, 14.1974120, 23.5874276, 14.4090240, 20.7562333, 23.8571983, 26.3276237, 23.7085262}
+anchors_optimal = {6, 5, 1, 0}
+exact point = {7, 7, 1}
+x_sol = {7.2472838, 7.2374247, 0.8263316}
+seed = 71
+------------------------------------------------------------
+PDOP = 2.404042 | it = 0
+r_noised_vec = {9.7942207, 12.4442758, 16.9700313, 15.3102488, 21.3590044, 22.8837749, 25.5095135, 24.3196878}
+anchors_optimal = {6, 2, 3, 1}
+exact point = {9, 7, 1}
+x_sol = {9.0900462, 6.9967905, 0.9538601}
+seed = 73
+------------------------------------------------------------
+PDOP = 4.339079 | it = 0
+r_noised_vec = {11.3525063, 10.6262416, 20.3378879, 16.2802898, 22.3047417, 21.8713174, 24.6283449, 25.0775345}
+anchors_optimal = {6, 4, 5, 3}
+exact point = {11, 7, 1}
+x_sol = {11.0038678, 7.1262935, 1.0090917}
+seed = 75
+------------------------------------------------------------
+PDOP = 2.980747 | it = 0
+r_noised_vec = {13.6721222, 9.1476062, 16.1010300, 17.7889830, 23.2858048, 21.1895591, 23.9368729, 25.9185978}
+anchors_optimal = {4, 5, 3, 1}
+exact point = {13, 7, 1}
+x_sol = {12.9534550, 6.8279493, 0.8863495}
+seed = 77
+------------------------------------------------------------
+PDOP = 4.480319 | it = 0
+r_noised_vec = {15.4979411, 7.7357648, 23.4998186, 19.0912022, 24.5030362, 20.6553247, 23.5491095, 26.9920479}
+anchors_optimal = {7, 4, 6, 3}
+exact point = {15, 7, 1}
+x_sol = {15.0792130, 7.1270560, 0.9185092}
+seed = 79
+------------------------------------------------------------
+PDOP = 2.862059 | it = 0
+r_noised_vec = {16.7895405, 6.7171446, 13.0465282, 20.5597513, 25.6026715, 20.3018145, 23.2053598, 28.1341779}
+anchors_optimal = {4, 3, 5, 1}
+exact point = {17, 7, 1}
+x_sol = {16.9035030, 6.9670992, 0.8409568}
+seed = 81
+------------------------------------------------------------
+PDOP = 3.710834 | it = 0
+r_noised_vec = {18.7570862, 6.1869629, 14.6652056, 22.2682223, 26.7833465, 20.1605523, 23.0911620, 29.3467452}
+anchors_optimal = {6, 3, 5, 1}
+exact point = {19, 7, 1}
+x_sol = {19.2063505, 7.1643712, 0.8113327}
+seed = 83
+------------------------------------------------------------
+PDOP = 4.319316 | it = 0
+r_noised_vec = {8.3329555, 20.6900468, 28.5459653, 10.9746651, 20.4936849, 28.0822433, 29.0512645, 22.0800370}
+anchors_optimal = {5, 7, 1, 4}
+exact point = {1, 9, 1}
+x_sol = {0.7994404, 8.7227128, 1.0122539}
+seed = 85
+------------------------------------------------------------
+PDOP = 4.078914 | it = 0
+r_noised_vec = {8.4075224, 18.9599054, 17.3061374, 11.1789240, 20.6387113, 26.7802129, 27.8556424, 22.1544072}
+anchors_optimal = {6, 5, 1, 3}
+exact point = {3, 9, 1}
+x_sol = {2.7824557, 8.9537628, 1.0867950}
+seed = 87
+------------------------------------------------------------
+PDOP = 2.279003 | it = 0
+r_noised_vec = {8.5859522, 17.0638401, 27.4613713, 11.9067745, 20.9104944, 25.5480280, 26.7457603, 22.3959614}
+anchors_optimal = {6, 1, 3, 0}
+exact point = {5, 9, 1}
+x_sol = {4.7774720, 8.7091394, 1.1287276}
+seed = 89
+------------------------------------------------------------
+PDOP = 3.295602 | it = 0
+r_noised_vec = {9.8979151, 15.3352187, 13.7652742, 12.3700674, 21.5186545, 24.3997894, 25.5412910, 22.8058486}
+anchors_optimal = {5, 4, 1, 3}
+exact point = {7, 9, 1}
+x_sol = {7.0184938, 9.1803455, 1.0215581}
+seed = 91
+------------------------------------------------------------
+PDOP = 3.309213 | it = 0
+r_noised_vec = {11.6876514, 13.5955022, 22.6302632, 13.6280628, 22.1730670, 23.3617470, 24.6156866, 23.3824079}
+anchors_optimal = {6, 7, 5, 1}
+exact point = {9, 9, 1}
+x_sol = {8.9422361, 8.9168210, 1.0017488}
+seed = 93
+------------------------------------------------------------
+PDOP = 3.013993 | it = 0
+r_noised_vec = {12.8467419, 11.9503521, 13.6388060, 14.9590558, 23.0801142, 22.4634999, 23.7622369, 24.1228611}
+anchors_optimal = {6, 5, 3, 1}
+exact point = {11, 9, 1}
+x_sol = {11.0507200, 8.9201296, 0.9790023}
+seed = 95
+------------------------------------------------------------
+PDOP = 3.195926 | it = 0
+r_noised_vec = {14.0427374, 10.5671092, 16.6193249, 16.1559545, 23.8855691, 21.6990852, 23.0360148, 24.9220823}
+anchors_optimal = {4, 6, 5, 1}
+exact point = {13, 9, 1}
+x_sol = {13.1228977, 8.9261136, 1.0477236}
+seed = 97
+------------------------------------------------------------
+PDOP = 2.044213 | it = 0
+r_noised_vec = {16.1463313, 9.2778168, 14.5829959, 17.8673994, 24.8955593, 21.0797710, 22.4558312, 25.9039610}
+anchors_optimal = {6, 3, 2, 1}
+exact point = {15, 9, 1}
+x_sol = {13.3047419, 7.1687925, 2.8263004}
+seed = 99
+------------------------------------------------------------
+PDOP = 2.020888 | it = 0
+r_noised_vec = {18.2633483, 8.4892012, 12.3118005, 19.4405966, 25.9334651, 20.8096894, 22.0145390, 27.0202932}
+anchors_optimal = {4, 6, 3, 1}
+exact point = {17, 9, 1}
+x_sol = {16.9970387, 8.9478214, 1.1949841}
+seed = 101
+------------------------------------------------------------
+PDOP = 4.111976 | it = 0
+r_noised_vec = {19.6145314, 7.9944975, 15.0838958, 21.0257157, 27.2858441, 20.5634173, 21.9385151, 28.2546972}
+anchors_optimal = {7, 4, 3, 5}
+exact point = {19, 9, 1}
+x_sol = {18.9648198, 9.0839308, 1.1250738}
+seed = 103
+------------------------------------------------------------
+PDOP = 2.373249 | it = 0
+r_noised_vec = {9.6398673, 21.4744043, 21.4456283, 9.0512804, 21.4671515, 28.5529227, 28.2418771, 20.9151199}
+anchors_optimal = {5, 2, 7, 0}
+exact point = {1, 11, 1}
+x_sol = {0.6998015, 10.6426213, 1.2911893}
+seed = 105
+------------------------------------------------------------
+PDOP = 2.441564 | it = 0
+r_noised_vec = {10.3400247, 19.8032953, 23.4816490, 9.2127618, 21.6572699, 27.2285619, 26.9233051, 21.0460234}
+anchors_optimal = {5, 4, 0, 3}
+exact point = {3, 11, 1}
+x_sol = {3.3327042, 11.0800297, 0.9704940}
+seed = 107
+------------------------------------------------------------
+PDOP = 2.192762 | it = 0
+r_noised_vec = {11.1062251, 18.0785048, 7.2806103, 9.6810779, 21.9271113, 25.9625302, 25.8129824, 21.3654970}
+anchors_optimal = {5, 1, 0, 3}
+exact point = {5, 11, 1}
+x_sol = {5.1451553, 11.2796044, 1.3626147}
+seed = 109
+------------------------------------------------------------
+PDOP = 3.051535 | it = 0
+r_noised_vec = {11.4652346, 16.5438298, 24.8888182, 11.0194175, 22.4777946, 25.0503168, 24.7305192, 21.8583111}
+anchors_optimal = {5, 6, 1, 0}
+exact point = {7, 11, 1}
+x_sol = {6.7566658, 10.9189419, 1.1889456}
+seed = 111
+------------------------------------------------------------
+PDOP = 2.917297 | it = 0
+r_noised_vec = {12.5034615, 14.9102533, 13.8366441, 11.9361266, 22.9136517, 24.0650804, 23.8162665, 22.5051165}
+anchors_optimal = {5, 6, 1, 0}
+exact point = {9, 11, 1}
+x_sol = {8.7637078, 10.8135142, 1.1101989}
+seed = 113
+------------------------------------------------------------
+PDOP = 2.182631 | it = 0
+r_noised_vec = {14.3879354, 13.5183905, 14.6924818, 13.4174620, 23.6315908, 23.2300177, 22.9076094, 23.4371128}
+anchors_optimal = {5, 0, 1, 3}
+exact point = {11, 11, 1}
+x_sol = {11.1385738, 11.2101158, 1.1082410}
+seed = 115
+------------------------------------------------------------
+PDOP = 2.239632 | it = 0
+r_noised_vec = {15.8822328, 12.2050036, 16.2536150, 15.1210041, 24.3908850, 22.5602796, 22.2647967, 24.3759906}
+anchors_optimal = {4, 0, 3, 1}
+exact point = {13, 11, 1}
+x_sol = {13.2179791, 11.1210672, 1.4823697}
+seed = 117
+------------------------------------------------------------
+PDOP = 2.857557 | it = 0
+r_noised_vec = {16.9165547, 11.1098554, 8.4027872, 16.5383317, 25.5550767, 22.0525938, 21.7765756, 25.4219287}
+anchors_optimal = {5, 6, 0, 1}
+exact point = {15, 11, 1}
+x_sol = {14.7826562, 10.8183592, 0.9503156}
+seed = 119
+------------------------------------------------------------
+PDOP = 2.098263 | it = 0
+r_noised_vec = {18.6540948, 10.4037550, 16.1032402, 18.3796084, 26.7849263, 21.7147645, 21.2740482, 26.5589559}
+anchors_optimal = {4, 6, 3, 1}
+exact point = {17, 11, 1}
+x_sol = {17.0055137, 10.9641482, 0.9740884}
+seed = 121
+------------------------------------------------------------
+PDOP = 4.805580 | it = 0
+r_noised_vec = {20.9137228, 9.9196689, 6.7412379, 20.1781670, 28.1655961, 21.5729247, 21.0923247, 27.7790552}
+anchors_optimal = {4, 7, 6, 3}
+exact point = {19, 11, 1}
+x_sol = {19.0997301, 11.0690763, 0.9074347}
+seed = 123
+------------------------------------------------------------
+PDOP = 5.381527 | it = 0
+r_noised_vec = {12.1604976, 22.4419015, 27.7055525, 6.9306924, 22.5786792, 29.5713935, 27.7642514, 20.3085375}
+anchors_optimal = {6, 4, 1, 7}
+exact point = {1, 13, 1}
+x_sol = {1.0725162, 13.0621068, 0.9104685}
+seed = 125
+------------------------------------------------------------
+PDOP = 2.091752 | it = 0
+r_noised_vec = {11.8175051, 20.7469492, 17.8529060, 7.3117888, 22.5832438, 28.2101549, 26.4157476, 20.3673736}
+anchors_optimal = {6, 4, 1, 3}
+exact point = {3, 13, 1}
+x_sol = {3.0689149, 12.9892741, 0.9750465}
+seed = 127
+------------------------------------------------------------
+PDOP = 3.466998 | it = 0
+r_noised_vec = {12.5460375, 19.2096238, 20.4832354, 8.0670857, 22.7812925, 27.1002503, 25.1124223, 20.6303293}
+anchors_optimal = {5, 4, 7, 0}
+exact point = {5, 13, 1}
+x_sol = {4.8306244, 12.9572843, 0.9846255}
+seed = 129
+------------------------------------------------------------
+PDOP = 3.610993 | it = 0
+r_noised_vec = {13.7805340, 17.7535126, 17.2814828, 9.0124199, 23.1737487, 26.0840342, 23.8872084, 21.0958580}
+anchors_optimal = {5, 6, 7, 1}
+exact point = {7, 13, 1}
+x_sol = {7.2030502, 13.3599843, 0.9260128}
+seed = 131
+------------------------------------------------------------
+PDOP = 3.550050 | it = 0
+r_noised_vec = {14.4653503, 16.2942380, 14.2528974, 10.8031823, 23.8390042, 25.1829448, 22.9886873, 21.5112706}
+anchors_optimal = {4, 6, 1, 0}
+exact point = {9, 13, 1}
+x_sol = {9.0195833, 13.0282687, 1.0512695}
+seed = 133
+------------------------------------------------------------
+PDOP = 3.026124 | it = 0
+r_noised_vec = {15.2501066, 15.1185045, 15.1488505, 12.1665534, 24.5396297, 24.4864425, 22.0649789, 22.3834669}
+anchors_optimal = {4, 7, 1, 3}
+exact point = {11, 13, 1}
+x_sol = {11.0428863, 13.1624693, 1.2106693}
+seed = 135
+------------------------------------------------------------
+PDOP = 4.260786 | it = 0
+r_noised_vec = {16.9882376, 14.1674721, 10.6519579, 13.8050093, 25.5093862, 23.5891691, 21.3323106, 23.3627959}
+anchors_optimal = {4, 7, 6, 1}
+exact point = {13, 13, 1}
+x_sol = {12.8882305, 13.2607514, 1.0458221}
+seed = 137
+------------------------------------------------------------
+PDOP = 3.303328 | it = 0
+r_noised_vec = {18.8057840, 13.0584343, 11.1022640, 15.7796601, 26.6982791, 23.0812061, 20.8516449, 24.4808393}
+anchors_optimal = {4, 5, 3, 1}
+exact point = {15, 13, 1}
+x_sol = {15.2383166, 13.1731859, 0.9679113}
+seed = 139
+------------------------------------------------------------
+PDOP = 3.479167 | it = 0
+r_noised_vec = {19.9222418, 12.3732738, 2.2512374, 17.3922277, 27.7022140, 22.7201039, 20.5094943, 25.7171928}
+anchors_optimal = {6, 0, 3, 1}
+exact point = {17, 13, 1}
+x_sol = {16.9157320, 12.9843719, 0.9750635}
+seed = 141
+------------------------------------------------------------
+PDOP = 2.363336 | it = 0
+r_noised_vec = {21.2801340, 11.9879398, 13.4838967, 19.2952529, 28.8105811, 22.5120594, 20.4068355, 27.0499768}
+anchors_optimal = {4, 6, 3, 1}
+exact point = {19, 13, 1}
+x_sol = {18.9500886, 12.9344022, 0.8885390}
+seed = 143
+------------------------------------------------------------
+PDOP = 61.144437 | it = 2
+r_noised_vec = {14.1355020, 23.3927929, 19.1410967, 5.0704776, 23.4956194, 30.2887395, 27.3889430, 19.6451927}
+anchors_optimal = {5, 6, 4, 7}
+exact point = {1, 15, 1}
+start_optimal = {0.885168, 14.901409, 1.050504}
+x_sol = {0.8851681, 14.9014089, 1.0584644}
+seed = 145
+------------------------------------------------------------
+PDOP = 2.732336 | it = 0
+r_noised_vec = {14.4723662, 21.9155271, 20.2553427, 5.3275476, 23.5695115, 29.0462325, 26.0998153, 19.7746773}
+anchors_optimal = {6, 1, 0, 3}
+exact point = {3, 15, 1}
+x_sol = {3.3726067, 15.2649111, 0.4479829}
+seed = 147
+------------------------------------------------------------
+PDOP = 2.367241 | it = 0
+r_noised_vec = {14.3708479, 20.3172306, 20.8059500, 6.4143643, 23.8924305, 27.8789497, 24.8872904, 20.0866585}
+anchors_optimal = {6, 7, 0, 3}
+exact point = {5, 15, 1}
+x_sol = {4.8183323, 14.8520316, 0.9650058}
+seed = 149
+------------------------------------------------------------
+PDOP = 3.061379 | it = 0
+r_noised_vec = {14.9330290, 19.0501268, 12.2708093, 7.9880192, 24.3304506, 26.7897174, 23.5957587, 20.5661749}
+anchors_optimal = {5, 4, 7, 3}
+exact point = {7, 15, 1}
+x_sol = {7.1916281, 14.9474546, 1.0484448}
+seed = 151
+------------------------------------------------------------
+PDOP = 2.959116 | it = 0
+r_noised_vec = {16.3624579, 17.7961108, 18.9246378, 9.2214098, 24.9877596, 25.9986489, 22.5392074, 21.4411184}
+anchors_optimal = {4, 7, 1, 3}
+exact point = {9, 15, 1}
+x_sol = {8.7368266, 14.8333308, 0.6398116}
+seed = 153
+------------------------------------------------------------
+PDOP = 2.459281 | it = 0
+r_noised_vec = {17.4635669, 16.6894877, 8.1681787, 11.3004899, 25.6693929, 25.1716325, 21.5612268, 22.2236328}
+anchors_optimal = {4, 0, 1, 3}
+exact point = {11, 15, 1}
+x_sol = {11.1957150, 15.1651341, 1.1857483}
+seed = 155
+------------------------------------------------------------
+PDOP = 3.537221 | it = 0
+r_noised_vec = {18.1591541, 15.8262100, 13.9285487, 13.0254918, 26.5891805, 24.4896572, 20.8144562, 23.1475446}
+anchors_optimal = {4, 7, 0, 1}
+exact point = {13, 15, 1}
+x_sol = {12.5864725, 15.0046237, 0.5729041}
+seed = 157
+------------------------------------------------------------
+PDOP = 2.423116 | it = 0
+r_noised_vec = {19.5864718, 14.9620679, 6.7810576, 14.7458998, 27.4389688, 23.9560563, 20.1613551, 24.1957250}
+anchors_optimal = {7, 6, 1, 2}
+exact point = {15, 15, 1}
+x_sol = {15.2092860, 15.1810720, 1.0132238}
+seed = 159
+------------------------------------------------------------
+PDOP = 5.072514 | it = 0
+r_noised_vec = {21.5745420, 14.4943165, 8.4762780, 16.8755464, 28.2819571, 23.7722713, 19.6701156, 25.3580736}
+anchors_optimal = {7, 5, 0, 6}
+exact point = {17, 15, 1}
+x_sol = {17.2399592, 15.1896694, 1.1374087}
+seed = 161
+------------------------------------------------------------
+PDOP = 4.176473 | it = 0
+r_noised_vec = {22.9640983, 14.0864889, 6.6602254, 18.6507456, 29.5405829, 23.5679788, 19.6087226, 26.6260456}
+anchors_optimal = {7, 0, 6, 3}
+exact point = {19, 15, 1}
+x_sol = {19.0380080, 15.2236711, 0.9974738}
+seed = 163
+------------------------------------------------------------
+PDOP = 3.824357 | it = 0
+r_noised_vec = {15.6600009, 24.8513971, 20.8959681, 2.9495100, 24.7903871, 31.2139086, 26.9532833, 19.1909335}
+anchors_optimal = {5, 1, 4, 3}
+exact point = {1, 17, 1}
+x_sol = {1.0330316, 17.0565140, 1.1127328}
+seed = 165
+------------------------------------------------------------
+PDOP = 2.361623 | it = 0
+r_noised_vec = {16.0199733, 23.3061063, 21.1747344, 3.6789837, 24.9556258, 30.0539306, 25.6115265, 19.2881718}
+anchors_optimal = {4, 1, 0, 3}
+exact point = {3, 17, 1}
+x_sol = {2.9596041, 16.8974901, 0.8646391}
+seed = 167
+------------------------------------------------------------
+PDOP = 2.926148 | it = 0
+r_noised_vec = {16.8489453, 21.7797601, 16.8291888, 4.9617873, 25.2656829, 29.0055517, 24.4032455, 19.6094681}
+anchors_optimal = {5, 4, 0, 3}
+exact point = {5, 17, 1}
+x_sol = {5.1587554, 17.3228322, 1.1719006}
+seed = 169
+------------------------------------------------------------
+PDOP = 4.813037 | it = 0
+r_noised_vec = {17.1338985, 20.5308478, 26.0619621, 6.7038423, 25.6186827, 28.0483342, 23.2875213, 19.8924310}
+anchors_optimal = {5, 4, 6, 1}
+exact point = {7, 17, 1}
+x_sol = {7.0686277, 16.9315896, 0.8896489}
+seed = 171
+------------------------------------------------------------
+PDOP = 4.574515 | it = 0
+r_noised_vec = {17.5251317, 19.2566602, 5.9861610, 8.7579558, 26.1908658, 27.2107961, 22.3430114, 20.6587532}
+anchors_optimal = {5, 4, 6, 1}
+exact point = {9, 17, 1}
+x_sol = {9.0666849, 16.8478228, 0.7734615}
+seed = 173
+------------------------------------------------------------
+PDOP = 3.432161 | it = 0
+r_noised_vec = {18.8817459, 18.3113538, 16.4721054, 10.2538968, 26.7427108, 26.5118910, 21.3108452, 21.5716712}
+anchors_optimal = {4, 5, 7, 3}
+exact point = {11, 17, 1}
+x_sol = {10.8234794, 17.0746207, 1.0211948}
+seed = 175
+------------------------------------------------------------
+PDOP = 2.424141 | it = 0
+r_noised_vec = {20.3605162, 17.4494514, 7.2014718, 12.4234277, 27.5400180, 25.9743025, 20.5949146, 22.6250289}
+anchors_optimal = {6, 0, 1, 2}
+exact point = {13, 17, 1}
+x_sol = {13.3965070, 17.1479515, 0.7029128}
+seed = 177
+------------------------------------------------------------
+PDOP = 4.106298 | it = 0
+r_noised_vec = {21.1874121, 16.7954650, 7.6865427, 14.3986969, 28.3547759, 25.3843628, 20.0388048, 23.7961619}
+anchors_optimal = {4, 5, 6, 1}
+exact point = {15, 17, 1}
+x_sol = {14.7007221, 16.8897941, 0.9663624}
+seed = 179
+------------------------------------------------------------
+PDOP = 4.078751 | it = 0
+r_noised_vec = {22.2794705, 16.4138703, 6.9404205, 16.1480101, 29.5089868, 25.1122299, 19.4970259, 25.0629407}
+anchors_optimal = {4, 5, 6, 1}
+exact point = {17, 17, 1}
+x_sol = {16.8199004, 17.0918439, 0.9945013}
+seed = 181
+------------------------------------------------------------
+PDOP = 4.592836 | it = 0
+r_noised_vec = {24.2130042, 16.1041380, 2.5100831, 18.3294903, 30.6890889, 24.9918951, 19.2549805, 26.4066770}
+anchors_optimal = {7, 6, 3, 1}
+exact point = {19, 17, 1}
+x_sol = {19.0936399, 17.0771411, 0.9909902}
+seed = 183
+------------------------------------------------------------
+PDOP = 5.033763 | it = 0
+r_noised_vec = {18.3260724, 26.3189902, 26.5552930, 1.0110854, 26.3181650, 32.5166174, 26.7807979, 19.0904342}
+anchors_optimal = {5, 4, 7, 1}
+exact point = {1, 19, 1}
+x_sol = {0.9030369, 19.1368719, 0.9362531}
+seed = 185
+------------------------------------------------------------
+PDOP = 3.654100 | it = 0
+r_noised_vec = {17.9276986, 24.7996178, 14.8537165, 2.1652134, 26.3267629, 31.2363719, 25.4515648, 19.1792814}
+anchors_optimal = {5, 7, 0, 3}
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+x_sol = {2.8381088, 18.8345850, 0.9432451}
+seed = 187
+------------------------------------------------------------
+PDOP = 2.816436 | it = 0
+r_noised_vec = {18.1435777, 23.4478923, 21.3143157, 4.1868056, 26.5388156, 30.2219673, 24.0942551, 19.4491241}
+anchors_optimal = {4, 1, 7, 3}
+exact point = {5, 19, 1}
+x_sol = {5.0727893, 19.0800080, 1.0068661}
+seed = 189
+------------------------------------------------------------
+PDOP = 2.428217 | it = 0
+r_noised_vec = {19.2048999, 22.1777293, 12.8048922, 6.0664003, 26.7754022, 29.2816935, 22.8061864, 20.1109085}
+anchors_optimal = {5, 7, 0, 2}
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+x_sol = {7.2354471, 19.1556822, 0.9069372}
+seed = 191
+------------------------------------------------------------
+PDOP = 3.080214 | it = 0
+r_noised_vec = {19.9548261, 20.9742208, 14.4536466, 8.0533947, 27.2922894, 28.4331079, 21.9119133, 20.7220578}
+anchors_optimal = {4, 1, 7, 3}
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+x_sol = {8.9317002, 18.8017205, 0.9066707}
+seed = 193
+------------------------------------------------------------
+PDOP = 3.878683 | it = 0
+r_noised_vec = {20.3182331, 20.0643810, 10.9613233, 10.2729117, 27.8492156, 27.6814790, 20.9820799, 21.5111368}
+anchors_optimal = {5, 6, 1, 3}
+exact point = {11, 19, 1}
+x_sol = {11.2623666, 19.0793843, 0.9293449}
+seed = 195
+------------------------------------------------------------
+PDOP = 5.010262 | it = 0
+r_noised_vec = {21.4213828, 19.1783175, 8.4066123, 11.9063164, 28.7805890, 27.0766611, 20.2595950, 22.4606889}
+anchors_optimal = {5, 7, 0, 3}
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+x_sol = {12.8276905, 18.8451388, 0.9546796}
+seed = 197
+------------------------------------------------------------
+PDOP = 4.144352 | it = 0
+r_noised_vec = {23.1108596, 18.6473968, 7.2416843, 14.0217628, 29.7232760, 26.5961604, 19.7037444, 23.5554464}
+anchors_optimal = {5, 7, 6, 1}
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+x_sol = {14.8847766, 18.8978475, 1.0360437}
+seed = 199
+------------------------------------------------------------
+PDOP = 4.598929 | it = 0
+r_noised_vec = {24.2443765, 18.2292878, -1.0051318, 16.1496063, 30.8608644, 26.2444434, 19.3651725, 24.7795708}
+anchors_optimal = {4, 7, 0, 6}
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+x_sol = {16.7899270, 19.4043637, 0.9051800}
+seed = 201
+------------------------------------------------------------
+PDOP = 2.852082 | it = 0
+r_noised_vec = {25.1225356, 18.0470401, 5.1529729, 17.9081318, 31.8425670, 26.0093142, 19.3117220, 26.1163905}
+anchors_optimal = {4, 6, 1, 3}
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+x_sol = {18.8685789, 19.0000124, 0.7566468}
+seed = 203
+------------------------------------------------------------
+PDOP = 2.865557 | it = 0
+r_noised_vec = {1.8937242, 19.2132000, 20.5387903, 19.1449274, 16.9978517, 25.4420683, 31.8824879, 25.4395905}
+anchors_optimal = {6, 1, 3, 4}
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+x_sol = {0.8923042, 0.9612203, 3.0033593}
+seed = 205
+------------------------------------------------------------
+PDOP = 4.254190 | it = 0
+r_noised_vec = {3.1786560, 17.1628743, 35.0615361, 19.2559611, 16.9913650, 23.9442560, 30.7671136, 25.5490462}
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+seed = 207
+------------------------------------------------------------
+PDOP = 2.041351 | it = 0
+r_noised_vec = {4.5208119, 15.2570311, 23.6047682, 19.4422710, 17.3662106, 22.5343906, 29.7490451, 25.6677162}
+anchors_optimal = {5, 3, 1, 0}
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+x_sol = {4.9121248, 1.0904168, 3.2625852}
+seed = 209
+------------------------------------------------------------
+PDOP = 2.317076 | it = 0
+r_noised_vec = {5.9668696, 13.1783013, 26.4596967, 20.0698534, 18.0138938, 21.2195635, 28.6318142, 26.1420308}
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+x_sol = {6.9980392, 0.9682657, 3.0287564}
+seed = 211
+------------------------------------------------------------
+PDOP = 4.445338 | it = 0
+r_noised_vec = {8.2562705, 11.2007307, 26.7516959, 20.7146586, 18.8159535, 20.2147201, 27.7258064, 26.7375214}
+anchors_optimal = {6, 3, 5, 4}
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+------------------------------------------------------------
+PDOP = 4.565927 | it = 0
+r_noised_vec = {10.5535461, 9.2075324, 20.1543055, 21.3364298, 19.7959195, 19.1782450, 27.0308650, 27.4495345}
+anchors_optimal = {7, 3, 2, 5}
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+seed = 215
+------------------------------------------------------------
+PDOP = 3.471013 | it = 0
+r_noised_vec = {12.0971747, 7.1833220, 27.5962791, 22.7612461, 21.0463552, 18.3273011, 26.3550339, 28.2673247}
+anchors_optimal = {7, 3, 5, 0}
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+------------------------------------------------------------
+PDOP = 5.056801 | it = 0
+r_noised_vec = {13.7983560, 5.3593800, 17.8497985, 23.6165195, 22.0860685, 17.6803255, 25.8297090, 29.1809856}
+anchors_optimal = {6, 3, 4, 5}
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+x_sol = {15.1105398, 1.1689485, 3.0096214}
+seed = 219
+------------------------------------------------------------
+PDOP = 2.030655 | it = 0
+r_noised_vec = {16.2491504, 3.4913230, 25.8648101, 24.8465725, 23.3216846, 17.2628990, 25.6535343, 30.1828900}
+anchors_optimal = {3, 5, 0, 1}
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+x_sol = {17.1275145, 1.2021769, 2.9784646}
+seed = 221
+------------------------------------------------------------
+PDOP = 4.267194 | it = 0
+r_noised_vec = {18.4336159, 2.2263692, 19.0507345, 26.3824967, 24.5725995, 17.0485421, 25.4550313, 31.2678710}
+anchors_optimal = {6, 4, 2, 5}
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+x_sol = {18.7410489, 1.0972149, 2.9992596}
+seed = 223
+------------------------------------------------------------
+PDOP = 120.316802 | it = 2
+r_noised_vec = {2.6510191, 19.1880519, 29.9962963, 17.0268658, 17.0060862, 25.6283460, 30.6044035, 24.0704691}
+anchors_optimal = {1, 5, 7, 3}
+exact point = {1, 3, 3}
+start_optimal = {1.018135, 3.055625, 2.882281}
+x_sol = {1.0176151, 3.0551054, 2.9044531}
+seed = 225
+------------------------------------------------------------
+PDOP = 4.285650 | it = 0
+r_noised_vec = {3.1708088, 17.3329489, 26.7075367, 17.2301503, 17.2134881, 24.2317369, 29.4494995, 24.2341844}
+anchors_optimal = {2, 5, 1, 4}
+exact point = {3, 3, 3}
+x_sol = {2.8454500, -0.3647737, 2.9540538}
+seed = 227
+------------------------------------------------------------
+PDOP = 3.837279 | it = 0
+r_noised_vec = {5.1242429, 15.3504867, 25.0536692, 17.6488144, 17.6595227, 22.9609487, 28.3927939, 24.3822260}
+anchors_optimal = {6, 7, 5, 1}
+exact point = {5, 3, 3}
+x_sol = {4.9300579, 3.1593269, 2.8271652}
+seed = 229
+------------------------------------------------------------
+PDOP = 3.972537 | it = 0
+r_noised_vec = {6.8891883, 13.5597338, 34.2145149, 18.0688871, 18.2420082, 21.5532781, 27.4675346, 24.7256728}
+anchors_optimal = {6, 7, 3, 1}
+exact point = {7, 3, 3}
+x_sol = {6.7340379, 2.9809247, 3.0033101}
+seed = 231
+------------------------------------------------------------
+PDOP = 2.985896 | it = 0
+r_noised_vec = {8.2183510, 11.4622339, 13.5922415, 18.9164782, 18.9300437, 20.4494387, 26.4695217, 25.2447881}
+anchors_optimal = {7, 5, 4, 1}
+exact point = {9, 3, 3}
+x_sol = {8.9254476, 3.1591376, 2.9527174}
+seed = 233
+------------------------------------------------------------
+PDOP = 1.835899 | it = 0
+r_noised_vec = {10.1804975, 9.5932857, 31.1145794, 19.8368915, 19.8576958, 19.4811733, 25.7637175, 25.9286449}
+anchors_optimal = {3, 5, 0, 1}
+exact point = {11, 3, 3}
+x_sol = {10.8055631, 2.8721123, 2.9346057}
+seed = 235
+------------------------------------------------------------
+PDOP = 1.941729 | it = 0
+r_noised_vec = {12.6301352, 7.5716123, 13.3165535, 20.6692762, 20.8498748, 18.6822140, 25.1536869, 26.7638321}
+anchors_optimal = {4, 3, 0, 1}
+exact point = {13, 3, 3}
+x_sol = {13.1892369, 3.4552983, 3.2579746}
+seed = 237
+------------------------------------------------------------
+PDOP = 2.843804 | it = 0
+r_noised_vec = {14.4449586, 5.6749528, 26.1154857, 22.2642733, 22.1018174, 17.8713112, 24.5683940, 27.7340915}
+anchors_optimal = {3, 4, 5, 1}
+exact point = {15, 3, 3}
+x_sol = {14.9501729, 2.7529946, 2.9426665}
+seed = 239
+------------------------------------------------------------
+PDOP = 2.583736 | it = 0
+r_noised_vec = {15.9205860, 4.0470347, 16.7223591, 23.4321561, 23.3184580, 17.4363455, 24.2200135, 28.8212059}
+anchors_optimal = {6, 3, 5, 1}
+exact point = {17, 3, 3}
+x_sol = {17.0816984, 3.0636076, 2.9303249}
+seed = 241
+------------------------------------------------------------
+PDOP = 40.644931 | it = 2
+r_noised_vec = {18.1126959, 2.7908786, 20.4174675, 24.7238609, 24.8337804, 17.2026912, 23.9819566, 30.0061473}
+anchors_optimal = {0, 7, 4, 3}
+exact point = {19, 3, 3}
+start_optimal = {18.916528, 3.035468, 2.892116}
+x_sol = {18.8969633, 3.0354678, 2.9040290}
+seed = 243
+------------------------------------------------------------
+PDOP = 4.280277 | it = 0
+r_noised_vec = {4.8169360, 19.4246139, 28.7594277, 15.2590592, 17.6221378, 25.8431150, 29.5482111, 22.6688395}
+anchors_optimal = {6, 5, 1, 4}
+exact point = {1, 5, 3}
+x_sol = {1.0966618, 5.0992055, 2.8539220}
+seed = 245
+------------------------------------------------------------
+PDOP = 2.484025 | it = 0
+r_noised_vec = {4.9504545, 17.4390100, 22.2073595, 15.2148762, 17.7087430, 24.3708253, 28.2357621, 22.7953908}
+anchors_optimal = {5, 7, 3, 0}
+exact point = {3, 5, 3}
+x_sol = {3.0975594, 5.0530142, 2.9174373}
+seed = 247
+------------------------------------------------------------
+PDOP = 3.443735 | it = 0
+r_noised_vec = {5.6472065, 15.6307441, 28.2263107, 15.6106145, 17.9636797, 22.9989470, 27.0227331, 23.1132614}
+anchors_optimal = {6, 5, 4, 1}
+exact point = {5, 5, 3}
+x_sol = {5.0721638, 5.2032490, 3.0096999}
+seed = 249
+------------------------------------------------------------
+PDOP = 2.441923 | it = 0
+r_noised_vec = {7.4897723, 13.8038054, 18.4349652, 16.3586387, 18.4520311, 21.7111226, 26.1006108, 23.5728910}
+anchors_optimal = {6, 4, 1, 0}
+exact point = {7, 5, 3}
+x_sol = {6.9618854, 5.0706295, 3.0162957}
+seed = 251
+------------------------------------------------------------
+PDOP = 1.890311 | it = 0
+r_noised_vec = {9.5164319, 11.9406983, 24.8519804, 17.0656657, 19.1181263, 20.5246352, 25.1527865, 24.1682578}
+anchors_optimal = {6, 4, 3, 1}
+exact point = {9, 5, 3}
+x_sol = {8.9407468, 5.0287291, 3.0743658}
+seed = 253
+------------------------------------------------------------
+PDOP = 2.775661 | it = 0
+r_noised_vec = {10.8903838, 10.2332165, 17.7466156, 18.1391473, 20.0706654, 19.4166940, 24.3891364, 24.8919640}
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+exact point = {11, 5, 3}
+x_sol = {10.8706921, 4.9624156, 3.3291093}
+seed = 255
+------------------------------------------------------------
+PDOP = 2.677934 | it = 0
+r_noised_vec = {12.4659224, 8.3911849, 20.4378622, 19.3197554, 21.0903725, 18.7499652, 23.7464573, 25.7371545}
+anchors_optimal = {6, 3, 5, 1}
+exact point = {13, 5, 3}
+x_sol = {12.8817875, 4.9122884, 3.1013365}
+seed = 257
+------------------------------------------------------------
+PDOP = 3.301316 | it = 0
+r_noised_vec = {14.8167469, 6.8353981, 18.1813563, 20.4006648, 22.4051391, 18.0584335, 23.2974020, 26.6979321}
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+exact point = {15, 5, 3}
+x_sol = {15.1285063, 4.9529127, 3.0669929}
+seed = 259
+------------------------------------------------------------
+PDOP = 2.574614 | it = 0
+r_noised_vec = {16.9334959, 5.4062910, 17.7188687, 22.1071641, 23.7162410, 17.5729821, 23.0360429, 27.7693267}
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+exact point = {17, 5, 3}
+x_sol = {17.1750102, 5.0829386, 3.1425864}
+seed = 261
+------------------------------------------------------------
+PDOP = 1.971560 | it = 0
+r_noised_vec = {18.3750486, 4.5363649, 23.7498132, 23.5806459, 25.2295975, 17.2947774, 22.7431969, 28.9478902}
+anchors_optimal = {4, 3, 6, 1}
+exact point = {19, 5, 3}
+x_sol = {19.1151031, 5.0238332, 2.9057878}
+seed = 263
+------------------------------------------------------------
+PDOP = 3.809883 | it = 0
+r_noised_vec = {6.0329466, 19.9681733, 17.3265931, 13.0171862, 18.0691267, 26.1486990, 28.7104328, 21.3121272}
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+exact point = {1, 7, 3}
+x_sol = {1.1054149, 7.1391204, 3.0063256}
+seed = 265
+------------------------------------------------------------
+PDOP = 2.243601 | it = 0
+r_noised_vec = {6.8530582, 17.9742411, 32.8614989, 13.4036064, 18.0366082, 24.7200705, 27.4250517, 21.3642670}
+anchors_optimal = {7, 4, 1, 0}
+exact point = {3, 7, 3}
+x_sol = {3.2339754, 7.0496666, 3.1748729}
+seed = 267
+------------------------------------------------------------
+PDOP = 1.584167 | it = 0
+r_noised_vec = {7.7385128, 16.2048263, 15.1224556, 13.7430804, 18.3364543, 23.3973015, 26.1406942, 21.6260173}
+anchors_optimal = {4, 1, 3, 0}
+exact point = {5, 7, 3}
+x_sol = {5.1654785, 7.1055874, 3.2278691}
+seed = 269
+------------------------------------------------------------
+PDOP = 2.992534 | it = 0
+r_noised_vec = {8.4563962, 14.3390375, 26.6708976, 14.3876795, 18.9278310, 22.1939060, 25.0051992, 22.0875342}
+anchors_optimal = {5, 7, 4, 3}
+exact point = {7, 7, 3}
+x_sol = {6.9656137, 7.0895689, 3.1091093}
+seed = 271
+------------------------------------------------------------
+PDOP = 3.135246 | it = 0
+r_noised_vec = {9.9860262, 12.6687148, 16.4758241, 15.4696716, 19.6528362, 21.1215625, 23.9387780, 22.7331258}
+anchors_optimal = {6, 7, 3, 1}
+exact point = {9, 7, 3}
+x_sol = {9.0192083, 6.9451450, 3.1977824}
+seed = 273
+------------------------------------------------------------
+PDOP = 3.131405 | it = 0
+r_noised_vec = {12.1280244, 11.0382226, 19.3132589, 16.4945516, 20.6757738, 20.1760870, 23.1642866, 23.5427621}
+anchors_optimal = {7, 6, 3, 1}
+exact point = {11, 7, 3}
+x_sol = {10.9651967, 7.0118316, 3.0739101}
+seed = 275
+------------------------------------------------------------
+PDOP = 3.725374 | it = 0
+r_noised_vec = {13.7278895, 9.4811773, 18.4348820, 17.7907810, 21.7198712, 19.4052406, 22.4016587, 24.4940297}
+anchors_optimal = {7, 6, 5, 0}
+exact point = {13, 7, 3}
+x_sol = {13.0821890, 7.2033961, 2.9675897}
+seed = 277
+------------------------------------------------------------
+PDOP = 3.309046 | it = 0
+r_noised_vec = {15.0400021, 8.2104237, 13.9489283, 19.4618249, 22.9856334, 18.8320169, 21.8123450, 25.5640251}
+anchors_optimal = {7, 4, 0, 2}
+exact point = {15, 7, 3}
+x_sol = {14.6265552, 7.2057885, 2.5490084}
+seed = 279
+------------------------------------------------------------
+PDOP = 2.577428 | it = 0
+r_noised_vec = {17.0944786, 7.0624866, 19.0825640, 20.5450560, 24.1247754, 18.2823023, 21.5740893, 26.7302759}
+anchors_optimal = {7, 3, 0, 1}
+exact point = {17, 7, 3}
+x_sol = {16.8774337, 7.0821545, 2.8050441}
+seed = 281
+------------------------------------------------------------
+PDOP = 2.545763 | it = 0
+r_noised_vec = {19.4187683, 6.5128452, 12.2174114, 22.3055070, 25.4457328, 18.1260436, 21.3984769, 28.1199797}
+anchors_optimal = {4, 6, 5, 1}
+exact point = {19, 7, 3}
+x_sol = {18.8929437, 7.0962801, 2.9700972}
+seed = 283
+------------------------------------------------------------
+PDOP = 3.418897 | it = 0
+r_noised_vec = {8.3004866, 20.7300717, 28.1515829, 11.2921898, 18.6206556, 26.8332205, 27.8071469, 20.4157509}
+anchors_optimal = {6, 5, 1, 0}
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+x_sol = {1.0042686, 9.0995870, 2.8608986}
+seed = 285
+------------------------------------------------------------
+PDOP = 1.957437 | it = 0
+r_noised_vec = {8.1367870, 18.8629838, 20.7709413, 11.2253271, 18.8175287, 25.4898372, 26.4760079, 20.5125922}
+anchors_optimal = {5, 2, 7, 0}
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+x_sol = {2.6817097, 8.7071140, 2.9623824}
+seed = 287
+------------------------------------------------------------
+PDOP = 2.904160 | it = 0
+r_noised_vec = {9.1681032, 17.0801209, 22.4365348, 11.9335956, 19.2081113, 24.2515428, 25.3051050, 20.7843062}
+anchors_optimal = {6, 5, 4, 0}
+exact point = {5, 9, 3}
+x_sol = {4.7319529, 9.1260260, 3.0026994}
+seed = 289
+------------------------------------------------------------
+PDOP = 2.880314 | it = 0
+r_noised_vec = {10.5456512, 15.2606498, 19.4975051, 12.7249017, 19.8294739, 22.8937109, 24.2572664, 21.2280826}
+anchors_optimal = {5, 7, 4, 3}
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+x_sol = {7.0548958, 8.9888564, 2.9024113}
+seed = 291
+------------------------------------------------------------
+PDOP = 3.124242 | it = 0
+r_noised_vec = {11.4291563, 13.6984875, 15.8886958, 13.6657327, 20.5091635, 21.8309547, 23.1035622, 21.8390116}
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+x_sol = {9.0272422, 8.9951579, 2.8962625}
+seed = 293
+------------------------------------------------------------
+PDOP = 2.798842 | it = 0
+r_noised_vec = {12.6240987, 12.1042390, 21.7598751, 15.0582644, 21.4559106, 20.8856824, 22.2425107, 22.6099627}
+anchors_optimal = {4, 5, 3, 1}
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+seed = 295
+------------------------------------------------------------
+PDOP = 2.734768 | it = 0
+r_noised_vec = {14.6754643, 10.8022571, 9.1460591, 16.3963931, 22.2801156, 20.0778223, 21.4876191, 23.5319746}
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+------------------------------------------------------------
+PDOP = 3.242120 | it = 0
+r_noised_vec = {16.5661787, 9.6692551, 21.1186332, 17.8994694, 23.3706062, 19.4374279, 20.8490799, 24.5950805}
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+seed = 299
+------------------------------------------------------------
+PDOP = 2.749730 | it = 0
+r_noised_vec = {17.8327029, 8.8006399, 7.9177416, 19.7504201, 24.4706342, 18.9955560, 20.4045445, 25.7942876}
+anchors_optimal = {7, 6, 5, 1}
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+seed = 301
+------------------------------------------------------------
+PDOP = 3.775886 | it = 0
+r_noised_vec = {19.5086821, 8.4280096, 17.9474498, 21.0888650, 25.9515482, 18.7427275, 20.1021375, 26.8894273}
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+------------------------------------------------------------
+PDOP = 2.853329 | it = 0
+r_noised_vec = {10.4127740, 21.5958665, 20.4064637, 9.1644946, 19.7376884, 27.2531621, 26.9678127, 19.0556603}
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+------------------------------------------------------------
+PDOP = 3.801983 | it = 0
+r_noised_vec = {10.6470710, 19.9194416, 23.0960896, 9.5709601, 19.9843600, 26.0159793, 25.5485849, 19.1954455}
+anchors_optimal = {6, 4, 1, 0}
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+------------------------------------------------------------
+PDOP = 1.829345 | it = 0
+r_noised_vec = {10.6981577, 18.1466839, 21.0640970, 9.9414613, 20.2297101, 24.7029406, 24.2326285, 19.5487411}
+anchors_optimal = {6, 4, 1, 3}
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+------------------------------------------------------------
+PDOP = 3.312681 | it = 0
+r_noised_vec = {11.6197106, 16.5022336, 16.1548069, 11.0134226, 20.6348319, 23.5046465, 23.1866123, 20.0990128}
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+------------------------------------------------------------
+PDOP = 1.892440 | it = 0
+r_noised_vec = {13.2523497, 14.9925949, 19.6979888, 12.2735999, 21.2229878, 22.4258763, 22.1600918, 20.8246320}
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+------------------------------------------------------------
+PDOP = 2.643336 | it = 0
+r_noised_vec = {14.4473647, 13.4920369, 12.2743552, 13.5216392, 22.0221454, 21.4516176, 21.3310656, 21.7019997}
+anchors_optimal = {7, 5, 1, 2}
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+------------------------------------------------------------
+PDOP = 3.305342 | it = 0
+r_noised_vec = {15.4304704, 12.0846343, 16.1819797, 15.1673970, 23.0679677, 20.8791021, 20.5274454, 22.7078738}
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+------------------------------------------------------------
+PDOP = 3.196071 | it = 0
+r_noised_vec = {17.2082645, 11.2696499, 11.1012534, 16.7761984, 24.1432717, 20.2874014, 20.0027536, 23.8190632}
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+------------------------------------------------------------
+PDOP = 3.614368 | it = 0
+r_noised_vec = {19.3092901, 10.5369469, 12.4288526, 18.1727160, 25.4392855, 19.8989629, 19.6902183, 25.2582764}
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+------------------------------------------------------------
+PDOP = 3.430009 | it = 0
+r_noised_vec = {20.7452305, 10.2629238, 9.0802602, 20.4083250, 26.9372626, 19.7252852, 19.3248268, 26.5306573}
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+------------------------------------------------------------
+PDOP = 2.945080 | it = 0
+r_noised_vec = {11.8208882, 22.7073744, 21.3417070, 7.2537459, 20.9190612, 28.1850750, 26.5060360, 18.5200199}
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+------------------------------------------------------------
+PDOP = 3.388580 | it = 0
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+------------------------------------------------------------
+PDOP = 2.595899 | it = 0
+r_noised_vec = {13.1506085, 19.5343352, 12.9892940, 8.4447118, 21.0653708, 25.7299409, 23.7004560, 18.8434893}
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+------------------------------------------------------------
+PDOP = 1.863767 | it = 0
+r_noised_vec = {13.5086446, 17.8854721, 23.8617723, 9.3647160, 21.5371702, 24.6786921, 22.4197819, 19.3253071}
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+------------------------------------------------------------
+PDOP = 3.095367 | it = 0
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+------------------------------------------------------------
+PDOP = 2.849037 | it = 0
+r_noised_vec = {15.8588997, 15.1207230, 18.1975024, 12.4527569, 23.0837376, 22.7530440, 20.3872294, 20.8773256}
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+------------------------------------------------------------
+PDOP = 2.943443 | it = 0
+r_noised_vec = {17.4042998, 13.9141732, 9.5677386, 13.9708103, 24.0978229, 22.0767810, 19.5500227, 21.9131457}
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+------------------------------------------------------------
+PDOP = 2.805220 | it = 0
+r_noised_vec = {18.3845780, 13.0661101, 11.7821348, 15.7893605, 25.1198770, 21.5636128, 18.9016227, 22.8225343}
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+------------------------------------------------------------
+PDOP = 2.808680 | it = 0
+r_noised_vec = {19.8104585, 12.3364359, 10.2690505, 17.5999598, 26.3509915, 21.2969786, 18.6119942, 24.1861693}
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+x_sol = {16.8228056, 12.6762021, 3.2575736}
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+------------------------------------------------------------
+PDOP = 4.131946 | it = 0
+r_noised_vec = {21.9355157, 12.1330978, 7.7557256, 19.1651455, 27.5019570, 20.8845152, 18.4467475, 25.6103290}
+anchors_optimal = {4, 7, 3, 6}
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+seed = 343
+------------------------------------------------------------
+PDOP = 2.085540 | it = 0
+r_noised_vec = {14.3966998, 23.6088477, 25.2797814, 5.5031181, 22.0185308, 29.1455625, 26.1554341, 17.6633438}
+anchors_optimal = {6, 1, 4, 3}
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+seed = 345
+------------------------------------------------------------
+PDOP = 2.694790 | it = 0
+r_noised_vec = {14.0313483, 22.1219331, 17.5672861, 5.7889165, 21.9725713, 27.8695037, 24.6344402, 17.8298068}
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+x_sol = {3.2605793, 15.2571153, 3.4338959}
+seed = 347
+------------------------------------------------------------
+PDOP = 3.436611 | it = 0
+r_noised_vec = {14.4838830, 20.7203305, 20.6779335, 6.5709072, 22.3398981, 26.6636999, 23.3622348, 18.2034985}
+anchors_optimal = {5, 6, 1, 0}
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+x_sol = {4.7223887, 14.8462863, 3.0889264}
+seed = 349
+------------------------------------------------------------
+PDOP = 2.081838 | it = 0
+r_noised_vec = {15.6485062, 19.2850795, 15.1551298, 8.1793906, 22.8851268, 25.5637789, 22.2662383, 18.7689386}
+anchors_optimal = {6, 1, 2, 3}
+exact point = {7, 15, 3}
+x_sol = {6.2164334, 14.2430614, 3.4971735}
+seed = 351
+------------------------------------------------------------
+PDOP = 3.516254 | it = 0
+r_noised_vec = {16.4139725, 18.0904990, 23.2849089, 9.6209096, 23.5452000, 24.5774450, 20.9160467, 19.5073859}
+anchors_optimal = {5, 4, 7, 0}
+exact point = {9, 15, 3}
+x_sol = {9.1927800, 15.0746931, 3.0011066}
+seed = 353
+------------------------------------------------------------
+PDOP = 1.823508 | it = 0
+r_noised_vec = {17.0073548, 16.8284352, 10.3508518, 11.2937327, 24.2513210, 23.7057653, 19.9170441, 20.3990790}
+anchors_optimal = {4, 6, 1, 3}
+exact point = {11, 15, 3}
+x_sol = {10.9709223, 15.0669179, 2.9464396}
+seed = 355
+------------------------------------------------------------
+PDOP = 3.947355 | it = 0
+r_noised_vec = {18.4328733, 15.8524432, 9.9885865, 13.2372493, 25.1582983, 22.9543429, 19.0508079, 21.4208271}
+anchors_optimal = {5, 7, 6, 0}
+exact point = {13, 15, 3}
+x_sol = {13.0241725, 14.8149625, 3.0513265}
+seed = 357
+------------------------------------------------------------
+PDOP = 3.972801 | it = 0
+r_noised_vec = {20.2313637, 14.9943469, 12.0667544, 14.9585752, 26.0500535, 22.5437491, 18.3615376, 22.7600100}
+anchors_optimal = {7, 5, 0, 1}
+exact point = {15, 15, 3}
+x_sol = {15.3546747, 15.0968475, 3.0423636}
+seed = 359
+------------------------------------------------------------
+PDOP = 3.546637 | it = 0
+r_noised_vec = {21.4140100, 14.3652143, 4.0548235, 16.8705999, 27.1711027, 22.1393393, 17.8434347, 23.9696150}
+anchors_optimal = {4, 0, 6, 1}
+exact point = {17, 15, 3}
+x_sol = {17.1368537, 14.9126373, 3.1392369}
+seed = 361
+------------------------------------------------------------
+PDOP = 3.958104 | it = 0
+r_noised_vec = {22.5499267, 14.1131279, 11.1985485, 18.8049889, 28.2896854, 21.9182389, 17.7275410, 25.2860554}
+anchors_optimal = {4, 0, 5, 3}
+exact point = {19, 15, 3}
+x_sol = {18.9183448, 14.5755680, 2.8208656}
+seed = 363
+------------------------------------------------------------
+PDOP = 3.626100 | it = 0
+r_noised_vec = {16.1206793, 24.7616785, 15.7756279, 3.4020500, 23.3172523, 29.9315054, 25.5811501, 17.2365685}
+anchors_optimal = {5, 4, 7, 0}
+exact point = {1, 17, 3}
+x_sol = {1.2315589, 16.9893411, 3.0311065}
+seed = 365
+------------------------------------------------------------
+PDOP = 1.887050 | it = 0
+r_noised_vec = {16.5895053, 23.3743277, 24.7801338, 4.1648001, 23.4485450, 28.8611445, 24.1145504, 17.3159334}
+anchors_optimal = {6, 4, 1, 3}
+exact point = {3, 17, 3}
+x_sol = {3.1224880, 17.0438994, 3.0310388}
+seed = 367
+------------------------------------------------------------
+PDOP = 2.733660 | it = 0
+r_noised_vec = {16.5610685, 21.9533058, 14.8568777, 5.4863277, 23.8370568, 27.6949265, 22.8589447, 17.6410069}
+anchors_optimal = {5, 4, 7, 3}
+exact point = {5, 17, 3}
+x_sol = {5.2683243, 17.2631619, 3.1024913}
+seed = 369
+------------------------------------------------------------
+PDOP = 2.092772 | it = 0
+r_noised_vec = {16.8720999, 20.7155367, 17.0311702, 6.8569548, 24.1782027, 26.6616763, 21.6145029, 18.1984584}
+anchors_optimal = {1, 7, 0, 3}
+exact point = {7, 17, 3}
+x_sol = {6.6982708, 16.7539454, 3.0219458}
+seed = 371
+------------------------------------------------------------
+PDOP = 3.623921 | it = 0
+r_noised_vec = {18.1066864, 19.5996881, 14.1616375, 8.8543933, 24.7150875, 25.7609459, 20.5422121, 18.9665158}
+anchors_optimal = {5, 4, 1, 3}
+exact point = {9, 17, 3}
+x_sol = {9.1107688, 17.1567555, 3.1453010}
+seed = 373
+------------------------------------------------------------
+PDOP = 605.644937 | it = 2
+r_noised_vec = {19.2884078, 18.5184052, 10.4073978, 10.6530477, 25.3081877, 25.0080129, 19.4932600, 19.9192366}
+anchors_optimal = {4, 5, 7, 6}
+exact point = {11, 17, 3}
+start_optimal = {10.941811, 16.958251, 3.045038}
+x_sol = {10.8974647, 16.9139048, 2.9914083}
+seed = 375
+------------------------------------------------------------
+PDOP = 3.226801 | it = 0
+r_noised_vec = {19.9415286, 17.7227947, 11.5666125, 12.4458448, 26.1706878, 24.3846144, 18.7245842, 20.8638956}
+anchors_optimal = {4, 0, 6, 3}
+exact point = {13, 17, 3}
+x_sol = {12.9086667, 16.8885661, 2.9410438}
+seed = 377
+------------------------------------------------------------
+PDOP = 3.560991 | it = 0
+r_noised_vec = {21.0656593, 16.9279395, 6.2837546, 14.5281194, 27.0637865, 23.9190779, 18.1295359, 22.1629624}
+anchors_optimal = {4, 0, 6, 3}
+exact point = {15, 17, 3}
+x_sol = {15.0019136, 16.6235724, 2.9029859}
+seed = 379
+------------------------------------------------------------
+PDOP = 3.609095 | it = 0
+r_noised_vec = {22.9210409, 16.4675088, 7.3053046, 16.3861348, 28.3030439, 23.6290659, 17.5504863, 23.5437573}
+anchors_optimal = {4, 7, 6, 3}
+exact point = {17, 17, 3}
+x_sol = {16.9812879, 16.9935206, 2.9788659}
+seed = 381
+------------------------------------------------------------
+PDOP = 4.258752 | it = 0
+r_noised_vec = {24.4206298, 16.1541631, 4.7378821, 18.3336782, 29.5264148, 23.5333084, 17.3393793, 24.9966459}
+anchors_optimal = {4, 7, 6, 1}
+exact point = {19, 17, 3}
+x_sol = {19.0310061, 16.9993913, 2.9559485}
+seed = 383
+------------------------------------------------------------
+PDOP = 2.675526 | it = 0
+r_noised_vec = {17.8637902, 26.1781367, 28.9800145, 2.5192021, 24.9463352, 31.2552926, 25.5238602, 17.1156632}
+anchors_optimal = {1, 6, 0, 3}
+exact point = {1, 19, 3}
+x_sol = {0.8636885, 18.7307532, 3.1594415}
+seed = 385
+------------------------------------------------------------
+PDOP = 4.147799 | it = 0
+r_noised_vec = {18.0070760, 24.8010357, 16.9031354, 2.8637375, 24.9096243, 30.1252985, 24.0474871, 17.2416962}
+anchors_optimal = {5, 4, 1, 3}
+exact point = {3, 19, 3}
+x_sol = {2.9462046, 18.9170040, 2.8041516}
+seed = 387
+------------------------------------------------------------
+PDOP = 4.114158 | it = 0
+r_noised_vec = {18.8290695, 23.3841137, 16.9857219, 4.5499890, 25.0725859, 29.0802774, 22.6182213, 17.5789991}
+anchors_optimal = {5, 4, 6, 0}
+exact point = {5, 19, 3}
+x_sol = {4.7887376, 19.2915421, 3.2868236}
+seed = 389
+------------------------------------------------------------
+PDOP = 427.222065 | it = 2
+r_noised_vec = {19.2461487, 22.2608312, 18.5881427, 6.5397946, 25.3373402, 28.1386412, 21.2653725, 18.1191565}
+anchors_optimal = {1, 6, 0, 7}
+exact point = {7, 19, 3}
+start_optimal = {7.207096, 19.122245, 3.017979}
+x_sol = {7.2070957, 19.1035387, 3.0366859}
+seed = 391
+------------------------------------------------------------
+PDOP = 3.804560 | it = 0
+r_noised_vec = {19.4899503, 21.1264884, 9.0186803, 8.1810674, 25.9213794, 27.1194703, 20.2293352, 18.8490941}
+anchors_optimal = {5, 4, 1, 7}
+exact point = {9, 19, 3}
+x_sol = {8.8276906, 18.8323569, 2.8911274}
+seed = 393
+------------------------------------------------------------
+PDOP = 2.075407 | it = 0
+r_noised_vec = {20.5716436, 20.2238457, 16.0210712, 10.2795015, 26.6882780, 26.3995602, 19.1706381, 19.8903312}
+anchors_optimal = {4, 1, 6, 3}
+exact point = {11, 19, 3}
+x_sol = {11.0449347, 19.0274553, 3.0644018}
+seed = 395
+------------------------------------------------------------
+PDOP = 2.166363 | it = 0
+r_noised_vec = {22.0534441, 19.4783501, 5.1048159, 12.2668233, 27.5568142, 25.7878080, 18.3166492, 20.8565763}
+anchors_optimal = {4, 1, 6, 3}
+exact point = {13, 19, 3}
+x_sol = {13.0650947, 19.0895992, 3.0658346}
+seed = 397
+------------------------------------------------------------
+PDOP = 62.668275 | it = 2
+r_noised_vec = {22.9536703, 18.8076037, 10.0842889, 14.0892223, 28.5215524, 25.3017719, 17.7408436, 22.0013795}
+anchors_optimal = {4, 5, 0, 1}
+exact point = {15, 19, 3}
+start_optimal = {15.056448, 19.064266, 2.961745}
+x_sol = {15.0605076, 19.0371997, 2.9576850}
+seed = 399
+------------------------------------------------------------
+PDOP = 2.654571 | it = 0
+r_noised_vec = {23.8282209, 18.4775942, 3.4643311, 16.2038958, 29.7168160, 24.9450588, 17.3214067, 23.2789754}
+anchors_optimal = {4, 0, 3, 2}
+exact point = {17, 19, 3}
+x_sol = {17.0938065, 18.5320493, 2.2024989}
+seed = 401
+------------------------------------------------------------
+PDOP = 4.169081 | it = 0
+r_noised_vec = {25.5271510, 18.1442329, 4.1176140, 18.1468689, 30.6619005, 24.7634060, 17.1729951, 24.6706459}
+anchors_optimal = {0, 7, 3, 1}
+exact point = {19, 19, 3}
+x_sol = {18.9847961, 18.9822786, 3.1491600}
+seed = 403
+------------------------------------------------------------
+PDOP = 3.887586 | it = 0
+r_noised_vec = {4.3387502, 19.4762807, 30.3556310, 19.3913454, 14.9687143, 24.1580188, 30.8196542, 24.0993240}
+anchors_optimal = {6, 5, 7, 0}
+exact point = {1, 1, 5}
+x_sol = {0.7875350, 0.8620733, 5.3496987}
+seed = 405
+------------------------------------------------------------
+PDOP = 3.036623 | it = 0
+r_noised_vec = {4.4236950, 17.4700488, 27.1316208, 19.7446502, 14.9352141, 22.5724897, 29.6912438, 24.1989075}
+anchors_optimal = {2, 7, 3, 0}
+exact point = {3, 1, 5}
+x_sol = {1.3875359, 0.7557333, 5.3490549}
+seed = 407
+------------------------------------------------------------
+PDOP = 3.890160 | it = 0
+r_noised_vec = {5.3263418, 15.4703734, 29.5819561, 19.7661473, 15.4170387, 21.0317197, 28.6392642, 24.4724679}
+anchors_optimal = {6, 7, 3, 4}
+exact point = {5, 1, 5}
+x_sol = {4.6761640, 0.9942999, 5.0210235}
+seed = 409
+------------------------------------------------------------
+PDOP = 2.833140 | it = 0
+r_noised_vec = {7.3137252, 13.3875746, 24.0943416, 20.2282004, 16.1406461, 19.7967091, 27.5116182, 24.9076631}
+anchors_optimal = {7, 3, 5, 0}
+exact point = {7, 1, 5}
+x_sol = {7.1524335, 1.1397496, 4.9418003}
+seed = 411
+------------------------------------------------------------
+PDOP = 3.746074 | it = 0
+r_noised_vec = {9.2576671, 11.5960406, 26.3209476, 21.1473019, 17.0987016, 18.5039517, 26.6182239, 25.4887901}
+anchors_optimal = {6, 7, 3, 5}
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+x_sol = {8.9512783, 0.8649048, 5.1718410}
+seed = 413
+------------------------------------------------------------
+PDOP = 2.656075 | it = 0
+r_noised_vec = {10.6163788, 9.6422199, 12.9419346, 21.7506529, 18.1354911, 17.3559210, 25.7940608, 26.2144306}
+anchors_optimal = {7, 4, 5, 1}
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+x_sol = {11.2281064, 1.0710438, 5.0195898}
+seed = 415
+------------------------------------------------------------
+PDOP = 1.967451 | it = 0
+r_noised_vec = {12.3612370, 8.0061029, 30.1535601, 22.8103553, 19.2445132, 16.3719266, 25.1665192, 27.1022975}
+anchors_optimal = {6, 3, 4, 1}
+exact point = {13, 1, 5}
+x_sol = {13.0422661, 1.0366181, 4.9829607}
+seed = 417
+------------------------------------------------------------
+PDOP = 2.089647 | it = 0
+r_noised_vec = {14.7612693, 6.3932717, 19.6928095, 24.0214184, 20.5355565, 15.7779297, 24.6183225, 28.0817030}
+anchors_optimal = {4, 2, 5, 1}
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+x_sol = {15.0464741, 1.3701888, 5.0244963}
+seed = 419
+------------------------------------------------------------
+PDOP = 2.701091 | it = 0
+r_noised_vec = {16.7470711, 5.0463274, 22.0081395, 25.0820127, 21.8682233, 15.2399842, 24.2065081, 29.1443529}
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+x_sol = {16.9726861, 1.0873718, 5.0581132}
+seed = 421
+------------------------------------------------------------
+PDOP = 2.397802 | it = 0
+r_noised_vec = {18.1964295, 4.2993472, 25.0789237, 26.4975142, 23.4126797, 14.9757760, 24.1718264, 30.2826687}
+anchors_optimal = {7, 0, 5, 1}
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+x_sol = {18.7269911, 0.4963028, 5.0844874}
+seed = 423
+------------------------------------------------------------
+PDOP = 3.634813 | it = 0
+r_noised_vec = {4.2575096, 19.6166706, 23.4810614, 17.4889172, 15.0291547, 24.2500394, 29.4964229, 22.7626142}
+anchors_optimal = {6, 5, 7, 0}
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+x_sol = {1.2394117, 3.0796171, 4.7622193}
+seed = 425
+------------------------------------------------------------
+PDOP = 3.831834 | it = 0
+r_noised_vec = {5.1766496, 17.7583609, 33.2293398, 17.5674565, 15.2672602, 22.7598014, 28.2703428, 22.8176457}
+anchors_optimal = {7, 1, 3, 4}
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+x_sol = {2.7552743, 2.9327442, 4.9202783}
+seed = 427
+------------------------------------------------------------
+PDOP = 3.991356 | it = 0
+r_noised_vec = {6.1688948, 15.7045743, 20.0555746, 18.0725813, 15.8317530, 21.3262637, 27.1893820, 23.0471845}
+anchors_optimal = {6, 7, 3, 1}
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+x_sol = {5.0110950, 2.9062386, 5.1169864}
+seed = 429
+------------------------------------------------------------
+PDOP = 3.689757 | it = 0
+r_noised_vec = {7.1781637, 13.7609566, 29.2244402, 18.4859027, 16.4101429, 20.0046014, 26.1932449, 23.4540622}
+anchors_optimal = {6, 5, 3, 4}
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+seed = 431
+------------------------------------------------------------
+PDOP = 2.512854 | it = 0
+r_noised_vec = {9.0464581, 11.8350283, 20.1980883, 19.0743120, 17.1599714, 18.8149694, 25.3583125, 23.9626329}
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+x_sol = {8.9331986, 2.8936594, 4.9045733}
+seed = 433
+------------------------------------------------------------
+PDOP = 2.249868 | it = 0
+r_noised_vec = {11.2788265, 9.8963186, 23.7618847, 20.2582280, 18.1033827, 17.8070720, 24.4567431, 24.6544440}
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+------------------------------------------------------------
+PDOP = 1.805856 | it = 0
+r_noised_vec = {12.8716280, 8.2204734, 21.5020859, 21.1468238, 19.2134924, 16.7321331, 23.8468711, 25.5070188}
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+------------------------------------------------------------
+PDOP = 3.512653 | it = 0
+r_noised_vec = {14.3620992, 6.5456955, 19.6402907, 22.3274339, 20.5607448, 16.0395779, 23.3730666, 26.5046512}
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+------------------------------------------------------------
+PDOP = 4.543279 | it = 0
+r_noised_vec = {16.6028552, 5.3376865, 21.8765581, 23.7769799, 21.9375726, 15.5690974, 22.8992239, 27.6294890}
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+x_sol = {16.9887528, 2.8765797, 5.0894133}
+seed = 441
+------------------------------------------------------------
+PDOP = 1.951535 | it = 0
+r_noised_vec = {18.8835125, 4.5665636, 18.7459345, 25.0243703, 23.5490060, 15.3543137, 22.6965252, 28.8624798}
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+------------------------------------------------------------
+PDOP = 3.625233 | it = 0
+r_noised_vec = {5.6120684, 19.8568725, 41.5806708, 15.5193949, 15.5591834, 24.5742183, 28.3953676, 21.1651639}
+anchors_optimal = {5, 7, 1, 4}
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+seed = 445
+------------------------------------------------------------
+PDOP = 1.540607 | it = 0
+r_noised_vec = {5.6713401, 18.0527128, 15.8249249, 15.6828603, 15.7987900, 23.0798774, 27.1317403, 21.2929826}
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+x_sol = {2.7700963, 4.8739998, 4.7779561}
+seed = 447
+------------------------------------------------------------
+PDOP = 3.103642 | it = 0
+r_noised_vec = {7.0268744, 16.1056816, 30.8905677, 15.7767990, 16.0644166, 21.6433544, 25.8582558, 21.5945987}
+anchors_optimal = {5, 6, 1, 4}
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+x_sol = {4.9732628, 5.2218975, 5.0081969}
+seed = 449
+------------------------------------------------------------
+PDOP = 2.546135 | it = 0
+r_noised_vec = {8.5584230, 14.3261915, 19.7966226, 16.7189840, 16.4966750, 20.2847687, 24.6688930, 22.2142387}
+anchors_optimal = {6, 7, 3, 0}
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+seed = 451
+------------------------------------------------------------
+PDOP = 2.108868 | it = 0
+r_noised_vec = {9.6481431, 12.4113994, 21.6908936, 17.5503772, 17.3278594, 19.0250713, 23.8343640, 22.8370067}
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+x_sol = {8.8763519, 4.8439717, 5.0482093}
+seed = 453
+------------------------------------------------------------
+PDOP = 2.086725 | it = 0
+r_noised_vec = {11.2017380, 10.6484239, 22.9988217, 18.3153827, 18.3963777, 17.9217559, 22.9743717, 23.6194100}
+anchors_optimal = {7, 3, 0, 1}
+exact point = {11, 5, 5}
+x_sol = {10.8181579, 4.9743603, 4.6467556}
+seed = 455
+------------------------------------------------------------
+PDOP = 1.711405 | it = 0
+r_noised_vec = {13.4633477, 8.9738120, 15.4505273, 19.7213570, 19.5720028, 16.9692378, 22.3111798, 24.5214888}
+anchors_optimal = {6, 3, 4, 1}
+exact point = {13, 5, 5}
+x_sol = {13.0483839, 4.9325254, 5.0869630}
+seed = 457
+------------------------------------------------------------
+PDOP = 3.346257 | it = 0
+r_noised_vec = {15.3545365, 7.4280716, 23.6894255, 20.9110755, 20.9769548, 16.1947761, 21.8176246, 25.5327111}
+anchors_optimal = {7, 6, 3, 1}
+exact point = {15, 5, 5}
+x_sol = {15.1292261, 5.0740463, 4.8514143}
+seed = 459
+------------------------------------------------------------
+PDOP = 2.445240 | it = 0
+r_noised_vec = {16.7320525, 6.3411887, 13.5282764, 22.2104428, 22.3600853, 15.5830914, 21.5144541, 26.6455552}
+anchors_optimal = {7, 6, 5, 1}
+exact point = {17, 5, 5}
+x_sol = {17.0029968, 4.7095001, 5.1678404}
+seed = 461
+------------------------------------------------------------
+PDOP = 2.829090 | it = 0
+r_noised_vec = {18.6524229, 5.6076753, 22.0055115, 23.8530911, 23.9209587, 15.4917083, 21.4471623, 27.8543007}
+anchors_optimal = {7, 4, 0, 1}
+exact point = {19, 5, 5}
+x_sol = {18.8280752, 5.1407946, 4.5973846}
+seed = 463
+------------------------------------------------------------
+PDOP = 3.494512 | it = 0
+r_noised_vec = {7.4847913, 20.2868596, 23.0488689, 13.5738520, 16.1647678, 24.8327052, 27.5553219, 19.8488699}
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+------------------------------------------------------------
+PDOP = 2.098056 | it = 0
+r_noised_vec = {7.6537858, 18.4461161, 26.0205872, 13.7235065, 16.2436450, 23.3052644, 26.2546688, 19.9295033}
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+exact point = {3, 7, 5}
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+------------------------------------------------------------
+PDOP = 3.002871 | it = 0
+r_noised_vec = {7.9447637, 16.6630507, 22.8615616, 14.2017638, 16.4722398, 21.8478343, 25.0245417, 20.2306104}
+anchors_optimal = {5, 1, 4, 3}
+exact point = {5, 7, 5}
+x_sol = {5.0791269, 7.0782627, 5.2455104}
+seed = 469
+------------------------------------------------------------
+PDOP = 3.211106 | it = 0
+r_noised_vec = {9.2599476, 14.9751189, 20.5783504, 14.6876863, 17.1629145, 20.6937288, 23.7455360, 20.5300717}
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+------------------------------------------------------------
+PDOP = 2.337811 | it = 0
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+------------------------------------------------------------
+PDOP = 2.097635 | it = 0
+r_noised_vec = {12.3969469, 11.6586701, 18.6334293, 17.0143755, 19.1185413, 18.4383934, 21.6456795, 22.0753687}
+anchors_optimal = {6, 5, 0, 1}
+exact point = {11, 7, 5}
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+------------------------------------------------------------
+PDOP = 1.655940 | it = 0
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+------------------------------------------------------------
+PDOP = 2.320317 | it = 0
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+------------------------------------------------------------
+PDOP = 2.582298 | it = 0
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+------------------------------------------------------------
+PDOP = 2.626893 | it = 0
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+exact point = {19, 7, 5}
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+------------------------------------------------------------
+PDOP = 2.154044 | it = 0
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+------------------------------------------------------------
+PDOP = 3.745141 | it = 0
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+exact point = {3, 9, 5}
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+------------------------------------------------------------
+PDOP = 2.227668 | it = 0
+r_noised_vec = {10.1091197, 17.4511151, 17.8418105, 12.3355014, 17.4855977, 22.7418678, 23.9410683, 19.2777669}
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+exact point = {5, 9, 5}
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+seed = 489
+------------------------------------------------------------
+PDOP = 2.138433 | it = 0
+r_noised_vec = {10.6245328, 15.7574472, 24.6191623, 13.4716765, 18.1989239, 21.5131325, 22.8151531, 19.7400111}
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+exact point = {7, 9, 5}
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+seed = 491
+------------------------------------------------------------
+PDOP = 2.321536 | it = 0
+r_noised_vec = {11.7129884, 14.2913025, 14.1212751, 14.0827201, 18.8907923, 20.4003208, 21.9384818, 20.3930106}
+anchors_optimal = {6, 7, 3, 0}
+exact point = {9, 9, 5}
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+------------------------------------------------------------
+PDOP = 1.624913 | it = 0
+r_noised_vec = {13.6091873, 12.7754243, 20.8447258, 15.3178880, 19.7387934, 19.4446071, 20.7507230, 21.2087171}
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+exact point = {11, 9, 5}
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+seed = 495
+------------------------------------------------------------
+PDOP = 2.420574 | it = 0
+r_noised_vec = {15.2218028, 11.6245589, 13.5180181, 16.9165505, 20.7313759, 18.4310064, 19.9877460, 22.1730805}
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+exact point = {13, 9, 5}
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+seed = 497
+------------------------------------------------------------
+PDOP = 2.417348 | it = 0
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+exact point = {15, 9, 5}
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+seed = 499
+------------------------------------------------------------
+PDOP = 2.135784 | it = 0
+r_noised_vec = {18.1137894, 9.5991283, 14.1972978, 19.8269049, 23.3238661, 17.3157768, 18.8405813, 24.4979069}
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+seed = 501
+------------------------------------------------------------
+PDOP = 2.921264 | it = 0
+r_noised_vec = {20.3696099, 9.0227030, 13.4729686, 21.5521683, 24.7297875, 17.0574805, 18.5625542, 25.8336011}
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+------------------------------------------------------------
+PDOP = 3.097414 | it = 0
+r_noised_vec = {10.9424117, 21.7703681, 24.7284361, 9.7599875, 18.0785456, 26.1869085, 25.8092261, 17.4483193}
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+seed = 505
+------------------------------------------------------------
+PDOP = 2.802823 | it = 0
+r_noised_vec = {10.6565529, 20.0478564, 12.1543833, 10.0844086, 18.3857321, 24.7484836, 24.3008763, 17.6006916}
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+------------------------------------------------------------
+PDOP = 2.545781 | it = 0
+r_noised_vec = {11.3660422, 18.2531356, 29.8541264, 10.6528472, 18.5696466, 23.3802135, 22.8905467, 17.7460098}
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+------------------------------------------------------------
+PDOP = 2.281221 | it = 0
+r_noised_vec = {12.6467080, 16.7857473, 11.1534956, 11.5003145, 19.0040222, 22.0936097, 21.7714967, 18.3628863}
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+seed = 511
+------------------------------------------------------------
+PDOP = 1.617217 | it = 0
+r_noised_vec = {13.4872491, 15.2520285, 22.5705690, 12.8938862, 19.5804370, 21.0967919, 20.6151921, 19.1682730}
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+------------------------------------------------------------
+PDOP = 1.976505 | it = 0
+r_noised_vec = {14.3676608, 14.0130454, 12.8304561, 14.0260967, 20.4942228, 20.0736265, 19.6578973, 20.1381250}
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+------------------------------------------------------------
+PDOP = 2.168632 | it = 0
+r_noised_vec = {16.1077489, 12.9011056, 14.8266057, 15.3954212, 21.6165299, 19.2219452, 18.8525353, 21.2449189}
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+seed = 517
+------------------------------------------------------------
+PDOP = 2.744799 | it = 0
+r_noised_vec = {17.9953184, 11.9413981, 14.6787320, 17.2656234, 22.8410220, 18.5512459, 18.2632771, 22.4632955}
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+------------------------------------------------------------
+PDOP = 2.389275 | it = 0
+r_noised_vec = {19.2496184, 11.3662098, 9.6806815, 18.7239287, 24.1894510, 18.0489638, 17.8995508, 23.7721970}
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+------------------------------------------------------------
+PDOP = 3.342713 | it = 0
+r_noised_vec = {20.6507951, 10.9028011, 15.3964846, 20.4745772, 25.5175106, 18.0062602, 17.5585666, 25.1553242}
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+------------------------------------------------------------
+PDOP = 2.594726 | it = 0
+r_noised_vec = {12.7401531, 22.9552323, 18.9247135, 8.1584125, 19.2995547, 26.9589315, 25.2881440, 16.5807437}
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+------------------------------------------------------------
+PDOP = 2.238715 | it = 0
+r_noised_vec = {13.1164667, 21.2116141, 25.0991389, 8.2368559, 19.2915368, 25.6004382, 23.8242405, 16.8673930}
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+------------------------------------------------------------
+PDOP = 2.514444 | it = 0
+r_noised_vec = {13.1246220, 19.5755782, 17.0931687, 9.0050114, 19.6086497, 24.3487514, 22.3461491, 17.1373484}
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+------------------------------------------------------------
+PDOP = 2.328882 | it = 0
+r_noised_vec = {13.7132740, 18.0807987, 18.9783658, 10.0857600, 19.9856892, 23.2017804, 21.0224949, 17.6450699}
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+------------------------------------------------------------
+PDOP = 2.537022 | it = 0
+r_noised_vec = {15.1554525, 16.5970144, 15.7954061, 11.3382724, 20.7722407, 22.1707984, 19.7691351, 18.3668447}
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+------------------------------------------------------------
+PDOP = 2.605656 | it = 0
+r_noised_vec = {16.3800641, 15.4485493, 14.0556432, 12.9610295, 21.7406859, 21.2913251, 18.8012846, 19.2818194}
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+------------------------------------------------------------
+PDOP = 2.230184 | it = 0
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+------------------------------------------------------------
+PDOP = 3.359035 | it = 0
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+------------------------------------------------------------
+PDOP = 2.940677 | it = 0
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+------------------------------------------------------------
+PDOP = 3.380086 | it = 0
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+------------------------------------------------------------
+PDOP = 2.854714 | it = 0
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+------------------------------------------------------------
+PDOP = 1.814472 | it = 0
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+------------------------------------------------------------
+PDOP = 2.434744 | it = 0
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+------------------------------------------------------------
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+------------------------------------------------------------
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+------------------------------------------------------------
+PDOP = 3.397122 | it = 0
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+------------------------------------------------------------
+PDOP = 3.325056 | it = 0
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+------------------------------------------------------------
+PDOP = 2.766179 | it = 0
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+------------------------------------------------------------
+PDOP = 1.846323 | it = 0
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+------------------------------------------------------------
+PDOP = 4.276698 | it = 0
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+------------------------------------------------------------
+PDOP = 3.720055 | it = 0
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+------------------------------------------------------------
+PDOP = 1.988912 | it = 0
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+------------------------------------------------------------
+PDOP = 2.411410 | it = 0
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+------------------------------------------------------------
+PDOP = 1.758139 | it = 0
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+------------------------------------------------------------
+PDOP = 2.448087 | it = 0
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+------------------------------------------------------------
+PDOP = 3.553480 | it = 0
+r_noised_vec = {19.0604578, 18.7979933, 6.6592766, 11.2100763, 23.9547125, 23.6526902, 17.8206163, 18.1807439}
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+------------------------------------------------------------
+PDOP = 2.920846 | it = 0
+r_noised_vec = {20.1774822, 17.8964414, 14.7060226, 12.8599206, 24.9034722, 22.9626082, 16.8703129, 19.3737330}
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+------------------------------------------------------------
+PDOP = 2.024311 | it = 0
+r_noised_vec = {21.8958715, 17.2224348, 6.6367059, 14.8111468, 26.0065454, 22.4482880, 16.2103786, 20.6989286}
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+exact point = {15, 17, 5}
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+seed = 579
+------------------------------------------------------------
+PDOP = 4.489171 | it = 0
+r_noised_vec = {23.1536259, 16.6524413, 8.1348541, 16.9193359, 27.2063793, 22.1236719, 15.7896770, 22.1258370}
+anchors_optimal = {4, 0, 7, 5}
+exact point = {17, 17, 5}
+x_sol = {17.0981636, 17.0956424, 5.1290348}
+seed = 581
+------------------------------------------------------------
+PDOP = 3.548890 | it = 0
+r_noised_vec = {24.1219406, 16.2099417, 7.3534441, 18.5513941, 28.4562339, 21.9668547, 15.3883641, 23.6306538}
+anchors_optimal = {0, 5, 3, 1}
+exact point = {19, 17, 5}
+x_sol = {18.8975214, 16.7556263, 4.7163027}
+seed = 583
+------------------------------------------------------------
+PDOP = 3.907707 | it = 0
+r_noised_vec = {18.3115994, 26.3866412, 19.4595385, 4.1460434, 23.6676480, 30.2103764, 24.2984850, 15.1085247}
+anchors_optimal = {5, 6, 2, 7}
+exact point = {1, 19, 5}
+x_sol = {0.9697670, 18.9802755, 4.9278228}
+seed = 585
+------------------------------------------------------------
+PDOP = 3.040434 | it = 0
+r_noised_vec = {18.8591402, 24.9814604, 23.4075290, 4.6576184, 23.5546072, 29.0397517, 22.7265720, 15.2790868}
+anchors_optimal = {4, 6, 0, 3}
+exact point = {3, 19, 5}
+x_sol = {2.7197022, 19.2887832, 5.2591487}
+seed = 587
+------------------------------------------------------------
+PDOP = 2.859315 | it = 0
+r_noised_vec = {18.9441951, 23.7852748, 14.7251592, 5.6460703, 23.7307360, 27.9868652, 21.2174275, 15.6833311}
+anchors_optimal = {5, 4, 0, 3}
+exact point = {5, 19, 5}
+x_sol = {4.7074529, 19.1053794, 5.1245973}
+seed = 589
+------------------------------------------------------------
+PDOP = 3.373080 | it = 0
+r_noised_vec = {19.0665056, 22.7103809, 18.6705543, 7.3293829, 23.9795764, 26.8415161, 19.7909348, 16.3059437}
+anchors_optimal = {5, 1, 6, 3}
+exact point = {7, 19, 5}
+x_sol = {6.9932721, 19.1522602, 5.1130109}
+seed = 591
+------------------------------------------------------------
+PDOP = 2.920760 | it = 0
+r_noised_vec = {20.0767622, 21.5700494, 12.2655123, 9.0168397, 24.6570263, 25.9760875, 18.4327848, 17.1255995}
+anchors_optimal = {1, 0, 6, 3}
+exact point = {9, 19, 5}
+x_sol = {8.8634040, 18.9677101, 5.3349077}
+seed = 593
+------------------------------------------------------------
+PDOP = 3.207480 | it = 0
+r_noised_vec = {21.3039588, 20.7446220, 12.7586612, 10.7741720, 25.4665269, 25.2316070, 17.4477675, 18.1194378}
+anchors_optimal = {4, 5, 0, 3}
+exact point = {11, 19, 5}
+x_sol = {10.8134210, 19.3888389, 5.3767018}
+seed = 595
+------------------------------------------------------------
+PDOP = 4.392554 | it = 0
+r_noised_vec = {21.9691934, 19.8056063, 10.0156444, 12.7001691, 26.4406337, 24.6281024, 16.4647981, 19.2661093}
+anchors_optimal = {5, 0, 1, 7}
+exact point = {13, 19, 5}
+x_sol = {12.8785110, 19.0722072, 4.8610162}
+seed = 597
+------------------------------------------------------------
+PDOP = 1.876758 | it = 0
+r_noised_vec = {22.8291518, 19.1897919, 6.8375269, 14.5499208, 27.4054103, 23.9849643, 15.7014040, 20.5476050}
+anchors_optimal = {0, 6, 3, 2}
+exact point = {15, 19, 5}
+x_sol = {14.8407480, 18.6439467, 5.2425706}
+seed = 599
+------------------------------------------------------------
+PDOP = 4.902864 | it = 0
+r_noised_vec = {24.4968169, 18.6699200, 9.7839761, 16.4045824, 28.4064475, 23.6776227, 15.3101645, 21.8856997}
+anchors_optimal = {4, 0, 5, 7}
+exact point = {17, 19, 5}
+x_sol = {16.9814853, 19.1300633, 5.0570469}
+seed = 601
+------------------------------------------------------------
+PDOP = 2.439161 | it = 0
+r_noised_vec = {26.0767846, 18.3435291, 1.9096951, 18.6271221, 29.5470192, 23.5105578, 15.0897521, 23.3336332}
+anchors_optimal = {4, 3, 1, 6}
+exact point = {19, 19, 5}
+x_sol = {19.1290834, 18.8531724, 5.0095761}
+seed = 603
+------------------------------------------------------------
+PDOP = 3.800370 | it = 0
+r_noised_vec = {5.8657142, 19.8368866, 38.6953146, 19.8378860, 12.9281314, 23.0649793, 29.9808794, 22.8789827}
+anchors_optimal = {5, 7, 1, 0}
+exact point = {1, 1, 7}
+x_sol = {1.0501193, 1.2749989, 6.8554947}
+seed = 605
+------------------------------------------------------------
+PDOP = 4.398446 | it = 0
+r_noised_vec = {6.0381925, 17.8309803, 21.6836587, 19.9964697, 13.1301911, 21.4064179, 28.6861451, 22.9652374}
+anchors_optimal = {6, 5, 3, 1}
+exact point = {3, 1, 7}
+x_sol = {3.0925239, 0.9368676, 6.8081350}
+seed = 607
+------------------------------------------------------------
+PDOP = 1.741030 | it = 0
+r_noised_vec = {7.3922910, 16.0805126, 33.5078577, 20.4201697, 13.5079490, 19.8339711, 27.6128006, 23.2424327}
+anchors_optimal = {3, 1, 4, 0}
+exact point = {5, 1, 7}
+x_sol = {5.1332390, 0.9648062, 7.1363495}
+seed = 609
+------------------------------------------------------------
+PDOP = 3.379847 | it = 0
+r_noised_vec = {8.7417390, 14.2390548, 23.1340170, 20.7250388, 14.3296703, 18.3356045, 26.6635008, 23.6986439}
+anchors_optimal = {7, 3, 4, 1}
+exact point = {7, 1, 7}
+x_sol = {7.0918494, 1.1240455, 7.0237239}
+seed = 611
+------------------------------------------------------------
+PDOP = 3.333157 | it = 0
+r_noised_vec = {9.7768439, 12.5381823, 26.7172595, 21.4883087, 15.4646546, 16.9306650, 25.5725545, 24.3175767}
+anchors_optimal = {6, 7, 4, 1}
+exact point = {9, 1, 7}
+x_sol = {8.8523419, 1.2318686, 6.6957753}
+seed = 613
+------------------------------------------------------------
+PDOP = 4.262141 | it = 0
+r_noised_vec = {11.4422181, 10.9220774, 25.4792225, 22.3301665, 16.5320845, 15.6306993, 24.7673026, 25.0802587}
+anchors_optimal = {7, 6, 3, 1}
+exact point = {11, 1, 7}
+x_sol = {10.9105289, 0.9277773, 7.0688673}
+seed = 615
+------------------------------------------------------------
+PDOP = 3.066177 | it = 0
+r_noised_vec = {13.6754732, 9.2964215, 21.5050672, 23.2220055, 17.7293014, 14.7124049, 24.0438084, 25.9664882}
+anchors_optimal = {3, 2, 4, 1}
+exact point = {13, 1, 7}
+x_sol = {12.5208848, 0.6040931, 6.5233934}
+seed = 617
+------------------------------------------------------------
+PDOP = 4.475392 | it = 0
+r_noised_vec = {15.4085912, 7.9867527, 26.3556727, 24.5227172, 19.0488090, 13.8315159, 23.5177522, 26.9520593}
+anchors_optimal = {6, 4, 7, 3}
+exact point = {15, 1, 7}
+x_sol = {15.0693806, 0.9226585, 7.1441417}
+seed = 619
+------------------------------------------------------------
+PDOP = 2.539466 | it = 0
+r_noised_vec = {16.8000504, 6.7751239, 19.6670675, 25.5958772, 20.5082263, 13.2049720, 23.1018387, 28.1987447}
+anchors_optimal = {3, 6, 5, 1}
+exact point = {17, 1, 7}
+x_sol = {17.0769200, 1.0441141, 7.1192373}
+seed = 621
+------------------------------------------------------------
+PDOP = 2.584927 | it = 0
+r_noised_vec = {18.8439758, 6.1573443, 25.2452057, 26.6951438, 22.1487160, 12.8577362, 22.7828848, 29.3917137}
+anchors_optimal = {7, 6, 5, 1}
+exact point = {19, 1, 7}
+x_sol = {19.5740262, 1.1910932, 7.1471450}
+seed = 623
+------------------------------------------------------------
+PDOP = 3.490410 | it = 0
+r_noised_vec = {6.6336177, 20.0196662, 27.2868182, 18.1675628, 13.0832471, 23.0752626, 28.5347583, 21.5546702}
+anchors_optimal = {5, 7, 1, 4}
+exact point = {1, 3, 7}
+x_sol = {0.9922003, 2.7780934, 7.0347183}
+seed = 625
+------------------------------------------------------------
+PDOP = 3.453183 | it = 0
+r_noised_vec = {6.7121512, 18.0463621, 28.2273834, 18.1044560, 13.3480865, 21.4371764, 27.2187673, 21.6169249}
+anchors_optimal = {5, 3, 1, 4}
+exact point = {3, 3, 7}
+x_sol = {3.0952337, 3.0399667, 6.9768067}
+seed = 627
+------------------------------------------------------------
+PDOP = 2.786197 | it = 0
+r_noised_vec = {7.1614922, 16.2132458, 23.4438181, 18.3955856, 13.7866562, 19.8923723, 26.0057576, 21.8538521}
+anchors_optimal = {6, 5, 1, 4}
+exact point = {5, 3, 7}
+x_sol = {5.0885635, 3.1159749, 7.0042859}
+seed = 629
+------------------------------------------------------------
+PDOP = 2.514388 | it = 0
+r_noised_vec = {8.6917478, 14.2965767, 23.4428977, 19.1024800, 14.5980377, 18.4532101, 25.0376702, 22.2664433}
+anchors_optimal = {7, 5, 4, 1}
+exact point = {7, 3, 7}
+x_sol = {7.1468880, 3.0607424, 6.9176617}
+seed = 631
+------------------------------------------------------------
+PDOP = 3.349347 | it = 0
+r_noised_vec = {10.5239433, 12.6305473, 28.3973963, 19.6661354, 15.4191668, 17.1465838, 24.1208257, 22.8518491}
+anchors_optimal = {6, 7, 3, 4}
+exact point = {9, 3, 7}
+x_sol = {8.9313888, 3.0143079, 6.9355230}
+seed = 633
+------------------------------------------------------------
+PDOP = 2.194343 | it = 0
+r_noised_vec = {11.8047201, 10.9289086, 16.5359291, 20.6028891, 16.5171818, 15.9561982, 23.4926105, 23.6037734}
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+exact point = {11, 3, 7}
+x_sol = {10.9793956, 2.6762504, 6.9431785}
+seed = 635
+------------------------------------------------------------
+PDOP = 3.039868 | it = 0
+r_noised_vec = {13.2434518, 9.4369085, 28.8233362, 21.7021581, 17.6627788, 14.9540709, 22.6034468, 24.5149451}
+anchors_optimal = {7, 3, 5, 0}
+exact point = {13, 3, 7}
+x_sol = {12.6516750, 2.7211935, 7.0789772}
+seed = 637
+------------------------------------------------------------
+PDOP = 3.231183 | it = 0
+r_noised_vec = {15.4424182, 8.1429730, 15.0237150, 22.8016877, 19.1428559, 14.1775525, 22.1257177, 25.3631224}
+anchors_optimal = {7, 6, 4, 1}
+exact point = {15, 3, 7}
+x_sol = {14.5458051, 3.2147619, 6.6473598}
+seed = 639
+------------------------------------------------------------
+PDOP = 2.400860 | it = 0
+r_noised_vec = {17.5125213, 7.0536472, 25.8568740, 24.1691923, 20.6852230, 13.6899323, 21.6238304, 26.5317280}
+anchors_optimal = {7, 6, 5, 1}
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+x_sol = {16.7195407, 3.1269527, 6.8773603}
+seed = 641
+------------------------------------------------------------
+PDOP = 2.088289 | it = 0
+r_noised_vec = {18.9481894, 6.5493310, 17.4863335, 25.5866101, 22.3775879, 13.2494148, 21.4737715, 27.8067452}
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+x_sol = {19.6816514, 3.5821546, 7.0091248}
+seed = 643
+------------------------------------------------------------
+PDOP = 3.404227 | it = 0
+r_noised_vec = {6.9248410, 20.3701795, 29.1372298, 15.9892381, 13.6704987, 23.4685949, 27.4965531, 19.7348341}
+anchors_optimal = {1, 7, 3, 4}
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+x_sol = {0.9771153, 5.1689173, 6.9787384}
+seed = 645
+------------------------------------------------------------
+PDOP = 3.478926 | it = 0
+r_noised_vec = {7.6608024, 18.5340224, 26.8847549, 16.3773353, 13.8880568, 21.9131450, 26.1271303, 19.8831246}
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+x_sol = {2.9392684, 5.1720915, 6.9032649}
+seed = 647
+------------------------------------------------------------
+PDOP = 2.548511 | it = 0
+r_noised_vec = {8.5031829, 16.6422323, 22.7898231, 16.6630452, 14.1747314, 20.4366139, 24.8152339, 20.2266826}
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+x_sol = {4.1389747, 5.0959748, 7.7728393}
+seed = 649
+------------------------------------------------------------
+PDOP = 3.036646 | it = 0
+r_noised_vec = {9.1612838, 14.7952178, 26.1564884, 17.1363381, 14.8255638, 18.8531889, 23.5836376, 20.7499681}
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+x_sol = {7.1940319, 4.9535833, 7.1703773}
+seed = 651
+------------------------------------------------------------
+PDOP = 2.562979 | it = 0
+r_noised_vec = {10.5495312, 13.1126959, 19.5084774, 18.1179483, 15.6069878, 17.5509538, 22.6644984, 21.4345420}
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+x_sol = {8.7746361, 4.7903305, 7.0479069}
+seed = 653
+------------------------------------------------------------
+PDOP = 2.194034 | it = 0
+r_noised_vec = {12.5844766, 11.3990822, 23.1984949, 18.9756091, 16.8183051, 16.3658853, 21.7075921, 22.2602086}
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+x_sol = {11.2481573, 4.7948908, 7.2240438}
+seed = 655
+------------------------------------------------------------
+PDOP = 2.273244 | it = 0
+r_noised_vec = {14.1787234, 10.0149599, 19.1085629, 20.0890396, 18.1441540, 15.3335424, 20.9498737, 23.4675355}
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+------------------------------------------------------------
+PDOP = 2.347479 | it = 0
+r_noised_vec = {15.4631902, 8.7103836, 26.7148685, 21.4212416, 19.6489303, 14.4902130, 20.4618663, 24.4934428}
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+------------------------------------------------------------
+PDOP = 1.808508 | it = 0
+r_noised_vec = {17.4180429, 7.8101564, 16.3565701, 22.4969555, 21.0892506, 13.9059646, 20.0954715, 25.6488178}
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+------------------------------------------------------------
+PDOP = 4.422707 | it = 0
+r_noised_vec = {19.6970209, 7.3421151, 17.7537531, 24.1591004, 22.7039220, 13.5783025, 19.9717579, 26.8950898}
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+------------------------------------------------------------
+PDOP = 3.361324 | it = 0
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+------------------------------------------------------------
+PDOP = 3.326146 | it = 0
+r_noised_vec = {8.3982909, 19.1215689, 19.1279037, 14.3076717, 14.3855415, 21.9996293, 25.1421874, 18.4928115}
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+------------------------------------------------------------
+PDOP = 2.868204 | it = 0
+r_noised_vec = {9.3517512, 17.2468533, 29.9066989, 14.9114255, 14.6622760, 20.6720826, 23.8817289, 18.7812471}
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+------------------------------------------------------------
+PDOP = 2.420591 | it = 0
+r_noised_vec = {10.7164011, 15.5853430, 15.9928851, 15.5894331, 15.4779427, 19.2321031, 22.5456097, 19.2892670}
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+------------------------------------------------------------
+PDOP = 2.103745 | it = 0
+r_noised_vec = {11.6377895, 13.9004275, 25.3919653, 16.2953802, 16.4294267, 17.9089041, 21.4579748, 20.0028953}
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+------------------------------------------------------------
+PDOP = 2.381840 | it = 0
+r_noised_vec = {12.7949215, 12.3153838, 16.4115173, 17.5289737, 17.6449499, 16.7144598, 20.4514375, 20.9082422}
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+------------------------------------------------------------
+PDOP = 2.378586 | it = 0
+r_noised_vec = {14.7735378, 10.7790259, 19.6686942, 18.6892120, 18.7802116, 15.8948565, 19.6488587, 21.7431329}
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+------------------------------------------------------------
+PDOP = 2.807636 | it = 0
+r_noised_vec = {16.6779118, 9.7387281, 17.9539523, 19.9769831, 20.0364702, 15.1068694, 18.9638583, 22.9666639}
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+------------------------------------------------------------
+PDOP = 2.206793 | it = 0
+r_noised_vec = {17.9838072, 8.7871573, 15.5731786, 21.5033501, 21.3775578, 14.5738194, 18.4575513, 24.2943772}
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+------------------------------------------------------------
+PDOP = 2.589683 | it = 0
+r_noised_vec = {19.6135475, 8.4865265, 18.7952384, 22.9103230, 22.9003935, 14.3201158, 18.3648967, 25.7090878}
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+x_sol = {18.9042712, 6.9071270, 6.9988267}
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+------------------------------------------------------------
+PDOP = 4.234473 | it = 0
+r_noised_vec = {10.1738523, 21.4595171, 23.2248871, 12.4269878, 15.2415733, 24.3747985, 25.4315815, 17.0547071}
+anchors_optimal = {6, 5, 1, 3}
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+x_sol = {1.0601215, 9.1148807, 6.9836860}
+seed = 685
+------------------------------------------------------------
+PDOP = 3.177403 | it = 0
+r_noised_vec = {10.4555541, 19.7695502, 25.4152568, 12.8594596, 15.3809064, 22.8735838, 23.9892458, 17.2010884}
+anchors_optimal = {2, 7, 4, 0}
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+x_sol = {-2.0608291, 8.9393378, 7.1512193}
+seed = 687
+------------------------------------------------------------
+PDOP = 1.796662 | it = 0
+r_noised_vec = {10.5543208, 18.2066814, 9.9071847, 13.0428100, 15.8385938, 21.4665318, 22.6939517, 17.5584647}
+anchors_optimal = {1, 7, 3, 0}
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+x_sol = {4.7081695, 8.9547051, 6.8635582}
+seed = 689
+------------------------------------------------------------
+PDOP = 1.949138 | it = 0
+r_noised_vec = {11.4399753, 16.5001134, 27.2710275, 13.8822616, 16.6598507, 20.1728090, 21.4720157, 18.1139330}
+anchors_optimal = {5, 1, 3, 0}
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+x_sol = {6.7794550, 8.8725223, 6.9555663}
+seed = 691
+------------------------------------------------------------
+PDOP = 2.903255 | it = 0
+r_noised_vec = {13.0585518, 15.0496699, 16.4914614, 14.9621383, 17.3288723, 18.8158712, 20.4115242, 18.8491044}
+anchors_optimal = {6, 5, 4, 3}
+exact point = {9, 9, 7}
+x_sol = {9.0856002, 8.8528076, 6.8416435}
+seed = 693
+------------------------------------------------------------
+PDOP = 1.900118 | it = 0
+r_noised_vec = {14.3225426, 13.5070121, 17.3552847, 15.9347752, 18.2445815, 17.7900706, 19.3146309, 19.9620183}
+anchors_optimal = {5, 3, 0, 1}
+exact point = {11, 9, 7}
+x_sol = {11.0972592, 9.2162675, 6.9724411}
+seed = 695
+------------------------------------------------------------
+PDOP = 1.567184 | it = 0
+r_noised_vec = {15.3387340, 12.2211458, 19.7349049, 17.3811776, 19.2562496, 16.9048094, 18.5244450, 20.9540417}
+anchors_optimal = {4, 6, 3, 1}
+exact point = {13, 9, 7}
+x_sol = {12.8736449, 8.8539362, 7.0460990}
+seed = 697
+------------------------------------------------------------
+PDOP = 3.026383 | it = 0
+r_noised_vec = {17.0705759, 11.1408602, 11.3413423, 18.8218510, 20.5902410, 16.2139887, 17.8995497, 22.0949181}
+anchors_optimal = {7, 6, 0, 5}
+exact point = {15, 9, 7}
+x_sol = {14.9155665, 8.9868302, 6.8347265}
+seed = 699
+------------------------------------------------------------
+PDOP = 2.027127 | it = 0
+r_noised_vec = {19.1715719, 10.2850867, 20.2975527, 20.2734684, 22.0771484, 15.7648959, 17.3208984, 23.3573998}
+anchors_optimal = {0, 6, 5, 1}
+exact point = {17, 9, 7}
+x_sol = {17.3885831, 9.1452217, 6.7434491}
+seed = 701
+------------------------------------------------------------
+PDOP = 2.741475 | it = 0
+r_noised_vec = {20.6754442, 9.9622661, 9.9950193, 21.9473608, 23.6354892, 15.3431260, 17.0696594, 24.7273017}
+anchors_optimal = {4, 3, 5, 1}
+exact point = {19, 9, 7}
+x_sol = {19.0059167, 8.9417088, 6.9167166}
+seed = 703
+------------------------------------------------------------
+PDOP = 26.577601 | it = 2
+r_noised_vec = {11.3446474, 22.1282301, 29.4105828, 10.8283181, 16.4945241, 25.1591709, 24.6554014, 15.7360677}
+anchors_optimal = {1, 5, 4, 0}
+exact point = {1, 11, 7}
+start_optimal = {1.002249, 10.801278, 6.727150}
+x_sol = {1.0022486, 10.7944271, 6.7282813}
+seed = 705
+------------------------------------------------------------
+PDOP = 3.632630 | it = 0
+r_noised_vec = {11.8000780, 20.5667696, 19.7078569, 10.8465356, 16.5661283, 23.6752079, 23.1737394, 15.8576254}
+anchors_optimal = {5, 6, 1, 3}
+exact point = {3, 11, 7}
+x_sol = {3.0828578, 11.1182440, 6.8809617}
+seed = 707
+------------------------------------------------------------
+PDOP = 2.731067 | it = 0
+r_noised_vec = {12.6511754, 18.9827409, 22.4657893, 11.6907213, 16.9588112, 22.2544134, 21.6831650, 16.2422168}
+anchors_optimal = {5, 1, 7, 0}
+exact point = {5, 11, 7}
+x_sol = {5.2291522, 11.3199235, 6.9496195}
+seed = 709
+------------------------------------------------------------
+PDOP = 2.557278 | it = 0
+r_noised_vec = {13.0940494, 17.4971060, 19.6236598, 12.3120612, 17.4325011, 20.9238565, 20.2767170, 16.8695697}
+anchors_optimal = {5, 1, 4, 7}
+exact point = {7, 11, 7}
+x_sol = {6.9759033, 11.0081504, 7.0352881}
+seed = 711
+------------------------------------------------------------
+PDOP = 2.135824 | it = 0
+r_noised_vec = {13.8233807, 16.1686722, 16.6698525, 13.3946057, 18.2298053, 19.7180792, 19.2056869, 17.4975690}
+anchors_optimal = {6, 2, 1, 0}
+exact point = {9, 11, 7}
+x_sol = {8.6489446, 10.0668942, 8.1059361}
+seed = 713
+------------------------------------------------------------
+PDOP = 2.549371 | it = 0
+r_noised_vec = {15.4354103, 14.8069062, 18.1122058, 14.8394340, 19.0738820, 18.6367160, 18.1219649, 18.6158912}
+anchors_optimal = {5, 7, 0, 1}
+exact point = {11, 11, 7}
+x_sol = {11.0001952, 11.0206104, 7.1294023}
+seed = 715
+------------------------------------------------------------
+PDOP = 2.202572 | it = 0
+r_noised_vec = {17.0397856, 13.7525186, 13.7515338, 16.0829659, 20.2934047, 17.7005163, 17.2533235, 19.8338699}
+anchors_optimal = {7, 0, 3, 1}
+exact point = {13, 11, 7}
+x_sol = {13.1637506, 11.3340131, 6.9547210}
+seed = 717
+------------------------------------------------------------
+PDOP = 3.126307 | it = 0
+r_noised_vec = {18.0974823, 12.7319645, 14.5908176, 17.6898176, 21.6732840, 17.1250526, 16.5989101, 21.1601774}
+anchors_optimal = {7, 0, 3, 5}
+exact point = {15, 11, 7}
+x_sol = {14.9493395, 10.8839268, 6.9520141}
+seed = 719
+------------------------------------------------------------
+PDOP = 2.123766 | it = 0
+r_noised_vec = {19.5128152, 12.0610342, 5.2015986, 19.3625086, 23.0405787, 16.5977847, 16.1708583, 22.5727411}
+anchors_optimal = {0, 5, 6, 1}
+exact point = {17, 11, 7}
+x_sol = {16.6916161, 10.8681526, 7.0784761}
+seed = 721
+------------------------------------------------------------
+PDOP = 3.749885 | it = 0
+r_noised_vec = {21.6178858, 11.6782263, 18.2779120, 20.9601403, 24.4130745, 16.3147850, 16.0251901, 24.0526015}
+anchors_optimal = {4, 7, 0, 5}
+exact point = {19, 11, 7}
+x_sol = {19.1796315, 10.9597517, 7.1140733}
+seed = 723
+------------------------------------------------------------
+PDOP = 3.484877 | it = 0
+r_noised_vec = {13.6744898, 23.1366761, 20.8114314, 9.3433885, 17.7332439, 25.8047307, 24.1314330, 14.8558831}
+anchors_optimal = {5, 6, 1, 7}
+exact point = {1, 13, 7}
+x_sol = {0.9834528, 12.6988966, 7.0637277}
+seed = 725
+------------------------------------------------------------
+PDOP = 2.300428 | it = 0
+r_noised_vec = {13.3521286, 21.5928019, 21.7719389, 9.5276169, 17.7357098, 24.3101080, 22.6327292, 14.9722526}
+anchors_optimal = {6, 4, 0, 3}
+exact point = {3, 13, 7}
+x_sol = {2.9950294, 12.8027330, 6.9137878}
+seed = 727
+------------------------------------------------------------
+PDOP = 2.844368 | it = 0
+r_noised_vec = {13.7769287, 19.9856994, 22.9051336, 9.8750881, 18.0815672, 23.1457558, 21.1870567, 15.3418675}
+anchors_optimal = {5, 6, 1, 0}
+exact point = {5, 13, 7}
+x_sol = {4.9835680, 12.7851222, 6.9132150}
+seed = 729
+------------------------------------------------------------
+PDOP = 2.677129 | it = 0
+r_noised_vec = {14.9459592, 18.6446106, 14.1354196, 11.1217827, 18.5440109, 21.8949263, 19.6931322, 15.9508217}
+anchors_optimal = {5, 1, 4, 7}
+exact point = {7, 13, 7}
+x_sol = {6.9340142, 12.8539902, 7.0324660}
+seed = 731
+------------------------------------------------------------
+PDOP = 1.951650 | it = 0
+r_noised_vec = {15.8025918, 17.3281900, 21.6313729, 12.2064624, 19.4094459, 20.7814967, 18.3940196, 16.8475367}
+anchors_optimal = {1, 7, 0, 3}
+exact point = {9, 13, 7}
+x_sol = {9.1698879, 13.1506364, 6.9515324}
+seed = 733
+------------------------------------------------------------
+PDOP = 2.893059 | it = 0
+r_noised_vec = {16.4544332, 16.1756373, 10.6100245, 13.5075711, 20.3495891, 19.8258392, 17.1744757, 17.8093416}
+anchors_optimal = {4, 7, 6, 1}
+exact point = {11, 13, 7}
+x_sol = {11.0844745, 13.0508718, 7.0725131}
+seed = 735
+------------------------------------------------------------
+PDOP = 2.932544 | it = 0
+r_noised_vec = {17.8637451, 15.2426185, 17.4721613, 15.2350457, 21.5364786, 19.0331357, 16.2773863, 18.9512566}
+anchors_optimal = {4, 5, 6, 3}
+exact point = {13, 13, 7}
+x_sol = {13.1726226, 13.0607091, 6.9629909}
+seed = 737
+------------------------------------------------------------
+PDOP = 2.332370 | it = 0
+r_noised_vec = {19.6916971, 14.3675051, 10.2274218, 16.7234197, 22.6249586, 18.4194188, 15.4580752, 20.2433777}
+anchors_optimal = {0, 5, 6, 2}
+exact point = {15, 13, 7}
+x_sol = {15.3115757, 13.1400764, 6.9644229}
+seed = 739
+------------------------------------------------------------
+PDOP = 3.478239 | it = 0
+r_noised_vec = {20.9674104, 13.8756752, 12.8828728, 18.4355205, 23.8201183, 18.0221722, 14.8540111, 21.6612332}
+anchors_optimal = {4, 7, 3, 1}
+exact point = {17, 13, 7}
+x_sol = {16.9611333, 13.0839213, 7.0962998}
+seed = 741
+------------------------------------------------------------
+PDOP = 3.222033 | it = 0
+r_noised_vec = {22.1348826, 13.4822787, 11.3431410, 20.2770380, 25.1270580, 17.8620330, 14.7420795, 23.1824214}
+anchors_optimal = {4, 7, 6, 1}
+exact point = {19, 13, 7}
+x_sol = {18.9235724, 12.9722205, 7.0920671}
+seed = 743
+------------------------------------------------------------
+PDOP = 2.670631 | it = 0
+r_noised_vec = {15.1964912, 24.3740299, 22.1974252, 7.7858667, 19.0243060, 26.9753096, 23.5068154, 13.8547719}
+anchors_optimal = {5, 6, 7, 3}
+exact point = {1, 15, 7}
+x_sol = {1.0101141, 15.1078147, 7.0438162}
+seed = 745
+------------------------------------------------------------
+PDOP = 3.683259 | it = 0
+r_noised_vec = {15.6829405, 22.8119874, 22.7155067, 8.0687767, 19.0802862, 25.6543745, 21.9862949, 14.0283803}
+anchors_optimal = {1, 6, 4, 7}
+exact point = {3, 15, 7}
+x_sol = {2.9578498, 14.9016281, 7.0717826}
+seed = 747
+------------------------------------------------------------
+PDOP = 1.877361 | it = 0
+r_noised_vec = {15.7304388, 21.2792937, 18.5779170, 8.9255654, 19.5469206, 24.4117148, 20.5055823, 14.4771335}
+anchors_optimal = {1, 0, 7, 3}
+exact point = {5, 15, 7}
+x_sol = {5.0957465, 14.9152892, 7.0810085}
+seed = 749
+------------------------------------------------------------
+PDOP = 2.302108 | it = 0
+r_noised_vec = {16.0531076, 19.9929659, 28.2533933, 9.6820991, 20.0836107, 23.2705714, 19.1602855, 15.1585657}
+anchors_optimal = {5, 4, 7, 3}
+exact point = {7, 15, 7}
+x_sol = {6.8639981, 15.0676133, 6.9200245}
+seed = 751
+------------------------------------------------------------
+PDOP = 2.272272 | it = 0
+r_noised_vec = {17.2743314, 18.6706460, 7.8977909, 11.2498889, 20.8986271, 22.3096091, 17.9828544, 16.1282183}
+anchors_optimal = {4, 1, 0, 3}
+exact point = {9, 15, 7}
+x_sol = {9.1791975, 15.0221717, 6.8592082}
+seed = 753
+------------------------------------------------------------
+PDOP = 3.540172 | it = 0
+r_noised_vec = {18.5268669, 17.6758754, 19.3604020, 12.7404610, 21.6157150, 21.1703259, 16.6629833, 17.2549146}
+anchors_optimal = {4, 2, 6, 3}
+exact point = {11, 15, 7}
+x_sol = {4.9077416, 21.0813143, 13.0571094}
+seed = 755
+------------------------------------------------------------
+PDOP = 2.589896 | it = 0
+r_noised_vec = {19.2708645, 16.7397836, 10.1702318, 14.2073685, 22.5424789, 20.4064835, 15.7001697, 18.5109760}
+anchors_optimal = {4, 0, 1, 3}
+exact point = {13, 15, 7}
+x_sol = {12.8985753, 14.9609710, 6.9000754}
+seed = 757
+------------------------------------------------------------
+PDOP = 2.700007 | it = 0
+r_noised_vec = {20.4019855, 16.0349503, 11.3959015, 16.1115037, 23.5264365, 19.7972888, 14.9190036, 19.8705262}
+anchors_optimal = {4, 5, 1, 6}
+exact point = {15, 15, 7}
+x_sol = {14.7515940, 14.9567362, 6.9522892}
+seed = 759
+------------------------------------------------------------
+PDOP = 2.890843 | it = 0
+r_noised_vec = {22.2574725, 15.6117094, 12.1013979, 17.8001413, 24.8257998, 19.3574682, 14.2529593, 21.3143076}
+anchors_optimal = {0, 7, 3, 6}
+exact point = {17, 15, 7}
+x_sol = {17.1092858, 15.1986856, 6.8827717}
+seed = 761
+------------------------------------------------------------
+PDOP = 3.378476 | it = 0
+r_noised_vec = {23.8383192, 15.5466036, 6.8237208, 19.5717314, 26.2381123, 19.1217407, 13.9124669, 22.8294828}
+anchors_optimal = {0, 7, 3, 1}
+exact point = {19, 15, 7}
+x_sol = {19.0939099, 15.3740208, 6.8649312}
+seed = 763
+------------------------------------------------------------
+PDOP = 2.016023 | it = 0
+r_noised_vec = {16.8788990, 25.6615444, 27.8317236, 6.7546586, 20.6893800, 27.9965166, 23.0217240, 13.3778795}
+anchors_optimal = {1, 6, 4, 3}
+exact point = {1, 17, 7}
+x_sol = {1.0942266, 17.2228962, 7.1590796}
+seed = 765
+------------------------------------------------------------
+PDOP = 1.859722 | it = 0
+r_noised_vec = {16.9804277, 24.2758317, 16.0830512, 6.9927554, 20.8003209, 26.6364349, 21.5284114, 13.4992373}
+anchors_optimal = {1, 6, 4, 3}
+exact point = {3, 17, 7}
+x_sol = {2.9837300, 17.2052399, 7.1064314}
+seed = 767
+------------------------------------------------------------
+PDOP = 3.969603 | it = 0
+r_noised_vec = {17.7957223, 22.7612791, 22.8348090, 7.7271691, 21.2351398, 25.3421353, 19.9308482, 13.8673789}
+anchors_optimal = {0, 1, 4, 6}
+exact point = {5, 17, 7}
+x_sol = {5.1753390, 17.2376202, 6.9423039}
+seed = 769
+------------------------------------------------------------
+PDOP = 2.154555 | it = 0
+r_noised_vec = {18.2945476, 21.4004831, 14.4674411, 9.1779625, 21.4960143, 24.3333978, 18.3736808, 14.5172297}
+anchors_optimal = {5, 7, 2, 3}
+exact point = {7, 17, 7}
+x_sol = {7.2086354, 17.2445378, 7.1706589}
+seed = 771
+------------------------------------------------------------
+PDOP = 3.412525 | it = 0
+r_noised_vec = {18.5921385, 20.2449748, 16.4100397, 10.3069036, 22.0667762, 23.2803878, 17.2417588, 15.4160811}
+anchors_optimal = {5, 4, 1, 6}
+exact point = {9, 17, 7}
+x_sol = {9.0517410, 16.9394266, 7.0232249}
+seed = 773
+------------------------------------------------------------
+PDOP = 2.657569 | it = 0
+r_noised_vec = {19.6605647, 19.0959104, 13.3481466, 12.0526608, 22.6977698, 22.3677575, 16.0696847, 16.5286997}
+anchors_optimal = {4, 5, 7, 3}
+exact point = {11, 17, 7}
+x_sol = {10.8913731, 16.8681800, 7.1333874}
+seed = 775
+------------------------------------------------------------
+PDOP = 3.082612 | it = 0
+r_noised_vec = {21.1790108, 18.3683993, 11.1877959, 13.8385427, 23.7585147, 21.6037924, 15.0681606, 17.8157274}
+anchors_optimal = {4, 5, 6, 3}
+exact point = {13, 17, 7}
+x_sol = {13.0721889, 16.8072206, 6.9924374}
+seed = 777
+------------------------------------------------------------
+PDOP = 2.549154 | it = 0
+r_noised_vec = {22.1801143, 17.6581438, 10.9943241, 15.4164852, 24.9172951, 21.1964910, 14.3070161, 19.2407787}
+anchors_optimal = {5, 7, 3, 6}
+exact point = {15, 17, 7}
+x_sol = {14.8557066, 16.9368557, 7.0121172}
+seed = 779
+------------------------------------------------------------
+PDOP = 1.983130 | it = 0
+r_noised_vec = {23.0964845, 17.3258205, 1.2884058, 17.3970997, 26.2280333, 20.7789169, 13.8116782, 20.7715533}
+anchors_optimal = {4, 3, 1, 6}
+exact point = {17, 17, 7}
+x_sol = {17.0739776, 17.0088454, 6.8706704}
+seed = 781
+------------------------------------------------------------
+PDOP = 2.146722 | it = 0
+r_noised_vec = {24.7813452, 17.1729168, 15.4153489, 19.2363058, 27.4804131, 20.5806288, 13.3970852, 22.3802521}
+anchors_optimal = {4, 3, 1, 6}
+exact point = {19, 17, 7}
+x_sol = {19.0633894, 17.0863792, 6.9511781}
+seed = 783
+------------------------------------------------------------
+PDOP = 2.250482 | it = 0
+r_noised_vec = {19.2926598, 26.9191822, 14.2394294, 6.0259513, 22.2355642, 29.1769974, 23.1280528, 13.0402134}
+anchors_optimal = {1, 0, 7, 3}
+exact point = {1, 19, 7}
+x_sol = {1.2253776, 19.3393324, 6.9806559}
+seed = 785
+------------------------------------------------------------
+PDOP = 1.998533 | it = 0
+r_noised_vec = {19.0644244, 25.6639799, 26.4183444, 6.4351309, 22.2766493, 27.9517005, 21.5228006, 13.2010819}
+anchors_optimal = {1, 4, 6, 3}
+exact point = {3, 19, 7}
+x_sol = {2.8130158, 19.0558830, 7.0864569}
+seed = 787
+------------------------------------------------------------
+PDOP = 2.565245 | it = 0
+r_noised_vec = {19.0742414, 24.2745037, 15.7462607, 7.2518085, 22.4813321, 26.8077361, 19.8810368, 13.7984499}
+anchors_optimal = {4, 6, 2, 3}
+exact point = {5, 19, 7}
+x_sol = {5.3590526, 18.5397544, 6.6233975}
+seed = 789
+------------------------------------------------------------
+PDOP = 154.758789 | it = 2
+r_noised_vec = {19.9660311, 23.1325055, 17.0875348, 8.3971987, 22.9736465, 25.7732964, 18.3955346, 14.5216011}
+anchors_optimal = {5, 1, 4, 0}
+exact point = {7, 19, 7}
+start_optimal = {6.908673, 19.075346, 7.101420}
+x_sol = {6.9085691, 19.0693439, 7.1013158}
+seed = 791
+------------------------------------------------------------
+PDOP = 2.949373 | it = 0
+r_noised_vec = {20.8967046, 21.9545886, 16.5851572, 10.2248063, 23.5186902, 24.8702071, 16.9694731, 15.4546501}
+anchors_optimal = {5, 1, 0, 3}
+exact point = {9, 19, 7}
+x_sol = {9.3070606, 19.2401474, 6.9072831}
+seed = 793
+------------------------------------------------------------
+PDOP = 3.221041 | it = 0
+r_noised_vec = {21.3312418, 20.9545439, 10.0342034, 11.6225108, 24.3725655, 24.1236562, 15.8169484, 16.5606819}
+anchors_optimal = {4, 5, 6, 3}
+exact point = {11, 19, 7}
+x_sol = {10.8176621, 19.2309192, 7.1535721}
+seed = 795
+------------------------------------------------------------
+PDOP = 3.264780 | it = 0
+r_noised_vec = {22.1637462, 20.1654641, 14.8049984, 13.4097622, 25.4599945, 23.3265609, 14.7008950, 17.8097221}
+anchors_optimal = {4, 5, 0, 3}
+exact point = {13, 19, 7}
+x_sol = {13.2390231, 18.6949979, 6.3689559}
+seed = 797
+------------------------------------------------------------
+PDOP = 4.051180 | it = 0
+r_noised_vec = {23.7429249, 19.4534071, 6.5285989, 15.3759433, 26.3777536, 22.8510881, 13.8136366, 19.1785327}
+anchors_optimal = {4, 0, 1, 6}
+exact point = {15, 19, 7}
+x_sol = {15.3760904, 18.9125762, 7.0247526}
+seed = 799
+------------------------------------------------------------
+PDOP = 3.438853 | it = 0
+r_noised_vec = {25.0786131, 19.1321261, 11.1826590, 17.0293263, 27.3994133, 22.5369213, 13.3542059, 20.6497838}
+anchors_optimal = {4, 5, 3, 6}
+exact point = {17, 19, 7}
+x_sol = {16.8898693, 19.1731054, 7.0486344}
+seed = 801
+------------------------------------------------------------
+PDOP = 3.374259 | it = 0
+r_noised_vec = {25.9476593, 18.8777281, 6.1660263, 19.0112974, 28.5056679, 22.3998617, 13.0410162, 22.2106321}
+anchors_optimal = {7, 5, 3, 6}
+exact point = {19, 19, 7}
+x_sol = {19.0107776, 19.2285710, 7.0250467}
+seed = 803
+------------------------------------------------------------
+PDOP = 3.547595 | it = 0
+r_noised_vec = {7.7746202, 20.5939370, 32.4873998, 20.6647068, 10.8861041, 21.9807908, 29.0461278, 21.9321992}
+anchors_optimal = {6, 5, 3, 4}
+exact point = {1, 1, 9}
+x_sol = {0.9040026, 1.0125690, 9.1315912}
+seed = 805
+------------------------------------------------------------
+PDOP = 3.663187 | it = 0
+r_noised_vec = {8.4888266, 18.8256306, 29.4473418, 20.6599400, 11.1261139, 20.3039737, 27.7857481, 21.8294291}
+anchors_optimal = {6, 7, 5, 0}
+exact point = {3, 1, 9}
+x_sol = {2.7230573, 1.0316723, 9.3245435}
+seed = 807
+------------------------------------------------------------
+PDOP = 3.470797 | it = 0
+r_noised_vec = {9.1297310, 17.0488462, 27.8522014, 21.0148396, 11.6516607, 18.6595852, 26.6725909, 22.1228337}
+anchors_optimal = {6, 7, 5, 0}
+exact point = {5, 1, 9}
+x_sol = {4.6577017, 0.9408687, 9.3731369}
+seed = 809
+------------------------------------------------------------
+PDOP = 1.921049 | it = 0
+r_noised_vec = {9.7270718, 15.4157076, 37.0293632, 21.5421951, 12.5846393, 17.0727766, 25.6778038, 22.5956835}
+anchors_optimal = {7, 1, 4, 0}
+exact point = {7, 1, 9}
+x_sol = {6.7361022, 1.2317956, 8.8221784}
+seed = 811
+------------------------------------------------------------
+PDOP = 2.627423 | it = 0
+r_noised_vec = {11.1731241, 13.6674335, 16.3294291, 21.9329220, 13.6439499, 15.5621808, 24.5975411, 23.2440271}
+anchors_optimal = {7, 3, 1, 0}
+exact point = {9, 1, 9}
+x_sol = {8.8694728, 1.1259378, 8.9412702}
+seed = 813
+------------------------------------------------------------
+PDOP = 3.355569 | it = 0
+r_noised_vec = {13.1021118, 12.1552798, 34.7680136, 23.0578330, 15.0004787, 14.1973630, 23.8099016, 24.0495301}
+anchors_optimal = {6, 3, 4, 5}
+exact point = {11, 1, 9}
+x_sol = {11.1170854, 0.8856237, 8.9553422}
+seed = 815
+------------------------------------------------------------
+PDOP = 3.208115 | it = 0
+r_noised_vec = {14.5141735, 10.6496593, 16.4431555, 23.8310178, 16.2937731, 12.9894786, 23.1192919, 24.9908876}
+anchors_optimal = {7, 3, 0, 5}
+exact point = {13, 1, 9}
+x_sol = {13.0937297, 1.0985216, 9.0098145}
+seed = 817
+------------------------------------------------------------
+PDOP = 1.933813 | it = 0
+r_noised_vec = {15.8137048, 9.4034524, 29.8086082, 24.8330726, 17.7938191, 11.9846807, 22.5179921, 26.0467592}
+anchors_optimal = {3, 6, 4, 1}
+exact point = {15, 1, 9}
+x_sol = {14.9449554, 1.0434665, 8.9398217}
+seed = 819
+------------------------------------------------------------
+PDOP = 4.199017 | it = 0
+r_noised_vec = {17.8476202, 8.5049034, 20.3015919, 26.2085235, 19.2708734, 11.2218512, 22.1160671, 27.1975265}
+anchors_optimal = {3, 6, 4, 5}
+exact point = {17, 1, 9}
+x_sol = {16.9588584, 0.9423557, 9.2455174}
+seed = 821
+------------------------------------------------------------
+PDOP = 4.487200 | it = 0
+r_noised_vec = {20.0150911, 7.9253188, 23.9593995, 27.3117694, 21.0327174, 10.9932496, 21.8481638, 28.4257738}
+anchors_optimal = {7, 3, 6, 1}
+exact point = {19, 1, 9}
+x_sol = {19.2021672, 1.2252706, 8.8660036}
+seed = 823
+------------------------------------------------------------
+PDOP = 2.466502 | it = 0
+r_noised_vec = {8.2350375, 20.6590910, 31.4437886, 18.7658969, 11.1769908, 21.9487866, 27.7194964, 20.2528018}
+anchors_optimal = {6, 5, 4, 0}
+exact point = {1, 3, 9}
+x_sol = {1.1098918, 2.9573356, 8.9971242}
+seed = 825
+------------------------------------------------------------
+PDOP = 1.879526 | it = 0
+r_noised_vec = {8.1698922, 18.7885090, 24.6921391, 18.9539630, 11.4529630, 20.2105404, 26.3297120, 20.5588916}
+anchors_optimal = {2, 7, 5, 0}
+exact point = {3, 3, 9}
+x_sol = {3.5427301, 3.1689911, 8.4646698}
+seed = 827
+------------------------------------------------------------
+PDOP = 1.854122 | it = 0
+r_noised_vec = {9.2280714, 17.1009368, 31.2391715, 19.1702633, 11.9450624, 18.5279662, 25.0503397, 20.8024893}
+anchors_optimal = {7, 5, 4, 0}
+exact point = {5, 3, 9}
+x_sol = {5.2210258, 2.8668672, 8.9861260}
+seed = 829
+------------------------------------------------------------
+PDOP = 2.993185 | it = 0
+r_noised_vec = {10.5029524, 15.4194757, 21.2956095, 19.7231754, 12.8161336, 17.1135351, 24.0342504, 21.2278494}
+anchors_optimal = {6, 3, 5, 4}
+exact point = {7, 3, 9}
+x_sol = {7.1152684, 3.0059972, 8.9204805}
+seed = 831
+------------------------------------------------------------
+PDOP = 1.901934 | it = 0
+r_noised_vec = {11.3762026, 13.7760966, 28.1500903, 20.5627368, 13.7327200, 15.6274445, 23.0289572, 21.8264773}
+anchors_optimal = {7, 1, 4, 0}
+exact point = {9, 3, 9}
+x_sol = {8.9115039, 2.9261181, 8.9429049}
+seed = 833
+------------------------------------------------------------
+PDOP = 2.311812 | it = 0
+r_noised_vec = {12.6752430, 12.3304604, 21.0596781, 21.1011331, 14.9543624, 14.2950911, 22.2129201, 22.5900343}
+anchors_optimal = {3, 4, 5, 1}
+exact point = {11, 3, 9}
+x_sol = {11.0074559, 3.2912043, 9.1234375}
+seed = 835
+------------------------------------------------------------
+PDOP = 3.489747 | it = 0
+r_noised_vec = {14.7200571, 10.8540750, 23.9680242, 22.3886283, 16.2286396, 13.1507190, 21.4618615, 23.5082247}
+anchors_optimal = {7, 3, 6, 4}
+exact point = {13, 3, 9}
+x_sol = {12.9217139, 2.8876872, 9.1477381}
+seed = 837
+------------------------------------------------------------
+PDOP = 3.265854 | it = 0
+r_noised_vec = {16.5079514, 9.7422397, 21.8852995, 23.4657141, 17.8609095, 12.2475740, 20.9624431, 24.5687721}
+anchors_optimal = {7, 3, 4, 1}
+exact point = {15, 3, 9}
+x_sol = {15.0030534, 3.0101981, 9.1056625}
+seed = 839
+------------------------------------------------------------
+PDOP = 2.218573 | it = 0
+r_noised_vec = {17.7975961, 8.7859413, 21.5057621, 24.5659961, 19.5293347, 11.5944910, 20.6545720, 25.7580631}
+anchors_optimal = {7, 4, 5, 1}
+exact point = {17, 3, 9}
+x_sol = {16.9990182, 3.0767658, 8.9936985}
+seed = 841
+------------------------------------------------------------
+PDOP = 1.873666 | it = 0
+r_noised_vec = {19.5724507, 8.2870560, 28.1237403, 26.1145743, 21.3293681, 11.2791216, 20.3253917, 27.0645861}
+anchors_optimal = {6, 0, 5, 1}
+exact point = {19, 3, 9}
+x_sol = {18.7738297, 2.9762377, 8.9593872}
+seed = 843
+------------------------------------------------------------
+PDOP = 2.332746 | it = 0
+r_noised_vec = {9.1837526, 20.9859644, 19.5087845, 16.9812104, 11.7927395, 22.4218427, 26.6616546, 18.3756264}
+anchors_optimal = {1, 7, 3, 0}
+exact point = {1, 5, 9}
+x_sol = {1.1297529, 5.1310475, 9.2025753}
+seed = 845
+------------------------------------------------------------
+PDOP = 1.898230 | it = 0
+r_noised_vec = {9.3522874, 19.0975825, 35.7585516, 17.0694461, 12.0034633, 20.8379205, 25.2423864, 18.5549912}
+anchors_optimal = {6, 1, 3, 4}
+exact point = {3, 5, 9}
+x_sol = {3.0467552, 4.9770622, 8.8529270}
+seed = 847
+------------------------------------------------------------
+PDOP = 1.772328 | it = 0
+r_noised_vec = {9.5278842, 17.4575473, 17.7517209, 17.5219183, 12.3127630, 19.0845136, 23.8831037, 18.9377450}
+anchors_optimal = {6, 3, 1, 4}
+exact point = {5, 5, 9}
+x_sol = {5.0191204, 4.9598662, 9.0496948}
+seed = 849
+------------------------------------------------------------
+PDOP = 2.384942 | it = 0
+r_noised_vec = {10.6275980, 15.6883609, 29.8231050, 18.0061611, 13.0769851, 17.5945591, 22.6223195, 19.5152320}
+anchors_optimal = {7, 3, 5, 4}
+exact point = {7, 5, 9}
+x_sol = {6.8536587, 4.9779806, 9.0099357}
+seed = 851
+------------------------------------------------------------
+PDOP = 2.318876 | it = 0
+r_noised_vec = {12.2933686, 14.0725040, 19.6914698, 18.7300148, 13.9786677, 16.2037377, 21.4394330, 20.2668863}
+anchors_optimal = {6, 7, 4, 0}
+exact point = {9, 5, 9}
+x_sol = {9.2130893, 4.8330650, 9.3348358}
+seed = 853
+------------------------------------------------------------
+PDOP = 2.201821 | it = 0
+r_noised_vec = {13.5109339, 12.7036795, 22.6851573, 19.9053072, 15.3605647, 14.9525781, 20.5998425, 21.1695309}
+anchors_optimal = {6, 4, 0, 1}
+exact point = {11, 5, 9}
+x_sol = {11.0568911, 4.9850415, 9.0946944}
+seed = 855
+------------------------------------------------------------
+PDOP = 2.221538 | it = 0
+r_noised_vec = {14.6578875, 11.5107489, 22.2810301, 20.6522458, 16.7981402, 13.6762520, 19.7609785, 22.2009523}
+anchors_optimal = {3, 4, 5, 1}
+exact point = {13, 5, 9}
+x_sol = {13.0036222, 5.2663087, 9.0646703}
+seed = 857
+------------------------------------------------------------
+PDOP = 3.250881 | it = 0
+r_noised_vec = {16.5694272, 10.3472224, 17.5226708, 22.0576849, 18.4368822, 12.7859690, 19.1234005, 23.3417979}
+anchors_optimal = {7, 4, 2, 0}
+exact point = {15, 5, 9}
+x_sol = {15.0374428, 5.1073447, 8.7796655}
+seed = 859
+------------------------------------------------------------
+PDOP = 2.534338 | it = 0
+r_noised_vec = {18.6460914, 9.6660508, 23.3573262, 23.4270699, 19.9178518, 12.1394818, 18.8197353, 24.5754499}
+anchors_optimal = {3, 4, 0, 1}
+exact point = {17, 5, 9}
+x_sol = {17.1906365, 5.2065558, 9.2093658}
+seed = 861
+------------------------------------------------------------
+PDOP = 2.266527 | it = 0
+r_noised_vec = {20.0917338, 9.0840774, 15.9914736, 24.6420288, 21.4775981, 11.7839952, 18.6408795, 26.1221121}
+anchors_optimal = {3, 0, 5, 1}
+exact point = {19, 5, 9}
+x_sol = {18.9515080, 5.1433732, 9.0173137}
+seed = 863
+------------------------------------------------------------
+PDOP = 3.229849 | it = 0
+r_noised_vec = {9.6856737, 21.5586768, 30.6038152, 15.3289411, 12.4211058, 22.7585111, 25.6197036, 17.1646184}
+anchors_optimal = {5, 1, 3, 4}
+exact point = {1, 7, 9}
+x_sol = {0.9298432, 6.9772146, 9.1007032}
+seed = 865
+------------------------------------------------------------
+PDOP = 2.171200 | it = 0
+r_noised_vec = {10.2576305, 19.7118801, 23.3643239, 15.4118984, 12.5862579, 21.0964666, 24.1199331, 17.2075765}
+anchors_optimal = {6, 3, 4, 0}
+exact point = {3, 7, 9}
+x_sol = {2.8407985, 7.0182203, 9.1001341}
+seed = 867
+------------------------------------------------------------
+PDOP = 2.636661 | it = 0
+r_noised_vec = {11.0747321, 17.9038523, 25.2170562, 15.7183160, 13.1297686, 19.4852099, 22.8188335, 17.4927942}
+anchors_optimal = {6, 5, 1, 4}
+exact point = {5, 7, 9}
+x_sol = {5.0451952, 6.7887958, 8.9440663}
+seed = 869
+------------------------------------------------------------
+PDOP = 2.209724 | it = 0
+r_noised_vec = {11.5523905, 16.3121229, 22.5636033, 16.4470603, 13.8942490, 17.9415398, 21.6271800, 18.0098641}
+anchors_optimal = {7, 5, 3, 4}
+exact point = {7, 7, 9}
+x_sol = {7.1092449, 7.0446039, 9.0829101}
+seed = 871
+------------------------------------------------------------
+PDOP = 2.361883 | it = 0
+r_noised_vec = {12.5199563, 14.6658959, 18.8204293, 17.2280332, 14.9326071, 16.4485964, 20.3280571, 18.7423037}
+anchors_optimal = {2, 7, 4, 0}
+exact point = {9, 7, 9}
+x_sol = {8.6797879, 7.1239160, 8.7570145}
+seed = 873
+------------------------------------------------------------
+PDOP = 1.894261 | it = 0
+r_noised_vec = {14.2985762, 13.3771134, 25.7870611, 18.1114258, 16.3008157, 15.3631724, 19.3153977, 19.6681599}
+anchors_optimal = {3, 4, 0, 1}
+exact point = {11, 7, 9}
+x_sol = {11.1711084, 7.2480404, 8.8877024}
+seed = 875
+------------------------------------------------------------
+PDOP = 2.280529 | it = 0
+r_noised_vec = {15.8809896, 12.1255382, 12.3575869, 19.6064624, 17.4349884, 14.2459698, 18.4111386, 20.7621916}
+anchors_optimal = {7, 4, 0, 5}
+exact point = {13, 7, 9}
+x_sol = {13.1587149, 7.1555321, 9.1375529}
+seed = 877
+------------------------------------------------------------
+PDOP = 2.425493 | it = 0
+r_noised_vec = {17.0055378, 11.1881692, 25.7800940, 20.6039776, 18.7765555, 13.3444197, 17.7165491, 21.9983104}
+anchors_optimal = {7, 3, 0, 1}
+exact point = {15, 7, 9}
+x_sol = {14.8161364, 6.9385374, 8.9367955}
+seed = 879
+------------------------------------------------------------
+PDOP = 2.072853 | it = 0
+r_noised_vec = {18.6402637, 10.5463737, 11.5773330, 22.0881367, 20.1455450, 12.6875166, 17.1905131, 23.3571974}
+anchors_optimal = {7, 6, 5, 1}
+exact point = {17, 7, 9}
+x_sol = {17.0801297, 6.9594563, 9.1908663}
+seed = 881
+------------------------------------------------------------
+PDOP = 2.463627 | it = 0
+r_noised_vec = {20.8276452, 10.1279059, 22.6794640, 23.7122298, 21.8102107, 12.5274774, 16.8419892, 24.6707261}
+anchors_optimal = {7, 4, 5, 1}
+exact point = {19, 7, 9}
+x_sol = {18.8880947, 7.0010675, 9.0693891}
+seed = 883
+------------------------------------------------------------
+PDOP = 3.122899 | it = 0
+r_noised_vec = {11.5025148, 22.2923918, 22.7774896, 13.4989576, 13.5696775, 23.3077982, 24.4799969, 15.5288669}
+anchors_optimal = {5, 1, 4, 3}
+exact point = {1, 9, 9}
+x_sol = {1.0495446, 9.3318834, 9.2815072}
+seed = 885
+------------------------------------------------------------
+PDOP = 3.647323 | it = 0
+r_noised_vec = {11.2218667, 20.4890369, 25.5342141, 13.7744973, 13.8016218, 21.7165516, 22.9327631, 15.7173037}
+anchors_optimal = {6, 5, 1, 3}
+exact point = {3, 9, 9}
+x_sol = {3.0166614, 9.0709734, 9.1366321}
+seed = 887
+------------------------------------------------------------
+PDOP = 2.580475 | it = 0
+r_noised_vec = {11.8551341, 18.8647953, 23.9681605, 14.2230006, 14.2777213, 20.2156839, 21.4921656, 16.1357315}
+anchors_optimal = {5, 1, 7, 0}
+exact point = {5, 9, 9}
+x_sol = {4.8332553, 8.7362039, 9.1107007}
+seed = 889
+------------------------------------------------------------
+PDOP = 2.922012 | it = 0
+r_noised_vec = {13.0971570, 17.2287242, 18.9808746, 14.8037276, 14.9101858, 18.8174888, 20.2654433, 16.7662767}
+anchors_optimal = {2, 5, 1, 7}
+exact point = {7, 9, 9}
+x_sol = {6.9096180, 8.8304036, 8.9929224}
+seed = 891
+------------------------------------------------------------
+PDOP = 2.433711 | it = 0
+r_noised_vec = {13.9534714, 15.6873590, 23.2204050, 15.8079801, 15.8420825, 17.5189306, 19.0980213, 17.5856868}
+anchors_optimal = {7, 4, 3, 1}
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+x_sol = {9.0661631, 8.9661894, 8.9377856}
+seed = 893
+------------------------------------------------------------
+PDOP = 2.556413 | it = 0
+r_noised_vec = {14.7929644, 14.3900270, 15.6712807, 16.9267731, 16.8401540, 16.3748228, 18.1418266, 18.5698716}
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+seed = 895
+------------------------------------------------------------
+PDOP = 2.427089 | it = 0
+r_noised_vec = {16.4457287, 13.1417804, 20.3227816, 17.9548576, 18.1150030, 15.4195029, 17.1354232, 19.6968808}
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+x_sol = {12.9827469, 9.1338179, 8.7739421}
+seed = 897
+------------------------------------------------------------
+PDOP = 2.078972 | it = 0
+r_noised_vec = {18.3142284, 12.3096864, 15.2456168, 19.6869660, 19.3887464, 14.8057578, 16.4796745, 20.9476157}
+anchors_optimal = {7, 6, 5, 1}
+exact point = {15, 9, 9}
+x_sol = {14.9006035, 9.1218629, 8.7188925}
+seed = 899
+------------------------------------------------------------
+PDOP = 2.962623 | it = 0
+r_noised_vec = {19.5910287, 11.6318935, 16.9824599, 20.9521680, 20.9790433, 13.9981392, 16.0669718, 22.3881168}
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+exact point = {17, 9, 9}
+x_sol = {16.9255883, 8.8631663, 8.8335106}
+seed = 901
+------------------------------------------------------------
+PDOP = 1.973116 | it = 0
+r_noised_vec = {20.9470065, 11.3604286, 13.7471997, 22.4851160, 22.6961999, 13.7498912, 15.6383505, 23.7790618}
+anchors_optimal = {0, 6, 2, 1}
+exact point = {19, 9, 9}
+x_sol = {18.6504669, 8.9229958, 9.0375656}
+seed = 903
+------------------------------------------------------------
+PDOP = 2.361799 | it = 0
+r_noised_vec = {12.8625428, 22.9938366, 23.3007452, 12.1620063, 14.9985543, 24.2760329, 23.7555613, 14.1449991}
+anchors_optimal = {5, 7, 0, 3}
+exact point = {1, 11, 9}
+x_sol = {0.7180483, 10.9613318, 9.1271947}
+seed = 905
+------------------------------------------------------------
+PDOP = 1.994703 | it = 0
+r_noised_vec = {13.2653890, 21.3388304, 28.5000073, 12.1333542, 15.0586642, 22.7910624, 22.0941970, 14.2524690}
+anchors_optimal = {6, 4, 7, 3}
+exact point = {3, 11, 9}
+x_sol = {2.9994560, 11.1218551, 9.0285635}
+seed = 907
+------------------------------------------------------------
+PDOP = 1.976954 | it = 0
+r_noised_vec = {13.3102701, 19.8711181, 15.3205196, 12.6775161, 15.4159827, 21.1646155, 20.6099043, 14.6542592}
+anchors_optimal = {5, 4, 0, 3}
+exact point = {5, 11, 9}
+x_sol = {4.9660940, 10.9327336, 8.9081781}
+seed = 909
+------------------------------------------------------------
+PDOP = 2.453623 | it = 0
+r_noised_vec = {13.8557797, 18.2978207, 27.1992721, 13.5161256, 15.9516271, 19.8077650, 19.1313800, 15.3256283}
+anchors_optimal = {6, 1, 7, 3}
+exact point = {7, 11, 9}
+x_sol = {7.0490838, 11.0523625, 9.1265992}
+seed = 911
+------------------------------------------------------------
+PDOP = 2.137071 | it = 0
+r_noised_vec = {15.2527480, 16.9513538, 12.6367930, 14.4046007, 16.8227274, 18.5465096, 17.6669280, 16.2309454}
+anchors_optimal = {5, 4, 7, 3}
+exact point = {9, 11, 9}
+x_sol = {8.8955562, 11.0147518, 9.0276035}
+seed = 913
+------------------------------------------------------------
+PDOP = 2.095570 | it = 0
+r_noised_vec = {16.5091867, 15.6516625, 22.1893613, 15.6628487, 17.7894472, 17.4066573, 16.7405297, 17.3298639}
+anchors_optimal = {5, 0, 3, 1}
+exact point = {11, 11, 9}
+x_sol = {11.2257554, 11.2165372, 8.9732321}
+seed = 915
+------------------------------------------------------------
+PDOP = 2.228508 | it = 0
+r_noised_vec = {17.3540717, 14.5235003, 13.4451623, 17.1314468, 19.1090557, 16.4271831, 15.7438907, 18.5823808}
+anchors_optimal = {7, 0, 3, 1}
+exact point = {13, 11, 9}
+x_sol = {12.8745195, 10.7020351, 9.1363576}
+seed = 917
+------------------------------------------------------------
+PDOP = 2.060370 | it = 0
+r_noised_vec = {18.7448101, 13.7057590, 16.3413692, 18.2692591, 20.4525146, 15.6542494, 15.0636488, 19.9244120}
+anchors_optimal = {4, 5, 6, 1}
+exact point = {15, 11, 9}
+x_sol = {15.0592060, 10.9774213, 8.9945344}
+seed = 919
+------------------------------------------------------------
+PDOP = 2.052478 | it = 0
+r_noised_vec = {20.7272255, 13.0178126, 15.3420736, 20.1467625, 22.0004355, 15.0944736, 14.5383339, 21.4565241}
+anchors_optimal = {4, 5, 6, 1}
+exact point = {17, 11, 9}
+x_sol = {17.2414744, 10.9336837, 8.9636924}
+seed = 921
+------------------------------------------------------------
+PDOP = 2.998249 | it = 0
+r_noised_vec = {22.2811905, 12.8081580, 12.5251644, 21.6710141, 23.4025902, 14.7680872, 14.3295279, 23.0375691}
+anchors_optimal = {0, 3, 6, 1}
+exact point = {19, 11, 9}
+x_sol = {19.2474352, 11.2057526, 8.7077616}
+seed = 923
+------------------------------------------------------------
+PDOP = 3.930706 | it = 0
+r_noised_vec = {14.1577296, 23.7876702, 27.4896290, 10.5202172, 16.2763740, 24.9991727, 23.0599727, 13.1631536}
+anchors_optimal = {5, 1, 6, 4}
+exact point = {1, 13, 9}
+x_sol = {1.0253083, 12.9525341, 8.9445952}
+seed = 925
+------------------------------------------------------------
+PDOP = 2.441971 | it = 0
+r_noised_vec = {14.4132333, 22.2931806, 19.8001378, 10.9259844, 16.2791934, 23.4619254, 21.5174729, 13.3150732}
+anchors_optimal = {5, 6, 7, 3}
+exact point = {3, 13, 9}
+x_sol = {2.9813036, 12.8015870, 8.9759463}
+seed = 927
+------------------------------------------------------------
+PDOP = 1.640858 | it = 0
+r_noised_vec = {15.2551083, 20.8707875, 23.2946298, 11.3226383, 16.6824829, 22.0192946, 20.0216831, 13.7438610}
+anchors_optimal = {1, 6, 4, 3}
+exact point = {5, 13, 9}
+x_sol = {4.8427606, 12.9319089, 8.9818273}
+seed = 929
+------------------------------------------------------------
+PDOP = 2.314822 | it = 0
+r_noised_vec = {15.7200845, 19.4418106, 18.0177088, 12.1640913, 17.2375248, 20.6761487, 18.4311718, 14.4283943}
+anchors_optimal = {6, 4, 0, 3}
+exact point = {7, 13, 9}
+x_sol = {6.7702165, 13.1093668, 9.1839157}
+seed = 931
+------------------------------------------------------------
+PDOP = 2.264063 | it = 0
+r_noised_vec = {16.1877287, 18.2614653, 25.7707130, 13.3705104, 18.1794984, 19.4223882, 17.0960720, 15.3389394}
+anchors_optimal = {1, 4, 0, 7}
+exact point = {9, 13, 9}
+x_sol = {8.6200380, 13.0055553, 8.6986420}
+seed = 933
+------------------------------------------------------------
+PDOP = 2.132756 | it = 0
+r_noised_vec = {17.5003849, 17.0177537, 14.0211208, 14.5596153, 19.1684545, 18.5521438, 15.8372727, 16.4441814}
+anchors_optimal = {4, 7, 6, 3}
+exact point = {11, 13, 9}
+x_sol = {11.0155762, 13.0531197, 8.9624025}
+seed = 935
+------------------------------------------------------------
+PDOP = 2.434312 | it = 0
+r_noised_vec = {19.0743539, 16.0937804, 13.8810895, 16.0300399, 20.4064137, 17.6604822, 14.7845135, 17.7180213}
+anchors_optimal = {5, 1, 3, 6}
+exact point = {13, 13, 9}
+x_sol = {12.9016633, 12.9555472, 9.1083457}
+seed = 937
+------------------------------------------------------------
+PDOP = 2.527995 | it = 0
+r_noised_vec = {20.0979635, 15.2757131, 17.5184642, 17.7629292, 21.5123077, 16.9781197, 13.8866223, 19.0273612}
+anchors_optimal = {0, 7, 3, 1}
+exact point = {15, 13, 9}
+x_sol = {14.9889664, 12.8264864, 9.2758206}
+seed = 939
+------------------------------------------------------------
+PDOP = 3.445284 | it = 0
+r_noised_vec = {21.2283975, 14.6768697, 8.3269649, 19.0303897, 22.8009290, 16.5291222, 13.2229978, 20.5027265}
+anchors_optimal = {0, 7, 3, 5}
+exact point = {17, 13, 9}
+x_sol = {16.7010274, 12.8286613, 8.9682616}
+seed = 941
+------------------------------------------------------------
+PDOP = 3.094553 | it = 0
+r_noised_vec = {23.1181519, 14.2267984, 18.2003183, 20.9658063, 24.1020031, 16.3162299, 13.0417693, 22.0806754}
+anchors_optimal = {4, 0, 1, 6}
+exact point = {19, 13, 9}
+x_sol = {19.2380830, 12.5729383, 9.2774314}
+seed = 943
+------------------------------------------------------------
+PDOP = 1.928991 | it = 0
+r_noised_vec = {16.4279408, 24.8082717, 17.6070878, 9.5030058, 17.7140217, 26.0728638, 22.4354939, 11.9504361}
+anchors_optimal = {1, 6, 4, 3}
+exact point = {1, 15, 9}
+x_sol = {1.0959468, 14.9155053, 9.0344672}
+seed = 945
+------------------------------------------------------------
+PDOP = 3.547289 | it = 0
+r_noised_vec = {16.1452832, 23.2108777, 27.0153996, 9.5203505, 17.9085296, 24.6945738, 20.7784140, 12.1431703}
+anchors_optimal = {1, 6, 4, 0}
+exact point = {3, 15, 9}
+x_sol = {3.1822454, 14.8959900, 8.9198615}
+seed = 947
+------------------------------------------------------------
+PDOP = 2.461172 | it = 0
+r_noised_vec = {16.3268209, 21.9639016, 17.2374758, 10.3287657, 18.3369471, 23.4223770, 19.2588142, 12.6602006}
+anchors_optimal = {6, 4, 2, 3}
+exact point = {5, 15, 9}
+x_sol = {5.4882323, 14.5997072, 8.5586486}
+seed = 949
+------------------------------------------------------------
+PDOP = 2.360386 | it = 0
+r_noised_vec = {17.3544003, 20.6992976, 19.7115591, 11.1846804, 18.8797244, 22.0759136, 17.7856462, 13.4597982}
+anchors_optimal = {5, 4, 0, 3}
+exact point = {7, 15, 9}
+x_sol = {7.0552114, 15.1336352, 9.0455583}
+seed = 951
+------------------------------------------------------------
+PDOP = 2.657559 | it = 0
+r_noised_vec = {18.2617309, 19.5658118, 17.3735227, 12.3065545, 19.7544106, 21.0091374, 16.4604693, 14.4894919}
+anchors_optimal = {5, 4, 0, 7}
+exact point = {9, 15, 9}
+x_sol = {9.1540232, 15.2445095, 9.0066863}
+seed = 953
+------------------------------------------------------------
+PDOP = 2.544971 | it = 0
+r_noised_vec = {18.7810323, 18.6480036, 13.7835971, 13.8059941, 20.4314992, 20.0714949, 15.1075895, 15.6952172}
+anchors_optimal = {0, 1, 6, 3}
+exact point = {11, 15, 9}
+x_sol = {10.6310299, 14.7663606, 9.3786072}
+seed = 955
+------------------------------------------------------------
+PDOP = 2.584667 | it = 0
+r_noised_vec = {19.8697422, 17.6787296, 16.0632162, 15.2487615, 21.4170022, 19.2929854, 14.0693965, 17.1867411}
+anchors_optimal = {4, 5, 1, 6}
+exact point = {13, 15, 9}
+x_sol = {12.7754921, 15.0860886, 8.9294262}
+seed = 957
+------------------------------------------------------------
+PDOP = 2.137260 | it = 0
+r_noised_vec = {21.5844506, 17.0693701, 10.8498886, 16.7540182, 22.4283409, 18.7538126, 13.2231555, 18.6619637}
+anchors_optimal = {4, 7, 6, 2}
+exact point = {15, 15, 9}
+x_sol = {15.0636065, 14.5726733, 8.9965326}
+seed = 959
+------------------------------------------------------------
+PDOP = 2.445574 | it = 0
+r_noised_vec = {22.9077546, 16.4559086, 13.4398690, 18.7778359, 23.8500541, 18.1069651, 12.4763569, 20.2108482}
+anchors_optimal = {4, 5, 1, 6}
+exact point = {17, 15, 9}
+x_sol = {16.8411288, 15.0316501, 8.9982827}
+seed = 961
+------------------------------------------------------------
+PDOP = 2.481838 | it = 0
+r_noised_vec = {23.9043703, 16.1714922, 11.0958553, 20.1869631, 25.3221798, 17.8920522, 12.1420668, 21.8144206}
+anchors_optimal = {4, 5, 1, 6}
+exact point = {19, 15, 9}
+x_sol = {18.9496647, 15.0446249, 8.9576745}
+seed = 963
+------------------------------------------------------------
+PDOP = 3.494617 | it = 0
+r_noised_vec = {17.7394510, 26.0563501, 30.6273626, 8.5408257, 19.5639539, 27.2151370, 22.1121086, 11.4987038}
+anchors_optimal = {5, 1, 4, 7}
+exact point = {1, 17, 9}
+x_sol = {1.0811740, 17.0928448, 8.8755184}
+seed = 965
+------------------------------------------------------------
+PDOP = 3.292077 | it = 0
+r_noised_vec = {18.2860755, 24.5209776, 19.0102288, 8.8825000, 19.6323829, 25.8256194, 20.4369785, 11.6304637}
+anchors_optimal = {5, 2, 0, 3}
+exact point = {3, 17, 9}
+x_sol = {3.0660528, 17.2232040, 9.1817878}
+seed = 967
+------------------------------------------------------------
+PDOP = 2.966319 | it = 0
+r_noised_vec = {18.4323894, 23.2561768, 18.9813465, 9.3182487, 19.8534883, 24.5264311, 18.7411626, 12.0989090}
+anchors_optimal = {5, 6, 0, 7}
+exact point = {5, 17, 9}
+x_sol = {5.1092743, 17.0872277, 9.0014403}
+seed = 969
+------------------------------------------------------------
+PDOP = 2.275744 | it = 0
+r_noised_vec = {18.5652561, 21.9452348, 21.3890668, 10.4842573, 20.2879648, 23.3276908, 17.1137014, 12.8719418}
+anchors_optimal = {5, 4, 7, 3}
+exact point = {7, 17, 9}
+x_sol = {7.0110621, 16.9714377, 9.0324412}
+seed = 971
+------------------------------------------------------------
+PDOP = 2.920374 | it = 0
+r_noised_vec = {19.5435464, 20.9499530, 11.4860660, 11.7432445, 20.9131374, 22.2318919, 15.7946386, 13.9055416}
+anchors_optimal = {1, 4, 6, 7}
+exact point = {9, 17, 9}
+x_sol = {9.0235127, 16.9209270, 9.0640710}
+seed = 973
+------------------------------------------------------------
+PDOP = 3.087960 | it = 0
+r_noised_vec = {20.8050737, 20.0064442, 19.9316595, 13.0831994, 21.8112603, 21.2485347, 14.4532079, 14.9385027}
+anchors_optimal = {4, 5, 0, 7}
+exact point = {11, 17, 9}
+x_sol = {11.1376540, 17.1466372, 9.3715794}
+seed = 975
+------------------------------------------------------------
+PDOP = 3.422952 | it = 0
+r_noised_vec = {21.5419474, 19.2424194, 8.4564402, 14.7724863, 22.7558348, 20.6014096, 13.3314292, 16.3562119}
+anchors_optimal = {4, 0, 1, 6}
+exact point = {13, 17, 9}
+x_sol = {12.9680209, 16.9820058, 9.0849337}
+seed = 977
+------------------------------------------------------------
+PDOP = 3.140863 | it = 0
+r_noised_vec = {22.4043807, 18.7128661, 15.7184084, 16.4010757, 23.9676092, 19.9639410, 12.4593985, 17.8855192}
+anchors_optimal = {4, 0, 1, 7}
+exact point = {15, 17, 9}
+x_sol = {14.4943399, 17.1988025, 8.5923680}
+seed = 979
+------------------------------------------------------------
+PDOP = 2.938059 | it = 0
+r_noised_vec = {24.0497868, 18.2158497, 8.7275455, 17.9523678, 25.4016198, 19.5204377, 11.8552276, 19.5164457}
+anchors_optimal = {7, 1, 3, 6}
+exact point = {17, 17, 9}
+x_sol = {16.8248745, 17.0756553, 8.9577857}
+seed = 981
+------------------------------------------------------------
+PDOP = 3.193777 | it = 0
+r_noised_vec = {25.6801076, 18.0698719, 11.5697597, 20.1150366, 26.6019484, 19.2747619, 11.6058464, 21.2237562}
+anchors_optimal = {4, 7, 1, 6}
+exact point = {19, 17, 9}
+x_sol = {18.8092672, 17.2688377, 8.7791781}
+seed = 983
+------------------------------------------------------------
+PDOP = 4.099752 | it = 0
+r_noised_vec = {19.5982371, 27.4125592, 23.6641249, 7.9870237, 21.1199650, 28.3740629, 22.0362418, 11.0086648}
+anchors_optimal = {5, 6, 4, 0}
+exact point = {1, 19, 9}
+x_sol = {1.0304900, 18.9289039, 8.8694204}
+seed = 985
+------------------------------------------------------------
+PDOP = 2.213438 | it = 0
+r_noised_vec = {19.5124878, 26.0398524, 19.9686605, 8.2454560, 21.0906849, 27.0387847, 20.3841403, 11.2276598}
+anchors_optimal = {1, 0, 7, 3}
+exact point = {3, 19, 9}
+x_sol = {2.6753491, 18.7302535, 8.9717684}
+seed = 987
+------------------------------------------------------------
+PDOP = 3.037119 | it = 0
+r_noised_vec = {20.2462014, 24.7321047, 21.5399849, 9.1254187, 21.3515135, 25.8252023, 18.7646227, 11.7759109}
+anchors_optimal = {5, 1, 0, 3}
+exact point = {5, 19, 9}
+x_sol = {5.1903070, 19.0956685, 9.0456823}
+seed = 989
+------------------------------------------------------------
+PDOP = 2.571738 | it = 0
+r_noised_vec = {20.8536115, 23.4771407, 15.9683840, 9.9595053, 21.8789345, 24.7326179, 17.0809151, 12.6062220}
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+exact point = {7, 19, 9}
+x_sol = {6.4000647, 19.3337202, 9.3469826}
+seed = 991
+------------------------------------------------------------
+PDOP = 3.083892 | it = 0
+r_noised_vec = {21.0708522, 22.4957838, 16.9648396, 11.3608415, 22.5257294, 23.7779035, 15.5801979, 13.6562984}
+anchors_optimal = {5, 4, 6, 3}
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+x_sol = {8.9742050, 18.9906876, 9.0343780}
+seed = 993
+------------------------------------------------------------
+PDOP = 3.037138 | it = 0
+r_noised_vec = {21.8595656, 21.5154409, 5.3816832, 12.9074242, 23.4103302, 22.9467623, 14.1536198, 15.1201868}
+anchors_optimal = {4, 5, 6, 3}
+exact point = {11, 19, 9}
+x_sol = {11.0655174, 19.0849723, 9.0470259}
+seed = 995
+------------------------------------------------------------
+PDOP = 3.962781 | it = 0
+r_noised_vec = {23.2924174, 20.8662308, 18.0865174, 14.3929204, 24.3149032, 22.2698126, 13.0244367, 16.4810518}
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+x_sol = {13.0071043, 19.0135103, 8.9067114}
+seed = 997
+------------------------------------------------------------
+PDOP = 1.872348 | it = 0
+r_noised_vec = {24.3598555, 20.3001241, 9.3776213, 16.1767327, 25.4439344, 21.7703295, 12.0043023, 17.9512319}
+anchors_optimal = {0, 5, 7, 2}
+exact point = {15, 19, 9}
+x_sol = {15.1547666, 19.1468855, 8.9887943}
+seed = 999
+------------------------------------------------------------
+PDOP = 4.313400 | it = 0
+r_noised_vec = {25.1181614, 19.9453730, 10.2330580, 17.9192080, 26.4814666, 21.4719893, 11.2507166, 19.5063508}
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+exact point = {17, 19, 9}
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+seed = 1001
+------------------------------------------------------------
+PDOP = 3.610118 | it = 0
+r_noised_vec = {26.5321438, 19.8337776, 12.3478069, 19.5126116, 27.7154227, 21.1640517, 11.0376469, 21.1332253}
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+exact point = {19, 19, 9}
+x_sol = {18.7487029, 19.0812482, 9.0647803}
+seed = 1003
+------------------------------------------------------------
+PDOP = 5.167610 | it = 0
+r_noised_vec = {10.2836954, 21.5225179, 26.1953015, 21.6202371, 8.8519909, 21.1150161, 28.2811173, 20.9999813}
+anchors_optimal = {6, 3, 1, 7}
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+x_sol = {1.0573057, 0.9463616, 11.1956695}
+seed = 1005
+------------------------------------------------------------
+PDOP = 3.149447 | it = 0
+r_noised_vec = {10.3026084, 19.8528909, 36.5605208, 21.5547980, 9.1623489, 19.3667074, 27.0305082, 21.0725016}
+anchors_optimal = {6, 3, 7, 4}
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+x_sol = {2.9579461, 1.0236398, 11.0410261}
+seed = 1007
+------------------------------------------------------------
+PDOP = 3.160122 | it = 0
+r_noised_vec = {10.4695915, 18.0580029, 23.1579982, 21.7361546, 9.8706434, 17.6662950, 25.8538289, 21.3507631}
+anchors_optimal = {6, 3, 7, 4}
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+seed = 1009
+------------------------------------------------------------
+PDOP = 3.998967 | it = 0
+r_noised_vec = {11.6067266, 16.4247129, 32.7891978, 22.4151458, 10.9220897, 15.8372995, 24.8130697, 21.8295990}
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+seed = 1011
+------------------------------------------------------------
+PDOP = 2.823568 | it = 0
+r_noised_vec = {13.1159178, 14.8520356, 23.7693523, 22.8598563, 12.1132062, 14.2681044, 23.9300963, 22.2529241}
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+seed = 1013
+------------------------------------------------------------
+PDOP = 2.151476 | it = 0
+r_noised_vec = {14.1464753, 13.3546296, 27.5116889, 23.6516250, 13.5665972, 12.7864624, 22.9412057, 23.1159587}
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+x_sol = {11.0730692, 1.2817109, 10.9229001}
+seed = 1015
+------------------------------------------------------------
+PDOP = 2.832079 | it = 0
+r_noised_vec = {15.3102443, 12.1718184, 25.5087300, 24.6691730, 14.9725304, 11.4452836, 22.2679379, 24.1079097}
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+x_sol = {13.0144313, 0.8982489, 10.9515433}
+seed = 1017
+------------------------------------------------------------
+PDOP = 2.164523 | it = 0
+r_noised_vec = {17.2512237, 11.0609635, 23.5676238, 25.5838185, 16.5928371, 10.3018059, 21.7274873, 25.2194281}
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+seed = 1019
+------------------------------------------------------------
+PDOP = 4.395817 | it = 0
+r_noised_vec = {19.1704487, 10.4219229, 26.1056119, 26.7797963, 18.1870292, 9.4716797, 21.2466637, 26.4307510}
+anchors_optimal = {3, 7, 6, 1}
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+x_sol = {17.0043126, 0.9900754, 10.9887603}
+seed = 1021
+------------------------------------------------------------
+PDOP = 2.527787 | it = 0
+r_noised_vec = {20.4950697, 10.0256015, 22.8935809, 28.2076486, 20.0779946, 9.0067040, 21.0081040, 27.7231256}
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+exact point = {19, 1, 11}
+x_sol = {19.3141852, 1.0205338, 11.0103149}
+seed = 1023
+------------------------------------------------------------
+PDOP = 3.625557 | it = 0
+r_noised_vec = {9.9114596, 21.5694633, 44.4896301, 19.5216247, 9.2343570, 21.0207020, 26.8850631, 19.2992341}
+anchors_optimal = {6, 5, 7, 0}
+exact point = {1, 3, 11}
+x_sol = {1.2803637, 3.1069289, 10.6766657}
+seed = 1025
+------------------------------------------------------------
+PDOP = 3.518142 | it = 0
+r_noised_vec = {10.5354826, 19.9124408, 18.7994069, 19.9139649, 9.5825019, 19.1599538, 25.5994212, 19.4019200}
+anchors_optimal = {6, 3, 7, 5}
+exact point = {3, 3, 11}
+x_sol = {3.1606351, 2.9150912, 11.0297763}
+seed = 1027
+------------------------------------------------------------
+PDOP = 2.737453 | it = 0
+r_noised_vec = {11.2174200, 18.4478606, 34.2585007, 20.1769524, 10.1356471, 17.5550131, 24.2575916, 19.6915355}
+anchors_optimal = {6, 3, 7, 4}
+exact point = {5, 3, 11}
+x_sol = {5.2191005, 2.9993361, 11.0092853}
+seed = 1029
+------------------------------------------------------------
+PDOP = 3.111453 | it = 0
+r_noised_vec = {11.6458878, 16.6320330, 23.3555261, 20.4888119, 11.0027121, 15.8410079, 23.0068645, 20.4248715}
+anchors_optimal = {2, 6, 3, 5}
+exact point = {7, 3, 11}
+x_sol = {7.1923898, 3.1742557, 10.9253891}
+seed = 1031
+------------------------------------------------------------
+PDOP = 2.931655 | it = 0
+r_noised_vec = {12.7291847, 15.1799821, 25.2166040, 21.3825902, 12.1358995, 14.2164930, 22.1089368, 20.9822913}
+anchors_optimal = {6, 3, 7, 5}
+exact point = {9, 3, 11}
+x_sol = {9.2224069, 2.9553575, 10.9462794}
+seed = 1033
+------------------------------------------------------------
+PDOP = 2.592516 | it = 0
+r_noised_vec = {14.5071724, 13.6260750, 27.1721238, 22.1023571, 13.5215533, 12.7041239, 21.2050153, 21.7526360}
+anchors_optimal = {7, 6, 0, 4}
+exact point = {11, 3, 11}
+x_sol = {11.1190658, 2.8593482, 11.2269907}
+seed = 1035
+------------------------------------------------------------
+PDOP = 3.043161 | it = 0
+r_noised_vec = {15.9434101, 12.2982668, 19.1711679, 23.0260110, 14.9411847, 11.5432315, 20.5187190, 22.6811614}
+anchors_optimal = {3, 7, 0, 5}
+exact point = {13, 3, 11}
+x_sol = {13.2680008, 3.2367142, 10.9147922}
+seed = 1037
+------------------------------------------------------------
+PDOP = 2.629726 | it = 0
+r_noised_vec = {17.0642194, 11.2797315, 28.2825507, 24.2558949, 16.7415065, 10.4312128, 19.9236828, 23.7518314}
+anchors_optimal = {6, 0, 4, 1}
+exact point = {15, 3, 11}
+x_sol = {14.8146116, 3.1149911, 10.7870932}
+seed = 1039
+------------------------------------------------------------
+PDOP = 2.857082 | it = 0
+r_noised_vec = {18.8204056, 10.4082093, 17.5270200, 25.3695610, 18.5080706, 9.6377073, 19.5911715, 24.9507360}
+anchors_optimal = {7, 6, 0, 5}
+exact point = {17, 3, 11}
+x_sol = {16.7822428, 2.8439842, 11.0946589}
+seed = 1041
+------------------------------------------------------------
+PDOP = 478.451877 | it = 2
+r_noised_vec = {20.9694963, 10.1475721, 26.6408518, 26.6946373, 20.4184734, 9.2332772, 19.5198230, 26.2636510}
+anchors_optimal = {7, 3, 0, 4}
+exact point = {19, 3, 11}
+start_optimal = {19.227912, 3.318845, 11.100151}
+x_sol = {19.2296412, 3.3188452, 11.1006393}
+seed = 1043
+------------------------------------------------------------
+PDOP = 3.174434 | it = 0
+r_noised_vec = {10.8773630, 21.6901916, 25.9651158, 18.2457513, 9.9362439, 21.4010318, 25.9056169, 17.4196072}
+anchors_optimal = {6, 1, 5, 4}
+exact point = {1, 5, 11}
+x_sol = {1.0453889, 4.8921889, 10.8279012}
+seed = 1045
+------------------------------------------------------------
+PDOP = 2.738170 | it = 0
+r_noised_vec = {10.6556642, 20.1001572, 29.0982534, 17.9748692, 10.0512562, 19.6653708, 24.4920328, 17.5548912}
+anchors_optimal = {6, 1, 5, 4}
+exact point = {3, 5, 11}
+x_sol = {2.9816038, 4.8912405, 10.9549871}
+seed = 1047
+------------------------------------------------------------
+PDOP = 3.035943 | it = 0
+r_noised_vec = {11.4311640, 18.5216701, 26.2598258, 18.4882817, 10.5065317, 17.9982514, 23.1344604, 17.9255862}
+anchors_optimal = {6, 1, 3, 0}
+exact point = {5, 5, 11}
+x_sol = {4.9110328, 4.9435513, 10.9998436}
+seed = 1049
+------------------------------------------------------------
+PDOP = 2.546856 | it = 0
+r_noised_vec = {12.6370074, 16.9503489, 24.0484427, 19.0998224, 11.4286094, 16.4150604, 21.7856463, 18.3678873}
+anchors_optimal = {3, 7, 1, 4}
+exact point = {7, 5, 11}
+x_sol = {7.0979663, 5.0587850, 11.2216824}
+seed = 1051
+------------------------------------------------------------
+PDOP = 2.443257 | it = 0
+r_noised_vec = {13.4237754, 15.5860530, 25.0239343, 19.5960699, 12.6658785, 14.9619525, 20.5894437, 19.1954041}
+anchors_optimal = {6, 3, 0, 4}
+exact point = {9, 5, 11}
+x_sol = {8.9291446, 5.1366261, 11.0203492}
+seed = 1053
+------------------------------------------------------------
+PDOP = 1.614377 | it = 0
+r_noised_vec = {14.3876723, 14.1249799, 8.6004362, 20.6778532, 14.0535720, 13.3995866, 19.4105067, 20.1732064}
+anchors_optimal = {3, 6, 1, 4}
+exact point = {11, 5, 11}
+x_sol = {11.1420220, 5.1404810, 11.1949739}
+seed = 1055
+------------------------------------------------------------
+PDOP = 2.626191 | it = 0
+r_noised_vec = {16.1679000, 12.9805273, 32.5795186, 21.6847016, 15.5978922, 12.1845007, 18.7529217, 21.2809752}
+anchors_optimal = {7, 6, 0, 5}
+exact point = {13, 5, 11}
+x_sol = {13.1633640, 5.1523681, 10.8087131}
+seed = 1057
+------------------------------------------------------------
+PDOP = 2.631566 | it = 0
+r_noised_vec = {17.9655465, 11.8981155, 12.8917912, 22.7510450, 17.3992248, 11.1864758, 18.0499036, 22.4963371}
+anchors_optimal = {3, 7, 4, 5}
+exact point = {15, 5, 11}
+x_sol = {15.1735732, 5.1486274, 10.8032860}
+seed = 1059
+------------------------------------------------------------
+PDOP = 1.805631 | it = 0
+r_noised_vec = {19.1943733, 11.1352765, 26.6868815, 24.1586697, 18.8631866, 10.4829863, 17.7387535, 23.8006473}
+anchors_optimal = {3, 4, 6, 1}
+exact point = {17, 5, 11}
+x_sol = {17.0895181, 4.9935459, 10.9888489}
+seed = 1061
+------------------------------------------------------------
+PDOP = 2.454429 | it = 0
+r_noised_vec = {20.6895202, 10.7576644, 17.7206520, 25.4687359, 20.4983034, 9.9373322, 17.4827226, 25.1801521}
+anchors_optimal = {3, 4, 1, 5}
+exact point = {19, 5, 11}
+x_sol = {18.9586808, 4.9342292, 10.9467572}
+seed = 1063
+------------------------------------------------------------
+PDOP = 4.309678 | it = 0
+r_noised_vec = {11.8018345, 22.1234677, 28.1378411, 16.1942082, 10.6243097, 21.9212061, 24.7185605, 15.8664593}
+anchors_optimal = {6, 1, 5, 3}
+exact point = {1, 7, 11}
+x_sol = {1.0878053, 7.0666327, 10.7344354}
+seed = 1065
+------------------------------------------------------------
+PDOP = 2.818485 | it = 0
+r_noised_vec = {12.0957417, 20.5366694, 28.8212346, 16.7358001, 10.8804410, 20.2059339, 23.2252510, 15.9620281}
+anchors_optimal = {1, 5, 3, 4}
+exact point = {3, 7, 11}
+x_sol = {2.8711639, 6.5992636, 10.8546059}
+seed = 1067
+------------------------------------------------------------
+PDOP = 2.792413 | it = 0
+r_noised_vec = {12.1456995, 18.8754119, 20.9102858, 16.7771666, 11.5058573, 18.5300674, 21.8666937, 16.4015073}
+anchors_optimal = {6, 1, 3, 0}
+exact point = {5, 7, 11}
+x_sol = {5.0062326, 6.9748604, 10.8180049}
+seed = 1069
+------------------------------------------------------------
+PDOP = 2.050755 | it = 0
+r_noised_vec = {12.8814487, 17.4417743, 28.4870638, 17.4217065, 12.4424856, 16.9104925, 20.6187830, 16.9121378}
+anchors_optimal = {3, 7, 5, 4}
+exact point = {7, 7, 11}
+x_sol = {7.0487024, 7.0472380, 10.9604066}
+seed = 1071
+------------------------------------------------------------
+PDOP = 2.197237 | it = 0
+r_noised_vec = {14.3634971, 16.0680904, 17.7066095, 18.3754330, 13.5599397, 15.4051808, 19.2881015, 17.6604510}
+anchors_optimal = {3, 7, 1, 0}
+exact point = {9, 7, 11}
+x_sol = {9.1349085, 7.0435134, 11.1780266}
+seed = 1073
+------------------------------------------------------------
+PDOP = 2.539898 | it = 0
+r_noised_vec = {15.5593042, 14.7805488, 25.2124752, 19.1023617, 14.7750208, 14.0119051, 18.2731825, 18.6121169}
+anchors_optimal = {7, 6, 1, 4}
+exact point = {11, 7, 11}
+x_sol = {10.8289921, 7.1286933, 10.8332916}
+seed = 1075
+------------------------------------------------------------
+PDOP = 2.892244 | it = 0
+r_noised_vec = {16.4795964, 13.7544776, 17.7853108, 20.3418979, 16.2022407, 12.7705666, 17.3719475, 19.7392052}
+anchors_optimal = {3, 7, 6, 1}
+exact point = {13, 7, 11}
+x_sol = {12.8118858, 6.9011712, 11.1356997}
+seed = 1077
+------------------------------------------------------------
+PDOP = 2.498425 | it = 0
+r_noised_vec = {18.0655466, 12.7562478, 20.9692033, 21.6223868, 17.6401323, 11.6933221, 16.5863163, 21.0143779}
+anchors_optimal = {0, 4, 6, 1}
+exact point = {15, 7, 11}
+x_sol = {14.8063715, 7.1427964, 10.8997290}
+seed = 1079
+------------------------------------------------------------
+PDOP = 2.772204 | it = 0
+r_noised_vec = {20.0779829, 12.1573135, 19.0940846, 22.8390312, 19.2855646, 11.1611789, 16.0608809, 22.4111613}
+anchors_optimal = {0, 4, 6, 1}
+exact point = {17, 7, 11}
+x_sol = {17.2190823, 6.7804205, 11.3208525}
+seed = 1081
+------------------------------------------------------------
+PDOP = 2.570855 | it = 0
+r_noised_vec = {21.5570893, 11.7251066, 18.3493986, 24.3852430, 20.8761101, 10.7562965, 15.7309616, 23.9045793}
+anchors_optimal = {3, 4, 1, 5}
+exact point = {19, 7, 11}
+x_sol = {18.9240542, 6.8934765, 11.0731635}
+seed = 1083
+------------------------------------------------------------
+PDOP = 2.096983 | it = 0
+r_noised_vec = {12.5093986, 22.8828400, 27.4964668, 14.8739936, 12.0292243, 22.3483739, 23.6935272, 14.1892515}
+anchors_optimal = {6, 3, 7, 4}
+exact point = {1, 9, 11}
+x_sol = {1.0250428, 9.0096679, 11.0237060}
+seed = 1085
+------------------------------------------------------------
+PDOP = 2.722657 | it = 0
+r_noised_vec = {12.9007570, 21.2437710, 14.8185955, 14.7721758, 12.3682618, 20.6365714, 22.0572454, 14.3019797}
+anchors_optimal = {6, 1, 7, 4}
+exact point = {3, 9, 11}
+x_sol = {3.0795934, 9.1428231, 10.9302224}
+seed = 1087
+------------------------------------------------------------
+PDOP = 2.547949 | it = 0
+r_noised_vec = {13.7231077, 19.5847359, 33.5726289, 15.5728331, 12.8245046, 19.1932512, 20.5199476, 14.8092547}
+anchors_optimal = {6, 1, 7, 4}
+exact point = {5, 9, 11}
+x_sol = {5.1906783, 9.0566814, 10.9563088}
+seed = 1089
+------------------------------------------------------------
+PDOP = 2.232468 | it = 0
+r_noised_vec = {14.1525084, 18.1931407, 14.3927668, 15.9952967, 13.5086142, 17.6612378, 19.2373556, 15.5237510}
+anchors_optimal = {6, 3, 0, 4}
+exact point = {7, 9, 11}
+x_sol = {7.0253376, 9.0379994, 10.9687062}
+seed = 1091
+------------------------------------------------------------
+PDOP = 2.026661 | it = 0
+r_noised_vec = {14.7913851, 16.7741627, 26.7441518, 16.7874867, 14.4567659, 16.2544475, 17.9515713, 16.4321166}
+anchors_optimal = {1, 7, 5, 4}
+exact point = {9, 9, 11}
+x_sol = {9.0471321, 8.8943059, 10.9517230}
+seed = 1093
+------------------------------------------------------------
+PDOP = 1.512279 | it = 0
+r_noised_vec = {16.2882962, 15.6352151, 16.9795806, 18.0482328, 15.5626698, 15.0003360, 16.8615625, 17.5038225}
+anchors_optimal = {3, 6, 1, 4}
+exact point = {11, 9, 11}
+x_sol = {11.0153047, 8.8763901, 11.0748641}
+seed = 1095
+------------------------------------------------------------
+PDOP = 2.264760 | it = 0
+r_noised_vec = {17.8514942, 14.6186990, 19.3386230, 19.0331824, 16.9390217, 13.9309080, 15.8703714, 18.7109751}
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+exact point = {13, 9, 11}
+x_sol = {13.2623549, 8.8376281, 11.3354050}
+seed = 1097
+------------------------------------------------------------
+PDOP = 3.011801 | it = 0
+r_noised_vec = {18.8839762, 13.7773152, 19.9016458, 20.3985663, 18.3513586, 13.0642907, 15.1613250, 20.0313363}
+anchors_optimal = {3, 7, 0, 5}
+exact point = {15, 9, 11}
+x_sol = {15.0021524, 8.9342908, 10.8907125}
+seed = 1099
+------------------------------------------------------------
+PDOP = 2.767321 | it = 0
+r_noised_vec = {20.2071694, 13.2781152, 14.3964184, 21.9159090, 20.0404727, 12.4747096, 14.6969594, 21.4486114}
+anchors_optimal = {3, 0, 6, 1}
+exact point = {17, 9, 11}
+x_sol = {16.6058251, 8.6058586, 11.3496079}
+seed = 1101
+------------------------------------------------------------
+PDOP = 3.395842 | it = 0
+r_noised_vec = {22.2274292, 12.8851321, 21.2816152, 23.2841242, 21.6929942, 12.2050648, 14.2916326, 22.9516077}
+anchors_optimal = {3, 7, 4, 6}
+exact point = {19, 9, 11}
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+seed = 1103
+------------------------------------------------------------
+PDOP = 2.934641 | it = 0
+r_noised_vec = {14.4063251, 23.7857420, 21.5323935, 13.4649659, 13.6131917, 23.5774674, 22.9419791, 12.7264348}
+anchors_optimal = {5, 6, 0, 4}
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+x_sol = {0.7479479, 11.2779622, 11.0848214}
+seed = 1105
+------------------------------------------------------------
+PDOP = 3.099364 | it = 0
+r_noised_vec = {14.1028493, 22.1255366, 28.1820711, 13.6123286, 13.6513735, 21.7489595, 21.2885170, 12.7888819}
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+seed = 1107
+------------------------------------------------------------
+PDOP = 2.713859 | it = 0
+r_noised_vec = {14.4623883, 20.5964410, 20.2982523, 13.8100585, 14.0302261, 20.2609068, 19.6655197, 13.2086140}
+anchors_optimal = {1, 2, 4, 3}
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+seed = 1109
+------------------------------------------------------------
+PDOP = 2.240183 | it = 0
+r_noised_vec = {15.5807195, 19.1930655, 22.5637491, 14.8513046, 14.5997488, 18.8593905, 18.1336963, 13.9256617}
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+seed = 1111
+------------------------------------------------------------
+PDOP = 2.365886 | it = 0
+r_noised_vec = {16.4466946, 17.8035082, 19.7697493, 15.6842494, 15.5729570, 17.5853780, 16.6719389, 14.8971858}
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+seed = 1113
+------------------------------------------------------------
+PDOP = 2.200374 | it = 0
+r_noised_vec = {17.0695704, 16.7481434, 18.3687999, 16.6363919, 16.6704641, 16.2321522, 15.5349586, 16.0764129}
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+------------------------------------------------------------
+PDOP = 1.527782 | it = 0
+r_noised_vec = {18.3898725, 15.6867381, 24.6185306, 18.1427063, 18.0822369, 15.2250747, 14.4176389, 17.4185359}
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+seed = 1117
+------------------------------------------------------------
+PDOP = 2.681207 | it = 0
+r_noised_vec = {20.1764145, 14.8857632, 8.8871084, 19.3879891, 19.4842714, 14.4060504, 13.5392822, 18.8838817}
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+------------------------------------------------------------
+PDOP = 1.944732 | it = 0
+r_noised_vec = {21.4660616, 14.4714728, 23.8806405, 20.8491155, 21.0814883, 13.8127654, 13.0544649, 20.4389962}
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+------------------------------------------------------------
+PDOP = 2.969438 | it = 0
+r_noised_vec = {22.5961216, 14.3348022, 9.1864231, 22.5502432, 22.5023897, 13.4863426, 12.7710231, 22.0557493}
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+seed = 1123
+------------------------------------------------------------
+PDOP = 3.198431 | it = 0
+r_noised_vec = {15.5570326, 24.6981455, 31.1698332, 12.1663075, 14.9694733, 24.1774994, 22.2428658, 11.5567198}
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+seed = 1125
+------------------------------------------------------------
+PDOP = 2.338271 | it = 0
+r_noised_vec = {16.0532442, 23.3252641, 20.4569290, 12.3626118, 14.9586920, 22.6005839, 20.5164625, 11.7437368}
+anchors_optimal = {5, 6, 3, 7}
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+seed = 1127
+------------------------------------------------------------
+PDOP = 2.545878 | it = 0
+r_noised_vec = {16.1378714, 21.7420485, 22.6264699, 13.0910334, 15.4384367, 21.0820853, 18.9563175, 12.2467100}
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+seed = 1129
+------------------------------------------------------------
+PDOP = 1.578499 | it = 0
+r_noised_vec = {16.4258949, 20.4133145, 21.8983330, 13.4083061, 16.1509893, 19.8291831, 17.4792666, 13.0245951}
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+seed = 1131
+------------------------------------------------------------
+PDOP = 2.299246 | it = 0
+r_noised_vec = {17.5870058, 19.0942069, 16.0245627, 14.6450647, 17.1028876, 18.5260645, 15.8934187, 14.0324744}
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+seed = 1133
+------------------------------------------------------------
+PDOP = 2.474105 | it = 0
+r_noised_vec = {18.8483434, 17.9024999, 21.2021202, 15.8677923, 18.1216725, 17.3764495, 14.5837648, 15.2277046}
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+------------------------------------------------------------
+PDOP = 2.734386 | it = 0
+r_noised_vec = {19.6112417, 17.0270331, 12.9316977, 16.9814151, 19.4677338, 16.3966882, 13.3922187, 16.5749803}
+anchors_optimal = {0, 1, 7, 5}
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+seed = 1137
+------------------------------------------------------------
+PDOP = 3.057725 | it = 0
+r_noised_vec = {20.6893729, 16.1974805, 18.4308563, 18.6555246, 20.5145332, 15.5879450, 12.4264116, 18.0471505}
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+seed = 1139
+------------------------------------------------------------
+PDOP = 2.019378 | it = 0
+r_noised_vec = {22.4941852, 15.8279290, 12.9049992, 20.1396088, 21.8708026, 15.2482680, 11.7014495, 19.6243299}
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+exact point = {17, 13, 11}
+x_sol = {17.2227640, 12.7101140, 11.2793444}
+seed = 1141
+------------------------------------------------------------
+PDOP = 2.962760 | it = 0
+r_noised_vec = {24.0975400, 15.5691243, 15.4727721, 21.6725661, 23.2054739, 14.9737433, 11.2552346, 21.3054902}
+anchors_optimal = {0, 3, 7, 6}
+exact point = {19, 13, 11}
+x_sol = {19.1116739, 13.4208241, 10.9151634}
+seed = 1143
+------------------------------------------------------------
+PDOP = 2.947132 | it = 0
+r_noised_vec = {17.0277434, 25.6394335, 24.6173405, 11.2476161, 16.5649756, 25.2072991, 21.5424877, 10.0955387}
+anchors_optimal = {2, 6, 0, 7}
+exact point = {1, 15, 11}
+x_sol = {0.9695032, 11.7128808, 14.2351230}
+seed = 1145
+------------------------------------------------------------
+PDOP = 3.735255 | it = 0
+r_noised_vec = {17.0848468, 24.2935102, 19.6289594, 11.3412140, 16.7743564, 23.7667033, 19.7666627, 10.3125306}
+anchors_optimal = {5, 6, 2, 0}
+exact point = {3, 15, 11}
+x_sol = {3.4594924, 15.0825061, 10.3572393}
+seed = 1147
+------------------------------------------------------------
+PDOP = 1.758336 | it = 0
+r_noised_vec = {17.8790347, 22.9045915, 27.4610336, 11.8587391, 17.2790341, 22.4119660, 18.0761798, 10.9073373}
+anchors_optimal = {6, 0, 3, 7}
+exact point = {5, 15, 11}
+x_sol = {5.0321508, 15.2113207, 11.0699918}
+seed = 1149
+------------------------------------------------------------
+PDOP = 2.349243 | it = 0
+r_noised_vec = {18.4210761, 21.7455242, 12.2704245, 12.9288329, 17.8043268, 21.1529315, 16.5713527, 11.8244833}
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+exact point = {7, 15, 11}
+x_sol = {7.0670406, 15.1625171, 11.0879472}
+seed = 1151
+------------------------------------------------------------
+PDOP = 2.395455 | it = 0
+r_noised_vec = {18.7253788, 20.4905762, 25.5990119, 13.6110838, 18.4920341, 20.0271373, 15.1002789, 12.9938913}
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+exact point = {9, 15, 11}
+x_sol = {8.8818948, 15.0556346, 10.9321156}
+seed = 1153
+------------------------------------------------------------
+PDOP = 2.658897 | it = 0
+r_noised_vec = {19.7403569, 19.4949580, 10.3379124, 14.9799701, 19.3643445, 19.0618697, 13.8123787, 14.3493383}
+anchors_optimal = {0, 1, 3, 6}
+exact point = {11, 15, 11}
+x_sol = {10.7533764, 14.8495312, 11.1312999}
+seed = 1155
+------------------------------------------------------------
+PDOP = 2.895496 | it = 0
+r_noised_vec = {21.2505284, 18.5695855, 20.2358900, 16.5264476, 20.4250208, 18.0855554, 12.5162864, 15.8366146}
+anchors_optimal = {0, 5, 3, 7}
+exact point = {13, 15, 11}
+x_sol = {13.1887509, 15.1963550, 11.0875029}
+seed = 1157
+------------------------------------------------------------
+PDOP = 2.873033 | it = 0
+r_noised_vec = {22.2953858, 17.8237143, 11.8321822, 17.7939346, 21.7175900, 17.4585720, 11.5759986, 17.4146506}
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+exact point = {15, 15, 11}
+x_sol = {15.2210378, 15.2489505, 10.5847613}
+seed = 1159
+------------------------------------------------------------
+PDOP = 3.615705 | it = 0
+r_noised_vec = {23.2016711, 17.3962373, 14.4990930, 19.5571588, 23.0308678, 17.0328503, 10.9234473, 19.0508881}
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+exact point = {17, 15, 11}
+x_sol = {17.0088927, 14.9074878, 11.0143717}
+seed = 1161
+------------------------------------------------------------
+PDOP = 2.898789 | it = 0
+r_noised_vec = {24.8336105, 17.0691959, 14.4341403, 21.2411085, 24.5546901, 16.8349191, 10.3929942, 20.9662198}
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+exact point = {19, 15, 11}
+x_sol = {19.2254749, 14.7986956, 11.0261233}
+seed = 1163
+------------------------------------------------------------
+PDOP = 3.233984 | it = 0
+r_noised_vec = {19.1717255, 26.7156324, 21.6307981, 10.3586623, 18.6219019, 26.6770261, 21.2719766, 9.6670209}
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+exact point = {1, 17, 11}
+x_sol = {1.0108015, 16.9693049, 10.9051168}
+seed = 1165
+------------------------------------------------------------
+PDOP = 3.499193 | it = 0
+r_noised_vec = {18.9899836, 25.3222937, 26.1355774, 10.6771472, 18.5868498, 25.0713673, 19.4301509, 9.8235129}
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+seed = 1167
+------------------------------------------------------------
+PDOP = 1.698388 | it = 0
+r_noised_vec = {18.9809716, 24.1062173, 17.4241432, 11.1845999, 18.8060311, 23.7660404, 17.7040191, 10.3690976}
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+x_sol = {5.0812076, 16.9775953, 10.9625550}
+seed = 1169
+------------------------------------------------------------
+PDOP = 2.810635 | it = 0
+r_noised_vec = {19.8329463, 22.9940743, 22.0044436, 12.0333703, 19.1930435, 22.5435351, 15.9768036, 11.2474873}
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+seed = 1171
+------------------------------------------------------------
+PDOP = 2.175848 | it = 0
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+exact point = {9, 17, 11}
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+seed = 1173
+------------------------------------------------------------
+PDOP = 2.784650 | it = 0
+r_noised_vec = {21.2708771, 21.0544307, 16.9465711, 14.3908438, 20.8540134, 20.4359191, 13.0004890, 13.7404836}
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+exact point = {11, 17, 11}
+x_sol = {10.9349454, 16.9566796, 10.9814604}
+seed = 1175
+------------------------------------------------------------
+PDOP = 2.837690 | it = 0
+r_noised_vec = {22.0738089, 20.1758766, 12.4447142, 15.8253613, 21.9150843, 19.6081529, 11.6903442, 15.2462257}
+anchors_optimal = {4, 1, 5, 7}
+exact point = {13, 17, 11}
+x_sol = {13.0206118, 17.0214608, 11.0943773}
+seed = 1177
+------------------------------------------------------------
+PDOP = 2.697014 | it = 0
+r_noised_vec = {23.6250044, 19.5902324, 11.8474859, 17.6034070, 23.1618756, 18.9425968, 10.6345146, 16.8732988}
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+exact point = {15, 17, 11}
+x_sol = {15.0161924, 17.1253755, 11.0702198}
+seed = 1179
+------------------------------------------------------------
+PDOP = 2.303496 | it = 0
+r_noised_vec = {25.0040147, 19.1044548, 17.3760601, 19.0140444, 24.3997525, 18.4492343, 9.9553610, 18.3392381}
+anchors_optimal = {1, 5, 7, 6}
+exact point = {17, 17, 11}
+x_sol = {16.7425906, 16.8490799, 11.1475249}
+seed = 1181
+------------------------------------------------------------
+PDOP = 2.722930 | it = 0
+r_noised_vec = {25.9029841, 18.8232659, 7.0092902, 20.8013674, 25.8258125, 18.3467800, 9.6070572, 20.1702512}
+anchors_optimal = {0, 1, 5, 6}
+exact point = {19, 17, 11}
+x_sol = {18.8328750, 16.9291787, 10.9660789}
+seed = 1183
+------------------------------------------------------------
+PDOP = 3.173844 | it = 0
+r_noised_vec = {20.3544997, 27.9742400, 31.8454849, 10.1254832, 20.1194062, 27.5909670, 21.2586642, 8.9447484}
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+exact point = {1, 19, 11}
+x_sol = {0.7125717, 18.6402805, 11.1570124}
+seed = 1185
+------------------------------------------------------------
+PDOP = 1.906327 | it = 0
+r_noised_vec = {20.9007756, 26.5652604, 15.6872049, 10.1737923, 20.2036691, 26.2176760, 19.3451171, 9.2244394}
+anchors_optimal = {0, 6, 3, 7}
+exact point = {3, 19, 11}
+x_sol = {2.8909665, 19.2720097, 10.9846255}
+seed = 1187
+------------------------------------------------------------
+PDOP = 3.395175 | it = 0
+r_noised_vec = {21.1779625, 25.4363206, 25.6984170, 10.8390727, 20.3694497, 24.9326280, 17.6612784, 9.9027328}
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+exact point = {5, 19, 11}
+x_sol = {4.8721937, 18.8381675, 10.9798759}
+seed = 1189
+------------------------------------------------------------
+PDOP = 3.005273 | it = 0
+r_noised_vec = {21.2019598, 24.2840494, 15.9722807, 11.7221848, 20.9487803, 23.9428847, 16.0659092, 10.9042543}
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+exact point = {7, 19, 11}
+x_sol = {6.9628860, 18.9197009, 10.9329823}
+seed = 1191
+------------------------------------------------------------
+PDOP = 2.981348 | it = 0
+r_noised_vec = {21.9293199, 23.3446664, 18.2400988, 12.5846325, 21.7047684, 22.8811411, 14.2875105, 12.1451741}
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+exact point = {9, 19, 11}
+x_sol = {8.8137269, 19.0155715, 10.7578448}
+seed = 1193
+------------------------------------------------------------
+PDOP = 3.101816 | it = 0
+r_noised_vec = {23.1630947, 22.5344583, 16.6685094, 14.3311617, 22.5870307, 21.9862351, 12.7721833, 13.5549986}
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+exact point = {11, 19, 11}
+x_sol = {11.2559775, 19.0904202, 11.1935526}
+seed = 1195
+------------------------------------------------------------
+PDOP = 2.999887 | it = 0
+r_noised_vec = {23.9494521, 21.7763918, 12.5176476, 15.6597778, 23.5024078, 21.2607464, 11.3148307, 15.0822813}
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+x_sol = {13.1406273, 19.0261564, 11.0582390}
+seed = 1197
+------------------------------------------------------------
+PDOP = 3.162751 | it = 0
+r_noised_vec = {24.6086977, 21.3142732, 15.9788048, 17.1108822, 24.6119610, 20.7233035, 10.2772135, 16.6841033}
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+seed = 1199
+------------------------------------------------------------
+PDOP = 1.969204 | it = 0
+r_noised_vec = {26.0079191, 20.8301032, 10.1228376, 19.0241497, 25.6699544, 20.3589213, 9.3967206, 18.5494890}
+anchors_optimal = {4, 1, 3, 6}
+exact point = {17, 19, 11}
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+seed = 1201
+------------------------------------------------------------
+PDOP = 2.944043 | it = 0
+r_noised_vec = {27.6518910, 20.6794992, 14.2433241, 20.5677746, 26.9450587, 20.1929101, 9.0959495, 20.2349562}
+anchors_optimal = {4, 1, 5, 6}
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+seed = 1203
+------------------------------------------------------------
+PDOP = 3.094118 | it = 0
+r_noised_vec = {12.0192586, 22.4726532, 30.6445361, 22.4254933, 6.8334326, 20.3389661, 27.6887770, 20.2681571}
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+seed = 1205
+------------------------------------------------------------
+PDOP = 2.085688 | it = 0
+r_noised_vec = {11.8601701, 20.7544993, 31.6602222, 22.6456454, 7.2432310, 18.5488492, 26.3564761, 20.3153046}
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+seed = 1207
+------------------------------------------------------------
+PDOP = 3.566797 | it = 0
+r_noised_vec = {12.6799672, 18.9665530, 27.3395200, 22.7715896, 8.0820503, 16.5979559, 25.1961916, 20.5744325}
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+------------------------------------------------------------
+PDOP = 2.890794 | it = 0
+r_noised_vec = {13.7165908, 17.5787355, 27.0153963, 23.2585833, 9.3754448, 14.8557882, 24.0904430, 21.0390624}
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+seed = 1211
+------------------------------------------------------------
+PDOP = 2.871529 | it = 0
+r_noised_vec = {14.3420999, 16.0507697, 32.8213544, 23.8728643, 10.7125863, 13.1694868, 23.1475244, 21.6959556}
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+seed = 1213
+------------------------------------------------------------
+PDOP = 1.978683 | it = 0
+r_noised_vec = {15.3335680, 14.9398349, 20.3234614, 24.3693369, 12.2098923, 11.5748834, 22.1844864, 22.5267354}
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+------------------------------------------------------------
+PDOP = 3.246367 | it = 0
+r_noised_vec = {17.0977247, 13.8777033, 33.6021865, 25.5577895, 13.8080982, 9.9250183, 21.5215363, 23.5114199}
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+------------------------------------------------------------
+PDOP = 2.258243 | it = 0
+r_noised_vec = {18.7050517, 13.0466974, 19.1622804, 26.5485066, 15.5693931, 8.6576755, 20.9981985, 24.4730255}
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+------------------------------------------------------------
+PDOP = 4.117066 | it = 0
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+------------------------------------------------------------
+PDOP = 2.374124 | it = 0
+r_noised_vec = {21.3954604, 12.1433637, 22.0131158, 28.8928188, 19.3049261, 7.1147355, 20.2963679, 27.1064537}
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+------------------------------------------------------------
+PDOP = 2.646067 | it = 0
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+------------------------------------------------------------
+PDOP = 2.587556 | it = 0
+r_noised_vec = {12.5321749, 20.9605468, 30.5468877, 20.8301554, 7.7488161, 18.4782422, 25.0178429, 18.5816428}
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+------------------------------------------------------------
+PDOP = 1.814873 | it = 0
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+------------------------------------------------------------
+PDOP = 1.957856 | it = 0
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+------------------------------------------------------------
+PDOP = 2.549403 | it = 0
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+------------------------------------------------------------
+PDOP = 2.414611 | it = 0
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+------------------------------------------------------------
+PDOP = 2.300380 | it = 0
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+------------------------------------------------------------
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+------------------------------------------------------------
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+------------------------------------------------------------
+PDOP = 2.131972 | it = 0
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+------------------------------------------------------------
+PDOP = 2.843160 | it = 0
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+------------------------------------------------------------
+PDOP = 1.816401 | it = 0
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+------------------------------------------------------------
+PDOP = 2.527888 | it = 0
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+------------------------------------------------------------
+PDOP = 2.438467 | it = 0
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+------------------------------------------------------------
+PDOP = 1.635081 | it = 0
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+------------------------------------------------------------
+PDOP = 2.598349 | it = 0
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+------------------------------------------------------------
+PDOP = 1.845150 | it = 0
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+------------------------------------------------------------
+PDOP = 2.666214 | it = 0
+r_noised_vec = {18.7002492, 13.5346168, 22.9806595, 23.6701006, 16.1988393, 9.6829559, 17.1819335, 21.7688267}
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+------------------------------------------------------------
+PDOP = 2.332073 | it = 0
+r_noised_vec = {20.1571575, 12.8569473, 20.4274979, 24.9374903, 17.9466707, 8.6599538, 16.6415052, 23.1414951}
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+------------------------------------------------------------
+PDOP = 2.492628 | it = 0
+r_noised_vec = {22.2068622, 12.6488849, 24.1356274, 26.4682811, 19.6618026, 8.2252444, 16.5355992, 24.5806429}
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+------------------------------------------------------------
+PDOP = 2.053889 | it = 0
+r_noised_vec = {13.6213004, 23.2359895, 26.4827265, 17.5819385, 9.1881480, 21.2595825, 24.0030136, 14.8785512}
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+------------------------------------------------------------
+PDOP = 2.701456 | it = 0
+r_noised_vec = {13.3242459, 21.6772575, 28.9488523, 17.8145708, 9.3182136, 19.5260402, 22.4974744, 14.9866055}
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+exact point = {3, 7, 13}
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+seed = 1267
+------------------------------------------------------------
+PDOP = 2.811661 | it = 0
+r_noised_vec = {13.8346295, 20.2361291, 13.7321995, 18.2106831, 10.0465502, 17.6444188, 21.0672713, 15.3506177}
+anchors_optimal = {6, 5, 7, 0}
+exact point = {5, 7, 13}
+x_sol = {5.0213564, 7.0130420, 12.8226293}
+seed = 1269
+------------------------------------------------------------
+PDOP = 1.980430 | it = 0
+r_noised_vec = {14.9644075, 18.7350136, 31.4762539, 18.5977292, 11.1895750, 15.9953199, 19.7545785, 15.9590614}
+anchors_optimal = {1, 3, 0, 4}
+exact point = {7, 7, 13}
+x_sol = {7.1561252, 7.2909990, 13.0980764}
+seed = 1271
+------------------------------------------------------------
+PDOP = 2.355710 | it = 0
+r_noised_vec = {15.7419217, 17.4810397, 20.8652931, 19.4518434, 12.3445082, 14.4092481, 18.5913939, 16.7930684}
+anchors_optimal = {3, 6, 7, 5}
+exact point = {9, 7, 13}
+x_sol = {8.8254531, 6.8680660, 13.0359754}
+seed = 1273
+------------------------------------------------------------
+PDOP = 2.282076 | it = 0
+r_noised_vec = {16.4458974, 16.1873031, 21.7590717, 20.3389899, 13.6519482, 12.9210937, 17.3546999, 17.7466678}
+anchors_optimal = {3, 7, 6, 5}
+exact point = {11, 7, 13}
+x_sol = {10.8620687, 6.9676067, 13.0981656}
+seed = 1275
+------------------------------------------------------------
+PDOP = 2.387608 | it = 0
+r_noised_vec = {17.9257654, 15.1573153, 25.0591713, 21.3594689, 15.1106003, 11.5748540, 16.4463878, 18.8980154}
+anchors_optimal = {7, 0, 6, 5}
+exact point = {13, 7, 13}
+x_sol = {12.7802977, 6.9077256, 13.1501186}
+seed = 1277
+------------------------------------------------------------
+PDOP = 1.615773 | it = 0
+r_noised_vec = {19.6901067, 14.3032555, 15.9363787, 22.7529102, 16.6637612, 10.4661978, 15.7058512, 20.2019310}
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+exact point = {15, 7, 13}
+x_sol = {14.9247274, 6.8912509, 13.0011005}
+seed = 1279
+------------------------------------------------------------
+PDOP = 2.447591 | it = 0
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+x_sol = {16.8305880, 6.9594150, 13.1322617}
+seed = 1281
+------------------------------------------------------------
+PDOP = 2.491123 | it = 0
+r_noised_vec = {22.1465431, 13.4163545, 14.8750617, 25.1239904, 20.1227377, 9.1604833, 14.7702974, 23.1654658}
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+exact point = {19, 7, 13}
+x_sol = {18.6702843, 6.7961704, 13.0285293}
+seed = 1283
+------------------------------------------------------------
+PDOP = 4.283696 | it = 0
+r_noised_vec = {14.4469218, 23.7326033, 32.7854327, 16.4213310, 10.6571969, 21.5501122, 22.9182659, 12.9575394}
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+exact point = {1, 9, 13}
+x_sol = {1.1732652, 8.8989585, 13.1007663}
+seed = 1285
+------------------------------------------------------------
+PDOP = 3.206642 | it = 0
+r_noised_vec = {14.8594622, 22.2728795, 23.1855556, 16.3329507, 10.8576936, 19.9864278, 21.3631527, 13.1476422}
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+exact point = {3, 9, 13}
+x_sol = {3.2558541, 9.4081887, 13.0427333}
+seed = 1287
+------------------------------------------------------------
+PDOP = 1.836072 | it = 0
+r_noised_vec = {14.8928156, 20.7833558, 26.2311577, 16.7283526, 11.5150833, 18.2785387, 19.7487361, 13.6275341}
+anchors_optimal = {5, 3, 7, 4}
+exact point = {5, 9, 13}
+x_sol = {5.1971623, 9.1023015, 12.9770551}
+seed = 1289
+------------------------------------------------------------
+PDOP = 2.170364 | it = 0
+r_noised_vec = {15.3334709, 19.4234020, 23.8132688, 17.4378329, 12.2481920, 16.6470334, 18.2200229, 14.3616785}
+anchors_optimal = {1, 6, 5, 4}
+exact point = {7, 9, 13}
+x_sol = {7.1551180, 9.0566971, 13.1353901}
+seed = 1291
+------------------------------------------------------------
+PDOP = 1.536678 | it = 0
+r_noised_vec = {16.6133129, 18.2272397, 20.9458818, 18.0709181, 13.2951017, 15.1014445, 17.0108545, 15.4523261}
+anchors_optimal = {1, 3, 6, 4}
+exact point = {9, 9, 13}
+x_sol = {8.9436365, 9.0929572, 13.0350190}
+seed = 1293
+------------------------------------------------------------
+PDOP = 2.107792 | it = 0
+r_noised_vec = {17.8170223, 17.0066528, 23.0346223, 19.1134504, 14.4554111, 13.8864519, 15.8046204, 16.5981282}
+anchors_optimal = {3, 7, 6, 5}
+exact point = {11, 9, 13}
+x_sol = {11.1766272, 9.0012505, 12.8638455}
+seed = 1295
+------------------------------------------------------------
+PDOP = 2.188414 | it = 0
+r_noised_vec = {18.5969832, 16.1421902, 18.7328118, 20.2512281, 15.9537307, 12.6691528, 14.8267181, 17.8858720}
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+exact point = {13, 9, 13}
+x_sol = {12.9740550, 8.7793976, 12.8738902}
+seed = 1297
+------------------------------------------------------------
+PDOP = 2.822515 | it = 0
+r_noised_vec = {19.8597715, 15.4546904, 19.7600537, 21.1860456, 17.5070011, 11.6922123, 14.0037523, 19.2767711}
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+exact point = {15, 9, 13}
+x_sol = {14.5937650, 9.0674210, 13.0573784}
+seed = 1299
+------------------------------------------------------------
+PDOP = 2.953916 | it = 0
+r_noised_vec = {21.7446645, 14.7565011, 9.8950541, 22.9435820, 19.2769382, 11.0122138, 13.4893288, 20.7508113}
+anchors_optimal = {3, 0, 7, 1}
+exact point = {17, 9, 13}
+x_sol = {17.2125292, 9.0900652, 13.0213627}
+seed = 1301
+------------------------------------------------------------
+PDOP = 2.931834 | it = 0
+r_noised_vec = {23.2715471, 14.3849359, 24.6509264, 24.3211355, 20.9759970, 10.6795176, 13.2962015, 22.2954566}
+anchors_optimal = {3, 7, 4, 5}
+exact point = {19, 9, 13}
+x_sol = {19.0773777, 8.9975017, 12.9850065}
+seed = 1303
+------------------------------------------------------------
+PDOP = 3.433753 | it = 0
+r_noised_vec = {15.3826886, 24.5180164, 24.1042316, 14.8558109, 12.3756934, 22.6088770, 22.2313865, 11.4302508}
+anchors_optimal = {2, 5, 0, 3}
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+x_sol = {1.0179247, 10.9192629, 12.7574908}
+seed = 1305
+------------------------------------------------------------
+PDOP = 2.174520 | it = 0
+r_noised_vec = {15.5806878, 22.8597277, 25.0466902, 15.2518306, 12.3876433, 20.9932058, 20.5687917, 11.5718377}
+anchors_optimal = {1, 3, 4, 7}
+exact point = {3, 11, 13}
+x_sol = {3.3841439, 11.0143758, 13.0976555}
+seed = 1307
+------------------------------------------------------------
+PDOP = 1.742330 | it = 0
+r_noised_vec = {16.3897054, 21.5554335, 26.9608592, 15.5045364, 12.8086852, 19.4606743, 18.9316258, 12.0615277}
+anchors_optimal = {6, 3, 4, 7}
+exact point = {5, 11, 13}
+x_sol = {4.8966841, 10.9889991, 12.9976368}
+seed = 1309
+------------------------------------------------------------
+PDOP = 2.683492 | it = 0
+r_noised_vec = {16.8569549, 20.1682237, 17.8468996, 16.0860907, 13.4223769, 18.1182846, 17.2891973, 12.8701333}
+anchors_optimal = {1, 5, 0, 7}
+exact point = {7, 11, 13}
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+seed = 1311
+------------------------------------------------------------
+PDOP = 2.402712 | it = 0
+r_noised_vec = {17.2645192, 19.0795790, 26.5398824, 17.0884572, 14.5146272, 16.5008775, 15.7818845, 13.7250854}
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+x_sol = {8.4512438, 10.6591646, 13.2273000}
+seed = 1313
+------------------------------------------------------------
+PDOP = 1.950909 | it = 0
+r_noised_vec = {18.4703597, 18.0830655, 15.0117786, 17.9854462, 15.7792679, 15.2769716, 14.3386807, 14.9850164}
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+exact point = {11, 11, 13}
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+seed = 1315
+------------------------------------------------------------
+PDOP = 1.882942 | it = 0
+r_noised_vec = {19.9956458, 17.1862996, 23.1506144, 19.1949560, 17.2336107, 14.2220980, 13.3001976, 16.4076072}
+anchors_optimal = {4, 1, 5, 6}
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+seed = 1317
+------------------------------------------------------------
+PDOP = 2.744712 | it = 0
+r_noised_vec = {21.0041382, 16.5953465, 15.6009973, 20.5452602, 18.6695796, 13.3974961, 12.3137520, 17.9552482}
+anchors_optimal = {0, 4, 1, 6}
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+seed = 1319
+------------------------------------------------------------
+PDOP = 2.679931 | it = 0
+r_noised_vec = {22.0582600, 15.9968634, 18.9634852, 21.7166597, 20.1327071, 12.6153767, 11.5876631, 19.5943637}
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+seed = 1321
+------------------------------------------------------------
+PDOP = 2.678008 | it = 0
+r_noised_vec = {23.8544258, 15.7906607, 17.5656061, 23.4678641, 21.7297982, 12.3067485, 11.4051491, 21.2974820}
+anchors_optimal = {0, 7, 5, 6}
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+seed = 1323
+------------------------------------------------------------
+PDOP = 3.571934 | it = 0
+r_noised_vec = {17.2693255, 25.5001636, 25.2229968, 14.0017398, 13.8249738, 23.5906370, 21.4144223, 9.9208527}
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+x_sol = {1.2360858, 10.8699678, 15.1742654}
+seed = 1325
+------------------------------------------------------------
+PDOP = 2.711503 | it = 0
+r_noised_vec = {17.0173122, 23.9761631, 26.1550755, 13.8876497, 13.8082786, 21.9834207, 19.7671907, 10.1354394}
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+seed = 1327
+------------------------------------------------------------
+PDOP = 2.150395 | it = 0
+r_noised_vec = {17.1485329, 22.5898289, 22.3163816, 14.5356717, 14.3886240, 20.4407511, 18.0338261, 10.7060956}
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+seed = 1329
+------------------------------------------------------------
+PDOP = 2.521696 | it = 0
+r_noised_vec = {18.1177791, 21.2054551, 32.9157964, 15.1602513, 15.1513804, 18.9965597, 16.4763298, 11.8163024}
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+------------------------------------------------------------
+PDOP = 2.289040 | it = 0
+r_noised_vec = {19.0293037, 20.1432858, 11.7636264, 15.9419294, 16.2060818, 17.6493534, 15.0873820, 12.9165840}
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+------------------------------------------------------------
+PDOP = 2.459842 | it = 0
+r_noised_vec = {19.5360552, 19.0824120, 24.7096038, 17.1913031, 17.2278427, 16.4222845, 13.4552491, 14.2087792}
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+------------------------------------------------------------
+PDOP = 1.901035 | it = 0
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+------------------------------------------------------------
+PDOP = 2.273956 | it = 0
+r_noised_vec = {22.2011596, 17.7281962, 17.1283696, 19.6940935, 19.6532981, 14.6900810, 11.1553078, 17.1772575}
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+------------------------------------------------------------
+PDOP = 1.684465 | it = 0
+r_noised_vec = {23.5317421, 17.2840729, 18.8664120, 21.2016910, 21.0908181, 14.0965071, 10.3203838, 18.8028426}
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+------------------------------------------------------------
+PDOP = 2.359147 | it = 0
+r_noised_vec = {24.5034178, 17.1546702, 12.5667127, 22.5993134, 22.7055446, 13.7723915, 9.8533756, 20.5022709}
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+------------------------------------------------------------
+PDOP = 2.738466 | it = 0
+r_noised_vec = {18.2698215, 26.5457639, 31.0380497, 12.9600187, 15.6111925, 24.3946428, 20.8416977, 8.5514193}
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+------------------------------------------------------------
+PDOP = 2.907419 | it = 0
+r_noised_vec = {18.8101530, 25.1976617, 19.1346873, 13.2970017, 15.8281887, 23.0597914, 18.9594721, 8.7897669}
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+------------------------------------------------------------
+PDOP = 3.048534 | it = 0
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+------------------------------------------------------------
+PDOP = 2.797938 | it = 0
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+------------------------------------------------------------
+PDOP = 2.647156 | it = 0
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+------------------------------------------------------------
+PDOP = 2.197091 | it = 0
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+------------------------------------------------------------
+PDOP = 2.938161 | it = 0
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+------------------------------------------------------------
+PDOP = 1.642773 | it = 0
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+------------------------------------------------------------
+PDOP = 3.370932 | it = 0
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+------------------------------------------------------------
+PDOP = 3.189672 | it = 0
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+------------------------------------------------------------
+PDOP = 3.604239 | it = 0
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+------------------------------------------------------------
+PDOP = 2.040325 | it = 0
+r_noised_vec = {19.8126644, 26.3752459, 29.6255530, 12.4273466, 17.6826772, 24.4931892, 18.6868176, 7.8957180}
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+------------------------------------------------------------
+PDOP = 2.578870 | it = 0
+r_noised_vec = {20.5107610, 25.0422621, 19.1475641, 13.1528533, 17.9007330, 23.1830449, 16.8201871, 8.7831044}
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+------------------------------------------------------------
+PDOP = 3.513495 | it = 0
+r_noised_vec = {21.1487877, 23.9557576, 20.7394297, 13.6581957, 18.4415548, 22.0259594, 15.0175954, 9.7935931}
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+------------------------------------------------------------
+PDOP = 2.856921 | it = 0
+r_noised_vec = {21.3820053, 22.8387885, 21.0756465, 14.7113740, 19.0613300, 20.6910220, 13.2460615, 11.0755999}
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+seed = 1373
+------------------------------------------------------------
+PDOP = 2.191794 | it = 0
+r_noised_vec = {22.1186267, 21.9131230, 14.2993901, 15.9952748, 20.0801885, 19.7063868, 11.7486583, 12.5458981}
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+seed = 1375
+------------------------------------------------------------
+PDOP = 2.988182 | it = 0
+r_noised_vec = {23.5221317, 21.1713608, 20.6898225, 17.1532250, 21.2662102, 18.8640882, 10.2420329, 14.1518486}
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+seed = 1377
+------------------------------------------------------------
+PDOP = 2.148869 | it = 0
+r_noised_vec = {24.6225413, 20.5013908, 11.7288004, 18.7019139, 22.5062174, 18.1850514, 8.9773211, 15.8588701}
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+seed = 1379
+------------------------------------------------------------
+PDOP = 2.645700 | it = 0
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+exact point = {17, 17, 13}
+x_sol = {16.9368296, 16.8843372, 13.1032487}
+seed = 1381
+------------------------------------------------------------
+PDOP = 2.999628 | it = 0
+r_noised_vec = {26.7360597, 19.9303519, 12.4837310, 21.8151496, 25.1585791, 17.4543476, 7.6771636, 19.4841832}
+anchors_optimal = {3, 1, 7, 2}
+exact point = {19, 17, 13}
+x_sol = {18.9225582, 16.8519839, 13.0333515}
+seed = 1383
+------------------------------------------------------------
+PDOP = 2.545769 | it = 0
+r_noised_vec = {21.8939539, 28.6570005, 26.5823060, 12.2025941, 19.2608530, 27.0090539, 20.3399558, 7.0390786}
+anchors_optimal = {1, 6, 3, 7}
+exact point = {1, 19, 13}
+x_sol = {0.9167060, 18.6093474, 13.1145967}
+seed = 1385
+------------------------------------------------------------
+PDOP = 2.161696 | it = 0
+r_noised_vec = {21.8539222, 27.5277946, 23.4212748, 12.2335201, 19.3575524, 25.5780755, 18.4481464, 7.1831246}
+anchors_optimal = {1, 4, 6, 3}
+exact point = {3, 19, 13}
+x_sol = {2.9507930, 18.9539631, 13.0314414}
+seed = 1387
+------------------------------------------------------------
+PDOP = 3.244125 | it = 0
+r_noised_vec = {21.7183726, 26.4880330, 21.3883081, 12.5456300, 19.5624051, 24.4164059, 16.6876054, 8.0572503}
+anchors_optimal = {0, 4, 6, 3}
+exact point = {5, 19, 13}
+x_sol = {4.9714905, 18.7709178, 12.8421057}
+seed = 1389
+------------------------------------------------------------
+PDOP = 3.262200 | it = 0
+r_noised_vec = {22.3678395, 25.3413763, 28.9785748, 13.5902930, 20.1973091, 23.1954143, 14.9736027, 9.2773079}
+anchors_optimal = {1, 5, 0, 3}
+exact point = {7, 19, 13}
+x_sol = {6.7667076, 18.8058994, 13.2410028}
+seed = 1391
+------------------------------------------------------------
+PDOP = 1.898938 | it = 0
+r_noised_vec = {23.3601364, 24.5150872, 10.0355820, 14.4165546, 20.9294980, 22.1001482, 13.1207742, 10.7317863}
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+exact point = {9, 19, 13}
+x_sol = {9.0004348, 18.8226799, 12.9385739}
+seed = 1393
+------------------------------------------------------------
+PDOP = 2.521051 | it = 0
+r_noised_vec = {23.8664175, 23.5179626, 25.7608310, 15.5915196, 21.9103344, 21.1403895, 11.5061002, 12.3326452}
+anchors_optimal = {0, 4, 7, 6}
+exact point = {11, 19, 13}
+x_sol = {11.0185209, 19.1307531, 12.8563981}
+seed = 1395
+------------------------------------------------------------
+PDOP = 3.161763 | it = 0
+r_noised_vec = {24.4381914, 22.8319351, 9.4250258, 17.0960795, 22.8156881, 20.5279214, 9.9746190, 14.0234728}
+anchors_optimal = {0, 4, 3, 6}
+exact point = {13, 19, 13}
+x_sol = {13.5556140, 18.5249807, 12.5176204}
+seed = 1397
+------------------------------------------------------------
+PDOP = 3.332049 | it = 0
+r_noised_vec = {25.7838444, 22.1932911, 20.2301491, 18.4093879, 23.8558789, 19.8964904, 8.6441037, 15.7710887}
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+exact point = {15, 19, 13}
+x_sol = {15.0332752, 19.0763438, 12.8731138}
+seed = 1399
+------------------------------------------------------------
+PDOP = 2.747671 | it = 0
+r_noised_vec = {27.2050275, 21.7135948, 12.0999009, 20.0176706, 24.9824102, 19.4856316, 7.6048331, 17.5575843}
+anchors_optimal = {4, 1, 7, 6}
+exact point = {17, 19, 13}
+x_sol = {17.0904021, 18.8118961, 13.0735437}
+seed = 1401
+------------------------------------------------------------
+PDOP = 4.512768 | it = 0
+r_noised_vec = {28.0779865, 21.5650958, 14.7352181, 21.6932604, 26.3153670, 19.2924271, 6.9718976, 19.3745014}
+anchors_optimal = {0, 1, 7, 5}
+exact point = {19, 19, 13}
+x_sol = {19.0084202, 18.9249055, 12.9435687}
+seed = 1403
+------------------------------------------------------------
+PDOP = 3.927346 | it = 0
+r_noised_vec = {13.7129007, 23.3933482, 35.3222868, 23.2836493, 4.8294677, 19.6334600, 27.2731619, 19.8004665}
+anchors_optimal = {6, 1, 5, 0}
+exact point = {1, 1, 15}
+x_sol = {1.0472343, 1.0696682, 14.7572629}
+seed = 1405
+------------------------------------------------------------
+PDOP = 3.189993 | it = 0
+r_noised_vec = {14.2537369, 21.9431312, 28.3392534, 23.7584064, 5.3905905, 17.7318361, 25.8764163, 19.7761548}
+anchors_optimal = {3, 1, 7, 4}
+exact point = {3, 1, 15}
+x_sol = {3.1558693, 0.9726886, 15.0622520}
+seed = 1407
+------------------------------------------------------------
+PDOP = 2.896892 | it = 0
+r_noised_vec = {14.8289145, 20.4325073, 35.5054649, 24.0322236, 6.4579762, 15.8546239, 24.6007916, 20.0086319}
+anchors_optimal = {3, 1, 7, 4}
+exact point = {5, 1, 15}
+x_sol = {5.2742243, 1.0621080, 15.1632216}
+seed = 1409
+------------------------------------------------------------
+PDOP = 3.244028 | it = 0
+r_noised_vec = {15.0758868, 19.1119703, 25.3469762, 24.1946324, 8.0115198, 14.0185616, 23.5440474, 20.4566610}
+anchors_optimal = {6, 7, 1, 5}
+exact point = {7, 1, 15}
+x_sol = {6.9250740, 1.0841553, 14.9407195}
+seed = 1411
+------------------------------------------------------------
+PDOP = 1.923168 | it = 0
+r_noised_vec = {15.8814493, 17.9119311, 32.6994912, 25.0201504, 9.5054852, 12.2464831, 22.5398914, 21.1055022}
+anchors_optimal = {6, 0, 5, 4}
+exact point = {9, 1, 15}
+x_sol = {8.9309974, 1.0770959, 14.7596364}
+seed = 1413
+------------------------------------------------------------
+PDOP = 3.057484 | it = 0
+r_noised_vec = {17.4001486, 16.7236052, 25.5839381, 25.6428639, 11.1698757, 10.3403103, 21.7242580, 21.9370745}
+anchors_optimal = {3, 7, 1, 4}
+exact point = {11, 1, 15}
+x_sol = {11.0633785, 1.1192339, 15.1400325}
+seed = 1415
+------------------------------------------------------------
+PDOP = 3.478983 | it = 0
+r_noised_vec = {18.6499971, 15.8368405, 28.7082351, 26.3879216, 12.8498173, 8.6930354, 20.9124533, 22.9298306}
+anchors_optimal = {3, 7, 6, 4}
+exact point = {13, 1, 15}
+x_sol = {12.8275376, 1.0089651, 14.9880336}
+seed = 1417
+------------------------------------------------------------
+PDOP = 2.466021 | it = 0
+r_noised_vec = {19.5689427, 14.9376073, 26.7853472, 27.5274203, 14.7622762, 7.2019084, 20.3943484, 24.0602075}
+anchors_optimal = {7, 6, 1, 5}
+exact point = {15, 1, 15}
+x_sol = {14.7885299, 0.9194221, 15.0069638}
+seed = 1419
+------------------------------------------------------------
+PDOP = 4.042608 | it = 0
+r_noised_vec = {21.0872008, 14.3983135, 26.5007186, 28.4860639, 16.7437614, 6.0037723, 20.0600191, 25.3042097}
+anchors_optimal = {3, 7, 0, 6}
+exact point = {17, 1, 15}
+x_sol = {16.7604911, 0.8477422, 15.0040212}
+seed = 1421
+------------------------------------------------------------
+PDOP = 3.307631 | it = 0
+r_noised_vec = {23.0618882, 14.0314712, 33.7095326, 29.6532091, 18.7321627, 5.1241482, 19.7187358, 26.6386666}
+anchors_optimal = {3, 7, 4, 5}
+exact point = {19, 1, 15}
+x_sol = {19.0430796, 1.0598780, 14.9656383}
+seed = 1423
+------------------------------------------------------------
+PDOP = 3.290784 | it = 0
+r_noised_vec = {14.2727717, 23.5922910, 22.8378144, 22.0561130, 5.4713331, 19.8036833, 26.0219417, 17.7391061}
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+x_sol = {0.9670951, 2.8124654, 14.8265874}
+seed = 1425
+------------------------------------------------------------
+PDOP = 3.562047 | it = 0
+r_noised_vec = {14.0031203, 22.0441487, 40.0012052, 21.9249284, 5.7512548, 17.8911537, 24.5365612, 17.9139426}
+anchors_optimal = {3, 7, 5, 0}
+exact point = {3, 3, 15}
+x_sol = {3.0316013, 3.0101287, 14.7050828}
+seed = 1427
+------------------------------------------------------------
+PDOP = 3.158624 | it = 0
+r_noised_vec = {14.6122486, 20.4488563, 21.5939613, 22.3703470, 6.7583851, 15.9811829, 23.1814161, 18.2821035}
+anchors_optimal = {6, 3, 7, 0}
+exact point = {5, 3, 15}
+x_sol = {5.1541384, 2.9496153, 14.8736084}
+seed = 1429
+------------------------------------------------------------
+PDOP = 2.384534 | it = 0
+r_noised_vec = {15.6558387, 19.1465629, 34.3110136, 22.9662562, 8.0255650, 14.0781004, 21.8733183, 18.8352148}
+anchors_optimal = {3, 1, 5, 4}
+exact point = {7, 3, 15}
+x_sol = {6.9793891, 2.7462825, 14.9315253}
+seed = 1431
+------------------------------------------------------------
+PDOP = 3.540618 | it = 0
+r_noised_vec = {16.2845686, 17.8401298, 24.1851607, 23.2858440, 9.4242484, 12.2326019, 20.6502292, 19.5593500}
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+exact point = {9, 3, 15}
+x_sol = {9.1030775, 3.2093853, 14.9442532}
+seed = 1433
+------------------------------------------------------------
+PDOP = 2.395041 | it = 0
+r_noised_vec = {17.0210638, 16.7649738, 27.3272460, 24.2380232, 11.2462910, 10.4398959, 19.8053709, 20.4392687}
+anchors_optimal = {3, 6, 4, 5}
+exact point = {11, 3, 15}
+x_sol = {10.9602009, 3.0457556, 15.1774057}
+seed = 1435
+------------------------------------------------------------
+PDOP = 2.792901 | it = 0
+r_noised_vec = {18.5598960, 15.8611627, 27.4044598, 25.1353012, 13.1382743, 8.7344585, 18.9536859, 21.4604185}
+anchors_optimal = {3, 6, 1, 5}
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+x_sol = {13.0593537, 3.0539093, 15.1127821}
+seed = 1437
+------------------------------------------------------------
+PDOP = 1.565006 | it = 0
+r_noised_vec = {20.1970227, 15.0576956, 22.3028670, 25.9970324, 15.1110159, 7.1708734, 18.3201714, 22.6099323}
+anchors_optimal = {6, 4, 1, 5}
+exact point = {15, 3, 15}
+x_sol = {15.1558256, 3.0208617, 15.1134940}
+seed = 1439
+------------------------------------------------------------
+PDOP = 3.586758 | it = 0
+r_noised_vec = {21.2927181, 14.6085921, 28.8426666, 27.2854905, 16.9971857, 6.1132279, 17.9718589, 23.8773782}
+anchors_optimal = {3, 7, 0, 5}
+exact point = {17, 3, 15}
+x_sol = {16.8589338, 2.8389961, 15.0886527}
+seed = 1441
+------------------------------------------------------------
+PDOP = 2.515158 | it = 0
+r_noised_vec = {22.6039466, 14.2304227, 20.9473146, 28.4454797, 18.8301296, 5.3813594, 17.8030502, 25.1827949}
+anchors_optimal = {3, 0, 1, 5}
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+x_sol = {18.6166704, 2.6524497, 15.0669974}
+seed = 1443
+------------------------------------------------------------
+PDOP = 2.037257 | it = 0
+r_noised_vec = {14.6687530, 24.0100574, 34.3852900, 20.4786932, 6.4159768, 19.9142152, 24.8881215, 15.6886623}
+anchors_optimal = {6, 7, 0, 4}
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+x_sol = {0.6767245, 5.1060693, 15.0791462}
+seed = 1445
+------------------------------------------------------------
+PDOP = 1.546056 | it = 0
+r_noised_vec = {14.9661388, 22.3828287, 27.2686044, 20.6352409, 6.6377161, 17.9866127, 23.2902934, 15.7935440}
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+x_sol = {3.1458168, 5.0953485, 15.2348957}
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+------------------------------------------------------------
+PDOP = 2.187993 | it = 0
+r_noised_vec = {14.9469928, 20.8332181, 29.3600075, 20.8108644, 7.5152350, 16.2774865, 21.9268421, 16.1679653}
+anchors_optimal = {6, 1, 5, 4}
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+x_sol = {5.0137419, 4.8202674, 14.9491160}
+seed = 1449
+------------------------------------------------------------
+PDOP = 1.979934 | it = 0
+r_noised_vec = {15.5039530, 19.4740328, 26.9964188, 21.2917314, 8.6688073, 14.4346373, 20.6608659, 16.7910169}
+anchors_optimal = {6, 1, 5, 4}
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+------------------------------------------------------------
+PDOP = 2.922671 | it = 0
+r_noised_vec = {16.8059281, 18.1098094, 23.0676901, 22.1830031, 10.2530325, 12.6701848, 19.3020537, 17.6327300}
+anchors_optimal = {3, 7, 0, 5}
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+x_sol = {8.9403468, 4.9829893, 15.2676963}
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+------------------------------------------------------------
+PDOP = 2.063709 | it = 0
+r_noised_vec = {17.8758901, 17.0760653, 31.2139236, 22.7144082, 12.0946240, 11.0047134, 18.2077467, 18.6586166}
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+seed = 1455
+------------------------------------------------------------
+PDOP = 1.755441 | it = 0
+r_noised_vec = {18.6404909, 16.0864392, 16.8255372, 23.7682699, 13.7399741, 9.4868819, 17.2136113, 19.8338047}
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+------------------------------------------------------------
+PDOP = 1.532695 | it = 0
+r_noised_vec = {20.0240354, 15.3939561, 31.6972459, 24.9262933, 15.4399591, 8.1421960, 16.5266457, 21.1255965}
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+------------------------------------------------------------
+PDOP = 2.549486 | it = 0
+r_noised_vec = {21.8894230, 14.9284275, 16.4581237, 25.9268979, 17.1887792, 7.1244494, 15.9636334, 22.6871608}
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+------------------------------------------------------------
+PDOP = 1.961650 | it = 0
+r_noised_vec = {23.2845655, 14.6246346, 28.5384057, 27.3289125, 18.9970446, 6.5855476, 15.5901015, 24.1227110}
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+------------------------------------------------------------
+PDOP = 2.102712 | it = 0
+r_noised_vec = {14.9537014, 24.4777954, 26.4815723, 19.1315996, 7.7479464, 20.7377714, 23.4845128, 14.0957652}
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+------------------------------------------------------------
+PDOP = 3.213909 | it = 0
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+------------------------------------------------------------
+PDOP = 2.267804 | it = 0
+r_noised_vec = {16.0400946, 21.4429575, 28.3305659, 19.7487174, 8.8136063, 17.0124916, 20.4143937, 14.6091573}
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+------------------------------------------------------------
+PDOP = 3.048828 | it = 0
+r_noised_vec = {16.4100040, 20.0257735, 23.2205923, 20.0219799, 9.8940620, 15.3063770, 19.0721788, 15.2425121}
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+------------------------------------------------------------
+PDOP = 1.966089 | it = 0
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+------------------------------------------------------------
+PDOP = 2.423864 | it = 0
+r_noised_vec = {18.2305553, 17.4261812, 20.4525932, 21.7165475, 12.7212065, 11.9537398, 16.8479985, 17.1471998}
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+------------------------------------------------------------
+PDOP = 2.157240 | it = 0
+r_noised_vec = {19.6874776, 16.6485127, 25.8002096, 22.4984449, 14.3047570, 10.5459776, 15.6772389, 18.3649649}
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+------------------------------------------------------------
+PDOP = 2.371144 | it = 0
+r_noised_vec = {20.6297768, 15.7932556, 20.6565439, 23.6363998, 15.8854989, 9.3302217, 14.9349514, 19.7299352}
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+------------------------------------------------------------
+PDOP = 2.802580 | it = 0
+r_noised_vec = {21.8036350, 15.4626436, 22.6713883, 25.0209800, 17.7300197, 8.4037641, 14.2523381, 21.0065529}
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+------------------------------------------------------------
+PDOP = 1.650089 | it = 0
+r_noised_vec = {23.6851305, 15.2477521, 19.5955266, 26.1772686, 19.5732090, 7.8730829, 13.9917197, 22.5741409}
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+------------------------------------------------------------
+PDOP = 2.436523 | it = 0
+r_noised_vec = {16.3942063, 24.9666596, 26.6571306, 17.8074094, 9.5142250, 21.1914893, 22.4973690, 11.9307016}
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+seed = 1485
+------------------------------------------------------------
+PDOP = 2.320160 | it = 0
+r_noised_vec = {16.0983735, 23.6191733, 32.8187454, 17.9576737, 9.7180631, 19.3834146, 20.8469312, 12.1389811}
+anchors_optimal = {6, 5, 0, 4}
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+x_sol = {3.0979997, 8.9505848, 14.8346547}
+seed = 1487
+------------------------------------------------------------
+PDOP = 2.553417 | it = 0
+r_noised_vec = {16.3682052, 22.1259162, 19.0727054, 18.2185327, 10.4062081, 17.6073056, 19.1827588, 12.6672480}
+anchors_optimal = {1, 6, 5, 7}
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+x_sol = {5.0389721, 8.9747099, 15.2247093}
+seed = 1489
+------------------------------------------------------------
+PDOP = 1.804560 | it = 0
+r_noised_vec = {17.3945209, 20.9080873, 32.1805671, 18.9058494, 11.1862801, 15.8425204, 17.5961243, 13.4741597}
+anchors_optimal = {6, 0, 7, 4}
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+x_sol = {7.1297208, 9.0152601, 15.1693815}
+seed = 1491
+------------------------------------------------------------
+PDOP = 2.109142 | it = 0
+r_noised_vec = {18.2138103, 19.5765479, 17.0256359, 19.5948626, 12.3268561, 14.4281508, 16.3162563, 14.5083632}
+anchors_optimal = {3, 6, 7, 5}
+exact point = {9, 9, 15}
+x_sol = {9.0334838, 8.9724031, 15.0648957}
+seed = 1493
+------------------------------------------------------------
+PDOP = 1.946728 | it = 0
+r_noised_vec = {18.7487659, 18.4851566, 27.6837093, 20.2577805, 13.5653878, 12.9324137, 14.9950330, 15.7191274}
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+exact point = {11, 9, 15}
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+seed = 1495
+------------------------------------------------------------
+PDOP = 2.409748 | it = 0
+r_noised_vec = {19.9229121, 17.5385305, 18.7212191, 21.5925908, 15.1913657, 11.6017654, 13.9023035, 17.0615587}
+anchors_optimal = {3, 0, 1, 5}
+exact point = {13, 9, 15}
+x_sol = {12.8505887, 8.6758539, 15.0526077}
+seed = 1497
+------------------------------------------------------------
+PDOP = 2.471311 | it = 0
+r_noised_vec = {21.6080088, 16.7213072, 22.0872549, 22.6409039, 16.8860343, 10.4819399, 13.0775439, 18.7477759}
+anchors_optimal = {0, 7, 4, 6}
+exact point = {15, 9, 15}
+x_sol = {15.2488671, 8.7541855, 15.2833655}
+seed = 1499
+------------------------------------------------------------
+PDOP = 2.849581 | it = 0
+r_noised_vec = {22.8507615, 16.3092923, 21.4785703, 23.8531627, 18.7031118, 9.8577567, 12.4937355, 20.2469404}
+anchors_optimal = {7, 4, 1, 6}
+exact point = {17, 9, 15}
+x_sol = {17.1801360, 8.9175736, 14.9745208}
+seed = 1501
+------------------------------------------------------------
+PDOP = 2.571208 | it = 0
+r_noised_vec = {23.8901409, 15.9814119, 18.2812905, 25.4156249, 20.4182465, 9.4281025, 12.2492077, 21.8262676}
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+exact point = {19, 9, 15}
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+seed = 1503
+------------------------------------------------------------
+PDOP = 3.136804 | it = 0
+r_noised_vec = {17.1148474, 25.5793613, 31.2522238, 16.6016182, 11.1907480, 21.9902116, 21.6440871, 10.3880631}
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+seed = 1505
+------------------------------------------------------------
+PDOP = 1.737566 | it = 0
+r_noised_vec = {17.6111135, 24.1655608, 23.5569633, 16.7391539, 11.3238536, 20.3136568, 19.9733088, 10.5275112}
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+exact point = {3, 11, 15}
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+seed = 1507
+------------------------------------------------------------
+PDOP = 2.740411 | it = 0
+r_noised_vec = {17.7056087, 22.8587870, 27.5651890, 17.1618387, 11.8008506, 18.7106468, 18.3251932, 11.0398781}
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+seed = 1509
+------------------------------------------------------------
+PDOP = 2.185298 | it = 0
+r_noised_vec = {17.9234420, 21.7051118, 22.5178189, 17.6801828, 12.4610923, 17.1719377, 16.6020677, 11.8797474}
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+seed = 1511
+------------------------------------------------------------
+PDOP = 2.313417 | it = 0
+r_noised_vec = {18.9804000, 20.5010331, 30.5871754, 18.4865362, 13.6906770, 15.7488643, 15.0739780, 12.9880080}
+anchors_optimal = {3, 5, 6, 4}
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+seed = 1513
+------------------------------------------------------------
+PDOP = 3.095729 | it = 0
+r_noised_vec = {20.1959802, 19.5747448, 19.2875988, 19.5499508, 15.0261065, 14.4738722, 13.6158842, 14.3076842}
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+seed = 1515
+------------------------------------------------------------
+PDOP = 2.143554 | it = 0
+r_noised_vec = {20.9208324, 18.6214989, 19.1628863, 20.3583189, 16.5877377, 13.4686842, 12.4193090, 15.8007724}
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+seed = 1517
+------------------------------------------------------------
+PDOP = 1.654081 | it = 0
+r_noised_vec = {21.8940120, 17.9395665, 24.1025618, 21.8227849, 18.0238598, 12.3163739, 11.3462526, 17.1768928}
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+seed = 1519
+------------------------------------------------------------
+PDOP = 2.319005 | it = 0
+r_noised_vec = {23.5971160, 17.4370778, 13.7032015, 23.1285895, 19.5362533, 11.6868131, 10.5547159, 18.8931152}
+anchors_optimal = {0, 7, 5, 6}
+exact point = {17, 11, 15}
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+seed = 1521
+------------------------------------------------------------
+PDOP = 2.138115 | it = 0
+r_noised_vec = {25.1699649, 17.1079987, 25.4584161, 24.4127774, 21.1024452, 11.3755704, 10.3040930, 20.6665948}
+anchors_optimal = {0, 1, 5, 6}
+exact point = {19, 11, 15}
+x_sol = {19.4695662, 11.1112966, 14.7968425}
+seed = 1523
+------------------------------------------------------------
+PDOP = 2.039375 | it = 0
+r_noised_vec = {18.2923484, 26.4079691, 20.9125561, 15.7312940, 12.8966122, 23.2276894, 20.7952115, 8.5886461}
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+exact point = {1, 13, 15}
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+seed = 1525
+------------------------------------------------------------
+PDOP = 1.818592 | it = 0
+r_noised_vec = {18.3012320, 24.9347007, 30.9890764, 15.7707023, 13.1205200, 21.4463383, 19.0227026, 8.8617411}
+anchors_optimal = {5, 3, 4, 7}
+exact point = {3, 13, 15}
+x_sol = {2.9263847, 12.9636208, 14.9785420}
+seed = 1527
+------------------------------------------------------------
+PDOP = 2.189603 | it = 0
+r_noised_vec = {19.0550296, 23.7286609, 21.2874636, 16.1137094, 13.5756721, 19.9087082, 17.3044479, 9.5438179}
+anchors_optimal = {1, 3, 4, 7}
+exact point = {5, 13, 15}
+x_sol = {4.9688604, 12.9530109, 14.9359782}
+seed = 1529
+------------------------------------------------------------
+PDOP = 2.238775 | it = 0
+r_noised_vec = {19.6059532, 22.5364465, 24.1693167, 16.8006199, 14.3750957, 18.4382901, 15.6589827, 10.5536030}
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+exact point = {7, 13, 15}
+x_sol = {7.2500522, 13.0069695, 15.1776323}
+seed = 1531
+------------------------------------------------------------
+PDOP = 285.333494 | it = 2
+r_noised_vec = {19.8774186, 21.4920623, 22.3781607, 17.4303992, 15.6057532, 17.0585134, 14.1245536, 11.8034562}
+anchors_optimal = {3, 0, 5, 6}
+exact point = {9, 13, 15}
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+x_sol = {8.9433508, 12.9024461, 14.7966200}
+seed = 1533
+------------------------------------------------------------
+PDOP = 2.724311 | it = 0
+r_noised_vec = {20.7974923, 20.6306254, 18.8352321, 18.5099865, 16.5077710, 15.8071882, 12.5027011, 13.2201237}
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+exact point = {11, 13, 15}
+x_sol = {11.1913917, 12.8662128, 14.7112942}
+seed = 1535
+------------------------------------------------------------
+PDOP = 2.743644 | it = 0
+r_noised_vec = {22.2515899, 19.7783664, 22.0705751, 19.8875378, 17.6936370, 14.7352843, 11.1927597, 14.9631754}
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+exact point = {13, 13, 15}
+x_sol = {13.2355125, 13.1215551, 15.0803993}
+seed = 1537
+------------------------------------------------------------
+PDOP = 2.407488 | it = 0
+r_noised_vec = {23.2890191, 19.2385627, 16.6628052, 20.8677900, 18.9434733, 13.8579883, 10.0676831, 16.5429974}
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+exact point = {15, 13, 15}
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+seed = 1539
+------------------------------------------------------------
+PDOP = 2.600169 | it = 0
+r_noised_vec = {24.1390565, 18.7148879, 20.0673049, 22.4023116, 20.4870342, 13.2114587, 9.1255122, 18.2070902}
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+seed = 1541
+------------------------------------------------------------
+PDOP = 1.885267 | it = 0
+r_noised_vec = {25.6758660, 18.4918522, 17.7657235, 23.9345272, 22.1599456, 13.0193357, 8.6418577, 19.9343329}
+anchors_optimal = {7, 1, 5, 6}
+exact point = {19, 13, 15}
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+seed = 1543
+------------------------------------------------------------
+PDOP = 2.909341 | it = 0
+r_noised_vec = {20.0881160, 27.4258040, 34.0420805, 14.7635962, 14.8889249, 24.0502031, 20.1691872, 7.0153476}
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+seed = 1545
+------------------------------------------------------------
+PDOP = 3.834427 | it = 0
+r_noised_vec = {19.9446065, 25.9955377, 22.8109007, 15.0494410, 15.0932572, 22.4672592, 18.3615842, 7.2716783}
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+seed = 1547
+------------------------------------------------------------
+PDOP = 1.836289 | it = 0
+r_noised_vec = {19.9026072, 24.7998336, 22.7612278, 15.4151193, 15.4463092, 20.9629752, 16.4666218, 8.0451812}
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+seed = 1549
+------------------------------------------------------------
+PDOP = 2.712883 | it = 0
+r_noised_vec = {20.6919571, 23.5625660, 26.1779041, 15.9827560, 16.1224253, 19.5269819, 14.6190324, 9.2091347}
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+seed = 1551
+------------------------------------------------------------
+PDOP = 3.172522 | it = 0
+r_noised_vec = {21.6498495, 22.6268058, 15.7478616, 16.9048575, 16.8555187, 18.4447364, 13.0321595, 10.6393556}
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+seed = 1553
+------------------------------------------------------------
+PDOP = 3.133299 | it = 0
+r_noised_vec = {22.1287536, 21.7222256, 25.8132519, 17.8765972, 17.8874521, 17.3186157, 11.4018421, 12.0556076}
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+------------------------------------------------------------
+PDOP = 2.895189 | it = 0
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+------------------------------------------------------------
+PDOP = 3.497412 | it = 0
+r_noised_vec = {24.3481167, 20.5101210, 22.4547501, 20.5872656, 20.3837147, 15.6598832, 8.6908147, 15.6771697}
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+------------------------------------------------------------
+PDOP = 2.370526 | it = 0
+r_noised_vec = {25.7264685, 20.0396875, 14.8713298, 21.7542215, 21.9474127, 15.1721347, 7.7789197, 17.5400915}
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+------------------------------------------------------------
+PDOP = 3.247821 | it = 0
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+------------------------------------------------------------
+PDOP = 2.322233 | it = 0
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+------------------------------------------------------------
+PDOP = 2.104830 | it = 0
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+------------------------------------------------------------
+PDOP = 2.556082 | it = 0
+r_noised_vec = {21.8499462, 25.9461426, 25.5425966, 14.8817988, 17.1691938, 22.5236750, 16.1870499, 7.1403092}
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+------------------------------------------------------------
+PDOP = 2.546799 | it = 0
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+------------------------------------------------------------
+PDOP = 1.779018 | it = 0
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+------------------------------------------------------------
+PDOP = 3.047428 | it = 0
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+------------------------------------------------------------
+PDOP = 2.762501 | it = 0
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+------------------------------------------------------------
+PDOP = 3.125856 | it = 0
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+------------------------------------------------------------
+PDOP = 1.967888 | it = 0
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+------------------------------------------------------------
+PDOP = 2.137587 | it = 0
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+------------------------------------------------------------
+PDOP = 3.103328 | it = 0
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+------------------------------------------------------------
+PDOP = 2.286935 | it = 0
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+------------------------------------------------------------
+PDOP = 2.236892 | it = 0
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+------------------------------------------------------------
+PDOP = 2.858458 | it = 0
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+------------------------------------------------------------
+PDOP = 2.577451 | it = 0
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+------------------------------------------------------------
+PDOP = 2.092651 | it = 0
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+------------------------------------------------------------
+PDOP = 3.283315 | it = 0
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+------------------------------------------------------------
+PDOP = 2.533251 | it = 0
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+------------------------------------------------------------
+PDOP = 2.292440 | it = 0
+r_noised_vec = {27.7159343, 22.8706062, 18.2203484, 21.1109792, 24.4350830, 18.7542873, 5.9002782, 16.9129200}
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+------------------------------------------------------------
+PDOP = 2.031306 | it = 0
+r_noised_vec = {28.8038018, 22.8011427, 15.3500989, 22.9236120, 25.8403086, 18.6943010, 5.1139221, 18.8056574}
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+------------------------------------------------------------
+PDOP = 6.199446 | it = 0
+r_noised_vec = {16.1814796, 24.8753792, 48.6053507, 24.8643049, 2.9835352, 19.1820398, 26.8131123, 19.3007914}
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+------------------------------------------------------------
+PDOP = 3.097564 | it = 0
+r_noised_vec = {16.3425396, 23.3963506, 22.7860388, 24.8169338, 3.6724469, 17.2034724, 25.5866613, 19.3711559}
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+------------------------------------------------------------
+PDOP = 2.901041 | it = 0
+r_noised_vec = {16.2752158, 22.0880740, 38.7126520, 25.2522998, 5.0912486, 15.2502836, 24.2591063, 19.6527111}
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+exact point = {5, 1, 17}
+x_sol = {5.1769688, 1.0182042, 17.1170945}
+seed = 1609
+------------------------------------------------------------
+PDOP = 4.783940 | it = 0
+r_noised_vec = {16.9056900, 20.6865597, 27.9717083, 25.5309170, 6.7219088, 13.3279582, 23.0242883, 20.0838573}
+anchors_optimal = {2, 3, 6, 1}
+exact point = {7, 1, 17}
+x_sol = {7.0634542, 1.1715076, 17.1394371}
+seed = 1611
+------------------------------------------------------------
+PDOP = 2.571281 | it = 0
+r_noised_vec = {18.1356079, 19.5363861, 29.7637830, 26.0558682, 8.5804371, 11.4134054, 22.1294086, 20.7162951}
+anchors_optimal = {3, 1, 0, 4}
+exact point = {9, 1, 17}
+x_sol = {9.1113129, 1.2892633, 17.2177993}
+seed = 1613
+------------------------------------------------------------
+PDOP = 1.882945 | it = 0
+r_noised_vec = {19.0096837, 18.3797839, 32.3796007, 26.8266732, 10.3953547, 9.5298363, 21.2502819, 21.5375943}
+anchors_optimal = {6, 1, 4, 5}
+exact point = {11, 1, 17}
+x_sol = {10.9538321, 1.0064026, 16.9999652}
+seed = 1615
+------------------------------------------------------------
+PDOP = 2.869216 | it = 0
+r_noised_vec = {19.7297488, 17.4352411, 23.8630114, 27.5718262, 12.1385330, 7.7056113, 20.6239394, 22.5281613}
+anchors_optimal = {7, 0, 1, 4}
+exact point = {13, 1, 17}
+x_sol = {12.7440883, 1.0217350, 16.8662896}
+seed = 1617
+------------------------------------------------------------
+PDOP = 3.076193 | it = 0
+r_noised_vec = {21.1629598, 16.7212924, 33.8282503, 28.4761145, 14.2123670, 5.9937580, 19.9478905, 23.6655230}
+anchors_optimal = {7, 0, 6, 5}
+exact point = {15, 1, 17}
+x_sol = {14.7668064, 0.9738632, 17.0738707}
+seed = 1619
+------------------------------------------------------------
+PDOP = 2.022494 | it = 0
+r_noised_vec = {22.9135643, 16.1376201, 22.4682529, 29.7117110, 16.2709716, 4.2869892, 19.6139921, 24.9263659}
+anchors_optimal = {7, 4, 1, 5}
+exact point = {17, 1, 17}
+x_sol = {16.9833221, 1.1163369, 16.8695923}
+seed = 1621
+------------------------------------------------------------
+PDOP = 2.255845 | it = 0
+r_noised_vec = {24.1335354, 15.9723429, 32.1700769, 30.5230754, 18.3774945, 3.2527326, 19.2712034, 26.2876957}
+anchors_optimal = {7, 6, 1, 5}
+exact point = {19, 1, 17}
+x_sol = {18.9122017, 1.0052892, 16.9351439}
+seed = 1623
+------------------------------------------------------------
+PDOP = 4.734480 | it = 0
+r_noised_vec = {15.8301870, 24.8083214, 29.9708666, 23.3875887, 3.7235203, 19.4696789, 25.7414541, 17.2417230}
+anchors_optimal = {2, 6, 5, 0}
+exact point = {1, 3, 17}
+x_sol = {0.9183167, 3.0380510, 16.7007997}
+seed = 1625
+------------------------------------------------------------
+PDOP = 2.575266 | it = 0
+r_noised_vec = {16.2460454, 23.4115709, 33.2925713, 23.5019197, 4.1626750, 17.5506601, 24.2927493, 17.3823007}
+anchors_optimal = {6, 1, 7, 4}
+exact point = {3, 3, 17}
+x_sol = {2.9212291, 3.0048285, 16.8889604}
+seed = 1627
+------------------------------------------------------------
+PDOP = 3.336918 | it = 0
+r_noised_vec = {16.9078266, 22.0458599, 30.7749298, 23.5750548, 5.3800356, 15.4519753, 22.8693395, 17.7283808}
+anchors_optimal = {3, 6, 7, 5}
+exact point = {5, 3, 17}
+x_sol = {5.0076000, 3.0199172, 16.8549401}
+seed = 1629
+------------------------------------------------------------
+PDOP = 2.093493 | it = 0
+r_noised_vec = {17.1583396, 20.7441319, 28.6119405, 24.1693753, 6.9208235, 13.5459179, 21.5712261, 18.4375291}
+anchors_optimal = {3, 7, 5, 4}
+exact point = {7, 3, 17}
+x_sol = {6.9317344, 2.8146137, 16.9267428}
+seed = 1631
+------------------------------------------------------------
+PDOP = 2.158680 | it = 0
+r_noised_vec = {17.7131038, 19.6469298, 29.9289238, 24.6886881, 8.7377466, 11.6344646, 20.3524659, 19.1945945}
+anchors_optimal = {3, 7, 5, 4}
+exact point = {9, 3, 17}
+x_sol = {8.9470381, 2.8135726, 16.8447069}
+seed = 1633
+------------------------------------------------------------
+PDOP = 1.799883 | it = 0
+r_noised_vec = {19.0670449, 18.5107128, 13.7282257, 25.3434853, 10.5350212, 9.7393021, 19.4427628, 20.1045019}
+anchors_optimal = {6, 0, 4, 5}
+exact point = {11, 3, 17}
+x_sol = {10.9245439, 3.0482364, 17.1464613}
+seed = 1635
+------------------------------------------------------------
+PDOP = 2.000959 | it = 0
+r_noised_vec = {20.3712429, 17.6821854, 38.4354436, 26.2876374, 12.5457121, 7.8811944, 18.5327586, 21.1480503}
+anchors_optimal = {3, 6, 1, 4}
+exact point = {13, 3, 17}
+x_sol = {13.0304204, 3.0730467, 17.1163359}
+seed = 1637
+------------------------------------------------------------
+PDOP = 2.436187 | it = 0
+r_noised_vec = {21.2162507, 16.8964479, 17.7718602, 27.1267056, 14.7160866, 6.1497195, 17.8418606, 22.3102681}
+anchors_optimal = {3, 6, 4, 5}
+exact point = {15, 3, 17}
+x_sol = {15.2037935, 3.1180805, 16.7837372}
+seed = 1639
+------------------------------------------------------------
+PDOP = 1.949546 | it = 0
+r_noised_vec = {22.4668488, 16.3831455, 32.4456904, 28.1876331, 16.5387564, 4.6424667, 17.5052622, 23.5793452}
+anchors_optimal = {7, 4, 1, 5}
+exact point = {17, 3, 17}
+x_sol = {17.1309991, 3.0669722, 16.9961832}
+seed = 1641
+------------------------------------------------------------
+PDOP = 2.701707 | it = 0
+r_noised_vec = {24.3447859, 16.1355088, 23.1930617, 29.6571360, 18.3966210, 3.6447074, 17.2809862, 24.9458883}
+anchors_optimal = {3, 0, 1, 5}
+exact point = {19, 3, 17}
+x_sol = {19.2451040, 2.9506021, 17.0018619}
+seed = 1643
+------------------------------------------------------------
+PDOP = 2.023011 | it = 0
+r_noised_vec = {16.7118129, 25.0441827, 32.0080655, 21.8213044, 4.9317898, 19.4700400, 24.4440941, 15.2795747}
+anchors_optimal = {1, 0, 7, 4}
+exact point = {1, 5, 17}
+x_sol = {1.3440422, 4.9962407, 17.2095300}
+seed = 1645
+------------------------------------------------------------
+PDOP = 2.258247 | it = 0
+r_noised_vec = {16.3986008, 23.6612767, 33.3305153, 22.0075887, 5.2695724, 17.6691691, 22.8938698, 15.4062113}
+anchors_optimal = {1, 3, 0, 4}
+exact point = {3, 5, 17}
+x_sol = {2.8436340, 4.8310565, 16.8459398}
+seed = 1647
+------------------------------------------------------------
+PDOP = 2.147307 | it = 0
+r_noised_vec = {16.7864582, 22.1972133, 25.1100284, 22.3953574, 6.3413404, 15.7157740, 21.5183376, 15.6006703}
+anchors_optimal = {1, 6, 5, 4}
+exact point = {5, 5, 17}
+x_sol = {5.0586065, 4.8143868, 16.9665981}
+seed = 1649
+------------------------------------------------------------
+PDOP = 2.865350 | it = 0
+r_noised_vec = {17.7947283, 20.9954155, 33.5304007, 22.6382597, 7.7413319, 13.7929080, 20.2382785, 16.2419012}
+anchors_optimal = {3, 1, 0, 5}
+exact point = {7, 5, 17}
+x_sol = {7.2327601, 5.3463566, 17.0937674}
+seed = 1651
+------------------------------------------------------------
+PDOP = 2.528688 | it = 0
+r_noised_vec = {18.4741832, 19.8378931, 22.3922188, 23.3758553, 9.4841091, 11.9040963, 18.8765094, 17.1036678}
+anchors_optimal = {1, 6, 0, 5}
+exact point = {9, 5, 17}
+x_sol = {9.1250906, 4.8522343, 17.1272235}
+seed = 1653
+------------------------------------------------------------
+PDOP = 2.092255 | it = 0
+r_noised_vec = {19.0189587, 18.9597975, 30.6291953, 24.1418647, 11.2293317, 10.2639082, 17.8102392, 18.1590789}
+anchors_optimal = {3, 7, 4, 5}
+exact point = {11, 5, 17}
+x_sol = {11.0460547, 5.1406775, 17.1599339}
+seed = 1655
+------------------------------------------------------------
+PDOP = 1.783802 | it = 0
+r_noised_vec = {20.2962741, 18.0201040, 23.0620799, 24.9453169, 13.1473070, 8.5456551, 16.8571602, 19.3732827}
+anchors_optimal = {0, 6, 4, 5}
+exact point = {13, 5, 17}
+x_sol = {13.1269332, 4.9437992, 16.7917647}
+seed = 1657
+------------------------------------------------------------
+PDOP = 3.318993 | it = 0
+r_noised_vec = {21.9179542, 17.4879976, 26.5707636, 26.0417043, 14.8890342, 7.0132890, 16.0837163, 20.7127589}
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+exact point = {15, 5, 17}
+x_sol = {15.2910135, 5.2954303, 17.0566311}
+seed = 1659
+------------------------------------------------------------
+PDOP = 3.447727 | it = 0
+r_noised_vec = {23.0313149, 16.8518512, 24.8462613, 27.1685922, 16.7456470, 5.7901522, 15.5235547, 22.1480785}
+anchors_optimal = {3, 0, 1, 4}
+exact point = {17, 5, 17}
+x_sol = {16.9856995, 5.0344491, 17.0795993}
+seed = 1661
+------------------------------------------------------------
+PDOP = 2.234439 | it = 0
+r_noised_vec = {24.1198355, 16.6207003, 24.0385845, 28.2083508, 18.5306397, 5.0990487, 15.1780783, 23.6549685}
+anchors_optimal = {3, 4, 1, 6}
+exact point = {19, 5, 17}
+x_sol = {18.8220253, 5.1519364, 17.0552640}
+seed = 1663
+------------------------------------------------------------
+PDOP = 3.783596 | it = 0
+r_noised_vec = {17.0830859, 25.5440241, 31.4497689, 20.7779937, 6.6377248, 20.1674349, 23.1693993, 13.3760171}
+anchors_optimal = {1, 6, 5, 0}
+exact point = {1, 7, 17}
+x_sol = {1.0088067, 7.0764307, 16.9676773}
+seed = 1665
+------------------------------------------------------------
+PDOP = 2.638594 | it = 0
+r_noised_vec = {17.4986527, 23.9755740, 18.6145796, 20.6576600, 6.9771153, 18.3287937, 21.5102965, 13.7699778}
+anchors_optimal = {1, 3, 5, 4}
+exact point = {3, 7, 17}
+x_sol = {2.9404069, 6.8374919, 16.7864072}
+seed = 1667
+------------------------------------------------------------
+PDOP = 2.358426 | it = 0
+r_noised_vec = {17.5066018, 22.6452297, 38.5847743, 20.9350281, 7.9026141, 16.5361116, 19.9569683, 14.1336691}
+anchors_optimal = {1, 3, 0, 4}
+exact point = {5, 7, 17}
+x_sol = {5.0703862, 7.0317291, 16.9218367}
+seed = 1669
+------------------------------------------------------------
+PDOP = 2.342447 | it = 0
+r_noised_vec = {17.8239596, 21.2594262, 18.7998369, 21.5842613, 9.0765978, 14.8228974, 18.6126484, 14.7846235}
+anchors_optimal = {1, 6, 7, 4}
+exact point = {7, 7, 17}
+x_sol = {7.1356424, 6.9157773, 16.8613944}
+seed = 1671
+------------------------------------------------------------
+PDOP = 2.231666 | it = 0
+r_noised_vec = {18.9583444, 20.2412714, 32.0691877, 22.0398088, 10.5876323, 12.9411374, 17.3054631, 15.6583337}
+anchors_optimal = {1, 0, 7, 4}
+exact point = {9, 7, 17}
+x_sol = {9.1765725, 6.9977512, 17.0084438}
+seed = 1673
+------------------------------------------------------------
+PDOP = 3.548934 | it = 0
+r_noised_vec = {20.0708892, 19.2249031, 22.2354456, 22.9079868, 12.0347469, 11.3256802, 16.1880543, 16.7215930}
+anchors_optimal = {2, 0, 1, 7}
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+x_sol = {11.3748342, 7.2153120, 17.0275544}
+seed = 1675
+------------------------------------------------------------
+PDOP = 2.659716 | it = 0
+r_noised_vec = {20.7456357, 18.4727395, 24.7959601, 23.9081997, 13.6995569, 9.8357418, 15.1113253, 17.9458575}
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+x_sol = {12.9658329, 6.9637909, 17.0069972}
+seed = 1677
+------------------------------------------------------------
+PDOP = 3.186680 | it = 0
+r_noised_vec = {21.8410480, 17.9126669, 25.9757955, 24.8742789, 15.3404669, 8.5527792, 14.3595439, 19.3067216}
+anchors_optimal = {2, 7, 4, 6}
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+x_sol = {14.8829736, 6.8836954, 22.8301434}
+seed = 1679
+------------------------------------------------------------
+PDOP = 2.390081 | it = 0
+r_noised_vec = {23.5853128, 17.4307459, 19.9131613, 26.1020682, 17.2843247, 7.3855939, 13.8490701, 20.7833560}
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+x_sol = {18.3153350, 6.8881646, 15.8878224}
+seed = 1681
+------------------------------------------------------------
+PDOP = 2.933289 | it = 0
+r_noised_vec = {25.0400844, 17.3043959, 27.7475667, 27.4736480, 19.2184546, 6.8401651, 13.4212582, 22.3579872}
+anchors_optimal = {3, 0, 1, 5}
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+seed = 1683
+------------------------------------------------------------
+PDOP = 3.364986 | it = 0
+r_noised_vec = {17.6764551, 26.1690568, 25.3712394, 19.2332671, 8.6844379, 20.8893244, 22.2043858, 11.3797730}
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+seed = 1685
+------------------------------------------------------------
+PDOP = 1.808901 | it = 0
+r_noised_vec = {17.8141283, 24.7604969, 32.5869282, 19.6419425, 8.8701665, 19.0636294, 20.4648026, 11.3614420}
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+seed = 1687
+------------------------------------------------------------
+PDOP = 1.763826 | it = 0
+r_noised_vec = {18.5728359, 23.3414485, 24.7805426, 19.8288903, 9.4448458, 17.2618082, 18.8151177, 11.9384490}
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+seed = 1689
+------------------------------------------------------------
+PDOP = 2.639319 | it = 0
+r_noised_vec = {19.0139821, 22.0198011, 27.4155993, 20.2225172, 10.3911229, 15.5348111, 17.1998850, 12.8035912}
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+------------------------------------------------------------
+PDOP = 2.736343 | it = 0
+r_noised_vec = {19.3294886, 20.9296423, 24.9561985, 21.1055578, 11.6258210, 13.8698473, 15.6578817, 13.9056681}
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+------------------------------------------------------------
+PDOP = 3.195182 | it = 0
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+------------------------------------------------------------
+PDOP = 2.017035 | it = 0
+r_noised_vec = {21.8237968, 19.1449818, 31.1369840, 22.7905450, 14.6859546, 10.8270244, 13.2818174, 16.6065100}
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+------------------------------------------------------------
+PDOP = 2.698106 | it = 0
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+------------------------------------------------------------
+PDOP = 2.731909 | it = 0
+r_noised_vec = {23.7077883, 18.1399000, 30.9404918, 25.1297005, 18.3349675, 8.9496407, 11.7849442, 19.7058176}
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+------------------------------------------------------------
+PDOP = 1.757711 | it = 0
+r_noised_vec = {25.3693587, 17.9981308, 14.6929604, 26.4744763, 20.0277427, 8.4569979, 11.4885890, 21.3427000}
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+------------------------------------------------------------
+PDOP = 3.488957 | it = 0
+r_noised_vec = {19.1613739, 26.8358313, 35.2587387, 18.5199523, 10.4520285, 21.4848154, 21.3796932, 9.7053702}
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+------------------------------------------------------------
+PDOP = 2.587126 | it = 0
+r_noised_vec = {18.9333098, 25.5505094, 24.6882189, 18.2942099, 10.5260195, 19.9083989, 19.5315587, 9.8201655}
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+seed = 1707
+------------------------------------------------------------
+PDOP = 2.091782 | it = 0
+r_noised_vec = {19.0005923, 24.1586101, 27.0566420, 18.8557042, 11.0733992, 18.2169759, 17.8727121, 10.3481588}
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+seed = 1709
+------------------------------------------------------------
+PDOP = 2.019539 | it = 0
+r_noised_vec = {19.8863856, 22.9871741, 26.9801565, 19.3710591, 12.0096053, 16.6180683, 16.2716302, 11.2181766}
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+seed = 1711
+------------------------------------------------------------
+PDOP = 2.775219 | it = 0
+r_noised_vec = {20.7661909, 21.8404687, 20.8921471, 19.9093995, 13.1433311, 15.1322327, 14.5660564, 12.3596376}
+anchors_optimal = {0, 3, 6, 4}
+exact point = {9, 11, 17}
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+seed = 1713
+------------------------------------------------------------
+PDOP = 1.991487 | it = 0
+r_noised_vec = {21.2221002, 20.8330781, 27.1099701, 20.9861531, 14.5225660, 13.7863300, 13.0989914, 13.7095566}
+anchors_optimal = {0, 4, 5, 6}
+exact point = {11, 11, 17}
+x_sol = {11.0484744, 10.9862979, 16.8019109}
+seed = 1715
+------------------------------------------------------------
+PDOP = 2.750366 | it = 0
+r_noised_vec = {22.1101353, 20.0779061, 18.4040865, 21.9300674, 15.9175371, 12.5951272, 11.7355819, 15.2173096}
+anchors_optimal = {0, 1, 7, 5}
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+x_sol = {12.7562045, 10.8370128, 16.9338181}
+seed = 1717
+------------------------------------------------------------
+PDOP = 2.206351 | it = 0
+r_noised_vec = {23.6678165, 19.3790504, 24.8859260, 23.0320690, 17.5616499, 11.6400355, 10.6773232, 16.8435737}
+anchors_optimal = {3, 4, 5, 6}
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+x_sol = {15.0505559, 11.0653999, 16.9092065}
+seed = 1719
+------------------------------------------------------------
+PDOP = 2.647781 | it = 0
+r_noised_vec = {24.9606978, 19.0618305, 19.0585853, 24.4033981, 19.0982733, 10.9835315, 9.8324154, 18.5579746}
+anchors_optimal = {0, 4, 7, 6}
+exact point = {17, 11, 17}
+x_sol = {17.0190007, 11.0354112, 17.2971683}
+seed = 1721
+------------------------------------------------------------
+PDOP = 3.062901 | it = 0
+r_noised_vec = {25.8672781, 18.8238526, 22.0158914, 25.6974104, 20.6273114, 10.7595240, 9.3206339, 20.1110025}
+anchors_optimal = {0, 7, 1, 5}
+exact point = {19, 11, 17}
+x_sol = {18.7836487, 11.1866734, 16.7781597}
+seed = 1723
+------------------------------------------------------------
+PDOP = 3.618770 | it = 0
+r_noised_vec = {19.8123811, 27.5850753, 28.5475336, 17.3679378, 12.2404816, 22.7402173, 20.4009332, 7.5194146}
+anchors_optimal = {1, 6, 3, 7}
+exact point = {1, 13, 17}
+x_sol = {1.0353558, 13.1219641, 16.9500965}
+seed = 1725
+------------------------------------------------------------
+PDOP = 2.003830 | it = 0
+r_noised_vec = {20.3400156, 26.3112617, 23.4238498, 17.7659103, 12.4908996, 21.1345277, 18.5414434, 7.8553116}
+anchors_optimal = {1, 6, 3, 4}
+exact point = {3, 13, 17}
+x_sol = {3.0734543, 12.9854259, 17.1855574}
+seed = 1727
+------------------------------------------------------------
+PDOP = 3.103330 | it = 0
+r_noised_vec = {20.5442177, 25.0322287, 32.4722844, 17.7813847, 13.0433222, 19.5925681, 16.7608659, 8.6414714}
+anchors_optimal = {1, 5, 3, 4}
+exact point = {5, 13, 17}
+x_sol = {4.8752508, 13.0445884, 16.8879934}
+seed = 1729
+------------------------------------------------------------
+PDOP = 2.338197 | it = 0
+r_noised_vec = {20.6161028, 23.9814827, 16.4783600, 18.4727305, 13.8489289, 18.1496998, 15.0787702, 9.7722505}
+anchors_optimal = {0, 5, 6, 7}
+exact point = {7, 13, 17}
+x_sol = {7.0296729, 13.1853235, 16.4864348}
+seed = 1731
+------------------------------------------------------------
+PDOP = 2.958724 | it = 0
+r_noised_vec = {21.4359671, 22.8529827, 31.4333198, 19.3063547, 14.7830825, 16.5981799, 13.4545977, 11.1391810}
+anchors_optimal = {1, 0, 4, 6}
+exact point = {9, 13, 17}
+x_sol = {8.8484701, 13.1387227, 16.8410831}
+seed = 1733
+------------------------------------------------------------
+PDOP = 2.976938 | it = 0
+r_noised_vec = {22.6422996, 21.9985579, 15.2899761, 20.0133224, 15.9827374, 15.3563081, 11.9910939, 12.6611894}
+anchors_optimal = {0, 1, 2, 7}
+exact point = {11, 13, 17}
+x_sol = {11.2562416, 17.0829784, 13.1898640}
+seed = 1735
+------------------------------------------------------------
+PDOP = 2.830101 | it = 0
+r_noised_vec = {23.3822562, 21.1907424, 26.6183242, 21.2366861, 17.1965505, 14.2662650, 10.4238213, 14.2861659}
+anchors_optimal = {0, 1, 4, 7}
+exact point = {13, 13, 17}
+x_sol = {13.0705880, 12.9112319, 17.1054884}
+seed = 1737
+------------------------------------------------------------
+PDOP = 3.069777 | it = 0
+r_noised_vec = {24.1219752, 20.5612131, 17.8308052, 22.4140340, 18.6483669, 13.3709948, 9.2410382, 15.9833758}
+anchors_optimal = {0, 1, 4, 6}
+exact point = {15, 13, 17}
+x_sol = {14.6870053, 13.2173315, 16.6607394}
+seed = 1739
+------------------------------------------------------------
+PDOP = 2.409813 | it = 0
+r_noised_vec = {25.6018411, 20.2180234, 20.9738751, 23.6232901, 20.0822567, 12.7238183, 8.3635916, 17.7347770}
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+exact point = {17, 13, 17}
+x_sol = {16.9361224, 12.8361769, 16.9088821}
+seed = 1741
+------------------------------------------------------------
+PDOP = 2.217426 | it = 0
+r_noised_vec = {27.2000549, 19.9089697, 21.3326011, 25.1166501, 21.8117226, 12.3803335, 7.7115498, 19.6038811}
+anchors_optimal = {3, 7, 5, 6}
+exact point = {19, 13, 17}
+x_sol = {19.0485304, 12.9685436, 16.9877358}
+seed = 1743
+------------------------------------------------------------
+PDOP = 52.242505 | it = 2
+r_noised_vec = {21.2228933, 28.2623337, 25.2200014, 16.7627052, 14.4594737, 23.7206457, 19.8664988, 5.8108211}
+anchors_optimal = {4, 2, 0, 6}
+exact point = {1, 15, 17}
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+x_sol = {1.0024154, 15.1123934, 16.8509164}
+seed = 1745
+------------------------------------------------------------
+PDOP = 2.457503 | it = 0
+r_noised_vec = {21.0675652, 27.1584029, 30.4255043, 16.7220118, 14.5931982, 22.0963590, 17.8495937, 6.0914234}
+anchors_optimal = {1, 5, 4, 7}
+exact point = {3, 15, 17}
+x_sol = {3.2555882, 15.1277893, 17.0613096}
+seed = 1747
+------------------------------------------------------------
+PDOP = 1.866260 | it = 0
+r_noised_vec = {21.7177273, 26.0006376, 21.6147652, 17.4148585, 14.9325289, 20.7179870, 16.0254645, 6.9684775}
+anchors_optimal = {5, 3, 4, 7}
+exact point = {5, 15, 17}
+x_sol = {5.0722483, 15.0900195, 17.2030952}
+seed = 1749
+------------------------------------------------------------
+PDOP = 4.357661 | it = 0
+r_noised_vec = {22.3633832, 24.9667343, 26.9082651, 17.7239153, 15.5624659, 19.2648759, 14.1076886, 8.2563643}
+anchors_optimal = {2, 1, 4, 6}
+exact point = {7, 15, 17}
+x_sol = {14.2863258, 7.8495550, 24.3165225}
+seed = 1751
+------------------------------------------------------------
+PDOP = 2.313837 | it = 0
+r_noised_vec = {22.5864909, 24.1296947, 20.8179885, 18.5243632, 16.3249797, 17.9397927, 12.1777733, 9.8003348}
+anchors_optimal = {1, 3, 6, 7}
+exact point = {9, 15, 17}
+x_sol = {9.1249579, 15.4168035, 17.0027756}
+seed = 1753
+------------------------------------------------------------
+PDOP = 3.110327 | it = 0
+r_noised_vec = {23.2432847, 23.1914214, 22.4776191, 19.6362567, 17.3990441, 16.7560570, 10.6546775, 11.5010583}
+anchors_optimal = {0, 1, 3, 5}
+exact point = {11, 15, 17}
+x_sol = {10.5633752, 14.5702028, 17.2651731}
+seed = 1755
+------------------------------------------------------------
+PDOP = 3.239614 | it = 0
+r_noised_vec = {24.5834748, 22.5834038, 18.6774965, 20.5259515, 18.5383816, 15.7169020, 9.0433543, 13.2975087}
+anchors_optimal = {0, 1, 5, 7}
+exact point = {13, 15, 17}
+x_sol = {12.9825554, 14.8298520, 17.4207663}
+seed = 1757
+------------------------------------------------------------
+PDOP = 2.037388 | it = 0
+r_noised_vec = {25.6792152, 21.8989932, 17.6073764, 21.8491257, 20.0211135, 15.1173895, 7.6675044, 15.1504770}
+anchors_optimal = {1, 2, 7, 6}
+exact point = {15, 15, 17}
+x_sol = {14.9933244, 14.9617421, 17.1112916}
+seed = 1759
+------------------------------------------------------------
+PDOP = 117.494370 | it = 2
+r_noised_vec = {26.4012945, 21.4914584, 24.7627365, 23.2273676, 21.5063285, 14.5692191, 6.5917298, 17.0176120}
+anchors_optimal = {7, 3, 1, 5}
+exact point = {17, 15, 17}
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+x_sol = {16.9827579, 14.9399206, 17.0766181}
+seed = 1761
+------------------------------------------------------------
+PDOP = 2.429526 | it = 0
+r_noised_vec = {27.6674306, 21.2438391, 12.6461911, 24.5392486, 23.1685933, 14.3010529, 6.0255794, 18.9839017}
+anchors_optimal = {0, 1, 5, 6}
+exact point = {19, 15, 17}
+x_sol = {18.7680531, 14.9266449, 16.9942259}
+seed = 1763
+------------------------------------------------------------
+PDOP = 2.845050 | it = 0
+r_noised_vec = {22.8654098, 29.3839552, 35.8302992, 16.2974429, 16.3450297, 24.9952633, 19.4800635, 4.3494944}
+anchors_optimal = {1, 5, 4, 7}
+exact point = {1, 17, 17}
+x_sol = {1.0893898, 17.0326815, 16.7803589}
+seed = 1765
+------------------------------------------------------------
+PDOP = 2.642602 | it = 0
+r_noised_vec = {22.8658732, 28.2085947, 19.3361907, 16.4875181, 16.3980953, 23.5434766, 17.6128893, 4.8160775}
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+exact point = {3, 17, 17}
+x_sol = {2.9468614, 16.7333499, 17.0432540}
+seed = 1767
+------------------------------------------------------------
+PDOP = 3.747662 | it = 0
+r_noised_vec = {22.7156655, 26.9705112, 30.1597749, 16.5717686, 16.6417077, 22.1695324, 15.7172085, 5.9534561}
+anchors_optimal = {1, 0, 4, 6}
+exact point = {5, 17, 17}
+x_sol = {4.9366575, 16.8506002, 16.7909216}
+seed = 1769
+------------------------------------------------------------
+PDOP = 2.001648 | it = 0
+r_noised_vec = {23.3022916, 26.0420117, 20.4722996, 17.4968326, 17.2621411, 20.9089511, 13.6863922, 7.4506450}
+anchors_optimal = {0, 3, 6, 7}
+exact point = {7, 17, 17}
+x_sol = {7.0314415, 16.7330958, 17.0954484}
+seed = 1771
+------------------------------------------------------------
+PDOP = 3.396127 | it = 0
+r_noised_vec = {24.2800929, 25.1368832, 23.1777504, 18.1198882, 17.9974335, 19.7863731, 11.8033184, 9.1266708}
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+exact point = {9, 17, 17}
+x_sol = {9.3857898, 17.3734885, 16.8253248}
+seed = 1773
+------------------------------------------------------------
+PDOP = 2.444854 | it = 0
+r_noised_vec = {24.7997488, 24.3850809, 22.2344091, 19.0118420, 19.1385636, 18.6298726, 9.9054135, 10.9003892}
+anchors_optimal = {4, 3, 5, 7}
+exact point = {11, 17, 17}
+x_sol = {11.0055912, 17.0122667, 16.8850434}
+seed = 1775
+------------------------------------------------------------
+PDOP = 2.214644 | it = 0
+r_noised_vec = {25.3224486, 23.8280235, 17.9698835, 20.3402496, 20.2900711, 17.7996791, 8.1672524, 12.7374028}
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+exact point = {13, 17, 17}
+x_sol = {12.8897117, 17.0822254, 17.2424395}
+seed = 1777
+------------------------------------------------------------
+PDOP = 1.800894 | it = 0
+r_noised_vec = {26.5947692, 23.2551741, 22.5339800, 21.4152074, 21.6705560, 17.1499767, 6.4686093, 14.5667290}
+anchors_optimal = {1, 4, 3, 6}
+exact point = {15, 17, 17}
+x_sol = {15.0470800, 17.2100277, 16.9205043}
+seed = 1779
+------------------------------------------------------------
+PDOP = 4.549203 | it = 0
+r_noised_vec = {28.0050004, 22.9861962, 16.1507230, 22.7990968, 22.8769319, 16.7137211, 5.0382698, 16.4437344}
+anchors_optimal = {1, 4, 3, 7}
+exact point = {17, 17, 17}
+x_sol = {16.9313477, 17.1567793, 17.0632215}
+seed = 1781
+------------------------------------------------------------
+PDOP = 2.830915 | it = 0
+r_noised_vec = {28.8792115, 22.6981482, 21.1627241, 24.3340735, 24.2459236, 16.5588193, 4.3299629, 18.3540343}
+anchors_optimal = {0, 4, 7, 6}
+exact point = {19, 17, 17}
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+seed = 1783
+------------------------------------------------------------
+PDOP = 4.802850 | it = 0
+r_noised_vec = {23.7967324, 30.7000950, 26.0991803, 15.9876771, 18.0765487, 26.3948900, 19.1991111, 3.0176115}
+anchors_optimal = {1, 5, 6, 3}
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+x_sol = {1.0577456, 19.1337987, 16.9685689}
+seed = 1785
+------------------------------------------------------------
+PDOP = 2.191966 | it = 0
+r_noised_vec = {24.2475454, 29.4514521, 26.5627098, 16.1588318, 18.2586876, 24.9994358, 17.2527456, 3.6121264}
+anchors_optimal = {0, 4, 6, 7}
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+x_sol = {3.0102691, 18.9297952, 17.1990469}
+seed = 1787
+------------------------------------------------------------
+PDOP = 3.615125 | it = 0
+r_noised_vec = {24.6861258, 28.2458233, 22.5552979, 16.6797955, 18.6685879, 23.6714404, 15.3366574, 4.9992640}
+anchors_optimal = {0, 5, 4, 6}
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+seed = 1789
+------------------------------------------------------------
+PDOP = 2.122660 | it = 0
+r_noised_vec = {24.6931118, 27.2978726, 21.4222109, 16.9271676, 19.2922507, 22.4250063, 13.4385345, 6.7195676}
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+seed = 1791
+------------------------------------------------------------
+PDOP = 4.012589 | it = 0
+r_noised_vec = {25.1249280, 26.3290788, 26.7920559, 18.0105992, 20.0203081, 21.2985264, 11.5889009, 8.5757439}
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+seed = 1793
+------------------------------------------------------------
+PDOP = 3.017460 | it = 0
+r_noised_vec = {26.2444041, 25.6674796, 14.7635445, 18.9353061, 20.8258669, 20.3089238, 9.5798784, 10.4889434}
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+seed = 1795
+------------------------------------------------------------
+PDOP = 1.861266 | it = 0
+r_noised_vec = {27.1319059, 25.0541005, 26.6556553, 19.9073292, 21.8622544, 19.4620781, 7.7784815, 12.4199865}
+anchors_optimal = {3, 5, 7, 6}
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+seed = 1797
+------------------------------------------------------------
+PDOP = 3.463486 | it = 0
+r_noised_vec = {27.6523581, 24.6181696, 13.3636135, 21.3811631, 22.9469969, 18.7707046, 6.0339128, 14.5116447}
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+------------------------------------------------------------
+PDOP = 2.684396 | it = 0
+r_noised_vec = {28.7226118, 24.3824885, 23.4148129, 22.6329944, 24.0286378, 18.4563433, 4.3738354, 16.4780808}
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+------------------------------------------------------------
+PDOP = 2.002181 | it = 0
+r_noised_vec = {30.3023109, 24.1609887, 15.7452133, 24.0513075, 25.5339599, 18.1907061, 3.3070426, 18.4339355}
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+------------------------------------------------------------
+PDOP = 306.024678 | it = 2
+r_noised_vec = {18.1523202, 26.3080181, 36.5901528, 26.2351659, 0.9994154, 18.9008175, 26.8028328, 19.1567215}
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+------------------------------------------------------------
+PDOP = 4.330355 | it = 0
+r_noised_vec = {17.8501167, 24.7937000, 35.1514360, 26.2239421, 2.3827272, 16.8630704, 25.4756449, 19.2226182}
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+------------------------------------------------------------
+PDOP = 4.199182 | it = 0
+r_noised_vec = {18.3295833, 23.4575353, 30.8561016, 26.3979170, 4.2425554, 15.0200837, 24.1211640, 19.4914683}
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+------------------------------------------------------------
+PDOP = 2.054337 | it = 0
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+------------------------------------------------------------
+PDOP = 2.185031 | it = 0
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+------------------------------------------------------------
+PDOP = 3.373223 | it = 0
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+------------------------------------------------------------
+PDOP = 2.527856 | it = 0
+r_noised_vec = {21.6169781, 19.1885660, 29.0123861, 28.8806736, 12.0023832, 7.0570806, 20.2713154, 22.2775015}
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+------------------------------------------------------------
+PDOP = 2.290837 | it = 0
+r_noised_vec = {23.0950617, 18.6568775, 37.0831140, 29.5605162, 13.9529161, 5.1105314, 19.6945712, 23.4283592}
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+------------------------------------------------------------
+PDOP = 3.312043 | it = 0
+r_noised_vec = {24.0516687, 18.2208891, 26.8007107, 30.7402466, 16.0567840, 3.2050492, 19.3471741, 24.6943051}
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+------------------------------------------------------------
+PDOP = 3.533829 | it = 0
+r_noised_vec = {25.1695390, 18.0365521, 27.5967044, 31.7856391, 18.0321929, 1.5037174, 19.2284156, 26.0670596}
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+------------------------------------------------------------
+PDOP = 3.537072 | it = 0
+r_noised_vec = {18.1892672, 26.3390047, 38.9614590, 24.6922524, 2.3710927, 19.2933062, 25.5710497, 16.9521117}
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+seed = 1825
+------------------------------------------------------------
+PDOP = 2.207499 | it = 0
+r_noised_vec = {18.4942165, 24.8592011, 26.5101036, 24.8895762, 3.0322478, 17.1904437, 24.1585193, 17.1153543}
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+seed = 1827
+------------------------------------------------------------
+PDOP = 2.035863 | it = 0
+r_noised_vec = {18.4239019, 23.6302463, 39.0652451, 25.0727588, 4.4906570, 15.2559504, 22.7906271, 17.4996825}
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+x_sol = {4.9058415, 2.9717661, 18.9843249}
+seed = 1829
+------------------------------------------------------------
+PDOP = 2.088714 | it = 0
+r_noised_vec = {18.8257452, 22.5353166, 24.3552834, 25.3208531, 6.2809507, 13.3212640, 21.4309028, 18.0860401}
+anchors_optimal = {1, 6, 5, 4}
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+x_sol = {6.8682702, 3.0834863, 19.1943269}
+seed = 1831
+------------------------------------------------------------
+PDOP = 1.944486 | it = 0
+r_noised_vec = {19.9638185, 21.2172075, 35.1821831, 26.2179882, 8.2461847, 11.3971789, 20.2355405, 18.8505954}
+anchors_optimal = {1, 6, 5, 4}
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+x_sol = {8.8711546, 3.1425944, 18.9282686}
+seed = 1833
+------------------------------------------------------------
+PDOP = 1.877624 | it = 0
+r_noised_vec = {20.9140851, 20.1489220, 26.0197485, 26.5940314, 10.1960774, 9.2979356, 19.1295955, 19.7575707}
+anchors_optimal = {1, 7, 4, 5}
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+x_sol = {10.9607471, 2.9631157, 18.9086172}
+seed = 1835
+------------------------------------------------------------
+PDOP = 1.874594 | it = 0
+r_noised_vec = {21.5236990, 19.3365002, 29.8238555, 27.4826224, 12.2679305, 7.4035634, 18.3536565, 21.0462924}
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+x_sol = {13.0181412, 3.0777907, 18.7307237}
+seed = 1837
+------------------------------------------------------------
+PDOP = 3.739221 | it = 0
+r_noised_vec = {22.6983070, 18.5488678, 28.7202979, 28.5603263, 14.2297668, 5.5358812, 17.6278460, 22.2102212}
+anchors_optimal = {0, 1, 6, 4}
+exact point = {15, 3, 19}
+x_sol = {15.0040170, 3.1471753, 18.7296547}
+seed = 1839
+------------------------------------------------------------
+PDOP = 2.918807 | it = 0
+r_noised_vec = {24.3995319, 18.2533835, 25.9503443, 29.3739022, 16.2951532, 3.7857360, 17.1183766, 23.4781751}
+anchors_optimal = {3, 1, 6, 5}
+exact point = {17, 3, 19}
+x_sol = {17.1035028, 3.1656048, 18.8909003}
+seed = 1841
+------------------------------------------------------------
+PDOP = 2.754434 | it = 0
+r_noised_vec = {25.6886715, 17.9751302, 30.0800060, 30.6351837, 18.1510976, 2.4570064, 17.0193446, 24.8363321}
+anchors_optimal = {3, 7, 6, 5}
+exact point = {19, 3, 19}
+x_sol = {19.1101395, 3.0362839, 18.9650286}
+seed = 1843
+------------------------------------------------------------
+PDOP = 2.684595 | it = 0
+r_noised_vec = {18.1803738, 26.4490828, 30.7524729, 23.4810594, 4.1011579, 19.4276793, 24.2023008, 15.0421710}
+anchors_optimal = {1, 3, 7, 4}
+exact point = {1, 5, 19}
+x_sol = {1.0883883, 4.9882260, 19.0550853}
+seed = 1845
+------------------------------------------------------------
+PDOP = 3.647622 | it = 0
+r_noised_vec = {18.4353526, 25.1348940, 33.4872855, 23.4486851, 4.4280160, 17.4451495, 22.7382606, 15.1381788}
+anchors_optimal = {3, 1, 0, 7}
+exact point = {3, 5, 19}
+x_sol = {2.8184035, 4.9853387, 18.9277605}
+seed = 1847
+------------------------------------------------------------
+PDOP = 2.200198 | it = 0
+r_noised_vec = {19.1449722, 23.8400414, 18.4285264, 23.8010136, 5.6790418, 15.4597508, 21.2783993, 15.5086965}
+anchors_optimal = {1, 6, 5, 4}
+exact point = {5, 5, 19}
+x_sol = {5.0591479, 4.8745689, 19.1669390}
+seed = 1849
+------------------------------------------------------------
+PDOP = 2.405346 | it = 0
+r_noised_vec = {19.4571160, 22.7613853, 36.6114733, 24.1898855, 7.2851236, 13.4620845, 19.9860150, 16.1373222}
+anchors_optimal = {3, 6, 5, 4}
+exact point = {7, 5, 19}
+x_sol = {7.1275081, 4.7575506, 18.7595910}
+seed = 1851
+------------------------------------------------------------
+PDOP = 3.547043 | it = 0
+r_noised_vec = {19.8119159, 21.5649538, 26.1595002, 24.5607282, 9.1037786, 11.6967751, 18.8349451, 17.0002709}
+anchors_optimal = {2, 3, 1, 7}
+exact point = {9, 5, 19}
+x_sol = {8.3660505, 4.7296785, 18.7689516}
+seed = 1853
+------------------------------------------------------------
+PDOP = 2.488714 | it = 0
+r_noised_vec = {20.9570331, 20.6625970, 26.9579229, 25.6478134, 10.8946044, 9.8041327, 17.5868103, 17.8267374}
+anchors_optimal = {3, 1, 4, 5}
+exact point = {11, 5, 19}
+x_sol = {11.0939839, 5.0185255, 19.2058395}
+seed = 1855
+------------------------------------------------------------
+PDOP = 2.222039 | it = 0
+r_noised_vec = {22.2909036, 19.7496361, 31.1028832, 26.2805343, 12.8219587, 7.9888002, 16.6700096, 19.0792742}
+anchors_optimal = {3, 6, 4, 5}
+exact point = {13, 5, 19}
+x_sol = {13.1468867, 4.8666239, 18.7156728}
+seed = 1857
+------------------------------------------------------------
+PDOP = 3.537554 | it = 0
+r_noised_vec = {23.1230736, 19.0611428, 21.2346376, 27.2121737, 14.5746165, 6.3021288, 15.9083941, 20.4512912}
+anchors_optimal = {0, 1, 6, 4}
+exact point = {15, 5, 19}
+x_sol = {15.0091938, 4.9208704, 18.9804496}
+seed = 1859
+------------------------------------------------------------
+PDOP = 3.257447 | it = 0
+r_noised_vec = {24.1269752, 18.6205553, 32.6557601, 28.4976291, 16.4691311, 5.0675993, 15.3207304, 21.9223863}
+anchors_optimal = {3, 4, 6, 7}
+exact point = {17, 5, 19}
+x_sol = {16.9618872, 4.9988364, 19.2325887}
+seed = 1861
+------------------------------------------------------------
+PDOP = 4.516624 | it = 0
+r_noised_vec = {25.8437473, 18.2897461, 20.4023331, 29.4731182, 18.2830527, 4.1860405, 14.9974730, 23.4685319}
+anchors_optimal = {3, 7, 1, 4}
+exact point = {19, 5, 19}
+x_sol = {18.8591556, 4.8025796, 18.8655975}
+seed = 1863
+------------------------------------------------------------
+PDOP = 34.132711 | it = 2
+r_noised_vec = {19.2473311, 26.7677942, 37.2456386, 22.1889117, 6.0266418, 19.8921177, 22.8590940, 13.0879881}
+anchors_optimal = {5, 1, 3, 7}
+exact point = {1, 7, 19}
+start_optimal = {1.048894, 6.948026, 18.948747}
+x_sol = {1.0467870, 6.9459187, 18.9425911}
+seed = 1865
+------------------------------------------------------------
+PDOP = 2.455812 | it = 0
+r_noised_vec = {18.9583430, 25.3435863, 27.7118913, 22.3611274, 6.4175428, 18.0145190, 21.3492886, 13.2554935}
+anchors_optimal = {1, 6, 7, 4}
+exact point = {3, 7, 19}
+x_sol = {3.1293680, 6.9599144, 18.9481183}
+seed = 1867
+------------------------------------------------------------
+PDOP = 2.258554 | it = 0
+r_noised_vec = {19.1368890, 24.1615682, 31.0183144, 22.5046326, 7.4308210, 16.1864272, 19.7470429, 13.6994346}
+anchors_optimal = {1, 6, 5, 4}
+exact point = {5, 7, 19}
+x_sol = {5.0583336, 7.1330190, 18.9679198}
+seed = 1869
+------------------------------------------------------------
+PDOP = 2.355521 | it = 0
+r_noised_vec = {20.0618146, 23.0353836, 28.9912219, 23.0116525, 8.6374539, 14.3705296, 18.2411430, 14.3935157}
+anchors_optimal = {1, 0, 7, 4}
+exact point = {7, 7, 19}
+x_sol = {7.1275660, 7.0113767, 19.1281788}
+seed = 1871
+------------------------------------------------------------
+PDOP = 1.922804 | it = 0
+r_noised_vec = {20.8184303, 21.9835338, 26.1277228, 23.7563109, 10.0599688, 12.6226776, 17.0273755, 15.5412738}
+anchors_optimal = {1, 6, 5, 4}
+exact point = {9, 7, 19}
+x_sol = {8.9702890, 7.0631704, 19.0248361}
+seed = 1873
+------------------------------------------------------------
+PDOP = 1.812487 | it = 0
+r_noised_vec = {21.2483055, 21.1580845, 28.7498408, 24.1441890, 11.6404392, 10.9668444, 15.8460178, 16.5704231}
+anchors_optimal = {1, 6, 4, 5}
+exact point = {11, 7, 19}
+x_sol = {10.9007407, 7.0572473, 19.1156016}
+seed = 1875
+------------------------------------------------------------
+PDOP = 1.923316 | it = 0
+r_noised_vec = {22.2555391, 20.2964369, 24.4387023, 25.3611334, 13.3700801, 9.4668178, 14.9032761, 17.7842888}
+anchors_optimal = {3, 1, 6, 4}
+exact point = {13, 7, 19}
+x_sol = {12.9722781, 6.8869693, 19.1087600}
+seed = 1877
+------------------------------------------------------------
+PDOP = 3.392595 | it = 0
+r_noised_vec = {23.8108102, 19.7434651, 41.4744077, 26.2690769, 15.0425462, 7.9307507, 14.0270309, 19.1336269}
+anchors_optimal = {3, 0, 7, 5}
+exact point = {15, 7, 19}
+x_sol = {15.2391883, 7.2602706, 19.0254927}
+seed = 1879
+------------------------------------------------------------
+PDOP = 2.623632 | it = 0
+r_noised_vec = {24.9757688, 19.2325216, 15.3314945, 27.2516306, 17.0851776, 6.8827888, 13.5133306, 20.5959898}
+anchors_optimal = {3, 7, 4, 5}
+exact point = {17, 7, 19}
+x_sol = {16.9350135, 7.0186447, 18.8804362}
+seed = 1881
+------------------------------------------------------------
+PDOP = 2.572499 | it = 0
+r_noised_vec = {25.8966241, 18.9715325, 31.2013866, 28.6953274, 19.0410755, 6.3045521, 13.3205766, 22.1545057}
+anchors_optimal = {7, 4, 1, 5}
+exact point = {19, 7, 19}
+x_sol = {18.9951363, 7.1247482, 18.9255702}
+seed = 1883
+------------------------------------------------------------
+PDOP = 3.804373 | it = 0
+r_noised_vec = {19.5834712, 27.3252866, 28.5074435, 21.0616283, 8.2672603, 20.8255602, 22.0447472, 10.9652422}
+anchors_optimal = {2, 6, 3, 4}
+exact point = {1, 9, 19}
+x_sol = {0.7873120, 9.2226015, 19.0974592}
+seed = 1885
+------------------------------------------------------------
+PDOP = 2.381757 | it = 0
+r_noised_vec = {20.0744431, 25.8765753, 29.4089774, 21.1424764, 8.4037319, 18.8517703, 20.3423164, 11.1539283}
+anchors_optimal = {1, 6, 7, 4}
+exact point = {3, 9, 19}
+x_sol = {2.8842179, 9.0845419, 18.6467032}
+seed = 1887
+------------------------------------------------------------
+PDOP = 3.038752 | it = 0
+r_noised_vec = {20.1687631, 24.6981457, 32.1183138, 21.5421922, 9.0058892, 17.0871668, 18.6484390, 11.6991762}
+anchors_optimal = {0, 6, 5, 7}
+exact point = {5, 9, 19}
+x_sol = {4.9501697, 9.0317629, 19.0710866}
+seed = 1889
+------------------------------------------------------------
+PDOP = 2.316452 | it = 0
+r_noised_vec = {20.3045510, 23.4873707, 22.5674477, 21.8938706, 9.9294234, 15.3537702, 17.0288762, 12.5579922}
+anchors_optimal = {1, 0, 7, 4}
+exact point = {7, 9, 19}
+x_sol = {6.8320582, 8.9444811, 18.7547722}
+seed = 1891
+------------------------------------------------------------
+PDOP = 2.215254 | it = 0
+r_noised_vec = {21.2383482, 22.5408853, 32.3624961, 22.5580673, 11.2484266, 13.6756807, 15.4862072, 13.5257104}
+anchors_optimal = {3, 6, 5, 7}
+exact point = {9, 9, 19}
+x_sol = {9.0032165, 9.1105692, 19.0768831}
+seed = 1893
+------------------------------------------------------------
+PDOP = 2.084120 | it = 0
+r_noised_vec = {22.3809604, 21.6790086, 20.2813849, 23.5475604, 12.8144475, 12.0822332, 13.9799822, 14.8689177}
+anchors_optimal = {3, 7, 4, 5}
+exact point = {11, 9, 19}
+x_sol = {10.9797291, 9.0032987, 19.2737601}
+seed = 1895
+------------------------------------------------------------
+PDOP = 2.064331 | it = 0
+r_noised_vec = {23.0394329, 20.9373856, 29.3844769, 24.0844425, 14.4639422, 10.6557156, 12.9891070, 16.3399542}
+anchors_optimal = {0, 7, 4, 5}
+exact point = {13, 9, 19}
+x_sol = {13.0174039, 8.9792506, 18.9634170}
+seed = 1897
+------------------------------------------------------------
+PDOP = 2.441126 | it = 0
+r_noised_vec = {23.8801426, 20.4513873, 21.5476389, 25.3762603, 16.2292136, 9.4285579, 11.9973469, 17.9043383}
+anchors_optimal = {3, 7, 4, 5}
+exact point = {15, 9, 19}
+x_sol = {15.0918335, 8.9953170, 19.0102436}
+seed = 1899
+------------------------------------------------------------
+PDOP = 2.389578 | it = 0
+r_noised_vec = {25.4497673, 19.9715686, 25.2896404, 26.5521271, 17.9343867, 8.4903736, 11.2504716, 19.5345264}
+anchors_optimal = {1, 7, 4, 5}
+exact point = {17, 9, 19}
+x_sol = {17.0672575, 8.9222238, 19.0993976}
+seed = 1901
+------------------------------------------------------------
+PDOP = 3.331553 | it = 0
+r_noised_vec = {26.9572898, 19.8286457, 24.0178202, 27.6024700, 19.8100189, 7.9071775, 11.0744970, 21.2117399}
+anchors_optimal = {0, 7, 4, 6}
+exact point = {19, 9, 19}
+x_sol = {19.1129849, 8.9868142, 19.2962796}
+seed = 1903
+------------------------------------------------------------
+PDOP = 3.310722 | it = 0
+r_noised_vec = {20.4737072, 28.0334747, 29.4066832, 20.2070381, 10.0343853, 21.4315285, 21.0854068, 9.1328406}
+anchors_optimal = {1, 5, 3, 4}
+exact point = {1, 11, 19}
+x_sol = {1.0625915, 10.9981525, 19.0938235}
+seed = 1905
+------------------------------------------------------------
+PDOP = 3.276347 | it = 0
+r_noised_vec = {20.4335590, 26.6845185, 30.7626326, 20.2315514, 10.0464356, 19.6429199, 19.2708384, 9.3247797}
+anchors_optimal = {0, 3, 6, 4}
+exact point = {3, 11, 19}
+x_sol = {3.1671314, 10.7161752, 18.8315649}
+seed = 1907
+------------------------------------------------------------
+PDOP = 3.303250 | it = 0
+r_noised_vec = {21.1354828, 25.4539382, 27.2184886, 20.4504122, 10.6888999, 17.9103898, 17.6050189, 9.9198926}
+anchors_optimal = {1, 0, 5, 7}
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+x_sol = {5.2054122, 11.0574594, 19.1084449}
+seed = 1909
+------------------------------------------------------------
+PDOP = 2.933778 | it = 0
+r_noised_vec = {21.6760057, 24.2351124, 38.6598419, 21.0624098, 11.6709581, 16.2374739, 15.9954190, 10.9397775}
+anchors_optimal = {1, 0, 3, 7}
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+x_sol = {7.4081198, 11.1901084, 19.0249046}
+seed = 1911
+------------------------------------------------------------
+PDOP = 2.936215 | it = 0
+r_noised_vec = {21.8939746, 23.3175254, 16.6652014, 21.6395863, 12.9092621, 14.8583275, 14.2684197, 12.0746193}
+anchors_optimal = {1, 0, 6, 4}
+exact point = {9, 11, 19}
+x_sol = {8.8062929, 11.2216346, 18.7288704}
+seed = 1913
+------------------------------------------------------------
+PDOP = 3.009326 | it = 0
+r_noised_vec = {22.6949957, 22.3742557, 30.7802994, 22.4680013, 14.2856801, 13.4320868, 12.8293328, 13.4252963}
+anchors_optimal = {3, 1, 4, 5}
+exact point = {11, 11, 19}
+x_sol = {11.1226237, 11.0119983, 18.9259569}
+seed = 1915
+------------------------------------------------------------
+PDOP = 2.887868 | it = 0
+r_noised_vec = {24.0616224, 21.7414731, 21.2857102, 23.6470743, 15.7045652, 12.1921181, 11.4883422, 14.9342638}
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+x_sol = {13.2921753, 10.7249658, 18.9499856}
+seed = 1917
+------------------------------------------------------------
+PDOP = 3.668919 | it = 0
+r_noised_vec = {25.0582415, 21.2027720, 23.2114202, 24.3784240, 17.2947572, 11.1912697, 10.3396896, 16.5629951}
+anchors_optimal = {3, 1, 4, 7}
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+x_sol = {14.9612063, 11.1519953, 18.9203882}
+seed = 1919
+------------------------------------------------------------
+PDOP = 3.032396 | it = 0
+r_noised_vec = {25.8219931, 20.9955113, 25.6996923, 25.7012775, 18.8466888, 10.4902920, 9.4852319, 18.2825822}
+anchors_optimal = {1, 4, 7, 6}
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+x_sol = {16.9285050, 11.0511807, 19.1815002}
+seed = 1921
+------------------------------------------------------------
+PDOP = 3.210974 | it = 0
+r_noised_vec = {27.2330030, 20.7202674, 18.5467178, 27.1141182, 20.5785143, 10.1246401, 8.9749557, 20.0697775}
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+------------------------------------------------------------
+PDOP = 3.782644 | it = 0
+r_noised_vec = {21.9071935, 29.0571059, 35.5140536, 19.1942777, 11.9058756, 22.5583644, 20.2401372, 7.0214918}
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+seed = 1925
+------------------------------------------------------------
+PDOP = 2.551167 | it = 0
+r_noised_vec = {21.7971711, 27.6040231, 23.3769811, 19.4589363, 12.1868225, 20.9529979, 18.3173804, 7.3286703}
+anchors_optimal = {0, 3, 6, 7}
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+seed = 1927
+------------------------------------------------------------
+PDOP = 3.343843 | it = 0
+r_noised_vec = {21.7144302, 26.4269537, 31.5480988, 19.7662276, 12.8777076, 19.5015092, 16.4655156, 8.0930588}
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+x_sol = {4.5298051, 12.8143120, 18.8703953}
+seed = 1929
+------------------------------------------------------------
+PDOP = 3.184734 | it = 0
+r_noised_vec = {22.4252161, 25.2295075, 23.2843886, 20.1490813, 13.5945987, 17.7884181, 14.7847619, 9.3261568}
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+x_sol = {6.9832176, 13.0747008, 18.9236903}
+seed = 1931
+------------------------------------------------------------
+PDOP = 2.267313 | it = 0
+r_noised_vec = {23.3546825, 24.1391297, 26.2606323, 20.9490267, 14.5197442, 16.4199934, 13.0823017, 10.7781240}
+anchors_optimal = {1, 5, 4, 6}
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+x_sol = {8.9528102, 13.0913043, 18.7389842}
+seed = 1933
+------------------------------------------------------------
+PDOP = 3.137726 | it = 0
+r_noised_vec = {23.8099542, 23.3372623, 24.0728919, 21.7495815, 15.6685175, 15.1833905, 11.5231246, 12.3714776}
+anchors_optimal = {2, 1, 5, 7}
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+x_sol = {7.5432052, 9.5822023, 18.7655912}
+seed = 1935
+------------------------------------------------------------
+PDOP = 2.567939 | it = 0
+r_noised_vec = {24.4528890, 22.5219010, 22.4256925, 22.5278996, 16.9125503, 14.1331206, 9.9828930, 14.0528042}
+anchors_optimal = {0, 1, 5, 6}
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+x_sol = {12.8870461, 13.1338670, 18.5918665}
+seed = 1937
+------------------------------------------------------------
+PDOP = 2.605380 | it = 0
+r_noised_vec = {25.8378811, 22.1209211, 23.4385238, 24.0513884, 18.3988463, 13.0834688, 8.7623031, 15.7910422}
+anchors_optimal = {1, 4, 7, 6}
+exact point = {15, 13, 19}
+x_sol = {15.0415541, 12.8463298, 19.0104385}
+seed = 1939
+------------------------------------------------------------
+PDOP = 1.922161 | it = 0
+r_noised_vec = {27.1814868, 21.7493829, 11.2125261, 25.0070278, 19.8933870, 12.4688971, 7.8455133, 17.5699316}
+anchors_optimal = {3, 1, 4, 6}
+exact point = {17, 13, 19}
+x_sol = {16.9014546, 12.8931445, 18.9353707}
+seed = 1941
+------------------------------------------------------------
+PDOP = 3.343213 | it = 0
+r_noised_vec = {28.0278234, 21.6625011, 31.8038759, 26.3328281, 21.6644359, 12.1367207, 7.1770719, 19.3823844}
+anchors_optimal = {4, 1, 7, 6}
+exact point = {19, 13, 19}
+x_sol = {19.0306964, 12.9650253, 19.0284904}
+seed = 1943
+------------------------------------------------------------
+PDOP = 4.872065 | it = 0
+r_noised_vec = {22.5481556, 29.7905945, 20.7275423, 18.8124296, 14.0761947, 23.6515572, 19.7216062, 5.1126076}
+anchors_optimal = {1, 5, 6, 3}
+exact point = {1, 15, 19}
+x_sol = {0.9442734, 14.9856423, 19.1337728}
+seed = 1945
+------------------------------------------------------------
+PDOP = 2.284262 | it = 0
+r_noised_vec = {23.0475946, 28.5254113, 34.1673810, 18.6969306, 14.3468313, 22.0413994, 17.7560690, 5.4752587}
+anchors_optimal = {1, 3, 6, 4}
+exact point = {3, 15, 19}
+x_sol = {2.9530224, 15.1668087, 18.9495362}
+seed = 1947
+------------------------------------------------------------
+PDOP = 3.668133 | it = 0
+r_noised_vec = {23.3812732, 27.4847285, 23.8271006, 19.1047198, 14.6533498, 20.5134965, 15.8246316, 6.3795010}
+anchors_optimal = {1, 0, 5, 6}
+exact point = {5, 15, 19}
+x_sol = {5.0072009, 14.9838045, 19.3054411}
+seed = 1949
+------------------------------------------------------------
+PDOP = 2.678206 | it = 0
+r_noised_vec = {23.3854634, 26.3234330, 25.6101285, 19.6887105, 15.2575473, 19.0613081, 13.8842185, 7.7382347}
+anchors_optimal = {1, 5, 4, 6}
+exact point = {7, 15, 19}
+x_sol = {7.0647179, 14.9884722, 19.1734121}
+seed = 1951
+------------------------------------------------------------
+PDOP = 3.125729 | it = 0
+r_noised_vec = {23.9684168, 25.4026894, 26.7247155, 20.2543205, 16.0236809, 17.7032547, 11.9571311, 9.3415410}
+anchors_optimal = {0, 3, 5, 4}
+exact point = {9, 15, 19}
+x_sol = {9.0092928, 14.8223027, 18.8612277}
+seed = 1953
+------------------------------------------------------------
+PDOP = 2.869950 | it = 0
+r_noised_vec = {25.1263805, 24.5119443, 19.5699459, 21.2121327, 17.1470506, 16.6555107, 10.2928536, 11.0915933}
+anchors_optimal = {1, 3, 5, 6}
+exact point = {11, 15, 19}
+x_sol = {11.0416412, 15.0121895, 19.0112994}
+seed = 1955
+------------------------------------------------------------
+PDOP = 2.486830 | it = 0
+r_noised_vec = {25.9286405, 23.7597733, 27.2007127, 22.2136389, 18.3431097, 15.6104530, 8.5655684, 12.9327438}
+anchors_optimal = {0, 3, 7, 6}
+exact point = {13, 15, 19}
+x_sol = {12.9707079, 15.2065433, 19.0839445}
+seed = 1957
+------------------------------------------------------------
+PDOP = 2.516547 | it = 0
+r_noised_vec = {26.5053206, 23.2737360, 17.5492066, 23.1189777, 19.8719736, 14.7842301, 7.0429152, 14.8303016}
+anchors_optimal = {1, 3, 7, 6}
+exact point = {15, 15, 19}
+x_sol = {14.9825050, 15.1714434, 18.7776127}
+seed = 1959
+------------------------------------------------------------
+PDOP = 3.450577 | it = 0
+r_noised_vec = {27.7378683, 22.8288291, 25.2029918, 24.7486354, 21.3550594, 14.1974816, 5.9081243, 16.7603842}
+anchors_optimal = {0, 1, 4, 6}
+exact point = {17, 15, 19}
+x_sol = {17.0324711, 15.0499665, 18.7460731}
+seed = 1961
+------------------------------------------------------------
+PDOP = 3.570580 | it = 0
+r_noised_vec = {29.3239858, 22.7594569, 18.8761907, 25.9383877, 23.0210505, 13.8517055, 5.2285393, 18.7053319}
+anchors_optimal = {3, 1, 2, 5}
+exact point = {19, 15, 19}
+x_sol = {18.8286679, 14.7547975, 19.0821878}
+seed = 1963
+------------------------------------------------------------
+PDOP = 1.750263 | it = 0
+r_noised_vec = {24.1573806, 30.5956897, 30.5412982, 18.1372648, 16.0713957, 24.8113896, 19.3828982, 3.1729498}
+anchors_optimal = {6, 3, 4, 7}
+exact point = {1, 17, 19}
+x_sol = {0.8781807, 17.0321618, 18.8919148}
+seed = 1965
+------------------------------------------------------------
+PDOP = 4.201513 | it = 0
+r_noised_vec = {23.8816753, 29.4799529, 27.7320380, 18.4828376, 16.1254455, 23.3071356, 17.3444073, 3.8976342}
+anchors_optimal = {1, 0, 5, 3}
+exact point = {3, 17, 19}
+x_sol = {2.6385997, 16.5189244, 19.0748699}
+seed = 1967
+------------------------------------------------------------
+PDOP = 3.312579 | it = 0
+r_noised_vec = {24.3856129, 28.4544056, 25.9092927, 18.6297159, 16.3424483, 21.9027576, 15.4459278, 5.2672238}
+anchors_optimal = {0, 5, 4, 6}
+exact point = {5, 17, 19}
+x_sol = {4.9038112, 16.8461607, 19.1205921}
+seed = 1969
+------------------------------------------------------------
+PDOP = 2.138295 | it = 0
+r_noised_vec = {25.1082074, 27.4280888, 34.4081984, 19.1710451, 17.0226366, 20.6148150, 13.5479371, 6.9437574}
+anchors_optimal = {1, 3, 4, 6}
+exact point = {7, 17, 19}
+x_sol = {6.8349009, 16.9604558, 19.0067403}
+seed = 1971
+------------------------------------------------------------
+PDOP = 2.057926 | it = 0
+r_noised_vec = {25.3572425, 26.6319901, 14.4874791, 20.0022433, 17.9076564, 19.4483830, 11.4836155, 8.7385747}
+anchors_optimal = {1, 3, 4, 6}
+exact point = {9, 17, 19}
+x_sol = {8.9162838, 17.0524196, 19.1420402}
+seed = 1973
+------------------------------------------------------------
+PDOP = 2.657798 | it = 0
+r_noised_vec = {25.7912876, 25.7662654, 32.1115232, 20.7575116, 18.9928334, 18.4181560, 9.5683410, 10.5868100}
+anchors_optimal = {0, 4, 5, 7}
+exact point = {11, 17, 19}
+x_sol = {11.0657698, 17.0433467, 18.5121788}
+seed = 1975
+------------------------------------------------------------
+PDOP = 4.088769 | it = 0
+r_noised_vec = {26.9740122, 25.1558543, 14.6292958, 21.8424226, 20.1236779, 17.5688363, 7.6451572, 12.4661617}
+anchors_optimal = {0, 1, 3, 6}
+exact point = {13, 17, 19}
+x_sol = {12.9942192, 17.0922608, 19.0227018}
+seed = 1977
+------------------------------------------------------------
+PDOP = 3.500031 | it = 0
+r_noised_vec = {28.1312727, 24.5972477, 26.9154094, 23.2348937, 21.3029180, 16.9318535, 5.8791798, 14.3701594}
+anchors_optimal = {0, 3, 4, 6}
+exact point = {15, 17, 19}
+x_sol = {14.9142457, 17.1186374, 19.3830051}
+seed = 1979
+------------------------------------------------------------
+PDOP = 3.465154 | it = 0
+r_noised_vec = {28.8018697, 24.1977243, 18.2955303, 24.0583362, 22.6562982, 16.3378651, 4.2534542, 16.2983769}
+anchors_optimal = {1, 4, 5, 7}
+exact point = {17, 17, 19}
+x_sol = {16.9837371, 17.0176515, 18.8843164}
+seed = 1981
+------------------------------------------------------------
+PDOP = 2.104893 | it = 0
+r_noised_vec = {29.8105095, 24.0557731, 21.1863911, 25.7200657, 24.0432031, 16.1417483, 3.1197912, 18.2529811}
+anchors_optimal = {3, 7, 5, 6}
+exact point = {19, 17, 19}
+x_sol = {19.0115322, 17.1006037, 19.1408016}
+seed = 1983
+------------------------------------------------------------
+PDOP = 2.809697 | it = 0
+r_noised_vec = {25.6096372, 31.6228816, 31.1302414, 18.0868846, 17.7785895, 26.3119502, 18.9906726, 1.1836037}
+anchors_optimal = {1, 6, 3, 4}
+exact point = {1, 19, 19}
+x_sol = {1.0600178, 18.7671559, 19.0581334}
+seed = 1985
+------------------------------------------------------------
+PDOP = 2.159741 | it = 0
+r_noised_vec = {25.7650732, 30.5653945, 23.9978153, 18.0057769, 18.0489909, 24.9395299, 16.9717173, 2.2523035}
+anchors_optimal = {5, 4, 3, 7}
+exact point = {3, 19, 19}
+x_sol = {2.7048927, 18.9392948, 18.8982929}
+seed = 1987
+------------------------------------------------------------
+PDOP = 2.902515 | it = 0
+r_noised_vec = {25.5765683, 29.4744232, 30.6282294, 18.5663793, 18.4732242, 23.6991277, 14.9975936, 4.0714470}
+anchors_optimal = {1, 5, 4, 7}
+exact point = {5, 19, 19}
+x_sol = {4.7002988, 19.0442982, 18.5813939}
+seed = 1989
+------------------------------------------------------------
+PDOP = 4.549573 | it = 0
+r_noised_vec = {25.9541147, 28.5817297, 20.7500102, 18.9920866, 19.1631923, 22.2769974, 13.0826967, 6.0321242}
+anchors_optimal = {1, 5, 4, 3}
+exact point = {7, 19, 19}
+x_sol = {7.1042981, 19.1099802, 18.9381753}
+seed = 1991
+------------------------------------------------------------
+PDOP = 1.853448 | it = 0
+r_noised_vec = {26.9076142, 27.7933828, 27.3087162, 19.6572015, 19.8427181, 21.1782210, 11.1533677, 8.0383994}
+anchors_optimal = {4, 3, 6, 7}
+exact point = {9, 19, 19}
+x_sol = {8.9267961, 19.1609893, 18.9681502}
+seed = 1993
+------------------------------------------------------------
+PDOP = 3.040343 | it = 0
+r_noised_vec = {27.5120123, 27.0342011, 20.5324911, 20.6888812, 20.6483364, 20.1989656, 9.2807457, 10.0607876}
+anchors_optimal = {0, 4, 5, 7}
+exact point = {11, 19, 19}
+x_sol = {10.9830417, 19.0561671, 19.1988691}
+seed = 1995
+------------------------------------------------------------
+PDOP = 3.330992 | it = 0
+r_noised_vec = {27.8916075, 26.5300846, 23.0665129, 21.6277761, 21.6140943, 19.3589777, 7.2115208, 12.0841340}
+anchors_optimal = {3, 4, 5, 6}
+exact point = {13, 19, 19}
+x_sol = {12.9315541, 18.9937890, 19.0093582}
+seed = 1997
+------------------------------------------------------------
+PDOP = 2.951965 | it = 0
+r_noised_vec = {28.9304661, 25.9724737, 21.2126867, 22.8139491, 22.7308881, 18.6996629, 5.3205427, 14.0988831}
+anchors_optimal = {0, 4, 5, 6}
+exact point = {15, 19, 19}
+x_sol = {14.8951547, 18.9570847, 18.9283841}
+seed = 1999
+------------------------------------------------------------
+PDOP = 2.672820 | it = 0
+r_noised_vec = {30.3373112, 25.7003223, 15.8549817, 24.3429666, 24.0634000, 18.2378209, 3.4823740, 16.0986999}
+anchors_optimal = {1, 3, 2, 6}
+exact point = {17, 19, 19}
+x_sol = {19.4789363, 21.2664769, 16.7961452}
+seed = 2001
+------------------------------------------------------------
+PDOP = 3.847112 | it = 0
+r_noised_vec = {31.2536703, 25.4769453, 27.4268245, 25.3080592, 25.4063381, 17.9730460, 1.7639750, 18.0751094}
+anchors_optimal = {0, 4, 3, 6}
+exact point = {19, 19, 19}
+x_sol = {18.5546411, 19.3498433, 19.2186813}
+----------------------------- End Simulation -------------------------------
+Counter = 999
+room point num = 999
+anchors num = 8
+LVM call number = 17.000000
+mean LVM call number = 0.017017
diff --git a/examples/example_results/optimization_test.txt b/examples/example_results/optimization_test.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1769d0b6b23e7002fdfceee8e4399cbcb9523ef4
--- /dev/null
+++ b/examples/example_results/optimization_test.txt
@@ -0,0 +1,99 @@
+**************** Testing the MicroPosMath-Lib!! 03/12/20 13:01:18 ****************
+***************** Optimization test *****************
+
+seeked_values_matrix = {
+ { 1.000, 1.000, 0.000},
+ { 1.000, 2.000, 0.000},
+ { 1.000, 3.000, 0.000},
+ { 2.000, 1.000, 0.000},
+ { 2.000, 2.000, 0.000},
+ { 2.000, 3.000, 0.000},
+ { 3.000, 1.000, 0.000},
+ { 3.000, 2.000, 0.000},
+ { 3.000, 3.000, 0.000}
+ };
+
+############## PARAMETERS #################
+eps = 1e-003
+tau = 1e-006
+fmin = 1e-011
+
+----------------------------------------- T1 ----------------------------------
+true vector value = {1.0000, 1.0000, 0.0000}
+start vector value = {0.9645166, 0.9894337, -0.1127879}
+Gauss-Newton solution = {0.9802478, 1.0010823, -0.0102076}
+iteration number = 3
+Levenberg-Marquardt solution = {0.9802478, 1.0010823, -0.0102076}
+iteration number = 3
+----------------------------------------- T2 ----------------------------------
+true vector value = {1.0000, 2.0000, 0.0000}
+start vector value = {0.9706874, 1.9937843, -0.0767517}
+Gauss-Newton solution = {0.9795361, 2.0017556, -0.0088006}
+iteration number = 3
+Levenberg-Marquardt solution = {0.9795361, 2.0017556, -0.0087994}
+iteration number = 2
+----------------------------------------- T3 ----------------------------------
+true vector value = {1.0000, 3.0000, 0.0000}
+start vector value = {0.9759567, 2.9980380, -0.0421651}
+Gauss-Newton solution = {0.9794494, 3.0021216, -0.0078297}
+iteration number = 2
+Levenberg-Marquardt solution = {0.9794494, 3.0021216, -0.0078297}
+iteration number = 2
+----------------------------------------- T4 ----------------------------------
+true vector value = {2.0000, 1.0000, 0.0000}
+start vector value = {1.9666907, 0.9892634, -0.1184331}
+Gauss-Newton solution = {1.9821901, 0.9982579, -0.0195254}
+iteration number = 3
+Levenberg-Marquardt solution = {1.9821896, 0.9982582, -0.0195230}
+iteration number = 2
+----------------------------------------- T5 ----------------------------------
+true vector value = {2.0000, 2.0000, 0.0000}
+start vector value = {1.9734193, 1.9945307, -0.0776960}
+Gauss-Newton solution = {1.9807405, 1.9997099, -0.0208893}
+iteration number = 3
+Levenberg-Marquardt solution = {1.9807406, 1.9997100, -0.0208879}
+iteration number = 2
+----------------------------------------- T6 ----------------------------------
+true vector value = {2.0000, 3.0000, 0.0000}
+start vector value = {1.9791861, 2.9997600, -0.0385668}
+Gauss-Newton solution = {1.9809479, 3.0014539, -0.0202003}
+iteration number = 2
+Levenberg-Marquardt solution = {1.9809479, 3.0014539, -0.0202003}
+iteration number = 2
+----------------------------------------- T7 ----------------------------------
+true vector value = {3.0000, 1.0000, 0.0000}
+start vector value = {2.9676093, 0.9886335, -0.1290797}
+Gauss-Newton solution = {2.9837993, 0.9951913, -0.0252817}
+iteration number = 3
+Levenberg-Marquardt solution = {2.9837980, 0.9951923, -0.0252798}
+iteration number = 2
+----------------------------------------- T8 ----------------------------------
+true vector value = {3.0000, 2.0000, 0.0000}
+start vector value = {2.9749588, 1.9950495, -0.0824135}
+Gauss-Newton solution = {2.9813853, 1.9981096, -0.0315086}
+iteration number = 3
+Levenberg-Marquardt solution = {2.9813854, 1.9981098, -0.0315072}
+iteration number = 2
+----------------------------------------- T9 ----------------------------------
+true vector value = {3.0000, 3.0000, 0.0000}
+start vector value = {2.9814874, 3.0015139, -0.0370967}
+Gauss-Newton solution = {2.9821952, 3.0019856, -0.0295741}
+iteration number = 2
+Levenberg-Marquardt solution = {2.9821952, 3.0019856, -0.0295741}
+iteration number = 2
+
+############### Test Gauss-Newton & LVM algorithms ###############
+
+Exponential Data:
+start value = {6.000000, 0.300000}
+Gauss-Newton solution = {7.000093, 0.262078}
+iteration number = 3
+Levenberg-Marquardt solution = {7.000090, 0.262078}
+iteration number = 3
+
+Sinusoidal Data:
+start value = {17.000000, 0.500000, 10.500000, 77.000000}
+Gauss-Newton solution = {16.552770, 0.465032, 10.837106, 76.292861}
+iteration number = 2
+Levenberg-Marquardt solution = {16.551824, 0.465067, 10.836856, 76.294166}
+iteration number = 2
diff --git a/examples/example_results/pinv_test.txt b/examples/example_results/pinv_test.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e92fb007e383e0dbdf0d40ad7bf9f90413554b99
--- /dev/null
+++ b/examples/example_results/pinv_test.txt
@@ -0,0 +1,137 @@
+**************** Testing the MicroPosMath-Lib!! 03/12/20 13:33:55 ****************
+
+
+++++++++++++++++++++++++++++++ QR Pseudo-Inverse ++++++++++++++++++++++++++++++
+
+************ Householder: MATRIX A ************
+Householder !!!!
+pinv_A = {
+ { 0.4443, 0.2321, -0.6020, 0.3083, 0.2243, -0.2235, -0.1356, -0.1991, 0.1551, 0.1044},
+ { -0.3757, 0.3558, 0.3456, -0.6042, 0.5472, -0.1283, 0.1363, 0.2453, 0.0728, -0.0866},
+ { 0.1020, -0.2385, 0.2072, 0.4753, 0.7903, 0.0340, 0.1776, -0.2598, -0.2873, -0.4797},
+ { 0.1923, 0.0776, -0.1805, -0.6930, -0.1703, 0.3056, 0.2575, 0.1059, 0.5269, -0.1320},
+ { -0.1350, -0.3361, 0.3667, 0.5515, -1.4222, 0.2822, -0.2158, 0.3005, -0.0908, 0.7449}
+ };
+
+************ Householder: MATRIX B ************
+Householder !!!!
+pinv_B = {
+ { 0.2150, 0.3125, -0.5303, 0.2803, 0.9696, -0.5553, -0.7392},
+ { 0.7550, 0.6248, -0.6419, -0.6979, 0.1876, 1.9666, -2.7736},
+ { 0.1937, -0.8510, -0.1891, 0.3615, 0.4971, 0.4637, -0.1897},
+ { -1.2069, -0.0661, 0.9477, 0.6014, -0.0246, -1.1941, 1.8148},
+ { 0.2754, -0.5344, 1.2077, -0.1488, -0.0477, -1.5360, 1.5157},
+ { 0.5698, 0.4190, 0.0174, 0.3728, -1.2926, 1.4093, -1.8186},
+ { -0.4571, 0.1207, 0.1235, -0.4794, -0.2530, -1.4440, 3.5404}
+ };
+
+************ Givens: MATRIX A ************
+Givens !!!
+pinv_A = {
+ { 0.4443, 0.2321, -0.6020, 0.3083, 0.2243, -0.2235, -0.1356, -0.1991, 0.1551, 0.1044},
+ { -0.3757, 0.3558, 0.3456, -0.6042, 0.5472, -0.1283, 0.1363, 0.2453, 0.0728, -0.0866},
+ { 0.1020, -0.2385, 0.2072, 0.4753, 0.7903, 0.0340, 0.1776, -0.2598, -0.2873, -0.4797},
+ { 0.1923, 0.0776, -0.1805, -0.6930, -0.1703, 0.3056, 0.2575, 0.1059, 0.5269, -0.1320},
+ { -0.1350, -0.3361, 0.3667, 0.5515, -1.4222, 0.2822, -0.2158, 0.3005, -0.0908, 0.7449}
+ };
+
+************ Givens: MATRIX B ************
+Givens !!!
+pinv_B = {
+ { 0.2150, 0.3125, -0.5303, 0.2803, 0.9696, -0.5553, -0.7392},
+ { 0.7550, 0.6248, -0.6419, -0.6979, 0.1876, 1.9666, -2.7736},
+ { 0.1937, -0.8510, -0.1891, 0.3615, 0.4971, 0.4637, -0.1897},
+ { -1.2069, -0.0661, 0.9477, 0.6014, -0.0246, -1.1941, 1.8148},
+ { 0.2754, -0.5344, 1.2077, -0.1488, -0.0477, -1.5360, 1.5157},
+ { 0.5698, 0.4190, 0.0174, 0.3728, -1.2926, 1.4093, -1.8186},
+ { -0.4571, 0.1207, 0.1235, -0.4794, -0.2530, -1.4440, 3.5404}
+ };
+
+
+
+++++++++++++++++++++++++++++++ Moore-Penrose Pseudo-Inverse ++++++++++++++++++++++++++++++
+
+pinv1 = {
+ { 0.1929222, -0.0153958, -0.0510431},
+ { 0.1665941, -0.0038045, -0.1302639},
+ { 0.0154620, -0.1582589, 0.0902300},
+ { -0.5018912, 0.0662716, 0.1090250}
+ };
+
+pinv2 = {
+ { 0.0016125, 0.0000280, 0.0018371},
+ { -0.0053906, -0.0191096, 0.0213637},
+ { 0.0102047, -0.0125148, -0.0056059},
+ { -0.0286827, 0.0022498, -0.0318171}
+ };
+
+########### Test 3: m < n : (2,3) ###########
+pinv3 = {
+ { 0.2833333, -0.1166667},
+ { 0.0666667, 0.2666667},
+ { 0.0833333, 0.0833333}
+ };
+
+########### Test 4: m > n : (3,2) ###########
+pinv4 = {
+ { -0.4117647, 0.1176471, 0.5882353},
+ { 0.5882353, 0.1176471, -0.4117647}
+ };
+
+########### Test 5: m = n : (4,4) ###########
+pinv5 = {
+ { 0.4677419, -0.9032258, 0.8064516, -0.3225806},
+ { 0.0537634, -0.1612903, 0.3225806, -0.1290323},
+ { 0.2903226, -0.8709677, 0.7419355, -0.0967742},
+ { -0.3010753, 0.9032258, -0.8064516, 0.3225806}
+ };
+
+########### Test 6: m < n : (4,7) ###########
+pinv6 = {
+ { -0.0409512, 0.0599057, -0.0593374, 0.1244804},
+ { 0.0753669, 0.0240347, -0.1214072, 0.0990684},
+ { 0.0233840, 0.0715069, -0.0926477, 0.0693273},
+ { 0.1306371, -0.0853891, 0.1341884, -0.2090739},
+ { 0.0306326, -0.0505254, 0.0423452, 0.0140961},
+ { -0.0498323, -0.0242453, 0.0931001, 0.0407283},
+ { -0.1645235, 0.1863886, -0.0220646, 0.1090861}
+ };
+
+########### Test 7: m = n (3, 3) ###########
+pinv7 = {
+ { -0.6666667, -1.3333333, 1.0000000},
+ { -0.6666667, 3.6666667, -2.0000000},
+ { 1.0000000, -2.0000000, 1.0000000}
+ };
+
+########### Test 8: m < n (5, 7) ###########
+pinv8 = {
+ { -0.0812286, 0.1577929, 0.1095004, -0.0051293, -0.0851231},
+ { 0.1566969, -0.2388769, -0.0036370, -0.0078878, 0.1456471},
+ { 0.1793644, -0.2239412, -0.2058249, 0.0778920, 0.1384461},
+ { -0.4761270, 0.5912117, 0.3612885, 0.2385908, -0.5533094},
+ { 0.2221671, -0.1203198, -0.0818366, -0.1881622, 0.1632612},
+ { -0.1422262, 0.1065645, -0.0301905, -0.0025897, 0.0749747},
+ { 0.0138054, 0.0468689, 0.1982004, -0.0854922, -0.0693175}
+ };
+
+########### Test 9: m > n (7, 5) ###########
+pinv9 = {
+ { -0.0434378, 0.0956633, -0.0139765, 0.0329355, 0.0904907, -0.2162322, -0.0376626},
+ { 0.0046990, -0.0780940, 0.1503789, -0.0671156, 0.0543225, 0.1227202, 0.0151531},
+ { 0.0067235, -0.0180006, -0.1017930, 0.1885946, -0.0524742, 0.0144159, -0.0656860},
+ { 0.0182215, -0.0192187, -0.0557228, 0.0494638, -0.0954845, 0.0267259, 0.1435169},
+ { 0.0880235, 0.0295377, 0.0871234, -0.2343556, 0.0105551, 0.1717566, 0.0318545}
+ };
+
+########### Test 10: m > n (5, 7) ###########
+pinv10 = {
+ { -0.1226635, 0.1929437, 0.1069447, 0.0267774, -0.1298527},
+ { 0.1801399, -0.2732942, -0.0437097, -0.0185220, 0.1933456},
+ { 0.1638409, -0.1960399, -0.1776830, 0.0541004, 0.1454298},
+ { -0.3690227, 0.4563202, 0.2833742, 0.2197539, -0.4939680},
+ { 0.2178785, -0.1275396, -0.1045516, -0.1784347, 0.1894125},
+ { -0.1376202, 0.0981498, 0.0033409, -0.0002629, 0.0628905},
+ { 0.0146783, 0.0532211, 0.1798108, -0.0884511, -0.0849223}
+ };
+
diff --git a/examples/example_results/pos_algos_common_test.txt b/examples/example_results/pos_algos_common_test.txt
new file mode 100644
index 0000000000000000000000000000000000000000..5f89b2b57df9f2214c34e2a0626c9562ffbef5ee
--- /dev/null
+++ b/examples/example_results/pos_algos_common_test.txt
@@ -0,0 +1,9 @@
+**************** Testing the MicroPosMath-Lib!! 03/11/20 12:29:50 ****************
+pdop_val = 8.4495751
+A_matrix = {
+ {1.0000000, -0.0000000, -0.0000000, -3.3400000},
+ {1.0000000, -9.0000000, -0.0000000, -1.5000000},
+ {1.0000000, -9.0000000, -8.9000000, -1.5000000},
+ {1.0000000, -0.0000000, -9.8400000, -1.7200000}
+ };
+
diff --git a/examples/example_results/position_optimization_test.txt b/examples/example_results/position_optimization_test.txt
new file mode 100644
index 0000000000000000000000000000000000000000..61334a4ac1fcaf7b45335dda569c5eff49bb4120
--- /dev/null
+++ b/examples/example_results/position_optimization_test.txt
@@ -0,0 +1,6 @@
+**************** Testing the MicroPosMath-Lib!! 03/12/20 13:53:15 ****************
+True position = {1.0000, 1.0000, 0.0000}
+Optimized position with Gauss-Newton algorithm = {0.9802478, 1.0010823, -0.0102076}
+iteration number = 3
+Optimized position with Levenberg-Marquardt algorithm = {0.9802478, 1.0010823, -0.0102076}
+iteration number = 3
diff --git a/examples/example_results/qr_givens.txt b/examples/example_results/qr_givens.txt
new file mode 100644
index 0000000000000000000000000000000000000000..79a797be3e9f301dbb0911d71425fb5b848a482f
--- /dev/null
+++ b/examples/example_results/qr_givens.txt
@@ -0,0 +1,94 @@
+**************** Testing the MicroPosMath-Lib!! 03/10/20 10:58:43 ****************
+c = 0.6097
+s = 0.7926
+t = 1.3000
+r = 164.0122
+************ MATRIX A ************
++++++++ Reduced QR-form +++++++
+red_Q = {
+ { 0.3655, -0.4666, 0.2411, -0.1772, 0.0735},
+ { 0.4064, 0.1403, -0.4483, -0.0432, 0.1830},
+ { 0.0570, 0.7001, 0.3279, 0.1421, -0.1997},
+ { 0.4098, -0.2673, 0.3313, 0.6320, -0.3003},
+ { 0.2837, 0.1996, 0.1277, 0.3120, 0.7745},
+ { 0.0437, 0.0461, 0.4879, -0.3315, -0.1537},
+ { 0.1249, 0.1454, 0.3595, -0.2337, 0.1175},
+ { 0.2454, 0.3579, -0.0908, -0.1353, -0.1637},
+ { 0.4296, -0.0454, 0.0366, -0.5136, 0.0494},
+ { 0.4329, 0.0878, -0.3611, 0.0560, -0.4056}
+ };
+
+red_R = {
+ { 2.2290, 1.9717, 1.4557, 0.9569, 1.6050},
+ { 0.0000, 1.2068, 0.4480, 0.0883, 0.5623},
+ { 0.0000, 0.0000, 1.3800, 0.9196, 0.5670},
+ { 0.0000, 0.0000, 0.0000, -0.9920, -0.1006},
+ { 0.0000, 0.0000, 0.0000, 0.0000, -0.5446}
+ };
++++++++ Full QR-form +++++++
+full_Q = {
+ { 0.3655, -0.4666, 0.2411, -0.1772, 0.0735, -0.5842, -0.2468, -0.0226, -0.3884, 0.0134},
+ { 0.4064, 0.1403, -0.4483, -0.0432, 0.1830, 0.2307, 0.0058, -0.5093, -0.3444, -0.3841},
+ { 0.0570, 0.7001, 0.3279, 0.1421, -0.1997, -0.4205, -0.2010, -0.3276, 0.0900, -0.0797},
+ { 0.4098, -0.2673, 0.3313, 0.6320, -0.3003, 0.2179, 0.1553, 0.0152, 0.1305, -0.2690},
+ { 0.2837, 0.1996, 0.1277, 0.3120, 0.7745, 0.0980, -0.1750, 0.1995, 0.0728, 0.2844},
+ { 0.0437, 0.0461, 0.4879, -0.3315, -0.1537, 0.6096, -0.4048, -0.0924, -0.2382, 0.1537},
+ { 0.1249, 0.1454, 0.3595, -0.2337, 0.1175, 0.0000, 0.8246, -0.0890, -0.2180, 0.1738},
+ { 0.2454, 0.3579, -0.0908, -0.1353, -0.1637, 0.0000, 0.0000, 0.7591, -0.2801, -0.3220},
+ { 0.4296, -0.0454, 0.0366, -0.5136, 0.0494, 0.0000, 0.0000, 0.0000, 0.7194, -0.1685},
+ { 0.4329, 0.0878, -0.3611, 0.0560, -0.4056, 0.0000, 0.0000, 0.0000, 0.0000, 0.7119}
+ };
+
+full_R = {
+ { 2.2290, 1.9717, 1.4557, 0.9569, 1.6050},
+ { 0.0000, 1.2068, 0.4480, 0.0883, 0.5623},
+ { 0.0000, 0.0000, 1.3800, 0.9196, 0.5670},
+ { 0.0000, 0.0000, 0.0000, -0.9920, -0.1006},
+ { 0.0000, 0.0000, 0.0000, 0.0000, -0.5446},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000}
+ };
+************ MATRIX B ************
++++++++ Reduced QR-form +++++++
+red_Q = {
+ { 0.4850, -0.1030, 0.1615, -0.7383, -0.3664, 0.1868, -0.1174},
+ { 0.5392, 0.1218, -0.7120, 0.0999, 0.3028, 0.2911, 0.0310},
+ { 0.0756, 0.5787, -0.0892, 0.3233, -0.7370, 0.0520, 0.0317},
+ { 0.5438, -0.4235, 0.4087, 0.5775, -0.0739, 0.0615, -0.1232},
+ { 0.3765, 0.2893, 0.0412, -0.0728, 0.1655, -0.8579, -0.0650},
+ { 0.0580, 0.5906, 0.4531, -0.0053, 0.4217, 0.3564, -0.3709},
+ { 0.1658, 0.1666, 0.2913, -0.0392, 0.1419, 0.1047, 0.9095}
+ };
+
+red_R = {
+ { 1.6798, 1.4417, 1.4571, 1.3083, 0.6039, 1.4164, 1.4034},
+ { 0.0000, 1.4789, 0.6963, 1.0763, 0.4720, 0.1135, 0.5475},
+ { 0.0000, 0.0000, 1.0233, 0.0774, -0.0054, 0.3097, 0.2588},
+ { 0.0000, 0.0000, 0.0000, 0.6779, -0.2445, 0.0929, -0.2062},
+ { 0.0000, 0.0000, 0.0000, 0.0000, -0.6319, -0.1504, 0.2334},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.5978, 0.3366},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.2569}
+ };
++++++++ Full QR-form +++++++
+full_Q = {
+ { 0.4850, -0.1030, 0.1615, -0.7383, -0.3664, 0.1868, -0.1174},
+ { 0.5392, 0.1218, -0.7120, 0.0999, 0.3028, 0.2911, 0.0310},
+ { 0.0756, 0.5787, -0.0892, 0.3233, -0.7370, 0.0520, 0.0317},
+ { 0.5438, -0.4235, 0.4087, 0.5775, -0.0739, 0.0615, -0.1232},
+ { 0.3765, 0.2893, 0.0412, -0.0728, 0.1655, -0.8579, -0.0650},
+ { 0.0580, 0.5906, 0.4531, -0.0053, 0.4217, 0.3564, -0.3709},
+ { 0.1658, 0.1666, 0.2913, -0.0392, 0.1419, 0.1047, 0.9095}
+ };
+
+full_R = {
+ { 1.6798, 1.4417, 1.4571, 1.3083, 0.6039, 1.4164, 1.4034},
+ { 0.0000, 1.4789, 0.6963, 1.0763, 0.4720, 0.1135, 0.5475},
+ { 0.0000, 0.0000, 1.0233, 0.0774, -0.0054, 0.3097, 0.2588},
+ { 0.0000, 0.0000, 0.0000, 0.6779, -0.2445, 0.0929, -0.2062},
+ { 0.0000, 0.0000, 0.0000, 0.0000, -0.6319, -0.1504, 0.2334},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.5978, 0.3366},
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.2569}
+ };
diff --git a/examples/example_results/solve_test.txt b/examples/example_results/solve_test.txt
new file mode 100644
index 0000000000000000000000000000000000000000..23fb7111e7738e4b7c18d105de50480b3aff49e6
--- /dev/null
+++ b/examples/example_results/solve_test.txt
@@ -0,0 +1,50 @@
+******************* Testing the MicroPosMath-Lib!! 03/29/19 22:32:25 *******************
+******* Determined system *******
+A1 = {
+ {2.0, 1.0, 1.0},
+ {-1.0, 1.0, -1.0},
+ {1.0, 2.0, 3.0}
+ };
+Moore Penrose:
+Moore Penrose !!!!
+
+x1 = {3.0, 1.0, -5.0}
+Householder:
+Householder !!!!
+
+x1 = {3.0, 1.0, -5.0}
+Givens:
+Givens !!!
+
+x1 = {3.0, 1.0, -5.0}
+******* Overdetermined system *******
+A2 = {
+ {25.0, 5.0, 1.0},
+ {64.0, 8.0, 1.0},
+ {100.0, 10.0, 1.0},
+ {144.0, 12.0, 1.0}
+ };
+Moore Penrose:
+Moore Penrose !!!!
+x2 = {0.0937, 23.2706, -12.4644}
+Householder:
+Householder !!!!
+x2 = {0.0937, 23.2706, -12.4644}
+Givens:
+Givens !!!
+x2 = {0.0937, 23.2706, -12.4644}
+******* Underdetermined system *******
+A3 = {
+ {2.0, -4.0, 2.0, -14.0},
+ {-1.0, 2.0, -2.0, 11.0},
+ {-1.0, 2.0, -1.0, 7.0}
+ };
+Moore Penrose:
+Moore Penrose !!!!
+x3 = {0.5957, -1.1915, -0.3617, -0.3404}
+Householder:
+Householder !!!!
+[solve_householder]: The equation is not solvable !!!
+Givens:
+Givens !!!
+[solve_givens]: The equation is not solvable !!!
diff --git a/examples/example_results/svd_test.txt b/examples/example_results/svd_test.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2a97bbe9fb0de284d09e61c3753d6bbf2f9d6a60
--- /dev/null
+++ b/examples/example_results/svd_test.txt
@@ -0,0 +1,309 @@
+******************* Testing the MicroPosMath-Lib!! 03/28/19 14:02:14 *******************
+########################## Test 1 ##########################
+matrix1 =
+{
+{ 1.0000, -3.6000, -1.2000, -2.8400},
+{ 1.0000, -7.2400, -7.1800, -2.2400},
+{ 1.0000, -12.0600, -1.3400, -3.6600}
+}
+U1 =
+{
+{-0.2791, -0.0695, -0.9577},
+{-0.5917, 0.7980, 0.1145},
+{-0.7563, -0.5986, 0.2638}
+}
+S1 =
+{
+{16.2937, 0.0000, 0.0000, 0.0000},
+{ 0.0000, 5.1678, 0.0000, 0.0000},
+{ 0.0000, 0.0000, 1.7021, 0.0000}
+}
+V1 =
+{
+{-0.0999, 0.0251, -0.3404, 0.9346},
+{ 0.8844, 0.3275, -0.3308, -0.0348},
+{ 0.3435, -0.9373, -0.0155, 0.0562},
+{ 0.2999, 0.1163, 0.8800, 0.3494}
+}
+s1 = {16.2937 , 5.1678 , 1.7021 , 0.0000 }
+########################## Test 2 ##########################
+matrix2 =
+{
+{ 1.0000, -22.0000, 30.0000, -20.0000},
+{ 1.0000, -26.0000, -42.0000, -10.0000},
+{ 1.0000, 18.0000, -30.0000, -14.0000}
+}
+U2 =
+{
+{ 0.4856, 0.6897, -0.5371},
+{-0.6969, 0.6764, 0.2385},
+{-0.5278, -0.2585, -0.8091}
+}
+S2 =
+{
+{59.8911, 0.0000, 0.0000, 0.0000},
+{ 0.0000, 41.0832, 0.0000, 0.0000},
+{ 0.0000, 0.0000, 21.7308, 0.0000}
+}
+V2 =
+{
+{-0.0123, 0.0270, -0.0510, -0.9983},
+{-0.0345, -0.9106, -0.4117, -0.0031},
+{ 0.9963, 0.0009, -0.0854, -0.0079},
+{ 0.0776, -0.4123, 0.9059, -0.0584}
+}
+s2 = {59.8911 , 41.0832 , 21.7308 , 0.0000 }
+######## Test 3: Singular Value Decomposition m < n : (2,3) ########
+########################## Test 3 ##########################
+matrix3 =
+{
+{ 3.0000, 1.0000, 1.0000},
+{-1.0000, 3.0000, 1.0000}
+}
+U3 =
+{
+{-0.7071, 0.7071},
+{-0.7071, -0.7071}
+}
+S3 =
+{
+{ 3.4641, 0.0000, 0.0000},
+{ 0.0000, 3.1623, 0.0000}
+}
+V3 =
+{
+{-0.4082, 0.8944, 0.1826},
+{-0.8165, -0.4472, 0.3651},
+{-0.4082, -0.0000, -0.9129}
+}
+s3 = {3.4641 , 3.1623 , 0.0000 }
+######## Test 4: Singular Value Decomposition m > n : (3,2) ########
+########################## Test 4 ##########################
+matrix4 =
+{
+{ 1.0000, 2.0000},
+{ 2.0000, 2.0000},
+{ 2.0000, 1.0000}
+}
+U4 =
+{
+{ 0.5145, -0.7071},
+{ 0.6860, 0.0000},
+{ 0.5145, 0.7071}
+}
+S4 =
+{
+{ 4.1231, 0.0000},
+{ 0.0000, 1.0000}
+}
+V4 =
+{
+{ 0.7071, 0.7071},
+{ 0.7071, -0.7071}
+}
+s4 = {4.1231 , 1.0000 }
+######## Test 5: Singular Value Decomposition m = n : (4,4) ########
+########################## Test 5 ##########################
+matrix5 =
+{
+{ 6.0000, 0.0000, 0.0000, 6.0000},
+{ 2.0000, 5.0000, 0.0000, 4.0000},
+{ 0.0000, 6.0000, 2.0000, 3.0000},
+{ 0.0000, 1.0000, 5.0000, 5.0000}
+}
+U5 =
+{
+{ 0.5517, -0.7792, 0.1068, -0.2777},
+{ 0.5086, 0.1759, 0.4722, 0.6981},
+{ 0.4717, 0.5854, 0.2019, -0.6277},
+{ 0.4631, 0.1387, -0.8514, 0.2035}
+}
+S5 =
+{
+{12.0734, 0.0000, 0.0000, 0.0000},
+{ 0.0000, 6.7089, 0.0000, 0.0000},
+{ 0.0000, 0.0000, 5.1011, 0.0000},
+{ 0.0000, 0.0000, 0.0000, 0.4502}
+}
+V5 =
+{
+{ 0.3584, -0.6444, 0.3107, -0.5998},
+{ 0.4834, 0.6753, 0.5334, -0.1604},
+{ 0.2699, 0.2779, -0.7554, -0.5285},
+{ 0.7517, -0.2268, -0.2199, 0.5789}
+}
+s5 = {12.0734 , 6.7089 , 5.1011 , 0.4502 }
+######## Test 6: Singular Value Decomposition m < n : (4,7) ########
+########################## Test 6 ##########################
+matrix6 =
+{
+{ 2.0000, 5.0000, 4.0000, 6.0000, 3.0000, 2.0000, 1.0000},
+{ 1.0000, 2.0000, 4.0000, 6.0000, 0.0000, 0.0000, 6.0000},
+{ 2.0000, 1.0000, 1.0000, 5.0000, 4.0000, 6.0000, 3.0000},
+{ 3.0000, 3.0000, 1.0000, 0.0000, 4.0000, 5.0000, 0.0000}
+}
+U6 =
+{
+{-0.5795, -0.0774, 0.7057, 0.4003},
+{-0.4884, -0.6948, -0.2003, -0.4884},
+{-0.5553, 0.2884, -0.6601, 0.4156},
+{-0.3425, 0.6542, 0.1618, -0.6546}
+}
+S6 =
+{
+{15.7749, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+{ 0.0000, 8.0819, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+{ 0.0000, 0.0000, 4.5200, 0.0000, 0.0000, 0.0000, 0.0000},
+{ 0.0000, 0.0000, 0.0000, 2.3248, 0.0000, 0.0000, 0.0000}
+}
+V6 =
+{
+{-0.2400, 0.2091, 0.0833, -0.3529, 0.8759, 0.0000, 0.0000},
+{-0.3459, 0.0587, 0.6533, -0.2252, -0.2616, -0.0906, 0.5680},
+{-0.3277, -0.2656, 0.3370, -0.2545, -0.1609, 0.4128, -0.6689},
+{-0.5822, -0.3949, -0.0593, 0.6664, 0.2089, 0.0143, 0.1172},
+{-0.3379, 0.4378, 0.0274, 0.1053, -0.1572, -0.6916, -0.4235},
+{-0.3932, 0.5997, -0.3850, 0.0091, -0.2106, 0.5251, 0.1318},
+{-0.3281, -0.4184, -0.5479, -0.5521, -0.1604, -0.2593, 0.1394}
+}
+s6 = {15.7749 , 8.0819 , 4.5200 , 2.3248 , 0.0000 }
+######## Test 7: Singular Value Decomposition m = n : (3,3) ########
+########################## Test 7 ##########################
+matrix7 =
+{
+{ 1.0000, 2.0000, 3.0000},
+{ 4.0000, 5.0000, 6.0000},
+{ 7.0000, 8.0000, 10.0000}
+}
+U7 =
+{
+{ 0.2093, 0.9644, -0.1617},
+{ 0.5038, 0.0353, 0.8631},
+{ 0.8380, -0.2621, -0.4785}
+}
+S7 =
+{
+{17.4125, 0.0000, 0.0000},
+{ 0.0000, 0.8752, 0.0000},
+{ 0.0000, 0.0000, 0.1969}
+}
+V7 =
+{
+{ 0.4647, -0.8333, -0.2995},
+{ 0.5538, 0.0095, 0.8326},
+{ 0.6910, 0.5528, -0.4659}
+}
+s7 = {17.4125 , 0.8752 , 0.1969 }
+######## Test 8: Singular Value Decomposition m < n : (5,7) ########
+########################## Test 8 ##########################
+matrix8 =
+{
+{ 6.0000, 2.0000, 7.0000, 3.0000, 6.0000, 0.0000, 1.0000},
+{ 7.0000, 1.0000, 6.0000, 3.0000, 6.0000, 4.0000, 0.0000},
+{ 3.0000, 5.0000, 1.0000, 1.0000, 0.0000, 2.0000, 3.0000},
+{ 5.0000, 5.0000, 7.0000, 3.0000, 1.0000, 3.0000, 0.0000},
+{ 6.0000, 5.0000, 4.0000, 1.0000, 2.0000, 7.0000, 1.0000}
+}
+U8 =
+{
+{-0.4811, 0.5418, 0.3805, 0.3085, -0.4848},
+{-0.5236, 0.3667, -0.4939, 0.0686, 0.5854},
+{-0.2268, -0.5127, 0.3728, 0.6476, 0.3569},
+{-0.4658, -0.1883, 0.4812, -0.6932, 0.1886},
+{-0.4754, -0.5232, -0.4906, -0.0176, -0.5092}
+}
+S8 =
+{
+{22.0562, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+{ 0.0000, 7.8623, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+{ 0.0000, 0.0000, 4.5429, 0.0000, 0.0000, 0.0000, 0.0000},
+{ 0.0000, 0.0000, 0.0000, 3.3732, 0.0000, 0.0000, 0.0000},
+{ 0.0000, 0.0000, 0.0000, 0.0000, 0.8324, 0.0000, 0.0000}
+}
+V8 =
+{
+{-0.5628, 0.0253, -0.1305, 0.2083, 0.1775, 0.7686, 0.0000},
+{-0.3321, -0.5940, 0.4589, 0.1096, -0.2437, -0.1192, -0.4906},
+{-0.5395, 0.2632, 0.3257, -0.5052, -0.2891, -0.1448, 0.4171},
+{-0.2318, 0.1431, 0.2170, -0.0943, 0.8595, -0.3106, -0.1859},
+{-0.3375, 0.5363, -0.2598, 0.4548, -0.2713, -0.3695, -0.3376},
+{-0.3297, -0.4815, -0.7089, -0.1877, 0.0682, -0.3109, 0.1429},
+{-0.0742, -0.1932, 0.2220, 0.6622, 0.0921, -0.2110, 0.6453}
+}
+s8 = {22.0562 , 7.8623 , 4.5429 , 3.3732 , 0.8324 , 0.0000 }
+######## Test 9: Singular Value Decomposition m > n : (7,5) ########
+########################## Test 9 ##########################
+matrix9 =
+{
+{ 6.3950, 2.8970, 7.3330, 3.7770, 6.5430},
+{ 7.6350, 1.2350, 6.3010, 3.3560, 6.7770},
+{ 3.5950, 5.9010, 1.4080, 1.6970, 0.5390},
+{ 5.5010, 5.5620, 7.2710, 3.9070, 1.6510},
+{ 6.1980, 5.0690, 4.2380, 1.3880, 2.8550},
+{ 0.0000, 1.9990, 4.1030, 0.5610, 2.9080},
+{ 3.8340, 3.1720, 0.0090, 7.0690, 1.0750}
+}
+U9 =
+{
+{ 0.5102, 0.3235, 0.1290, 0.1239, 0.1815},
+{ 0.4888, 0.4208, 0.3600, -0.3166, -0.1020},
+{ 0.2377, -0.4802, -0.3410, -0.2860, 0.4013},
+{ 0.4529, -0.2095, -0.3568, 0.4311, -0.6507},
+{ 0.3797, -0.1215, -0.3098, -0.5047, 0.0424},
+{ 0.1745, 0.2302, -0.2810, 0.5547, 0.5906},
+{ 0.2539, -0.6132, 0.6598, 0.2331, 0.1471}
+}
+S9 =
+{
+{24.2351, 0.0000, 0.0000, 0.0000, 0.0000},
+{ 0.0000, 7.7588, 0.0000, 0.0000, 0.0000},
+{ 0.0000, 0.0000, 5.7846, 0.0000, 0.0000},
+{ 0.0000, 0.0000, 0.0000, 3.6211, 0.0000},
+{ 0.0000, 0.0000, 0.0000, 0.0000, 2.3081}
+}
+V9 =
+{
+{ 0.5640, -0.0905, 0.1720, -0.6948, -0.4018},
+{ 0.3748, -0.5985, -0.5562, -0.0089, 0.4382},
+{ 0.5272, 0.4186, -0.4010, 0.4929, -0.3782},
+{ 0.3367, -0.4349, 0.6568, 0.5145, -0.0379},
+{ 0.3875, 0.5189, 0.2625, -0.0978, 0.7085}
+}
+s9 = {24.2351 , 7.7588 , 5.7846 , 3.6211 , 2.3081 }
+######## Test 10: Singular Value Decomposition m > n : (5,7) ########
+########################## Test 10 ##########################
+matrix10 =
+{
+{ 6.3950, 2.8970, 7.3330, 3.7770, 6.5430, 0.0000, 1.9990},
+{ 7.6350, 1.2350, 6.3010, 3.3560, 6.7770, 4.1030, 0.5610},
+{ 3.5950, 5.9010, 1.4080, 1.6970, 0.5390, 2.9080, 3.8340},
+{ 5.5010, 5.5620, 7.2710, 3.9070, 1.6510, 3.1720, 0.0090},
+{ 6.1980, 5.0690, 4.2380, 1.3880, 2.8550, 7.0690, 1.0750}
+}
+U10 =
+{
+{-0.4874, 0.5058, 0.4552, 0.2782, -0.4712},
+{-0.5142, 0.3948, -0.4900, 0.1408, 0.5655},
+{-0.2769, -0.5923, 0.3700, 0.5647, 0.3416},
+{-0.4638, -0.1675, 0.3646, -0.7638, 0.2013},
+{-0.4541, -0.4577, -0.5319, -0.0224, -0.5486}
+}
+S10 =
+{
+{24.4099, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+{ 0.0000, 7.9272, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000},
+{ 0.0000, 0.0000, 4.9730, 0.0000, 0.0000, 0.0000, 0.0000},
+{ 0.0000, 0.0000, 0.0000, 3.8946, 0.0000, 0.0000, 0.0000},
+{ 0.0000, 0.0000, 0.0000, 0.0000, 0.9255, 0.0000, 0.0000}
+}
+V10 =
+{
+{-0.5491, 0.0455, -0.1590, 0.1398, 0.2592, 0.7644, 0.0000},
+{-0.3508, -0.6048, 0.4482, -0.0126, -0.3370, -0.0062, -0.4433},
+{-0.5121, 0.2781, 0.2350, -0.4944, -0.2940, -0.1455, 0.5031},
+{-0.2654, 0.1186, 0.2793, -0.1369, 0.7811, -0.3795, -0.2541},
+{-0.3640, 0.5149, -0.2130, 0.4504, -0.3242, -0.3089, -0.3918},
+{-0.3112, -0.4881, -0.7113, -0.0926, 0.0805, -0.3527, 0.1393},
+{-0.1154, -0.1932, 0.2986, 0.7111, 0.1049, -0.1749, 0.5594}
+}
+s10 = {24.4099 , 7.9272 , 4.9730 , 3.8946 , 0.9255 , 0.0000 }
diff --git a/examples/example_results/tmp.txt b/examples/example_results/tmp.txt
new file mode 100644
index 0000000000000000000000000000000000000000..2ef806294ee5e3331b6b68eb03b2502919f96577
--- /dev/null
+++ b/examples/example_results/tmp.txt
@@ -0,0 +1,165 @@
+**************** Testing the MicroPosMath-Lib!! 01/09/20 15:13:36 ****************
+************* MILPS: Real positioning of paper experiment (Three Anchors) *************
+***** Real positioning of paper experiment (On MCU: Three Anchors) *****
+############## PARAMETERS #################
+eps = 1e-003
+tau = 1e-006
+fmin = 1e-003
+**********************************************************************************
+Sensor8a1:
+B_vec = {52.5070000, 3.3031000, 1.7160000}
+
+---------------------------- Sensor8a1: ----------------------------
+true position = {102.0000, 18.0000, 0.6550}
+start position = {102.0905149, 18.0292459, 1.0790493}
+Gauss-Newton = {101.9283962, 18.0457408, 1.0790493}
+iteration number = 3
+Levenberg-Marquardt = {101.9283686, 18.0455982, 1.0794787}
+iteration number = 2
+
+-----------------------------------------------------------------------------
+**********************************************************************************
+Sensor8a2:
+B_vec = {52.1430000, 3.2310000, 1.4700000}
+
+---------------------------- Sensor8a2: ----------------------------
+true position = {102.0000, 18.0000, 1.4230}
+start position = {101.6974329, 18.0366298, 1.9765389}
+Gauss-Newton = {101.7162507, 17.9891733, 2.4568367}
+iteration number = 2
+Levenberg-Marquardt = {101.7160239, 17.9904800, 2.4560520}
+iteration number = 3
+
+-----------------------------------------------------------------------------
+**********************************************************************************
+Sensor8a3:
+B_vec = {43.2630000, 3.0620000, 1.4890000}
+
+---------------------------- Sensor8a3: ----------------------------
+true position = {102.0000, 18.0000, 2.3080}
+start position = {101.7988503, 17.9812062, 2.5227716}
+Gauss-Newton = {101.8317628, 17.9321926, 2.6741388}
+iteration number = 2
+Levenberg-Marquardt = {101.8317628, 17.9321926, 2.6741389}
+iteration number = 2
+
+-----------------------------------------------------------------------------
+**********************************************************************************
+Sensor12a1:
+B_vec = {7.7690000, 2.1510000, 2.9050000}
+
+---------------------------- Sensor12a1: ----------------------------
+true position = {104.0000, 18.0000, 0.6550}
+start position = {103.9518494, 18.0188884, 1.4051588}
+The minimum rank-value of a matrix is one
+Gauss-Newton = {103.9486032, 18.0220887, 1.2577644}
+iteration number = 14
+Levenberg-Marquardt = {103.9413939, 18.0248890, 1.0598070}
+iteration number = 3
+
+-----------------------------------------------------------------------------
+**********************************************************************************
+Sensor12a2:
+B_vec = {7.7480000, 2.1280000, 2.8820000}
+
+---------------------------- Sensor12a2: ----------------------------
+true position = {104.0000, 18.0000, 1.4230}
+start position = {103.9460100, 18.0083354, 1.4996519}
+The minimum rank-value of a matrix is one
+Gauss-Newton = {103.9460100, 18.0083354, 1.4996519}
+iteration number = 8
+Levenberg-Marquardt = {103.9517046, 18.0054312, 1.0042607}
+iteration number = 2
+
+-----------------------------------------------------------------------------
+**********************************************************************************
+Sensor12a3:
+B_vec = {7.5030000, 2.0440000, 2.7600000}
+
+---------------------------- Sensor12a3: ----------------------------
+true position = {104.0000, 18.0000, 2.3080}
+start position = {103.9568950, 17.9414253, 2.3897192}
+Gauss-Newton = {103.9682921, 17.9382284, 2.4539023}
+iteration number = 2
+Levenberg-Marquardt = {103.9568950, 17.9414253, 2.3897192}
+iteration number = 0
+
+-----------------------------------------------------------------------------
+**********************************************************************************
+Sensor8b1:
+B_vec = {9.4650000, 13.9740000, 3.3310000}
+
+---------------------------- Sensor8b1: ----------------------------
+true position = {102.0000, 20.0000, 0.6550}
+start position = {102.0262678, 19.9733240, 1.0756360}
+Gauss-Newton = {101.8652610, 19.9910786, 1.0756360}
+iteration number = 3
+Levenberg-Marquardt = {101.8652640, 19.9910796, 1.0813598}
+iteration number = 3
+
+-----------------------------------------------------------------------------
+**********************************************************************************
+Sensor8b2:
+B_vec = {9.2240000, 13.7440000, 3.2460000}
+
+---------------------------- Sensor8b2: ----------------------------
+true position = {102.0000, 20.0000, 1.4230}
+start position = {101.9842702, 19.9817579, 1.0756874}
+Gauss-Newton = {101.9197808, 19.9921115, 1.0756874}
+iteration number = 2
+Levenberg-Marquardt = {101.9197977, 19.9921073, 1.0781073}
+iteration number = 2
+
+-----------------------------------------------------------------------------
+**********************************************************************************
+Sensor8b3:
+B_vec = {8.7350000, 13.1390000, 3.1640000}
+
+---------------------------- Sensor8b3: ----------------------------
+true position = {102.0000, 20.0000, 2.3080}
+start position = {101.9619519, 19.9981048, 2.2787830}
+Gauss-Newton = {101.9608138, 20.0044513, 2.2592678}
+iteration number = 1
+Levenberg-Marquardt = {101.9619519, 19.9981048, 2.2787830}
+iteration number = 0
+
+-----------------------------------------------------------------------------
+**********************************************************************************
+Sensor12b1:
+B_vec = {3.7550000, 5.5710000, 9.0800000}
+
+---------------------------- Sensor12b1: ----------------------------
+true position = {104.0000, 20.0000, 0.6550}
+start position = {103.9302551, 20.0017760, 1.5535869}
+Gauss-Newton = {103.9281799, 20.0057060, 1.9735674}
+iteration number = 5
+Levenberg-Marquardt = {103.9281780, 20.0055105, 1.9838842}
+iteration number = 2
+
+-----------------------------------------------------------------------------
+**********************************************************************************
+Sensor12b2:
+B_vec = {3.6620000, 5.5510000, 9.1490000}
+
+---------------------------- Sensor12b2: ----------------------------
+true position = {104.0000, 20.0000, 1.4230}
+start position = {103.9343889, 20.0341990, 1.6600619}
+Gauss-Newton = {103.9429796, 20.0345795, 2.2738341}
+iteration number = 5
+Levenberg-Marquardt = {103.9429980, 20.0346843, 2.2759125}
+iteration number = 3
+
+-----------------------------------------------------------------------------
+**********************************************************************************
+Sensor12b3:
+B_vec = {3.5300000, 5.5070000, 8.8960000}
+
+---------------------------- Sensor12b3: ----------------------------
+true position = {104.0000, 20.0000, 2.3080}
+start position = {103.9215386, 20.0822974, 2.4845738}
+Gauss-Newton = {103.9392940, 20.0804785, 2.7232693}
+iteration number = 3
+Levenberg-Marquardt = {103.9393186, 20.0804830, 2.7240359}
+iteration number = 2
+
+-----------------------------------------------------------------------------
diff --git a/examples/example_results/utils_tests.txt b/examples/example_results/utils_tests.txt
new file mode 100644
index 0000000000000000000000000000000000000000..1e449ddf0a473589b06b4de7a02115da5545cfba
--- /dev/null
+++ b/examples/example_results/utils_tests.txt
@@ -0,0 +1,14 @@
+******************* Testing the MicroPosMath-Lib!! 09/18/19 22:26:21 *******************
+
+########### Test: utiles ###########
+arr = { 4, 8, 6, -1, -2, -3, -1, 3, 4, 5}
+win_size = 5
+mv_av_arr = {0.8000, 2.4000, 3.6000, 3.4000, 3.0000, 1.6000, -0.2000, -0.8000, 0.2000, 1.6000}
+mean = 2.3000
+!!! Median algorithm !!!
+arr1 = {100, 91, 92, 85, 40, 77, 92, 91, 94}
+median1 = 91.0000
+arr2 = {0.4854, 0.8003, 0.1419, 0.4218, 0.9157, 0.7922, 0.9595, 0.6557, 0.0357, 0.8491, 0.9340, 0.6787, 0.7577}
+median2 = 0.7577
+arr3 = {0.9502, 0.0344, -0.4387, 0.3816, 0.7655, 0.7952, 0.1869, 0.4898, 0.4456, 0.6463, -0.7094, 0.7547}
+median3 = 0.4677
diff --git a/examples/linear_algebra/basic_operations/include/matrix_test.h b/examples/linear_algebra/basic_operations/include/matrix_test.h
new file mode 100644
index 0000000000000000000000000000000000000000..bb7b23a35cf136ed1d7adf469cba041089877684
--- /dev/null
+++ b/examples/linear_algebra/basic_operations/include/matrix_test.h
@@ -0,0 +1,45 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @ingroup examples
+ * @{
+ *
+ * @file
+ * @brief Examples of matrix computations.
+ *
+ * @details Matrix computation examples (see @ref matrix.h "matrix" functions).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#ifndef MATRIX_TEST_H_
+#define MATRIX_TEST_H_
+
+/**
+ * @brief Test some matrix operations.
+ *
+ */
+void matrix_test(void);
+
+/**
+ * @brief Examples of the inverse of triangular matrices.
+ *
+ */
+void inv_triangular_matrices_test(void);
+
+/**
+ * @brief Examples of triangular matrices.
+ *
+ */
+void triangular_matrices_test(void);
+
+#endif /* MATRIX_TEST_H_ */
diff --git a/examples/linear_algebra/basic_operations/include/vector_test.h b/examples/linear_algebra/basic_operations/include/vector_test.h
new file mode 100644
index 0000000000000000000000000000000000000000..1523ec574e2323214d3ac569e5efbc7e8a4631ef
--- /dev/null
+++ b/examples/linear_algebra/basic_operations/include/vector_test.h
@@ -0,0 +1,33 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @ingroup examples
+ * @{
+ *
+ * @file
+ * @brief Examples of vector computations.
+ *
+ * @details Vector computation examples (see @ref vector.h "vector" functions).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#ifndef VECTOR_TEST_H_
+#define VECTOR_TEST_H_
+
+/**
+ * @brief Examples of vector operations.
+ *
+ */
+void vector_test(void);
+
+#endif /* VECTOR_TEST_H_ */
diff --git a/examples/linear_algebra/basic_operations/matrix_test.c b/examples/linear_algebra/basic_operations/matrix_test.c
new file mode 100644
index 0000000000000000000000000000000000000000..09624a57a135e7dd49ebfb734973a89322900c19
--- /dev/null
+++ b/examples/linear_algebra/basic_operations/matrix_test.c
@@ -0,0 +1,298 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @{
+ *
+ * @file
+ * @brief Examples of matrix computations.
+ *
+ * @details Matrix computation examples of the (see @ref matrix.h "matrix" functions).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#include <stdio.h>
+#include <stdint.h>
+#include <inttypes.h>
+#include <math.h>
+
+#include "utils.h"
+#include "matrix.h"
+
+void matrix_test(void)
+{
+ puts("############ Basic Matrix Algebra ###############");
+ uint8_t m = 3;
+ uint8_t n = 4;
+ matrix_t diag_elem = M_PI;
+
+ matrix_t matrix1[3][4] = { { 0.2785, 0.9649, 0.9572, 0.1419 },
+ { 0.5469, 0.1576, 0.4854, 0.4218 },
+ { 0.9575, 0.9706, 0.8003, 0.9157 },
+ };
+
+ matrix_t matrix2[3][4] = { { 0.7922, 0.0357, 0.6787, 0.3922 },
+ { 0.9595, 0.8491, 0.7577, 0.6555 },
+ { 0.6557, 0.9340, 0.7431, 0.1712 },
+ };
+ matrix_t res_matrix[m][n];
+ matrix_t trans_matrix[n][m];
+ matrix_t res_mul_matrix[m][m];
+ matrix_t diag_vec[3] = { 1.1, 2.3, 3.5 };
+
+ matrix_add(m, n, matrix1, matrix2, res_matrix);
+ printf("matrix1 + matrix2 = ");
+ matrix_flex_print(m, n, res_matrix, 7, 4);
+
+ matrix_sub(m, n, matrix1, matrix2, res_matrix);
+ printf("matrix1 - matrix2 = ");
+ matrix_flex_print(m, n, res_matrix, 7, 4);
+
+ matrix_transpose(m, n, matrix2, trans_matrix);
+ printf("trans(matrix2) = ");
+ matrix_flex_print(n, m, trans_matrix, 7, 4);
+
+ matrix_mul(m, n, matrix1, n, m, trans_matrix, res_mul_matrix);
+ printf("matrix1 x matrix2 = ");
+ matrix_flex_print(m, m, res_mul_matrix, 7, 4);
+
+ matrix_get_diag_mat(m, n, diag_elem, res_matrix);
+ printf("dig_matrix = ");
+ matrix_flex_print(m, n, res_matrix, 7, 4);
+
+ matrix_get_diag_mat_new(m, n, res_matrix, m, diag_vec);
+ printf("dig_matrix = ");
+ matrix_flex_print(m, n, res_matrix, 7, 4);
+
+ matrix_t matrix3[5][5] = {
+ { 0.8147, 0.0975, 0.1576, 0.1419, 0.6557 },
+ { 0.9058, 0.2785, 0.9706, 0.4218, 0.0357 },
+ { 0.1270, 0.5469, 0.9572, 0.9157, 0.8491 },
+ { 0.9595, 0.8491, 0.7577, 0.6555, 0.6787 },
+ { 0.6557, 0.9340, 0.7431, 0.1712, 0.9595 },
+ };
+
+ matrix_swap_rows(5, matrix3, 3, 1);
+ printf("swapped matrix3 = ");
+ matrix_flex_print(5, 5, matrix3, 7, 4);
+
+ puts(" *** Test Partial Matrix Multiplication *** ");
+ matrix_t A[11][7] =
+ {
+ { 0.8147, 0.9706, 0.8491, 0.0462, 0.1869, 0.4984, 0.5472 },
+ { 0.9058, 0.9572, 0.9340, 0.0971, 0.4898, 0.9597, 0.1386 },
+ { 0.1270, 0.4854, 0.6787, 0.8235, 0.4456, 0.3404, 0.1493 },
+ { 0.9134, 0.8003, 0.7577, 0.6948, 0.6463, 0.5853, 0.2575 },
+ { 0.6324, 0.1419, 0.7431, 0.3171, 0.7094, 0.2238, 0.8407 },
+ { 0.0975, 0.4218, 0.3922, 0.9502, 0.7547, 0.7513, 0.2543 },
+ { 0.2785, 0.9157, 0.6555, 0.0344, 0.2760, 0.2551, 0.8143 },
+ { 0.5469, 0.7922, 0.1712, 0.4387, 0.6797, 0.5060, 0.2435 },
+ { 0.9575, 0.9595, 0.7060, 0.3816, 0.6551, 0.6991, 0.9293 },
+ { 0.9649, 0.6557, 0.0318, 0.7655, 0.1626, 0.8909, 0.3500 },
+ { 0.1576, 0.0357, 0.2769, 0.7952, 0.1190, 0.9593, 0.1966 }
+ };
+
+ matrix_t B[7][5] = {
+ { 0.2511, 0.9172, 0.0540, 0.0119, 0.6020 },
+ { 0.6160, 0.2858, 0.5308, 0.3371, 0.2630 },
+ { 0.4733, 0.7572, 0.7792, 0.1622, 0.6541 },
+ { 0.3517, 0.7537, 0.9340, 0.7943, 0.6892 },
+ { 0.8308, 0.3804, 0.1299, 0.3112, 0.7482 },
+ { 0.5853, 0.5678, 0.5688, 0.5285, 0.4505 },
+ { 0.5497, 0.0759, 0.4694, 0.1656, 0.0838 }
+ };
+
+ uint8_t l;
+ uint8_t a_row_begin, a_row_end, a_col_begin, a_col_end;
+ uint8_t b_row_begin, b_row_end, b_col_begin, b_col_end;
+ m = 11;
+ n = 7;
+ l = 5;
+ matrix_t C[5][3];
+
+ a_row_begin = 3, a_row_end = 7;
+ a_col_begin = 2, a_col_end = 4;
+ b_row_begin = 3, b_row_end = 5;
+ b_col_begin = 1, b_col_end = 3;
+ matrix_part_mul(n, A, l, B,
+ a_row_begin, a_row_end, a_col_begin, a_col_end,
+ b_row_begin, b_row_end, b_col_begin, b_col_end,
+ 3, C);
+
+ printf("part_A = ");
+ matrix_flex_part_print(m, n, A, a_row_begin, a_row_end, a_col_begin,
+ a_col_end, 7, 4);
+ printf("part_B = ");
+ matrix_flex_part_print(n, l, B, b_row_begin, b_row_end, b_col_begin,
+ b_col_end, 7, 4);
+
+ printf("C = ");
+ matrix_flex_print(5, 3, C, 7, 4);
+
+ puts(" *** Test The 2-norm of a Matrix, *** ");
+
+ double two_norm = matrix_get_two_norm(m, n, A);
+ printf("A_two_norm = %7.4f\n", two_norm);
+
+ matrix_t D[7][5] = {
+ { -0.2743, -4.9913, 0.3375, -6.5684, -6.9048 },
+ { -4.9657, -2.0716, -4.7133, -2.7536, -4.3030 },
+ { -0.4857, -3.2137, -0.9424, -0.7667, -5.7025 },
+ { -5.0518, -4.1867, -0.9702, 0.4721, -0.6457 },
+ { 0.4341, -0.3534, -3.9564, -5.9608, -4.5103 },
+ { -4.2001, -2.3179, -2.4574, -2.4494, -2.7717 },
+ { -5.4272, -2.6022, -6.3932, -3.2449, -5.6748 }
+ };
+ m = 7;
+ n = 5;
+ two_norm = matrix_get_two_norm(m, n, D);
+ printf("D_two_norm = %7.4f\n", two_norm);
+
+ double frob_norm = matrix_get_frob_norm(m, n, D);
+ printf("D_frob_norm = %7.4f\n", frob_norm);
+}
+
+void inv_triangular_matrices_test(void)
+{
+
+ puts(
+ "*********** Test the Inverse of Upper Triangular Matrices ***********");
+ matrix_t U[11][7] =
+ {
+ { 0.8147, 0.9706, 0.8491, 0.0462, 0.1869, 0.4984, 0.5472 },
+ { 0.0000, 0.9572, 0.9340, 0.0971, 0.4898, 0.9597, 0.1386 },
+ { 0.0000, 0.0000, 0.6787, 0.8235, 0.4456, 0.3404, 0.1493 },
+ { 0.0000, 0.0000, 0.0000, 0.6948, 0.6463, 0.5853, 0.2575 },
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.7094, 0.2238, 0.8407 },
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.7513, 0.2543 },
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.8143 },
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000 },
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000 },
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000 },
+ { 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000 }
+ };
+ uint8_t m, n;
+
+ puts("Square Matrix:");
+ m = 7;
+ n = 7;
+ printf("U1 = ");
+ matrix_flex_print(m, n, U, 7, 4);
+ matrix_t inv_U1[n][m];
+ matrix_get_inv_upp_triang(m, n, U, inv_U1);
+ printf("inv_U1 = ");
+ matrix_flex_print(n, m, inv_U1, 7, 4);
+
+ puts("Rectangular Matrix:");
+ m = 11;
+ n = 7;
+ printf("U2 = ");
+ matrix_flex_print(m, n, U, 7, 4);
+ matrix_t inv_U2[n][m];
+ matrix_get_inv_upp_triang(m, n, U, inv_U2);
+ printf("inv_U2 = ");
+ matrix_flex_print(n, m, inv_U2, 7, 4);
+
+ puts(
+ "*********** Test the Inverse of Lower Triangular Matrices ***********");
+ matrix_t L[11][7] =
+ {
+ { 0.8147, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000 },
+ { 0.9058, 0.9572, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000 },
+ { 0.1270, 0.4854, 0.6787, 0.0000, 0.0000, 0.0000, 0.0000 },
+ { 0.9134, 0.8003, 0.7577, 0.6948, 0.0000, 0.0000, 0.0000 },
+ { 0.6324, 0.1419, 0.7431, 0.3171, 0.7094, 0.0000, 0.0000 },
+ { 0.0975, 0.4218, 0.3922, 0.9502, 0.7547, 0.7513, 0.0000 },
+ { 0.2785, 0.9157, 0.6555, 0.0344, 0.2760, 0.2551, 0.8143 },
+ { 0.5469, 0.7922, 0.1712, 0.4387, 0.6797, 0.5060, 0.2435 },
+ { 0.9575, 0.9595, 0.7060, 0.3816, 0.6551, 0.6991, 0.9293 },
+ { 0.9649, 0.6557, 0.0318, 0.7655, 0.1626, 0.8909, 0.3500 },
+ { 0.1576, 0.0357, 0.2769, 0.7952, 0.1190, 0.9593, 0.1966 }
+ };
+ m = 7;
+ n = 7;
+ puts("Square Matrix:");
+ printf("L1 = ");
+ matrix_flex_print(m, n, L, 7, 4);
+ matrix_t inv_L1[n][m];
+ matrix_get_inv_low_triang(m, n, L, inv_L1);
+ printf("inv_L1 = ");
+ matrix_flex_print(n, m, inv_L1, 7, 4);
+
+ puts("Rectangular Matrix:");
+ m = 11;
+ n = 7;
+ printf("L2 = ");
+ matrix_flex_print(m, n, L, 7, 4);
+ matrix_t inv_L2[n][m];
+ matrix_get_inv_low_triang(m, n, L, inv_L2);
+ printf("inv_L2 = ");
+ matrix_flex_print(n, m, inv_L2, 7, 4);
+}
+
+void triangular_matrices_test(void)
+{
+ matrix_t A[10][5] = {
+ { 0.8147, 0.1576, 0.6557, 0.7060, 0.4387 },
+ { 0.9058, 0.9706, 0.0357, 0.0318, 0.3816 },
+ { 0.1270, 0.9572, 0.8491, 0.2769, 0.7655 },
+ { 0.9134, 0.4854, 0.9340, 0.0462, 0.7952 },
+ { 0.6324, 0.8003, 0.6787, 0.0971, 0.1869 },
+ { 0.0975, 0.1419, 0.7577, 0.8235, 0.4898 },
+ { 0.2785, 0.4218, 0.7431, 0.6948, 0.4456 },
+ { 0.5469, 0.9157, 0.3922, 0.3171, 0.6463 },
+ { 0.9575, 0.7922, 0.6555, 0.9502, 0.7094 },
+ { 0.9649, 0.9595, 0.1712, 0.0344, 0.7547 }
+ };
+
+ uint8_t m = 10, n = 5;
+ matrix_t copy_A[m][n];
+
+ matrix_copy(m, n, A, copy_A);
+ matrix_t B[m][n];
+ matrix_t C[n][m];
+ matrix_t D[n][m];
+
+ puts("++++++++++ upper triangular ++++++++++");
+ matrix_transpose(m, n, A, C);
+ matrix_get_upp_triang(m, n, A, B);
+ matrix_get_upp_triang(m, n, A, A);
+ matrix_get_upp_triang(n, m, C, D);
+
+ printf("A = ");
+ matrix_flex_print(m, n, A, 7, 4);
+ printf("B = ");
+ matrix_flex_print(m, n, B, 7, 4);
+ printf("C = ");
+ matrix_flex_print(n, m, C, 7, 4);
+ printf("D = ");
+ matrix_flex_print(n, m, D, 7, 4);
+
+ puts("++++++++++ lower triangular ++++++++++");
+ matrix_copy(m, n, copy_A, A);
+ printf("A = ");
+ matrix_flex_print(m, n, A, 7, 4);
+ matrix_transpose(m, n, A, C);
+ matrix_get_low_triang(m, n, A, B);
+ matrix_get_low_triang(m, n, A, A);
+ matrix_get_low_triang(n, m, C, D);
+
+ printf("A = ");
+ matrix_flex_print(m, n, A, 7, 4);
+ printf("B = ");
+ matrix_flex_print(m, n, B, 7, 4);
+ printf("C = ");
+ matrix_flex_print(n, m, C, 7, 4);
+ printf("D = ");
+ matrix_flex_print(n, m, D, 7, 4);
+
+}
diff --git a/examples/linear_algebra/basic_operations/vector_test.c b/examples/linear_algebra/basic_operations/vector_test.c
new file mode 100644
index 0000000000000000000000000000000000000000..afaa4cc89d6ee00cdafd3b1bd997b0f0f6e4a0cf
--- /dev/null
+++ b/examples/linear_algebra/basic_operations/vector_test.c
@@ -0,0 +1,88 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @{
+ *
+ * @file
+ * @brief Examples of vector computations.
+ *
+ * @details Vector computation examples of the @ref vector.h functions.
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#include <stdio.h>
+#include <stdint.h>
+#include <inttypes.h>
+#include <math.h>
+
+#include "vector.h"
+
+void vector_test(void)
+{
+ puts("############ Test Vector Algebra ###############");
+ vector_t a[5] = { 0.0975, 0.2785, 0.5469, 0.9575, 0.9649 };
+ vector_t b[5] = { 0.1576, 0.9706, 0.9572, 0.4854, 0.8003 };
+ vector_t c[5];
+ vector_t d[5] = { 0.1576, 0.9706, 0.9572, 0.4854, 0.8003 };
+
+ uint8_t size = 5;
+
+ vector_add(size, a, b, c);
+ printf("c = a + b = ");
+ vector_flex_print(size, c, 3, 4);
+ puts("");
+
+ vector_sub(size, a, b, c);
+ printf("c = a - b = ");
+ vector_flex_print(size, c, 3, 4);
+ puts("");
+
+ vector_mul(size, a, b, c);
+ printf("c = a * b = ");
+ vector_flex_print(size, c, 3, 4);
+ puts("");
+
+ vector_t mean = vector_get_mean_value(size, a);
+ printf("mean(a) = %.4f\n", mean);
+
+ vector_t norm2 = vector_get_norm2(size, a);
+ printf("norm2(a) = %.4f\n", norm2);
+
+ vector_t squ_norm2 = vector_get_square_norm2(size, b);
+ printf("squ_norm2(b) = %.4f\n", squ_norm2);
+
+ vector_t scal = vector_get_scalar_product(size, a, b);
+ printf("scal(a) = %.4f\n", scal);
+
+ vector_t sum = vector_get_sum(size, a);
+ printf("sum(a) = %.4f\n", sum);
+
+ vector_t euc_dist = vector_get_euclidean_distance(size, a, b);
+ printf("euc_dist(a,b) = %.4f\n", euc_dist);
+
+ if (vector_is_equal(size, b, d)) {
+ puts("vectors are equal !!");
+ }
+ else {
+ puts("vectors are not equal !!");
+ }
+
+ vector_copy(size, a, d);
+ vector_flex_print(size, d, 3, 4);
+ puts("");
+
+ vector_clear(size, d);
+ vector_flex_print(size, d, 3, 4);
+ puts("");
+
+}
diff --git a/examples/linear_algebra/matrix_decompositions/givens_test.c b/examples/linear_algebra/matrix_decompositions/givens_test.c
new file mode 100644
index 0000000000000000000000000000000000000000..4845ffa53ac275390b35f3932ec0964fd09b3e06
--- /dev/null
+++ b/examples/linear_algebra/matrix_decompositions/givens_test.c
@@ -0,0 +1,115 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @{
+ *
+ * @file
+ * @brief Examples of the Givens algorithm.
+ *
+ * @details Givens algorithm examples (see @ref qr_givens.h the "Givens" approach).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#include <stdio.h>
+
+#include "qr_givens.h"
+#include "matrix.h"
+
+void givens_test(void)
+{
+ matrix_t xj, xij;
+
+ xj = 100;
+ xij = 130;
+
+ matrix_t c_s_t_r_vec[4];
+ qr_givens_get_params(xj, xij, c_s_t_r_vec);
+
+ printf("c = %7.4f\n", c_s_t_r_vec[0]);
+ printf("s = %7.4f\n", c_s_t_r_vec[1]);
+ printf("t = %7.4f\n", c_s_t_r_vec[2]);
+ printf("r = %7.4f\n", c_s_t_r_vec[3]);
+
+ puts("************ MATRIX A ************");
+ matrix_t A[10][5] = {
+ { 0.8147, 0.1576, 0.6557, 0.7060, 0.4387 },
+ { 0.9058, 0.9706, 0.0357, 0.0318, 0.3816 },
+ { 0.1270, 0.9572, 0.8491, 0.2769, 0.7655 },
+ { 0.9134, 0.4854, 0.9340, 0.0462, 0.7952 },
+ { 0.6324, 0.8003, 0.6787, 0.0971, 0.1869 },
+ { 0.0975, 0.1419, 0.7577, 0.8235, 0.4898 },
+ { 0.2785, 0.4218, 0.7431, 0.6948, 0.4456 },
+ { 0.5469, 0.9157, 0.3922, 0.3171, 0.6463 },
+ { 0.9575, 0.7922, 0.6555, 0.9502, 0.7094 },
+ { 0.9649, 0.9595, 0.1712, 0.0344, 0.7547 }
+ };
+
+ uint8_t m, n;
+ m = 10;
+ n = 5;
+
+ matrix_t copy_A[m][n];
+
+ puts("+++++++ Reduced QR-form +++++++");
+ matrix_copy(m, n, A, copy_A);
+ matrix_t red_Q[m][n];
+ qr_givens_decomp(m, n, copy_A, n, red_Q, true);
+ printf("red_Q = ");
+ matrix_flex_print(m, n, red_Q, 7, 4);
+ puts("");
+ printf("red_R = ");
+ matrix_flex_print(n, n, copy_A, 7, 4);
+ puts("+++++++ Full QR-form +++++++");
+ matrix_copy(m, n, A, copy_A);
+ matrix_t full_Q[m][m];
+ qr_givens_decomp(m, n, copy_A, m, full_Q, false);
+ printf("full_Q = ");
+ matrix_flex_print(m, m, full_Q, 7, 4);
+ puts("");
+ printf("full_R = ");
+ matrix_flex_print(m, n, copy_A, 7, 4);
+
+ puts("************ MATRIX B ************");
+ matrix_t B[7][7] =
+ {
+ { 0.8147, 0.5469, 0.8003, 0.0357, 0.6555, 0.8235, 0.7655 },
+ { 0.9058, 0.9575, 0.1419, 0.8491, 0.1712, 0.6948, 0.7952 },
+ { 0.1270, 0.9649, 0.4218, 0.9340, 0.7060, 0.3171, 0.1869 },
+ { 0.9134, 0.1576, 0.9157, 0.6787, 0.0318, 0.9502, 0.4898 },
+ { 0.6324, 0.9706, 0.7922, 0.7577, 0.2769, 0.0344, 0.4456 },
+ { 0.0975, 0.9572, 0.9595, 0.7431, 0.0462, 0.4387, 0.6463 },
+ { 0.2785, 0.4854, 0.6557, 0.3922, 0.0971, 0.3816, 0.7094 }
+ };
+ m = 7;
+ n = 7;
+ matrix_t copy_B[m][n];
+ puts("+++++++ Reduced QR-form +++++++");
+ matrix_copy(m, n, B, copy_B);
+ matrix_t red_Q1[m][n];
+ qr_givens_decomp(m, n, copy_B, n, red_Q1, true);
+ printf("red_Q = ");
+ matrix_flex_print(m, n, red_Q1, 7, 4);
+ puts("");
+ printf("red_R = ");
+ matrix_flex_print(n, n, copy_B, 7, 4);
+ puts("+++++++ Full QR-form +++++++");
+ matrix_copy(m, n, B, copy_B);
+ matrix_t full_Q1[m][m];
+ qr_givens_decomp(m, n, copy_B, m, full_Q1, false);
+ printf("full_Q = ");
+ matrix_flex_print(m, m, full_Q1, 7, 4);
+ puts("");
+ printf("full_R = ");
+ matrix_flex_print(m, n, copy_B, 7, 4);
+
+}
diff --git a/examples/linear_algebra/matrix_decompositions/householder_test.c b/examples/linear_algebra/matrix_decompositions/householder_test.c
new file mode 100644
index 0000000000000000000000000000000000000000..c5153135dfef1fb733d2d66916f1f7565657eca2
--- /dev/null
+++ b/examples/linear_algebra/matrix_decompositions/householder_test.c
@@ -0,0 +1,79 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @{
+ *
+ * @file
+ * @brief Examples of the Householder algorithm.
+ *
+ * @details Householder algorithm examples (see the @ref qr_householder.h
+ * "Householder" approach).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#include <stdbool.h>
+#include <stdio.h>
+
+#include "matrix.h"
+#include "qr_householder.h"
+
+
+void householder_test(void)
+{
+
+ matrix_t A[10][5] = { { 0.8147, 0.1576, 0.6557, 0.7060, 0.4387 },
+ { 0.9058, 0.9706, 0.0357, 0.0318, 0.3816 },
+ { 0.1270, 0.9572, 0.8491, 0.2769, 0.7655 },
+ { 0.9134, 0.4854, 0.9340, 0.0462, 0.7952 },
+ { 0.6324, 0.8003, 0.6787, 0.0971, 0.1869 },
+ { 0.0975, 0.1419, 0.7577, 0.8235, 0.4898 },
+ { 0.2785, 0.4218, 0.7431, 0.6948, 0.4456 },
+ { 0.5469, 0.9157, 0.3922, 0.3171, 0.6463 },
+ { 0.9575, 0.7922, 0.6555, 0.9502, 0.7094 },
+ { 0.9649, 0.9595, 0.1712, 0.0344, 0.7547 } };
+ uint8_t m = 10, n = 5;
+ matrix_t copy_A[m][n];
+ matrix_t Q_red[m][n];
+ matrix_t Q[m][m];
+
+ matrix_copy(m, n, A, copy_A);
+ matrix_clear(m, n, Q_red);
+ qr_householder_decomp(m, n, copy_A, n, Q_red, true);
+ printf("Q_red = ");
+ matrix_flex_print(m, n, Q_red, 7, 4);
+ printf("R_red = ");
+ matrix_flex_print(n, n, copy_A, 7, 4);
+
+ matrix_copy(m, n, A, copy_A);
+ matrix_clear(m, m, Q);
+ qr_householder_decomp(m, n, copy_A, m, Q, false);
+ printf("Q = ");
+ matrix_flex_print(m, m, Q, 7, 4);
+ printf("R = ");
+ matrix_flex_print(m, n, copy_A, 7, 4);
+
+ matrix_t B[4][4] = {
+ { 6, 0, 0, 6 },
+ { 2, 5, 0, 4 },
+ { 0, 6, 2, 3 },
+ { 0, 1, 5, 5 }
+ };
+ m = 4;
+ n = 4;
+ matrix_t Q1_red[m][n];
+ qr_householder_decomp(m, n, B, m, Q1_red, true);
+ printf("Q1 = ");
+ matrix_flex_print(m, m, Q1_red, 7, 4);
+ printf("R1 = ");
+ matrix_flex_print(m, n, B, 7, 4);
+}
diff --git a/examples/linear_algebra/matrix_decompositions/include/givens_test.h b/examples/linear_algebra/matrix_decompositions/include/givens_test.h
new file mode 100644
index 0000000000000000000000000000000000000000..df1e4fbca0ffdab87fcc4f688e0d4718fe49aab7
--- /dev/null
+++ b/examples/linear_algebra/matrix_decompositions/include/givens_test.h
@@ -0,0 +1,33 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @ingroup examples
+ * @{
+ *
+ * @file
+ * @brief Examples of the Givens algorithm.
+ *
+ * @details Givens algorithm examples (see @ref qr_givens.h the "Givens" approach).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#ifndef GIVENS_TEST_H_
+#define GIVENS_TEST_H_
+
+/**
+ * @brief Examples of the Givens algorithm.
+ *
+ */
+void givens_test(void);
+
+#endif /* GIVENS_TEST_H_ */
diff --git a/examples/linear_algebra/matrix_decompositions/include/householder_test.h b/examples/linear_algebra/matrix_decompositions/include/householder_test.h
new file mode 100644
index 0000000000000000000000000000000000000000..b2552af31cab7a4793bffd26417f1d73d6ea9561
--- /dev/null
+++ b/examples/linear_algebra/matrix_decompositions/include/householder_test.h
@@ -0,0 +1,34 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @ingroup examples
+ * @{
+ *
+ * @file
+ * @brief Examples of the Householder algorithm.
+ *
+ * @details Householder algorithm examples (see the @ref qr_householder.h
+ * "Householder" approach).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#ifndef HOUSEHOLDER_TEST_H_
+#define HOUSEHOLDER_TEST_H_
+
+/**
+ * @brief Examples of the Householder algorithm.
+ *
+ */
+void householder_test(void);
+
+#endif /* HOUSEHOLDER_TEST_H_ */
diff --git a/examples/linear_algebra/matrix_decompositions/include/lu_decomp_test.h b/examples/linear_algebra/matrix_decompositions/include/lu_decomp_test.h
new file mode 100644
index 0000000000000000000000000000000000000000..78b37d830af63dc8465c9ef9ed57e8f3be8bc3b7
--- /dev/null
+++ b/examples/linear_algebra/matrix_decompositions/include/lu_decomp_test.h
@@ -0,0 +1,34 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @ingroup examples
+ * @{
+ *
+ * @file
+ * @brief Examples of the LU algorithm with pivoting.
+ *
+ * @details LU algorithm with pivoting examples (see the @ref lu_decomp.h
+ * "Gaussian Elimination with pivoting" approach).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#ifndef LU_DECOMP_TEST_H_
+#define LU_DECOMP_TEST_H_
+
+/**
+ * @brief Examples of the LU algorithm with pivoting.
+ *
+ */
+void lu_decomp_test(void);
+
+#endif /* LU_DECOMP_TEST_H_ */
diff --git a/examples/linear_algebra/matrix_decompositions/include/svd_test.h b/examples/linear_algebra/matrix_decompositions/include/svd_test.h
new file mode 100644
index 0000000000000000000000000000000000000000..19e86acbda9cbde201ac0c5889f9b962c39418e2
--- /dev/null
+++ b/examples/linear_algebra/matrix_decompositions/include/svd_test.h
@@ -0,0 +1,34 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @ingroup examples
+ * @{
+ *
+ * @file
+ * @brief Examples of the SVD algorithm.
+ *
+ * @details SVD algorithm examples (see the @ref svd.h
+ * "Singular Value Decomposition (SVD)" approach).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#ifndef SVD_TEST_H_
+#define SVD_TEST_H_
+
+/**
+ * @brief Examples of the Givens algorithm.
+ *
+ */
+void svd_test(void);
+
+#endif /* SVD_TEST_H_ */
diff --git a/examples/linear_algebra/matrix_decompositions/lu_decomp_test.c b/examples/linear_algebra/matrix_decompositions/lu_decomp_test.c
new file mode 100644
index 0000000000000000000000000000000000000000..985304fa39af5674583e03c2f68c458e808684e1
--- /dev/null
+++ b/examples/linear_algebra/matrix_decompositions/lu_decomp_test.c
@@ -0,0 +1,84 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @{
+ *
+ * @file
+ * @brief Examples of the LU algorithm with pivoting.
+ *
+ * @details LU algorithm with pivoting examples (see the @ref lu_decomp.h
+ * "Gaussian Elimination with pivoting" approach).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#include <stdio.h>
+
+#include "matrix.h"
+#include "lu_decomp.h"
+
+void lu_decomp_test(void)
+{
+ matrix_t A[5][5] = { { 0.8147, 0.1576, 0.6557, 0.7060, 0.4387 },
+ { 0.9058, 0.9706, 0.0357, 0.0318, 0.3816 },
+ { 0.1270, 0.9572, 0.8491, 0.2769, 0.7655 },
+ { 0.9134, 0.4854, 0.9340, 0.0462, 0.7952 },
+ { 0.6324, 0.8003, 0.6787, 0.0971, 0.1869 }, };
+ uint8_t n;
+
+ n = 5;
+ matrix_t L[n][n];
+ matrix_t P[n][n];
+ lu_decomp(n, A, L, P);
+ printf("L = ");
+ matrix_flex_print(n, n, L, 7, 4);
+ printf("U = ");
+ matrix_flex_print(n, n, A, 7, 4);
+ printf("P = ");
+ matrix_flex_print(n, n, P, 7, 4);
+
+ matrix_t B[11][11] = {
+ { 0.4387, 0.6797, 0.5060, 0.2435, 0.9172, 0.1299, 0.2630, 0.9961, 0.2599, 0.1450,
+ 0.4173 },
+ { 0.3816, 0.6551, 0.6991, 0.9293, 0.2858, 0.5688, 0.6541, 0.0782, 0.8001, 0.8530,
+ 0.0497 },
+ { 0.7655, 0.1626, 0.8909, 0.3500, 0.7572, 0.4694, 0.6892, 0.4427, 0.4314, 0.6221,
+ 0.9027 },
+ { 0.7952, 0.1190, 0.9593, 0.1966, 0.7537, 0.0119, 0.7482, 0.1067, 0.9106, 0.3510,
+ 0.9448 },
+ { 0.1869, 0.4984, 0.5472, 0.2511, 0.3804, 0.3371, 0.4505, 0.9619, 0.1818, 0.5132,
+ 0.4909 },
+ { 0.4898, 0.9597, 0.1386, 0.6160, 0.5678, 0.1622, 0.0838, 0.0046, 0.2638, 0.4018,
+ 0.4893 },
+ { 0.4456, 0.3404, 0.1493, 0.4733, 0.0759, 0.7943, 0.2290, 0.7749, 0.1455, 0.0760,
+ 0.3377 },
+ { 0.6463, 0.5853, 0.2575, 0.3517, 0.0540, 0.3112, 0.9133, 0.8173, 0.1361, 0.2399,
+ 0.9001 },
+ { 0.7094, 0.2238, 0.8407, 0.8308, 0.5308, 0.5285, 0.1524, 0.8687, 0.8693, 0.1233,
+ 0.3692 },
+ { 0.7547, 0.7513, 0.2543, 0.5853, 0.7792, 0.1656, 0.8258, 0.0844, 0.5797, 0.1839,
+ 0.1112 },
+ { 0.2760, 0.2551, 0.8143, 0.5497, 0.9340, 0.6020, 0.5383, 0.3998, 0.5499, 0.2400,
+ 0.7803 }
+ };
+
+ n = 11;
+ matrix_t L1[n][n];
+ matrix_t P1[n][n];
+ lu_decomp(n, B, L1, P1);
+ printf("L1 = ");
+ matrix_flex_print(n, n, L1, 7, 4);
+ printf("U1 = ");
+ matrix_flex_print(n, n, B, 7, 4);
+ printf("P1 = ");
+ matrix_flex_print(n, n, P1, 7, 4);
+}
diff --git a/examples/linear_algebra/matrix_decompositions/svd_test.c b/examples/linear_algebra/matrix_decompositions/svd_test.c
new file mode 100644
index 0000000000000000000000000000000000000000..9bb507987716c2db2e6601c0f236e7e3d7d44f28
--- /dev/null
+++ b/examples/linear_algebra/matrix_decompositions/svd_test.c
@@ -0,0 +1,159 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @{
+ *
+ * @file
+ * @brief Examples of the SVD algorithm.
+ *
+ * @details SVD algorithm examples (see the @ref svd.h
+ * "Singular Value Decomposition (SVD)" approach).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#include <stdio.h>
+#include <inttypes.h>
+
+#include "svd.h"
+#include "matrix.h"
+#include "vector.h"
+
+
+void svd_test(void)
+{
+ uint8_t m, n;
+ uint8_t i = 0;
+
+ //m<n
+ matrix_t matrix1_arr[3][4] = { { 1.0000, -3.6000, -1.2000, -2.8400 },
+ { 1.0000, -7.2400, -7.1800, -2.2400 },
+ { 1.0000, -12.0600, -1.3400, -3.6600 } };
+
+ m = 3;
+ n = 4;
+ matrix_t matrix2_arr[3][4] = {
+ { 1, -22, 30, -20 },
+ { 1, -26, -42, -10 },
+ { 1, 18, -30, -14 }
+ };
+ svd_compute_print_U_S_V_s(m, n, matrix1_arr, ++i);
+ svd_compute_print_U_S_V_s(m, n, matrix2_arr, ++i);
+
+ printf(
+ "######## Test %d: Singular Value Decomposition m < n : (2,3) ########\n",
+ ++i);
+ matrix_t matrix3_arr[2][3] = {
+ { 3, 1, 1 },
+ { -1, 3, 1 }
+ };
+ m = 2;
+ n = 3;
+ svd_compute_print_U_S_V_s(m, n, matrix3_arr, i);
+
+ printf(
+ "######## Test %d: Singular Value Decomposition m > n : (3,2) ########\n",
+ ++i);
+ matrix_t matrix4_arr[3][2] = {
+ { 1, 2 },
+ { 2, 2 },
+ { 2, 1 }
+ };
+ m = 3;
+ n = 2;
+ svd_compute_print_U_S_V_s(m, n, matrix4_arr, i);
+
+ printf(
+ "######## Test %d: Singular Value Decomposition m = n : (4,4) ########\n",
+ ++i);
+
+ matrix_t matrix5_arr[4][4] = {
+ { 6, 0, 0, 6 },
+ { 2, 5, 0, 4 },
+ { 0, 6, 2, 3 },
+ { 0, 1, 5, 5 }
+ };
+ m = 4;
+ n = 4;
+ svd_compute_print_U_S_V_s(m, n, matrix5_arr, i);
+
+ printf(
+ "######## Test %d: Singular Value Decomposition m < n : (4,7) ########\n",
+ ++i);
+ matrix_t matrix6_arr[4][7] = {
+ { 2, 5, 4, 6, 3, 2, 1 },
+ { 1, 2, 4, 6, 0, 0, 6 },
+ { 2, 1, 1, 5, 4, 6, 3 },
+ { 3, 3, 1, 0, 4, 5, 0 }
+ };
+ m = 4;
+ n = 7;
+ svd_compute_print_U_S_V_s(m, n, matrix6_arr, i);
+
+ printf(
+ "######## Test %d: Singular Value Decomposition m = n : (3,3) ########\n",
+ ++i);
+ matrix_t matrix7_arr[3][3] = {
+ { 1., 2., 3 },
+ { 4., 5., 6. },
+ { 7., 8., 10. }
+ };
+ m = 3;
+ n = 3;
+ svd_compute_print_U_S_V_s(m, n, matrix7_arr, i);
+
+ printf(
+ "######## Test %d: Singular Value Decomposition m < n : (5,7) ########\n",
+ ++i);
+ matrix_t matrix8_arr[5][7] = {
+ { 6, 2, 7, 3, 6, 0, 1 },
+ { 7, 1, 6, 3, 6, 4, 0 },
+ { 3, 5, 1, 1, 0, 2, 3 },
+ { 5, 5, 7, 3, 1, 3, 0 },
+ { 6, 5, 4, 1, 2, 7, 1 }
+ };
+ m = 5;
+ n = 7;
+ svd_compute_print_U_S_V_s(m, n, matrix8_arr, i);
+
+ //m>n
+ printf(
+ "######## Test %d: Singular Value Decomposition m > n : (7,5) ########\n",
+ ++i);
+ matrix_t matrix9_arr[7][5] = {
+ { 6.395, 2.897, 7.333, 3.777, 6.543 },
+ { 7.635, 1.235, 6.301, 3.356, 6.777 },
+ { 3.595, 5.901, 1.408, 1.697, 0.539 },
+ { 5.501, 5.562, 7.271, 3.907, 1.651 },
+ { 6.198, 5.069, 4.238, 1.388, 2.855 },
+ { 0.000, 1.999, 4.103, 0.561, 2.908 },
+ { 3.834, 3.172, 0.009, 7.069, 1.075 }
+ };
+
+ m = 7;
+ n = 5;
+ svd_compute_print_U_S_V_s(m, n, matrix9_arr, i);
+
+ printf(
+ "######## Test %d: Singular Value Decomposition m > n : (5,7) ########\n",
+ ++i);
+ matrix_t matrix10_arr[5][7] = {
+ { 6.395, 2.897, 7.333, 3.777, 6.543, 0.000, 1.999 },
+ { 7.635, 1.235, 6.301, 3.356, 6.777, 4.103, 0.561 },
+ { 3.595, 5.901, 1.408, 1.697, 0.539, 2.908, 3.834 },
+ { 5.501, 5.562, 7.271, 3.907, 1.651, 3.172, 0.009 },
+ { 6.198, 5.069, 4.238, 1.388, 2.855, 7.069, 1.075 }
+ };
+ m = 5;
+ n = 7;
+ svd_compute_print_U_S_V_s(m, n, matrix10_arr, i);
+}
diff --git a/examples/linear_algebra/pseudo_inverse/include/moore_penrose_pinv_test.h b/examples/linear_algebra/pseudo_inverse/include/moore_penrose_pinv_test.h
new file mode 100644
index 0000000000000000000000000000000000000000..4f7c2a0035576a6973549bd3b3e6677c30ad4f2c
--- /dev/null
+++ b/examples/linear_algebra/pseudo_inverse/include/moore_penrose_pinv_test.h
@@ -0,0 +1,34 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @ingroup examples
+ * @{
+ *
+ * @file
+ * @brief Examples of the Moore--Penrose algorithm.
+ *
+ * @details Moore--Penrose algorithm examples (see the @ref moore_penrose_pseudo_inverse.h
+ * "Moore--Penrose" approach).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#ifndef MOORE_PENROSE_PINV_TEST_H_
+#define MOORE_PENROSE_PINV_TEST_H_
+
+/**
+ * @brief Examples of the Moore--Penrose algorithm.
+ *
+ */
+void moore_penrose_pinv_test(void);
+
+#endif /* MOORE_PENROSE_PINV_TEST_H_ */
diff --git a/examples/linear_algebra/pseudo_inverse/include/qr_pinv_test.h b/examples/linear_algebra/pseudo_inverse/include/qr_pinv_test.h
new file mode 100644
index 0000000000000000000000000000000000000000..375fe6d553ae9157c17c5e0a7e9d76566e628096
--- /dev/null
+++ b/examples/linear_algebra/pseudo_inverse/include/qr_pinv_test.h
@@ -0,0 +1,34 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @ingroup examples
+ * @{
+ *
+ * @file
+ * @brief Examples of the QR-based pseudo-inverse algorithm.
+ *
+ * @details QR-based pseudo-inverse algorithm examples (see the
+ * @ref qr_pseudo_inverse.h "QR Pseudo-Inverse" approach).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#ifndef QR_PINV_TEST_H_
+#define QR_PINV_TEST_H_
+
+/**
+ * @brief Examples of the QR-based pseudo-inverse algorithm.
+ *
+ */
+void qr_pinv_test(void);
+
+#endif /* TESTS_QR_PINV_TEST_H_ */
diff --git a/examples/linear_algebra/pseudo_inverse/moore_penrose_pinv_test.c b/examples/linear_algebra/pseudo_inverse/moore_penrose_pinv_test.c
new file mode 100644
index 0000000000000000000000000000000000000000..87fd3a7fcafc51ae29e4fbb841881c97bf31c430
--- /dev/null
+++ b/examples/linear_algebra/pseudo_inverse/moore_penrose_pinv_test.c
@@ -0,0 +1,159 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @{
+ *
+ * @file
+ * @brief Examples of the Moore--Penrose algorithm.
+ *
+ * @details Moore--Penrose algorithm examples (see the @ref moore_penrose_pseudo_inverse.h
+ * "Moore--Penrose" approach).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#include <stdio.h>
+#include <inttypes.h>
+
+#include "moore_penrose_pseudo_inverse.h"
+#include "matrix.h"
+
+void moore_penrose_pinv_test(void)
+{
+ puts("\n\n++++++++++++++++++++++++++++++ Moore-Penrose Pseudo-Inverse ++++++++++++++++++++++++++++++\n");
+ uint8_t m, n;
+ uint8_t i = 0;
+
+ //m<n
+ matrix_t matrix1_arr[3][4] = { { 1.0000, -3.6000, -1.2000, -2.8400 },
+ { 1.0000, -7.2400, -7.1800, -2.2400 },
+ { 1.0000, -12.0600, -1.3400, -3.6600 } };
+
+ m = 3;
+ n = 4;
+ moore_penrose_pinv_compute_print(m, n, matrix1_arr, ++i);
+ matrix_t matrix2_arr[3][4] = {
+ { 1, -22, 30, -20 },
+ { 1, -26, -42, -10 },
+ { 1, 18, -30, -14 }
+ };
+ moore_penrose_pinv_compute_print(m, n, matrix2_arr, ++i);
+
+ printf(
+ "########### Test %d: m < n : (2,3) ###########\n",
+ ++i);
+ matrix_t matrix3_arr[2][3] = {
+ { 3, 1, 1 },
+ { -1, 3, 1 }
+ };
+ m = 2;
+ n = 3;
+ moore_penrose_pinv_compute_print(m, n, matrix3_arr, i);
+
+ printf(
+ "########### Test %d: m > n : (3,2) ###########\n",
+ ++i);
+ matrix_t matrix4_arr[3][2] = {
+ { 1, 2 },
+ { 2, 2 },
+ { 2, 1 }
+ };
+ m = 3;
+ n = 2;
+ moore_penrose_pinv_compute_print(m, n, matrix4_arr, i);
+
+ printf(
+ "########### Test %d: m = n : (4,4) ###########\n",
+ ++i);
+
+ matrix_t matrix5_arr[4][4] = {
+ { 6, 0, 0, 6 },
+ { 2, 5, 0, 4 },
+ { 0, 6, 2, 3 },
+ { 0, 1, 5, 5 }
+ };
+ m = 4;
+ n = 4;
+ moore_penrose_pinv_compute_print(m, n, matrix5_arr, i);
+
+ printf(
+ "########### Test %d: m < n : (4,7) ###########\n",
+ ++i);
+ matrix_t matrix6_arr[4][7] = {
+ { 2, 5, 4, 6, 3, 2, 1 },
+ { 1, 2, 4, 6, 0, 0, 6 },
+ { 2, 1, 1, 5, 4, 6, 3 },
+ { 3, 3, 1, 0, 4, 5, 0 }
+ };
+ m = 4;
+ n = 7;
+ moore_penrose_pinv_compute_print(m, n, matrix6_arr, i);
+
+ printf(
+ "########### Test %d: m = n (3, 3) ###########\n",
+ ++i);
+ matrix_t matrix7_arr[3][3] = {
+ { 1., 2., 3 },
+ { 4., 5., 6. },
+ { 7., 8., 10. }
+ };
+ m = 3;
+ n = 3;
+ moore_penrose_pinv_compute_print(m, n, matrix7_arr, i);
+
+ printf(
+ "########### Test %d: m < n (5, 7) ###########\n",
+ ++i);
+ matrix_t matrix8_arr[5][7] = {
+ { 6, 2, 7, 3, 6, 0, 1 },
+ { 7, 1, 6, 3, 6, 4, 0 },
+ { 3, 5, 1, 1, 0, 2, 3 },
+ { 5, 5, 7, 3, 1, 3, 0 },
+ { 6, 5, 4, 1, 2, 7, 1 }
+ };
+ m = 5;
+ n = 7;
+ moore_penrose_pinv_compute_print(m, n, matrix8_arr, i);
+
+ //m>n
+ printf(
+ "########### Test %d: m > n (7, 5) ###########\n",
+ ++i);
+ matrix_t matrix9_arr[7][5] = {
+ { 6.395, 2.897, 7.333, 3.777, 6.543 },
+ { 7.635, 1.235, 6.301, 3.356, 6.777 },
+ { 3.595, 5.901, 1.408, 1.697, 0.539 },
+ { 5.501, 5.562, 7.271, 3.907, 1.651 },
+ { 6.198, 5.069, 4.238, 1.388, 2.855 },
+ { 0.000, 1.999, 4.103, 0.561, 2.908 },
+ { 3.834, 3.172, 0.009, 7.069, 1.075 }
+ };
+
+ m = 7;
+ n = 5;
+ moore_penrose_pinv_compute_print(m, n, matrix9_arr, i);
+
+ printf(
+ "########### Test %d: m > n (5, 7) ###########\n",
+ ++i);
+ matrix_t matrix10_arr[5][7] = {
+ { 6.395, 2.897, 7.333, 3.777, 6.543, 0.000, 1.999 },
+ { 7.635, 1.235, 6.301, 3.356, 6.777, 4.103, 0.561 },
+ { 3.595, 5.901, 1.408, 1.697, 0.539, 2.908, 3.834 },
+ { 5.501, 5.562, 7.271, 3.907, 1.651, 3.172, 0.009 },
+ { 6.198, 5.069, 4.238, 1.388, 2.855, 7.069, 1.075 }
+ };
+ m = 5;
+ n = 7;
+ moore_penrose_pinv_compute_print(m, n, matrix10_arr, i);
+
+}
diff --git a/examples/linear_algebra/pseudo_inverse/qr_pinv_test.c b/examples/linear_algebra/pseudo_inverse/qr_pinv_test.c
new file mode 100644
index 0000000000000000000000000000000000000000..5450f2190a72861a2a87a19e23938078b74ca349
--- /dev/null
+++ b/examples/linear_algebra/pseudo_inverse/qr_pinv_test.c
@@ -0,0 +1,102 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @{
+ *
+ * @file
+ * @brief Examples of the QR-based pseudo-inverse algorithm.
+ *
+ * @details QR-based pseudo-inverse algorithm examples (see the
+ * @ref qr_pseudo_inverse.h "QR Pseudo-Inverse" approach).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#include <qr_pseudo_inverse.h>
+#include <stdio.h>
+
+#include "matrix.h"
+#include "qr_common.h"
+
+void qr_pinv_test(void)
+{
+ puts("\n\n++++++++++++++++++++++++++++++ QR Pseudo-Inverse ++++++++++++++++++++++++++++++\n");
+ puts("************ Householder: MATRIX A ************");
+ matrix_t A[10][5] = {
+ { 0.8147, 0.1576, 0.6557, 0.7060, 0.4387 },
+ { 0.9058, 0.9706, 0.0357, 0.0318, 0.3816 },
+ { 0.1270, 0.9572, 0.8491, 0.2769, 0.7655 },
+ { 0.9134, 0.4854, 0.9340, 0.0462, 0.7952 },
+ { 0.6324, 0.8003, 0.6787, 0.0971, 0.1869 },
+ { 0.0975, 0.1419, 0.7577, 0.8235, 0.4898 },
+ { 0.2785, 0.4218, 0.7431, 0.6948, 0.4456 },
+ { 0.5469, 0.9157, 0.3922, 0.3171, 0.6463 },
+ { 0.9575, 0.7922, 0.6555, 0.9502, 0.7094 },
+ { 0.9649, 0.9595, 0.1712, 0.0344, 0.7547 }
+ };
+
+ uint8_t m, n;
+ m = 10;
+ n = 5;
+ matrix_t pinv_A[n][m];
+
+ qr_get_pinv(m, n, A, pinv_A, QR_Householder);
+
+ printf("pinv_A = ");
+ matrix_flex_print(n, m, pinv_A, 8, 4);
+ puts("");
+
+ puts("************ Householder: MATRIX B ************");
+ matrix_t B[7][7] =
+ {
+ { 0.8147, 0.5469, 0.8003, 0.0357, 0.6555, 0.8235, 0.7655 },
+ { 0.9058, 0.9575, 0.1419, 0.8491, 0.1712, 0.6948, 0.7952 },
+ { 0.1270, 0.9649, 0.4218, 0.9340, 0.7060, 0.3171, 0.1869 },
+ { 0.9134, 0.1576, 0.9157, 0.6787, 0.0318, 0.9502, 0.4898 },
+ { 0.6324, 0.9706, 0.7922, 0.7577, 0.2769, 0.0344, 0.4456 },
+ { 0.0975, 0.9572, 0.9595, 0.7431, 0.0462, 0.4387, 0.6463 },
+ { 0.2785, 0.4854, 0.6557, 0.3922, 0.0971, 0.3816, 0.7094 }
+ };
+
+ m = 7;
+ n = 7;
+ matrix_t pinv_B[m][n];
+
+ qr_get_pinv(m, n, B, pinv_B, QR_Householder);
+
+ printf("pinv_B = ");
+ matrix_flex_print(n, m, pinv_B, 8, 4);
+ puts("");
+
+ puts("************ Givens: MATRIX A ************");
+
+ m = 10;
+ n = 5;
+
+ qr_get_pinv(m, n, A, pinv_A, QR_Givens);
+
+ printf("pinv_A = ");
+ matrix_flex_print(n, m, pinv_A, 8, 4);
+ puts("");
+
+ puts("************ Givens: MATRIX B ************");
+
+ m = 7;
+ n = 7;
+
+ qr_get_pinv(m, n, B, pinv_B, QR_Givens);
+
+ printf("pinv_B = ");
+ matrix_flex_print(n, m, pinv_B, 8, 4);
+ puts("");
+
+}
diff --git a/examples/linear_algebra/solve_linear_equations/include/solve_test.h b/examples/linear_algebra/solve_linear_equations/include/solve_test.h
new file mode 100644
index 0000000000000000000000000000000000000000..6e176d97d7fecca0b7044689a71f41e56e601381
--- /dev/null
+++ b/examples/linear_algebra/solve_linear_equations/include/solve_test.h
@@ -0,0 +1,39 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @ingroup examples
+ * @{
+ *
+ * @file
+ * @brief Examples of solving linear equation systems.
+ *
+ * @details Solving linear equation systems examples (see @ref solve.h "solve" functions).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#ifndef SOLVE_TEST_H_
+#define SOLVE_TEST_H_
+
+/**
+ * @brief Examples of solving linear equation systems.
+ *
+ */
+void solve_test(void);
+
+/**
+ * @brief Example of solving an (10,5) linear equation system.
+ *
+ */
+void solve_big_matrix_test(void);
+
+#endif /* SOLVE_TEST_H_ */
diff --git a/examples/linear_algebra/solve_linear_equations/solve_test.c b/examples/linear_algebra/solve_linear_equations/solve_test.c
new file mode 100644
index 0000000000000000000000000000000000000000..523daa1bdc2fdb9fd3eb79c965d53807f39075ce
--- /dev/null
+++ b/examples/linear_algebra/solve_linear_equations/solve_test.c
@@ -0,0 +1,274 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @{
+ *
+ * @file
+ * @brief Examples of solving linear equation systems.
+ *
+ * @details Solving linear equation systems examples (see @ref solve.h "solve" functions).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#include <stdio.h>
+
+#include "solve.h"
+#include "matrix.h"
+#include "vector.h"
+
+void solve_test(void)
+{
+ int8_t error_no;
+
+ puts("############ Solve Linear Algebra Module ############");
+
+ puts("******* Determined system *******");
+ uint8_t m = 3;
+ uint8_t n = m;
+ enum ALGORITHM algo = Moore_Penrose;
+ matrix_t A1[3][3] = { { 2, 1, 1 },
+ { -1, 1, -1 },
+ { 1, 2, 3 } };
+ matrix_t copy_A1[m][n];
+ matrix_t b1[3] = { 2, 3, -10 };
+ matrix_t x[3];
+
+ printf("A1 = ");
+ matrix_flex_print(m, n, A1, 3, 1);
+
+ puts("Moore Penrose: ");
+ matrix_copy(m, n, A1, copy_A1);
+ error_no = solve(m, n, copy_A1, b1, x, algo);
+ puts("");
+
+ if (error_no > 0) {
+ printf("x1 = ");
+ vector_flex_print(n, x, 3, 1);
+ puts("");
+ }
+
+ puts("Householder: ");
+ algo = Householder;
+ matrix_copy(m, n, A1, copy_A1);
+ error_no = solve(m, n, copy_A1, b1, x, algo);
+
+ if (error_no > 0) {
+ puts("");
+ printf("x1 = ");
+ vector_flex_print(n, x, 3, 1);
+ puts("");
+ }
+
+ puts("Givens: ");
+ algo = Givens;
+ matrix_copy(m, n, A1, copy_A1);
+ error_no = solve(m, n, copy_A1, b1, x, algo);
+
+ if (error_no > 0) {
+ puts("");
+ printf("x1 = ");
+ vector_flex_print(n, x, 3, 1);
+ puts("");
+ }
+
+ puts("Gauss: ");
+ algo = Gauss;
+ matrix_copy(m, n, A1, copy_A1);
+ error_no = solve(m, n, copy_A1, b1, x, algo);
+
+ if (error_no > 0) {
+ puts("");
+ printf("x1 = ");
+ vector_flex_print(n, x, 3, 1);
+ puts("");
+ }
+
+ puts("******* Overdetermined system *******");
+ m = 4;
+ n = 3;
+ matrix_t A2[4][3] = { { 25, 5, 1 },
+ { 64, 8, 1 },
+ { 100, 10, 1 },
+ { 144, 12, 1 }, };
+ matrix_t copy_A2[m][n];
+ matrix_t b2[4] = { 106.8, 177.2, 232.6, 279.2 };
+ printf("A2 = ");
+ matrix_flex_print(m, n, A2, 3, 1);
+
+ puts("Moore Penrose: ");
+ algo = Moore_Penrose;
+ matrix_copy(m, n, A2, copy_A2);
+ error_no = solve(m, n, copy_A2, b2, x, algo);
+
+ if (error_no > 0) {
+ printf("x2 = ");
+ vector_flex_print(n, x, 3, 4);
+ puts("");
+ }
+
+ puts("Householder: ");
+ algo = Householder;
+ matrix_copy(m, n, A2, copy_A2);
+ error_no = solve(m, n, copy_A2, b2, x, algo);
+
+ if (error_no > 0) {
+ printf("x2 = ");
+ vector_flex_print(n, x, 3, 4);
+ puts("");
+ }
+
+ puts("Givens: ");
+ algo = Givens;
+ matrix_copy(m, n, A2, copy_A2);
+ error_no = solve(m, n, copy_A2, b2, x, algo);
+
+ if (error_no > 0) {
+ printf("x2 = ");
+ vector_flex_print(n, x, 3, 4);
+ puts("");
+ }
+
+ puts("******* Underdetermined system *******");
+ m = 3;
+ n = 4;
+ matrix_t A3[3][4] = { { 2, -4, 2, -14 },
+ { -1, 2, -2, 11 },
+ { -1, 2, -1, 7 } };
+ matrix_t copy_A3[m][n];
+ matrix_t b3[3] = { 10, -6, -5 };
+ printf("A3 = ");
+ matrix_flex_print(m, n, A3, 3, 1);
+
+ puts("Moore Penrose: ");
+ algo = Moore_Penrose;
+ matrix_copy(m, n, A3, copy_A3);
+ error_no = solve(m, n, A3, b3, x, algo);
+
+ if (error_no > 0) {
+ printf("x3 = ");
+ vector_flex_print(n, x, 3, 4);
+ puts("");
+ }
+
+ puts("Householder: ");
+ algo = Householder;
+ matrix_copy(m, n, A3, copy_A3);
+ error_no = solve(m, n, copy_A3, b3, x, algo);
+
+ if (error_no > 0) {
+ printf("x3 = ");
+ vector_flex_print(n, x, 3, 4);
+ puts("");
+ }
+
+ puts("Givens: ");
+ algo = Givens;
+ matrix_copy(m, n, A3, copy_A3);
+ error_no = solve(m, n, copy_A3, b3, x, algo);
+
+ if (error_no > 0) {
+ printf("x3 = ");
+ vector_flex_print(n, x, 3, 4);
+ puts("");
+ }
+
+ puts("*** Test: Solve with LU decomposition ***");
+ algo = Gauss;
+ matrix_t A4[5][5] = {
+ { 0.1712, 0.0971, 0.0344, 0.1869, 0.7547 },
+ { 0.7060, 0.8235, 0.4387, 0.4898, 0.2760 },
+ { 0.0318, 0.6948, 0.3816, 0.4456, 0.6797 },
+ { 0.2769, 0.3171, 0.7655, 0.6463, 0.6551 },
+ { 0.0462, 0.9502, 0.7952, 0.7094, 0.1626 }
+ };
+ matrix_t x4[5];
+ matrix_t b4[5] = { 0.1190, 0.4984, 0.9597, 0.3404, 0.5853 };
+
+ m = 5;
+ n = 5;
+ matrix_t copy_A4[m][m];
+ matrix_copy(m, n, A4, copy_A4);
+ error_no = solve(m, n, copy_A4, b4, x4, algo);
+
+ if (error_no > 0) {
+ printf("x4 = ");
+ vector_flex_print(n, x4, 3, 4);
+ puts("");
+ }
+
+ matrix_t dot_b4[5];
+ matrix_mul_vec(m, m, A4, x4, dot_b4);
+ printf("dot_b4 = ");
+ vector_flex_print(n, dot_b4, 3, 4);
+ puts("");
+}
+
+void solve_big_matrix_test(void)
+{
+ matrix_t A[10][5] = { { 0.8147, 0.1576, 0.6557, 0.7060, 0.4387 },
+ { 0.9058, 0.9706, 0.0357, 0.0318, 0.3816 },
+ { 0.1270, 0.9572, 0.8491, 0.2769, 0.7655 },
+ { 0.9134, 0.4854, 0.9340, 0.0462, 0.7952 },
+ { 0.6324, 0.8003, 0.6787, 0.0971, 0.1869 },
+ { 0.0975, 0.1419, 0.7577, 0.8235, 0.4898 },
+ { 0.2785, 0.4218, 0.7431, 0.6948, 0.4456 },
+ { 0.5469, 0.9157, 0.3922, 0.3171, 0.6463 },
+ { 0.9575, 0.7922, 0.6555, 0.9502, 0.7094 },
+ { 0.9649, 0.9595, 0.1712, 0.0344, 0.7547 } };
+ uint8_t m = 10, n = 5;
+ int8_t error_no;
+ enum ALGORITHM algo;
+ matrix_t copy_A[m][n];
+ matrix_t b[10] = { 1.2902, 0.8819, 0.9721, 1.2347, 0.9185, 0.9844, 1.0627,
+ 1.0280, 1.7283, 1.0618 };
+ matrix_t x[n];
+
+ printf("A = ");
+ matrix_flex_print(m, n, A, 3, 4);
+
+ puts("Moore Penrose: ");
+ algo = Moore_Penrose;
+ matrix_copy(m, n, A, copy_A);
+ error_no = solve(m, n, copy_A, b, x, algo);
+ puts("");
+
+ if (error_no > 0) {
+ printf("x = ");
+ vector_flex_print(n, x, 3, 4);
+ puts("");
+ }
+
+ puts("Householder: ");
+ algo = Householder;
+ matrix_copy(m, n, A, copy_A);
+ error_no = solve(m, n, copy_A, b, x, algo);
+
+ if (error_no > 0) {
+ puts("");
+ printf("x = ");
+ vector_flex_print(n, x, 3, 4);
+ puts("");
+ }
+
+ puts("Givens: ");
+ algo = Givens;
+ matrix_copy(m, n, A, copy_A);
+ error_no = solve(m, n, copy_A, b, x, algo);
+
+ if (error_no > 0) {
+ puts("");
+ printf("x = ");
+ vector_flex_print(n, x, 3, 4);
+ puts("");
+ }
+}
diff --git a/examples/linear_algebra/utilities/include/utils_test.h b/examples/linear_algebra/utilities/include/utils_test.h
new file mode 100644
index 0000000000000000000000000000000000000000..9390b51182f10d3dde4c4ad6c598707ab6c7af5a
--- /dev/null
+++ b/examples/linear_algebra/utilities/include/utils_test.h
@@ -0,0 +1,33 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @ingroup examples
+ * @{
+ *
+ * @file
+ * @brief Examples of the utility functions.
+ *
+ * @details Utility examples (see @ref utils.h "utilities" functions).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#ifndef UTILS_TEST_H_
+#define UTILS_TEST_H_
+
+/**
+ * @brief Examples of the utility functions.
+ *
+ */
+void utils_test(void);
+
+#endif /* UTILS_TEST_H_*/
diff --git a/examples/linear_algebra/utilities/utils_test.c b/examples/linear_algebra/utilities/utils_test.c
new file mode 100644
index 0000000000000000000000000000000000000000..473bfecb75a9ac18af024eb6604cec1e02b3417b
--- /dev/null
+++ b/examples/linear_algebra/utilities/utils_test.c
@@ -0,0 +1,92 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @{
+ *
+ * @file
+ * @brief Examples of the utility functions.
+ *
+ * @details Utility examples (see @ref utils.h "utilities" functions).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#include <stdio.h>
+
+#include "utils.h"
+#include "vector.h"
+
+void utils_test(void)
+{
+ puts("############ Test Utils ###############");
+ double deg_ang = 45;
+ double rad_ang = utils_to_radian(deg_ang);
+ printf("rad_ang = %.4f\n", rad_ang);
+
+ float f1 = 4.78;
+ float f2 = 11.77;
+ float f_max = (float)utils_max(f1, f2);
+ printf("f_max = %.4f\n", f_max);
+
+ float f_min = (float)utils_min(f1, f2);
+ printf("f_min = %.4f\n", f_min);
+
+ uint8_t a1 = 9;
+ uint8_t b1 = 13;
+ utils_swap(&a1, &b1);
+ printf("a1 = %u, b1 = %u\n", a1, b1);
+
+ printf("sind(45) = %.4f\n", utils_sind(deg_ang));
+
+ vector_t arr[10] = { 4, 8, 6, -1, -2, -3, -1, 3, 4, 5 };
+ vector_t mv_aver_arr[10];
+ uint8_t win_size = 5;
+ double mean = 0.0;
+
+ printf("arr = ");
+ vector_flex_print(10, arr, 3, 0);
+ puts("");
+ printf("win_size = %u\n", win_size);
+ utils_moving_average(10, arr, win_size, mv_aver_arr);
+ printf("mv_av_arr = ");
+ vector_flex_print(10, mv_aver_arr, 3, 4);
+ puts("");
+ mean = utils_mean(10, arr);
+ printf("mean = %3.4f\n", mean);
+
+ puts("!!! Median algorithm !!!");
+ vector_t arr1[9] = { 100, 91, 92, 85, 40, 77, 92, 91, 94 };
+ vector_t median_val = 0.0;
+
+ printf("arr1 = ");
+ vector_flex_print(9, arr1, 3, 0);
+ puts("");
+ median_val = utils_get_median(arr1, 9);
+ printf("median1 = %3.4f\n", median_val);
+
+ vector_t arr2[13] = { 0.4854, 0.8003, 0.1419, 0.4218, 0.9157, 0.7922,
+ 0.9595, 0.6557, 0.0357, 0.8491, 0.9340, 0.6787,
+ 0.7577 };
+ printf("arr2 = ");
+ vector_flex_print(13, arr2, 3, 4);
+ puts("");
+ median_val = utils_get_median(arr2, 13);
+ printf("median2 = %3.4f\n", median_val);
+
+ vector_t arr3[12] = { 0.9502, 0.0344, -0.4387, 0.3816, 0.7655, 0.7952,
+ 0.1869, 0.4898, 0.4456, 0.6463, -0.7094, 0.7547 };
+ printf("arr3 = ");
+ vector_flex_print(12, arr3, 3, 4);
+ puts("");
+ median_val = utils_get_median(arr3, 12);
+ printf("median3 = %3.4f\n", median_val);
+}
diff --git a/examples/localization/position_algos/distance_based/distance_based_test.c b/examples/localization/position_algos/distance_based/distance_based_test.c
new file mode 100644
index 0000000000000000000000000000000000000000..46db3bbfacdb9f4ea4acbc129603f96636c54420
--- /dev/null
+++ b/examples/localization/position_algos/distance_based/distance_based_test.c
@@ -0,0 +1,58 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @{
+ *
+ * @file
+ * @brief Examples of localization algorithms of distance-based positioning systems.
+ *
+ * @details Localization algorithms examples using distance measures (see the
+ * @ref dist_based_position.h "methods of distance-based" localization systems).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * @author Abdelmoumen Norrdine <a.norrdine@googlemail.com>
+ *
+ * @}
+ */
+
+#include <stdio.h>
+
+#include "trilateration.h"
+#include "matrix.h"
+#include "vector.h"
+#include "dist_based_position.h"
+
+void distance_based_test(void)
+{
+ puts("***************** Distance-based system example *****************");
+ matrix_t ref_pos_matrix[4][3] = { { 0, 0, 1.67 }, // P1
+ { 4.5, 0, 0.75 }, // P2
+ { 4.5, 4.45, 0.75 }, // P3
+ { 0, 4.92, 0.86 } // P4
+ };
+
+ matrix_t true_pos[3] = { 1.0000, 3.0000, 0.0000 }; // is usually unknown
+ /* measured distances to the reference stations */
+ matrix_t measured_dist_arr[4] = { 3.577157155, 4.685985423, 3.883094303,
+ 2.320377599 };
+ /* estimated position */
+ matrix_t est_pos[4];
+ uint8_t ref_point_num = 4;
+ trilateration2(ref_point_num, ref_pos_matrix, measured_dist_arr,
+ est_pos, NULL);
+
+ printf("true position = ");
+ vector_flex_print(3, true_pos, 5, 4);
+ puts("");
+
+ printf("estimated position = ");
+ vector_flex_print(3, &est_pos[1], 5, 7);
+ puts("");
+}
diff --git a/examples/localization/position_algos/distance_based/include/distance_based_test.h b/examples/localization/position_algos/distance_based/include/distance_based_test.h
new file mode 100644
index 0000000000000000000000000000000000000000..69e86ca3cb50870bbbfd53149944b6a472ab882b
--- /dev/null
+++ b/examples/localization/position_algos/distance_based/include/distance_based_test.h
@@ -0,0 +1,36 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @ingroup examples
+ * @{
+ *
+ * @file
+ * @brief Examples of localization algorithms of distance-based positioning systems.
+ *
+ * @details Localization algorithms examples using distance measures (see the
+ * @ref dist_based_position.h "methods of distance-based" localization systems).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * @author Abdelmoumen Norrdine <a.norrdine@googlemail.com>
+ *
+ * @}
+ */
+
+#ifndef DISTANCE_BASED_TEST_H_
+#define DISTANCE_BASED_TEST_H_
+
+/**
+ * @brief Example of a distance-based localization system.
+ * @details This example shows how to use the trilateration algorithm, whereby an estimated
+ * position is calculated based on the distance measurements.
+ */
+void distance_based_test(void);
+
+#endif /* DISTANCE_BASED_TEST_H_ */
diff --git a/examples/localization/position_algos/magnetic_based/include/magnetic_based_test.h b/examples/localization/position_algos/magnetic_based/include/magnetic_based_test.h
new file mode 100644
index 0000000000000000000000000000000000000000..51672315795941c6886fd202308394e74fcffee3
--- /dev/null
+++ b/examples/localization/position_algos/magnetic_based/include/magnetic_based_test.h
@@ -0,0 +1,36 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @ingroup examples
+ * @{
+ *
+ * @file
+ * @brief Examples of localization algorithms of magnetic-based positioning systems.
+ *
+ * @details Localization algorithms examples using artificially generated DC-pulsed, magnetic
+ * signals (see the @ref magnetic_based_position.h "methods of magnetic-based" localization
+ * systems).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * @author Abdelmoumen Norrdine <a.norrdine@googlemail.com>
+ *
+ * @}
+ */
+
+#ifndef MAGNETIC_BASED_TEST_H_
+#define MAGNETIC_BASED_TEST_H_
+
+/**
+ * @brief Example of a magnetic-based localization system.
+ *
+ */
+void magnetic_based_test(void);
+
+#endif /* MAGNETIC_BASED_TEST_H_ */
diff --git a/examples/localization/position_algos/magnetic_based/magnetic_based_test.c b/examples/localization/position_algos/magnetic_based/magnetic_based_test.c
new file mode 100644
index 0000000000000000000000000000000000000000..bd39ad41661e4ffde244a9a85a40078e516ecb7e
--- /dev/null
+++ b/examples/localization/position_algos/magnetic_based/magnetic_based_test.c
@@ -0,0 +1,73 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @{
+ *
+ * @file
+ * @brief Examples of localization algorithms of magnetic-based positioning systems.
+ *
+ * @details Localization algorithms examples using artificially generated DC-pulsed, magnetic
+ * signals (see the @ref magnetic_based_position.h "methods of magnetic-based"
+ * localization systems).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * @author Abdelmoumen Norrdine <a.norrdine@googlemail.com>
+ *
+ * @}
+ */
+
+#include <stdio.h>
+
+#include "matrix.h"
+#include "vector.h"
+#include "utils.h"
+#include "trilateration.h"
+#include "magnetic_based_position.h"
+
+void magnetic_based_test(void)
+{
+ puts("***************** Magnetic-based system example *****************");
+ matrix_t ref_pos_matrix[4][3] = {
+ { 100.395, 16.781, 1.084 }, //P1
+ { 100.937, 22.941, 1.072 }, //P2
+ { 106.229, 22.716, 1.064 }, //P3
+ { 106.3, 16.8, 2.35 } //P4
+ };
+
+ matrix_t true_pos[3] = { 102, 18, 2.308 }; // is usually unknown // Sensor8a3
+
+ /* magnetic field strengths to the reference stations */
+ matrix_t B_vec[4] = { 43.2630, 3.0620, 1.4890, 4.5361 };
+ /* Elevation angles to the reference stations */
+ matrix_t theta_vec[4] = { 31.3710, 12.4870, 11.7280, 0.5352 };
+ uint8_t ref_point_num = 4;
+ matrix_t r0_vec[ref_point_num];
+
+ for (uint8_t i = 0; i < ref_point_num; i++) {
+
+ r0_vec[i] = magnetic_based_get_r(B_vec[i],
+ utils_to_radian(theta_vec[i]), K_T);
+
+ }
+
+ /* estimated position */
+ matrix_t est_pos[4];
+ trilateration2(ref_point_num, ref_pos_matrix, r0_vec,
+ est_pos, NULL);
+
+ printf("true position = ");
+ vector_flex_print(3, true_pos, 5, 4);
+ puts("");
+
+ printf("estimated position = ");
+ vector_flex_print(3, &est_pos[1], 5, 7);
+ puts("");
+
+}
diff --git a/examples/localization/position_algos/pos_algos_common/include/pos_algos_common_test.h b/examples/localization/position_algos/pos_algos_common/include/pos_algos_common_test.h
new file mode 100644
index 0000000000000000000000000000000000000000..d531bd6c8f1e1d50a55fd54cc00bbac1d28bb29a
--- /dev/null
+++ b/examples/localization/position_algos/pos_algos_common/include/pos_algos_common_test.h
@@ -0,0 +1,34 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @ingroup examples
+ * @{
+ *
+ * @file
+ * @brief Examples of common algorithms of localization systems.
+ *
+ * @details Common algorithms examples of positioning systems (see the
+ * @ref pos_algos_common "positioning algorithms common" module).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#ifndef POS_ALGOS_COMMON_TEST_H_
+#define POS_ALGOS_COMMON_TEST_H_
+
+/**
+ * @brief Example of common localization algorithms.
+ *
+ */
+void pos_algos_common_test(void);
+
+#endif /* POS_ALGOS_COMMON_TEST_H_ */
diff --git a/examples/localization/position_algos/pos_algos_common/pos_algos_common_test.c b/examples/localization/position_algos/pos_algos_common/pos_algos_common_test.c
new file mode 100644
index 0000000000000000000000000000000000000000..da9d42c9c98b3d02b9a5a89381d65b3e88c2c589
--- /dev/null
+++ b/examples/localization/position_algos/pos_algos_common/pos_algos_common_test.c
@@ -0,0 +1,50 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @{
+ *
+ * @file
+ * @brief Examples of common algorithms of localization systems.
+ *
+ * @details Common algorithms examples of positioning systems (see the
+ * @ref pos_algos_common "positioning algorithms common" module).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#include <stdio.h>
+
+#include "DOP.h"
+#include "matrix.h"
+#include "trilateration.h"
+
+void pos_algos_common_test(void)
+{
+ matrix_t ref_pos_matrix[4][3] = { { 0, 0, 1.67 }, // P1
+ { 4.5, 0, 0.75 }, // P2
+ { 4.5, 4.45, 0.75 }, // P3
+ { 0, 4.92, 0.86 } // P4
+ };
+
+ uint8_t m = 4;
+ double A_matrix[m][4];
+ double true_pos[] = { 1, 1, 0 };
+
+ double pdop_val = get_PDOP(m, ref_pos_matrix, true_pos);
+
+ printf("pdop_val = %.7f\n", pdop_val);
+
+ trilateration_get_A_matrix(m, ref_pos_matrix, A_matrix);
+ printf("A_matrix = ");
+ matrix_flex_print(m, 4, A_matrix, 3, 7);
+ puts("");
+}
diff --git a/examples/localization/position_optimization/include/multipath_algo_own_norm_distr_test.h b/examples/localization/position_optimization/include/multipath_algo_own_norm_distr_test.h
new file mode 100644
index 0000000000000000000000000000000000000000..4848303d489db8ec9a27b1dd7b966909f225da1a
--- /dev/null
+++ b/examples/localization/position_optimization/include/multipath_algo_own_norm_distr_test.h
@@ -0,0 +1,34 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @ingroup examples
+ * @{
+ *
+ * @file
+ * @brief Example of the algorithm for the recognition and mitigation of multipath effects.
+ *
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * @author Naouar Guerchali
+ * @author Abdelmoumen Norrdine <a.norrdine@googlemail.com>
+ *
+ * @}
+ */
+
+#ifndef MULTIPATH_ALGO_OWN_NORM_DISTR_TEST_H_
+#define MULTIPATH_ALGO_OWN_NORM_DISTR_TEST_H_
+
+/**
+ * @brief Example of the algorithm for the recognition and mitigation of multipath effects.
+ *
+ */
+void multipath_algo_own_norm_distr_test(void);
+
+#endif /* MULTIPATH_ALGO_OWN_NORM_DISTR_TEST_H_ */
diff --git a/examples/localization/position_optimization/include/position_optimization_test.h b/examples/localization/position_optimization/include/position_optimization_test.h
new file mode 100644
index 0000000000000000000000000000000000000000..ca1b9835d0ddd63c276a8270fa898f9a4a28e0b4
--- /dev/null
+++ b/examples/localization/position_optimization/include/position_optimization_test.h
@@ -0,0 +1,37 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @ingroup examples
+ * @{
+ *
+ * @file
+ * @brief Examples of optimization algorithms for localization systems.
+ *
+ * @details Optimization algorithms examples for localization systems. (see the @ref
+ * loc_gauss_newton.h "modified GN" and @ref loc_levenberg_marquardt.h "LVM"
+ * optimization methods).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * @author Naouar Guerchali
+ * @author Abdelmoumen Norrdine <a.norrdine@googlemail.com>
+ *
+ * @}
+ */
+
+#ifndef POSITION_OPTIMIZATION_TEST_H_
+#define POSITION_OPTIMIZATION_TEST_H_
+
+/**
+ * @brief Examples of optimization algorithms of a localization system.
+ *
+ */
+void position_optimization_test(void);
+
+#endif /* POSITION_OPTIMIZATION_TEST_H_ */
diff --git a/examples/localization/position_optimization/multipath_algo_own_norm_distr_test.c b/examples/localization/position_optimization/multipath_algo_own_norm_distr_test.c
new file mode 100644
index 0000000000000000000000000000000000000000..354bb6a7a5f325c712e188cdf85c6e1d0d94ab8e
--- /dev/null
+++ b/examples/localization/position_optimization/multipath_algo_own_norm_distr_test.c
@@ -0,0 +1,217 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @{
+ *
+ * @file
+ * @brief Example of the algorithm for the recognition and mitigation of multipath effects.
+ *
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * @author Naouar Guerchali
+ * @author Abdelmoumen Norrdine <a.norrdine@googlemail.com>
+ *
+ * @}
+ */
+
+#include <float.h>
+#include <stdio.h>
+#include <unistd.h>
+#include <inttypes.h>
+
+#include "multipath_dist_detection_mitigation.h"
+#include "loc_levenberg_marquardt.h"
+#include "norm_dist_rnd_generator.h"
+#include "dist_based_jacobian.h"
+#include "dist_based_fi.h"
+#include "shell_sort.h"
+#include "vector.h"
+#include "DOP.h"
+
+void multipath_algo_own_norm_distr_test(void)
+{
+ //to get the console output in the debugging mode.
+ setvbuf(stdout, NULL, _IONBF, 0);
+ setvbuf(stderr, NULL, _IONBF, 0);
+ uint8_t n = 8; //length of alphabet
+ uint8_t k = 4; //length of figures
+
+ matrix_t ref_matrix[][3] = { { 1, 1, 1 },
+ { 20, 1, 1 },
+ { 20, 20, 1 },
+ { 1, 20, 1 },
+ { 1, 1, 20 },
+ { 20, 1, 20 },
+ { 20, 20, 20 },
+ { 1, 20, 20 } };
+
+ matrix_t opt_noised_r_vec[k];
+
+ matrix_t sol_x[3];
+ matrix_t optimal_start_pos[3];
+ matrix_t tmp_start_optimal[3];
+ uint8_t optimal_anchor_combi_arr[k];
+ uint8_t PDOP_Threshold = 8;
+ uint8_t maxit = 100;
+ uint8_t it = 0;
+ matrix_t tau = 1e-6;
+ matrix_t eps = 1e-5;
+ matrix_t beta0 = 0.2;
+ matrix_t beta1 = 0.8;
+ uint8_t d_max = 19;
+ uint8_t grid_cell_length = 2;
+ uint8_t axis_point_num = d_max / grid_cell_length;
+ uint32_t exact_point[3];
+ //matrix_t multipath[] = {5,3};
+ //matrix_t multipath[] = {4,3}; // for 4 anchors
+ matrix_t multipath[] = { 3 }; // for 4 anchors
+ uint8_t anchor_num = n;
+ uint32_t room_point_num;
+ matrix_t noised_r_vec[anchor_num];
+ uint32_t counter = 0;
+ matrix_t mean_lvm_call_num = 0;
+ matrix_t sigma = 0.1;
+ int32_t initial_seed_val = 3;
+ int32_t seed = 0;
+
+ /************************************************/
+
+ puts("################ START ################");
+
+ // initialize seed's value
+ seed = initial_seed_val;
+
+ //Sampling the room
+ for (uint32_t z = 0; z <= axis_point_num; z++) {
+ exact_point[2] = ref_matrix[0][2] + grid_cell_length * z;
+
+ for (uint32_t y = 0; y <= axis_point_num; y++) {
+ exact_point[1] = ref_matrix[0][1]
+ + grid_cell_length * y;
+
+ for (uint32_t x = 0; x <= axis_point_num; x++) {
+ exact_point[0] = ref_matrix[0][0]
+ + grid_cell_length * x;
+
+ if (!is_anchor(anchor_num, ref_matrix,
+ exact_point)) {
+ printf("seed = %ld\n", (long) seed);
+ sim_UWB_dist(n, ref_matrix, exact_point,
+ sigma, 2, multipath,
+ seed, noised_r_vec);
+ seed = 2 * initial_seed_val + 1;
+ initial_seed_val++;
+
+ recog_mitigate_multipath(k, n,
+ ref_matrix,
+ noised_r_vec,
+ optimal_anchor_combi_arr,
+ optimal_start_pos);
+
+ // PDOP & Levenberg
+ matrix_t opt_ref_matrix_comb_matrix[k][3];
+
+ get_optimal_partial_ref_matrix(n,
+ ref_matrix, k,
+ optimal_anchor_combi_arr,
+ opt_ref_matrix_comb_matrix);
+ matrix_t PDOP =
+ get_PDOP(k,
+ opt_ref_matrix_comb_matrix,
+ optimal_start_pos);
+
+ get_optimal_partial_r_noised_vec(k,
+ noised_r_vec,
+ optimal_anchor_combi_arr,
+ opt_noised_r_vec);
+
+ if (PDOP > PDOP_Threshold) {
+ vector_get_elements(
+ noised_r_vec, k,
+ optimal_anchor_combi_arr,
+ opt_noised_r_vec);
+ vector_copy(3,
+ optimal_start_pos,
+ tmp_start_optimal);
+ it =
+ loc_levenberg_marquardt(
+ 3,
+ opt_ref_matrix_comb_matrix,
+ optimal_start_pos,
+ opt_noised_r_vec,
+ eps,
+ tau,
+ beta0,
+ beta1,
+ maxit,
+ sol_x,
+ dist_based_f_i,
+ dist_based_jacobian_get_JTJ,
+ dist_based_jacobian_get_JTf,
+ dist_based_jacobian_get_J_mul_s);
+ mean_lvm_call_num++;
+
+ }
+ else {
+ it = 0;
+ vector_copy(3,
+ optimal_start_pos,
+ sol_x);
+ }
+
+ puts(
+ "------------------------------------------------------------");
+ printf("PDOP = %f | it = %d\n", PDOP,
+ it);
+
+ printf("r_noised_vec = ");
+ //matrix_print_array(r_noised_vec, n, 7);
+ vector_flex_print(n, noised_r_vec, 5,
+ 7);
+ puts("");
+ printf(
+ "anchors_optimal = {%u, %u, %u, %u}\n",
+ optimal_anchor_combi_arr[0],
+ optimal_anchor_combi_arr[1],
+ optimal_anchor_combi_arr[2],
+ optimal_anchor_combi_arr[3]);
+ printf(
+ "exact point = {%lu, %lu, %lu}\n",
+ (unsigned long)exact_point[0],
+ (unsigned long)exact_point[1],
+ (unsigned long)exact_point[2]);
+ if (it != 0) {
+ printf(
+ "start_optimal = {%f, %f, %f}\n",
+ tmp_start_optimal[0],
+ tmp_start_optimal[1],
+ tmp_start_optimal[2]);
+ }
+
+ printf("x_sol = {%.7f, %.7f, %.7f}\n",
+ sol_x[0],
+ sol_x[1],
+ sol_x[2]);
+ counter++;
+ }//x
+ }//if
+ }//y
+ }//Z
+
+ room_point_num = counter;
+ puts(
+ "----------------------------- End Simulation -------------------------------");
+ printf("Counter = %lu\n", (unsigned long) counter);
+ printf("room point num = %lu\n", (unsigned long) room_point_num);
+ printf("anchors num = %u\n", n);
+ printf("LVM call number = %f\n", mean_lvm_call_num);
+ printf("mean LVM call number = %f\n",
+ mean_lvm_call_num / room_point_num);
+}
diff --git a/examples/localization/position_optimization/position_optimization_test.c b/examples/localization/position_optimization/position_optimization_test.c
new file mode 100644
index 0000000000000000000000000000000000000000..9ee14af6e85121c6c294d4038a3beecec782be0f
--- /dev/null
+++ b/examples/localization/position_optimization/position_optimization_test.c
@@ -0,0 +1,84 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @{
+ *
+ * @file
+ * @brief Examples of optimization algorithms for localization systems.
+ *
+ * @details Optimization algorithms examples for localization systems. (see the
+ * @ref loc_gauss_newton.h "modified GN" and @ref loc_levenberg_marquardt.h "LVM"
+ * optimization methods).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * @author Naouar Guerchali
+ * @author Abdelmoumen Norrdine <a.norrdine@googlemail.com>
+ *
+ * @}
+ */
+
+#include <stdio.h>
+#include <stdint.h>
+
+#include "loc_levenberg_marquardt.h"
+#include "loc_gauss_newton.h"
+#include "dist_based_fi.h"
+#include "dist_based_position.h"
+#include "dist_based_jacobian.h"
+#include "vector.h"
+
+void position_optimization_test(void)
+{
+ matrix_t ref_pos_matrix[4][3] = { { 0, 0, 1.67 }, // P1
+ { 4.5, 0, 0.75 }, // P2
+ { 4.5, 4.45, 0.75 }, // P3
+ { 0, 4.92, 0.86 } // P4
+ };
+
+ uint8_t ref_num = 4;
+ double true_pos[] = { 1.0000, 1.0000, 0.0000 };
+ double measured_dist_arr[] = { 2.1893555, 3.7321172, 4.9925183, 4.1269400 };
+ vector_t start_pos[] = { 0.9645166, 0.9894337, -0.1127879 };
+ double est_pos[3];
+
+ uint8_t iter_num;
+ matrix_t fmin = 1e-11;
+ matrix_t eps = 1e-3;
+ matrix_t beta0 = 0.2;
+ matrix_t beta1 = 0.8;
+ matrix_t tau = 1e-6;
+ uint8_t max_iter_num = 100;
+
+ iter_num = loc_gauss_newton(ref_num, ref_pos_matrix, start_pos,
+ measured_dist_arr, eps, fmin, max_iter_num, est_pos,
+ &dist_based_f_i, &dist_based_jacobian_get_JTJ,
+ &dist_based_jacobian_get_JTf);
+ printf("True position = ");
+ vector_flex_print(3, true_pos, 3, 4);
+ puts("");
+ printf("Optimized position with Gauss-Newton algorithm = ");
+ vector_flex_print(3, est_pos, 5, 7);
+ puts("");
+ printf("iteration number = %u\n", iter_num);
+
+ vector_clear((uint8_t) 3, est_pos);
+
+ iter_num = loc_levenberg_marquardt(ref_num, ref_pos_matrix, start_pos,
+ measured_dist_arr, eps, tau, beta0, beta1, max_iter_num,
+ est_pos,
+ &dist_based_f_i, &dist_based_jacobian_get_JTJ,
+ &dist_based_jacobian_get_JTf,
+ &dist_based_jacobian_get_J_mul_s);
+ printf("Optimized position with Levenberg-Marquardt algorithm = ");
+ vector_flex_print(3, est_pos, 5, 7);
+ puts("");
+ printf("iteration number = %u\n", iter_num);
+
+}
diff --git a/examples/non_linear_algebra/optimization/include/optimization_test.h b/examples/non_linear_algebra/optimization/include/optimization_test.h
new file mode 100644
index 0000000000000000000000000000000000000000..7a7daf6ea081533c8a79cc3b7eaff72f5c41734a
--- /dev/null
+++ b/examples/non_linear_algebra/optimization/include/optimization_test.h
@@ -0,0 +1,61 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @ingroup examples
+ * @{
+ *
+ * @file
+ * @brief Examples of optimization algorithms.
+ *
+ * @details Optimization algorithms examples (see the @ref modified_gauss_newton.h
+ * "modified GN" and @ref levenberg_marquardt.h "LVM" optimization methods).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#ifndef EXAMPLES_OPTIMIZATION_TEST_H_
+#define EXAMPLES_OPTIMIZATION_TEST_H_
+
+/**
+ * @brief Examples of optimization algorithms using the LVM and GN algorithms.
+ *
+ */
+void optimization_test(void);
+
+
+/**
+ * @brief Examples of optimization algorithms using exponential data.
+ * @details The model function is:
+ * \f$
+ * g(\vec{x}, t) = x_1 \mathrm{e}^{x_2t},
+ * \f$ where \f$\vec{x} = [x_1, x_2]^T\f$ and \f$ \vec{x_0} = [6,.3]\f$ is the initial
+ * guess. The data set is \f$ d(t_i, y_i)\f$, whereby \f$ t_i \f$ is equal to
+ * \f$ \lbrace 1, \hdots, 8 \rbrace\f$ and \f$ y_i\f$ is equal to \f$\lbrace 8.3, 11.0,
+ * 14.7, 19.7, 26.7, 35.2, 44.4, 55.9 \rbrace \f$.
+ *
+ */
+void optimization_exponential_data_test(void);
+
+/**
+ * @brief Examples of optimization algorithms using sinusoidal data.
+ * @details The model function is:
+ * \f$
+ * g(\vec{x}, t) = x_1 \sin\left( x_2t +x_3\right) + x_4,
+ * \f$ whereby \f$\vec{x} = [x_1, x_2, x_3, x_4]^T\f$ and \f$\vec{x_0} =
+ * [17, 0.5, 10.5, 77]\f$ is the initial guess. The set of data points is
+ * \f$ d(t_i, y_i) \f$, where \f$t_i \f$ is equal to \f$\lbrace 1, \hdots,
+ * 12 \rbrace\f$ and \f$y_i\f$ is equal to \f$\lbrace 61, 65, 72, 78, 85, 90, 92, 92,
+ * 88, 81, 72, 63 \rbrace\f$.
+ */
+void optimization_sinusoidal_data_test(void);
+
+#endif /* EXAMPLES_OPTIMIZATION_TEST_H_ */
diff --git a/examples/non_linear_algebra/optimization/optimization_test.c b/examples/non_linear_algebra/optimization/optimization_test.c
new file mode 100644
index 0000000000000000000000000000000000000000..0d5a74d9635730fff9f689922cb6070f0e49eadd
--- /dev/null
+++ b/examples/non_linear_algebra/optimization/optimization_test.c
@@ -0,0 +1,421 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @{
+ *
+ * @file
+ * @brief Examples of optimization algorithms.
+ *
+ * @details Optimization algorithms examples (see the @ref modified_gauss_newton.h
+ * "modified GN" and @ref levenberg_marquardt.h "LVM" optimization methods).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#include <stdio.h>
+#include <math.h>
+
+#include "matrix.h"
+#include "vector.h"
+#include "levenberg_marquardt.h"
+#include "modified_gauss_newton.h"
+
+/**
+ * @brief Calculate the Jacobian matrix of the function @ref optimization_get_f_error.
+ *
+ * @param[in] x0_vec[] start values.
+ * @param[out] J[][] calculated Jacobian matrix.
+ *
+ */
+void optimization_get_J(vector_t x0_vec[], matrix_t J[][3])
+{
+ uint8_t i;
+ matrix_t denom;
+ uint8_t row_num = 4;
+
+ matrix_t ref_value_matrix[4][3] = { { 0, 0, 1.67 },
+ { 4.5, 0, 0.75 },
+ { 4.5, 4.45, 0.75 },
+ { 0, 4.92, 0.86 } };
+
+ for (i = 0; i < row_num; i++) {
+ denom = sqrt(pow(x0_vec[0] - ref_value_matrix[i][0], 2) +
+ pow(x0_vec[1] - ref_value_matrix[i][1], 2) +
+ pow(x0_vec[2] - ref_value_matrix[i][2], 2));
+ if (denom != 0) {
+ J[i][0] = (x0_vec[0] - ref_value_matrix[i][0]) / denom;
+ J[i][1] = (x0_vec[1] - ref_value_matrix[i][1]) / denom;
+ J[i][2] = (x0_vec[2] - ref_value_matrix[i][2]) / denom;
+ }
+ }
+}
+
+/**
+ * @brief Calculate the error vector of the approximation.
+ *
+ * @param[in] x0_vec[] start values.
+ * @param[in] measured_data_vec[] measured data vector.
+ * @param[out] f_vec[] calculated error vector.
+ *
+ */
+void optimization_get_f_error(vector_t x0_vec[], vector_t measured_data_vec[],
+ vector_t f_vec[])
+{
+ uint8_t i;
+ uint8_t row_num = 4;
+ matrix_t ref_point_mat[4][3] = { { 0, 0, 1.67 },
+ { 4.5, 0, 0.75 },
+ { 4.5, 4.45, 0.75 },
+ { 0, 4.92, 0.86 } };
+
+ for (i = 0; i < row_num; i++) {
+ f_vec[i] =
+ sqrt(
+ (x0_vec[0] - ref_point_mat[i][0])
+ * (x0_vec[0]
+ - ref_point_mat[i][0])
+ +
+ (x0_vec[1]
+ - ref_point_mat[i][1])
+ * (x0_vec[1]
+ - ref_point_mat[i][1])
+ +
+ (x0_vec[2]
+ - ref_point_mat[i][2])
+ * (x0_vec[2]
+ - ref_point_mat[i][2])
+ )
+ - measured_data_vec[i];
+ }
+}
+
+void optimization_test(void)
+{
+ puts(
+ "***************** Optimization test *****************");
+
+ matrix_t true_values_matrix[9][3] = {
+ { 1, 1, 0 }, // T1
+ { 1, 2, 0 }, // T2
+ { 1, 3, 0 }, // T3
+ { 2, 1, 0 }, // T4
+ { 2, 2, 0 }, // T5
+ { 2, 3, 0 }, // T6
+ { 3, 1, 0 }, // T7
+ { 3, 2, 0 }, // T8
+ { 3, 3, 0 }, // T9
+ };
+
+ matrix_t x0_matrix[9][3] = {
+ { 0.9645166, 0.9894337, -0.1127879 }, // X0_1
+ { 0.9706874, 1.9937843, -0.0767517 }, // X0_2
+ { 0.9759567, 2.9980380, -0.0421651 }, // X0_3
+ { 1.9666907, 0.9892634, -0.1184331 }, // X0_4
+ { 1.9734193, 1.9945307, -0.0776960 }, // X0_5
+ { 1.9791861, 2.9997600, -0.0385668 }, // X0_6
+ { 2.9676093, 0.9886335, -0.1290797 }, // X0_7
+ { 2.9749588, 1.9950495, -0.0824135 }, // X0_8
+ { 2.9814874, 3.0015139, -0.0370967 }, // X0_9
+ };
+
+ matrix_t measured_values_matrix[9][4] = {
+ { 2.189355547, 3.732117187, 4.992518309, 4.126940038 }, // M1
+ { 2.791860082, 4.115904867, 4.358726079, 3.195059925 }, // M2
+ { 3.577157155, 4.685985423, 3.883094303, 2.320377599 }, // M3
+ { 2.791860082, 2.810684972, 4.347183679, 4.474971454 }, // M4
+ { 3.285646100, 3.303836609, 3.600904464, 3.633252051 }, // M5
+ { 3.974524884, 3.992093430, 3.006899725, 2.893757310 }, // M6
+ { 3.577157155, 1.968162419, 3.857113556, 5.001588788 }, // M7
+ { 3.974524884, 2.625676627, 2.990106568, 4.264874121 }, // M8
+ { 4.560484620, 3.452531771, 2.238079928, 3.655150652 }, // M9
+ };
+
+ uint8_t vector_values_num = 9;
+ uint8_t f_length = 4;
+ uint8_t i;
+
+ //GN & LVM-parameters
+ matrix_t fmin = 1e-11;
+ matrix_t eps = 1e-3;
+ matrix_t beta0 = 0.2;
+ matrix_t beta1 = 0.8;
+ matrix_t tau = 1e-6;
+ uint8_t max_iter_num = 100;
+ uint8_t iter_num;
+ matrix_t est_values_vec[3];
+
+ printf("\nseeked_values_matrix = ");
+ matrix_flex_print(vector_values_num, 3, true_values_matrix, 7, 3);
+ puts("");
+
+ puts("############## PARAMETERS #################");
+ printf("eps = %.0e\ntau = %.0e\nfmin = %.0e\n", eps, tau, fmin);
+
+ for (i = 0; i < vector_values_num; i++) {
+ /************************************** Gauss-Newton **************************************/
+
+ printf(
+ "\n----------------------------------------- T%u ----------------------------------\n",
+ i + 1);
+ printf("true vector value = {%.4f, %.4f, %.4f}\n",
+ true_values_matrix[i][0],
+ true_values_matrix[i][1],
+ true_values_matrix[i][2]);
+ printf("start vector value = ");
+ vector_flex_print(3, x0_matrix[i], 5, 7);
+ puts("");
+
+ iter_num = modified_gauss_newton(f_length, 3, x0_matrix[i],
+ measured_values_matrix[i], eps, fmin,
+ max_iter_num, est_values_vec,
+ &optimization_get_f_error, &optimization_get_J);
+ printf("Gauss-Newton solution = ");
+ vector_flex_print(3, est_values_vec, 5, 7);
+ puts("");
+ printf("iteration number = %u\n", iter_num);
+
+ vector_clear((uint8_t)3, est_values_vec);
+ iter_num = opt_levenberg_marquardt(f_length, 3, x0_matrix[i],
+ measured_values_matrix[i], eps, tau,
+ beta0, beta1, max_iter_num,
+ est_values_vec, &optimization_get_f_error,
+ optimization_get_J);
+ printf("Levenberg-Marquardt solution = ");
+ vector_flex_print(3, est_values_vec, 5, 7);
+ puts("");
+ printf("iteration number = %u", iter_num);
+ }
+}
+
+
+/**
+ * @brief Calculate the error vector using exponential data.
+ * @details The error function is:
+ * \f$
+ * \vec{f}(x_1, x_2) =
+ * \begin{bmatrix}
+ * x_1 \mathrm{e}^{x_2} - y_1, ~\hdots, x_1\mathrm{e}^{8x_2}-y_8
+ * \end{bmatrix}^{T},
+ * \f$
+ *
+ * @param[in] x_vec[] start vector.
+ * @param[in] data_vec[] data vector.
+ * @param[out] f_vec[] calculated error vector.
+ *
+ */
+void optimization_get_exp_f(vector_t x_vec[], vector_t data_vec[],
+ vector_t f_vec[])
+{
+ vector_t x1, x2;
+ uint8_t i;
+
+ x1 = x_vec[0];
+ x2 = x_vec[1];
+ for (i = 1; i < 9; i++) {
+ f_vec[i - 1] = x1 * exp(i * x2) - data_vec[i - 1];
+ }
+}
+
+/**
+ * @brief Calculate the Jacobian matrix using exponential data.
+ * @details The Jacobian matrix is:
+ * \f$
+ * {J_f} =
+ * \begin{bmatrix}
+ * \frac{\partial f_1}{\partial x1} & \frac{\partial f_1}{\partial x_2} \\
+ * \frac{\partial f_2}{\partial x1} & \frac{\partial f_2}{\partial x_2} \\
+ * \vdots & \vdots & \\
+ * \frac{\partial f_n}{\partial x1} & \frac{\partial f_n}{\partial x_2} \\
+ * \end{bmatrix} =
+ * \begin{bmatrix}
+ * \mathrm{e}^{x_2} & \mathrm{e}^{x_2} x_1\\
+ * \mathrm{e}^{2 x_2} & 2\mathrm{e}^{2x_2} x_1 \\
+ * \vdots & \vdots & \\
+ * \mathrm{e}^{8 x_2} & 8\mathrm{e}^{8x_2} x_1 \\
+ * \end{bmatrix}.
+ * \f$
+ *
+ * @param[in] x_vec[] start vector.
+ * @param[in] J[] Jacobian matrix.
+ *
+ */
+void optimization_get_exp_Jacobian(vector_t x_vec[], matrix_t J[][2])
+{
+ vector_t x1, x2;
+ uint8_t i;
+
+ x1 = x_vec[0];
+ x2 = x_vec[1];
+ for (i = 1; i < 9; i++) {
+ J[i - 1][0] = exp(i * x2);
+ J[i - 1][1] = i * x1 * exp(i * x2);
+ }
+}
+
+void optimization_exponential_data_test(void)
+{
+ vector_t d_vec[] = { 8.3, 11.0, 14.7, 19.7, 26.7, 35.2, 44.4, 55.9 };
+ vector_t start_x_vec[] = { 6, .3 };
+ vector_t f_vec[8];
+ matrix_t J[8][2];
+
+ // Parameters of GNM & LVM
+ matrix_t beta0 = 0.2;
+ matrix_t beta1 = 0.8;
+ matrix_t eps = 1e-3;
+ matrix_t tau = 1e-6;
+ matrix_t f_min = 1e-11;
+ uint8_t max_it_num = 3;
+ uint8_t iter_num = 0;
+ matrix_t est_x_vec[2];
+
+ optimization_get_exp_f(start_x_vec, d_vec, f_vec);
+ optimization_get_exp_Jacobian(start_x_vec, J);
+
+ puts(
+ "\n\n############### Test Gauss-Newton & LVM algorithms ###############");
+ puts("\nExponential Data:");
+ iter_num = modified_gauss_newton(8, 2, start_x_vec, d_vec, eps, f_min,
+ max_it_num, est_x_vec,
+ &optimization_get_exp_f,
+ &optimization_get_exp_Jacobian);
+ printf("start value = {%.6f, %.6f}\n", start_x_vec[0], start_x_vec[1]);
+ printf("Gauss-Newton solution = {%.6f, %.6f}\n", est_x_vec[0], est_x_vec[1]);
+ printf("iteration number = %d\n", iter_num);
+
+ iter_num = 0;
+ vector_clear(2, est_x_vec);
+
+ iter_num = opt_levenberg_marquardt(8, 2, start_x_vec, d_vec, eps, tau,
+ beta0, beta1, max_it_num,
+ est_x_vec, &optimization_get_exp_f,
+ &optimization_get_exp_Jacobian);
+ printf("Levenberg-Marquardt solution = {%.6f, %.6f}\n", est_x_vec[0],
+ est_x_vec[1]);
+ printf("iteration number = %d\n", iter_num);
+
+}
+
+/**
+ * @brief Calculate the error vector using sinusoidal data.
+ * @details The error function is:
+ * \f$
+ * \vec{f}(x_1, x_2, x_3, x_4)=
+ * \begin{bmatrix}
+ * x_1 \sin\left( x_2 +x_3\right) +x_4 - y_1 \\
+ * \vdots \\
+ * x_1 \sin\left( 12 x_2 +x_3\right) +x_4 - y_{12}
+ * \end{bmatrix}.
+ * \f$
+ *
+ * @param[in] x_vec[] start vector.
+ * @param[in] data_vec[] data vector.
+ * @param[out] f_vec[] calculated error vector.
+ *
+ */
+void optimization_get_sin_f(vector_t x_vec[], vector_t data_vec[],
+ vector_t f_vec[])
+{
+ vector_t x1, x2, x3, x4;
+ uint8_t i;
+
+ x1 = x_vec[0];
+ x2 = x_vec[1];
+ x3 = x_vec[2];
+ x4 = x_vec[3];
+ for (i = 1; i < 13; i++) {
+ f_vec[i - 1] = x1 * sin(x2 * i + x3) + x4 - data_vec[i - 1];
+ }
+}
+
+/**
+ * @brief Calculate the Jacobian matrix using sinusoidal data.
+ * @details The Jacobian matrix is
+ * \f$
+ * J_f =
+ * \left[\begin{matrix}
+ * \sin\left( x_2 +x_3\right) & x_1 \cos\left( x_2 +x_3\right) &
+ * x_1\cos\left( x_2 +x_3\right) \\
+ * \sin\left( 2 x_2 +x_3\right) & 2 x_1 \cos\left( 2 x_2 +x_3\right) &
+ * x_1 \cos\left( 2 x_2 +x_3\right)\\
+ * \vdots & \vdots \\
+ * \sin\left( 12 x_2 +x_3\right) & 12 x_1 \cos\left( 12 x_2 +x_3\right) &
+ * x_1 \cos\left( 12 x_2 +x_3\right)
+ * \end{matrix}\right].
+ * \f$
+ *
+ * @param[in] x_vec[] start vector.
+ * @param[in] J[] Jacobian matrix.
+ *
+ */
+void optimization_get_sin_Jacobian(vector_t x_vec[], matrix_t J[][4])
+{
+ vector_t x1, x2, x3;
+ uint8_t i;
+
+ x1 = x_vec[0];
+ x2 = x_vec[1];
+ x3 = x_vec[2];
+ for (i = 1; i < 13; i++) {
+ J[i - 1][0] = sin(i * x2 + x3);
+ J[i - 1][1] = i * x1 * cos(i * x2 + x3);
+ J[i - 1][2] = x1 * cos(i * x2 + x3);
+ J[i - 1][3] = 1;
+ }
+}
+
+void optimization_sinusoidal_data_test(void)
+{
+ vector_t d_vec[] = { 61, 65, 72, 78, 85, 90, 92, 92, 88, 81, 72, 63 };
+ vector_t start_x_vec[] = { 17, 0.5, 10.5, 77 };
+ vector_t f_vec[12];
+ matrix_t J[12][4];
+
+ // Parameters of GNM & LVM
+ matrix_t beta0 = 0.2;
+ matrix_t beta1 = 0.8;
+ matrix_t eps = 1e-3;
+ matrix_t tau = 1e-6;
+ matrix_t f_min = 1e-11;
+ uint8_t max_it_num = 2;
+ uint8_t iter_num = 0;
+ matrix_t est_x_vec[4];
+
+ optimization_get_sin_f(start_x_vec, d_vec, f_vec);
+ optimization_get_sin_Jacobian(start_x_vec, J);
+
+// puts("############### Test Gauss-Newton & LVM algorithms ###############");
+ puts("\nSinusoidal Data:");
+ iter_num = modified_gauss_newton(12, 4, start_x_vec, d_vec, eps, f_min,
+ max_it_num, est_x_vec,
+ &optimization_get_sin_f,
+ &optimization_get_sin_Jacobian);
+ printf("start value = {%.6f, %.6f, %.6f, %.6f}\n", start_x_vec[0],
+ start_x_vec[1],
+ start_x_vec[2], start_x_vec[3]);
+ printf("Gauss-Newton solution = {%.6f, %.6f, %.6f, %.6f}\n", est_x_vec[0],
+ est_x_vec[1],
+ est_x_vec[2], est_x_vec[3]);
+ printf("iteration number = %d\n", iter_num);
+
+ iter_num = 0;
+ vector_clear(4, est_x_vec);
+
+ iter_num = opt_levenberg_marquardt(12, 4, start_x_vec, d_vec, eps, tau,
+ beta0, beta1, max_it_num,
+ est_x_vec, &optimization_get_sin_f,
+ &optimization_get_sin_Jacobian);
+ printf("Levenberg-Marquardt solution = {%.6f, %.6f, %.6f, %.6f}\n", est_x_vec[0],
+ est_x_vec[1],
+ est_x_vec[2], est_x_vec[3]);
+ printf("iteration number = %d\n", iter_num);
+}
diff --git a/examples/non_linear_algebra/solve_non_linear_equations/fsolve_test.c b/examples/non_linear_algebra/solve_non_linear_equations/fsolve_test.c
new file mode 100644
index 0000000000000000000000000000000000000000..c8c402e889ffd3383ee75c5d6d83d43e425e3b6d
--- /dev/null
+++ b/examples/non_linear_algebra/solve_non_linear_equations/fsolve_test.c
@@ -0,0 +1,368 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @{
+ *
+ * @file
+ * @brief Examples of solving non-linear equation systems.
+ *
+ * @details Solving non-linear equation systems examples (see @ref fsolve.h "fsolve" functions).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <complex.h>
+#include <float.h>
+
+#include "vector.h"
+#include "matrix.h"
+#include "damped_newton_raphson.h"
+#include "newton_raphson.h"
+#include "fsolve.h"
+
+/********************** f1 ******************************/
+
+/*
+ * f1(x1,x2) = [x1^3 + x2 - 1;
+ * x2^3 - x1 + 1]
+ */
+/**
+ *
+ * @brief The non-linear system f1.
+ * @details \f$ f_1 \left(x_1, x_2 \right) =
+ * \begin{bmatrix}
+ * x_1^3 + x_2 - 1 \\
+ * x_2^3 - x_1 + 1 \\
+ * \end{bmatrix} \f$
+ *
+ * @param[in] x_arr[] pointer to the \f$ x_1 \f$ and \f$ x_2 \f$ values.
+ * @param[in] f1_vec[] pointer to the \f$ f_1 \f$ function values.
+ *
+ */
+void get_non_lin_sys_f1_(vector_t x_arr[], vector_t f1_vec[])
+{
+
+ f1_vec[0] = pow(x_arr[0], 3) + x_arr[1] - 1;
+ f1_vec[1] = pow(x_arr[1], 3) - x_arr[0] + 1;
+
+}
+
+/*
+ * J1(x1,x2) = [3*x1^2, 1;
+ * -1, 3*x2^2]
+ */
+
+/**
+ *
+ * @brief The Jacobian matrix of the non-linear system \f$ f_1 \f$.
+ * @details \f$ J_1 \left( x_1, x_2\right) =
+ * \begin{bmatrix}
+ * 3 \times x_1^2 & 1 \\
+ * -1 & 3 \times x_2^2 \\
+ * \end{bmatrix} \f$
+ *
+ * @param[in] x_arr[] pointer to the \f$ x_1 \f$ and \f$ x_2 \f$ values.
+ * @param[in] J1[][] pointer to the Jacobian function \f$ J_1 \f$.
+ *
+ */
+void get_non_lin_sys_J1_(vector_t x_arr[], matrix_t J1[][2])
+{
+ J1[0][0] = 3 * pow(x_arr[0], 2);
+ J1[0][1] = 1;
+ J1[1][0] = -1;
+ J1[1][1] = 3 * pow(x_arr[1], 2);
+}
+
+/****************************** f2 ********************************/
+
+/*
+ * f2(x1,x2,x3) = [3*x1-cos(x2*x3)-1/2;
+ * x1^2-81*(x2+0.1)^2+sin(x3)+1.06;
+ * exp(-x1*x2)+20*x3+(10*pi-3)/3
+ * ]
+ */
+/**
+ *
+ * @brief The non-linear system \f$ f_2 \f$.
+ * @details \f$ f_2 \left( x_1, x_2, x_3 \right) =
+ * \begin{bmatrix}
+ * 3 x_1 - \cos\left( x_2 \times x_3 \right) - \dfrac{1}{2} \\
+ * x_1^2 - 81 \left( x_2 + 0.1 \right)^2 + \sin(x_3) + 1.06 \\
+ * \exp \left( -x1 \times x_2 \right) + 20 x_3 + \dfrac{10 \pi -3}{3} \\
+ * \end{bmatrix} \f$
+ *
+ * @param[in] x_arr[] pointer to the \f$ x_1 \f$, \f$ x_2 \f$, and \f$ x_3 \f$ values.
+ * @param[in] f2_vec[] pointer to the \f$ f_2 \f$ function values.
+ *
+ */
+void get_non_lin_sys_f2_(vector_t x_arr[], vector_t f2_vec[])
+{
+
+ f2_vec[0] = 3 * x_arr[0] - cos(x_arr[1] * x_arr[2]) - 0.5;
+ f2_vec[1] = pow(x_arr[0], 2) - 81 * pow((x_arr[1] + 0.1), 2)
+ + sin(x_arr[2]) + 1.06;
+ f2_vec[2] = exp(-x_arr[0] * x_arr[1]) + 20 * x_arr[2]
+ + (10 * M_PI - 3) / 3;
+}
+
+/*
+ * [ 3, x3*sin(x2*x3), x2*sin(x2*x3)]
+ * Jf2 = [ 2*x1, -162*x2 - 81/5, cos(x3)]
+ * [ -x2*exp(-x1*x2), -x1*exp(-x1*x2), 20]
+ */
+/**
+ *
+ * @brief The Jacobian matrix of the non-linear system \f$ f_2 \f$.
+ * @details \f$ J_2 \left( x_1, x_2, x_3 \right) =
+ * \begin{bmatrix}
+ * 3 & x_3 \sin\left( x_2 x_3 \right) & x_2 \sin\left( x_2 x_3 \right) \\
+ * 2 x_1 & -162 x2 - \dfrac{81}{5} & \cos(x_3) \\
+ * -x_2 \exp\left( -x_1 x_2 \right) & -x_1 \exp\left( -x_1 x_2 \right) & 20
+ * \end{bmatrix} \f$
+ *
+ * @param[in] x_arr[] pointer to the \f$ x_1 \f$, \f$ x_2 \f$, and \f$ x_3 \f$ values.
+ * @param[in] J2[][] pointer to the Jacobian function \f$ J_2 \f$.
+ *
+ */
+void get_non_lin_sys_J2_(vector_t x_arr[], matrix_t J2[][3])
+{
+ J2[0][0] = 3;
+ J2[0][1] = x_arr[2] * sin(x_arr[1] * x_arr[2]);
+ J2[0][2] = x_arr[1] * sin(x_arr[1] * x_arr[2]);
+ J2[1][0] = 2 * x_arr[0];
+ J2[1][1] = -162 * x_arr[1] - 16.2;
+ J2[1][2] = cos(x_arr[2]);
+ J2[2][0] = -x_arr[1] * exp(-x_arr[0] * x_arr[1]);
+ J2[2][1] = -x_arr[0] * exp(-x_arr[0] * x_arr[1]);
+ J2[2][2] = 20;
+}
+
+/****************************** f3 ********************************/
+/*
+ *
+ * f3(x1,x2,x3) = [exp(-x1*x2) + log(x1)-exp(-2);
+ * exp(x1)-sqrt(x3)/x1-exp(1)+2;
+ * x1 + x2 - x2*x3+5
+ * ]
+ */
+/**
+ *
+ * @brief The non-linear system \f$ f_3 \f$.
+ * @details \f$ f_3 \left( x_1, x_2, x_3 \right) =
+ * \begin{bmatrix}
+ * \exp \left( -x_1 x_2 \right) + \log \left( x_1 \right)-\exp \left( -2 \right) \\
+ * \exp \left( x_1 \right) - \dfrac{\sqrt{x_3}}{x_1} - \exp \left( 1 \right) + 2\\
+ * x_1 + x_2 - x_2 x_3 + 5 \\
+ * \end{bmatrix} \f$
+ *
+ * @param[in] x_arr[] pointer to the \f$ x_1 \f$, \f$ x_2 \f$, and \f$ x_3 \f$ values.
+ * @param[in] f3_vec[] pointer to the \f$ f_3 \f$ function values.
+ *
+ */
+void get_non_lin_sys_f3_(vector_t x_arr[], vector_t f3_vec[])
+{
+ double complex z;
+
+ f3_vec[0] = exp(-x_arr[0] * x_arr[1]) + log(x_arr[0]) - exp(-2);
+ if (x_arr[2] < 0) {
+ z = csqrtl(x_arr[2]);
+ f3_vec[1] = exp(x_arr[0]) - creal(z) / x_arr[0] - exp(1) + 2;
+ }
+ else {
+ f3_vec[1] = exp(x_arr[0]) - sqrt(x_arr[2]) / x_arr[0] - exp(1)
+ + 2;
+ }
+
+ f3_vec[2] = x_arr[0] + x_arr[1] - x_arr[1] * x_arr[2] + 5;
+}
+
+/*
+ * [ 1/x1 - x2*exp(-x1*x2), -x1*exp(-x1*x2), 0]
+ * Jf3 = [ exp(x1) + x3^(1/2)/x1^2, 0, -1/(2*x1*x3^(1/2))]
+ * [ 1, 1 - x3, -x2]
+ */
+/**
+ *
+ * @brief The Jacobian matrix of the non-linear system \f$ f_3 \f$.
+ * @details \f$ J_3 \left( x_1, x_2, x_3 \right) =
+ * \begin{bmatrix}
+ * \dfrac{1}{x_1}-x_2 \exp\left(-x_1 x_2\right) & -x_1\exp\left(-x_1 x_2\right) & 0 \\
+ * \exp\left(x_1\right) + \dfrac{\sqrt{x_3}}{x_1^2} & 0 & \dfrac{-1}{2x_1\sqrt{x_3}} \\
+ * 1 & 1-x_3 & -x_2
+ * \end{bmatrix} \f$
+ *
+ * @param[in] x_arr[] pointer to the \f$ x_1 \f$, \f$ x_2 \f$, and \f$ x_3 \f$ values.
+ * @param[in] J3[][] pointer to the Jacobian function \f$ J_3 \f$.
+ *
+ */
+void get_non_lin_sys_J3_(vector_t x_arr[], matrix_t J3[][3])
+{
+ double complex z;
+
+ J3[0][0] = 1 / x_arr[0] - x_arr[1] * exp(-x_arr[0] * x_arr[1]);
+ J3[0][1] = -x_arr[0] * exp(-x_arr[0] * x_arr[1]);
+ J3[0][2] = 0;
+ if (x_arr[2] < 0) {
+ z = csqrtl(x_arr[2]);
+ J3[1][0] = exp(x_arr[0]) + creal(z) / pow(x_arr[0], 2);
+ }
+ else {
+ J3[1][0] = exp(x_arr[0]) + sqrt(x_arr[2]) / pow(x_arr[0], 2);
+ }
+ J3[1][1] = 0;
+ if (x_arr[2] < 0) {
+ z = csqrtl(x_arr[2]);
+ if ((x_arr[0] == 0) || (creal(z) == 0)) {
+ //J3[1][2] = -1;
+ J3[1][2] = -DBL_MAX;
+ }
+ else {
+ J3[1][2] = -1 / (2 * x_arr[0] * creal(z));
+ }
+
+ }
+ else {
+ J3[1][2] = -1 / (2 * x_arr[0] * sqrt(x_arr[2]));
+ }
+
+ J3[2][0] = 1;
+ J3[2][1] = 1 - x_arr[2];
+ J3[2][2] = -x_arr[1];
+}
+
+void fsolve_test(void)
+{
+ puts("############ Test Solve Non-linear Algebra Module ############");
+ puts(
+ "\n******************************* f1 ******************************");
+ vector_t f1_vec[2];
+ vector_t x1_arr[2] = { 3, 2 };
+ matrix_t J1[2][2];
+ get_non_lin_sys_f1_(x1_arr, f1_vec);
+ get_non_lin_sys_J1_(x1_arr, J1);
+ uint8_t f1_length = 2;
+ vector_t x0_arr1[2] = { .5, .5 };
+ uint8_t n = 2;
+ vector_t est_x1[n];
+ uint8_t iter_num;
+ enum NON_LIN_ALGORITHM algo;
+
+ algo = Newton_Raphson;
+ iter_num = fsolve(f1_length, n, x0_arr1, algo, est_x1,
+ &get_non_lin_sys_f1_, &get_non_lin_sys_J1_);
+// iter_num = newton_raphson(f1_length, n, x0_arr1, eps, max_it_num, est_x1,
+// &get_non_lin_sys_f1_, &get_non_lin_sys_J1_);
+ printf("iter_num = %u\nx1 = ", iter_num);
+ vector_flex_print(n, est_x1, 3, 3);
+ puts("");
+ get_non_lin_sys_f1_(est_x1, f1_vec);
+ printf("f1(x1) = ");
+ vector_flex_print(f1_length, f1_vec, 3, 3);
+
+ puts("\nDamped Newton");
+ iter_num = 0;
+ vector_clear(n, est_x1);
+ vector_clear(f1_length, f1_vec);
+ algo = Damped_Newton_Raphson;
+ iter_num = fsolve(f1_length, n, x0_arr1, algo, est_x1,
+ &get_non_lin_sys_f1_, &get_non_lin_sys_J1_);
+ printf("iter_num = %u\nx1 = ", iter_num);
+ vector_flex_print(n, est_x1, 3, 3);
+ puts("");
+ get_non_lin_sys_f1_(est_x1, f1_vec);
+ printf("f1(x1) = ");
+ vector_flex_print(f1_length, f1_vec, 3, 3);
+
+ puts(
+ "/\n******************************** f2 ******************************/");
+ vector_t f2_vec[3];
+ matrix_t J2[3][3];
+ vector_t x2_arr[3] = { 0.1, 0.2, 0.3 };
+ get_non_lin_sys_f2_(x2_arr, f2_vec);
+ get_non_lin_sys_J2_(x2_arr, J2);
+ uint8_t f2_length = 3;
+ n = 3;
+ vector_t est_x2[n];
+ vector_t x0_arr2[3] = { 1, 1, 1 };
+ algo = Newton_Raphson;
+ iter_num = fsolve(f2_length, n, x0_arr2, algo, est_x2,
+ &get_non_lin_sys_f2_, &get_non_lin_sys_J2_);
+// iter_num = newton_raphson(f2_length, n, x0_arr2, eps, max_it_num, est_x2,
+// &get_non_lin_sys_f2_, &get_non_lin_sys_J2_);
+ printf("iter_num = %u\nx2 = ", iter_num);
+ vector_flex_print(n, est_x2, 3, 9);
+ puts("");
+ get_non_lin_sys_f2_(est_x2, f2_vec);
+ printf("f2(x2) = ");
+ vector_flex_print(f2_length, f2_vec, 3, 3);
+ puts("");
+
+ puts("\nDamped Newton");
+ iter_num = 0;
+ vector_clear(n, est_x2);
+ vector_clear(f2_length, f2_vec);
+ algo = Damped_Newton_Raphson;
+ iter_num = fsolve(f2_length, n, x0_arr2, algo, est_x2,
+ &get_non_lin_sys_f2_, &get_non_lin_sys_J2_);
+ printf("iter_num = %u\nx2 = ", iter_num);
+ vector_flex_print(n, est_x2, 3, 9);
+ puts("");
+ get_non_lin_sys_f2_(est_x2, f2_vec);
+ printf("f2(x2) = ");
+ vector_flex_print(f2_length, f2_vec, 3, 3);
+
+ puts(
+ "/\n******************************** f3 ******************************/");
+
+ vector_t f3_vec[3];
+ vector_t x3_arr[3] = { 1e1, 2e2, 3e3 };
+ matrix_t J3[3][3];
+ get_non_lin_sys_f3_(x3_arr, f3_vec);
+ get_non_lin_sys_J3_(x3_arr, J3);
+
+ uint8_t f3_length = 3;
+ n = 3;
+ vector_t est_x3[n];
+ vector_t x0_arr3[3] = { 1, 1, 1 };
+ algo = Newton_Raphson;
+ iter_num = fsolve(f3_length, n, x0_arr3, algo, est_x3,
+ &get_non_lin_sys_f3_,
+ &get_non_lin_sys_J3_);
+// iter_num = newton_raphson(f3_length, n, x0_arr3, eps, max_it_num, est_x3,
+// &get_non_lin_sys_f3_, &get_non_lin_sys_J3_);
+ printf("iter_num = %u\nx2 = ", iter_num);
+ vector_flex_print(n, est_x3, 3, 9);
+ puts("");
+ get_non_lin_sys_f3_(est_x3, f3_vec);
+ printf("f3(x3) = ");
+ vector_flex_print(f3_length, f3_vec, 3, 3);
+ puts("");
+
+ puts("\nDamped Newton");
+ iter_num = 0;
+ vector_clear(n, est_x3);
+ vector_clear(f3_length, f3_vec);
+ iter_num = fsolve(f3_length, n, x0_arr3, algo, est_x3,
+ &get_non_lin_sys_f3_,
+ &get_non_lin_sys_J3_);
+ printf("iter_num = %u\nx3 = ", iter_num);
+ vector_flex_print(n, est_x3, 3, 9);
+ puts("");
+ get_non_lin_sys_f3_(est_x3, f3_vec);
+ printf("f3(x3) = ");
+ vector_flex_print(f3_length, f3_vec, 3, 3);
+ puts("");
+
+}
diff --git a/examples/non_linear_algebra/solve_non_linear_equations/include/fsolve_test.h b/examples/non_linear_algebra/solve_non_linear_equations/include/fsolve_test.h
new file mode 100644
index 0000000000000000000000000000000000000000..1ec71dfbb9aa5de3cd64cceb4e3ecf1acb7153ba
--- /dev/null
+++ b/examples/non_linear_algebra/solve_non_linear_equations/include/fsolve_test.h
@@ -0,0 +1,33 @@
+/*
+ * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ * 2020 Freie Universität Berlin
+ *
+ * This file is subject to the terms and conditions of the GNU Lesser General
+ * Public License v2.1. See the file LICENSE in the top level directory for more
+ * details.
+ */
+
+/**
+ * @ingroup examples
+ * @{
+ *
+ * @file
+ * @brief Examples of solving non-linear equation systems.
+ *
+ * @details Solving non-linear equation systems examples (see @ref fsolve.h "fsolve" functions).
+ *
+ * @author Zakaria Kasmi <zkasmi@inf.fu-berlin.de>
+ *
+ * @}
+ */
+
+#ifndef FSOLVE_TEST_H_
+#define FSOLVE_TEST_H_
+
+/**
+ * @brief Examples of solving non-linear equation systems.
+ *
+ */
+void fsolve_test(void);
+
+#endif /* FSOLVE_TEST_H_ */