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<div class="title">modified_gauss_newton.c</div> </div>
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<a href="modified__gauss__newton_8c.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">/*</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment"> * Copyright (C) 2020 Zakaria Kasmi <zkasmi@inf.fu-berlin.de></span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment"> * 2020 Freie Universität Berlin</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment"> *</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment"> * This file is subject to the terms and conditions of the GNU Lesser General</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment"> * Public License v2.1. See the file LICENSE in the top level directory for more</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment"> * details.</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span>  </div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="preprocessor">#include <stdio.h></span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="preprocessor">#include <math.h></span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  </div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span> <span class="preprocessor">#include "<a class="code" href="utils_8h.html">utils.h</a>"</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> <span class="preprocessor">#include "<a class="code" href="matrix_8h.html">matrix.h</a>"</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> <span class="preprocessor">#include "<a class="code" href="vector_8h.html">vector.h</a>"</span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> <span class="preprocessor">#include "<a class="code" href="moore__penrose__pseudo__inverse_8h.html">moore_penrose_pseudo_inverse.h</a>"</span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  </div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> <span class="comment">//n is the size of x0 that is equal to the column number of J</span></div>
<div class="line"><a name="l00032"></a><span class="lineno"><a class="line" href="modified__gauss__newton_8c.html#a7376799043ad2c27fac02371624051bc"> 32</a></span> uint8_t <a class="code" href="modified__gauss__newton_8c.html#a7376799043ad2c27fac02371624051bc">modified_gauss_newton</a>(uint8_t f_length, uint8_t n,</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  <a class="code" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> x0_vec[n],</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <a class="code" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> data_vec[f_length],</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <a class="code" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> eps, <a class="code" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> fmin, uint8_t max_iter_num,</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <a class="code" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> est_x_vec[n],</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="keywordtype">void</span> (*get_f_error)(<a class="code" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> x0_vec[],</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <a class="code" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> data_vec[],</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <a class="code" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> f_vec[]),</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="keywordtype">void</span> (*get_jacobian)(<a class="code" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> x0_vec[],</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <a class="code" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> J[][n])</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  )</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  </div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span> {</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <a class="code" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> J[f_length][n];</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <a class="code" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> JT_J[n][n];</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <a class="code" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> JT_f[n];</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <a class="code" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> f_vec[f_length];</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <a class="code" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> f_error;</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <a class="code" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> pinv_JTJ_mat[n][n];</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <a class="code" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> correction_vec[n];</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <a class="code" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> x_vec[n];</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <a class="code" href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a> next_x_vec[n];</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <a class="code" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> max_error, min_error;</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <a class="code" href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a> step;</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  uint8_t iter_num;</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  </div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  get_f_error(x0_vec, data_vec, f_vec);</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  f_error = <a class="code" href="vector_8h.html#a4cfc452fdff3e32a601ccff140cd9ae6">vector_get_norm2</a>(f_length, f_vec);</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  max_error = f_error;</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  min_error = max_error;</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  step = eps;</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  </div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <a class="code" href="vector_8h.html#ae9d3378f23ba835c727245b434b8a7f6">vector_copy</a>(n, x0_vec, x_vec);</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <a class="code" href="vector_8h.html#ae9d3378f23ba835c727245b434b8a7f6">vector_copy</a>(n, x0_vec, est_x_vec);</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  iter_num = 0;</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  </div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keywordflow">while</span> ((step >= eps) && (iter_num < max_iter_num) && (f_error > fmin)) {</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="comment">/*</span></div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span> <span class="comment"> * Compute then correction terms & next x_vec values</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="comment">//JT_J = J'*J</span></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  get_jacobian(x_vec, J);</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <a class="code" href="matrix_8h.html#a0107887a6c40980fa639750be8262f01">matrix_trans_mul_itself</a>(f_length, n, J, JT_J);</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  </div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="comment">//JT_f = J'*f</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  get_f_error(x_vec, data_vec, f_vec);</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <a class="code" href="matrix_8h.html#a53b0a1829b2085414fb66a9e9bd6c7b7">matrix_trans_mul_vec</a>(f_length, n, J, f_length, f_vec, JT_f);</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  </div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="comment">//solve: J'J*s = -J'*f</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <a class="code" href="moore__penrose__pseudo__inverse_8h.html#a0ddd46446f074a0d38c04157686f5fce">moore_penrose_get_pinv</a>(n, n, JT_J, pinv_JTJ_mat);</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="comment">//s = (J'J)\J'*f</span></div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <a class="code" href="matrix_8h.html#ad610bcce232c69ca302550f57b1ad9fb">matrix_mul_vec</a>(n, n, pinv_JTJ_mat, JT_f, correction_vec);</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  </div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="comment">// x = x - s</span></div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <a class="code" href="vector_8h.html#a3bbd999b10064c2ede2bd427aa040b63">vector_sub</a>(n, x_vec, correction_vec, next_x_vec);</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  </div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="comment">//next step</span></div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  step = <a class="code" href="vector_8h.html#abbb6bf046e47a8634c15c43a508cacb9">vector_get_euclidean_distance</a>(n, x_vec, next_x_vec);</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  </div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="comment">// x_vec = next_x_vec</span></div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <a class="code" href="vector_8h.html#ae9d3378f23ba835c727245b434b8a7f6">vector_copy</a>(n, next_x_vec, x_vec);</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  </div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="comment">//error vector</span></div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  get_f_error(x_vec, data_vec, f_vec);</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  </div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  f_error = <a class="code" href="vector_8h.html#a4cfc452fdff3e32a601ccff140cd9ae6">vector_get_norm2</a>(f_length, f_vec);</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  </div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="keywordflow">if</span> (min_error > f_error) { <span class="comment">//store the x_vec value with the minimum error in est_x_vec</span></div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <a class="code" href="vector_8h.html#ae9d3378f23ba835c727245b434b8a7f6">vector_copy</a>(n, x_vec, est_x_vec);</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  min_error = f_error; <span class="comment">// update min_error</span></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  }</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  </div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  max_error = <a class="code" href="utils_8h.html#a0ae8ea233ea6c519cd0434f8c5bde5e5">utils_max</a>(f_error, max_error); <span class="comment">// update max_error</span></div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  iter_num++;</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keywordflow">if</span> ((max_error - min_error) > 10) {</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  }</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  </div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  } <span class="comment">//while</span></div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  </div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keywordflow">return</span> iter_num;</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span> }</div>
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</div><!-- doc-content -->
<div class="ttc" id="amoore__penrose__pseudo__inverse_8h_html_a0ddd46446f074a0d38c04157686f5fce"><div class="ttname"><a href="moore__penrose__pseudo__inverse_8h.html#a0ddd46446f074a0d38c04157686f5fce">moore_penrose_get_pinv</a></div><div class="ttdeci">int8_t moore_penrose_get_pinv(uint8_t m, uint8_t n, matrix_t A[m][n], matrix_t pinv_A[n][m])</div><div class="ttdoc">Calculate the Moore–Penrose inverse of a rectangular matrix.</div><div class="ttdef"><b>Definition:</b> <a href="moore__penrose__pseudo__inverse_8c_source.html#l00038">moore_penrose_pseudo_inverse.c:38</a></div></div>
<div class="ttc" id="avector_8h_html_a4cfc452fdff3e32a601ccff140cd9ae6"><div class="ttname"><a href="vector_8h.html#a4cfc452fdff3e32a601ccff140cd9ae6">vector_get_norm2</a></div><div class="ttdeci">vector_t vector_get_norm2(uint8_t length, vector_t arr[])</div><div class="ttdoc">Compute the 2-norm norm of a vector.</div><div class="ttdef"><b>Definition:</b> <a href="vector_8c_source.html#l00042">vector.c:42</a></div></div>
<div class="ttc" id="amatrix_8h_html_ad610bcce232c69ca302550f57b1ad9fb"><div class="ttname"><a href="matrix_8h.html#ad610bcce232c69ca302550f57b1ad9fb">matrix_mul_vec</a></div><div class="ttdeci">void matrix_mul_vec(uint8_t m, uint8_t n, matrix_t matrix[m][n], matrix_t vec[n], matrix_t dst_arr[m])</div><div class="ttdoc">Compute the multiplication of a matrix with a column vector.</div><div class="ttdef"><b>Definition:</b> <a href="matrix_8c_source.html#l00434">matrix.c:434</a></div></div>
<div class="ttc" id="avector_8h_html_abbb6bf046e47a8634c15c43a508cacb9"><div class="ttname"><a href="vector_8h.html#abbb6bf046e47a8634c15c43a508cacb9">vector_get_euclidean_distance</a></div><div class="ttdeci">vector_t vector_get_euclidean_distance(uint8_t length, vector_t vec1[], vector_t vec2[])</div><div class="ttdoc">Compute the Euclidean distance between two vectors.</div><div class="ttdef"><b>Definition:</b> <a href="vector_8c_source.html#l00163">vector.c:163</a></div></div>
<div class="ttc" id="avector_8h_html_acb41430bc5720dda7d1c45d91a0b0221"><div class="ttname"><a href="vector_8h.html#acb41430bc5720dda7d1c45d91a0b0221">vector_t</a></div><div class="ttdeci">#define vector_t</div><div class="ttdoc">Define the data type of the vector elements.</div><div class="ttdef"><b>Definition:</b> <a href="vector_8h_source.html#l00033">vector.h:33</a></div></div>
<div class="ttc" id="amatrix_8h_html_a0107887a6c40980fa639750be8262f01"><div class="ttname"><a href="matrix_8h.html#a0107887a6c40980fa639750be8262f01">matrix_trans_mul_itself</a></div><div class="ttdeci">void matrix_trans_mul_itself(uint8_t m, uint8_t n, matrix_t A[m][n], matrix_t AT_mul_A[n][n])</div><div class="ttdoc">Compute the multiplication of the transpose of a matrix with itself.</div><div class="ttdef"><b>Definition:</b> <a href="matrix_8c_source.html#l00545">matrix.c:545</a></div></div>
<div class="ttc" id="amatrix_8h_html_a53b0a1829b2085414fb66a9e9bd6c7b7"><div class="ttname"><a href="matrix_8h.html#a53b0a1829b2085414fb66a9e9bd6c7b7">matrix_trans_mul_vec</a></div><div class="ttdeci">void matrix_trans_mul_vec(uint8_t m, uint8_t n, matrix_t A[m][n], uint8_t b_size, matrix_t b_vec[m], matrix_t c_vec[n])</div><div class="ttdoc">Compute the multiplication of transposed matrix with column vector.</div><div class="ttdef"><b>Definition:</b> <a href="matrix_8c_source.html#l00511">matrix.c:511</a></div></div>
<div class="ttc" id="amatrix_8h_html"><div class="ttname"><a href="matrix_8h.html">matrix.h</a></div><div class="ttdoc">Matrix computations.</div></div>
<div class="ttc" id="amoore__penrose__pseudo__inverse_8h_html"><div class="ttname"><a href="moore__penrose__pseudo__inverse_8h.html">moore_penrose_pseudo_inverse.h</a></div><div class="ttdoc">Moore–Penrose algorithm to compute the pseudo-inverse of a matrix.</div></div>
<div class="ttc" id="autils_8h_html"><div class="ttname"><a href="utils_8h.html">utils.h</a></div><div class="ttdoc">Utilities for linear algebra.</div></div>
<div class="ttc" id="autils_8h_html_a0ae8ea233ea6c519cd0434f8c5bde5e5"><div class="ttname"><a href="utils_8h.html#a0ae8ea233ea6c519cd0434f8c5bde5e5">utils_max</a></div><div class="ttdeci">double utils_max(double a, double b)</div><div class="ttdoc">Returns the greater of two real numbers.</div><div class="ttdef"><b>Definition:</b> <a href="utils_8c_source.html#l00055">utils.c:55</a></div></div>
<div class="ttc" id="avector_8h_html_ae9d3378f23ba835c727245b434b8a7f6"><div class="ttname"><a href="vector_8h.html#ae9d3378f23ba835c727245b434b8a7f6">vector_copy</a></div><div class="ttdeci">void vector_copy(uint8_t size, vector_t src_arr[], vector_t dest_arr[])</div><div class="ttdoc">Copy the elements of the source vector to the destination vector.</div><div class="ttdef"><b>Definition:</b> <a href="vector_8c_source.html#l00037">vector.c:37</a></div></div>
<div class="ttc" id="amodified__gauss__newton_8c_html_a7376799043ad2c27fac02371624051bc"><div class="ttname"><a href="modified__gauss__newton_8c.html#a7376799043ad2c27fac02371624051bc">modified_gauss_newton</a></div><div class="ttdeci">uint8_t modified_gauss_newton(uint8_t f_length, uint8_t n, vector_t x0_vec[n], vector_t data_vec[f_length], matrix_t eps, matrix_t fmin, uint8_t max_iter_num, vector_t est_x_vec[n], void(*get_f_error)(vector_t x0_vec[], vector_t data_vec[], vector_t f_vec[]), void(*get_jacobian)(vector_t x0_vec[], matrix_t J[][n]))</div><div class="ttdoc">Implements the modified Gauss–Newton algorithm.</div><div class="ttdef"><b>Definition:</b> <a href="modified__gauss__newton_8c_source.html#l00032">modified_gauss_newton.c:32</a></div></div>
<div class="ttc" id="amatrix_8h_html_af38ac6b76d645fea9abd6caeb4d9dd31"><div class="ttname"><a href="matrix_8h.html#af38ac6b76d645fea9abd6caeb4d9dd31">matrix_t</a></div><div class="ttdeci">#define matrix_t</div><div class="ttdoc">Define the data type of the matrix elements.</div><div class="ttdef"><b>Definition:</b> <a href="matrix_8h_source.html#l00038">matrix.h:38</a></div></div>
<div class="ttc" id="avector_8h_html"><div class="ttname"><a href="vector_8h.html">vector.h</a></div><div class="ttdoc">Vector computations.</div></div>
<div class="ttc" id="avector_8h_html_a3bbd999b10064c2ede2bd427aa040b63"><div class="ttname"><a href="vector_8h.html#a3bbd999b10064c2ede2bd427aa040b63">vector_sub</a></div><div class="ttdeci">void vector_sub(uint8_t size, vector_t a_vec[], vector_t b_vec[], vector_t a_minus_b[])</div><div class="ttdoc">Compute the subtraction of two vectors.</div><div class="ttdef"><b>Definition:</b> <a href="vector_8c_source.html#l00094">vector.c:94</a></div></div>
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