From 32deb0b85a5309550ae45da479063a06760d13e2 Mon Sep 17 00:00:00 2001
From: penrose <penrose@mi.fu-berlin.de>
Date: Wed, 5 May 2021 01:53:08 +0200
Subject: [PATCH] init of matrices and vectors
---
.../five_point_stencil-checkpoint.ipynb | 155 ++++++++++++++++++
five_point_stencil.ipynb | 155 ++++++++++++++++++
2 files changed, 310 insertions(+)
create mode 100644 .ipynb_checkpoints/five_point_stencil-checkpoint.ipynb
create mode 100644 five_point_stencil.ipynb
diff --git a/.ipynb_checkpoints/five_point_stencil-checkpoint.ipynb b/.ipynb_checkpoints/five_point_stencil-checkpoint.ipynb
new file mode 100644
index 0000000..2846fb8
--- /dev/null
+++ b/.ipynb_checkpoints/five_point_stencil-checkpoint.ipynb
@@ -0,0 +1,155 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "First, the components of the following equation will be assembled:\n",
+ "\n",
+ "$$A \\underline{u} = \\underline{f} + B\\underline{g}$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def u(x,y):\n",
+ " return pow(x,4)*pow(y,5)-17*np.sin(x*y)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def f(x,y):\n",
+ " return -(12*pow(x,2)*pow(y,5)+20*pow(x,4)*pow(y,3)+(pow(x,2)+pow(y,2))*17*np.sin(x*y))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "n = 2\n",
+ "h = pow(2,-n)\n",
+ "N = pow(2,n)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def matrix_A(h):\n",
+ " N = int(1/h)\n",
+ " m = pow(N-1,2)\n",
+ " A = np.zeros((m,m))\n",
+ " return A"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
+ " [0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
+ " [0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
+ " [0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
+ " [0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
+ " [0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
+ " [0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
+ " [0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
+ " [0., 0., 0., 0., 0., 0., 0., 0., 0.]])"
+ ]
+ },
+ "execution_count": 30,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "matrix_A(h)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def matrix_B(h):\n",
+ " N = int(1/h)\n",
+ " m = pow(N-1,2)\n",
+ " l = 4*N\n",
+ " B = np.zeros((m,l))\n",
+ " return B"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def vector_g(h):\n",
+ " N = int(1/h)\n",
+ " l = 4*N\n",
+ " g = np.zeros(l)\n",
+ " g[-1] = u(1,1)\n",
+ " return g "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.8"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/five_point_stencil.ipynb b/five_point_stencil.ipynb
new file mode 100644
index 0000000..2846fb8
--- /dev/null
+++ b/five_point_stencil.ipynb
@@ -0,0 +1,155 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "First, the components of the following equation will be assembled:\n",
+ "\n",
+ "$$A \\underline{u} = \\underline{f} + B\\underline{g}$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def u(x,y):\n",
+ " return pow(x,4)*pow(y,5)-17*np.sin(x*y)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def f(x,y):\n",
+ " return -(12*pow(x,2)*pow(y,5)+20*pow(x,4)*pow(y,3)+(pow(x,2)+pow(y,2))*17*np.sin(x*y))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "n = 2\n",
+ "h = pow(2,-n)\n",
+ "N = pow(2,n)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 29,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def matrix_A(h):\n",
+ " N = int(1/h)\n",
+ " m = pow(N-1,2)\n",
+ " A = np.zeros((m,m))\n",
+ " return A"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 30,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
+ " [0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
+ " [0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
+ " [0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
+ " [0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
+ " [0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
+ " [0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
+ " [0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
+ " [0., 0., 0., 0., 0., 0., 0., 0., 0.]])"
+ ]
+ },
+ "execution_count": 30,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "matrix_A(h)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 31,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def matrix_B(h):\n",
+ " N = int(1/h)\n",
+ " m = pow(N-1,2)\n",
+ " l = 4*N\n",
+ " B = np.zeros((m,l))\n",
+ " return B"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "def vector_g(h):\n",
+ " N = int(1/h)\n",
+ " l = 4*N\n",
+ " g = np.zeros(l)\n",
+ " g[-1] = u(1,1)\n",
+ " return g "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.8"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
--
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