init of matrices and vectors

32deb0b8 · penrose · 3f05036c · 32deb0b8 · 32deb0b8
Commit 32deb0b8 authored 4 years ago by penrose
--- a/.ipynb_checkpoints/five_point_stencil-checkpoint.ipynb
+++ b/.ipynb_checkpoints/five_point_stencil-checkpoint.ipynb
+{
+ "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
+}
+%% Cell type:markdown id: tags:
+
+
+%% Cell type:code id: tags:
+
+``` python
+import numpy as np
+```
+
+%% Cell type:markdown id: tags:
+
+First, the components of the following equation will be assembled:
+
+$$A \underline{u} = \underline{f} + B\underline{g}$$
+
+%% Cell type:code id: tags:
+
+``` python
+def u(x,y):
+    return pow(x,4)*pow(y,5)-17*np.sin(x*y)
+```
+
+%% Cell type:code id: tags:
+
+``` python
+def f(x,y):
+    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 id: tags:
+
+``` python
+n = 2
+h = pow(2,-n)
+N = pow(2,n)
+```
+
+%% Cell type:code id: tags:
+
+``` python
+def matrix_A(h):
+    N = int(1/h)
+    m = pow(N-1,2)
+    A = np.zeros((m,m))
+    return A
+```
+
+%% Cell type:code id: tags:
+
+``` python
+matrix_A(h)
+```
+
+%% Output
+
+    array([[0., 0., 0., 0., 0., 0., 0., 0., 0.],
+           [0., 0., 0., 0., 0., 0., 0., 0., 0.],
+           [0., 0., 0., 0., 0., 0., 0., 0., 0.],
+           [0., 0., 0., 0., 0., 0., 0., 0., 0.],
+           [0., 0., 0., 0., 0., 0., 0., 0., 0.],
+           [0., 0., 0., 0., 0., 0., 0., 0., 0.],
+           [0., 0., 0., 0., 0., 0., 0., 0., 0.],
+           [0., 0., 0., 0., 0., 0., 0., 0., 0.],
+           [0., 0., 0., 0., 0., 0., 0., 0., 0.]])
+
+%% Cell type:code id: tags:
+
+``` python
+def matrix_B(h):
+    N = int(1/h)
+    m = pow(N-1,2)
+    l = 4*N
+    B = np.zeros((m,l))
+    return B
+```
+
+%% Cell type:code id: tags:
+
+``` python
+def vector_g(h):
+    N = int(1/h)
+    l = 4*N
+    g = np.zeros(l)
+    g[-1] = u(1,1)
+    return g
+```
+
+%% Cell type:code id: tags:
+
+``` python
+```
--- a/five_point_stencil.ipynb
+++ b/five_point_stencil.ipynb
+{
+ "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
+}
+%% Cell type:markdown id: tags:
+
+
+%% Cell type:code id: tags:
+
+``` python
+import numpy as np
+```
+
+%% Cell type:markdown id: tags:
+
+First, the components of the following equation will be assembled:
+
+$$A \underline{u} = \underline{f} + B\underline{g}$$
+
+%% Cell type:code id: tags:
+
+``` python
+def u(x,y):
+    return pow(x,4)*pow(y,5)-17*np.sin(x*y)
+```
+
+%% Cell type:code id: tags:
+
+``` python
+def f(x,y):
+    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 id: tags:
+
+``` python
+n = 2
+h = pow(2,-n)
+N = pow(2,n)
+```
+
+%% Cell type:code id: tags:
+
+``` python
+def matrix_A(h):
+    N = int(1/h)
+    m = pow(N-1,2)
+    A = np.zeros((m,m))
+    return A
+```
+
+%% Cell type:code id: tags:
+
+``` python
+matrix_A(h)
+```
+
+%% Output
+
+    array([[0., 0., 0., 0., 0., 0., 0., 0., 0.],
+           [0., 0., 0., 0., 0., 0., 0., 0., 0.],
+           [0., 0., 0., 0., 0., 0., 0., 0., 0.],
+           [0., 0., 0., 0., 0., 0., 0., 0., 0.],
+           [0., 0., 0., 0., 0., 0., 0., 0., 0.],
+           [0., 0., 0., 0., 0., 0., 0., 0., 0.],
+           [0., 0., 0., 0., 0., 0., 0., 0., 0.],
+           [0., 0., 0., 0., 0., 0., 0., 0., 0.],
+           [0., 0., 0., 0., 0., 0., 0., 0., 0.]])
+
+%% Cell type:code id: tags:
+
+``` python
+def matrix_B(h):
+    N = int(1/h)
+    m = pow(N-1,2)
+    l = 4*N
+    B = np.zeros((m,l))
+    return B
+```
+
+%% Cell type:code id: tags:
+
+``` python
+def vector_g(h):
+    N = int(1/h)
+    l = 4*N
+    g = np.zeros(l)
+    g[-1] = u(1,1)
+    return g
+```
+
+%% Cell type:code id: tags:
+
+``` python
+```