notes

commit dcfa6316d2dd13b2f4f9c2fb3635f2bd36fcd092
parent a22856d713f9558189bb47e6b22f3375fabb908f
Author: miksa234 <milutin@popovic.xyz>
Date:   Mon, 25 Apr 2022 12:29:42 +0200

prb 6 done

Diffstat:
A
num_ana/prog/.ipynb_checkpoints/prb6_p-checkpoint.ipynb
 | 
6
++++++
A
num_ana/prog/prb6_p.ipynb
 | 
196
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

2 files changed, 202 insertions(+), 0 deletions(-)
diff --git a/num_ana/prog/.ipynb_checkpoints/prb6_p-checkpoint.ipynb b/num_ana/prog/.ipynb_checkpoints/prb6_p-checkpoint.ipynb
@@ -0,0 +1,6 @@
+{
+ "cells": [],
+ "metadata": {},
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/num_ana/prog/prb6_p.ipynb b/num_ana/prog/prb6_p.ipynb
@@ -0,0 +1,196 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "9518bc9b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "from matplotlib import pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 56,
+   "id": "1f94b10c",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[6488 6480]\t1.9987623950544455\n"
+     ]
+    }
+   ],
+   "source": [
+    "def power_iter(A: np.ndarray, x_0 :np.array, N :int=10):\n",
+    "    x_k = x_0\n",
+    "    for i in range(N):\n",
+    "        x_k1 = A@x_k\n",
+    "        r_k = (x_k1 @ x_k)/(x_k @ x_k)\n",
+    "        x_k = x_k1\n",
+    "    return x_k, r_k\n",
+    "A = np.array([[1, 1], [2, 0]])\n",
+    "x_0 = np.random.randint(10, size=len(A))\n",
+    "x_k, r_k = power_iter(A, x_0)\n",
+    "print(x_k, r_k, sep='\\t')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 187,
+   "id": "742e8c5e",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[1.8852459  0.26229508]\t[ 1.26229508 -0.8852459 ]\n"
+     ]
+    }
+   ],
+   "source": [
+    "def QR_alg(A:np.ndarray, N:int=10):\n",
+    "    A_k = A\n",
+    "    for i in range(N):\n",
+    "        Q, R = np.linalg.qr(A_k)\n",
+    "        A_k = R@Q\n",
+    "    return A_k, Q, R\n",
+    "    \n",
+    "A_k, Q, R = QR_alg(A, N=3)\n",
+    "print(A_k[:,0], A_k[:,1], sep='\\t')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 188,
+   "id": "04812e53",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[ 37375.,  25025.],\n",
+       "       [  5200., -17550.]])"
+      ]
+     },
+     "execution_count": 188,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "A_k*np.sqrt(793)*5*5*np.sqrt(793)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 154,
+   "id": "233539a6",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "a1 = 1/5*np.array([7, 4])\n",
+    "e1 = a1/np.linalg.norm(a1)\n",
+    "a2 = 1/5 * np.array([9, -2])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 177,
+   "id": "3e998ed0",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[135., -25.],\n",
+       "       [ 40., -70.]])"
+      ]
+     },
+     "execution_count": 177,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "A_k*np.sqrt(65)*np.sqrt(65)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 179,
+   "id": "26fc5985",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "140.80127840328723"
+      ]
+     },
+     "execution_count": 179,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "135**2 + 40**2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 169,
+   "id": "4cd82a72",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "55"
+      ]
+     },
+     "execution_count": 169,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "9*7-4*2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4c09f8ff",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "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": "3.10.4"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}