Add files via upload

Defective_matrix_eigen_vectors.ipynb

@@ -0,0 +1,166 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "6a2895e6",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np \n",
+    "import matplotlib.pylab as plt\n",
+    "from tqdm.auto import tqdm\n",
+    "from pint import UnitRegistry\n",
+    "%config InlineBackend.figure_format = 'retina'"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "72978ada",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "\n",
+    "def shrinkList(lst):\n",
+    "    tup_list = []\n",
+    "    i, index = 0, 0\n",
+    "    while(index < len(lst)):\n",
+    "        element_count = 0\n",
+    "        while(i < len(lst) and lst[i] == lst[index]):\n",
+    "            element_count += 1\n",
+    "            i += 1\n",
+    "        tup_list.append((lst[index], element_count))\n",
+    "        index += element_count\n",
+    "          \n",
+    "    return tup_list\n",
+    "def generalized_eig(A,eigen_val,multi):\n",
+    "    from scipy.linalg import null_space\n",
+    "    coef=A-eigen_val*np.eye(np.shape(A)[0])\n",
+    "    ns=null_space(np.linalg.matrix_power(coef,multi))\n",
+    "    M=np.zeros((np.shape(A)[0],multi))\n",
+    "    M[:,0]=ns[:,0].T\n",
+    "    for i in range(1,multi):\n",
+    "        eig=M[:,i-1]\n",
+    "        eig2=np.matmul(coef,eig)\n",
+    "        M[:,i]=eig2\n",
+    "    return M\n",
+    "def defective_eigenvec(A):\n",
+    "    omega, M = np.linalg.eig(A)\n",
+    "    shrink_eig=shrinkList(omega)\n",
+    "    eig_vec=np.zeros((np.shape(A)[0],1))\n",
+    "    for i in range(1,np.shape(shrink_eig)[0]+1):\n",
+    "        temp=generalized_eig(A,shrink_eig[i-1][0],shrink_eig[i-1][1])\n",
+    "        eig_vec=np.concatenate((eig_vec,temp),axis=1)\n",
+    "        eig_vec_trim=eig_vec[:,1:]\n",
+    "    return eig_vec_trim\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "c943cab4",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[ 1.00000000e+00 -1.00000000e+00  1.00000000e+00 -9.39618477e-01]\n",
+      " [ 0.00000000e+00  1.11022302e-15 -1.11022302e-15  2.68462422e-01]\n",
+      " [ 0.00000000e+00  0.00000000e+00  6.16297582e-31 -2.01346817e-01]\n",
+      " [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  6.71156055e-02]]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "array([[ 1.00000000e+00,  9.00719925e+14, -1.97032484e+15,\n",
+       "        -9.00719925e+15],\n",
+       "       [ 0.00000000e+00,  9.00719925e+14,  1.62259277e+30,\n",
+       "         4.86777830e+30],\n",
+       "       [ 0.00000000e+00,  0.00000000e+00,  1.62259277e+30,\n",
+       "         4.86777830e+30],\n",
+       "       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00,\n",
+       "         1.48996644e+01]])"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "AA=[[5,1,-2,4],[0,5,2,2],[0,0,5,3],[0,0,0,4]]\n",
+    "omega, M = np.linalg.eig(AA)\n",
+    "print(M)\n",
+    "np.linalg.inv(M)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "7aa72b9e",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[[ 0.         -2.          2.          0.93961848]\n",
+      " [ 0.          2.          0.         -0.26846242]\n",
+      " [ 1.          0.          0.          0.20134682]\n",
+      " [ 0.          0.          0.         -0.06711561]]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "array([[  0.        ,   0.        ,   1.        ,   3.        ],\n",
+       "       [  0.        ,   0.5       ,   0.        ,  -2.        ],\n",
+       "       [  0.5       ,   0.5       ,   0.        ,   5.        ],\n",
+       "       [ -0.        ,  -0.        ,  -0.        , -14.89966443]])"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "test=defective_eigenvec(AA)\n",
+    "print(test)\n",
+    "np.linalg.inv(test)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "18e0ca79",
+   "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": "3.8.13"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}