Mat1b

01002 - Matematik 1b/Funktioner 1/Funktioner1.ipynb

@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": null,
    "id": "d2493461",
    "metadata": {},
    "outputs": [
@@ -24,6 +24,80 @@
     "print(sympy.Max(h,0))\n",
     "print(relu)"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "de59fd98",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\left[\\begin{matrix}x_{1} \\left(11 x_{1} - 12 x_{2}\\right) - 20 x_{1} + x_{2} \\left(- 12 x_{1} + 4 x_{2}\\right) + 40 x_{2} - 60\\end{matrix}\\right]$"
+      ],
+      "text/plain": [
+       "Matrix([[x_1*(11*x_1 - 12*x_2) - 20*x_1 + x_2*(-12*x_1 + 4*x_2) + 40*x_2 - 60]])"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\left[\\begin{matrix}x_{1} \\left(11 x_{1} - 24 x_{2}\\right) - 20 x_{1} + 4 x_{2}^{2} + 40 x_{2} - 60\\end{matrix}\\right]$"
+      ],
+      "text/plain": [
+       "Matrix([[x_1*(11*x_1 - 24*x_2) - 20*x_1 + 4*x_2**2 + 40*x_2 - 60]])"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\left[\\begin{matrix}x_{1} \\left(14.6 x_{1} - 7.2 x_{2}\\right) - 44 x_{1} + x_{2} \\left(- 7.2 x_{1} + 10.4 x_{2}\\right) + 8 x_{2} - 60\\end{matrix}\\right]$"
+      ],
+      "text/plain": [
+       "Matrix([[x_1*(14.6*x_1 - 7.2*x_2) - 44*x_1 + x_2*(-7.2*x_1 + 10.4*x_2) + 8*x_2 - 60]])"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import sympy as sp\n",
+    "import numpy\n",
+    "\n",
+    "x_1, x_2 = sp.symbols('x_1, x_2')\n",
+    "\n",
+    "A_1 = sp.Matrix([[11,-12],[-12,4]])\n",
+    "A_2 = sp.Matrix([[11,0],[-24,4]])\n",
+    "A_3 = sp.Matrix([[73/5,-36/5],[-36/5,52/5]])\n",
+    "\n",
+    "b_1 = sp.Matrix([-20,40])\n",
+    "b_2 = b_1\n",
+    "b_3 = sp.Matrix([-44,8])\n",
+    "\n",
+    "x = sp.Matrix([x_1,x_2])\n",
+    "\n",
+    "c = sp.Matrix([-60])\n",
+    "\n",
+    "q_1 = x.T * A_1 * x + b_1.T * x + c\n",
+    "\n",
+    "q_2 = x.T * A_2 * x + b_2.T * x + c\n",
+    "\n",
+    "q_3 = x.T * A_3 * x + b_3.T * x + c\n",
+    "\n",
+    "display(q_1)\n",
+    "\n",
+    "display(q_2)\n",
+    "\n",
+    "display(q_3)\n"
+   ]
   }
  ],
  "metadata": {