HW1

.~lock.ssh-keygen -t ed25519 -C "ssham033@ucr.edu".pub#

@@ -0,0 +1 @@
+,samaneh,samaneh-N552VW,27.09.2024 14:32,file:///home/samaneh/.config/libreoffice/4;

Computational Astrophysics.ipynb

@@ -0,0 +1,173 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "3767ec62",
+   "metadata": {},
+   "source": [
+    "###Problem 1.3\n",
+    "##Part a)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "4412eec9",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Schwarzschild radius of the Sun: 2954.126555055405 meter\n"
+     ]
+    }
+   ],
+   "source": [
+    "\n",
+    "UR = UnitRegistry()\n",
+    "\n",
+    "G = 6.67430e-11 * UR.meter**3 / (UR.kilogram * UR.second**2)\n",
+    "M_sun = 1.989e30 * UR.kilogram\n",
+    "c = 299792458 * UR.meter / UR.second\n",
+    "\n",
+    "R_s = 2 * G * M_sun / c**2\n",
+    "print(R_s.to(UR.meter))\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ea10a00a",
+   "metadata": {},
+   "source": [
+    "##Part b) Matrix Multiplication"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "6ba49d93",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from pint import UnitRegistry\n",
+    "import numpy as np\n",
+    "import time"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "657814a6",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def matrix_multiply_for_loops(X, Y):\n",
+    "    rows_X, cols_X = len(X), len(X[0])\n",
+    "    rows_Y, cols_Y = len(Y), len(Y[0])\n",
+    "    \n",
+    "    result = [[0 for _ in range(cols_Y)] for _ in range(rows_X)]\n",
+    "    \n",
+    "    for i in range(rows_X):\n",
+    "        for j in range(cols_Y):\n",
+    "            for k in range(cols_X):\n",
+    "                result[i][j] += X[i][k] * Y[k][j]\n",
+    "    \n",
+    "    return result\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "2fc57baa",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def matrix_multiply_list_comprehension(X, Y):\n",
+    "    return [[sum(X[i][k] * Y[k][j] for k in range(len(X[0]))) for j in range(len(Y[0]))] for i in range(len(X))]\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b434e35b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def matrix_multiply_numpy(X, Y):\n",
+    "    return np.dot(X, Y)\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2997814c",
+   "metadata": {},
+   "source": [
+    "##Part C"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ec4d0e2a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "\n",
+    "\n",
+    "def generate_random_matrix(size):\n",
+    "    return np.random.rand(size, size)\n",
+    "\n",
+    "def test_multiplication_routines(matrix_size):\n",
+    "    A = generate_random_matrix(matrix_size)\n",
+    "    A_inv = np.linalg.inv(A)\n",
+    "    A_list = A.tolist()\n",
+    "    A_inv_list = A_inv.tolist()\n",
+    "\n",
+    "    start_time = time.time()\n",
+    "    result_for_loops = matrix_multiply_for_loops(A_list, A_inv_list)\n",
+    "    time_for_loops = time.time() - start_time\n",
+    "\n",
+    "    start_time = time.time()\n",
+    "    result_list_comprehension = matrix_multiply_list_comprehension(A_list, A_inv_list)\n",
+    "    time_list_comprehension = time.time() - start_time\n",
+    "\n",
+    "    start_time = time.time()\n",
+    "    result_numpy = matrix_multiply_numpy(A, A_inv)\n",
+    "    time_numpy = time.time() - start_time\n",
+    "\n",
+    "    identity_matrix = np.identity(matrix_size)\n",
+    "    result_for_loops = np.array(result_for_loops)\n",
+    "    result_list_comprehension = np.array(result_list_comprehension)\n",
+    "\n",
+    "    print(f\"Time for loops: {time_for_loops:.6f} seconds, Correct: {np.allclose(result_for_loops, identity_matrix)}\")\n",
+    "    print(f\"Time list comprehension: {time_list_comprehension:.6f} seconds, Correct: {np.allclose(result_list_comprehension, identity_matrix)}\")\n",
+    "    print(f\"Time numpy: {time_numpy:.6f} seconds, Correct: {np.allclose(result_numpy, identity_matrix)}\")\n",
+    "\n",
+    "test_multiplication_routines(100)\n"
+   ]
+  }
+ ],
+ "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": "3.8.8"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}