{"cells": [{"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": ["#! /usr/bin/env python3\n", "#\n", "def linalg_solve_bench ( n, verbose = True ):"]}, {"cell_type": "markdown", "metadata": {}, "source": ["****************************************************************************80<br>\n", "<br>\n", " linalg_solve_bench() uses scipy.linalg.solve() for the LINPACK benchmark.<br>\n", "<br>\n", " Licensing:<br>\n", "<br>\n", "   This code is distributed under the MIT license.<br>\n", "<br>\n", " Modified:<br>\n", "<br>\n", "   07 February 2025<br>\n", "<br>\n", " Author:<br>\n", "<br>\n", "   John Burkardt.<br>\n", "<br>\n", " Input:<br>\n", "<br>\n", "   integer N, the order of the matrix.<br>\n", ""]}, {"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": ["  from scipy.linalg import solve\n", "  from time import perf_counter\n", "  import numpy as np\n", "  import platform"]}, {"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": ["  if ( verbose ):\n", "    print ( '' )\n", "    print ( 'linalg_solve_bench():' )\n", "    print ( '  python version: ' + platform.python_version ( ) )\n", "    print ( '  numpy version:  ' + np.version.version )\n", "    print ( '  Test scipy.linalg.solve() on the LINPACK benchmark.' )\n", "    print ( '  Datatype: float64' )\n", "    print ( '  Matrix order N = ', n )\n", "#\n", "#  Set the matrix A, a solution x, and a right hand side.\n", "#\n", "  A = 2.0 * np.random.random ( [ n, n ] ) - 1.0\n", "  x_exact = np.ones ( n )\n", "  b = np.matmul ( A, x_exact )\n", "#\n", "#  Solve the system.\n", "#\n", "  cpu = perf_counter ( )\n", "  x = solve ( A, b )\n", "  cpu = perf_counter ( ) - cpu\n", "#\n", "#  Compute residual.\n", "#\n", "  r = np.matmul ( A, x ) - b\n", "#\n", "#  Take infinity norms.\n", "#\n", "  a_norm = np.linalg.norm ( A, np.inf )\n", "  r_norm = np.linalg.norm ( r, np.inf )\n", "  x_norm = np.linalg.norm ( x, np.inf )\n", "#\n", "#  Report.\n", "#\n", "  eps = np.finfo(float).eps\n", "  ratio = r_norm / ( a_norm * x_norm * eps )"]}, {"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": ["  ops = ( 2 * n * n * n ) / 3.0 + 2.0 * n * n\n", "  mflops = ops / ( 1000000 * cpu )\n", "  unit = 2.0 / mflops"]}, {"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": ["  cray = 0.056\n", "  cray_ratio = cpu / cray"]}, {"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": ["  if ( verbose ):\n", "    print ( '' )\n", "    print ( '  Normalized residual = ', ratio )\n", "    print ( '  Residual norm       = ', r_norm )\n", "    print ( '  Machine epsilon     = ', eps )\n", "    print ( '  First X[]           = ', x[0] )\n", "    print ( '  Last X[]            = ', x[-1] )\n", "    print ( '  CPU seconds         = ', cpu )\n", "    print ( '  MegaFLOPS           = ', mflops )\n", "    print ( '  Unit                = ', unit )\n", "    print ( '  Cray ratio          = ', cray_ratio )\n", "#\n", "#  Terminate.\n", "#\n", "  if ( verbose ):\n", "    print ( '' )\n", "    print ( 'linalg_solve_bench():' )\n", "    print ( '  Normal end of execution.' )"]}, {"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": ["  return mflops"]}, {"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": ["def timestamp ( ):"]}, {"cell_type": "markdown", "metadata": {}, "source": ["****************************************************************************80<br>\n", "<br>\n", " timestamp() prints the date as a timestamp.<br>\n", "<br>\n", " Licensing:<br>\n", "<br>\n", "   This code is distributed under the MIT license. <br>\n", "<br>\n", " Modified:<br>\n", "<br>\n", "   06 April 2013<br>\n", "<br>\n", " Author:<br>\n", "<br>\n", "   John Burkardt<br>\n", ""]}, {"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": ["  import time"]}, {"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": ["  t = time.time ( )\n", "  print ( time.ctime ( t ) )"]}, {"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": ["  return"]}, {"cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": ["if ( __name__ == '__main__' ):\n", "  timestamp ( )\n", "  n = 1000\n", "  linalg_solve_bench ( n )\n", "  timestamp ( )"]}], "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": "3.6.4"}}, "nbformat": 4, "nbformat_minor": 2}