{"nbformat_minor": 0, "metadata": {"signature": "sha256:afe0e41dee5e49ae4789c0568a07e740996c82654f1aa667a754b9111f07314f", "name": ""}, "nbformat": 3, "worksheets": [{"metadata": {}, "cells": [{"source": ["# Relative cost of matrix operations"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "cell_type": "code", "outputs": [], "prompt_number": 2, "metadata": {}, "input": ["import numpy as np\n", "import scipy.linalg as spla\n", "import scipy as sp\n", "\n", "import matplotlib.pyplot as pt\n", "\n", "from time import time\n", "\n", "np.alterdot()"], "language": "python"}, {"collapsed": false, "cell_type": "code", "outputs": [{"output_type": "pyout", "text": ["array([ 100,  122,  150,  185,  227,  279,  343,  421,  517,  636,  781,\n", "        959, 1178, 1447, 1778], dtype=int32)"], "metadata": {}, "prompt_number": 8}], "prompt_number": 8, "metadata": {}, "input": ["n_values = (10**np.linspace(2, 3.25, 15)).astype(np.int32)\n", "n_values"], "language": "python"}, {"collapsed": false, "cell_type": "code", "outputs": [{"output_type": "stream", "text": ["-----> lu\n", "100\n", "122\n", "150\n", "185\n", "227\n", "279\n", "343\n", "421\n", "517"], "stream": "stdout"}, {"output_type": "stream", "text": ["\n", "636\n", "781"], "stream": "stdout"}, {"output_type": "stream", "text": ["\n", "959"], "stream": "stdout"}, {"output_type": "stream", "text": ["\n", "1178"], "stream": "stdout"}, {"output_type": "stream", "text": ["\n", "1447"], "stream": "stdout"}, {"output_type": "stream", "text": ["\n", "1778"], "stream": "stdout"}, {"output_type": "stream", "text": ["\n", "----->"], "stream": "stdout"}, {"output_type": "stream", "text": [" qr\n", "100\n", "122\n", "150\n", "185\n", "227\n", "279\n", "343"], "stream": "stdout"}, {"output_type": "stream", "text": ["\n", "421\n", "517"], "stream": "stdout"}, {"output_type": "stream", "text": ["\n", "636"], "stream": "stdout"}, {"output_type": "stream", "text": ["\n", "781"], "stream": "stdout"}, 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2OGGxeOdiOs/oTKdrOvFs42ejZjU4OEmjXz9Yvx4WLozdpGFMLMsxcahq9wjF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\nYus4TKyyxGGMMSYgUZ84Ap2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"metadata": {}, "text": ["<matplotlib.figure.Figure at 0x7fab4838fb38>"]}], "prompt_number": 9, "metadata": {}, "input": ["\n", "def mat_mul(A):\n", "    return A.dot(A)\n", "\n", "for name, f in [\n", "        (\"lu\", spla.lu_factor),\n", "        (\"qr\", spla.qr),\n", "        ]:\n", "\n", "    times = []\n", "    print(\"----->\", name)\n", "    \n", "    for n in n_values:\n", "        print(n)\n", "\n", "        A = np.random.randn(n, n)\n", "        \n", "        start_time = time()\n", "        f(A)\n", "        times.append(time() - start_time)\n", "        \n", "    pt.loglog(n_values, times, label=name)\n", "\n", "pt.grid()\n", "pt.legend(loc=\"best\")\n", "pt.xlabel(\"Matrix size $n$\")\n", "pt.ylabel(\"Wall time [s]\")"], "language": "python"}, {"source": ["* Can we see the asymptotic cost ($O(n^3)$) of these algorithms from the plot?"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "cell_type": "code", "outputs": [], "prompt_number": 3, "metadata": {}, "input": [], "language": "python"}]}]}