{"nbformat_minor": 0, "cells": [{"source": "The incomplete gamma isn't stable in the real domain:", "cell_type": "markdown", "metadata": {}}, {"execution_count": 43, "cell_type": "code", "source": "%display latex\nvar('k')\nR10 = RealField(1000)\nf(k, x) = log(gamma(k, x * k))\nf", "outputs": [{"execution_count": 43, "output_type": "execute_result", "data": {"text/plain": "(k, x) |--> log(gamma(k, k*x))", "text/html": ""}, "metadata": {}}], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 40, "cell_type": "code", "source": "def plot1(f): return sum(\n plot_semilogy(\n ## float: see http://trac.sagemath.org/ticket/18210\n f(R10(k)),\n (x, R10(0), R10(5/2)),\n color=color,\n legend_label='k=%i' % k,\n figsize=6,\n aspect_ratio=1.0,\n )\n for k, color in zip(\n [1, 2, 4, 8, 17, 26, 35, 48, 51, 100],\n ['blue', 'brown', 'red', 'green', 'black', 'yellow', 'orange', 'cyan', 'purple', 'magenta'],\n )\n)\nplot1(f)", "outputs": [{"output_type": "stream", "name": "stdout", "text": "verbose 0 (2691: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 12 points.\nverbose 0 (2691: plot.py, generate_plot_points) Last error message: 'can't convert complex to float'\nverbose 0 (2691: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 45 points.\nverbose 0 (2691: plot.py, generate_plot_points) Last error message: 'can't convert complex to float'\nverbose 0 (2691: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 50 points.\nverbose 0 (2691: plot.py, generate_plot_points) Last error message: 'can't convert complex to float'\nverbose 0 (2691: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 52 points.\nverbose 0 (2691: plot.py, generate_plot_points) Last error message: 'can't convert complex to float'\nverbose 0 (2691: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 65 points.\nverbose 0 (2691: plot.py, generate_plot_points) Last error message: 'can't convert complex to float'\n"}, {"execution_count": 40, "output_type": "execute_result", "data": {"image/png": 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Z2KetyWJCX3gTnhzbNAoNtAotNAqNvWiVzsddnaMSVQxhRESDXECFIi7eSI6s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\nKCIiIiICwFBEREREBIChiIiIiAgA8H8TmyLmIkYgfQAAAABJRU5ErkJggg==\n", "text/plain": "Graphics object consisting of 18 graphics primitives"}, "metadata": {}}], "metadata": {"collapsed": false, "trusted": true}}, {"source": "There's an obvious bite out of that plot.\nThe correct output is smooth and real.", "cell_type": "markdown", "metadata": {}}, {"source": "A 3d plot of the same:", "cell_type": "markdown", "metadata": {}}, {"execution_count": 44, "cell_type": "code", "source": "def plot2(f): return plot3d(f, (x, 0, 5/2), (k, 1, 101))\nplot2(f)", "outputs": [{"execution_count": 44, "output_type": "execute_result", "data": {"text/plain": "Graphics3d Object", "text/html": "\n\n"}, "metadata": {}}], "metadata": {"collapsed": false, "trusted": true}}, {"source": "Again, there's an obvious bite out of the function.\n\nWithin that domain, the output is *negative*, when it shouldn't be, in the real, positive domain.\nIf I take the absolute value, the output is closer to correct, but still wrong:", "cell_type": "markdown", "metadata": {}}, {"execution_count": 27, "cell_type": "code", "source": "g = log(abs(gamma(k, x*k)))\ng", "outputs": [{"execution_count": 27, "output_type": "execute_result", "data": {"text/plain": "log(abs(gamma(k, k*x)))", "text/html": ""}, "metadata": {}}], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 28, "cell_type": "code", "source": "plot1(g)", "outputs": [{"execution_count": 28, "output_type": "execute_result", "data": {"image/png": 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z55gxQRMuMQ8rHZHW+Gs3+jYUEZEuWbbQ3XMDTJ9GMevl5bO2w/DZ/8Knv4a6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\n7T3iGGq1Ghs3bpyIcolokhNlKCIiAoCzZ89i9uzZUCqVcHR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4uDh89NFHllgFIppEGIqI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\nRU5ErkJggg==\n", 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