{ "cells": [ { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "import sys; sys.path.append('..')\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "from conformalmapping import *" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "G = Splinep.from_complex_list([ \n", " 0.2398 + 0.6023j, 0.3567 + 1.0819j, 0.2632 + 1.5965j,\n", " -0.5205 + 1.7485j, -1.0585 + 1.1170j, -1.0702 + 0.5088j,\n", " -0.5906 + 0.0994j, -0.7778 - 0.4269j, -1.2924 - 0.6140j,\n", " -1.4561 - 1.2456j, -0.5439 - 1.3509j, 0.2515 - 1.0702j,\n", " 0.3099 - 0.6023j, 0.7427 - 0.5906j, 1.1053 - 0.1813j,\n", " 1.2807 + 0.3567j \n", "])" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Starting bisection ...\n", "Bisection finished in 14 steps\n", "Starting Newton iteration ...\n", "\n", "Newton iteration finished in 5 steps...\n", "\n", "label: 4/256 points with |f| > eps, max|f| = 0.0000 \n", "\n", "\n" ] }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAQoAAAD7CAYAAACSctrBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzsnXWYnPXxwD8Tx4MTgmvxIkULDW7FCRT3SXEpWiz8cHdo\n", "prhbgZLikAbXQoES3IsXDyFAyPz+mO8mm83u3u7d2t29n+fZ5+52X5nd23fe+Y6Ku5ORkZFRjh7N\n", "FiAjI6P1yRRFRkZGm2SKIiMjo00yRZGRkdEmmaLIyMhok0xRZGRktEmvZguQQ0SyOG1GRpNwd2lr\n", "g5Z4hCgdPsbQZr+PVpGjFWRoFTkyGcrLUcm1ly09MjIy2iRTFBkZGW3SMj6KGjGy2QIkRjZbAErI\n", "ICICDAQWAOZNj7mA6YH+6TFV3i4O/AR8lR5fAx8B7wBvp8c77v5LNXI0mJHNFoDWkAHaKYekNUrT\n", "ERH3thwqGVUjIlMDg4CVgGXTYzzwOnGxvwO8D3xBKIGvge8JBZGjH6FIco/ZgfkIJTM/MBPwAvBs\n", "eoxw94/q+84yakUl116mKLogIrIAMBhYB1gOeAZ4BPhXenzkNfzHi0h/YOl0rhWANYD/AvcB/wAe\n", "dvfxtTpfRm3JFEU3QkRmBLYBtifu9DcDdxEX6egGy9IT+A2hqDYHZgSuA65x95caKUtG22SKohsg\n", 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"plt.subplot(1,2,1)\n", "G.plot()\n", "zs = G(t)\n", "plt.plot(zs.real, zs.imag, 'ro')\n", "plt.gca().set_aspect('equal')\n", "plt.gca().axis(G.plotbox())\n", "\n", "plt.subplot(1,2,2)\n", "c = Circle(0, 1)\n", "c.plot()\n", "zs = np.exp(1.0j * S.theta(t))\n", "plt.plot(zs.real, zs.imag, 'ro')\n", "plt.gca().set_aspect('equal')\n", "plt.gca().axis(c.plotbox())" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Starting bisection ...\n", "Bisection finished in 14 steps\n", "Starting Newton iteration ...\n", "\n", "Newton iteration finished in 3 steps...\n", "\n", "label: 0/20 points wit |f| > eps, max|f| = 0.0000 \n", "\n", "\n" ] }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEACAYAAAC08h1NAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", 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"plt.subplot(1,2,2)\n", "val = G(S.invtheta(2*np.pi*t))\n", "G.plot()\n", "plt.plot(val.real, val.imag, 'rd')" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Starting bisection ...\n", "Bisection finished in 14 steps\n", "Starting Newton iteration ...\n", "\n", "Newton iteration finished in 5 steps...\n", "\n", "label: 6/512 points wit |f| > eps, max|f| = 0.0000 \n", "\n", "\n" ] } ], "source": [ "np.set_printoptions(precision=4, suppress=True, linewidth=15)\n", "N = 512\n", "th= 2*np.pi*np.arange(N)/float(N)\n", "t = S.invtheta(th)\n", "w = G(t)\n", "c = np.fft.fft(w)/float(N)\n", "f = lambda z : np.polyval(helpers.flipud(c),z)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ 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"zcjoZPw/duiUDlnKAOoAAAAASUVORK5CYII=\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gd = unitdisk().grid()\n", "lst = []\n", "for curve in gd.curves:\n", " newcurve = f(curve)\n", " lst.append(newcurve)\n", "gc = GridCurves(lst)\n", "gc.plot()\n", "G.plot()\n", "plt.gca().set_aspect('equal')\n", "plt.gca().axis(G.plotbox())\n", "ax = plt.gca()\n", "ax.set_xticks([]) \n", "ax.set_yticks([]) " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.9" } }, "nbformat": 4, "nbformat_minor": 0 }