{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Complex Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%plot gnuplot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "clear all\n",
    "Lx = 4.0;  Ly = 4.0;\n",
    "dx = 0.1;\n",
    "x = -Lx:dx:Lx;\n",
    "y = -Ly:dx:Ly;\n",
    "\n",
    "[xx,yy] = meshgrid(x,y);\n",
    "zz = xx + 1i*yy;  %%%Up to this point the complex mesh is created\n",
    "phi=log(zz);\n",
    "\n",
    "figure(1001)\n",
    "surf(xx,yy,real(phi))\n",
    "axis([-Lx Lx -Ly Ly])\n",
    "xlabel('Re(z)-axis')\n",
    "ylabel('Im(z)-axis')\n",
    "title('Surface plot of Re(log(z))','fontsize',16)\n",
    "print -dpng a.png\n",
    "\n",
    "figure(1002)\n",
    "zz = xx + 1i*yy;  %%%Up to this point the complex mesh is created\n",
    "surf(xx,yy,imag(phi))\n",
    "axis([-Lx Lx -Ly Ly])\n",
    "xlabel('Re(z)-axis')\n",
    "ylabel('Im(z)-axis')\n",
    "title('Surface plot of Im(log(z))','fontsize',16)\n",
    "print -dpng b.png\n",
    "\n",
    "contn = 10; %How may contours you want to plot?\n",
    "%  imag part \n",
    "figure(12);  clf;\n",
    "contourf(x,y,imag(phi),contn);  hold on\n",
    "contour(x,y,real(phi),contn,'w');  \n",
    "hold off\n",
    "colorbar\n",
    "axis equal\n",
    "axis([-Lx Lx -Ly Ly])\n",
    "xlabel('Re(z)-axis')\n",
    "ylabel('Im(z)-axis')\n",
    "title('contours of Im(log(z))','fontsize',16)\n",
    "print -dpng c.png\n",
    "\n",
    "%  real part\n",
    "figure(22);  clf;\n",
    "contourf(x,y,real(phi),contn);  hold on\n",
    "contour(x,y,imag(phi),contn,'w');  \n",
    "colorbar\n",
    "axis equal\n",
    "axis([-Lx Lx -Ly Ly])\n",
    "xlabel('Re(z)-axis')\n",
    "ylabel('Im(z)-axis')\n",
    "title('contours of Re(log(z))','fontsize',12)\n",
    "print -dpng d.png"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    " <table style=\"width:100%\">\n",
    "  <tr>\n",
    "    <th>\n",
    "    <img src=\"images/Relogz.png\" alt=\"contours of Im(log(z))\" style=\"width:400px;height:300px;\">\n",
    "</th>\n",
    "    <th>\n",
    "    <img src=\"images/Imlogz.png\" alt=\"contours of Im(log(z))\" style=\"width:400px;height:300px;\">\n",
    "</th>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td>\n",
    "    <img src=\"images/Recontlogz.png\" alt=\"contours of Im(log(z))\" style=\"width:400px;height:300px;\">\n",
    "</td>\n",
    "    <td>\n",
    "    <img src=\"images/Imcontlogz.png\" alt=\"contours of Im(log(z))\" style=\"width:400px;height:300px;\">\n",
    "    </td>\n",
    "  </tr>\n",
    "  </table> \n"
   ]
  }
 ],
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    {
     "text": "MetaKernel Magics",
     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
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