{
 "metadata": {
  "name": "plot_intro"
 }, 
 "nbformat": 2, 
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown", 
     "source": [
      "#New Plotting Framework for SymPy"
     ]
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "", 
      "", 
      "## Structure of the Module", 
      "", 
      "", 
      "", 
      "This module implements a new plotting framework for SymPy. The central class of the module is the `Plot` class that connects the data representations (subclasses of `BaseSeries`) with different plotting backends. It's not imported by default for backward compatibility with the old module.", 
      "", 
      "", 
      "", 
      "Then there are the `plot_*()` functions for plotting different kinds of plots and is better suited for interactive work.", 
      "", 
      "", 
      "", 
      "* ``plot``: Plots line plots in 2D.", 
      "", 
      "* ``plot_parametric``: Plots parametric line plots in 2D.", 
      "", 
      "* ``plot_implicit`` : Plots implicit equations and region plots in 2D", 
      "", 
      "* ``plot3d`` : Plots functions of two variables in 3D", 
      "", 
      "* ``plot3d_parametric_line``: Plots line parametric plots in 3D", 
      "", 
      "* ``plot3d_parametric_surface``   : Plots surface parametric plots of functions with two variables in 3D."
     ]
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "##General examples"
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": true, 
     "input": [
      "from sympy.plotting import plot, plot_parametric, plot3d, plot3d_parametric_line, plot3d_parametric_surface"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 8
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "p = plot(x)"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 9
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "p # the Plot object"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 10
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "p[0] # one of the data series objects"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 11
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "p[0].label # an option of the data series"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 12
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "p.legend # a global option of the plot"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 13
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "p.legend = True", 
      "", 
      "p.show()"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 14
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "You can plot 2D different functions in the same plot."
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "p1 = plot_parametric(x*sin(x),x*cos(x), show=False)", 
      "", 
      "p1.extend(p) # Plot objects are just like lists.", 
      "", 
      "p1.show()"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 15
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "p1.legend = True", 
      "", 
      "p1.show()"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 16
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "p1[0].line_color='r'", 
      "", 
      "p1[1].line_color='b' # a constant color", 
      "", 
      "p1.show()"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 17
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "p1[0].line_color = lambda a : a # color dependent on the parameter", 
      "", 
      "p1.show()"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 18
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "p1.title = 'Big title'", 
      "", 
      "p1.xlabel = 'the x axis'", 
      "", 
      "p1[1].label = 'straight line'", 
      "", 
      "p1.show()"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 19
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "p1.aspect_ratio"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 20
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "p1.aspect_ratio = (1,1)", 
      "", 
      "p1.xlim = (-15,20)", 
      "", 
      "p1.show()"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 21
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "Hm, `xlim` does not work in the notebook. Hopefully it works in IPython."
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": true, 
     "input": [
      "p1._backend.ax.get_xlim()"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 17
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "Yeah, the backend got the command, but the `inline` backend does not honour it."
     ]
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "## Adding expressions to a plot"
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "p = plot(x)", 
      "", 
      "p"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 23
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "p.extend(plot(x+1, show=False))", 
      "", 
      "p.show()", 
      "", 
      "p"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 24
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "p.append(plot(x+3, x**2, show=False)[1])", 
      "", 
      "p.show()", 
      "", 
      "p"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 25
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "## Different types of plots"
     ]
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "###``plot``", 
      "", 
      "The ``plot`` by default uses an recursive adaptive algorithm to plot line plots. The default depth of recursion is 12, which means the function will be sampled at a maximum of $2^{12}$ points."
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "help(plot)"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 26
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "plot(sin(x**2)) # plots with adaptive sampling and default range of (-10, 10)"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 28
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "You can also specify the depth of the recursion. It is also possible to disable adaptive sampling and use uniform sampling with ``nb_of_points``."
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "plot(sin(x**2), depth=7)  #specifying the depth of recursion."
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 30
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "plot(sin(x**2), adaptive=False, nb_of_points=500)"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 31
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "###``plot_parametric``", 
      "", 
      "``plot_parametric`` uses an recursive adaptive sampling algorithm to plot."
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "help(plot_parametric)"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 32
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "plot_parametric(cos(x), sin(x))"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 33
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "Multiple plots."
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "plot_parametric((cos(x), sin(x)), (x, cos(x)))"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 34
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "We can combine parametric and line plots into a single plot."
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "p = plot(sin(x), show=False)", 
      "", 
      "", 
      "", 
      "p.extend(plot_parametric(cos(x), sin(x), show=False))", 
      "", 
      "p.show()"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 35
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "###``plot3d``"
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "help(plot3d)"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 36
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "plot3d(x*y)"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 37
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "plot3d(x*y, nb_of_points_x=100, nb_of_points_y=50) "
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 38
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "###``plot3_parametric_line``"
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "help(plot3d_parametric_line)"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 39
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "plot3d_parametric_line(cos(x), sin(x), x)"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 40
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "###``plot3d_parametric_surface``"
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "help(plot3d_parametric_surface)"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 41
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "plot3d_parametric_surface(cos(x + y), sin(x - y), x - y)"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 42
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "## Complex values", 
      "", 
      "If complex values are encountered, they are discarded while plotting."
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "plot(sqrt(x), (x, -5, 5))"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 43
    }, 
    {
     "cell_type": "markdown", 
     "source": [
      "", 
      "", 
      "## Textplot", 
      "", 
      "", 
      "", 
      "There is also the textplot backend that permits plotting in the terminal."
     ]
    }, 
    {
     "cell_type": "code", 
     "collapsed": true, 
     "input": [
      "pt = plot(sin(x),show=False)"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 44
    }, 
    {
     "cell_type": "code", 
     "collapsed": true, 
     "input": [
      "pt.backend = plot_backends['text']"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 45
    }, 
    {
     "cell_type": "code", 
     "collapsed": false, 
     "input": [
      "pt.show()"
     ], 
     "language": "python", 
     "outputs": [], 
     "prompt_number": 46
    }
   ]
  }
 ]
}