examples/sample.py

   1 """
   2 Utility functions for plotting sympy functions.
   3
   4 See examples\mplot2d.py and examples\mplot3d.py for usable 2d and 3d
   5 graphing functions using matplotlib.
   6 """
   7
   8 from numpy import repeat, arange, empty, ndarray, array
   9 from sympy import Symbol, Basic, Real, Rational, I, sympify
  10
  11 def sample2d(f, x_args):
  12     """
  13     Samples a 2d function f over specified intervals and returns two
  14     arrays (X, Y) suitable for plotting with matlab (matplotlib)
  15     syntax. See examples\mplot2d.py.
  16
  17     f is a function of one variable, such as x**2.
  18     x_args is an interval given in the form (var, min, max, n)
  19     """
  20     try:
  21         f = sympify(f)
  22     except:
  23         raise ValueError("f could not be interpretted as a SymPy function")
  24     try:
  25         x, x_min, x_max, x_n = x_args
  26     except:
  27         raise ValueError("x_args must be a tuple of the form (var, min, max, n)")
  28
  29     x_l = float(x_max - x_min)
  30     x_d = x_l/float(x_n)
  31     X = arange(float(x_min), float(x_max)+x_d, x_d)
  32
  33     Y = empty(len(X))
  34     for i in range(len(X)):
  35         try:
  36             Y[i] = float(f.subs(x, X[i]))
  37         except:
  38             Y[i] = None
  39     return X, Y
  40
  41 def sample3d(f, x_args, y_args):
  42     """
  43     Samples a 3d function f over specified intervals and returns three
  44     2d arrays (X, Y, Z) suitable for plotting with matlab (matplotlib)
  45     syntax. See examples\mplot3d.py.
  46
  47     f is a function of two variables, such as x**2 + y**2.
  48     x_args and y_args are intervals given in the form (var, min, max, n)
  49     """
  50     x, x_min, x_max, x_n = None, None, None, None
  51     y, y_min, y_max, y_n = None, None, None, None
  52     try:
  53         f = sympify(f)
  54     except:
  55         raise ValueError("f could not be interpretted as a SymPy function")
  56     try:
  57         x, x_min, x_max, x_n = x_args
  58         y, y_min, y_max, y_n = y_args
  59     except:
  60         raise ValueError("x_args and y_args must be tuples of the form (var, min, max, intervals)")
  61
  62     x_l = float(x_max - x_min)
  63     x_d = x_l/float(x_n)
  64     x_a = arange(float(x_min), float(x_max)+x_d, x_d)
  65
  66     y_l = float(y_max - y_min)
  67     y_d = y_l/float(y_n)
  68     y_a = arange(float(y_min), float(y_max)+y_d, y_d)
  69
  70     def meshgrid(x, y):
  71         """
  72         Taken from matplotlib.mlab.meshgrid.
  73         """
  74         x = array(x)
  75         y = array(y)
  76         numRows, numCols = len(y), len(x)
  77         x.shape = 1, numCols
  78         X = repeat(x, numRows, 0)
  79
  80         y.shape = numRows, 1
  81         Y = repeat(y, numCols, 1)
  82         return X, Y
  83
  84     X, Y = meshgrid(x_a, y_a)
  85
  86     Z = ndarray((len(X), len(X[0])))
  87     for j in range(len(X)):
  88         for k in range(len(X[0])):
  89             try:
  90                 Z[j][k] = float( f.subs(x, X[j][k]).subs(y, Y[j][k]) )
  91             except:
  92                 Z[j][k] = 0
  93     return X, Y, Z
  94
  95 def sample(f, *var_args):
  96     """
  97     Samples a 2d or 3d function over specified intervals and returns
  98     a dataset suitable for plotting with matlab (matplotlib) syntax.
  99     Wrapper for sample2d and sample3d.
 100
 101     f is a function of one or two variables, such as x**2.
 102     var_args are intervals for each variable given in the form (var, min, max, n)
 103     """
 104     if len(var_args) == 1:
 105         return sample2d(f, var_args[0])
 106     elif len(var_args) == 2:
 107         return sample3d(f, var_args[0], var_args[1])
 108     else:
 109         raise ValueError("Only 2d and 3d sampling are supported at this time.")