Plotting mathematica data with python
Question: This question is related to my previous question on ["publication quality
plots in python"](http://stackoverflow.com/q/15988413/957560).

I am trying to write a post processor (a bash script/python combo) that would
comb through the thousands (literally!) of data files I have and plot data.
The trouble is, my data files are from mathematica.

I have interpolating function polynomials in Mathematica (mma) as a result of
an NDSolve operation on a non-linear partial differential equation. I was able
to deconstruct/extract discrete data out of my mma polynomials.

The data when plotted in mma results in 3D profile plots such as this: ![3D
plot from mathematica using
<code>ListPlot3D</code>](http://i.stack.imgur.com/jDCHn.png)

Now this is a profile plot at a certain time step that I am interested in. It
is constituted of X and Y coordinate values (data included at the end of this
post) which I extracted and when plotted look like this:

![X data](http://i.stack.imgur.com/7Yg41.png)

![Y data](http://i.stack.imgur.com/IFEGe.png)

How do I plot this X, Y data with python? In other words, what is the best way
of going about it?

I have tried the following python code for surface plots and wireframe plots
but they all **need a Z coordinate which I don't have**.

## Edit

My full data for this particular 3D profile plot is
[here](http://dl.dropboxusercontent.com/u/13223318/data3d.dat). I am trying to
figure out how to arrange this in rows and columns now...

## Example wireframe plot:

    
    
    from numpy import *
    from numpy.random import rand
    from pylab import pcolor, show, colorbar, xticks, yticks
    from pylab import *
    from mpl_toolkits.mplot3d import axes3d
    from matplotlib import *
    #from matplotlib.ticker import LinearLocator, FormatStrFormatter
    import matplotlib.pyplot as plt
    import numpy as np
    
    fig = plt.figure()
    ax = fig.add_subplot(111, projection='3d')
    X, Y, Z = axes3d.get_test_data(0.05)
    ax.plot_wireframe(X, Y,Z, rstride=10, cstride=10, cmap="binary")
    
    plt.show()
    

![Python wireframe plot](http://i.stack.imgur.com/xesVc.jpg)

## Surface plot

    
    
    from numpy import *
    from numpy.random import rand
    from pylab import pcolor, show, colorbar, xticks, yticks
    from pylab import *
    from mpl_toolkits.mplot3d import Axes3D
    from matplotlib import *
    #from matplotlib.ticker import LinearLocator, FormatStrFormatter
    import matplotlib.pyplot as plt
    import numpy as np
    
    fig = plt.figure()
    ax = fig.gca(projection='3d')
    X = np.arange(-5, 5, 0.25)
    Y = np.arange(-5, 5, 0.25)
    X, Y = np.meshgrid(X, Y)
    R = np.sqrt(X**2 + Y**2)
    Z = np.sin(R)
    surf = ax.plot_surface(X,Y,Z, rstride=1, cstride=1, cmap="binary",
            linewidth=0, antialiased=False)
    #ax.set_zlim(-1.01, 1.01)
    
    #ax.zaxis.set_major_locator(LinearLocator(10))
    #ax.zaxis.set_major_formatter(FormatStrFormatter('%.02f'))
    
    fig.colorbar(surf, shrink=0.5, aspect=5)
    
    plt.show()
    

![Python surface plot](http://i.stack.imgur.com/bIByR.png)

## X, Y data:

X:

    
    
    {0.132737, 0.13191, 0.129746, 0.127106, 0.125117, 0.12483, 0.126976, \
    0.131958, 0.140068, 0.151781, 0.167899, 0.189295, 0.216319, 0.248189, \
    0.282795, 0.317034, 0.347415, 0.370662, 0.384156, 0.386236, 0.376402, \
    0.355467, 0.325648, 0.290526, 0.254685, 0.222845, 0.198549, 0.183281, \
    0.177335, 0.182392, 0.203451, 0.246983, 0.315549, 0.405471, 0.509765, \
    0.621364, 0.73459, 0.845401, 0.951138, 1.05018, 1.14164, 1.22514, \
    1.30063, 1.3683, 1.42847, 1.48156, 1.52802, 1.56836, 1.60306, \
    1.63263, 1.65754, 1.67825, 1.69521, 1.70884, 1.71951, 1.72761, \
    1.73347, 1.7374, 1.73971, 1.74066, 1.74049, 1.73944, 1.7377, 1.73545, \
    1.73286, 1.73009, 1.72724, 1.72445, 1.7218, 1.71938, 1.71726, 1.7155, \
    1.71414, 1.71322, 1.71275, 1.71275, 1.71322, 1.71415, 1.71551, \
    1.71727, 1.71939, 1.72181, 1.72446, 1.72726, 1.7301, 1.73288, \
    1.73547, 1.73772, 1.73947, 1.74052, 1.74069, 1.73974, 1.73744, \
    1.7335, 1.72765, 1.71955, 1.70888, 1.69525, 1.67829, 1.65757, \
    1.63266, 1.60309, 1.56838, 1.52803, 1.48156, 1.42846, 1.36828, \
    1.30059, 1.22507, 1.14155, 1.05005, 0.950968, 0.845186, 0.734326, \
    0.621052, 0.509426, 0.405163, 0.31538, 0.247033, 0.203632, 0.18257, \
    0.177457, 0.183338, 0.198563, 0.222852, 0.254712, 0.290571, 0.325696, \
    0.355504, 0.376422, 0.386237, 0.38414, 0.370635, 0.347385, 0.317008, \
    0.282778, 0.24818, 0.216314, 0.189287, 0.167886, 0.151767, 0.140056, \
    0.131952, 0.126973, 0.124829, 0.125116, 0.127103, 0.129743, 0.131907, \
    0.132737}
    

Y:

    
    
    {0.132737, 0.160814, 0.248665, 0.386715, 0.554857, 0.736199, \
    0.919228, 1.09676, 1.26441, 1.41958, 1.56072, 1.68695, 1.79781, \
    1.89307, 1.97268, 2.03665, 2.08504, 2.11789, 2.13527, 2.1372, \
    2.12369, 2.0947, 2.05018, 1.99008, 1.91432, 1.82288, 1.71579, 1.5932, \
    1.45551, 1.30345, 1.13838, 0.962571, 0.779892, 0.596757, 0.423678, \
    0.276942, 0.177388, 0.136833, 0.13817, 0.160097, 0.190941, 0.222093, \
    0.247023, 0.261917, 0.265986, 0.261225, 0.251781, 0.243058, 0.240757, \
    0.250172, 0.275704, 0.320022, 0.382994, 0.461711, 0.551722, 0.648374, \
    0.747602, 0.846211, 0.941863, 1.03295, 1.11842, 1.19768, 1.27043, \
    1.33662, 1.39633, 1.4498, 1.49731, 1.53921, 1.57586, 1.60765, \
    1.63497, 1.65821, 1.67774, 1.69392, 1.70711, 1.71765, 1.72583, \
    1.73197, 1.73635, 1.73922, 1.74084, 1.74142, 1.74119, 1.74032, 1.739, \
    1.73739, 1.73562, 1.73382, 1.73211, 1.73057, 1.72928, 1.72831, \
    1.72768, 1.72744, 1.72759, 1.72812, 1.72901, 1.73023, 1.73172, \
    1.7334, 1.73518, 1.73697, 1.73864, 1.74005, 1.74105, 1.74146, \
    1.74111, 1.73977, 1.73724, 1.73326, 1.72759, 1.71994, 1.71003, \
    1.69753, 1.68213, 1.66347, 1.64119, 1.61492, 1.58428, 1.54888, \
    1.50832, 1.46224, 1.41028, 1.35213, 1.28756, 1.21644, 1.13877, \
    1.05479, 0.965005, 0.870346, 0.772266, 0.672914, 0.575269, 0.483202, \
    0.401281, 0.334109, 0.285083, 0.255065, 0.242016, 0.241877, 0.249537, \
    0.25934, 0.265716, 0.264102, 0.251884, 0.229106, 0.198813, 0.166855, \
    0.141209, 0.132737}
    


Answer: Use the `plot` or `scatter` method to plot x, y data. In your case, x is time
and y is either one of X or Y. To generate your time coordinates use the
[range](http://docs.python.org/2.7/library/functions.html?highlight=range#range)
function:

    
    
    range(5) -> [0, 1, 2, 3, 4]
    

Here is an example.

    
    
    #!python2
    
    import matplotlib.pyplot as plt
    
    X = [0.132737, 0.13191, 0.129746, 0.127106, 0.125117, 0.12483, 0.126976,
    0.131958, 0.140068, 0.151781, 0.167899, 0.189295, 0.216319, 0.248189,
    0.282795, 0.317034, 0.347415, 0.370662, 0.384156, 0.386236, 0.376402,
    0.355467, 0.325648, 0.290526, 0.254685, 0.222845, 0.198549, 0.183281,
    0.177335, 0.182392, 0.203451, 0.246983, 0.315549, 0.405471, 0.509765,
    0.621364, 0.73459, 0.845401, 0.951138, 1.05018, 1.14164, 1.22514,
    1.30063, 1.3683, 1.42847, 1.48156, 1.52802, 1.56836, 1.60306,
    1.63263, 1.65754, 1.67825, 1.69521, 1.70884, 1.71951, 1.72761,
    1.73347, 1.7374, 1.73971, 1.74066, 1.74049, 1.73944, 1.7377, 1.73545,
    1.73286, 1.73009, 1.72724, 1.72445, 1.7218, 1.71938, 1.71726, 1.7155,
    1.71414, 1.71322, 1.71275, 1.71275, 1.71322, 1.71415, 1.71551,
    1.71727, 1.71939, 1.72181, 1.72446, 1.72726, 1.7301, 1.73288,
    1.73547, 1.73772, 1.73947, 1.74052, 1.74069, 1.73974, 1.73744,
    1.7335, 1.72765, 1.71955, 1.70888, 1.69525, 1.67829, 1.65757,
    1.63266, 1.60309, 1.56838, 1.52803, 1.48156, 1.42846, 1.36828,
    1.30059, 1.22507, 1.14155, 1.05005, 0.950968, 0.845186, 0.734326,
    0.621052, 0.509426, 0.405163, 0.31538, 0.247033, 0.203632, 0.18257,
    0.177457, 0.183338, 0.198563, 0.222852, 0.254712, 0.290571, 0.325696,
    0.355504, 0.376422, 0.386237, 0.38414, 0.370635, 0.347385, 0.317008,
    0.282778, 0.24818, 0.216314, 0.189287, 0.167886, 0.151767, 0.140056,
    0.131952, 0.126973, 0.124829, 0.125116, 0.127103, 0.129743, 0.131907,
    0.132737]
    
    
    ax = plt.subplot(111)
    ax.plot(range(len(X)), X)
    #ax.scatter(range(len(X)), X)
    plt.show()
    

## Edit in answer to the comment

    
    
    #!python2
    
    import matplotlib.pyplot as plt
    from mpl_toolkits.mplot3d import Axes3D
    import numpy as np
    
    DATA = 'test0005.dat'
    
    def get_data(fname=DATA):
        '''Read 2d array of z coordinates from file. Convert to float values
        and wrap in a numpy array.'''
        with open(fname) as f:
            data = [map(float, line.split()) for line in f]
        return np.array(data)
    
    
    def plot(x, y, z):
        '''Surface plot of 3d data.'''
        fig = plt.figure()
        ax = fig.gca(projection='3d')
        ax.plot_surface(x, y, z, rstride=4, cstride=4)
        plt.show()
    
    
    if __name__ == '__main__':
        z = get_data()
        x = range(z.shape[0])
        y = range(z.shape[1])
        x, y = np.meshgrid(x, y)
        plot(x, y, z)
    

