How to plot contours from multidimensional data in MatPlotLib (NumPy)?

Question

I have many measurements of several quantities in an array, like this:

m = array([[2, 1, 3, 2, 1, 4, 2], # measurements for quantity A
[8, 7, 6, 7, 5, 6, 8], # measurements for quantity B
[0, 1, 2, 0, 3, 2, 1], # measurements for quantity C
[5, 6, 7, 5, 6, 5, 7]] # measurements for quantity D
)

The quantities are correlated and I need to plot various contour plots. Like "contours of B vs. D x A".

It is true that in the general case the functions might be not well defined -- for example in the above data, columns 0 and 3 show that for the same (D=5,A=2) point there are two distinct values for B (B=8 and B=7). But still, for some combinations I know there is a functional dependence, which I need plotted.

The contour() function from MatPlotLib expects three arrays: X and Y can be 1D arrays, and Z has to be a 2D array with corresponding values. How should I prepare/extract these arrays from m?

Answer 1

You will probably want to use something like scipy.interpolate.griddata to prepare your Z arrays. This will interpolate your data to a regularly spaced 2D array, given your input X and Y, and a set of sorted, regularly spaced X and Y arrays which you will need for eventual plotting. For example, if X and Y contain data points between 1 and 10, then you need to construct a set of new X and Y with a step size that makes sense for your data, e.g.

Xout = numpy.linspace(1,10,10)
Yout = numpy.linspace(1,10,10)

To turn your Xout and Yout arrays into 2D arrays you can use numpy.meshgrid, e.g.

Xout_2d, Yout_2d = numpy.meshgrid(Xout,Yout)

Then you can use those new regularly spaced arrays to construct your interpolated Z array that you can use for plotting, e.g.

Zout = scipy.interpolate.griddata((X,Y),Z,(Xout_2d,Yout_2d))

This interpolated 2D Zout should be usable for a contour plot with Xout_2d and Yout_2d.

Extracting your arrays from m is simple, you just do something like this:

A, B, C, D = (row for row in m)