Multidimensional symbolic matrix in Python

Question

I would like to create a 3D matrix of specific size by calculating a value for each combination of indexes. Each value in the matrix will be symbolic.

What I tried up to now:

import numpy as np
import sympy as sp

var1 = np.arange(1,10,2)
var2 = np.arange(1,10,2)
var3 = np.arange(20,50,5)

myMatrix = np.zeros(shape = (len(var1), len(var2), len(var3)))
t = sp.symbols('t')

for ii in range(len(var1)):
    for jj in range(len(var2)):
        for kk in range(len(var3)):
            myMatrix[ii][jj][kk] = var1[ii] * var2[jj] * var3[kk] * t

This gives me the error:

TypeError: can't convert expression to float

which as far as I understand is due to combining numpy and sympy. Therefore, I tried:

myMatrix = sp.MatrixSymbol('temp', len(var1), len(var2), len(var3))

instead of:

myMatrix = np.zeros(shape = (len(var1), len(var2), len(var3)))

and got an error:

TypeError: new() takes exactly 4 arguments (5 given)

To sum up, my question is: how can I create a 3D matrix with any variables inside to be able to use it in the nested loop, which involves symbolic calculation?

(This is my first post in this community, so please let me know if I did anything wrong.)

Answer 1

The first error you get is, as you suggested, because you try to save a sympy type object into a numpy zeros array which is of type numbers. One option would be to use a numpy array of objects, which works as follows,

import numpy as np
import sympy as sp

var1 = np.arange(1,10,2)
var2 = np.arange(1,10,2)
var3 = np.arange(20,50,5)

myMatrix = np.empty((len(var1), len(var2), len(var3)), dtype=object)
t = sp.symbols('t')

for ii in range(len(var1)):
    for jj in range(len(var2)):
        for kk in range(len(var3)):
            myMatrix[ii][jj][kk] = var1[ii] * var2[jj] * var3[kk] * t

Although for large sizes this isn't too efficient and not the way numpy should work. For sympy arrays this may be the only way to go however as it seems that, at least in my version of sympy (0.7.1.rc1), 3D arrays are not supported. For

myMatrix = sp.zeros((len(var1), len(var2), len(var3)))

I get the following error

ValueError: Matrix dimensions should be a two-element tuple of ints or a single int!