How to create symbolic matrix and do substitute in batch with sympy?

Question

I need to create completely symbolic matrices, are there ready made functions for that in sympy?

For example, if I were to create a 2x2 matrix manually, I would do

from sympy import *

a00, a01, a10, a11 = symbols('a00 a01 a10 a11')
A = Matrix([[a00, a01],[a10, a11]])

The problem is I do not know the dimension prior to simulation and creating every symbol manually gets old fast when dimension gets higher. Ideally I want to be able to create a 10x10 matrix with A=Matrix(10,10) with A[0,0]=Symbol('A00'), etc.

Also, if the above is possible, it'd be really nice to be able to do substitution in batch as well. For example, I want something like some_equation.subs([(A,numpy.random.rand(2,2))])

Answer 1

You can use subs method to do the substitution.

In [5]: A = MatrixSymbol('A', 2, 2)

In [6]: B = MatrixSymbol('B', 2, 2)

In [7]: C = A*B

In [8]: C.subs({A: Matrix([[0, 1], [1, 0]]), B: Matrix([[2, 3], [4, 5]])})
Out[8]: 
Matrix([
[0, 1],
[1, 0]])*Matrix([
[2, 3],
[4, 5]])

Probably you need symbolic dimension for your MatrixSymbol objects.

Answer 2

I think you might have been trying to make all the elments of a matrix separate symbols? Here's something I tried to make an array rho that is "states x states" in size:

rho = np.array([[Symbol("rho{}{}".format(i,j)) for j in range(len(states))] for i in range(len(states))])