Problem

Within SymPy, I am trying to create a set of X_i matrices each of size n_i x p where i = 1, ... M (Pinheiro and Bates, 2000, pg. 58). Is this something that can be done? I’d also like to be able to print the set of matrices to see each one… Eventually, every X_i matrix is going to become part of further operations…

I tried looking at the documentation for Indexed, but my understanding is that this just gives me a Symbol that I can index over.

Attempted Solutions

For example,

import sympy as sm
sm.init_printing()

M = sm.symbols('M', integer = True) # M groups
i = sm.Idx('i', (1, M))
X = sm.IndexedBase('X')
X[i].ranges

Gives

[(1, M)]

However, this is not a set of matrices and each matrix does not have a variable number of rows (depending on $n_i$).

So then I tried to search further online and asked ChatGPT, then I got the following responses, which seems to say that I can’t set an arbitrary upper limit to the index.

ChatGPT gave this template to work from, although this is by assigning p = 2 and M = 5; and with a constant number of rows for each Matrix (5).

n = 5
p = 2
M = 5
X=[sm.Matrix(n, p, lambda r, c: f'a_{r+1}{c+1}_{i}') for i in range(1,M+1)]
X

Giving

⎡⎡a₁₁ ₁  a₁₂ ₁⎤  ⎡a₁₁ ₂  a₁₂ ₂⎤  ⎡a₁₁ ₃  a₁₂ ₃⎤  ⎡a₁₁ ₄  a₁₂ ₄⎤  ⎡a₁₁ ₅  a₁₂ ₅
⎢⎢            ⎥  ⎢            ⎥  ⎢            ⎥  ⎢            ⎥  ⎢            
⎢⎢a₂₁ ₁  a₂₂ ₁⎥  ⎢a₂₁ ₂  a₂₂ ₂⎥  ⎢a₂₁ ₃  a₂₂ ₃⎥  ⎢a₂₁ ₄  a₂₂ ₄⎥  ⎢a₂₁ ₅  a₂₂ ₅
⎢⎢            ⎥  ⎢            ⎥  ⎢            ⎥  ⎢            ⎥  ⎢            
⎢⎢a₃₁ ₁  a₃₂ ₁⎥, ⎢a₃₁ ₂  a₃₂ ₂⎥, ⎢a₃₁ ₃  a₃₂ ₃⎥, ⎢a₃₁ ₄  a₃₂ ₄⎥, ⎢a₃₁ ₅  a₃₂ ₅
⎢⎢            ⎥  ⎢            ⎥  ⎢            ⎥  ⎢            ⎥  ⎢            
⎢⎢a₄₁ ₁  a₄₂ ₁⎥  ⎢a₄₁ ₂  a₄₂ ₂⎥  ⎢a₄₁ ₃  a₄₂ ₃⎥  ⎢a₄₁ ₄  a₄₂ ₄⎥  ⎢a₄₁ ₅  a₄₂ ₅
⎢⎢            ⎥  ⎢            ⎥  ⎢            ⎥  ⎢            ⎥  ⎢            
⎣⎣a₅₁ ₁  a₅₂ ₁⎦  ⎣a₅₁ ₂  a₅₂ ₂⎦  ⎣a₅₁ ₃  a₅₂ ₃⎦  ⎣a₅₁ ₄  a₅₂ ₄⎦  ⎣a₅₁ ₅  a₅₂ ₅

⎤⎤
⎥⎥
⎥⎥
⎥⎥
⎥⎥
⎥⎥
⎥⎥
⎥⎥
⎦⎦

Although further tweaking could probably give a set of M matrices each with a different number of n rows, my suspicion is that (1) this will not work with the rest of the SymPy operations (matrix algebra, vector calculus and more); and (2) that this is not idiomatic SymPy given the absence of any invocation of Idx or IndexedBase. Any help would be greatly appreciated.

Acceptable, but Less Preferred, Solutions

• M is a defined integer to create a concrete upper limit, like M = 5
• Each i of n_i and p are defined integers, like (n = [10, 10, 12, 12, 24]; p = 5) so that each X_i matrix is concretely defined