CODEWITHSUNDEEP
pythonnumpylinear-algebra
K Jackson
K Jackson

Reputation: 191

LinAlgError: Last 2 dimensions of the array must be square

I need to solve a set of simultaneous equations of the form Ax = B for x. I've used the numpy.linalg.solve function, inputting A and B, but I get the error

LinAlgError: Last 2 dimensions of the array must be square

Here's my code:

A = numpy.matrix([(-0.56, -0.52), (0.44, 0.46), (0.69, 0.71)])
B = [(-0.38, -24.09, 0.0)]
x = numpy.linalg.solve(A, B)

x should have the form (x1,x2,0).

How do I fix this?

Upvotes: 19

Views: 104389

Answers (3)

Keivan
Keivan

Reputation: 752

In case you still haven't found an answer, or in case someone in the future has this question.

To solve Ax=b:

numpy.linalg.solve uses LAPACK gesv. As mentioned in the documentation of LAPACK, gesv requires A to be square:

LA_GESV computes the solution to a real or complex linear system of equations AX = B, where A is a square matrix and X and B are rectangular matrices or vectors. Gaussian elimination with row interchanges is used to factor A as A = PL*U , where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the above system.

If A matrix is not square, it means that you either have more variables than your equations or the other way around. In these situations, you can have the cases of no solution or infinite number of solutions. What determines the solution space is the rank of the matrix compared to the number of columns. Therefore, you first have to check the rank of the matrix.

That being said, you can use another method to solve your system of linear equations. I suggest having a look at factorization methods like LU or QR or even SVD. In LAPACK you can use getrs, in Python you can different things:

  • first do the factorization like QR and then feed the resulting matrices to a method like scipy.linalg.solve_triangular
  • solve the least-squares using numpy.linalg.lstsq

Also have a look here where a simple example is formulated and solved.

Upvotes: 34

cottontail
cottontail

Reputation: 23041

Another common way this error may occur is when an operation that was intended to be performed element-wise is called on a numpy.matrix() object. The following example reproduces this error. In this case, arr is a numpy ndarray, while mat is a numpy matrix object. As you can see, element-wise squaring works for arr but it doesn't work for mat because **2 is a matrix square which is equivalent to dot product. To get around the issue, convert the matrix to ndarray.

import numpy as np
arr = np.array([[1,2]])
mat = np.matrix([[1,2]])

x1 = arr**2             # array([[1, 4]])
y1 = mat**2             # LinAlgError: Last 2 dimensions of the array must be square
y2 = np.array(mat)**2   # array([[1, 4]])

Upvotes: 0

ashish trehan
ashish trehan

Reputation: 433

A square matrix is a matrix with the same number of rows and columns. The matrix you are doing is a 3 by 2. Add a column of zeroes to fix this problem.

Upvotes: 5

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