torch.linalg.matrix_power

torch.linalg.matrix_power(A, n, *, out=None) → Tensor

Computes the n-th power of a square matrix for an integer n.

Supports input of float, double, cfloat and cdouble dtypes. Also supports batches of matrices, and if A is a batch of matrices then the output has the same batch dimensions.

If n= 0, it returns the identity matrix (or batch) of the same shape as A. If n is negative, it returns the inverse of each matrix (if invertible) raised to the power of abs(n).

Note

Consider using torch.linalg.solve() if possible for multiplying a matrix on the left by a negative power as, if n> 0:

matrix_power(torch.linalg.solve(A, B), n) == matrix_power(A, -n)  @ B

It is always preferred to use solve() when possible, as it is faster and more numerically stable than computing $A^{-n}$ explicitly.

See also

torch.linalg.solve() computes A.inverse() @ B with a numerically stable algorithm.

Parameters:

• A (Tensor) – tensor of shape (*, m, m) where * is zero or more batch dimensions.

• n (int) – the exponent.

Keyword Arguments:

out (Tensor, optional) – output tensor. Ignored if None. Default: None.

Raises:

RuntimeError – if n< 0 and the matrix A or any matrix in the batch of matrices A is not invertible.

Examples:

>>> A = torch.randn(3, 3)
>>> torch.linalg.matrix_power(A, 0)
tensor([[1., 0., 0.],
        [0., 1., 0.],
        [0., 0., 1.]])
>>> torch.linalg.matrix_power(A, 3)
tensor([[ 1.0756,  0.4980,  0.0100],
        [-1.6617,  1.4994, -1.9980],
        [-0.4509,  0.2731,  0.8001]])
>>> torch.linalg.matrix_power(A.expand(2, -1, -1), -2)
tensor([[[ 0.2640,  0.4571, -0.5511],
        [-1.0163,  0.3491, -1.5292],
        [-0.4899,  0.0822,  0.2773]],
        [[ 0.2640,  0.4571, -0.5511],
        [-1.0163,  0.3491, -1.5292],
        [-0.4899,  0.0822,  0.2773]]])