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 asA
. Ifn
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, ifn
> 0:torch.linalg.solve(matrix_power(A, n), B) == matrix_power(A, -n) @ B
It is always preferred to use
solve()
when possible, as it is faster and more numerically stable than computing explicitly.See also
torch.linalg.solve()
computesA
.inverse() @B
with a numerically stable algorithm.- Parameters
- Keyword Arguments
out (Tensor, optional) – output tensor. Ignored if None. Default: None.
- Raises
RuntimeError – if
n
< 0 and the matrixA
or any matrix in the batch of matricesA
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]]])