inv(A, *, out=None) → Tensor¶
Computes the inverse of a square matrix if it exists. Throws a RuntimeError if the matrix is not invertible.
Letting be or , for a matrix , its inverse matrix (if it exists) is defined as
where is the n-dimensional identity matrix.
The inverse matrix exists if and only if is invertible. In this case, the inverse is unique.
Supports input of float, double, cfloat and cdouble dtypes. Also supports batches of matrices, and if
Ais a batch of matrices then the output has the same batch dimensions.
When inputs are on a CUDA device, this function synchronizes that device with the CPU.
torch.linalg.solve()if possible for multiplying a matrix on the left by the inverse, as:
torch.linalg.solve(A, B) == A.inv() @ B
It is always prefered to use
solve()when possible, as it is faster and more numerically stable than computing the inverse explicitly.
torch.linalg.pinv()computes the pseudoinverse (Moore-Penrose inverse) of matrices of any shape.
Bwith a numerically stable algorithm.
A (Tensor) – tensor of shape (*, n, n) where * is zero or more batch dimensions consisting of invertible matrices.
- Keyword Arguments
out (Tensor, optional) – output tensor. Ignored if None. Default: None.
RuntimeError – if the matrix
Aor any matrix in the batch of matrices
Ais not invertible.
>>> A = torch.randn(4, 4) >>> Ainv = torch.linalg.inv(A) >>> torch.dist(A @ Ainv, torch.eye(4)) tensor(1.1921e-07) >>> A = torch.randn(2, 3, 4, 4) # Batch of matrices >>> Ainv = torch.linalg.inv(A) >>> torch.dist(A @ Ainv, torch.eye(4))) tensor(1.9073e-06) >>> A = torch.randn(4, 4, dtype=torch.complex128) # Complex matrix >>> Ainv = torch.linalg.inv(A) >>> torch.dist(A @ Ainv, torch.eye(4)) tensor(7.5107e-16, dtype=torch.float64)