torch.linalg.matrix_rank¶
- torch.linalg.matrix_rank(A, *, atol=None, rtol=None, hermitian=False, out=None) Tensor ¶
Computes the numerical rank of a matrix.
The matrix rank is computed as the number of singular values (or eigenvalues in absolute value when
hermitian
= True) that are greater than threshold, where is the largest singular value (or eigenvalue).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
hermitian
= True,A
is assumed to be Hermitian if complex or symmetric if real, but this is not checked internally. Instead, just the lower triangular part of the matrix is used in the computations.If
rtol
is not specified andA
is a matrix of dimensions (m, n), the relative tolerance is set to be and is the epsilon value for the dtype ofA
(seefinfo
). Ifrtol
is not specified andatol
is specified to be larger than zero thenrtol
is set to zero.If
atol
orrtol
is atorch.Tensor
, its shape must be broadcastable to that of the singular values ofA
as returned bytorch.linalg.svdvals()
.Note
This function has NumPy compatible variant linalg.matrix_rank(A, tol, hermitian=False). However, use of the positional argument
tol
is deprecated in favor ofatol
andrtol
.Note
The matrix rank is computed using a singular value decomposition
torch.linalg.svdvals()
ifhermitian
= False (default) and the eigenvalue decompositiontorch.linalg.eigvalsh()
whenhermitian
= True. When inputs are on a CUDA device, this function synchronizes that device with the CPU.- Parameters
- Keyword Arguments
atol (float, Tensor, optional) – the absolute tolerance value. When None it’s considered to be zero. Default: None.
rtol (float, Tensor, optional) – the relative tolerance value. See above for the value it takes when None. Default: None.
hermitian (bool) – indicates whether
A
is Hermitian if complex or symmetric if real. Default: False.out (Tensor, optional) – output tensor. Ignored if None. Default: None.
Examples:
>>> A = torch.eye(10) >>> torch.linalg.matrix_rank(A) tensor(10) >>> B = torch.eye(10) >>> B[0, 0] = 0 >>> torch.linalg.matrix_rank(B) tensor(9) >>> A = torch.randn(4, 3, 2) >>> torch.linalg.matrix_rank(A) tensor([2, 2, 2, 2]) >>> A = torch.randn(2, 4, 2, 3) >>> torch.linalg.matrix_rank(A) tensor([[2, 2, 2, 2], [2, 2, 2, 2]]) >>> A = torch.randn(2, 4, 3, 3, dtype=torch.complex64) >>> torch.linalg.matrix_rank(A) tensor([[3, 3, 3, 3], [3, 3, 3, 3]]) >>> torch.linalg.matrix_rank(A, hermitian=True) tensor([[3, 3, 3, 3], [3, 3, 3, 3]]) >>> torch.linalg.matrix_rank(A, atol=1.0, rtol=0.0) tensor([[3, 2, 2, 2], [1, 2, 1, 2]]) >>> torch.linalg.matrix_rank(A, atol=1.0, rtol=0.0, hermitian=True) tensor([[2, 2, 2, 1], [1, 2, 2, 2]])