linalg_tensorinv: Computes the multiplicative inverse of 'torch_tensordot()'

In torch: Tensors and Neural Networks with 'GPU' Acceleration

Computes the multiplicative inverse of torch_tensordot()

Description

If m is the product of the first ind dimensions of A and n is the product of the rest of the dimensions, this function expects m and n to be equal. If this is the case, it computes a tensor X such that tensordot(A, X, ind) is the identity matrix in dimension m.

Usage

linalg_tensorinv(A, ind = 3L)

Arguments

A	(Tensor): tensor to invert.
ind	(int): index at which to compute the inverse of torch_tensordot(). Default: 3.

Details

Supports input of float, double, cfloat and cdouble dtypes.

Note

Consider using linalg_tensorsolve() if possible for multiplying a tensor on the left by the tensor inverse as ⁠linalg_tensorsolve(A, B) == torch_tensordot(linalg_tensorinv(A), B))⁠

It is always prefered to use linalg_tensorsolve() when possible, as it is faster and more numerically stable than computing the pseudoinverse explicitly.

See Also

• linalg_tensorsolve() computes ⁠torch_tensordot(linalg_tensorinv(A), B))⁠.

Other linalg: linalg_cholesky_ex(), linalg_cholesky(), linalg_det(), linalg_eigh(), linalg_eigvalsh(), linalg_eigvals(), linalg_eig(), linalg_householder_product(), linalg_inv_ex(), linalg_inv(), linalg_lstsq(), linalg_matrix_norm(), linalg_matrix_power(), linalg_matrix_rank(), linalg_multi_dot(), linalg_norm(), linalg_pinv(), linalg_qr(), linalg_slogdet(), linalg_solve(), linalg_svdvals(), linalg_svd(), linalg_tensorsolve(), linalg_vector_norm()

Examples

if (torch_is_installed()) {
A <- torch_eye(4 * 6)$reshape(c(4, 6, 8, 3))
Ainv <- linalg_tensorinv(A, ind = 3)
Ainv$shape
B <- torch_randn(4, 6)
torch_allclose(torch_tensordot(Ainv, B), linalg_tensorsolve(A, B))

A <- torch_randn(4, 4)
Atensorinv <- linalg_tensorinv(A, 2)
Ainv <- linalg_inv(A)
torch_allclose(Atensorinv, Ainv)
}

torch documentation built on June 7, 2023, 6:19 p.m.