linalg_tensorsolve function

Computes the solution X to the system torch_tensordot(A, X) = B.

If m is the product of the first B\ .ndim dimensions of A and n is the product of the rest of the dimensions, this function expects m and n to be equal. The returned tensor x satisfies tensordot(A, x, dims=x$ndim) == B.

linalg_tensorsolve(A, B, dims = NULL)

Arguments

• A: (Tensor): tensor to solve for.
• B: (Tensor): the solution
• dims: (Tuple[int], optional): dimensions of A to be moved. If NULL, no dimensions are moved. Default: NULL.

Details

If dims is specified, A will be reshaped as A = movedim(A, dims, seq(len(dims) - A$ndim + 1, 0))

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

Examples

if (torch_is_installed()) {
A <- torch_eye(2 * 3 * 4)$reshape(c(2 * 3, 4, 2, 3, 4))
B <- torch_randn(2 * 3, 4)
X <- linalg_tensorsolve(A, B)
X$shape
torch_allclose(torch_tensordot(A, X, dims = X$ndim), B)

A <- torch_randn(6, 4, 4, 3, 2)
B <- torch_randn(4, 3, 2)
X <- linalg_tensorsolve(A, B, dims = c(1, 3))
A <- A$permute(c(2, 4, 5, 1, 3))
torch_allclose(torch_tensordot(A, X, dims = X$ndim), B, atol = 1e-6)
}

See Also

• linalg_tensorinv() computes the multiplicative inverse of torch_tensordot().

Other linalg: linalg_cholesky(), linalg_cholesky_ex(), linalg_det(), linalg_eig(), linalg_eigh(), linalg_eigvals(), linalg_eigvalsh(), linalg_householder_product(), linalg_inv(), linalg_inv_ex(), 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_solve_triangular(), linalg_svd(), linalg_svdvals(), linalg_tensorinv(), linalg_vector_norm()