torch.linalg

Common linear algebra operations.

See Linear algebra (torch.linalg) for some common numerical edge-cases.

Matrix Properties

norm	Computes a vector or matrix norm.
vector_norm	Computes a vector norm.
matrix_norm	Computes a matrix norm.
diagonal	Alias for torch.diagonal() with defaults dim1= -2, dim2= -1.
det	Computes the determinant of a square matrix.
slogdet	Computes the sign and natural logarithm of the absolute value of the determinant of a square matrix.
cond	Computes the condition number of a matrix with respect to a matrix norm.
matrix_rank	Computes the numerical rank of a matrix.

Decompositions

cholesky	Computes the Cholesky decomposition of a complex Hermitian or real symmetric positive-definite matrix.
qr	Computes the QR decomposition of a matrix.
lu	Computes the LU decomposition with partial pivoting of a matrix.
lu_factor	Computes a compact representation of the LU factorization with partial pivoting of a matrix.
eig	Computes the eigenvalue decomposition of a square matrix if it exists.
eigvals	Computes the eigenvalues of a square matrix.
eigh	Computes the eigenvalue decomposition of a complex Hermitian or real symmetric matrix.
eigvalsh	Computes the eigenvalues of a complex Hermitian or real symmetric matrix.
svd	Computes the singular value decomposition (SVD) of a matrix.
svdvals	Computes the singular values of a matrix.

Solvers

solve	Computes the solution of a square system of linear equations with a unique solution.
solve_triangular	Computes the solution of a triangular system of linear equations with a unique solution.
lu_solve	Computes the solution of a square system of linear equations with a unique solution given an LU decomposition.
lstsq	Computes a solution to the least squares problem of a system of linear equations.

Inverses

inv	Computes the inverse of a square matrix if it exists.
pinv	Computes the pseudoinverse (Moore-Penrose inverse) of a matrix.

Matrix Functions

matrix_exp	Computes the matrix exponential of a square matrix.
matrix_power	Computes the n-th power of a square matrix for an integer n.

Matrix Products

cross	Computes the cross product of two 3-dimensional vectors.
matmul	Alias for torch.matmul()
vecdot	Computes the dot product of two batches of vectors along a dimension.
multi_dot	Efficiently multiplies two or more matrices by reordering the multiplications so that the fewest arithmetic operations are performed.
householder_product	Computes the first n columns of a product of Householder matrices.

Tensor Operations

tensorinv	Computes the multiplicative inverse of torch.tensordot().
tensorsolve	Computes the solution X to the system torch.tensordot(A, X) = B.

Misc

vander

Generates a Vandermonde matrix.

Experimental Functions

cholesky_ex	Computes the Cholesky decomposition of a complex Hermitian or real symmetric positive-definite matrix.
inv_ex	Computes the inverse of a square matrix if it is invertible.
solve_ex	A version of solve() that does not perform error checks unless check_errors= True.
lu_factor_ex	This is a version of lu_factor() that does not perform error checks unless check_errors= True.
ldl_factor	Computes a compact representation of the LDL factorization of a Hermitian or symmetric (possibly indefinite) matrix.
ldl_factor_ex	This is a version of ldl_factor() that does not perform error checks unless check_errors= True.
ldl_solve	Computes the solution of a system of linear equations using the LDL factorization.