torch.linalg — PyTorch 2.7 documentation (original) (raw)

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

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.