module

linalg

39 members

lucid.linalg

lucid.linalg: linear algebra operations.

Functions

fninv→ Tensor

Compute the multiplicative inverse of a square matrix.

fndet→ Tensor

Compute the determinant of a square matrix.

fnsolve→ Tensor

Solve a square linear system $AX = B$.

fncholesky→ Tensor

Cholesky decomposition of a symmetric positive-definite matrix.

fnnorm→ Tensor

Compute a vector or matrix norm.

fnsvd→ Tensor

Singular value decomposition of a matrix.

fnsvdvals→ Tensor

Compute only the singular values of a matrix.

fnqr→ Tensor

QR decomposition of a matrix.

fnmatrix_power→ Tensor

Raise a square matrix to an integer power.

fnpinv→ Tensor

Moore-Penrose pseudo-inverse of a matrix.

fneig→ Tensor

Eigenvalue decomposition of a general square matrix.

fneigvals→ Tensor

Compute only the eigenvalues of a general square matrix.

fneigh→ Tensor

Eigendecomposition of a Hermitian / symmetric matrix.

fneigvalsh→ Tensor

Eigenvalues of a Hermitian / symmetric matrix.

fnlu_factor→ Tensor

LU factorization with partial pivoting (packed form).

fnslogdet→ Tensor

Sign and natural log of the absolute determinant.

fnmatrix_rank→ Tensor

Compute the numerical rank of a matrix.

fncond→ Tensor

Compute the condition number of a matrix.

fnmulti_dot→ Tensor

Multiply a sequence of matrices as a single chained product.

fnsolve_triangular→ Tensor

Solve a triangular linear system by back/forward substitution.

fnvander→ Tensor

Construct a Vandermonde matrix from a 1-D vector.

fnvector_norm→ Tensor

Compute a vector $p$-norm along an axis.

fncross→ Tensor

Compute the cross product of two 3-D vectors.

fnvecdot→ Tensor

Compute a batched vector dot product along an axis.

fndot→ Tensor

Dot product of two 1-D tensors.

fninner→ Tensor

Inner product over the last axes of two tensors.

fnouter→ Tensor

Outer product of two 1-D tensors.

fnmatrix_norm→ Tensor

Compute a matrix norm.

fnlstsq→ Tensor

Solve a least-squares linear system.

fnlu_solve→ Tensor

Solve a linear system from a precomputed LU factorization.

fnhouseholder_product→ Tensor

Reconstruct an orthogonal matrix from Householder reflectors.

fnldl_factor→ Tensor

LDL factorization of a symmetric (or Hermitian) matrix.

fncholesky_ex→ Tensor

Cholesky factorization with an explicit success flag.

fninv_ex→ Tensor

Matrix inverse with an explicit success flag.

fnsolve_ex→ Tensor

Solve $AX = B$ with an explicit success flag.

fnlu→ Tensor

Full LU decomposition with explicit factors $(P, L, U)$.

fnldl_solve→ Tensor

Solve a symmetric linear system using an LDL factorization.

fnmatrix_exp→ Tensor

Matrix exponential $e^A$.

fndiagonal→ Tensor

Extract a (off-)diagonal from each matrix in a batched input.