Crate lax

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§Linear Algebra eXtension (LAX)

ndarray-free safe Rust wrapper for LAPACK FFI

As the property of $A$, several types of triangular factorization are used:

LU-decomposition for general matrix
- $PA = LU$, where $L$ is lower matrix, $U$ is upper matrix, and $P$ is permutation matrix
Bunch-Kaufman diagonal pivoting method for nonpositive-definite Hermitian matrix
- $A = U D U^\dagger$, where $U$ is upper matrix, $D$ is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

matrix type	Triangler factorization (TRF)	Solve (TRS)	Inverse matrix (TRI)	Reciprocal condition number (CON)
General (GE)	lu	solve	inv	rcond
Symmetric (SY) / Hermitian (HE)	bk	solveh	invh	-

Solve eigenvalue problem for a matrix $A$

$$ Av_i = \lambda_i v_i $$

or generalized eigenvalue problem

$$ Av_i = \lambda_i B v_i $$

matrix type	Eigenvalue (EV)	Generalized Eigenvalue Problem (EG)
General (GE)	eig	-
Symmetric (SY) / Hermitian (HE)	eigh	eigh_generalized

matrix type	Singular Value Decomposition (SVD)	SVD with divided-and-conquer (SDD)	Least square problem (LSD)
General (GE)	svd	svddc	least_squares

LUFactorizedTridiagonal: Represents the LU factorization of a tridiagonal matrix A as A = P*L*U.
LeastSquaresOutput: Result of LeastSquares
SVDOutput: Result of SVD
Tridiagonal: Represents a tridiagonal matrix as 3 one-dimensional vectors.

Diag
NormType
Transpose
UPLO: Upper/Lower specification for seveal usages
UVTFlag: Specifies how many of the columns of U and rows of Vᵀ are computed and returned.