linalg.h File Reference

linear algebra functions More...

#include "a.h"

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Functions
void	a_linalg_T1 (a_float *A, a_uint n)
	transpose an n x n square matrix in-place.
void	a_linalg_T2 (a_float *__restrict T, a_float const *__restrict A, a_uint m, a_uint n)
	transpose a given m x n matrix A into an n x m matrix T.
a_float	a_linalg_dot (a_float const *X, a_float const *Y, a_size n)
	compute the dot product of two vectors.
void	a_linalg_mulmm (a_float *__restrict Z, a_float const *__restrict X, a_float const *__restrict Y, a_uint row, a_uint c_r, a_uint col)
	multiply two matrices X and Y, storing the result in Z.
void	a_linalg_mulTm (a_float *__restrict Z, a_float const *__restrict X, a_float const *__restrict Y, a_uint c_r, a_uint row, a_uint col)
	multiply the transpose of matrix X with matrix Y, storing the result in Z.
void	a_linalg_mulmT (a_float *__restrict Z, a_float const *__restrict X, a_float const *__restrict Y, a_uint row, a_uint col, a_uint c_r)
	multiply matrix X with the transpose of matrix Y, storing the result in Z.
void	a_linalg_mulTT (a_float *__restrict Z, a_float const *__restrict X, a_float const *__restrict Y, a_uint row, a_uint c_r, a_uint col)
	multiply the transpose of matrix X with the transpose of matrix Y, storing the result in Z.
int	a_linalg_plu (a_float *A, a_uint n, a_uint *p, int *sign)
	compute LU decomposition of a square matrix with partial pivoting.
void	a_linalg_plu_get_P (a_uint const *p, a_uint n, a_float *P)
	construct the permutation matrix P from a permutation vector p.
void	a_linalg_plu_get_L (a_float const *A, a_uint n, a_float *L)
	extract the lower triangular matrix L from matrix A.
void	a_linalg_plu_get_U (a_float const *A, a_uint n, a_float *U)
	extract the upper triangular matrix U from matrix A.
void	a_linalg_plu_apply (a_uint const *p, a_uint n, a_float const *b, a_float *Pb)
	apply the permutation P to the vector b, producing Pb.
void	a_linalg_plu_lower (a_float const *L, a_uint n, a_float *y)
	solve the lower triangular system Ly = Pb for y.
void	a_linalg_plu_upper (a_float const *U, a_uint n, a_float *x)
	solve the upper triangular system Ux = y for x.
void	a_linalg_plu_solve (a_float const *A, a_uint n, a_uint const *p, a_float const *b, a_float *x)
	solve the linear system Ax = b using LU decomposition with partial pivoting.
void	a_linalg_plu_inv (a_float const *A, a_uint n, a_uint const *p, a_float *b, a_float *I)
	compute the inverse of a matrix using its LU decomposition and permutation matrix.
a_float	a_linalg_plu_det (a_float const *A, a_uint n, int sign)
	compute the determinant of a matrix using its LU decomposition.
a_float	a_linalg_plu_lndet (a_float const *A, a_uint n)
	compute the natural logarithm of the absolute value of the determinant of a matrix using its LU decomposition.
int	a_linalg_plu_sgndet (a_float const *A, a_uint n, int sign)
	compute the sign of the determinant of a matrix using its LU decomposition.
int	a_linalg_cho (a_float *A, a_uint n)
	compute Cholesky decomposition of a symmetric positive-definite matrix.
void	a_linalg_cho_get_L (a_float const *A, a_uint n, a_float *L)
	extract the lower triangular matrix L from matrix A.
void	a_linalg_cho_lower (a_float const *L, a_uint n, a_float *y)
	solve the lower triangular system Ly = b for y.
void	a_linalg_cho_upper (a_float const *L, a_uint n, a_float *x)
	solve the upper triangular system L^T x = y for x.
void	a_linalg_cho_solve (a_float const *A, a_uint n, a_float *x)
	solve the linear system Ax = b using the Cholesky factorization A = LL^T.
void	a_linalg_cho_inv (a_float const *A, a_uint n, a_float *b, a_float *I)
	compute the inverse of a matrix using its Cholesky factorization A = LL^T.

Detailed Description

linear algebra functions