linalg.h File Reference

linear algebra functions More...

#include "a.h"

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Functions
void	a_real_T1 (a_uint n, a_real *A)
	transpose an n x n square matrix in-place.
void	a_real_T2 (a_uint m, a_uint n, a_real const *__restrict A, a_real *__restrict T)
	transpose a given m x n matrix A into an n x m matrix T.
void	a_real_eye1 (a_uint n, a_real *E)
	generate an m x n matrix with ones on the diagonal and zeros elsewhere.
void	a_real_eye2 (a_uint m, a_uint n, a_real *E)
	generate an m x n matrix with ones on the diagonal and zeros elsewhere.
void	a_real_tri1 (a_uint n, a_real *L)
	generate an m x n matrix with ones in the lower triangular part and zeros elsewhere.
void	a_real_tri2 (a_uint m, a_uint n, a_real *L)
	generate an m x n matrix with ones in the lower triangular part and zeros elsewhere.
void	a_real_diag (a_uint n, a_real const *__restrict a, a_real *__restrict A)
	compute a diagonal matrix from a given diagonal vector.
void	a_real_diag1 (a_uint n, a_real const *__restrict A, a_real *__restrict a)
	extract a diagonal vector from a given diagonal matrix.
void	a_real_diag2 (a_uint m, a_uint n, a_real const *__restrict A, a_real *__restrict a)
	extract a diagonal vector from a given diagonal matrix.
void	a_real_triL (a_uint n, a_real const *__restrict A, a_real *__restrict L)
	extract the lower triangular part of a square matrix, including the diagonal.
void	a_real_triL1 (a_uint n, a_real const *__restrict A, a_real *__restrict L)
	extract the lower triangular part of a square matrix, set the diagonal to 1.
void	a_real_triL2 (a_uint m, a_uint n, a_real const *__restrict A, a_real *__restrict L)
	extract the lower triangular part of a square matrix, including the diagonal.
void	a_real_triU (a_uint n, a_real const *__restrict A, a_real *__restrict U)
	extract the upper triangular part of a square matrix, including the diagonal.
void	a_real_triU1 (a_uint n, a_real const *__restrict A, a_real *__restrict U)
	extract the upper triangular part of a square matrix, set the diagonal to 1.
void	a_real_triU2 (a_uint m, a_uint n, a_real const *__restrict A, a_real *__restrict U)
	extract the upper triangular part of a square matrix, including the diagonal.
void	a_real_mulmm (a_uint row, a_uint c_r, a_uint col, a_real const *__restrict X, a_real const *__restrict Y, a_real *__restrict Z)
	multiply two matrices X and Y, storing the result in Z.
void	a_real_mulTm (a_uint c_r, a_uint row, a_uint col, a_real const *__restrict X, a_real const *__restrict Y, a_real *__restrict Z)
	multiply the transpose of matrix X with matrix Y, storing the result in Z.
void	a_real_mulmT (a_uint row, a_uint col, a_uint c_r, a_real const *__restrict X, a_real const *__restrict Y, a_real *__restrict Z)
	multiply matrix X with the transpose of matrix Y, storing the result in Z.
void	a_real_mulTT (a_uint row, a_uint c_r, a_uint col, a_real const *__restrict X, a_real const *__restrict Y, a_real *__restrict Z)
	multiply the transpose of matrix X with the transpose of matrix Y, storing the result in Z.
int	a_real_plu (a_uint n, a_real *A, a_uint *p, int *sign)
	compute LU decomposition of a square matrix with partial pivoting.
void	a_real_plu_P (a_uint n, a_uint const *__restrict p, a_real *__restrict P)
	construct the permutation matrix P from a permutation vector p.
void	a_real_plu_P_ (a_uint n, a_uint const *__restrict p, a_real *__restrict P)
void	a_real_plu_L (a_uint n, a_real const *__restrict A, a_real *__restrict L)
	extract the lower triangular matrix L from matrix A.
void	a_real_plu_U (a_uint n, a_real const *__restrict A, a_real *__restrict U)
	extract the upper triangular matrix U from matrix A.
void	a_real_plu_apply (a_uint n, a_uint const *__restrict p, a_real const *__restrict b, a_real *__restrict Pb)
	apply the permutation P to the vector b, producing Pb.
void	a_real_plu_lower (a_uint n, a_real const *L, a_real *y)
	solve the lower triangular system Ly = Pb for y.
void	a_real_plu_lower_ (a_uint n, a_real const *L, a_real *y)
void	a_real_plu_upper (a_uint n, a_real const *U, a_real *x)
	solve the upper triangular system Ux = y for x.
void	a_real_plu_upper_ (a_uint n, a_real const *U, a_real *x)
void	a_real_plu_solve (a_uint n, a_real const *A, a_uint const *p, a_real const *b, a_real *x)
	solve the linear system Ax = b using LU decomposition with partial pivoting.
void	a_real_plu_inv (a_uint n, a_real const *A, a_uint const *p, a_real *b, a_real *I)
	compute the inverse of a matrix using its LU decomposition and permutation matrix.
void	a_real_plu_inv_ (a_uint n, a_real const *A, a_uint const *p, a_real *I)
a_real	a_real_plu_det (a_uint n, a_real const *A, int sign)
	compute the determinant of a matrix using its LU decomposition.
a_real	a_real_plu_lndet (a_uint n, a_real const *A)
	compute the natural logarithm of the absolute value of the determinant of a matrix using its LU decomposition.
int	a_real_plu_sgndet (a_uint n, a_real const *A, int sign)
	compute the sign of the determinant of a matrix using its LU decomposition.
int	a_real_ldl (a_uint n, a_real *A)
	compute LDL decomposition of a symmetric matrix.
void	a_real_ldl_L (a_uint n, a_real const *__restrict A, a_real *__restrict L)
	extract the lower triangular matrix L from matrix A.
void	a_real_ldl_D (a_uint n, a_real const *__restrict A, a_real *__restrict d)
	extract the diagonal vector D from matrix A.
void	a_real_ldl_lower (a_uint n, a_real const *L, a_real *y)
	solve the lower triangular system Ly = b for y.
void	a_real_ldl_lower_ (a_uint n, a_real const *L, a_real *y)
void	a_real_ldl_upper (a_uint n, a_real const *L, a_real *x)
	solve the upper triangular system D L^T x = y for x.
void	a_real_ldl_upper_ (a_uint n, a_real const *L, a_real *x)
void	a_real_ldl_solve (a_uint n, a_real const *A, a_real *x)
	solve the linear system Ax = b using the LDL factorization A = LDL^T.
void	a_real_ldl_inv (a_uint n, a_real const *A, a_real *b, a_real *I)
	compute the inverse of a matrix using its LDL factorization A = LDL^T.
void	a_real_ldl_inv_ (a_uint n, a_real const *A, a_real *I)
a_real	a_real_ldl_det (a_uint n, a_real const *A)
	compute the determinant of a matrix using its LDL decomposition.
a_real	a_real_ldl_lndet (a_uint n, a_real const *A)
	compute the natural logarithm of the absolute value of the determinant of a matrix using its LDL decomposition.
int	a_real_ldl_sgndet (a_uint n, a_real const *A)
	compute the sign of the determinant of a matrix using its LDL decomposition.
int	a_real_llt (a_uint n, a_real *A)
	compute Cholesky decomposition of a symmetric positive-definite matrix.
void	a_real_llt_L (a_uint n, a_real const *__restrict A, a_real *__restrict L)
	extract the lower triangular matrix L from matrix A.
void	a_real_llt_lower (a_uint n, a_real const *L, a_real *y)
	solve the lower triangular system Ly = b for y.
void	a_real_llt_lower_ (a_uint n, a_real const *L, a_real *y)
void	a_real_llt_upper (a_uint n, a_real const *L, a_real *x)
	solve the upper triangular system L^T x = y for x.
void	a_real_llt_upper_ (a_uint n, a_real const *L, a_real *x)
void	a_real_llt_solve (a_uint n, a_real const *A, a_real *x)
	solve the linear system Ax = b using the Cholesky factorization A = LL^T.
void	a_real_llt_inv (a_uint n, a_real const *A, a_real *b, a_real *I)
	compute the inverse of a matrix using its Cholesky factorization A = LL^T.
void	a_real_llt_inv_ (a_uint n, a_real const *A, a_real *I)
a_real	a_real_llt_det (a_uint n, a_real const *A)
	compute the determinant of a matrix using its Cholesky decomposition.
a_real	a_real_llt_lndet (a_uint n, a_real const *A)
	compute the natural logarithm of the absolute value of the determinant of a matrix using its Cholesky decomposition.

Detailed Description

linear algebra functions