dd/d46/linalg_8h_source.html

#ifndef LIBA_LINALG_H

#define LIBA_LINALG_H


#include "a.h"


#if defined(__cplusplus)

extern "C" {

#endif /* __cplusplus */


A_EXTERN void a_real_T1(a_uint n, a_real *A);


A_EXTERN void a_real_T2(a_uint m, a_uint n, a_real const *__restrict A, a_real *__restrict T);


A_EXTERN void a_real_eye1(a_uint n, a_real *E);


A_EXTERN void a_real_eye2(a_uint m, a_uint n, a_real *E);


A_EXTERN void a_real_tri1(a_uint n, a_real *L);


A_EXTERN void a_real_tri2(a_uint m, a_uint n, a_real *L);


A_EXTERN void a_real_diag(a_uint n, a_real const *__restrict a, a_real *__restrict A);


A_EXTERN void a_real_diag1(a_uint n, a_real const *__restrict A, a_real *__restrict a);


A_EXTERN void a_real_diag2(a_uint m, a_uint n, a_real const *__restrict A, a_real *__restrict a);


A_EXTERN void a_real_triL(a_uint n, a_real const *__restrict A, a_real *__restrict L);


A_EXTERN void a_real_triL1(a_uint n, a_real const *__restrict A, a_real *__restrict L);


A_EXTERN void a_real_triL2(a_uint m, a_uint n, a_real const *__restrict A, a_real *__restrict L);


A_EXTERN void a_real_triU(a_uint n, a_real const *__restrict A, a_real *__restrict U);


A_EXTERN void a_real_triU1(a_uint n, a_real const *__restrict A, a_real *__restrict U);


A_EXTERN void a_real_triU2(a_uint m, a_uint n, a_real const *__restrict A, a_real *__restrict U);


A_EXTERN 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);


A_EXTERN 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);


A_EXTERN 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);


A_EXTERN 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);


A_EXTERN int a_real_plu(a_uint n, a_real *A, a_uint *p, int *sign);


A_EXTERN void a_real_plu_P(a_uint n, a_uint const *__restrict p, a_real *__restrict P);

A_EXTERN void a_real_plu_P_(a_uint n, a_uint const *__restrict p, a_real *__restrict P);


A_EXTERN void a_real_plu_L(a_uint n, a_real const *__restrict A, a_real *__restrict L);


A_EXTERN void a_real_plu_U(a_uint n, a_real const *__restrict A, a_real *__restrict U);


A_EXTERN void a_real_plu_apply(a_uint n, a_uint const *__restrict p, a_real const *__restrict b, a_real *__restrict Pb);


A_EXTERN void a_real_plu_lower(a_uint n, a_real const *L, a_real *y);

A_EXTERN void a_real_plu_lower_(a_uint n, a_real const *L, a_real *y);


A_EXTERN void a_real_plu_upper(a_uint n, a_real const *U, a_real *x);

A_EXTERN void a_real_plu_upper_(a_uint n, a_real const *U, a_real *x);


A_EXTERN void a_real_plu_solve(a_uint n, a_real const *A, a_uint const *p, a_real const *b, a_real *x);


A_EXTERN void a_real_plu_inv(a_uint n, a_real const *A, a_uint const *p, a_real *b, a_real *I);

A_EXTERN void a_real_plu_inv_(a_uint n, a_real const *A, a_uint const *p, a_real *I);


A_EXTERN a_real a_real_plu_det(a_uint n, a_real const *A, int sign);


A_EXTERN a_real a_real_plu_lndet(a_uint n, a_real const *A);


A_EXTERN int a_real_plu_sgndet(a_uint n, a_real const *A, int sign);


A_EXTERN int a_real_ldl(a_uint n, a_real *A);


A_EXTERN void a_real_ldl_L(a_uint n, a_real const *__restrict A, a_real *__restrict L);


A_EXTERN void a_real_ldl_D(a_uint n, a_real const *__restrict A, a_real *__restrict d);


A_EXTERN void a_real_ldl_lower(a_uint n, a_real const *L, a_real *y);

A_EXTERN void a_real_ldl_lower_(a_uint n, a_real const *L, a_real *y);


A_EXTERN void a_real_ldl_upper(a_uint n, a_real const *L, a_real *x);

A_EXTERN void a_real_ldl_upper_(a_uint n, a_real const *L, a_real *x);


A_EXTERN void a_real_ldl_solve(a_uint n, a_real const *A, a_real *x);


A_EXTERN void a_real_ldl_inv(a_uint n, a_real const *A, a_real *b, a_real *I);

A_EXTERN void a_real_ldl_inv_(a_uint n, a_real const *A, a_real *I);


A_EXTERN a_real a_real_ldl_det(a_uint n, a_real const *A);


A_EXTERN a_real a_real_ldl_lndet(a_uint n, a_real const *A);


A_EXTERN int a_real_ldl_sgndet(a_uint n, a_real const *A);


A_EXTERN int a_real_llt(a_uint n, a_real *A);


A_EXTERN void a_real_llt_L(a_uint n, a_real const *__restrict A, a_real *__restrict L);


A_EXTERN void a_real_llt_lower(a_uint n, a_real const *L, a_real *y);

A_EXTERN void a_real_llt_lower_(a_uint n, a_real const *L, a_real *y);


A_EXTERN void a_real_llt_upper(a_uint n, a_real const *L, a_real *x);

A_EXTERN void a_real_llt_upper_(a_uint n, a_real const *L, a_real *x);


A_EXTERN void a_real_llt_solve(a_uint n, a_real const *A, a_real *x);


A_EXTERN void a_real_llt_inv(a_uint n, a_real const *A, a_real *b, a_real *I);

A_EXTERN void a_real_llt_inv_(a_uint n, a_real const *A, a_real *I);


A_EXTERN a_real a_real_llt_det(a_uint n, a_real const *A);


A_EXTERN a_real a_real_llt_lndet(a_uint n, a_real const *A);


#if defined(__cplusplus)

} /* extern "C" */

#endif /* __cplusplus */


#endif /* a/linalg.h */

a.h
algorithm library

a_real_llt_solve
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.

a_real_ldl_L
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.

a_real_tri2
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.

a_real_triL
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.

a_real_ldl_sgndet
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.

a_real_T2
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.

a_real_plu_solve
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.

a_real_eye2
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.

a_real_T1
void a_real_T1(a_uint n, a_real *A)
transpose an n x n square matrix in-place.

a_real_ldl_upper
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.

a_real_ldl_inv
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.

a_real_diag2
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.

a_real_plu_inv
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.

a_real_plu
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.

a_real_plu_L
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.

a_real_plu_U
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.

a_real_llt
int a_real_llt(a_uint n, a_real *A)
compute Cholesky decomposition of a symmetric positive-definite matrix.

a_real_plu_lndet
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 decom...

a_real_ldl_lndet
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 deco...

a_real_plu_sgndet
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.

a_real_tri1
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.

a_real_plu_det
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_llt_L
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.

a_real_ldl
int a_real_ldl(a_uint n, a_real *A)
compute LDL decomposition of a symmetric matrix.

a_real_plu_upper
void a_real_plu_upper(a_uint n, a_real const *U, a_real *x)
solve the upper triangular system Ux = y for x.

a_real_eye1
void a_real_eye1(a_uint n, a_real *E)
generate an m x n matrix with ones on the diagonal and zeros elsewhere.

a_real_triU1
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.

a_real_ldl_D
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.

a_real_diag1
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.

a_real_ldl_lower
void a_real_ldl_lower(a_uint n, a_real const *L, a_real *y)
solve the lower triangular system Ly = b for y.

a_real_mulmT
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.

a_real_plu_lower
void a_real_plu_lower(a_uint n, a_real const *L, a_real *y)
solve the lower triangular system Ly = Pb for y.

a_real_ldl_det
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_mulTm
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.

a_real_triL2
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.

a_real_llt_det
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_ldl_solve
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.

a_real_llt_lndet
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...

a_real_llt_inv
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.

a_real_llt_lower
void a_real_llt_lower(a_uint n, a_real const *L, a_real *y)
solve the lower triangular system Ly = b for y.

a_real_mulTT
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.

a_real_llt_upper
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.

a_real_triL1
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.

a_real_plu_apply
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.

a_real_triU
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.

a_real_diag
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.

a_real_mulmm
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.

a_real_plu_P
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.

a_real_triU2
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.

a_real
double a_real
compiler built-in floating-point number type
Definition a.h:1006

a_uint
unsigned int a_uint
unsigned integer type is guaranteed to be at least 16 bits
Definition a.h:337