/usr/include/trfac.h is in libalglib-dev 2.6.0-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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Copyright (c) 1992-2007 The University of Tennessee. All rights reserved.
Contributors:
* Sergey Bochkanov (ALGLIB project). Translation from FORTRAN to
pseudocode.
See subroutines comments for additional copyrights.
>>> SOURCE LICENSE >>>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation (www.fsf.org); either version 2 of the
License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
A copy of the GNU General Public License is available at
http://www.fsf.org/licensing/licenses
>>> END OF LICENSE >>>
*************************************************************************/
#ifndef _trfac_h
#define _trfac_h
#include "ap.h"
#include "ialglib.h"
#include "reflections.h"
#include "creflections.h"
#include "hqrnd.h"
#include "matgen.h"
#include "ablasf.h"
#include "ablas.h"
/*************************************************************************
LU decomposition of a general real matrix with row pivoting
A is represented as A = P*L*U, where:
* L is lower unitriangular matrix
* U is upper triangular matrix
* P = P0*P1*...*PK, K=min(M,N)-1,
Pi - permutation matrix for I and Pivots[I]
This is cache-oblivous implementation of LU decomposition.
It is optimized for square matrices. As for rectangular matrices:
* best case - M>>N
* worst case - N>>M, small M, large N, matrix does not fit in CPU cache
INPUT PARAMETERS:
A - array[0..M-1, 0..N-1].
M - number of rows in matrix A.
N - number of columns in matrix A.
OUTPUT PARAMETERS:
A - matrices L and U in compact form:
* L is stored under main diagonal
* U is stored on and above main diagonal
Pivots - permutation matrix in compact form.
array[0..Min(M-1,N-1)].
-- ALGLIB routine --
10.01.2010
Bochkanov Sergey
*************************************************************************/
void rmatrixlu(ap::real_2d_array& a,
int m,
int n,
ap::integer_1d_array& pivots);
/*************************************************************************
LU decomposition of a general complex matrix with row pivoting
A is represented as A = P*L*U, where:
* L is lower unitriangular matrix
* U is upper triangular matrix
* P = P0*P1*...*PK, K=min(M,N)-1,
Pi - permutation matrix for I and Pivots[I]
This is cache-oblivous implementation of LU decomposition. It is optimized
for square matrices. As for rectangular matrices:
* best case - M>>N
* worst case - N>>M, small M, large N, matrix does not fit in CPU cache
INPUT PARAMETERS:
A - array[0..M-1, 0..N-1].
M - number of rows in matrix A.
N - number of columns in matrix A.
OUTPUT PARAMETERS:
A - matrices L and U in compact form:
* L is stored under main diagonal
* U is stored on and above main diagonal
Pivots - permutation matrix in compact form.
array[0..Min(M-1,N-1)].
-- ALGLIB routine --
10.01.2010
Bochkanov Sergey
*************************************************************************/
void cmatrixlu(ap::complex_2d_array& a,
int m,
int n,
ap::integer_1d_array& pivots);
/*************************************************************************
Cache-oblivious Cholesky decomposition
The algorithm computes Cholesky decomposition of a Hermitian positive-
definite matrix. The result of an algorithm is a representation of A as
A=U'*U or A=L*L' (here X' detones conj(X^T)).
INPUT PARAMETERS:
A - upper or lower triangle of a factorized matrix.
array with elements [0..N-1, 0..N-1].
N - size of matrix A.
IsUpper - if IsUpper=True, then A contains an upper triangle of
a symmetric matrix, otherwise A contains a lower one.
OUTPUT PARAMETERS:
A - the result of factorization. If IsUpper=True, then
the upper triangle contains matrix U, so that A = U'*U,
and the elements below the main diagonal are not modified.
Similarly, if IsUpper = False.
RESULT:
If the matrix is positive-definite, the function returns True.
Otherwise, the function returns False. Contents of A is not determined
in such case.
-- ALGLIB routine --
15.12.2009
Bochkanov Sergey
*************************************************************************/
bool hpdmatrixcholesky(ap::complex_2d_array& a, int n, bool isupper);
/*************************************************************************
Cache-oblivious Cholesky decomposition
The algorithm computes Cholesky decomposition of a symmetric positive-
definite matrix. The result of an algorithm is a representation of A as
A=U^T*U or A=L*L^T
INPUT PARAMETERS:
A - upper or lower triangle of a factorized matrix.
array with elements [0..N-1, 0..N-1].
N - size of matrix A.
IsUpper - if IsUpper=True, then A contains an upper triangle of
a symmetric matrix, otherwise A contains a lower one.
OUTPUT PARAMETERS:
A - the result of factorization. If IsUpper=True, then
the upper triangle contains matrix U, so that A = U^T*U,
and the elements below the main diagonal are not modified.
Similarly, if IsUpper = False.
RESULT:
If the matrix is positive-definite, the function returns True.
Otherwise, the function returns False. Contents of A is not determined
in such case.
-- ALGLIB routine --
15.12.2009
Bochkanov Sergey
*************************************************************************/
bool spdmatrixcholesky(ap::real_2d_array& a, int n, bool isupper);
void rmatrixlup(ap::real_2d_array& a,
int m,
int n,
ap::integer_1d_array& pivots);
void cmatrixlup(ap::complex_2d_array& a,
int m,
int n,
ap::integer_1d_array& pivots);
void rmatrixplu(ap::real_2d_array& a,
int m,
int n,
ap::integer_1d_array& pivots);
void cmatrixplu(ap::complex_2d_array& a,
int m,
int n,
ap::integer_1d_array& pivots);
#endif
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