/usr/include/matgen.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) 2007, Sergey Bochkanov (ALGLIB project).
>>> 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 _matgen_h
#define _matgen_h
#include "ap.h"
#include "ialglib.h"
#include "reflections.h"
#include "creflections.h"
#include "hqrnd.h"
/*************************************************************************
Generation of a random uniformly distributed (Haar) orthogonal matrix
INPUT PARAMETERS:
N - matrix size, N>=1
OUTPUT PARAMETERS:
A - orthogonal NxN matrix, array[0..N-1,0..N-1]
-- ALGLIB routine --
04.12.2009
Bochkanov Sergey
*************************************************************************/
void rmatrixrndorthogonal(int n, ap::real_2d_array& a);
/*************************************************************************
Generation of random NxN matrix with given condition number and norm2(A)=1
INPUT PARAMETERS:
N - matrix size
C - condition number (in 2-norm)
OUTPUT PARAMETERS:
A - random matrix with norm2(A)=1 and cond(A)=C
-- ALGLIB routine --
04.12.2009
Bochkanov Sergey
*************************************************************************/
void rmatrixrndcond(int n, double c, ap::real_2d_array& a);
/*************************************************************************
Generation of a random Haar distributed orthogonal complex matrix
INPUT PARAMETERS:
N - matrix size, N>=1
OUTPUT PARAMETERS:
A - orthogonal NxN matrix, array[0..N-1,0..N-1]
-- ALGLIB routine --
04.12.2009
Bochkanov Sergey
*************************************************************************/
void cmatrixrndorthogonal(int n, ap::complex_2d_array& a);
/*************************************************************************
Generation of random NxN complex matrix with given condition number C and
norm2(A)=1
INPUT PARAMETERS:
N - matrix size
C - condition number (in 2-norm)
OUTPUT PARAMETERS:
A - random matrix with norm2(A)=1 and cond(A)=C
-- ALGLIB routine --
04.12.2009
Bochkanov Sergey
*************************************************************************/
void cmatrixrndcond(int n, double c, ap::complex_2d_array& a);
/*************************************************************************
Generation of random NxN symmetric matrix with given condition number and
norm2(A)=1
INPUT PARAMETERS:
N - matrix size
C - condition number (in 2-norm)
OUTPUT PARAMETERS:
A - random matrix with norm2(A)=1 and cond(A)=C
-- ALGLIB routine --
04.12.2009
Bochkanov Sergey
*************************************************************************/
void smatrixrndcond(int n, double c, ap::real_2d_array& a);
/*************************************************************************
Generation of random NxN symmetric positive definite matrix with given
condition number and norm2(A)=1
INPUT PARAMETERS:
N - matrix size
C - condition number (in 2-norm)
OUTPUT PARAMETERS:
A - random SPD matrix with norm2(A)=1 and cond(A)=C
-- ALGLIB routine --
04.12.2009
Bochkanov Sergey
*************************************************************************/
void spdmatrixrndcond(int n, double c, ap::real_2d_array& a);
/*************************************************************************
Generation of random NxN Hermitian matrix with given condition number and
norm2(A)=1
INPUT PARAMETERS:
N - matrix size
C - condition number (in 2-norm)
OUTPUT PARAMETERS:
A - random matrix with norm2(A)=1 and cond(A)=C
-- ALGLIB routine --
04.12.2009
Bochkanov Sergey
*************************************************************************/
void hmatrixrndcond(int n, double c, ap::complex_2d_array& a);
/*************************************************************************
Generation of random NxN Hermitian positive definite matrix with given
condition number and norm2(A)=1
INPUT PARAMETERS:
N - matrix size
C - condition number (in 2-norm)
OUTPUT PARAMETERS:
A - random HPD matrix with norm2(A)=1 and cond(A)=C
-- ALGLIB routine --
04.12.2009
Bochkanov Sergey
*************************************************************************/
void hpdmatrixrndcond(int n, double c, ap::complex_2d_array& a);
/*************************************************************************
Multiplication of MxN matrix by NxN random Haar distributed orthogonal matrix
INPUT PARAMETERS:
A - matrix, array[0..M-1, 0..N-1]
M, N- matrix size
OUTPUT PARAMETERS:
A - A*Q, where Q is random NxN orthogonal matrix
-- ALGLIB routine --
04.12.2009
Bochkanov Sergey
*************************************************************************/
void rmatrixrndorthogonalfromtheright(ap::real_2d_array& a, int m, int n);
/*************************************************************************
Multiplication of MxN matrix by MxM random Haar distributed orthogonal matrix
INPUT PARAMETERS:
A - matrix, array[0..M-1, 0..N-1]
M, N- matrix size
OUTPUT PARAMETERS:
A - Q*A, where Q is random MxM orthogonal matrix
-- ALGLIB routine --
04.12.2009
Bochkanov Sergey
*************************************************************************/
void rmatrixrndorthogonalfromtheleft(ap::real_2d_array& a, int m, int n);
/*************************************************************************
Multiplication of MxN complex matrix by NxN random Haar distributed
complex orthogonal matrix
INPUT PARAMETERS:
A - matrix, array[0..M-1, 0..N-1]
M, N- matrix size
OUTPUT PARAMETERS:
A - A*Q, where Q is random NxN orthogonal matrix
-- ALGLIB routine --
04.12.2009
Bochkanov Sergey
*************************************************************************/
void cmatrixrndorthogonalfromtheright(ap::complex_2d_array& a, int m, int n);
/*************************************************************************
Multiplication of MxN complex matrix by MxM random Haar distributed
complex orthogonal matrix
INPUT PARAMETERS:
A - matrix, array[0..M-1, 0..N-1]
M, N- matrix size
OUTPUT PARAMETERS:
A - Q*A, where Q is random MxM orthogonal matrix
-- ALGLIB routine --
04.12.2009
Bochkanov Sergey
*************************************************************************/
void cmatrixrndorthogonalfromtheleft(ap::complex_2d_array& a, int m, int n);
/*************************************************************************
Symmetric multiplication of NxN matrix by random Haar distributed
orthogonal matrix
INPUT PARAMETERS:
A - matrix, array[0..N-1, 0..N-1]
N - matrix size
OUTPUT PARAMETERS:
A - Q'*A*Q, where Q is random NxN orthogonal matrix
-- ALGLIB routine --
04.12.2009
Bochkanov Sergey
*************************************************************************/
void smatrixrndmultiply(ap::real_2d_array& a, int n);
/*************************************************************************
Hermitian multiplication of NxN matrix by random Haar distributed
complex orthogonal matrix
INPUT PARAMETERS:
A - matrix, array[0..N-1, 0..N-1]
N - matrix size
OUTPUT PARAMETERS:
A - Q^H*A*Q, where Q is random NxN orthogonal matrix
-- ALGLIB routine --
04.12.2009
Bochkanov Sergey
*************************************************************************/
void hmatrixrndmultiply(ap::complex_2d_array& a, int n);
#endif
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