/usr/include/reflections.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 _reflections_h
#define _reflections_h
#include "ap.h"
#include "ialglib.h"
/*************************************************************************
Generation of an elementary reflection transformation
The subroutine generates elementary reflection H of order N, so that, for
a given X, the following equality holds true:
( X(1) ) ( Beta )
H * ( .. ) = ( 0 )
( X(n) ) ( 0 )
where
( V(1) )
H = 1 - Tau * ( .. ) * ( V(1), ..., V(n) )
( V(n) )
where the first component of vector V equals 1.
Input parameters:
X - vector. Array whose index ranges within [1..N].
N - reflection order.
Output parameters:
X - components from 2 to N are replaced with vector V.
The first component is replaced with parameter Beta.
Tau - scalar value Tau. If X is a null vector, Tau equals 0,
otherwise 1 <= Tau <= 2.
This subroutine is the modification of the DLARFG subroutines from
the LAPACK library.
MODIFICATIONS:
24.12.2005 sign(Alpha) was replaced with an analogous to the Fortran SIGN code.
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
*************************************************************************/
void generatereflection(ap::real_1d_array& x, int n, double& tau);
/*************************************************************************
Application of an elementary reflection to a rectangular matrix of size MxN
The algorithm pre-multiplies the matrix by an elementary reflection transformation
which is given by column V and scalar Tau (see the description of the
GenerateReflection procedure). Not the whole matrix but only a part of it
is transformed (rows from M1 to M2, columns from N1 to N2). Only the elements
of this submatrix are changed.
Input parameters:
C - matrix to be transformed.
Tau - scalar defining the transformation.
V - column defining the transformation.
Array whose index ranges within [1..M2-M1+1].
M1, M2 - range of rows to be transformed.
N1, N2 - range of columns to be transformed.
WORK - working array whose indexes goes from N1 to N2.
Output parameters:
C - the result of multiplying the input matrix C by the
transformation matrix which is given by Tau and V.
If N1>N2 or M1>M2, C is not modified.
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
*************************************************************************/
void applyreflectionfromtheleft(ap::real_2d_array& c,
double tau,
const ap::real_1d_array& v,
int m1,
int m2,
int n1,
int n2,
ap::real_1d_array& work);
/*************************************************************************
Application of an elementary reflection to a rectangular matrix of size MxN
The algorithm post-multiplies the matrix by an elementary reflection transformation
which is given by column V and scalar Tau (see the description of the
GenerateReflection procedure). Not the whole matrix but only a part of it
is transformed (rows from M1 to M2, columns from N1 to N2). Only the
elements of this submatrix are changed.
Input parameters:
C - matrix to be transformed.
Tau - scalar defining the transformation.
V - column defining the transformation.
Array whose index ranges within [1..N2-N1+1].
M1, M2 - range of rows to be transformed.
N1, N2 - range of columns to be transformed.
WORK - working array whose indexes goes from M1 to M2.
Output parameters:
C - the result of multiplying the input matrix C by the
transformation matrix which is given by Tau and V.
If N1>N2 or M1>M2, C is not modified.
-- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
*************************************************************************/
void applyreflectionfromtheright(ap::real_2d_array& c,
double tau,
const ap::real_1d_array& v,
int m1,
int m2,
int n1,
int n2,
ap::real_1d_array& work);
#endif
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