/usr/include/vtk-5.8/alglib/reflections.h is in libvtk5-dev 5.8.0-5.
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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.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
- Redistributions of source code must retain the above copyright
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- Redistributions in binary form must reproduce the above copyright
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*************************************************************************/
#ifndef _reflections_h
#define _reflections_h
#include "alglib/ap.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. It has a similar functionality except for the
fact that it doesn�t handle errors when the intermediate results
cause an overflow.
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
*************************************************************************/
ALGLIB_EXPORT
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
*************************************************************************/
ALGLIB_EXPORT
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
*************************************************************************/
ALGLIB_EXPORT
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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