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qr.h
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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
notice, this list of conditions and the following disclaimer.
- Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer listed
in this license in the documentation and/or other materials
provided with the distribution.
- Neither the name of the copyright holders nor the names of its
contributors may be used to endorse or promote products derived from
this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*************************************************************************/
#ifndef _qr_h
#define _qr_h
#include "ap.h"
#include "amp.h"
#include "reflections.h"
namespace qr
{
template<unsigned int Precision>
void rmatrixqr(ap::template_2d_array< amp::ampf<Precision> >& a,
int m,
int n,
ap::template_1d_array< amp::ampf<Precision> >& tau);
template<unsigned int Precision>
void rmatrixqrunpackq(const ap::template_2d_array< amp::ampf<Precision> >& a,
int m,
int n,
const ap::template_1d_array< amp::ampf<Precision> >& tau,
int qcolumns,
ap::template_2d_array< amp::ampf<Precision> >& q);
template<unsigned int Precision>
void rmatrixqrunpackr(const ap::template_2d_array< amp::ampf<Precision> >& a,
int m,
int n,
ap::template_2d_array< amp::ampf<Precision> >& r);
template<unsigned int Precision>
void qrdecomposition(ap::template_2d_array< amp::ampf<Precision> >& a,
int m,
int n,
ap::template_1d_array< amp::ampf<Precision> >& tau);
template<unsigned int Precision>
void unpackqfromqr(const ap::template_2d_array< amp::ampf<Precision> >& a,
int m,
int n,
const ap::template_1d_array< amp::ampf<Precision> >& tau,
int qcolumns,
ap::template_2d_array< amp::ampf<Precision> >& q);
template<unsigned int Precision>
void qrdecompositionunpacked(ap::template_2d_array< amp::ampf<Precision> > a,
int m,
int n,
ap::template_2d_array< amp::ampf<Precision> >& q,
ap::template_2d_array< amp::ampf<Precision> >& r);
/*************************************************************************
QR decomposition of a rectangular matrix of size MxN
Input parameters:
A - matrix A whose indexes range within [0..M-1, 0..N-1].
M - number of rows in matrix A.
N - number of columns in matrix A.
Output parameters:
A - matrices Q and R in compact form (see below).
Tau - array of scalar factors which are used to form
matrix Q. Array whose index ranges within [0.. Min(M-1,N-1)].
Matrix A is represented as A = QR, where Q is an orthogonal matrix of size
MxM, R - upper triangular (or upper trapezoid) matrix of size M x N.
The elements of matrix R are located on and above the main diagonal of
matrix A. The elements which are located in Tau array and below the main
diagonal of matrix A are used to form matrix Q as follows:
Matrix Q is represented as a product of elementary reflections
Q = H(0)*H(2)*...*H(k-1),
where k = min(m,n), and each H(i) is in the form
H(i) = 1 - tau * v * (v^T)
where tau is a scalar stored in Tau[I]; v - real vector,
so that v(0:i-1) = 0, v(i) = 1, v(i+1:m-1) stored in A(i+1:m-1,i).
-- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992.
Translation from FORTRAN to pseudocode (AlgoPascal)
by Sergey Bochkanov, ALGLIB project, 2005-2007.
*************************************************************************/
template<unsigned int Precision>
void rmatrixqr(ap::template_2d_array< amp::ampf<Precision> >& a,
int m,
int n,
ap::template_1d_array< amp::ampf<Precision> >& tau)
{
ap::template_1d_array< amp::ampf<Precision> > work;
ap::template_1d_array< amp::ampf<Precision> > t;
int i;
int k;
int minmn;
amp::ampf<Precision> tmp;
if( m<=0 || n<=0 )
{
return;
}
minmn = ap::minint(m, n);
work.setbounds(0, n-1);
t.setbounds(1, m);
tau.setbounds(0, minmn-1);
//
// Test the input arguments
//
k = minmn;
for(i=0; i<=k-1; i++)
{
//
// Generate elementary reflector H(i) to annihilate A(i+1:m,i)
//
ap::vmove(t.getvector(1, m-i), a.getcolumn(i, i, m-1));
reflections::generatereflection<Precision>(t, m-i, tmp);
tau(i) = tmp;
ap::vmove(a.getcolumn(i, i, m-1), t.getvector(1, m-i));
t(1) = 1;
if( i<n )
{
//
// Apply H(i) to A(i:m-1,i+1:n-1) from the left
//
reflections::applyreflectionfromtheleft<Precision>(a, tau(i), t, i, m-1, i+1, n-1, work);
}
}
}
/*************************************************************************
Partial unpacking of matrix Q from the QR decomposition of a matrix A
Input parameters:
A - matrices Q and R in compact form.
Output of RMatrixQR subroutine.
M - number of rows in given matrix A. M>=0.
N - number of columns in given matrix A. N>=0.
Tau - scalar factors which are used to form Q.
Output of the RMatrixQR subroutine.
QColumns - required number of columns of matrix Q. M>=QColumns>=0.
Output parameters:
Q - first QColumns columns of matrix Q.
Array whose indexes range within [0..M-1, 0..QColumns-1].
If QColumns=0, the array remains unchanged.
-- ALGLIB --
Copyright 2005 by Bochkanov Sergey
*************************************************************************/
template<unsigned int Precision>
void rmatrixqrunpackq(const ap::template_2d_array< amp::ampf<Precision> >& a,
int m,
int n,
const ap::template_1d_array< amp::ampf<Precision> >& tau,
int qcolumns,
ap::template_2d_array< amp::ampf<Precision> >& q)
{
int i;
int j;
int k;
int minmn;
ap::template_1d_array< amp::ampf<Precision> > v;
ap::template_1d_array< amp::ampf<Precision> > work;
ap::ap_error::make_assertion(qcolumns<=m);
if( m<=0 || n<=0 || qcolumns<=0 )
{
return;
}
//
// init
//
minmn = ap::minint(m, n);
k = ap::minint(minmn, qcolumns);
q.setbounds(0, m-1, 0, qcolumns-1);
v.setbounds(1, m);
work.setbounds(0, qcolumns-1);
for(i=0; i<=m-1; i++)
{
for(j=0; j<=qcolumns-1; j++)
{
if( i==j )
{
q(i,j) = 1;
}
else
{
q(i,j) = 0;
}
}
}
//
// unpack Q
//
for(i=k-1; i>=0; i--)
{
//
// Apply H(i)
//
ap::vmove(v.getvector(1, m-i), a.getcolumn(i, i, m-1));
v(1) = 1;
reflections::applyreflectionfromtheleft<Precision>(q, tau(i), v, i, m-1, 0, qcolumns-1, work);
}
}
/*************************************************************************
Unpacking of matrix R from the QR decomposition of a matrix A
Input parameters:
A - matrices Q and R in compact form.
Output of RMatrixQR subroutine.
M - number of rows in given matrix A. M>=0.
N - number of columns in given matrix A. N>=0.
Output parameters:
R - matrix R, array[0..M-1, 0..N-1].
-- ALGLIB --
Copyright 2005 by Bochkanov Sergey
*************************************************************************/
template<unsigned int Precision>
void rmatrixqrunpackr(const ap::template_2d_array< amp::ampf<Precision> >& a,
int m,
int n,
ap::template_2d_array< amp::ampf<Precision> >& r)
{
int i;
int k;
if( m<=0 || n<=0 )
{
return;
}
k = ap::minint(m, n);
r.setbounds(0, m-1, 0, n-1);
for(i=0; i<=n-1; i++)
{
r(0,i) = 0;
}
for(i=1; i<=m-1; i++)
{
ap::vmove(r.getrow(i, 0, n-1), r.getrow(0, 0, n-1));
}
for(i=0; i<=k-1; i++)
{
ap::vmove(r.getrow(i, i, n-1), a.getrow(i, i, n-1));
}
}
/*************************************************************************
Obsolete 1-based subroutine. See RMatrixQR for 0-based replacement.
*************************************************************************/
template<unsigned int Precision>
void qrdecomposition(ap::template_2d_array< amp::ampf<Precision> >& a,
int m,
int n,
ap::template_1d_array< amp::ampf<Precision> >& tau)
{
ap::template_1d_array< amp::ampf<Precision> > work;
ap::template_1d_array< amp::ampf<Precision> > t;
int i;
int k;
int mmip1;
int minmn;
amp::ampf<Precision> tmp;
minmn = ap::minint(m, n);
work.setbounds(1, n);
t.setbounds(1, m);
tau.setbounds(1, minmn);
//
// Test the input arguments
//
k = ap::minint(m, n);
for(i=1; i<=k; i++)
{
//
// Generate elementary reflector H(i) to annihilate A(i+1:m,i)
//
mmip1 = m-i+1;
ap::vmove(t.getvector(1, mmip1), a.getcolumn(i, i, m));
reflections::generatereflection<Precision>(t, mmip1, tmp);
tau(i) = tmp;
ap::vmove(a.getcolumn(i, i, m), t.getvector(1, mmip1));
t(1) = 1;
if( i<n )
{
//
// Apply H(i) to A(i:m,i+1:n) from the left
//
reflections::applyreflectionfromtheleft<Precision>(a, tau(i), t, i, m, i+1, n, work);
}
}
}
/*************************************************************************
Obsolete 1-based subroutine. See RMatrixQRUnpackQ for 0-based replacement.
*************************************************************************/
template<unsigned int Precision>
void unpackqfromqr(const ap::template_2d_array< amp::ampf<Precision> >& a,
int m,
int n,
const ap::template_1d_array< amp::ampf<Precision> >& tau,
int qcolumns,
ap::template_2d_array< amp::ampf<Precision> >& q)
{
int i;
int j;
int k;
int minmn;
ap::template_1d_array< amp::ampf<Precision> > v;
ap::template_1d_array< amp::ampf<Precision> > work;
int vm;
ap::ap_error::make_assertion(qcolumns<=m);
if( m==0 || n==0 || qcolumns==0 )
{
return;
}
//
// init
//
minmn = ap::minint(m, n);
k = ap::minint(minmn, qcolumns);
q.setbounds(1, m, 1, qcolumns);
v.setbounds(1, m);
work.setbounds(1, qcolumns);
for(i=1; i<=m; i++)
{
for(j=1; j<=qcolumns; j++)
{
if( i==j )
{
q(i,j) = 1;
}
else
{
q(i,j) = 0;
}
}
}
//
// unpack Q
//
for(i=k; i>=1; i--)
{
//
// Apply H(i)
//
vm = m-i+1;
ap::vmove(v.getvector(1, vm), a.getcolumn(i, i, m));
v(1) = 1;
reflections::applyreflectionfromtheleft<Precision>(q, tau(i), v, i, m, 1, qcolumns, work);
}
}
/*************************************************************************
Obsolete 1-based subroutine. See RMatrixQR for 0-based replacement.
*************************************************************************/
template<unsigned int Precision>
void qrdecompositionunpacked(ap::template_2d_array< amp::ampf<Precision> > a,
int m,
int n,
ap::template_2d_array< amp::ampf<Precision> >& q,
ap::template_2d_array< amp::ampf<Precision> >& r)
{
int i;
int k;
ap::template_1d_array< amp::ampf<Precision> > tau;
ap::template_1d_array< amp::ampf<Precision> > work;
ap::template_1d_array< amp::ampf<Precision> > v;
k = ap::minint(m, n);
if( n<=0 )
{
return;
}
work.setbounds(1, m);
v.setbounds(1, m);
q.setbounds(1, m, 1, m);
r.setbounds(1, m, 1, n);
//
// QRDecomposition
//
qrdecomposition<Precision>(a, m, n, tau);
//
// R
//
for(i=1; i<=n; i++)
{
r(1,i) = 0;
}
for(i=2; i<=m; i++)
{
ap::vmove(r.getrow(i, 1, n), r.getrow(1, 1, n));
}
for(i=1; i<=k; i++)
{
ap::vmove(r.getrow(i, i, n), a.getrow(i, i, n));
}
//
// Q
//
unpackqfromqr<Precision>(a, m, n, tau, m, q);
}
} // namespace
#endif
amp.h
ap.h
m
int m
Definition cfEzgcd.cc:128
i
int i
Definition cfEzgcd.cc:132
k
int k
Definition cfEzgcd.cc:99
tau
void tau(int **points, int sizePoints, int k)
Definition cfNewtonPolygon.cc:461
amp::ampf
Definition amp.h:82
ap::ap_error::make_assertion
static void make_assertion(bool bClause)
Definition ap.h:49
ap::template_1d_array
Definition ap.h:657
ap::template_1d_array::getvector
raw_vector< T > getvector(int iStart, int iEnd)
Definition ap.h:776
ap::template_1d_array::setbounds
void setbounds(int iLow, int iHigh)
Definition ap.h:735
ap::template_2d_array
Definition ap.h:807
v
const Variable & v
< [in] a sqrfree bivariate poly
Definition facBivar.h:39
j
int j
Definition facHensel.cc:110
ap::vmove
void vmove(raw_vector< T > vdst, const_raw_vector< T > vsrc)
Definition ap.h:237
ap::minint
int minint(int m1, int m2)
Definition ap.cpp:167
qr
Definition qr.h:46
qr::rmatrixqr
void rmatrixqr(ap::template_2d_array< amp::ampf< Precision > > &a, int m, int n, ap::template_1d_array< amp::ampf< Precision > > &tau)
Definition qr.h:123
qr::rmatrixqrunpackq
void rmatrixqrunpackq(const ap::template_2d_array< amp::ampf< Precision > > &a, int m, int n, const ap::template_1d_array< amp::ampf< Precision > > &tau, int qcolumns, ap::template_2d_array< amp::ampf< Precision > > &q)
Definition qr.h:193
qr::qrdecomposition
void qrdecomposition(ap::template_2d_array< amp::ampf< Precision > > &a, int m, int n, ap::template_1d_array< amp::ampf< Precision > > &tau)
Definition qr.h:303
qr::unpackqfromqr
void unpackqfromqr(const ap::template_2d_array< amp::ampf< Precision > > &a, int m, int n, const ap::template_1d_array< amp::ampf< Precision > > &tau, int qcolumns, ap::template_2d_array< amp::ampf< Precision > > &q)
Definition qr.h:354
qr::rmatrixqrunpackr
void rmatrixqrunpackr(const ap::template_2d_array< amp::ampf< Precision > > &a, int m, int n, ap::template_2d_array< amp::ampf< Precision > > &r)
Definition qr.h:269
qr::qrdecompositionunpacked
void qrdecompositionunpacked(ap::template_2d_array< amp::ampf< Precision > > a, int m, int n, ap::template_2d_array< amp::ampf< Precision > > &q, ap::template_2d_array< amp::ampf< Precision > > &r)
Definition qr.h:420
reflections::generatereflection
void generatereflection(ap::template_1d_array< amp::ampf< Precision > > &x, int n, amp::ampf< Precision > &tau)
Definition reflections.h:112
reflections::applyreflectionfromtheleft
void applyreflectionfromtheleft(ap::template_2d_array< amp::ampf< Precision > > &c, amp::ampf< Precision > tau, const ap::template_1d_array< amp::ampf< Precision > > &v, int m1, int m2, int n1, int n2, ap::template_1d_array< amp::ampf< Precision > > &work)
Definition reflections.h:207
reflections.h