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svd.h
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/*************************************************************************
Copyright (c) 2005-2007, Sergey Bochkanov (ALGLIB project).
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 _svd_h
#define _svd_h
/*MAKEHEADER*/
#include "ap.h"
/*MAKEHEADER*/
#include "amp.h"
/*MAKEHEADER*/
#include "reflections.h"
/*MAKEHEADER*/
#include "bidiagonal.h"
/*MAKEHEADER*/
#include "qr.h"
/*MAKEHEADER*/
#include "lq.h"
/*MAKEHEADER*/
#include "blas.h"
/*MAKEHEADER*/
#include "rotations.h"
/*MAKEHEADER*/
#include "bdsvd.h"
namespace svd
{
template<unsigned int Precision>
bool rmatrixsvd(ap::template_2d_array< amp::ampf<Precision> > a,
int m,
int n,
int uneeded,
int vtneeded,
int additionalmemory,
ap::template_1d_array< amp::ampf<Precision> >& w,
ap::template_2d_array< amp::ampf<Precision> >& u,
ap::template_2d_array< amp::ampf<Precision> >& vt);
template<unsigned int Precision>
bool svddecomposition(ap::template_2d_array< amp::ampf<Precision> > a,
int m,
int n,
int uneeded,
int vtneeded,
int additionalmemory,
ap::template_1d_array< amp::ampf<Precision> >& w,
ap::template_2d_array< amp::ampf<Precision> >& u,
ap::template_2d_array< amp::ampf<Precision> >& vt);
/*************************************************************************
Singular value decomposition of a rectangular matrix.
The algorithm calculates the singular value decomposition of a matrix of
size MxN: A = U * S * V^T
The algorithm finds the singular values and, optionally, matrices U and V^T.
The algorithm can find both first min(M,N) columns of matrix U and rows of
matrix V^T (singular vectors), and matrices U and V^T wholly (of sizes MxM
and NxN respectively).
Take into account that the subroutine does not return matrix V but V^T.
Input parameters:
A - matrix to be decomposed.
Array whose indexes range within [0..M-1, 0..N-1].
M - number of rows in matrix A.
N - number of columns in matrix A.
UNeeded - 0, 1 or 2. See the description of the parameter U.
VTNeeded - 0, 1 or 2. See the description of the parameter VT.
AdditionalMemory -
If the parameter:
* equals 0, the algorithm doesn't use additional
memory (lower requirements, lower performance).
* equals 1, the algorithm uses additional
memory of size min(M,N)*min(M,N) of real numbers.
It often speeds up the algorithm.
* equals 2, the algorithm uses additional
memory of size M*min(M,N) of real numbers.
It allows to get a maximum performance.
The recommended value of the parameter is 2.
Output parameters:
W - contains singular values in descending order.
U - if UNeeded=0, U isn't changed, the left singular vectors
are not calculated.
if Uneeded=1, U contains left singular vectors (first
min(M,N) columns of matrix U). Array whose indexes range
within [0..M-1, 0..Min(M,N)-1].
if UNeeded=2, U contains matrix U wholly. Array whose
indexes range within [0..M-1, 0..M-1].
VT - if VTNeeded=0, VT isn't changed, the right singular vectors
are not calculated.
if VTNeeded=1, VT contains right singular vectors (first
min(M,N) rows of matrix V^T). Array whose indexes range
within [0..min(M,N)-1, 0..N-1].
if VTNeeded=2, VT contains matrix V^T wholly. Array whose
indexes range within [0..N-1, 0..N-1].
-- ALGLIB --
Copyright 2005 by Bochkanov Sergey
*************************************************************************/
template<unsigned int Precision>
bool rmatrixsvd(ap::template_2d_array< amp::ampf<Precision> > a,
int m,
int n,
int uneeded,
int vtneeded,
int additionalmemory,
ap::template_1d_array< amp::ampf<Precision> >& w,
ap::template_2d_array< amp::ampf<Precision> >& u,
ap::template_2d_array< amp::ampf<Precision> >& vt)
{
bool result;
ap::template_1d_array< amp::ampf<Precision> > tauq;
ap::template_1d_array< amp::ampf<Precision> > taup;
ap::template_1d_array< amp::ampf<Precision> > tau;
ap::template_1d_array< amp::ampf<Precision> > e;
ap::template_1d_array< amp::ampf<Precision> > work;
ap::template_2d_array< amp::ampf<Precision> > t2;
bool isupper;
int minmn;
int ncu;
int nrvt;
int nru;
int ncvt;
int i;
int j;
int im1;
amp::ampf<Precision> sm;
result = true;
if( m==0 || n==0 )
{
return result;
}
ap::ap_error::make_assertion(uneeded>=0 && uneeded<=2);
ap::ap_error::make_assertion(vtneeded>=0 && vtneeded<=2);
ap::ap_error::make_assertion(additionalmemory>=0 && additionalmemory<=2);
//
// initialize
//
minmn = ap::minint(m, n);
w.setbounds(1, minmn);
ncu = 0;
nru = 0;
if( uneeded==1 )
{
nru = m;
ncu = minmn;
u.setbounds(0, nru-1, 0, ncu-1);
}
if( uneeded==2 )
{
nru = m;
ncu = m;
u.setbounds(0, nru-1, 0, ncu-1);
}
nrvt = 0;
ncvt = 0;
if( vtneeded==1 )
{
nrvt = minmn;
ncvt = n;
vt.setbounds(0, nrvt-1, 0, ncvt-1);
}
if( vtneeded==2 )
{
nrvt = n;
ncvt = n;
vt.setbounds(0, nrvt-1, 0, ncvt-1);
}
//
// M much larger than N
// Use bidiagonal reduction with QR-decomposition
//
if( m>amp::ampf<Precision>("1.6")*n )
{
if( uneeded==0 )
{
//
// No left singular vectors to be computed
//
qr::rmatrixqr<Precision>(a, m, n, tau);
for(i=0; i<=n-1; i++)
{
for(j=0; j<=i-1; j++)
{
a(i,j) = 0;
}
}
bidiagonal::rmatrixbd<Precision>(a, n, n, tauq, taup);
bidiagonal::rmatrixbdunpackpt<Precision>(a, n, n, taup, nrvt, vt);
bidiagonal::rmatrixbdunpackdiagonals<Precision>(a, n, n, isupper, w, e);
result = bdsvd::rmatrixbdsvd<Precision>(w, e, n, isupper, false, u, 0, a, 0, vt, ncvt);
return result;
}
else
{
//
// Left singular vectors (may be full matrix U) to be computed
//
qr::rmatrixqr<Precision>(a, m, n, tau);
qr::rmatrixqrunpackq<Precision>(a, m, n, tau, ncu, u);
for(i=0; i<=n-1; i++)
{
for(j=0; j<=i-1; j++)
{
a(i,j) = 0;
}
}
bidiagonal::rmatrixbd<Precision>(a, n, n, tauq, taup);
bidiagonal::rmatrixbdunpackpt<Precision>(a, n, n, taup, nrvt, vt);
bidiagonal::rmatrixbdunpackdiagonals<Precision>(a, n, n, isupper, w, e);
if( additionalmemory<1 )
{
//
// No additional memory can be used
//
bidiagonal::rmatrixbdmultiplybyq<Precision>(a, n, n, tauq, u, m, n, true, false);
result = bdsvd::rmatrixbdsvd<Precision>(w, e, n, isupper, false, u, m, a, 0, vt, ncvt);
}
else
{
//
// Large U. Transforming intermediate matrix T2
//
work.setbounds(1, ap::maxint(m, n));
bidiagonal::rmatrixbdunpackq<Precision>(a, n, n, tauq, n, t2);
blas::copymatrix<Precision>(u, 0, m-1, 0, n-1, a, 0, m-1, 0, n-1);
blas::inplacetranspose<Precision>(t2, 0, n-1, 0, n-1, work);
result = bdsvd::rmatrixbdsvd<Precision>(w, e, n, isupper, false, u, 0, t2, n, vt, ncvt);
blas::matrixmatrixmultiply<Precision>(a, 0, m-1, 0, n-1, false, t2, 0, n-1, 0, n-1, true, amp::ampf<Precision>("1.0"), u, 0, m-1, 0, n-1, amp::ampf<Precision>("0.0"), work);
}
return result;
}
}
//
// N much larger than M
// Use bidiagonal reduction with LQ-decomposition
//
if( n>amp::ampf<Precision>("1.6")*m )
{
if( vtneeded==0 )
{
//
// No right singular vectors to be computed
//
lq::rmatrixlq<Precision>(a, m, n, tau);
for(i=0; i<=m-1; i++)
{
for(j=i+1; j<=m-1; j++)
{
a(i,j) = 0;
}
}
bidiagonal::rmatrixbd<Precision>(a, m, m, tauq, taup);
bidiagonal::rmatrixbdunpackq<Precision>(a, m, m, tauq, ncu, u);
bidiagonal::rmatrixbdunpackdiagonals<Precision>(a, m, m, isupper, w, e);
work.setbounds(1, m);
blas::inplacetranspose<Precision>(u, 0, nru-1, 0, ncu-1, work);
result = bdsvd::rmatrixbdsvd<Precision>(w, e, m, isupper, false, a, 0, u, nru, vt, 0);
blas::inplacetranspose<Precision>(u, 0, nru-1, 0, ncu-1, work);
return result;
}
else
{
//
// Right singular vectors (may be full matrix VT) to be computed
//
lq::rmatrixlq<Precision>(a, m, n, tau);
lq::rmatrixlqunpackq<Precision>(a, m, n, tau, nrvt, vt);
for(i=0; i<=m-1; i++)
{
for(j=i+1; j<=m-1; j++)
{
a(i,j) = 0;
}
}
bidiagonal::rmatrixbd<Precision>(a, m, m, tauq, taup);
bidiagonal::rmatrixbdunpackq<Precision>(a, m, m, tauq, ncu, u);
bidiagonal::rmatrixbdunpackdiagonals<Precision>(a, m, m, isupper, w, e);
work.setbounds(1, ap::maxint(m, n));
blas::inplacetranspose<Precision>(u, 0, nru-1, 0, ncu-1, work);
if( additionalmemory<1 )
{
//
// No additional memory available
//
bidiagonal::rmatrixbdmultiplybyp<Precision>(a, m, m, taup, vt, m, n, false, true);
result = bdsvd::rmatrixbdsvd<Precision>(w, e, m, isupper, false, a, 0, u, nru, vt, n);
}
else
{
//
// Large VT. Transforming intermediate matrix T2
//
bidiagonal::rmatrixbdunpackpt<Precision>(a, m, m, taup, m, t2);
result = bdsvd::rmatrixbdsvd<Precision>(w, e, m, isupper, false, a, 0, u, nru, t2, m);
blas::copymatrix<Precision>(vt, 0, m-1, 0, n-1, a, 0, m-1, 0, n-1);
blas::matrixmatrixmultiply<Precision>(t2, 0, m-1, 0, m-1, false, a, 0, m-1, 0, n-1, false, amp::ampf<Precision>("1.0"), vt, 0, m-1, 0, n-1, amp::ampf<Precision>("0.0"), work);
}
blas::inplacetranspose<Precision>(u, 0, nru-1, 0, ncu-1, work);
return result;
}
}
//
// M<=N
// We can use inplace transposition of U to get rid of columnwise operations
//
if( m<=n )
{
bidiagonal::rmatrixbd<Precision>(a, m, n, tauq, taup);
bidiagonal::rmatrixbdunpackq<Precision>(a, m, n, tauq, ncu, u);
bidiagonal::rmatrixbdunpackpt<Precision>(a, m, n, taup, nrvt, vt);
bidiagonal::rmatrixbdunpackdiagonals<Precision>(a, m, n, isupper, w, e);
work.setbounds(1, m);
blas::inplacetranspose<Precision>(u, 0, nru-1, 0, ncu-1, work);
result = bdsvd::rmatrixbdsvd<Precision>(w, e, minmn, isupper, false, a, 0, u, nru, vt, ncvt);
blas::inplacetranspose<Precision>(u, 0, nru-1, 0, ncu-1, work);
return result;
}
//
// Simple bidiagonal reduction
//
bidiagonal::rmatrixbd<Precision>(a, m, n, tauq, taup);
bidiagonal::rmatrixbdunpackq<Precision>(a, m, n, tauq, ncu, u);
bidiagonal::rmatrixbdunpackpt<Precision>(a, m, n, taup, nrvt, vt);
bidiagonal::rmatrixbdunpackdiagonals<Precision>(a, m, n, isupper, w, e);
if( additionalmemory<2 || uneeded==0 )
{
//
// We cant use additional memory or there is no need in such operations
//
result = bdsvd::rmatrixbdsvd<Precision>(w, e, minmn, isupper, false, u, nru, a, 0, vt, ncvt);
}
else
{
//
// We can use additional memory
//
t2.setbounds(0, minmn-1, 0, m-1);
blas::copyandtranspose<Precision>(u, 0, m-1, 0, minmn-1, t2, 0, minmn-1, 0, m-1);
result = bdsvd::rmatrixbdsvd<Precision>(w, e, minmn, isupper, false, u, 0, t2, m, vt, ncvt);
blas::copyandtranspose<Precision>(t2, 0, minmn-1, 0, m-1, u, 0, m-1, 0, minmn-1);
}
return result;
}
/*************************************************************************
Obsolete 1-based subroutine.
See RMatrixSVD for 0-based replacement.
*************************************************************************/
template<unsigned int Precision>
bool svddecomposition(ap::template_2d_array< amp::ampf<Precision> > a,
int m,
int n,
int uneeded,
int vtneeded,
int additionalmemory,
ap::template_1d_array< amp::ampf<Precision> >& w,
ap::template_2d_array< amp::ampf<Precision> >& u,
ap::template_2d_array< amp::ampf<Precision> >& vt)
{
bool result;
ap::template_1d_array< amp::ampf<Precision> > tauq;
ap::template_1d_array< amp::ampf<Precision> > taup;
ap::template_1d_array< amp::ampf<Precision> > tau;
ap::template_1d_array< amp::ampf<Precision> > e;
ap::template_1d_array< amp::ampf<Precision> > work;
ap::template_2d_array< amp::ampf<Precision> > t2;
bool isupper;
int minmn;
int ncu;
int nrvt;
int nru;
int ncvt;
int i;
int j;
int im1;
amp::ampf<Precision> sm;
result = true;
if( m==0 || n==0 )
{
return result;
}
ap::ap_error::make_assertion(uneeded>=0 && uneeded<=2);
ap::ap_error::make_assertion(vtneeded>=0 && vtneeded<=2);
ap::ap_error::make_assertion(additionalmemory>=0 && additionalmemory<=2);
//
// initialize
//
minmn = ap::minint(m, n);
w.setbounds(1, minmn);
ncu = 0;
nru = 0;
if( uneeded==1 )
{
nru = m;
ncu = minmn;
u.setbounds(1, nru, 1, ncu);
}
if( uneeded==2 )
{
nru = m;
ncu = m;
u.setbounds(1, nru, 1, ncu);
}
nrvt = 0;
ncvt = 0;
if( vtneeded==1 )
{
nrvt = minmn;
ncvt = n;
vt.setbounds(1, nrvt, 1, ncvt);
}
if( vtneeded==2 )
{
nrvt = n;
ncvt = n;
vt.setbounds(1, nrvt, 1, ncvt);
}
//
// M much larger than N
// Use bidiagonal reduction with QR-decomposition
//
if( m>amp::ampf<Precision>("1.6")*n )
{
if( uneeded==0 )
{
//
// No left singular vectors to be computed
//
qr::qrdecomposition<Precision>(a, m, n, tau);
for(i=2; i<=n; i++)
{
for(j=1; j<=i-1; j++)
{
a(i,j) = 0;
}
}
bidiagonal::tobidiagonal<Precision>(a, n, n, tauq, taup);
bidiagonal::unpackptfrombidiagonal<Precision>(a, n, n, taup, nrvt, vt);
bidiagonal::unpackdiagonalsfrombidiagonal<Precision>(a, n, n, isupper, w, e);
result = bdsvd::bidiagonalsvddecomposition<Precision>(w, e, n, isupper, false, u, 0, a, 0, vt, ncvt);
return result;
}
else
{
//
// Left singular vectors (may be full matrix U) to be computed
//
qr::qrdecomposition<Precision>(a, m, n, tau);
qr::unpackqfromqr<Precision>(a, m, n, tau, ncu, u);
for(i=2; i<=n; i++)
{
for(j=1; j<=i-1; j++)
{
a(i,j) = 0;
}
}
bidiagonal::tobidiagonal<Precision>(a, n, n, tauq, taup);
bidiagonal::unpackptfrombidiagonal<Precision>(a, n, n, taup, nrvt, vt);
bidiagonal::unpackdiagonalsfrombidiagonal<Precision>(a, n, n, isupper, w, e);
if( additionalmemory<1 )
{
//
// No additional memory can be used
//
bidiagonal::multiplybyqfrombidiagonal<Precision>(a, n, n, tauq, u, m, n, true, false);
result = bdsvd::bidiagonalsvddecomposition<Precision>(w, e, n, isupper, false, u, m, a, 0, vt, ncvt);
}
else
{
//
// Large U. Transforming intermediate matrix T2
//
work.setbounds(1, ap::maxint(m, n));
bidiagonal::unpackqfrombidiagonal<Precision>(a, n, n, tauq, n, t2);
blas::copymatrix<Precision>(u, 1, m, 1, n, a, 1, m, 1, n);
blas::inplacetranspose<Precision>(t2, 1, n, 1, n, work);
result = bdsvd::bidiagonalsvddecomposition<Precision>(w, e, n, isupper, false, u, 0, t2, n, vt, ncvt);
blas::matrixmatrixmultiply<Precision>(a, 1, m, 1, n, false, t2, 1, n, 1, n, true, amp::ampf<Precision>("1.0"), u, 1, m, 1, n, amp::ampf<Precision>("0.0"), work);
}
return result;
}
}
//
// N much larger than M
// Use bidiagonal reduction with LQ-decomposition
//
if( n>amp::ampf<Precision>("1.6")*m )
{
if( vtneeded==0 )
{
//
// No right singular vectors to be computed
//
lq::lqdecomposition<Precision>(a, m, n, tau);
for(i=1; i<=m-1; i++)
{
for(j=i+1; j<=m; j++)
{
a(i,j) = 0;
}
}
bidiagonal::tobidiagonal<Precision>(a, m, m, tauq, taup);
bidiagonal::unpackqfrombidiagonal<Precision>(a, m, m, tauq, ncu, u);
bidiagonal::unpackdiagonalsfrombidiagonal<Precision>(a, m, m, isupper, w, e);
work.setbounds(1, m);
blas::inplacetranspose<Precision>(u, 1, nru, 1, ncu, work);
result = bdsvd::bidiagonalsvddecomposition<Precision>(w, e, m, isupper, false, a, 0, u, nru, vt, 0);
blas::inplacetranspose<Precision>(u, 1, nru, 1, ncu, work);
return result;
}
else
{
//
// Right singular vectors (may be full matrix VT) to be computed
//
lq::lqdecomposition<Precision>(a, m, n, tau);
lq::unpackqfromlq<Precision>(a, m, n, tau, nrvt, vt);
for(i=1; i<=m-1; i++)
{
for(j=i+1; j<=m; j++)
{
a(i,j) = 0;
}
}
bidiagonal::tobidiagonal<Precision>(a, m, m, tauq, taup);
bidiagonal::unpackqfrombidiagonal<Precision>(a, m, m, tauq, ncu, u);
bidiagonal::unpackdiagonalsfrombidiagonal<Precision>(a, m, m, isupper, w, e);
work.setbounds(1, ap::maxint(m, n));
blas::inplacetranspose<Precision>(u, 1, nru, 1, ncu, work);
if( additionalmemory<1 )
{
//
// No additional memory available
//
bidiagonal::multiplybypfrombidiagonal<Precision>(a, m, m, taup, vt, m, n, false, true);
result = bdsvd::bidiagonalsvddecomposition<Precision>(w, e, m, isupper, false, a, 0, u, nru, vt, n);
}
else
{
//
// Large VT. Transforming intermediate matrix T2
//
bidiagonal::unpackptfrombidiagonal<Precision>(a, m, m, taup, m, t2);
result = bdsvd::bidiagonalsvddecomposition<Precision>(w, e, m, isupper, false, a, 0, u, nru, t2, m);
blas::copymatrix<Precision>(vt, 1, m, 1, n, a, 1, m, 1, n);
blas::matrixmatrixmultiply<Precision>(t2, 1, m, 1, m, false, a, 1, m, 1, n, false, amp::ampf<Precision>("1.0"), vt, 1, m, 1, n, amp::ampf<Precision>("0.0"), work);
}
blas::inplacetranspose<Precision>(u, 1, nru, 1, ncu, work);
return result;
}
}
//
// M<=N
// We can use inplace transposition of U to get rid of columnwise operations
//
if( m<=n )
{
bidiagonal::tobidiagonal<Precision>(a, m, n, tauq, taup);
bidiagonal::unpackqfrombidiagonal<Precision>(a, m, n, tauq, ncu, u);
bidiagonal::unpackptfrombidiagonal<Precision>(a, m, n, taup, nrvt, vt);
bidiagonal::unpackdiagonalsfrombidiagonal<Precision>(a, m, n, isupper, w, e);
work.setbounds(1, m);
blas::inplacetranspose<Precision>(u, 1, nru, 1, ncu, work);
result = bdsvd::bidiagonalsvddecomposition<Precision>(w, e, minmn, isupper, false, a, 0, u, nru, vt, ncvt);
blas::inplacetranspose<Precision>(u, 1, nru, 1, ncu, work);
return result;
}
//
// Simple bidiagonal reduction
//
bidiagonal::tobidiagonal<Precision>(a, m, n, tauq, taup);
bidiagonal::unpackqfrombidiagonal<Precision>(a, m, n, tauq, ncu, u);
bidiagonal::unpackptfrombidiagonal<Precision>(a, m, n, taup, nrvt, vt);
bidiagonal::unpackdiagonalsfrombidiagonal<Precision>(a, m, n, isupper, w, e);
if( additionalmemory<2 || uneeded==0 )
{
//
// We cant use additional memory or there is no need in such operations
//
result = bdsvd::bidiagonalsvddecomposition<Precision>(w, e, minmn, isupper, false, u, nru, a, 0, vt, ncvt);
}
else
{
//
// We can use additional memory
//
t2.setbounds(1, minmn, 1, m);
blas::copyandtranspose<Precision>(u, 1, m, 1, minmn, t2, 1, minmn, 1, m);
result = bdsvd::bidiagonalsvddecomposition<Precision>(w, e, minmn, isupper, false, u, 0, t2, m, vt, ncvt);
blas::copyandtranspose<Precision>(t2, 1, minmn, 1, m, u, 1, m, 1, minmn);
}
return result;
}
} // namespace
#endif
amp.h
ap.h
bdsvd.h
bidiagonal.h
blas.h
m
int m
Definition cfEzgcd.cc:128
i
int i
Definition cfEzgcd.cc:132
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::setbounds
void setbounds(int iLow, int iHigh)
Definition ap.h:735
ap::template_2d_array
Definition ap.h:807
ap::template_2d_array::setbounds
void setbounds(int iLow1, int iHigh1, int iLow2, int iHigh2)
Definition ap.h:890
result
return result
Definition facAbsBiFact.cc:76
w
const CanonicalForm & w
Definition facAbsFact.cc:51
j
int j
Definition facHensel.cc:110
lq.h
ap::maxint
int maxint(int m1, int m2)
Definition ap.cpp:162
ap::minint
int minint(int m1, int m2)
Definition ap.cpp:167
bdsvd::bidiagonalsvddecomposition
bool bidiagonalsvddecomposition(ap::template_1d_array< amp::ampf< Precision > > &d, ap::template_1d_array< amp::ampf< Precision > > e, int n, bool isupper, bool isfractionalaccuracyrequired, ap::template_2d_array< amp::ampf< Precision > > &u, int nru, ap::template_2d_array< amp::ampf< Precision > > &c, int ncc, ap::template_2d_array< amp::ampf< Precision > > &vt, int ncvt)
Definition bdsvd.h:229
bdsvd::rmatrixbdsvd
bool rmatrixbdsvd(ap::template_1d_array< amp::ampf< Precision > > &d, ap::template_1d_array< amp::ampf< Precision > > e, int n, bool isupper, bool isfractionalaccuracyrequired, ap::template_2d_array< amp::ampf< Precision > > &u, int nru, ap::template_2d_array< amp::ampf< Precision > > &c, int ncc, ap::template_2d_array< amp::ampf< Precision > > &vt, int ncvt)
Definition bdsvd.h:186
bidiagonal::unpackptfrombidiagonal
void unpackptfrombidiagonal(const ap::template_2d_array< amp::ampf< Precision > > &qp, int m, int n, const ap::template_1d_array< amp::ampf< Precision > > &taup, int ptrows, ap::template_2d_array< amp::ampf< Precision > > &pt)
Definition bidiagonal.h:1196
bidiagonal::multiplybyqfrombidiagonal
void multiplybyqfrombidiagonal(const ap::template_2d_array< amp::ampf< Precision > > &qp, int m, int n, const ap::template_1d_array< amp::ampf< Precision > > &tauq, ap::template_2d_array< amp::ampf< Precision > > &z, int zrows, int zcolumns, bool fromtheright, bool dotranspose)
Definition bidiagonal.h:1055
bidiagonal::rmatrixbdunpackpt
void rmatrixbdunpackpt(const ap::template_2d_array< amp::ampf< Precision > > &qp, int m, int n, const ap::template_1d_array< amp::ampf< Precision > > &taup, int ptrows, ap::template_2d_array< amp::ampf< Precision > > &pt)
Definition bidiagonal.h:575
bidiagonal::unpackqfrombidiagonal
void unpackqfrombidiagonal(const ap::template_2d_array< amp::ampf< Precision > > &qp, int m, int n, const ap::template_1d_array< amp::ampf< Precision > > &tauq, int qcolumns, ap::template_2d_array< amp::ampf< Precision > > &q)
Definition bidiagonal.h:981
bidiagonal::rmatrixbdunpackq
void rmatrixbdunpackq(const ap::template_2d_array< amp::ampf< Precision > > &qp, int m, int n, const ap::template_1d_array< amp::ampf< Precision > > &tauq, int qcolumns, ap::template_2d_array< amp::ampf< Precision > > &q)
Definition bidiagonal.h:348
bidiagonal::rmatrixbdmultiplybyq
void rmatrixbdmultiplybyq(const ap::template_2d_array< amp::ampf< Precision > > &qp, int m, int n, const ap::template_1d_array< amp::ampf< Precision > > &tauq, ap::template_2d_array< amp::ampf< Precision > > &z, int zrows, int zcolumns, bool fromtheright, bool dotranspose)
Definition bidiagonal.h:422
bidiagonal::unpackdiagonalsfrombidiagonal
void unpackdiagonalsfrombidiagonal(const ap::template_2d_array< amp::ampf< Precision > > &b, int m, int n, bool &isupper, ap::template_1d_array< amp::ampf< Precision > > &d, ap::template_1d_array< amp::ampf< Precision > > &e)
Definition bidiagonal.h:1413
bidiagonal::rmatrixbdunpackdiagonals
void rmatrixbdunpackdiagonals(const ap::template_2d_array< amp::ampf< Precision > > &b, int m, int n, bool &isupper, ap::template_1d_array< amp::ampf< Precision > > &d, ap::template_1d_array< amp::ampf< Precision > > &e)
Definition bidiagonal.h:805
bidiagonal::tobidiagonal
void tobidiagonal(ap::template_2d_array< amp::ampf< Precision > > &a, int m, int n, ap::template_1d_array< amp::ampf< Precision > > &tauq, ap::template_1d_array< amp::ampf< Precision > > &taup)
Definition bidiagonal.h:850
bidiagonal::rmatrixbd
void rmatrixbd(ap::template_2d_array< amp::ampf< Precision > > &a, int m, int n, ap::template_1d_array< amp::ampf< Precision > > &tauq, ap::template_1d_array< amp::ampf< Precision > > &taup)
Definition bidiagonal.h:194
bidiagonal::rmatrixbdmultiplybyp
void rmatrixbdmultiplybyp(const ap::template_2d_array< amp::ampf< Precision > > &qp, int m, int n, const ap::template_1d_array< amp::ampf< Precision > > &taup, ap::template_2d_array< amp::ampf< Precision > > &z, int zrows, int zcolumns, bool fromtheright, bool dotranspose)
Definition bidiagonal.h:649
bidiagonal::multiplybypfrombidiagonal
void multiplybypfrombidiagonal(const ap::template_2d_array< amp::ampf< Precision > > &qp, int m, int n, const ap::template_1d_array< amp::ampf< Precision > > &taup, ap::template_2d_array< amp::ampf< Precision > > &z, int zrows, int zcolumns, bool fromtheright, bool dotranspose)
Definition bidiagonal.h:1270
blas::matrixmatrixmultiply
void matrixmatrixmultiply(const ap::template_2d_array< amp::ampf< Precision > > &a, int ai1, int ai2, int aj1, int aj2, bool transa, const ap::template_2d_array< amp::ampf< Precision > > &b, int bi1, int bi2, int bj1, int bj2, bool transb, amp::ampf< Precision > alpha, ap::template_2d_array< amp::ampf< Precision > > &c, int ci1, int ci2, int cj1, int cj2, amp::ampf< Precision > beta, ap::template_1d_array< amp::ampf< Precision > > &work)
Definition blas.h:505
blas::copyandtranspose
void copyandtranspose(const ap::template_2d_array< amp::ampf< Precision > > &a, int is1, int is2, int js1, int js2, ap::template_2d_array< amp::ampf< Precision > > &b, int id1, int id2, int jd1, int jd2)
Definition blas.h:351
blas::inplacetranspose
void inplacetranspose(ap::template_2d_array< amp::ampf< Precision > > &a, int i1, int i2, int j1, int j2, ap::template_1d_array< amp::ampf< Precision > > &work)
Definition blas.h:318
blas::copymatrix
void copymatrix(const ap::template_2d_array< amp::ampf< Precision > > &a, int is1, int is2, int js1, int js2, ap::template_2d_array< amp::ampf< Precision > > &b, int id1, int id2, int jd1, int jd2)
Definition blas.h:288
lq::rmatrixlq
void rmatrixlq(ap::template_2d_array< amp::ampf< Precision > > &a, int m, int n, ap::template_1d_array< amp::ampf< Precision > > &tau)
Definition lq.h:113
lq::lqdecomposition
void lqdecomposition(ap::template_2d_array< amp::ampf< Precision > > &a, int m, int n, ap::template_1d_array< amp::ampf< Precision > > &tau)
Definition lq.h:288
lq::rmatrixlqunpackq
void rmatrixlqunpackq(const ap::template_2d_array< amp::ampf< Precision > > &a, int m, int n, const ap::template_1d_array< amp::ampf< Precision > > &tau, int qrows, ap::template_2d_array< amp::ampf< Precision > > &q)
Definition lq.h:177
lq::unpackqfromlq
void unpackqfromlq(const ap::template_2d_array< amp::ampf< Precision > > &a, int m, int n, const ap::template_1d_array< amp::ampf< Precision > > &tau, int qrows, ap::template_2d_array< amp::ampf< Precision > > &q)
Definition lq.h:342
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
svd
Definition svd.h:64
svd::rmatrixsvd
bool rmatrixsvd(ap::template_2d_array< amp::ampf< Precision > > a, int m, int n, int uneeded, int vtneeded, int additionalmemory, ap::template_1d_array< amp::ampf< Precision > > &w, ap::template_2d_array< amp::ampf< Precision > > &u, ap::template_2d_array< amp::ampf< Precision > > &vt)
Definition svd.h:140
svd::svddecomposition
bool svddecomposition(ap::template_2d_array< amp::ampf< Precision > > a, int m, int n, int uneeded, int vtneeded, int additionalmemory, ap::template_1d_array< amp::ampf< Precision > > &w, ap::template_2d_array< amp::ampf< Precision > > &u, ap::template_2d_array< amp::ampf< Precision > > &vt)
Definition svd.h:408
qr.h
reflections.h
rotations.h