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/*
* Copyright (c) 2014, Michael Lehn
*
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1) Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2) Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
* 3) Neither the name of the FLENS development group 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.
*/
/* Based on
*
SUBROUTINE ZHETRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO )
*
* -- LAPACK routine (version 3.3.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* -- April 2011 --
*/
#ifndef FLENS_LAPACK_HE_TRD_TCC
#define FLENS_LAPACK_HE_TRD_TCC 1
#include <flens/blas/blas.h>
#include <flens/lapack/lapack.h>
namespace flens { namespace lapack {
//== generic lapack implementation =============================================
namespace generic {
template <typename MA>
typename MA::IndexType
trd_wsq_impl(const HeMatrix<MA> &A)
{
typedef typename MA::IndexType IndexType;
typedef typename MA::ElementType T;
const IndexType n = A.dim();
const char upLo[1] = { cxxf77blas::getF77BlasChar(A.upLo()) };
//
// Determine the block size.
//
const IndexType nb = ilaenv<T>(1, "HETRD", upLo, n);
return n*nb;
}
template <typename MA, typename VD, typename VE, typename VTAU, typename VWORK>
void
trd_impl(HeMatrix<MA> &A,
DenseVector<VD> &d,
DenseVector<VE> &e,
DenseVector<VTAU> &tau,
DenseVector<VWORK> &work)
{
using std::real;
typedef typename MA::IndexType IndexType;
typedef typename MA::ElementType T;
typedef typename ComplexTrait<T>::PrimitiveType PT;
const PT One(1);
const T COne(1);
const Underscore<IndexType> _;
const char upLo[1] = { cxxf77blas::getF77BlasChar(A.upLo()) };
const IndexType n = A.numRows();
//
// Determine the block size.
//
IndexType nb = ilaenv<T>(1, "HETRD", upLo, n);
const IndexType lWorkOpt = trd_wsq(A);
if (work.length()==0) {
work.resize(lWorkOpt);
}
const IndexType lWork = work.length();
IndexType ldWork = -1;
//
// Quick return if possible
//
if (n==0) {
work(1) = 1;
return;
}
IndexType nx = n;
IndexType iws = 1;
if (nb>1 && nb<n) {
//
// Determine when to cross over from blocked to unblocked code
// (last block is always handled by unblocked code).
//
nx = max(nb, ilaenv<T>(3, "HETRD", upLo, n));
if (nx<n) {
//
// Determine if workspace is large enough for blocked code.
//
ldWork = n;
iws = ldWork*nb;
if (lWork < iws) {
//
// Not enough workspace to use optimal NB: determine the
// minimum value of NB, and reduce NB or force use of
// unblocked code by setting NX = N.
//
nb = max(lWork/ldWork, IndexType(1));
IndexType nbMin = ilaenv<T>(2, "HETRD", upLo, n);
if (nb<nbMin) {
nx = n;
}
}
} else {
nx = n;
}
} else {
nb = 1;
}
if (A.upLo()==Upper) {
//
// Reduce the upper triangle of A.
// Columns 1:kk are handled by the unblocked method.
//
IndexType kk = n - ((n-nx+nb-1)/nb)*nb;
for (IndexType i=n-nb+1; i>=kk+1; i-=nb) {
//
// Reduce columns i:i+nb-1 to tridiagonal form and form the
// matrix W which is needed to update the unreduced part of
// the matrix
//
auto A_ = A(_(1,i+nb-1),_(1,i+nb-1)).upper().hermitian();
auto e_ = e(_(1,i+nb-2));
auto tau_ = tau(_(1,i+nb-2));
ASSERT(ldWork!=-1);
typename GeMatrix<MA>::View Work(i+nb-1, nb, work, ldWork);
latrd(A_, e_, tau_, Work);
//
// Update the unreduced submatrix A(1:i-1,1:i-1), using an
// update of the form: A := A - V*W**H - W*V**H
//
auto __A = A(_(1,i-1),_(1,i-1)).upper().hermitian();
auto __V = A(_(1,i-1),_(i,i+nb-1));
auto __W = Work(_(1,i-1),_);
blas::r2k(NoTrans, -COne, __V, __W, One, __A);
//
// Copy superdiagonal elements back into A, and diagonal
// elements into D
//
for (IndexType j=i; j<=i+nb-1; ++j) {
A(j-1,j) = e(j-1);
d(j) = real(A(j,j));
}
}
//
// Use unblocked code to reduce the last or only block
//
auto A_ = A(_(1,kk),_(1,kk)).upper().hermitian();
auto d_ = d(_(1,kk));
auto e_ = e(_(1,kk-1));
auto tau_ = tau(_(1,kk-1));
td2(A_, d_, e_, tau_);
} else {
//
// Reduce the lower triangle of A
//
IndexType i;
for (i=1; i<=n-nx; i+=nb) {
//
// Reduce columns i:i+nb-1 to tridiagonal form and form the
// matrix W which is needed to update the unreduced part of
// the matrix
//
auto A_ = A(_(i,n),_(i,n)).lower().hermitian();
auto e_ = e(_(i,n-1));
auto tau_ = tau(_(i,n-1));
ASSERT(ldWork!=-1);
typename GeMatrix<MA>::View Work(n-i+1, nb, work, ldWork);
latrd(A_, e_, tau_, Work);
//
// Update the unreduced submatrix A(i+nb:n,i+nb:n), using
// an update of the form: A := A - V*W**H - W*V**H
//
auto __A = A(_(i+nb,n),_(i+nb,n)).lower().hermitian();
auto __V = A(_(i+nb,n),_(i,i+nb-1));
typename GeMatrix<MA>::View __Work(n-i-nb+1, nb,
work(_(nb+1, lWork)),
ldWork);
blas::r2k(NoTrans, -COne, __V, __Work, One, __A);
//
// Copy subdiagonal elements back into A, and diagonal
// elements into D
//
for (IndexType j=i; j<=i+nb-1; ++j) {
A(j+1, j) = e(j);
d(j) = real(A(j,j));
}
}
//
// Use unblocked code to reduce the last or only block
//
auto A_ = A(_(i,n),_(i,n)).lower().hermitian();
auto d_ = d(_(i,n));
auto e_ = e(_(i,n-1));
auto tau_ = tau(_(i,n-1));
td2(A_, d_, e_, tau_);
}
work(1) = lWorkOpt;
}
} // namespace generic
//== interface for native lapack ===============================================
#ifdef USE_CXXLAPACK
namespace external {
//-- (he)trf [complex variant] -------------------------------------------------
template <typename MA>
typename MA::IndexType
trd_wsq_impl(const HeMatrix<MA> &A)
{
using std::real;
typedef typename HeMatrix<MA>::IndexType IndexType;
typedef typename HeMatrix<MA>::ElementType T;
typedef typename ComplexTrait<T>::PrimitiveType PT;
T DUMMY;
PT RDUMMY;
T WORK;
IndexType LWORK = -1;
cxxlapack::hetrd<IndexType>(getF77Char(A.upLo()),
A.dim(),
&DUMMY, A.leadingDimension(),
&RDUMMY,
&RDUMMY,
&DUMMY,
&WORK,
LWORK);
return IndexType(real(WORK));
}
template <typename MA, typename VD, typename VE, typename VTAU, typename VWORK>
void
trd_impl(HeMatrix<MA> &A,
DenseVector<VD> &d,
DenseVector<VE> &e,
DenseVector<VTAU> &tau,
DenseVector<VWORK> &work)
{
typedef typename HeMatrix<MA>::IndexType IndexType;
if (work.length()==0) {
work.resize(trd_wsq_impl(A));
}
cxxlapack::hetrd<IndexType>(getF77Char(A.upLo()),
A.dim(),
A.data(), A.leadingDimension(),
d.data(),
e.data(),
tau.data(),
work.data(),
work.length());
}
} // namespace external
#endif // USE_CXXLAPACK
//== public interface ==========================================================
//-- (he)trd -------------------------------------------------------------------
template <typename MA, typename VD, typename VE, typename VTAU, typename VWORK>
typename RestrictTo<IsHeMatrix<MA>::value
&& IsRealDenseVector<VD>::value
&& IsRealDenseVector<VE>::value
&& IsComplexDenseVector<VTAU>::value
&& IsComplexDenseVector<VWORK>::value,
void>::Type
trd(MA &&A,
VD &&d,
VE &&e,
VTAU &&tau,
VWORK &&work)
{
//
// Remove references from rvalue types
//
# ifdef CHECK_CXXLAPACK
typedef typename RemoveRef<MA>::Type MatrixA;
typedef typename RemoveRef<VD>::Type VectorD;
typedef typename RemoveRef<VE>::Type VectorE;
typedef typename RemoveRef<VTAU>::Type VectorTau;
typedef typename RemoveRef<VWORK>::Type VectorWork;
# endif
# ifndef NDEBUG
//
// Test the input parameters
//
ASSERT(A.firstRow()==1);
ASSERT(A.firstCol()==1);
ASSERT(d.firstIndex()==1);
ASSERT(d.length()==A.numRows());
ASSERT(e.firstIndex()==1);
ASSERT(e.length()==A.numRows()-1);
ASSERT(tau.firstIndex()==1);
ASSERT(tau.length()==A.numRows()-1);
ASSERT(work.firstIndex()==1);
ASSERT(work.length()==0 || work.length()>=1);
# endif
//
// Resize output arguments if they are empty and needed
//
if (work.length()==0) {
work.resize(trd_wsq(A));
}
//
// Make copies of output arguments
//
# ifdef CHECK_CXXLAPACK
typename MatrixA::NoView A_org = A;
typename VectorD::NoView d_org = d;
typename VectorE::NoView e_org = e;
typename VectorTau::NoView tau_org = tau;
typename VectorWork::NoView work_org = work;
# endif
//
// Call implementation
//
LAPACK_SELECT::trd_impl(A, d, e, tau, work);
# ifdef CHECK_CXXLAPACK
//
// Compare results
//
typename MatrixA::NoView A_generic = A;
typename VectorD::NoView d_generic = d;
typename VectorE::NoView e_generic = e;
typename VectorTau::NoView tau_generic = tau;
typename VectorWork::NoView work_generic = work;
A = A_org;
d = d_org;
e = e_org;
tau = tau_org;
work = work_org;
external::trd_impl(A, d, e, tau, work);
bool failed = false;
if (! isIdentical(A_generic, A, "A_generic", "A")) {
std::cerr << "CXXLAPACK: A_generic = " << A_generic << std::endl;
std::cerr << "F77LAPACK: A = " << A << std::endl;
failed = true;
}
if (! isIdentical(d_generic, d, "d_generic", "d")) {
std::cerr << "CXXLAPACK: d_generic = " << d_generic << std::endl;
std::cerr << "F77LAPACK: d = " << d << std::endl;
failed = true;
}
if (! isIdentical(e_generic, e, "e_generic", "e")) {
std::cerr << "CXXLAPACK: e_generic = " << e_generic << std::endl;
std::cerr << "F77LAPACK: e = " << e << std::endl;
failed = true;
}
if (! isIdentical(tau_generic, tau, "tau_generic", "tau")) {
std::cerr << "CXXLAPACK: tau_generic = " << tau_generic << std::endl;
std::cerr << "F77LAPACK: tau = " << tau << std::endl;
failed = true;
}
if (! isIdentical(work_generic, work, "work_generic", "work")) {
std::cerr << "CXXLAPACK: work_generic = " << work_generic << std::endl;
std::cerr << "F77LAPACK: work = " << work << std::endl;
failed = true;
}
if (failed) {
ASSERT(0);
}
# endif
}
//-- (he)trd [workspace query] -------------------------------------------------
template <typename MA>
typename RestrictTo<IsHeMatrix<MA>::value,
typename MA::IndexType>::Type
trd_wsq(const MA &A)
{
# ifndef NDEBUG
//
// Test the input parameters
//
ASSERT(A.firstRow()==1);
ASSERT(A.firstCol()==1);
# endif
const auto ws = LAPACK_SELECT::trd_wsq_impl(A);
# ifdef CHECK_CXXLAPACK
//
// Compare results
//
const auto optWorkSize = external::trd_wsq_impl(A);
if (! isIdentical(optWorkSize, ws, "optWorkSize", "ws")) {
ASSERT(0);
}
# endif
return ws;
}
} } // namespace lapack, flens
#endif // FLENS_LAPACK_HE_TRD_TCC
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