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/*
* Copyright (c) 2011, 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 DPOTF2( UPLO, N, A, LDA, INFO )
SUBROUTINE ZPOTF2( UPLO, N, A, LDA, 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_PO_POTF2_TCC
#define FLENS_LAPACK_PO_POTF2_TCC 1
#include <cxxstd/algorithm.h>
#include <flens/blas/blas.h>
#include <flens/lapack/lapack.h>
namespace flens { namespace lapack {
//== generic lapack implementation =============================================
namespace generic {
//-- potf2 [real variant] ------------------------------------------------------
template <typename MA>
typename SyMatrix<MA>::IndexType
potf2_impl(SyMatrix<MA> &A)
{
using std::isnan;
using std::sqrt;
typedef typename SyMatrix<MA>::ElementType T;
typedef typename SyMatrix<MA>::IndexType IndexType;
const Underscore<IndexType> _;
const IndexType n = A.dim();
const bool upper = (A.upLo()==Upper);
const T Zero(0), One(1);
IndexType info = 0;
//
// Quick return if possible
//
if (n==0) {
return info;
}
if (upper) {
//
// Compute the Cholesky factorization A = U**T *U.
//
for (IndexType j=1; j<=n; ++j) {
//
// Partition matrix
//
const auto range1 = _(1,j-1);
const auto range3 = _(j+1,n);
const auto a12 = A(range1,j);
const auto A13 = A(range1,range3);
auto a23 = A(j,range3);
//
// Compute U(J,J) and test for non-positive-definiteness.
//
T a22 = A(j,j) - a12*a12;
if (a22<=Zero || isnan(a22)) {
A(j,j) = a22;
info = j;
break;
}
a22 = sqrt(a22);
A(j,j) = a22;
//
// Compute elements J+1:N of row J.
//
if (j<n) {
blas::mv(Trans, -One, A13, a12, One, a23);
a23 *= One / a22;
}
}
} else {
//
// Compute the Cholesky factorization A = L*L**T.
//
for (IndexType j=1; j<=n; ++j) {
//
// Partition matrix
//
const auto range1 = _(1,j-1);
const auto range3 = _(j+1,n);
const auto a21 = A(j,range1);
const auto A31 = A(range3,range1);
auto a32 = A(range3,j);
//
// Compute L(J,J) and test for non-positive-definiteness.
//
T a22 = A(j,j) - a21*a21;
if (a22<=Zero || isnan(a22)) {
A(j,j) = a22;
info = j;
break;
}
a22 = sqrt(a22);
A(j,j) = a22;
//
// Compute elements J+1:N of column J.
//
if (j<n) {
blas::mv(NoTrans, -One, A31, a21, One, a32);
a32 *= One / a22;
}
}
}
return info;
}
//-- potf2 [complex variant] ---------------------------------------------------
template <typename MA>
typename HeMatrix<MA>::IndexType
potf2_impl(HeMatrix<MA> &A)
{
using std::imag;
using std::real;
using std::isnan;
using std::sqrt;
typedef typename HeMatrix<MA>::ElementType T;
typedef typename ComplexTrait<T>::PrimitiveType PT;
typedef typename HeMatrix<MA>::IndexType IndexType;
const Underscore<IndexType> _;
const IndexType n = A.dim();
const bool upper = (A.upLo()==Upper);
const PT Zero(0), One(1);
const T COne(1);
IndexType info = 0;
//
// Quick return if possible
//
if (n==0) {
return info;
}
if (upper) {
//
// Compute the Cholesky factorization A = U**T *U.
//
for (IndexType j=1; j<=n; ++j) {
//
// Partition matrix
//
const auto range1 = _(1,j-1);
const auto range3 = _(j+1,n);
auto a12 = A(range1,j);
const auto A13 = A(range1,range3);
auto a23 = A(j,range3);
//
// Compute U(J,J) and test for non-positive-definiteness.
//
PT a22 = real(A(j,j) - blas::dotc(a12,a12));
if (a22<=Zero || isnan(a22)) {
A(j,j) = a22;
info = j;
break;
}
a22 = sqrt(a22);
A(j,j) = a22;
//
// Compute elements J+1:N of row J.
//
if (j<n) {
imag(a12) *= -One;
blas::mv(Trans, -COne, A13, a12, COne, a23);
imag(a12) *= -One;
a23 *= One / a22;
}
}
} else {
//
// Compute the Cholesky factorization A = L*L**T.
//
for (IndexType j=1; j<=n; ++j) {
//
// Partition matrix
//
const auto range1 = _(1,j-1);
const auto range3 = _(j+1,n);
auto a21 = A(j,range1);
const auto A31 = A(range3,range1);
auto a32 = A(range3,j);
//
// Compute L(J,J) and test for non-positive-definiteness.
//
PT a22 = real(A(j,j) - blas::dotc(a21,a21));
if (a22<=Zero || isnan(a22)) {
A(j,j) = a22;
info = j;
break;
}
a22 = sqrt(a22);
A(j,j) = a22;
//
// Compute elements J+1:N of column J.
//
if (j<n) {
imag(a21) *= -One;
blas::mv(NoTrans, -COne, A31, a21, COne, a32);
imag(a21) *= -One;
a32 *= One / a22;
}
}
}
return info;
}
} // namespace generic
//== interface for native lapack ===============================================
#ifdef USE_CXXLAPACK
namespace external {
template <typename MA>
typename SyMatrix<MA>::IndexType
potf2_impl(SyMatrix<MA> &A)
{
typedef typename SyMatrix<MA>::IndexType IndexType;
IndexType info = cxxlapack::potf2<IndexType>(getF77Char(A.upLo()),
A.dim(),
A.data(),
A.leadingDimension());
ASSERT(info>=0);
return info;
}
template <typename MA>
typename HeMatrix<MA>::IndexType
potf2_impl(HeMatrix<MA> &A)
{
typedef typename HeMatrix<MA>::IndexType IndexType;
IndexType info = cxxlapack::potf2<IndexType>(getF77Char(A.upLo()),
A.dim(),
A.data(),
A.leadingDimension());
ASSERT(info>=0);
return info;
}
} // namespace external
#endif // USE_CXXLAPACK
//== public interface ==========================================================
template <typename MA>
typename RestrictTo<IsRealSyMatrix<MA>::value
|| IsHeMatrix<MA>::value,
typename RemoveRef<MA>::Type::IndexType>::Type
potf2(MA &&A)
{
//
// Remove references from rvalue types
//
typedef typename RemoveRef<MA>::Type MatrixA;
typedef typename MatrixA::IndexType IndexType;
//
// Test the input parameters
//
ASSERT(A.firstRow()==1);
ASSERT(A.firstCol()==1);
# ifdef CHECK_CXXLAPACK
//
// Make copies of output arguments
//
typename MatrixA::GeneralNoView A_org = A.general();
# endif
//
// Call implementation
//
IndexType info = LAPACK_SELECT::potf2_impl(A);
# ifdef CHECK_CXXLAPACK
//
// Make copies of generic results
//
typename MatrixA::GeneralNoView A_generic = A.general();
//
// Restore output arguments
//
A.general() = A_org;
//
// Compare results
//
IndexType info_ = external::potf2_impl(A);
bool failed = false;
if (! isIdentical(A_generic, A.general(), "A_generic", "A_")) {
std::cerr << "CXXLAPACK: A_generic = " << A_generic << std::endl;
std::cerr << "F77LAPACK: A = " << A.general() << std::endl;
failed = true;
}
if (! isIdentical(info, info_, " info", "info_")) {
std::cerr << "CXXLAPACK: info = " << info << std::endl;
std::cerr << "F77LAPACK: info_ = " << info_ << std::endl;
failed = true;
}
if (failed) {
ASSERT(0);
}
# endif
return info;
}
} } // namespace lapack, flens
#endif // FLENS_LAPACK_PO_POTF2_TCC
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