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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
*
DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E )
*
* -- LAPACK auxiliary routine (version 3.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2006
*/
#ifndef FLENS_LAPACK_LA_LANST_TCC
#define FLENS_LAPACK_LA_LANST_TCC 1
#include <flens/blas/blas.h>
#include <flens/lapack/lapack.h>
namespace flens { namespace lapack {
//== generic lapack implementation =============================================
namespace generic {
template <typename VD, typename VE>
typename VD::ElementType
lanst_impl(Norm norm,
const DenseVector<VD> &d,
const DenseVector<VE> &e)
{
using std::abs;
using std::max;
using std::sqrt;
typedef typename VD::ElementType T;
typedef typename VD::IndexType IndexType;
const T Zero(0), One(1);
const Underscore<IndexType> _;
const IndexType n = d.length();
T normA = 0;
if (n==0) {
normA = Zero;
} else if (norm==MaximumNorm) {
//
// Find max(abs(A(i,j))).
//
normA = abs(d(n));
for (IndexType i=1; i<=n-1; ++i) {
normA = max(normA, abs(d(i)));
normA = max(normA, abs(e(i)));
}
} else if (norm==OneNorm || norm==InfinityNorm) {
//
// Find norm1(A).
//
if (n==1) {
normA = abs(d(1));
} else {
normA = max(abs(d(1)) +abs(e(1)),
abs(e(n-1))+abs(d(n)));
for (IndexType i=2; i<=n-1; ++i) {
normA = max(normA, abs(d(i))+abs(e(i))+abs(e(i-1)));
}
}
} else if (norm==FrobeniusNorm) {
//
// Find normF(A).
//
T scale = Zero;
T sum = One;
if (n>1) {
lassq(e(_(1,n-1)), scale, sum);
sum *= 2;
}
lassq(d, scale, sum);
normA = scale*sqrt(sum);
}
return normA;
}
} // namespace generic
//== interface for native lapack ===============================================
#ifdef USE_CXXLAPACK
namespace external {
template <typename VD, typename VE>
typename VD::ElementType
lanst_impl(Norm norm,
const DenseVector<VD> &d,
const DenseVector<VE> &e)
{
typedef typename VD::IndexType IndexType;
return cxxlapack::lanst<IndexType>(getF77Char(norm),
d.length(),
d.data(),
e.data());
}
} // namespace external
#endif
//== public interface ==========================================================
template <typename VD, typename VE>
typename RestrictTo<IsRealDenseVector<VD>::value
&& IsRealDenseVector<VE>::value,
typename VD::ElementType>::Type
lanst(Norm norm,
const VD &d,
const VE &e)
{
typedef typename VD::ElementType T;
//
// Test the input parameters
//
ASSERT(d.firstIndex()==1);
ASSERT(e.firstIndex()==1);
ASSERT(d.length()==e.length()+1 || d.length()==0);
//
// Call implementation
//
T result = LAPACK_SELECT::lanst_impl(norm, d, e);
# ifdef CHECK_CXXLAPACK
//
// Compare results
//
T result_ = external::lanst_impl(norm, d, e);
if (! isIdentical(result, result_, " result", "result_")) {
ASSERT(0);
}
# endif
return result;
}
} } // namespace lapack, flens
#endif // FLENS_LAPACK_LA_LANST_TCC
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