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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#include "main.h"
template<typename T> bool isFinite(const T& x)
{
return x==x && x>=NumTraits<T>::lowest() && x<=NumTraits<T>::highest();
}
template<typename MatrixType> void stable_norm(const MatrixType& m)
{
/* this test covers the following files:
StableNorm.h
*/
typedef typename MatrixType::Index Index;
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
// Check the basic machine-dependent constants.
{
int ibeta, it, iemin, iemax;
ibeta = std::numeric_limits<RealScalar>::radix; // base for floating-point numbers
it = std::numeric_limits<RealScalar>::digits; // number of base-beta digits in mantissa
iemin = std::numeric_limits<RealScalar>::min_exponent; // minimum exponent
iemax = std::numeric_limits<RealScalar>::max_exponent; // maximum exponent
VERIFY( (!(iemin > 1 - 2*it || 1+it>iemax || (it==2 && ibeta<5) || (it<=4 && ibeta <= 3 ) || it<2))
&& "the stable norm algorithm cannot be guaranteed on this computer");
}
Index rows = m.rows();
Index cols = m.cols();
Scalar big = ei_random<Scalar>() * (std::numeric_limits<RealScalar>::max() * RealScalar(1e-4));
Scalar small = static_cast<RealScalar>(1)/big;
MatrixType vzero = MatrixType::Zero(rows, cols),
vrand = MatrixType::Random(rows, cols),
vbig(rows, cols),
vsmall(rows,cols);
vbig.fill(big);
vsmall.fill(small);
VERIFY_IS_MUCH_SMALLER_THAN(vzero.norm(), static_cast<RealScalar>(1));
VERIFY_IS_APPROX(vrand.stableNorm(), vrand.norm());
VERIFY_IS_APPROX(vrand.blueNorm(), vrand.norm());
VERIFY_IS_APPROX(vrand.hypotNorm(), vrand.norm());
RealScalar size = static_cast<RealScalar>(m.size());
// test isFinite
VERIFY(!isFinite( std::numeric_limits<RealScalar>::infinity()));
VERIFY(!isFinite(ei_sqrt(-ei_abs(big))));
// test overflow
VERIFY(isFinite(ei_sqrt(size)*ei_abs(big)));
#ifdef EIGEN_VECTORIZE_SSE
// since x87 FPU uses 80bits of precision overflow is not detected
if(ei_packet_traits<Scalar>::size>1)
{
VERIFY_IS_NOT_APPROX(static_cast<Scalar>(vbig.norm()), ei_sqrt(size)*big); // here the default norm must fail
}
#endif
VERIFY_IS_APPROX(vbig.stableNorm(), ei_sqrt(size)*ei_abs(big));
VERIFY_IS_APPROX(vbig.blueNorm(), ei_sqrt(size)*ei_abs(big));
VERIFY_IS_APPROX(vbig.hypotNorm(), ei_sqrt(size)*ei_abs(big));
// test underflow
VERIFY(isFinite(ei_sqrt(size)*ei_abs(small)));
#ifdef EIGEN_VECTORIZE_SSE
// since x87 FPU uses 80bits of precision underflow is not detected
if(ei_packet_traits<Scalar>::size>1)
{
VERIFY_IS_NOT_APPROX(static_cast<Scalar>(vsmall.norm()), ei_sqrt(size)*small); // here the default norm must fail
}
#endif
VERIFY_IS_APPROX(vsmall.stableNorm(), ei_sqrt(size)*ei_abs(small));
VERIFY_IS_APPROX(vsmall.blueNorm(), ei_sqrt(size)*ei_abs(small));
VERIFY_IS_APPROX(vsmall.hypotNorm(), ei_sqrt(size)*ei_abs(small));
// Test compilation of cwise() version
VERIFY_IS_APPROX(vrand.colwise().stableNorm(), vrand.colwise().norm());
VERIFY_IS_APPROX(vrand.colwise().blueNorm(), vrand.colwise().norm());
VERIFY_IS_APPROX(vrand.colwise().hypotNorm(), vrand.colwise().norm());
VERIFY_IS_APPROX(vrand.rowwise().stableNorm(), vrand.rowwise().norm());
VERIFY_IS_APPROX(vrand.rowwise().blueNorm(), vrand.rowwise().norm());
VERIFY_IS_APPROX(vrand.rowwise().hypotNorm(), vrand.rowwise().norm());
}
void test_stable_norm()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( stable_norm(Matrix<float, 1, 1>()) );
CALL_SUBTEST_2( stable_norm(Vector4d()) );
CALL_SUBTEST_3( stable_norm(VectorXd(ei_random<int>(10,2000))) );
CALL_SUBTEST_4( stable_norm(VectorXf(ei_random<int>(10,2000))) );
CALL_SUBTEST_5( stable_norm(VectorXcd(ei_random<int>(10,2000))) );
}
}
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