193 lines
7.8 KiB
C++
193 lines
7.8 KiB
C++
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2009-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#include "main.h"
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template<typename T> EIGEN_DONT_INLINE T copy(const T& x)
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{
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return x;
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}
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template<typename MatrixType> void stable_norm(const MatrixType& m)
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{
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/* this test covers the following files:
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StableNorm.h
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*/
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using std::sqrt;
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using std::abs;
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typedef typename MatrixType::Index Index;
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typedef typename MatrixType::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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bool complex_real_product_ok = true;
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// Check the basic machine-dependent constants.
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{
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int ibeta, it, iemin, iemax;
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ibeta = std::numeric_limits<RealScalar>::radix; // base for floating-point numbers
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it = std::numeric_limits<RealScalar>::digits; // number of base-beta digits in mantissa
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iemin = std::numeric_limits<RealScalar>::min_exponent; // minimum exponent
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iemax = std::numeric_limits<RealScalar>::max_exponent; // maximum exponent
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VERIFY( (!(iemin > 1 - 2*it || 1+it>iemax || (it==2 && ibeta<5) || (it<=4 && ibeta <= 3 ) || it<2))
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&& "the stable norm algorithm cannot be guaranteed on this computer");
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Scalar inf = std::numeric_limits<RealScalar>::infinity();
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if(NumTraits<Scalar>::IsComplex && (numext::isnan)(inf*RealScalar(1)) )
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{
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complex_real_product_ok = false;
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static bool first = true;
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if(first)
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std::cerr << "WARNING: compiler mess up complex*real product, " << inf << " * " << 1.0 << " = " << inf*RealScalar(1) << std::endl;
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first = false;
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}
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}
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Index rows = m.rows();
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Index cols = m.cols();
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// get a non-zero random factor
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Scalar factor = internal::random<Scalar>();
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while(numext::abs2(factor)<RealScalar(1e-4))
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factor = internal::random<Scalar>();
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Scalar big = factor * ((std::numeric_limits<RealScalar>::max)() * RealScalar(1e-4));
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factor = internal::random<Scalar>();
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while(numext::abs2(factor)<RealScalar(1e-4))
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factor = internal::random<Scalar>();
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Scalar small = factor * ((std::numeric_limits<RealScalar>::min)() * RealScalar(1e4));
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MatrixType vzero = MatrixType::Zero(rows, cols),
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vrand = MatrixType::Random(rows, cols),
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vbig(rows, cols),
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vsmall(rows,cols);
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vbig.fill(big);
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vsmall.fill(small);
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VERIFY_IS_MUCH_SMALLER_THAN(vzero.norm(), static_cast<RealScalar>(1));
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VERIFY_IS_APPROX(vrand.stableNorm(), vrand.norm());
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VERIFY_IS_APPROX(vrand.blueNorm(), vrand.norm());
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VERIFY_IS_APPROX(vrand.hypotNorm(), vrand.norm());
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RealScalar size = static_cast<RealScalar>(m.size());
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// test numext::isfinite
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VERIFY(!(numext::isfinite)( std::numeric_limits<RealScalar>::infinity()));
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VERIFY(!(numext::isfinite)(sqrt(-abs(big))));
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// test overflow
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VERIFY((numext::isfinite)(sqrt(size)*abs(big)));
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VERIFY_IS_NOT_APPROX(sqrt(copy(vbig.squaredNorm())), abs(sqrt(size)*big)); // here the default norm must fail
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VERIFY_IS_APPROX(vbig.stableNorm(), sqrt(size)*abs(big));
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VERIFY_IS_APPROX(vbig.blueNorm(), sqrt(size)*abs(big));
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VERIFY_IS_APPROX(vbig.hypotNorm(), sqrt(size)*abs(big));
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// test underflow
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VERIFY((numext::isfinite)(sqrt(size)*abs(small)));
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VERIFY_IS_NOT_APPROX(sqrt(copy(vsmall.squaredNorm())), abs(sqrt(size)*small)); // here the default norm must fail
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VERIFY_IS_APPROX(vsmall.stableNorm(), sqrt(size)*abs(small));
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VERIFY_IS_APPROX(vsmall.blueNorm(), sqrt(size)*abs(small));
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VERIFY_IS_APPROX(vsmall.hypotNorm(), sqrt(size)*abs(small));
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// Test compilation of cwise() version
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VERIFY_IS_APPROX(vrand.colwise().stableNorm(), vrand.colwise().norm());
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VERIFY_IS_APPROX(vrand.colwise().blueNorm(), vrand.colwise().norm());
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VERIFY_IS_APPROX(vrand.colwise().hypotNorm(), vrand.colwise().norm());
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VERIFY_IS_APPROX(vrand.rowwise().stableNorm(), vrand.rowwise().norm());
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VERIFY_IS_APPROX(vrand.rowwise().blueNorm(), vrand.rowwise().norm());
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VERIFY_IS_APPROX(vrand.rowwise().hypotNorm(), vrand.rowwise().norm());
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// test NaN, +inf, -inf
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MatrixType v;
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Index i = internal::random<Index>(0,rows-1);
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Index j = internal::random<Index>(0,cols-1);
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// NaN
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{
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v = vrand;
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v(i,j) = std::numeric_limits<RealScalar>::quiet_NaN();
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VERIFY(!(numext::isfinite)(v.squaredNorm())); VERIFY((numext::isnan)(v.squaredNorm()));
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VERIFY(!(numext::isfinite)(v.norm())); VERIFY((numext::isnan)(v.norm()));
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VERIFY(!(numext::isfinite)(v.stableNorm())); VERIFY((numext::isnan)(v.stableNorm()));
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VERIFY(!(numext::isfinite)(v.blueNorm())); VERIFY((numext::isnan)(v.blueNorm()));
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VERIFY(!(numext::isfinite)(v.hypotNorm())); VERIFY((numext::isnan)(v.hypotNorm()));
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}
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// +inf
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{
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v = vrand;
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v(i,j) = std::numeric_limits<RealScalar>::infinity();
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VERIFY(!(numext::isfinite)(v.squaredNorm())); VERIFY(isPlusInf(v.squaredNorm()));
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VERIFY(!(numext::isfinite)(v.norm())); VERIFY(isPlusInf(v.norm()));
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VERIFY(!(numext::isfinite)(v.stableNorm()));
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if(complex_real_product_ok){
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VERIFY(isPlusInf(v.stableNorm()));
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}
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VERIFY(!(numext::isfinite)(v.blueNorm())); VERIFY(isPlusInf(v.blueNorm()));
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VERIFY(!(numext::isfinite)(v.hypotNorm())); VERIFY(isPlusInf(v.hypotNorm()));
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}
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// -inf
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{
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v = vrand;
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v(i,j) = -std::numeric_limits<RealScalar>::infinity();
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VERIFY(!(numext::isfinite)(v.squaredNorm())); VERIFY(isPlusInf(v.squaredNorm()));
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VERIFY(!(numext::isfinite)(v.norm())); VERIFY(isPlusInf(v.norm()));
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VERIFY(!(numext::isfinite)(v.stableNorm()));
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if(complex_real_product_ok) {
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VERIFY(isPlusInf(v.stableNorm()));
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}
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VERIFY(!(numext::isfinite)(v.blueNorm())); VERIFY(isPlusInf(v.blueNorm()));
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VERIFY(!(numext::isfinite)(v.hypotNorm())); VERIFY(isPlusInf(v.hypotNorm()));
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}
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// mix
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{
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Index i2 = internal::random<Index>(0,rows-1);
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Index j2 = internal::random<Index>(0,cols-1);
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v = vrand;
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v(i,j) = -std::numeric_limits<RealScalar>::infinity();
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v(i2,j2) = std::numeric_limits<RealScalar>::quiet_NaN();
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VERIFY(!(numext::isfinite)(v.squaredNorm())); VERIFY((numext::isnan)(v.squaredNorm()));
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VERIFY(!(numext::isfinite)(v.norm())); VERIFY((numext::isnan)(v.norm()));
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VERIFY(!(numext::isfinite)(v.stableNorm())); VERIFY((numext::isnan)(v.stableNorm()));
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VERIFY(!(numext::isfinite)(v.blueNorm())); VERIFY((numext::isnan)(v.blueNorm()));
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VERIFY(!(numext::isfinite)(v.hypotNorm())); VERIFY((numext::isnan)(v.hypotNorm()));
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}
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// stableNormalize[d]
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{
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VERIFY_IS_APPROX(vrand.stableNormalized(), vrand.normalized());
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MatrixType vcopy(vrand);
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vcopy.stableNormalize();
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VERIFY_IS_APPROX(vcopy, vrand.normalized());
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VERIFY_IS_APPROX((vrand.stableNormalized()).norm(), RealScalar(1));
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VERIFY_IS_APPROX(vcopy.norm(), RealScalar(1));
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VERIFY_IS_APPROX((vbig.stableNormalized()).norm(), RealScalar(1));
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VERIFY_IS_APPROX((vsmall.stableNormalized()).norm(), RealScalar(1));
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RealScalar big_scaling = ((std::numeric_limits<RealScalar>::max)() * RealScalar(1e-4));
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VERIFY_IS_APPROX(vbig/big_scaling, (vbig.stableNorm() * vbig.stableNormalized()).eval()/big_scaling);
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VERIFY_IS_APPROX(vsmall, vsmall.stableNorm() * vsmall.stableNormalized());
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}
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}
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void test_stable_norm()
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{
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for(int i = 0; i < g_repeat; i++) {
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CALL_SUBTEST_1( stable_norm(Matrix<float, 1, 1>()) );
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CALL_SUBTEST_2( stable_norm(Vector4d()) );
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CALL_SUBTEST_3( stable_norm(VectorXd(internal::random<int>(10,2000))) );
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CALL_SUBTEST_4( stable_norm(VectorXf(internal::random<int>(10,2000))) );
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CALL_SUBTEST_5( stable_norm(VectorXcd(internal::random<int>(10,2000))) );
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}
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}
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