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260 lines
10 KiB
C++
260 lines
10 KiB
C++
// 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>
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EIGEN_DONT_INLINE T copy(const T& x) {
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return x;
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}
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template <typename MatrixType>
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void stable_norm(const MatrixType& m) {
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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::abs;
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using std::sqrt;
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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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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 << " = "
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<< 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)) 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)) factor = internal::random<Scalar>();
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Scalar small = factor * ((std::numeric_limits<RealScalar>::min)() * RealScalar(1e4));
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Scalar one(1);
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MatrixType vzero = MatrixType::Zero(rows, cols), vrand = MatrixType::Random(rows, cols), 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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// test with expressions as input
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VERIFY_IS_APPROX((one * vrand).stableNorm(), vrand.norm());
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VERIFY_IS_APPROX((one * vrand).blueNorm(), vrand.norm());
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VERIFY_IS_APPROX((one * vrand).hypotNorm(), vrand.norm());
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VERIFY_IS_APPROX((one * vrand + one * vrand - one * vrand).stableNorm(), vrand.norm());
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VERIFY_IS_APPROX((one * vrand + one * vrand - one * vrand).blueNorm(), vrand.norm());
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VERIFY_IS_APPROX((one * vrand + one * vrand - one * 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()));
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VERIFY((numext::isnan)(v.squaredNorm()));
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VERIFY(!(numext::isfinite)(v.norm()));
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VERIFY((numext::isnan)(v.norm()));
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VERIFY(!(numext::isfinite)(v.stableNorm()));
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VERIFY((numext::isnan)(v.stableNorm()));
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VERIFY(!(numext::isfinite)(v.blueNorm()));
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VERIFY((numext::isnan)(v.blueNorm()));
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VERIFY(!(numext::isfinite)(v.hypotNorm()));
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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()));
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VERIFY(isPlusInf(v.squaredNorm()));
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VERIFY(!(numext::isfinite)(v.norm()));
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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()));
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VERIFY(isPlusInf(v.blueNorm()));
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VERIFY(!(numext::isfinite)(v.hypotNorm()));
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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()));
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VERIFY(isPlusInf(v.squaredNorm()));
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VERIFY(!(numext::isfinite)(v.norm()));
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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()));
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VERIFY(isPlusInf(v.blueNorm()));
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VERIFY(!(numext::isfinite)(v.hypotNorm()));
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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()));
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VERIFY((numext::isnan)(v.squaredNorm()));
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VERIFY(!(numext::isfinite)(v.norm()));
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VERIFY((numext::isnan)(v.norm()));
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VERIFY(!(numext::isfinite)(v.stableNorm()));
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VERIFY((numext::isnan)(v.stableNorm()));
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VERIFY(!(numext::isfinite)(v.blueNorm()));
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VERIFY((numext::isnan)(v.blueNorm()));
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if (i2 != i || j2 != j) {
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// hypot propagates inf over NaN.
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VERIFY(!(numext::isfinite)(v.hypotNorm()));
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VERIFY((numext::isinf)(v.hypotNorm()));
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} else {
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// inf is overwritten by NaN, expect norm to be NaN.
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VERIFY(!(numext::isfinite)(v.hypotNorm()));
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VERIFY((numext::isnan)(v.hypotNorm()));
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}
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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_empty() {
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Eigen::VectorXf empty(0);
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VERIFY_IS_EQUAL(empty.stableNorm(), 0.0f);
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}
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template <typename Scalar>
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void test_hypot() {
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typedef typename NumTraits<Scalar>::Real RealScalar;
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Scalar factor = internal::random<Scalar>();
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while (numext::abs2(factor) < RealScalar(1e-4)) 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)) factor = internal::random<Scalar>();
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Scalar small = factor * ((std::numeric_limits<RealScalar>::min)() * RealScalar(1e4));
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Scalar one(1), zero(0), sqrt2(std::sqrt(2)), nan(std::numeric_limits<RealScalar>::quiet_NaN());
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Scalar a = internal::random<Scalar>(-1, 1);
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Scalar b = internal::random<Scalar>(-1, 1);
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VERIFY_IS_APPROX(numext::hypot(a, b), std::sqrt(numext::abs2(a) + numext::abs2(b)));
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VERIFY_IS_EQUAL(numext::hypot(zero, zero), zero);
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VERIFY_IS_APPROX(numext::hypot(one, one), sqrt2);
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VERIFY_IS_APPROX(numext::hypot(big, big), sqrt2 * numext::abs(big));
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VERIFY_IS_APPROX(numext::hypot(small, small), sqrt2 * numext::abs(small));
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VERIFY_IS_APPROX(numext::hypot(small, big), numext::abs(big));
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VERIFY((numext::isnan)(numext::hypot(nan, a)));
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VERIFY((numext::isnan)(numext::hypot(a, nan)));
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}
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EIGEN_DECLARE_TEST(stable_norm) {
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CALL_SUBTEST_1(test_empty());
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for (int i = 0; i < g_repeat; i++) {
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CALL_SUBTEST_3(test_hypot<double>());
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CALL_SUBTEST_4(test_hypot<float>());
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CALL_SUBTEST_5(test_hypot<std::complex<double> >());
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CALL_SUBTEST_6(test_hypot<std::complex<float> >());
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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_3(stable_norm(MatrixXd(internal::random<int>(10, 200), internal::random<int>(10, 200))));
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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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CALL_SUBTEST_6(stable_norm(VectorXcf(internal::random<int>(10, 2000))));
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}
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}
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