test/stable_norm.cpp

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009-2014 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include "main.h"

template<typename T> EIGEN_DONT_INLINE T copy(const T& x)
{
  return x;
}

template<typename MatrixType> void stable_norm(const MatrixType& m)
{
  /* this test covers the following files:
     StableNorm.h
  */
  using std::sqrt;
  using std::abs;
  typedef typename MatrixType::Scalar Scalar;
  typedef typename NumTraits<Scalar>::Real RealScalar;
  
  bool complex_real_product_ok = true;

  // 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");
    
    Scalar inf = std::numeric_limits<RealScalar>::infinity();
    if(NumTraits<Scalar>::IsComplex && (numext::isnan)(inf*RealScalar(1)) )
    {
      complex_real_product_ok = false;
      static bool first = true;
      if(first)
        std::cerr << "WARNING: compiler mess up complex*real product, " << inf << " * " << 1.0 << " = " << inf*RealScalar(1) << std::endl;
      first = false;
    }
  }


  Index rows = m.rows();
  Index cols = m.cols();

  // get a non-zero random factor
  Scalar factor = internal::random<Scalar>();
  while(numext::abs2(factor)<RealScalar(1e-4))
    factor = internal::random<Scalar>();
  Scalar big = factor * ((std::numeric_limits<RealScalar>::max)() * RealScalar(1e-4));
  
  factor = internal::random<Scalar>();
  while(numext::abs2(factor)<RealScalar(1e-4))
    factor = internal::random<Scalar>();
  Scalar small = factor * ((std::numeric_limits<RealScalar>::min)() * RealScalar(1e4));

  Scalar one(1);

  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());

  // test with expressions as input
  VERIFY_IS_APPROX((one*vrand).stableNorm(),      vrand.norm());
  VERIFY_IS_APPROX((one*vrand).blueNorm(),        vrand.norm());
  VERIFY_IS_APPROX((one*vrand).hypotNorm(),       vrand.norm());
  VERIFY_IS_APPROX((one*vrand+one*vrand-one*vrand).stableNorm(),      vrand.norm());
  VERIFY_IS_APPROX((one*vrand+one*vrand-one*vrand).blueNorm(),        vrand.norm());
  VERIFY_IS_APPROX((one*vrand+one*vrand-one*vrand).hypotNorm(),       vrand.norm());

  RealScalar size = static_cast<RealScalar>(m.size());

  // test numext::isfinite
  VERIFY(!(numext::isfinite)( std::numeric_limits<RealScalar>::infinity()));
  VERIFY(!(numext::isfinite)(sqrt(-abs(big))));

  // test overflow
  VERIFY((numext::isfinite)(sqrt(size)*abs(big)));
  VERIFY_IS_NOT_APPROX(sqrt(copy(vbig.squaredNorm())), abs(sqrt(size)*big)); // here the default norm must fail
  VERIFY_IS_APPROX(vbig.stableNorm(), sqrt(size)*abs(big));
  VERIFY_IS_APPROX(vbig.blueNorm(),   sqrt(size)*abs(big));
  VERIFY_IS_APPROX(vbig.hypotNorm(),  sqrt(size)*abs(big));

  // test underflow
  VERIFY((numext::isfinite)(sqrt(size)*abs(small)));
  VERIFY_IS_NOT_APPROX(sqrt(copy(vsmall.squaredNorm())),   abs(sqrt(size)*small)); // here the default norm must fail
  VERIFY_IS_APPROX(vsmall.stableNorm(), sqrt(size)*abs(small));
  VERIFY_IS_APPROX(vsmall.blueNorm(),   sqrt(size)*abs(small));
  VERIFY_IS_APPROX(vsmall.hypotNorm(),  sqrt(size)*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());
  
  // test NaN, +inf, -inf 
  MatrixType v;
  Index i = internal::random<Index>(0,rows-1);
  Index j = internal::random<Index>(0,cols-1);

  // NaN
  {
    v = vrand;
    v(i,j) = std::numeric_limits<RealScalar>::quiet_NaN();
    VERIFY(!(numext::isfinite)(v.squaredNorm()));   VERIFY((numext::isnan)(v.squaredNorm()));
    VERIFY(!(numext::isfinite)(v.norm()));          VERIFY((numext::isnan)(v.norm()));
    VERIFY(!(numext::isfinite)(v.stableNorm()));    VERIFY((numext::isnan)(v.stableNorm()));
    VERIFY(!(numext::isfinite)(v.blueNorm()));      VERIFY((numext::isnan)(v.blueNorm()));
    VERIFY(!(numext::isfinite)(v.hypotNorm()));     VERIFY((numext::isnan)(v.hypotNorm()));
  }
  
  // +inf
  {
    v = vrand;
    v(i,j) = std::numeric_limits<RealScalar>::infinity();
    VERIFY(!(numext::isfinite)(v.squaredNorm()));   VERIFY(isPlusInf(v.squaredNorm()));
    VERIFY(!(numext::isfinite)(v.norm()));          VERIFY(isPlusInf(v.norm()));
    VERIFY(!(numext::isfinite)(v.stableNorm()));
    if(complex_real_product_ok){
      VERIFY(isPlusInf(v.stableNorm()));
    }
    VERIFY(!(numext::isfinite)(v.blueNorm()));      VERIFY(isPlusInf(v.blueNorm()));
    VERIFY(!(numext::isfinite)(v.hypotNorm()));     VERIFY(isPlusInf(v.hypotNorm()));
  }
  
  // -inf
  {
    v = vrand;
    v(i,j) = -std::numeric_limits<RealScalar>::infinity();
    VERIFY(!(numext::isfinite)(v.squaredNorm()));   VERIFY(isPlusInf(v.squaredNorm()));
    VERIFY(!(numext::isfinite)(v.norm()));          VERIFY(isPlusInf(v.norm()));
    VERIFY(!(numext::isfinite)(v.stableNorm()));
    if(complex_real_product_ok) {
      VERIFY(isPlusInf(v.stableNorm()));
    }
    VERIFY(!(numext::isfinite)(v.blueNorm()));      VERIFY(isPlusInf(v.blueNorm()));
    VERIFY(!(numext::isfinite)(v.hypotNorm()));     VERIFY(isPlusInf(v.hypotNorm()));
  }
  
  // mix
  {
    Index i2 = internal::random<Index>(0,rows-1);
    Index j2 = internal::random<Index>(0,cols-1);
    v = vrand;
    v(i,j) = -std::numeric_limits<RealScalar>::infinity();
    v(i2,j2) = std::numeric_limits<RealScalar>::quiet_NaN();
    VERIFY(!(numext::isfinite)(v.squaredNorm()));   VERIFY((numext::isnan)(v.squaredNorm()));
    VERIFY(!(numext::isfinite)(v.norm()));          VERIFY((numext::isnan)(v.norm()));
    VERIFY(!(numext::isfinite)(v.stableNorm()));    VERIFY((numext::isnan)(v.stableNorm()));
    VERIFY(!(numext::isfinite)(v.blueNorm()));      VERIFY((numext::isnan)(v.blueNorm()));
    if (i2 != i || j2 != j) {
      // hypot propagates inf over NaN.
      VERIFY(!(numext::isfinite)(v.hypotNorm()));     VERIFY((numext::isinf)(v.hypotNorm()));
    } else {
      // inf is overwritten by NaN, expect norm to be NaN.
      VERIFY(!(numext::isfinite)(v.hypotNorm()));     VERIFY((numext::isnan)(v.hypotNorm()));
    }
  }

  // stableNormalize[d]
  {
    VERIFY_IS_APPROX(vrand.stableNormalized(), vrand.normalized());
    MatrixType vcopy(vrand);
    vcopy.stableNormalize();
    VERIFY_IS_APPROX(vcopy, vrand.normalized());
    VERIFY_IS_APPROX((vrand.stableNormalized()).norm(), RealScalar(1));
    VERIFY_IS_APPROX(vcopy.norm(), RealScalar(1));
    VERIFY_IS_APPROX((vbig.stableNormalized()).norm(), RealScalar(1));
    VERIFY_IS_APPROX((vsmall.stableNormalized()).norm(), RealScalar(1));
    RealScalar big_scaling = ((std::numeric_limits<RealScalar>::max)() * RealScalar(1e-4));
    VERIFY_IS_APPROX(vbig/big_scaling, (vbig.stableNorm() * vbig.stableNormalized()).eval()/big_scaling);
    VERIFY_IS_APPROX(vsmall, vsmall.stableNorm() * vsmall.stableNormalized());
  }
}

template<typename Scalar>
void test_hypot()
{
  typedef typename NumTraits<Scalar>::Real RealScalar;
  Scalar factor = internal::random<Scalar>();
  while(numext::abs2(factor)<RealScalar(1e-4))
    factor = internal::random<Scalar>();
  Scalar big = factor * ((std::numeric_limits<RealScalar>::max)() * RealScalar(1e-4));
  
  factor = internal::random<Scalar>();
  while(numext::abs2(factor)<RealScalar(1e-4))
    factor = internal::random<Scalar>();
  Scalar small = factor * ((std::numeric_limits<RealScalar>::min)() * RealScalar(1e4));

  Scalar  one   (1),
          zero  (0),
          sqrt2 (std::sqrt(2)),
          nan   (std::numeric_limits<RealScalar>::quiet_NaN());

  Scalar a = internal::random<Scalar>(-1,1);
  Scalar b = internal::random<Scalar>(-1,1);
  VERIFY_IS_APPROX(numext::hypot(a,b),std::sqrt(numext::abs2(a)+numext::abs2(b)));
  VERIFY_IS_EQUAL(numext::hypot(zero,zero), zero);
  VERIFY_IS_APPROX(numext::hypot(one, one), sqrt2);
  VERIFY_IS_APPROX(numext::hypot(big,big), sqrt2*numext::abs(big));
  VERIFY_IS_APPROX(numext::hypot(small,small), sqrt2*numext::abs(small));
  VERIFY_IS_APPROX(numext::hypot(small,big), numext::abs(big));
  VERIFY((numext::isnan)(numext::hypot(nan,a)));
  VERIFY((numext::isnan)(numext::hypot(a,nan)));
}

EIGEN_DECLARE_TEST(stable_norm)
{
  for(int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST_3( test_hypot<double>() );
    CALL_SUBTEST_4( test_hypot<float>() );
    CALL_SUBTEST_5( test_hypot<std::complex<double> >() );
    CALL_SUBTEST_6( test_hypot<std::complex<float> >() );

    CALL_SUBTEST_1( stable_norm(Matrix<float, 1, 1>()) );
    CALL_SUBTEST_2( stable_norm(Vector4d()) );
    CALL_SUBTEST_3( stable_norm(VectorXd(internal::random<int>(10,2000))) );
    CALL_SUBTEST_3( stable_norm(MatrixXd(internal::random<int>(10,200), internal::random<int>(10,200))) );
    CALL_SUBTEST_4( stable_norm(VectorXf(internal::random<int>(10,2000))) );
    CALL_SUBTEST_5( stable_norm(VectorXcd(internal::random<int>(10,2000))) );
    CALL_SUBTEST_6( stable_norm(VectorXcf(internal::random<int>(10,2000))) );
  }
}