void TestBigFill (const size_t size, const T magic)
{
vector<T> vbig (size);
fill (vbig.begin() + 1, vbig.end(), magic); // offset to test prealignment loop
typename vector<T>::const_iterator iMismatch;
iMismatch = find_if (vbig.begin() + 1, vbig.end(), bind1st (not_equal_to<T>(), magic));
if (iMismatch == vbig.end())
cout << "works\n";
else
cout.format ("does not work: mismatch at %zd, =0x%lX\n", abs_distance (vbig.begin(), iMismatch), (unsigned long)(*iMismatch));
}
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 = internal::random<Scalar>() * (std::numeric_limits<RealScalar>::max() * RealScalar(1e-4));
Scalar small = internal::random<Scalar>() * (std::numeric_limits<RealScalar>::min() * RealScalar(1e4));
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(internal::sqrt(-internal::abs(big))));
// test overflow
VERIFY(isFinite(internal::sqrt(size)*internal::abs(big)));
VERIFY_IS_NOT_APPROX(internal::sqrt(copy(vbig.squaredNorm())), internal::abs(internal::sqrt(size)*big)); // here the default norm must fail
VERIFY_IS_APPROX(vbig.stableNorm(), internal::sqrt(size)*internal::abs(big));
VERIFY_IS_APPROX(vbig.blueNorm(), internal::sqrt(size)*internal::abs(big));
VERIFY_IS_APPROX(vbig.hypotNorm(), internal::sqrt(size)*internal::abs(big));
// test underflow
VERIFY(isFinite(internal::sqrt(size)*internal::abs(small)));
VERIFY_IS_NOT_APPROX(internal::sqrt(copy(vsmall.squaredNorm())), internal::abs(internal::sqrt(size)*small)); // here the default norm must fail
VERIFY_IS_APPROX(vsmall.stableNorm(), internal::sqrt(size)*internal::abs(small));
VERIFY_IS_APPROX(vsmall.blueNorm(), internal::sqrt(size)*internal::abs(small));
VERIFY_IS_APPROX(vsmall.hypotNorm(), internal::sqrt(size)*internal::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());
}