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eigen/test/stable_norm.cpp
Rasmus Munk Larsen c1faa74738 Add boundary test coverage: stableNorm, LinSpaced, complex GEMV, triangular solve 
libeigen/eigen!2291

Co-authored-by: Rasmus Munk Larsen <rmlarsen@gmail.com>
2026-03-12 18:15:30 -07:00

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// 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::abs;
using std::sqrt;
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 random factor bounded away from zero: |factor| >= 0.1.
Scalar factor = internal::random<Scalar>(Scalar(RealScalar(0.1)), Scalar(RealScalar(1)));
Scalar big = factor * ((std::numeric_limits<RealScalar>::max)() * RealScalar(1e-4));
factor = internal::random<Scalar>(Scalar(RealScalar(0.1)), Scalar(RealScalar(1)));
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());
}
}
void test_empty() {
Eigen::VectorXf empty(0);
VERIFY_IS_EQUAL(empty.stableNorm(), 0.0f);
}
template <typename Scalar>
void test_hypot() {
typedef typename NumTraits<Scalar>::Real RealScalar;
// Get a random factor bounded away from zero: |factor| >= 0.1.
Scalar factor = internal::random<Scalar>(Scalar(RealScalar(0.1)), Scalar(RealScalar(1)));
Scalar big = factor * ((std::numeric_limits<RealScalar>::max)() * RealScalar(1e-4));
factor = internal::random<Scalar>(Scalar(RealScalar(0.1)), Scalar(RealScalar(1)));
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)));
}
// Test stableNorm at the 4096-element block boundary.
// stable_norm_impl_inner_step processes vectors in blocks of 4096.
// Sizes near this boundary exercise the transition between full blocks
// and the remainder tail, including scale propagation across blocks.
template <typename Scalar>
void stable_norm_block_boundary() {
using std::abs;
using std::sqrt;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, Dynamic, 1> VecType;
// Test sizes around the 4096 block boundary.
const Index sizes[] = {4095, 4096, 4097, 8191, 8192, 8193, 12288};
for (int si = 0; si < 7; ++si) {
Index n = sizes[si];
VecType v = VecType::Random(n);
VERIFY_IS_APPROX(v.stableNorm(), v.norm());
VERIFY_IS_APPROX(v.blueNorm(), v.norm());
}
// Test scale transitions across blocks: first block has tiny values,
// second block has huge values. This exercises the scale/invScale
// update logic when maxCoeff > scale in stable_norm_kernel.
{
RealScalar tiny = (std::numeric_limits<RealScalar>::min)() * RealScalar(1e4);
RealScalar huge_val = (std::numeric_limits<RealScalar>::max)() * RealScalar(1e-4);
Index n = 8192;
VecType v(n);
// First 4096 elements: tiny. Second 4096 elements: huge.
v.head(4096).setConstant(Scalar(tiny));
v.tail(4096).setConstant(Scalar(huge_val));
// The huge part dominates, so the expected norm is sqrt(4096)*huge_val.
RealScalar expected = sqrt(RealScalar(4096)) * abs(huge_val);
VERIFY_IS_APPROX(v.stableNorm(), expected);
VERIFY_IS_APPROX(v.blueNorm(), expected);
}
// Reverse: first block huge, second block tiny.
{
RealScalar tiny = (std::numeric_limits<RealScalar>::min)() * RealScalar(1e4);
RealScalar huge_val = (std::numeric_limits<RealScalar>::max)() * RealScalar(1e-4);
Index n = 8192;
VecType v(n);
v.head(4096).setConstant(Scalar(huge_val));
v.tail(4096).setConstant(Scalar(tiny));
RealScalar expected = sqrt(RealScalar(4096)) * abs(huge_val);
VERIFY_IS_APPROX(v.stableNorm(), expected);
VERIFY_IS_APPROX(v.blueNorm(), expected);
}
// Matrix version: columns with different magnitudes.
// Scale must propagate correctly across columns.
{
RealScalar tiny = (std::numeric_limits<RealScalar>::min)() * RealScalar(1e4);
RealScalar huge_val = (std::numeric_limits<RealScalar>::max)() * RealScalar(1e-4);
typedef Matrix<Scalar, Dynamic, Dynamic> MatType;
MatType m(100, 2);
m.col(0).setConstant(Scalar(tiny));
m.col(1).setConstant(Scalar(huge_val));
RealScalar expected = sqrt(RealScalar(100)) * abs(huge_val);
VERIFY_IS_APPROX(m.stableNorm(), expected);
VERIFY_IS_APPROX(m.blueNorm(), expected);
}
}
EIGEN_DECLARE_TEST(stable_norm) {
CALL_SUBTEST_1(test_empty());
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))));
}
// Block boundary and scale transition tests (deterministic, outside g_repeat).
CALL_SUBTEST_7(stable_norm_block_boundary<float>());
CALL_SUBTEST_7(stable_norm_block_boundary<double>());
}
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