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eigen/test/redux.cpp

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2015 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/.
#define TEST_ENABLE_TEMPORARY_TRACKING
#define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8
// ^^ see bug 1449
#include "main.h"
template<typename MatrixType> void matrixRedux(const MatrixType& m)
{
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
Index rows = m.rows();
Index cols = m.cols();
MatrixType m1 = MatrixType::Random(rows, cols);
// The entries of m1 are uniformly distributed in [0,1], so m1.prod() is very small. This may lead to test
// failures if we underflow into denormals. Thus, we scale so that entries are close to 1.
MatrixType m1_for_prod = MatrixType::Ones(rows, cols) + RealScalar(0.2) * m1;
Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> m2(rows,rows);
m2.setRandom();
VERIFY_IS_MUCH_SMALLER_THAN(MatrixType::Zero(rows, cols).sum(), Scalar(1));
VERIFY_IS_APPROX(MatrixType::Ones(rows, cols).sum(), Scalar(float(rows*cols))); // the float() here to shut up excessive MSVC warning about int->complex conversion being lossy
Scalar s(0), p(1), minc(numext::real(m1.coeff(0))), maxc(numext::real(m1.coeff(0)));
for(int j = 0; j < cols; j++)
for(int i = 0; i < rows; i++)
{
s += m1(i,j);
p *= m1_for_prod(i,j);
minc = (std::min)(numext::real(minc), numext::real(m1(i,j)));
maxc = (std::max)(numext::real(maxc), numext::real(m1(i,j)));
}
const Scalar mean = s/Scalar(RealScalar(rows*cols));
VERIFY_IS_APPROX(m1.sum(), s);
VERIFY_IS_APPROX(m1.mean(), mean);
VERIFY_IS_APPROX(m1_for_prod.prod(), p);
VERIFY_IS_APPROX(m1.real().minCoeff(), numext::real(minc));
VERIFY_IS_APPROX(m1.real().maxCoeff(), numext::real(maxc));
// test that partial reduction works if nested expressions is forced to evaluate early
VERIFY_IS_APPROX((m1.matrix() * m1.matrix().transpose()) .cwiseProduct(m2.matrix()).rowwise().sum().sum(),
(m1.matrix() * m1.matrix().transpose()).eval().cwiseProduct(m2.matrix()).rowwise().sum().sum());
// test slice vectorization assuming assign is ok
Index r0 = internal::random<Index>(0,rows-1);
Index c0 = internal::random<Index>(0,cols-1);
Index r1 = internal::random<Index>(r0+1,rows)-r0;
Index c1 = internal::random<Index>(c0+1,cols)-c0;
VERIFY_IS_APPROX(m1.block(r0,c0,r1,c1).sum(), m1.block(r0,c0,r1,c1).eval().sum());
VERIFY_IS_APPROX(m1.block(r0,c0,r1,c1).mean(), m1.block(r0,c0,r1,c1).eval().mean());
VERIFY_IS_APPROX(m1_for_prod.block(r0,c0,r1,c1).prod(), m1_for_prod.block(r0,c0,r1,c1).eval().prod());
VERIFY_IS_APPROX(m1.block(r0,c0,r1,c1).real().minCoeff(), m1.block(r0,c0,r1,c1).real().eval().minCoeff());
VERIFY_IS_APPROX(m1.block(r0,c0,r1,c1).real().maxCoeff(), m1.block(r0,c0,r1,c1).real().eval().maxCoeff());
// regression for bug 1090
const int R1 = MatrixType::RowsAtCompileTime>=2 ? MatrixType::RowsAtCompileTime/2 : 6;
const int C1 = MatrixType::ColsAtCompileTime>=2 ? MatrixType::ColsAtCompileTime/2 : 6;
if(R1<=rows-r0 && C1<=cols-c0)
{
VERIFY_IS_APPROX( (m1.template block<R1,C1>(r0,c0).sum()), m1.block(r0,c0,R1,C1).sum() );
}
// test empty objects
VERIFY_IS_APPROX(m1.block(r0,c0,0,0).sum(), Scalar(0));
VERIFY_IS_APPROX(m1.block(r0,c0,0,0).prod(), Scalar(1));
// test nesting complex expression
VERIFY_EVALUATION_COUNT( (m1.matrix()*m1.matrix().transpose()).sum(), (MatrixType::IsVectorAtCompileTime && MatrixType::SizeAtCompileTime!=1 ? 0 : 1) );
VERIFY_EVALUATION_COUNT( ((m1.matrix()*m1.matrix().transpose())+m2).sum(),(MatrixType::IsVectorAtCompileTime && MatrixType::SizeAtCompileTime!=1 ? 0 : 1));
}
template<typename VectorType> void vectorRedux(const VectorType& w)
{
using std::abs;
typedef typename VectorType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
Index size = w.size();
VectorType v = VectorType::Random(size);
VectorType v_for_prod = VectorType::Ones(size) + Scalar(0.2) * v; // see comment above declaration of m1_for_prod
for(int i = 1; i < size; i++)
{
Scalar s(0), p(1);
RealScalar minc(numext::real(v.coeff(0))), maxc(numext::real(v.coeff(0)));
for(int j = 0; j < i; j++)
{
s += v[j];
p *= v_for_prod[j];
minc = (std::min)(minc, numext::real(v[j]));
maxc = (std::max)(maxc, numext::real(v[j]));
}
VERIFY_IS_MUCH_SMALLER_THAN(abs(s - v.head(i).sum()), Scalar(1));
VERIFY_IS_APPROX(p, v_for_prod.head(i).prod());
VERIFY_IS_APPROX(minc, v.real().head(i).minCoeff());
VERIFY_IS_APPROX(maxc, v.real().head(i).maxCoeff());
}
for(int i = 0; i < size-1; i++)
{
Scalar s(0), p(1);
RealScalar minc(numext::real(v.coeff(i))), maxc(numext::real(v.coeff(i)));
for(int j = i; j < size; j++)
{
s += v[j];
p *= v_for_prod[j];
minc = (std::min)(minc, numext::real(v[j]));
maxc = (std::max)(maxc, numext::real(v[j]));
}
VERIFY_IS_MUCH_SMALLER_THAN(abs(s - v.tail(size-i).sum()), Scalar(1));
VERIFY_IS_APPROX(p, v_for_prod.tail(size-i).prod());
VERIFY_IS_APPROX(minc, v.real().tail(size-i).minCoeff());
VERIFY_IS_APPROX(maxc, v.real().tail(size-i).maxCoeff());
}
for(int i = 0; i < size/2; i++)
{
Scalar s(0), p(1);
RealScalar minc(numext::real(v.coeff(i))), maxc(numext::real(v.coeff(i)));
for(int j = i; j < size-i; j++)
{
s += v[j];
p *= v_for_prod[j];
minc = (std::min)(minc, numext::real(v[j]));
maxc = (std::max)(maxc, numext::real(v[j]));
}
VERIFY_IS_MUCH_SMALLER_THAN(abs(s - v.segment(i, size-2*i).sum()), Scalar(1));
VERIFY_IS_APPROX(p, v_for_prod.segment(i, size-2*i).prod());
VERIFY_IS_APPROX(minc, v.real().segment(i, size-2*i).minCoeff());
VERIFY_IS_APPROX(maxc, v.real().segment(i, size-2*i).maxCoeff());
}
// test empty objects
VERIFY_IS_APPROX(v.head(0).sum(), Scalar(0));
VERIFY_IS_APPROX(v.tail(0).prod(), Scalar(1));
VERIFY_RAISES_ASSERT(v.head(0).mean());
VERIFY_RAISES_ASSERT(v.head(0).minCoeff());
VERIFY_RAISES_ASSERT(v.head(0).maxCoeff());
}
EIGEN_DECLARE_TEST(redux)
{
// the max size cannot be too large, otherwise reduxion operations obviously generate large errors.
int maxsize = (std::min)(100,EIGEN_TEST_MAX_SIZE);
TEST_SET_BUT_UNUSED_VARIABLE(maxsize);
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( matrixRedux(Matrix<float, 1, 1>()) );
CALL_SUBTEST_1( matrixRedux(Array<float, 1, 1>()) );
CALL_SUBTEST_2( matrixRedux(Matrix2f()) );
CALL_SUBTEST_2( matrixRedux(Array2f()) );
CALL_SUBTEST_2( matrixRedux(Array22f()) );
CALL_SUBTEST_3( matrixRedux(Matrix4d()) );
CALL_SUBTEST_3( matrixRedux(Array4d()) );
CALL_SUBTEST_3( matrixRedux(Array44d()) );
CALL_SUBTEST_4( matrixRedux(MatrixXcf(internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
CALL_SUBTEST_4( matrixRedux(ArrayXXcf(internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
CALL_SUBTEST_5( matrixRedux(MatrixXd (internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
CALL_SUBTEST_5( matrixRedux(ArrayXXd (internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
CALL_SUBTEST_6( matrixRedux(MatrixXi (internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
CALL_SUBTEST_6( matrixRedux(ArrayXXi (internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
}
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_7( vectorRedux(Vector4f()) );
CALL_SUBTEST_7( vectorRedux(Array4f()) );
CALL_SUBTEST_5( vectorRedux(VectorXd(internal::random<int>(1,maxsize))) );
CALL_SUBTEST_5( vectorRedux(ArrayXd(internal::random<int>(1,maxsize))) );
CALL_SUBTEST_8( vectorRedux(VectorXf(internal::random<int>(1,maxsize))) );
CALL_SUBTEST_8( vectorRedux(ArrayXf(internal::random<int>(1,maxsize))) );
}
}
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