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eigen/test/basicstuff.cpp

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// 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 EIGEN_NO_STATIC_ASSERT
#include "main.h"
template<typename MatrixType> void basicStuff(const MatrixType& m)
{
typedef typename MatrixType::Index Index;
typedef typename MatrixType::Scalar Scalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
Index rows = m.rows();
Index cols = m.cols();
// this test relies a lot on Random.h, and there's not much more that we can do
// to test it, hence I consider that we will have tested Random.h
MatrixType m1 = MatrixType::Random(rows, cols),
m2 = MatrixType::Random(rows, cols),
m3(rows, cols),
mzero = MatrixType::Zero(rows, cols),
square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>::Random(rows, rows);
VectorType v1 = VectorType::Random(rows),
vzero = VectorType::Zero(rows);
SquareMatrixType sm1 = SquareMatrixType::Random(rows,rows), sm2(rows,rows);
Scalar x = 0;
while(x == Scalar(0)) x = internal::random<Scalar>();
Index r = internal::random<Index>(0, rows-1),
c = internal::random<Index>(0, cols-1);
m1.coeffRef(r,c) = x;
VERIFY_IS_APPROX(x, m1.coeff(r,c));
m1(r,c) = x;
VERIFY_IS_APPROX(x, m1(r,c));
v1.coeffRef(r) = x;
VERIFY_IS_APPROX(x, v1.coeff(r));
v1(r) = x;
VERIFY_IS_APPROX(x, v1(r));
v1[r] = x;
VERIFY_IS_APPROX(x, v1[r]);
VERIFY_IS_APPROX( v1, v1);
VERIFY_IS_NOT_APPROX( v1, 2*v1);
VERIFY_IS_MUCH_SMALLER_THAN( vzero, v1);
VERIFY_IS_MUCH_SMALLER_THAN( vzero, v1.squaredNorm());
VERIFY_IS_NOT_MUCH_SMALLER_THAN(v1, v1);
VERIFY_IS_APPROX( vzero, v1-v1);
VERIFY_IS_APPROX( m1, m1);
VERIFY_IS_NOT_APPROX( m1, 2*m1);
VERIFY_IS_MUCH_SMALLER_THAN( mzero, m1);
VERIFY_IS_NOT_MUCH_SMALLER_THAN(m1, m1);
VERIFY_IS_APPROX( mzero, m1-m1);
// always test operator() on each read-only expression class,
// in order to check const-qualifiers.
// indeed, if an expression class (here Zero) is meant to be read-only,
// hence has no _write() method, the corresponding MatrixBase method (here zero())
// should return a const-qualified object so that it is the const-qualified
// operator() that gets called, which in turn calls _read().
VERIFY_IS_MUCH_SMALLER_THAN(MatrixType::Zero(rows,cols)(r,c), static_cast<Scalar>(1));
// now test copying a row-vector into a (column-)vector and conversely.
square.col(r) = square.row(r).eval();
Matrix<Scalar, 1, MatrixType::RowsAtCompileTime> rv(rows);
Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> cv(rows);
rv = square.row(r);
cv = square.col(r);
VERIFY_IS_APPROX(rv, cv.transpose());
if(cols!=1 && rows!=1 && MatrixType::SizeAtCompileTime!=Dynamic)
{
VERIFY_RAISES_ASSERT(m1 = (m2.block(0,0, rows-1, cols-1)));
}
if(cols!=1 && rows!=1)
{
VERIFY_RAISES_ASSERT(m1[0]);
VERIFY_RAISES_ASSERT((m1+m1)[0]);
}
VERIFY_IS_APPROX(m3 = m1,m1);
MatrixType m4;
VERIFY_IS_APPROX(m4 = m1,m1);
m3.real() = m1.real();
VERIFY_IS_APPROX(static_cast<const MatrixType&>(m3).real(), static_cast<const MatrixType&>(m1).real());
VERIFY_IS_APPROX(static_cast<const MatrixType&>(m3).real(), m1.real());
// check == / != operators
VERIFY(m1==m1);
VERIFY(m1!=m2);
VERIFY(!(m1==m2));
VERIFY(!(m1!=m1));
m1 = m2;
VERIFY(m1==m2);
VERIFY(!(m1!=m2));
// check automatic transposition
sm2.setZero();
for(typename MatrixType::Index i=0;i<rows;++i)
sm2.col(i) = sm1.row(i);
VERIFY_IS_APPROX(sm2,sm1.transpose());
sm2.setZero();
for(typename MatrixType::Index i=0;i<rows;++i)
sm2.col(i).noalias() = sm1.row(i);
VERIFY_IS_APPROX(sm2,sm1.transpose());
sm2.setZero();
for(typename MatrixType::Index i=0;i<rows;++i)
sm2.col(i).noalias() += sm1.row(i);
VERIFY_IS_APPROX(sm2,sm1.transpose());
sm2.setZero();
for(typename MatrixType::Index i=0;i<rows;++i)
sm2.col(i).noalias() -= sm1.row(i);
VERIFY_IS_APPROX(sm2,-sm1.transpose());
// check ternary usage
{
bool b = internal::random<int>(0,10)>5;
m3 = b ? m1 : m2;
if(b) VERIFY_IS_APPROX(m3,m1);
else VERIFY_IS_APPROX(m3,m2);
m3 = b ? -m1 : m2;
if(b) VERIFY_IS_APPROX(m3,-m1);
else VERIFY_IS_APPROX(m3,m2);
m3 = b ? m1 : -m2;
if(b) VERIFY_IS_APPROX(m3,m1);
else VERIFY_IS_APPROX(m3,-m2);
}
}
template<typename MatrixType> void basicStuffComplex(const MatrixType& m)
{
typedef typename MatrixType::Index Index;
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime> RealMatrixType;
Index rows = m.rows();
Index cols = m.cols();
Scalar s1 = internal::random<Scalar>(),
s2 = internal::random<Scalar>();
VERIFY(numext::real(s1)==numext::real_ref(s1));
VERIFY(numext::imag(s1)==numext::imag_ref(s1));
numext::real_ref(s1) = numext::real(s2);
numext::imag_ref(s1) = numext::imag(s2);
VERIFY(internal::isApprox(s1, s2, NumTraits<RealScalar>::epsilon()));
// extended precision in Intel FPUs means that s1 == s2 in the line above is not guaranteed.
RealMatrixType rm1 = RealMatrixType::Random(rows,cols),
rm2 = RealMatrixType::Random(rows,cols);
MatrixType cm(rows,cols);
cm.real() = rm1;
cm.imag() = rm2;
VERIFY_IS_APPROX(static_cast<const MatrixType&>(cm).real(), rm1);
VERIFY_IS_APPROX(static_cast<const MatrixType&>(cm).imag(), rm2);
rm1.setZero();
rm2.setZero();
rm1 = cm.real();
rm2 = cm.imag();
VERIFY_IS_APPROX(static_cast<const MatrixType&>(cm).real(), rm1);
VERIFY_IS_APPROX(static_cast<const MatrixType&>(cm).imag(), rm2);
cm.real().setZero();
VERIFY(static_cast<const MatrixType&>(cm).real().isZero());
VERIFY(!static_cast<const MatrixType&>(cm).imag().isZero());
}
#ifdef EIGEN_TEST_PART_2
void casting()
{
Matrix4f m = Matrix4f::Random(), m2;
Matrix4d n = m.cast<double>();
VERIFY(m.isApprox(n.cast<float>()));
m2 = m.cast<float>(); // check the specialization when NewType == Type
VERIFY(m.isApprox(m2));
}
#endif
template <typename Scalar>
void fixedSizeMatrixConstruction()
{
Scalar raw[4];
for(int k=0; k<4; ++k)
raw[k] = internal::random<Scalar>();
{
Matrix<Scalar,4,1> m(raw);
Array<Scalar,4,1> a(raw);
for(int k=0; k<4; ++k) VERIFY(m(k) == raw[k]);
for(int k=0; k<4; ++k) VERIFY(a(k) == raw[k]);
VERIFY_IS_EQUAL(m,(Matrix<Scalar,4,1>(raw[0],raw[1],raw[2],raw[3])));
VERIFY((a==(Array<Scalar,4,1>(raw[0],raw[1],raw[2],raw[3]))).all());
}
{
Matrix<Scalar,3,1> m(raw);
Array<Scalar,3,1> a(raw);
for(int k=0; k<3; ++k) VERIFY(m(k) == raw[k]);
for(int k=0; k<3; ++k) VERIFY(a(k) == raw[k]);
VERIFY_IS_EQUAL(m,(Matrix<Scalar,3,1>(raw[0],raw[1],raw[2])));
VERIFY((a==Array<Scalar,3,1>(raw[0],raw[1],raw[2])).all());
}
{
Matrix<Scalar,2,1> m(raw), m2( (DenseIndex(raw[0])), (DenseIndex(raw[1])) );
Array<Scalar,2,1> a(raw), a2( (DenseIndex(raw[0])), (DenseIndex(raw[1])) );
for(int k=0; k<2; ++k) VERIFY(m(k) == raw[k]);
for(int k=0; k<2; ++k) VERIFY(a(k) == raw[k]);
VERIFY_IS_EQUAL(m,(Matrix<Scalar,2,1>(raw[0],raw[1])));
VERIFY((a==Array<Scalar,2,1>(raw[0],raw[1])).all());
for(int k=0; k<2; ++k) VERIFY(m2(k) == DenseIndex(raw[k]));
for(int k=0; k<2; ++k) VERIFY(a2(k) == DenseIndex(raw[k]));
}
{
Matrix<Scalar,1,2> m(raw),
m2( (DenseIndex(raw[0])), (DenseIndex(raw[1])) ),
m3( (int(raw[0])), (int(raw[1])) ),
m4( (float(raw[0])), (float(raw[1])) );
Array<Scalar,1,2> a(raw), a2( (DenseIndex(raw[0])), (DenseIndex(raw[1])) );
for(int k=0; k<2; ++k) VERIFY(m(k) == raw[k]);
for(int k=0; k<2; ++k) VERIFY(a(k) == raw[k]);
VERIFY_IS_EQUAL(m,(Matrix<Scalar,1,2>(raw[0],raw[1])));
VERIFY((a==Array<Scalar,1,2>(raw[0],raw[1])).all());
for(int k=0; k<2; ++k) VERIFY(m2(k) == DenseIndex(raw[k]));
for(int k=0; k<2; ++k) VERIFY(a2(k) == DenseIndex(raw[k]));
for(int k=0; k<2; ++k) VERIFY(m3(k) == int(raw[k]));
for(int k=0; k<2; ++k) VERIFY((m4(k)) == Scalar(float(raw[k])));
}
{
Matrix<Scalar,1,1> m(raw), m1(raw[0]), m2( (DenseIndex(raw[0])) ), m3( (int(raw[0])) );
Array<Scalar,1,1> a(raw), a1(raw[0]), a2( (DenseIndex(raw[0])) );
VERIFY(m(0) == raw[0]);
VERIFY(a(0) == raw[0]);
VERIFY(m1(0) == raw[0]);
VERIFY(a1(0) == raw[0]);
VERIFY(m2(0) == DenseIndex(raw[0]));
VERIFY(a2(0) == DenseIndex(raw[0]));
VERIFY(m3(0) == int(raw[0]));
VERIFY_IS_EQUAL(m,(Matrix<Scalar,1,1>(raw[0])));
VERIFY((a==Array<Scalar,1,1>(raw[0])).all());
}
}
void test_basicstuff()
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( basicStuff(Matrix<float, 1, 1>()) );
CALL_SUBTEST_2( basicStuff(Matrix4d()) );
CALL_SUBTEST_3( basicStuff(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_4( basicStuff(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_5( basicStuff(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_6( basicStuff(Matrix<float, 100, 100>()) );
CALL_SUBTEST_7( basicStuff(Matrix<long double,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE),internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_3( basicStuffComplex(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_5( basicStuffComplex(MatrixXcd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
}
CALL_SUBTEST_1(fixedSizeMatrixConstruction<unsigned char>());
CALL_SUBTEST_1(fixedSizeMatrixConstruction<float>());
CALL_SUBTEST_1(fixedSizeMatrixConstruction<double>());
CALL_SUBTEST_1(fixedSizeMatrixConstruction<int>());
CALL_SUBTEST_1(fixedSizeMatrixConstruction<long int>());
CALL_SUBTEST_1(fixedSizeMatrixConstruction<std::ptrdiff_t>());
CALL_SUBTEST_2(casting());
}
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