template<typename MatrixType> void determinant(const MatrixType& m)
{
/* this test covers the following files:
Determinant.h
*/
typedef typename MatrixType::Index Index;
Index size = m.rows();
MatrixType m1(size, size), m2(size, size);
m1.setRandom();
m2.setRandom();
typedef typename MatrixType::Scalar Scalar;
Scalar x = ei_random<Scalar>();
VERIFY_IS_APPROX(MatrixType::Identity(size, size).determinant(), Scalar(1));
VERIFY_IS_APPROX((m1*m2).eval().determinant(), m1.determinant() * m2.determinant());
if(size==1) return;
Index i = ei_random<Index>(0, size-1);
Index j;
do {
j = ei_random<Index>(0, size-1);
} while(j==i);
m2 = m1;
m2.row(i).swap(m2.row(j));
VERIFY_IS_APPROX(m2.determinant(), -m1.determinant());
m2 = m1;
m2.col(i).swap(m2.col(j));
VERIFY_IS_APPROX(m2.determinant(), -m1.determinant());
VERIFY_IS_APPROX(m2.determinant(), m2.transpose().determinant());
VERIFY_IS_APPROX(ei_conj(m2.determinant()), m2.adjoint().determinant());
m2 = m1;
m2.row(i) += x*m2.row(j);
VERIFY_IS_APPROX(m2.determinant(), m1.determinant());
m2 = m1;
m2.row(i) *= x;
VERIFY_IS_APPROX(m2.determinant(), m1.determinant() * x);
// check empty matrix
VERIFY_IS_APPROX(m2.block(0,0,0,0).determinant(), Scalar(1));
}
template<typename Scalar> void trmm(int size,int /*othersize*/)
{
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar,Dynamic,Dynamic,ColMajor> MatrixColMaj;
typedef Matrix<Scalar,Dynamic,Dynamic,RowMajor> MatrixRowMaj;
DenseIndex rows = size;
DenseIndex cols = ei_random<DenseIndex>(1,size);
MatrixColMaj triV(rows,cols), triH(cols,rows), upTri(cols,rows), loTri(rows,cols),
unitUpTri(cols,rows), unitLoTri(rows,cols), strictlyUpTri(cols,rows), strictlyLoTri(rows,cols);
MatrixColMaj ge1(rows,cols), ge2(cols,rows), ge3;
MatrixRowMaj rge3;
Scalar s1 = ei_random<Scalar>(),
s2 = ei_random<Scalar>();
triV.setRandom();
triH.setRandom();
loTri = triV.template triangularView<Lower>();
upTri = triH.template triangularView<Upper>();
unitLoTri = triV.template triangularView<UnitLower>();
unitUpTri = triH.template triangularView<UnitUpper>();
strictlyLoTri = triV.template triangularView<StrictlyLower>();
strictlyUpTri = triH.template triangularView<StrictlyUpper>();
ge1.setRandom();
ge2.setRandom();
VERIFY_IS_APPROX( ge3 = triV.template triangularView<Lower>() * ge2, loTri * ge2);
VERIFY_IS_APPROX( ge3 = ge2 * triV.template triangularView<Lower>(), ge2 * loTri);
VERIFY_IS_APPROX( ge3 = triH.template triangularView<Upper>() * ge1, upTri * ge1);
VERIFY_IS_APPROX( ge3 = ge1 * triH.template triangularView<Upper>(), ge1 * upTri);
VERIFY_IS_APPROX( ge3 = (s1*triV.adjoint()).template triangularView<Upper>() * (s2*ge1), s1*loTri.adjoint() * (s2*ge1));
VERIFY_IS_APPROX( ge3 = ge1 * triV.adjoint().template triangularView<Upper>(), ge1 * loTri.adjoint());
VERIFY_IS_APPROX( ge3 = triH.adjoint().template triangularView<Lower>() * ge2, upTri.adjoint() * ge2);
VERIFY_IS_APPROX( ge3 = ge2 * triH.adjoint().template triangularView<Lower>(), ge2 * upTri.adjoint());
VERIFY_IS_APPROX( ge3 = triV.template triangularView<Lower>() * ge1.adjoint(), loTri * ge1.adjoint());
VERIFY_IS_APPROX( ge3 = ge1.adjoint() * triV.template triangularView<Lower>(), ge1.adjoint() * loTri);
VERIFY_IS_APPROX( ge3 = triH.template triangularView<Upper>() * ge2.adjoint(), upTri * ge2.adjoint());
VERIFY_IS_APPROX(rge3.noalias() = triH.template triangularView<Upper>() * ge2.adjoint(), upTri * ge2.adjoint());
VERIFY_IS_APPROX( ge3 = (s1*triV).adjoint().template triangularView<Upper>() * ge2.adjoint(), ei_conj(s1) * loTri.adjoint() * ge2.adjoint());
VERIFY_IS_APPROX(rge3.noalias() = triV.adjoint().template triangularView<Upper>() * ge2.adjoint(), loTri.adjoint() * ge2.adjoint());
VERIFY_IS_APPROX( ge3 = triH.adjoint().template triangularView<Lower>() * ge1.adjoint(), upTri.adjoint() * ge1.adjoint());
VERIFY_IS_APPROX(rge3.noalias() = triH.adjoint().template triangularView<Lower>() * ge1.adjoint(), upTri.adjoint() * ge1.adjoint());
VERIFY_IS_APPROX( ge3 = triV.template triangularView<UnitLower>() * ge2, unitLoTri * ge2);
VERIFY_IS_APPROX( rge3.noalias() = ge2 * triV.template triangularView<UnitLower>(), ge2 * unitLoTri);
VERIFY_IS_APPROX( ge3 = ge2 * triV.template triangularView<UnitLower>(), ge2 * unitLoTri);
VERIFY_IS_APPROX( ge3 = (s1*triV).adjoint().template triangularView<UnitUpper>() * ge2.adjoint(), ei_conj(s1) * unitLoTri.adjoint() * ge2.adjoint());
VERIFY_IS_APPROX( ge3 = triV.template triangularView<StrictlyLower>() * ge2, strictlyLoTri * ge2);
VERIFY_IS_APPROX( rge3.noalias() = ge2 * triV.template triangularView<StrictlyLower>(), ge2 * strictlyLoTri);
VERIFY_IS_APPROX( ge3 = ge2 * triV.template triangularView<StrictlyLower>(), ge2 * strictlyLoTri);
VERIFY_IS_APPROX( ge3 = (s1*triV).adjoint().template triangularView<StrictlyUpper>() * ge2.adjoint(), ei_conj(s1) * strictlyLoTri.adjoint() * ge2.adjoint());
}
template<typename MatrixType> void adjoint(const MatrixType& m)
{
/* this test covers the following files:
Transpose.h Conjugate.h Dot.h
*/
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
int rows = m.rows();
int cols = m.cols();
RealScalar largerEps = test_precision<RealScalar>();
if (ei_is_same_type<RealScalar,float>::ret)
largerEps = RealScalar(1e-3f);
MatrixType m1 = MatrixType::Random(rows, cols),
m2 = MatrixType::Random(rows, cols),
m3(rows, cols),
mzero = MatrixType::Zero(rows, cols),
identity = SquareMatrixType::Identity(rows, rows),
square = SquareMatrixType::Random(rows, rows);
VectorType v1 = VectorType::Random(rows),
v2 = VectorType::Random(rows),
v3 = VectorType::Random(rows),
vzero = VectorType::Zero(rows);
Scalar s1 = ei_random<Scalar>(),
s2 = ei_random<Scalar>();
// check basic compatibility of adjoint, transpose, conjugate
VERIFY_IS_APPROX(m1.transpose().conjugate().adjoint(), m1);
VERIFY_IS_APPROX(m1.adjoint().conjugate().transpose(), m1);
// check multiplicative behavior
VERIFY_IS_APPROX((m1.adjoint() * m2).adjoint(), m2.adjoint() * m1);
VERIFY_IS_APPROX((s1 * m1).adjoint(), ei_conj(s1) * m1.adjoint());
// check basic properties of dot, norm, norm2
typedef typename NumTraits<Scalar>::Real RealScalar;
VERIFY(ei_isApprox((s1 * v1 + s2 * v2).dot(v3), s1 * v1.dot(v3) + s2 * v2.dot(v3), largerEps));
VERIFY(ei_isApprox(v3.dot(s1 * v1 + s2 * v2), ei_conj(s1)*v3.dot(v1)+ei_conj(s2)*v3.dot(v2), largerEps));
VERIFY_IS_APPROX(ei_conj(v1.dot(v2)), v2.dot(v1));
VERIFY_IS_APPROX(ei_abs(v1.dot(v1)), v1.squaredNorm());
if(NumTraits<Scalar>::HasFloatingPoint)
VERIFY_IS_APPROX(v1.squaredNorm(), v1.norm() * v1.norm());
VERIFY_IS_MUCH_SMALLER_THAN(ei_abs(vzero.dot(v1)), static_cast<RealScalar>(1));
if(NumTraits<Scalar>::HasFloatingPoint)
VERIFY_IS_MUCH_SMALLER_THAN(vzero.norm(), static_cast<RealScalar>(1));
// check compatibility of dot and adjoint
VERIFY(ei_isApprox(v1.dot(square * v2), (square.adjoint() * v1).dot(v2), largerEps));
// like in testBasicStuff, test operator() to check const-qualification
int r = ei_random<int>(0, rows-1),
c = ei_random<int>(0, cols-1);
VERIFY_IS_APPROX(m1.conjugate()(r,c), ei_conj(m1(r,c)));
VERIFY_IS_APPROX(m1.adjoint()(c,r), ei_conj(m1(r,c)));
if(NumTraits<Scalar>::HasFloatingPoint)
{
// check that Random().normalized() works: tricky as the random xpr must be evaluated by
// normalized() in order to produce a consistent result.
VERIFY_IS_APPROX(VectorType::Random(rows).normalized().norm(), RealScalar(1));
}
// check inplace transpose
m3 = m1;
m3.transposeInPlace();
VERIFY_IS_APPROX(m3,m1.transpose());
m3.transposeInPlace();
VERIFY_IS_APPROX(m3,m1);
}
