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TriangularMatrix: extend to rectangular matrices

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This commit is contained in:
Benoit Jacob 2009-11-19 17:07:55 -05:00
parent 2275f98d7b
commit a20a744adc
2 changed files with 193 additions and 83 deletions
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93
Eigen/src/Core/TriangularMatrix.h
View File

@ -26,22 +26,11 @@
#ifndef EIGEN_TRIANGULARMATRIX_H #ifndef EIGEN_TRIANGULARMATRIX_H
#define EIGEN_TRIANGULARMATRIX_H #define EIGEN_TRIANGULARMATRIX_H
/** \nonstableyet /** \internal
*
* \class TriangularBase * \class TriangularBase
* *
* \brief Expression of a triangular matrix extracted from a given matrix * \brief Base class for triangular part in a matrix
*
* \param MatrixType the type of the object in which we are taking the triangular part
* \param Mode the kind of triangular matrix expression to construct. Can be UpperTriangular,
* LowerTriangular, UpperSelfadjoint, or LowerSelfadjoint. This is in fact a bit field;
* it must have either UpperBit or LowerBit, and additionnaly it may have either
* TraingularBit or SelfadjointBit.
*
* This class represents an expression of the upper or lower triangular part of
* a square matrix, possibly with a further assumption on the diagonal. It is the return type
* of MatrixBase::part() and most of the time this is the only way it is used.
*
* \sa MatrixBase::part()
*/ */
template<typename Derived> class TriangularBase : public AnyMatrixBase<Derived> template<typename Derived> class TriangularBase : public AnyMatrixBase<Derived>
{ {
@ -115,19 +104,21 @@ template<typename Derived> class TriangularBase : public AnyMatrixBase<Derived>
}; };
/** \class TriangularView /** \class TriangularView
* \nonstableyet
* *
* \brief Expression of a triangular part of a dense matrix * \brief Base class for triangular part in a matrix
* *
* \param MatrixType the type of the dense matrix storing the coefficients * \param MatrixType the type of the object in which we are taking the triangular part
* \param Mode the kind of triangular matrix expression to construct. Can be UpperTriangular,
* LowerTriangular, UpperSelfadjoint, or LowerSelfadjoint. This is in fact a bit field;
* it must have either UpperBit or LowerBit, and additionnaly it may have either
* TraingularBit or SelfadjointBit.
* *
* This class is an expression of a triangular part of a matrix with given dense * This class represents a triangular part of a matrix, not necessarily square. Strictly speaking, for rectangular
* storage of the coefficients. It is the return type of MatrixBase::triangularPart() * matrices one should speak ok "trapezoid" parts. This class is the return type
* and most of the time this is the only way that it is used. * of MatrixBase::triangularView() and most of the time this is the only way it is used.
* *
* \sa class TriangularBase, MatrixBase::triangularPart(), class DiagonalWrapper * \sa MatrixBase::triangularView()
*/ */
template<typename MatrixType, unsigned int _Mode> template<typename MatrixType, unsigned int _Mode>
struct ei_traits<TriangularView<MatrixType, _Mode> > : ei_traits<MatrixType> struct ei_traits<TriangularView<MatrixType, _Mode> > : ei_traits<MatrixType>
@ -155,7 +146,7 @@ template<typename _MatrixType, unsigned int _Mode> class TriangularView
typedef TriangularBase<TriangularView> Base; typedef TriangularBase<TriangularView> Base;
typedef typename ei_traits<TriangularView>::Scalar Scalar; typedef typename ei_traits<TriangularView>::Scalar Scalar;
typedef _MatrixType MatrixType; typedef _MatrixType MatrixType;
typedef typename MatrixType::PlainMatrixType PlainMatrixType; typedef typename MatrixType::PlainMatrixType DenseMatrixType;
typedef typename MatrixType::Nested MatrixTypeNested; typedef typename MatrixType::Nested MatrixTypeNested;
typedef typename ei_cleantype<MatrixTypeNested>::type _MatrixTypeNested; typedef typename ei_cleantype<MatrixTypeNested>::type _MatrixTypeNested;
@ -244,9 +235,9 @@ template<typename _MatrixType, unsigned int _Mode> class TriangularView
inline const TriangularView<NestByValue<Transpose<MatrixType> >,TransposeMode> transpose() const inline const TriangularView<NestByValue<Transpose<MatrixType> >,TransposeMode> transpose() const
{ return m_matrix.transpose().nestByValue(); } { return m_matrix.transpose().nestByValue(); }
PlainMatrixType toDense() const DenseMatrixType toDenseMatrix() const
{ {
PlainMatrixType res(rows(), cols()); DenseMatrixType res(rows(), cols());
res = *this; res = *this;
return res; return res;
} }
@ -351,6 +342,7 @@ struct ei_triangular_assignment_selector
} }
} }
}; };
template<typename Derived1, typename Derived2, unsigned int Mode, bool ClearOpposite> template<typename Derived1, typename Derived2, unsigned int Mode, bool ClearOpposite>
struct ei_triangular_assignment_selector<Derived1, Derived2, Mode, 1, ClearOpposite> struct ei_triangular_assignment_selector<Derived1, Derived2, Mode, 1, ClearOpposite>
{ {
@ -365,6 +357,7 @@ struct ei_triangular_assignment_selector<Derived1, Derived2, Mode, 1, ClearOppos
dst.copyCoeff(0, 0, src); dst.copyCoeff(0, 0, src);
} }
}; };
// prevent buggy user code from causing an infinite recursion // prevent buggy user code from causing an infinite recursion
template<typename Derived1, typename Derived2, unsigned int Mode, bool ClearOpposite> template<typename Derived1, typename Derived2, unsigned int Mode, bool ClearOpposite>
struct ei_triangular_assignment_selector<Derived1, Derived2, Mode, 0, ClearOpposite> struct ei_triangular_assignment_selector<Derived1, Derived2, Mode, 0, ClearOpposite>
@ -379,14 +372,16 @@ struct ei_triangular_assignment_selector<Derived1, Derived2, UpperTriangular, Dy
{ {
for(int j = 0; j < dst.cols(); ++j) for(int j = 0; j < dst.cols(); ++j)
{ {
for(int i = 0; i <= j; ++i) int maxi = std::min(j, dst.rows()-1);
for(int i = 0; i <= maxi; ++i)
dst.copyCoeff(i, j, src); dst.copyCoeff(i, j, src);
if (ClearOpposite) if (ClearOpposite)
for(int i = j+1; i < dst.rows(); ++i) for(int i = maxi+1; i < dst.rows(); ++i)
dst.coeffRef(i, j) = 0; dst.coeffRef(i, j) = 0;
} }
} }
}; };
template<typename Derived1, typename Derived2, bool ClearOpposite> template<typename Derived1, typename Derived2, bool ClearOpposite>
struct ei_triangular_assignment_selector<Derived1, Derived2, LowerTriangular, Dynamic, ClearOpposite> struct ei_triangular_assignment_selector<Derived1, Derived2, LowerTriangular, Dynamic, ClearOpposite>
{ {
@ -396,8 +391,9 @@ struct ei_triangular_assignment_selector<Derived1, Derived2, LowerTriangular, Dy
{ {
for(int i = j; i < dst.rows(); ++i) for(int i = j; i < dst.rows(); ++i)
dst.copyCoeff(i, j, src); dst.copyCoeff(i, j, src);
int maxi = std::min(j, dst.rows());
if (ClearOpposite) if (ClearOpposite)
for(int i = 0; i < j; ++i) for(int i = 0; i < maxi; ++i)
dst.coeffRef(i, j) = 0; dst.coeffRef(i, j) = 0;
} }
} }
@ -410,14 +406,16 @@ struct ei_triangular_assignment_selector<Derived1, Derived2, StrictlyUpperTriang
{ {
for(int j = 0; j < dst.cols(); ++j) for(int j = 0; j < dst.cols(); ++j)
{ {
for(int i = 0; i < j; ++i) int maxi = std::min(j, dst.rows());
for(int i = 0; i < maxi; ++i)
dst.copyCoeff(i, j, src); dst.copyCoeff(i, j, src);
if (ClearOpposite) if (ClearOpposite)
for(int i = j; i < dst.rows(); ++i) for(int i = maxi; i < dst.rows(); ++i)
dst.coeffRef(i, j) = 0; dst.coeffRef(i, j) = 0;
} }
} }
}; };
template<typename Derived1, typename Derived2, bool ClearOpposite> template<typename Derived1, typename Derived2, bool ClearOpposite>
struct ei_triangular_assignment_selector<Derived1, Derived2, StrictlyLowerTriangular, Dynamic, ClearOpposite> struct ei_triangular_assignment_selector<Derived1, Derived2, StrictlyLowerTriangular, Dynamic, ClearOpposite>
{ {
@ -427,8 +425,9 @@ struct ei_triangular_assignment_selector<Derived1, Derived2, StrictlyLowerTriang
{ {
for(int i = j+1; i < dst.rows(); ++i) for(int i = j+1; i < dst.rows(); ++i)
dst.copyCoeff(i, j, src); dst.copyCoeff(i, j, src);
int maxi = std::min(j, dst.rows());
if (ClearOpposite) if (ClearOpposite)
for(int i = 0; i <= j; ++i) for(int i = 0; i <= maxi; ++i)
dst.coeffRef(i, j) = 0; dst.coeffRef(i, j) = 0;
} }
} }
@ -441,11 +440,12 @@ struct ei_triangular_assignment_selector<Derived1, Derived2, UnitUpperTriangular
{ {
for(int j = 0; j < dst.cols(); ++j) for(int j = 0; j < dst.cols(); ++j)
{ {
for(int i = 0; i < j; ++i) int maxi = std::min(j, dst.rows());
for(int i = 0; i < maxi; ++i)
dst.copyCoeff(i, j, src); dst.copyCoeff(i, j, src);
if (ClearOpposite) if (ClearOpposite)
{ {
for(int i = j+1; i < dst.rows(); ++i) for(int i = maxi+1; i < dst.rows(); ++i)
dst.coeffRef(i, j) = 0; dst.coeffRef(i, j) = 0;
dst.coeffRef(j, j) = 1; dst.coeffRef(j, j) = 1;
} }
@ -459,11 +459,12 @@ struct ei_triangular_assignment_selector<Derived1, Derived2, UnitLowerTriangular
{ {
for(int j = 0; j < dst.cols(); ++j) for(int j = 0; j < dst.cols(); ++j)
{ {
for(int i = j+1; i < dst.rows(); ++i) int maxi = std::min(j, dst.rows());
for(int i = maxi+1; i < dst.rows(); ++i)
dst.copyCoeff(i, j, src); dst.copyCoeff(i, j, src);
if (ClearOpposite) if (ClearOpposite)
{ {
for(int i = 0; i < j; ++i) for(int i = 0; i < maxi; ++i)
dst.coeffRef(i, j) = 0; dst.coeffRef(i, j) = 0;
dst.coeffRef(j, j) = 1; dst.coeffRef(j, j) = 1;
} }
@ -514,7 +515,7 @@ TriangularView<MatrixType, Mode>::operator=(const TriangularBase<OtherDerived>&
ei_assert(Mode == OtherDerived::Mode); ei_assert(Mode == OtherDerived::Mode);
if(ei_traits<OtherDerived>::Flags & EvalBeforeAssigningBit) if(ei_traits<OtherDerived>::Flags & EvalBeforeAssigningBit)
{ {
typename OtherDerived::PlainMatrixType other_evaluated(other.rows(), other.cols()); typename OtherDerived::DenseMatrixType other_evaluated(other.rows(), other.cols());
other_evaluated.template triangularView<Mode>().lazyAssign(other.derived()); other_evaluated.template triangularView<Mode>().lazyAssign(other.derived());
lazyAssign(other_evaluated); lazyAssign(other_evaluated);
} }
@ -633,17 +634,20 @@ const TriangularView<Derived, Mode> MatrixBase<Derived>::triangularView() const
template<typename Derived> template<typename Derived>
bool MatrixBase<Derived>::isUpperTriangular(RealScalar prec) const bool MatrixBase<Derived>::isUpperTriangular(RealScalar prec) const
{ {
if(cols() != rows()) return false;
RealScalar maxAbsOnUpperTriangularPart = static_cast<RealScalar>(-1); RealScalar maxAbsOnUpperTriangularPart = static_cast<RealScalar>(-1);
for(int j = 0; j < cols(); ++j) for(int j = 0; j < cols(); ++j)
for(int i = 0; i <= j; ++i) {
int maxi = std::min(j, rows()-1);
for(int i = 0; i <= maxi; ++i)
{ {
RealScalar absValue = ei_abs(coeff(i,j)); RealScalar absValue = ei_abs(coeff(i,j));
if(absValue > maxAbsOnUpperTriangularPart) maxAbsOnUpperTriangularPart = absValue; if(absValue > maxAbsOnUpperTriangularPart) maxAbsOnUpperTriangularPart = absValue;
} }
for(int j = 0; j < cols()-1; ++j) }
RealScalar threshold = maxAbsOnUpperTriangularPart * prec;
for(int j = 0; j < cols(); ++j)
for(int i = j+1; i < rows(); ++i) for(int i = j+1; i < rows(); ++i)
if(!ei_isMuchSmallerThan(coeff(i, j), maxAbsOnUpperTriangularPart, prec)) return false; if(ei_abs(coeff(i, j)) > threshold) return false;
return true; return true;
} }
@ -655,7 +659,6 @@ bool MatrixBase<Derived>::isUpperTriangular(RealScalar prec) const
template<typename Derived> template<typename Derived>
bool MatrixBase<Derived>::isLowerTriangular(RealScalar prec) const bool MatrixBase<Derived>::isLowerTriangular(RealScalar prec) const
{ {
if(cols() != rows()) return false;
RealScalar maxAbsOnLowerTriangularPart = static_cast<RealScalar>(-1); RealScalar maxAbsOnLowerTriangularPart = static_cast<RealScalar>(-1);
for(int j = 0; j < cols(); ++j) for(int j = 0; j < cols(); ++j)
for(int i = j; i < rows(); ++i) for(int i = j; i < rows(); ++i)
@ -663,9 +666,13 @@ bool MatrixBase<Derived>::isLowerTriangular(RealScalar prec) const
RealScalar absValue = ei_abs(coeff(i,j)); RealScalar absValue = ei_abs(coeff(i,j));
if(absValue > maxAbsOnLowerTriangularPart) maxAbsOnLowerTriangularPart = absValue; if(absValue > maxAbsOnLowerTriangularPart) maxAbsOnLowerTriangularPart = absValue;
} }
RealScalar threshold = maxAbsOnLowerTriangularPart * prec;
for(int j = 1; j < cols(); ++j) for(int j = 1; j < cols(); ++j)
for(int i = 0; i < j; ++i) {
if(!ei_isMuchSmallerThan(coeff(i, j), maxAbsOnLowerTriangularPart, prec)) return false; int maxi = std::min(j, rows()-1);
for(int i = 0; i < maxi; ++i)
if(ei_abs(coeff(i, j)) > threshold) return false;
}
return true; return true;
} }

183
test/triangular.cpp
View File

@ -24,7 +24,9 @@
#include "main.h" #include "main.h"
template<typename MatrixType> void triangular(const MatrixType& m)
template<typename MatrixType> void triangular_square(const MatrixType& m)
{ {
typedef typename MatrixType::Scalar Scalar; typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar; typedef typename NumTraits<Scalar>::Real RealScalar;
@ -51,8 +53,8 @@ template<typename MatrixType> void triangular(const MatrixType& m)
v2 = VectorType::Random(rows), v2 = VectorType::Random(rows),
vzero = VectorType::Zero(rows); vzero = VectorType::Zero(rows);
MatrixType m1up = m1.template triangularView<Eigen::UpperTriangular>(); MatrixType m1up = m1.template triangularView<UpperTriangular>();
MatrixType m2up = m2.template triangularView<Eigen::UpperTriangular>(); MatrixType m2up = m2.template triangularView<UpperTriangular>();
if (rows*cols>1) if (rows*cols>1)
{ {
@ -66,20 +68,20 @@ template<typename MatrixType> void triangular(const MatrixType& m)
// test overloaded operator+= // test overloaded operator+=
r1.setZero(); r1.setZero();
r2.setZero(); r2.setZero();
r1.template triangularView<Eigen::UpperTriangular>() += m1; r1.template triangularView<UpperTriangular>() += m1;
r2 += m1up; r2 += m1up;
VERIFY_IS_APPROX(r1,r2); VERIFY_IS_APPROX(r1,r2);
// test overloaded operator= // test overloaded operator=
m1.setZero(); m1.setZero();
m1.template triangularView<Eigen::UpperTriangular>() = m2.transpose() + m2; m1.template triangularView<UpperTriangular>() = m2.transpose() + m2;
m3 = m2.transpose() + m2; m3 = m2.transpose() + m2;
VERIFY_IS_APPROX(m3.template triangularView<Eigen::LowerTriangular>().transpose().toDense(), m1); VERIFY_IS_APPROX(m3.template triangularView<LowerTriangular>().transpose().toDenseMatrix(), m1);
// test overloaded operator= // test overloaded operator=
m1.setZero(); m1.setZero();
m1.template triangularView<Eigen::LowerTriangular>() = m2.transpose() + m2; m1.template triangularView<LowerTriangular>() = m2.transpose() + m2;
VERIFY_IS_APPROX(m3.template triangularView<Eigen::LowerTriangular>().toDense(), m1); VERIFY_IS_APPROX(m3.template triangularView<LowerTriangular>().toDenseMatrix(), m1);
m1 = MatrixType::Random(rows, cols); m1 = MatrixType::Random(rows, cols);
for (int i=0; i<rows; ++i) for (int i=0; i<rows; ++i)
@ -87,49 +89,143 @@ template<typename MatrixType> void triangular(const MatrixType& m)
Transpose<MatrixType> trm4(m4); Transpose<MatrixType> trm4(m4);
// test back and forward subsitution with a vector as the rhs // test back and forward subsitution with a vector as the rhs
m3 = m1.template triangularView<Eigen::UpperTriangular>(); m3 = m1.template triangularView<UpperTriangular>();
VERIFY(v2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Eigen::LowerTriangular>().solve(v2)), largerEps)); VERIFY(v2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<LowerTriangular>().solve(v2)), largerEps));
m3 = m1.template triangularView<Eigen::LowerTriangular>(); m3 = m1.template triangularView<LowerTriangular>();
VERIFY(v2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Eigen::UpperTriangular>().solve(v2)), largerEps)); VERIFY(v2.isApprox(m3.transpose() * (m1.transpose().template triangularView<UpperTriangular>().solve(v2)), largerEps));
m3 = m1.template triangularView<Eigen::UpperTriangular>(); m3 = m1.template triangularView<UpperTriangular>();
VERIFY(v2.isApprox(m3 * (m1.template triangularView<Eigen::UpperTriangular>().solve(v2)), largerEps)); VERIFY(v2.isApprox(m3 * (m1.template triangularView<UpperTriangular>().solve(v2)), largerEps));
m3 = m1.template triangularView<Eigen::LowerTriangular>(); m3 = m1.template triangularView<LowerTriangular>();
VERIFY(v2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Eigen::LowerTriangular>().solve(v2)), largerEps)); VERIFY(v2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<LowerTriangular>().solve(v2)), largerEps));
// test back and forward subsitution with a matrix as the rhs // test back and forward subsitution with a matrix as the rhs
m3 = m1.template triangularView<Eigen::UpperTriangular>(); m3 = m1.template triangularView<UpperTriangular>();
VERIFY(m2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Eigen::LowerTriangular>().solve(m2)), largerEps)); VERIFY(m2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<LowerTriangular>().solve(m2)), largerEps));
m3 = m1.template triangularView<Eigen::LowerTriangular>(); m3 = m1.template triangularView<LowerTriangular>();
VERIFY(m2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Eigen::UpperTriangular>().solve(m2)), largerEps)); VERIFY(m2.isApprox(m3.transpose() * (m1.transpose().template triangularView<UpperTriangular>().solve(m2)), largerEps));
m3 = m1.template triangularView<Eigen::UpperTriangular>(); m3 = m1.template triangularView<UpperTriangular>();
VERIFY(m2.isApprox(m3 * (m1.template triangularView<Eigen::UpperTriangular>().solve(m2)), largerEps)); VERIFY(m2.isApprox(m3 * (m1.template triangularView<UpperTriangular>().solve(m2)), largerEps));
m3 = m1.template triangularView<Eigen::LowerTriangular>(); m3 = m1.template triangularView<LowerTriangular>();
VERIFY(m2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Eigen::LowerTriangular>().solve(m2)), largerEps)); VERIFY(m2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<LowerTriangular>().solve(m2)), largerEps));
// check M * inv(L) using in place API // check M * inv(L) using in place API
m4 = m3; m4 = m3;
m3.transpose().template triangularView<Eigen::UpperTriangular>().solveInPlace(trm4); m3.transpose().template triangularView<UpperTriangular>().solveInPlace(trm4);
VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>())); VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>()));
// check M * inv(U) using in place API // check M * inv(U) using in place API
m3 = m1.template triangularView<Eigen::UpperTriangular>(); m3 = m1.template triangularView<UpperTriangular>();
m4 = m3; m4 = m3;
m3.transpose().template triangularView<Eigen::LowerTriangular>().solveInPlace(trm4); m3.transpose().template triangularView<LowerTriangular>().solveInPlace(trm4);
VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>())); VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>()));
// check solve with unit diagonal // check solve with unit diagonal
m3 = m1.template triangularView<Eigen::UnitUpperTriangular>(); m3 = m1.template triangularView<UnitUpperTriangular>();
VERIFY(m2.isApprox(m3 * (m1.template triangularView<Eigen::UnitUpperTriangular>().solve(m2)), largerEps)); VERIFY(m2.isApprox(m3 * (m1.template triangularView<UnitUpperTriangular>().solve(m2)), largerEps));
// VERIFY(( m1.template triangularView<Eigen::UpperTriangular>() // VERIFY(( m1.template triangularView<UpperTriangular>()
// * m2.template triangularView<Eigen::UpperTriangular>()).isUpperTriangular()); // * m2.template triangularView<UpperTriangular>()).isUpperTriangular());
// test swap // test swap
m1.setOnes(); m1.setOnes();
m2.setZero(); m2.setZero();
m2.template triangularView<Eigen::UpperTriangular>().swap(m1); m2.template triangularView<UpperTriangular>().swap(m1);
m3.setZero(); m3.setZero();
m3.template triangularView<Eigen::UpperTriangular>().setOnes(); m3.template triangularView<UpperTriangular>().setOnes();
VERIFY_IS_APPROX(m2,m3);
}
template<typename MatrixType> void triangular_rect(const MatrixType& m)
{
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
int rows = m.rows();
int cols = m.cols();
MatrixType m1 = MatrixType::Random(rows, cols),
m2 = MatrixType::Random(rows, cols),
m3(rows, cols),
m4(rows, cols),
r1(rows, cols),
r2(rows, cols),
mzero = MatrixType::Zero(rows, cols),
mones = MatrixType::Ones(rows, cols),
identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
::Identity(rows, rows),
square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
::Random(rows, rows);
VectorType v1 = VectorType::Random(rows),
v2 = VectorType::Random(rows),
vzero = VectorType::Zero(rows);
MatrixType m1up = m1.template triangularView<UpperTriangular>();
MatrixType m2up = m2.template triangularView<UpperTriangular>();
if (rows*cols>1)
{
VERIFY(m1up.isUpperTriangular());
VERIFY(m2up.transpose().isLowerTriangular());
VERIFY(!m2.isLowerTriangular());
}
// VERIFY_IS_APPROX(m1up.transpose() * m2, m1.upper().transpose().lower() * m2);
// test overloaded operator+=
r1.setZero();
r2.setZero();
r1.template triangularView<UpperTriangular>() += m1;
r2 += m1up;
VERIFY_IS_APPROX(r1,r2);
// test overloaded operator=
m1.setZero();
m1.template triangularView<UpperTriangular>() = 3 * m2;
m3 = 3 * m2;
VERIFY_IS_APPROX(m3.template triangularView<UpperTriangular>().toDenseMatrix(), m1);
m1.setZero();
m1.template triangularView<LowerTriangular>() = 3 * m2;
VERIFY_IS_APPROX(m3.template triangularView<LowerTriangular>().toDenseMatrix(), m1);
m1.setZero();
m1.template triangularView<StrictlyUpperTriangular>() = 3 * m2;
VERIFY_IS_APPROX(m3.template triangularView<StrictlyUpperTriangular>().toDenseMatrix(), m1);
m1.setZero();
m1.template triangularView<StrictlyLowerTriangular>() = 3 * m2;
VERIFY_IS_APPROX(m3.template triangularView<StrictlyLowerTriangular>().toDenseMatrix(), m1);
m1.setRandom();
m2 = m1.template triangularView<UpperTriangular>();
VERIFY(m2.isUpperTriangular());
VERIFY(!m2.isLowerTriangular());
m2 = m1.template triangularView<StrictlyUpperTriangular>();
VERIFY(m2.isUpperTriangular());
VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
m2 = m1.template triangularView<UnitUpperTriangular>();
VERIFY(m2.isUpperTriangular());
m2.diagonal().cwise() -= Scalar(1);
VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
m2 = m1.template triangularView<LowerTriangular>();
VERIFY(m2.isLowerTriangular());
VERIFY(!m2.isUpperTriangular());
m2 = m1.template triangularView<StrictlyLowerTriangular>();
VERIFY(m2.isLowerTriangular());
VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
m2 = m1.template triangularView<UnitLowerTriangular>();
VERIFY(m2.isLowerTriangular());
m2.diagonal().cwise() -= Scalar(1);
VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
// test swap
m1.setOnes();
m2.setZero();
m2.template triangularView<UpperTriangular>().swap(m1);
m3.setZero();
m3.template triangularView<UpperTriangular>().setOnes();
VERIFY_IS_APPROX(m2,m3); VERIFY_IS_APPROX(m2,m3);
} }
@ -137,12 +233,19 @@ template<typename MatrixType> void triangular(const MatrixType& m)
void test_triangular() void test_triangular()
{ {
for(int i = 0; i < g_repeat ; i++) { for(int i = 0; i < g_repeat ; i++) {
CALL_SUBTEST_1( triangular(Matrix<float, 1, 1>()) ); CALL_SUBTEST_1( triangular_square(Matrix<float, 1, 1>()) );
CALL_SUBTEST_2( triangular(Matrix<float, 2, 2>()) ); CALL_SUBTEST_2( triangular_square(Matrix<float, 2, 2>()) );
CALL_SUBTEST_3( triangular(Matrix3d()) ); CALL_SUBTEST_3( triangular_square(Matrix3d()) );
CALL_SUBTEST_4( triangular(MatrixXcf(4, 4)) ); CALL_SUBTEST_4( triangular_square(MatrixXcf(4, 4)) );
CALL_SUBTEST_5( triangular(Matrix<std::complex<float>,8, 8>()) ); CALL_SUBTEST_5( triangular_square(Matrix<std::complex<float>,8, 8>()) );
CALL_SUBTEST_6( triangular(MatrixXcd(17,17)) ); CALL_SUBTEST_6( triangular_square(MatrixXcd(17,17)) );
CALL_SUBTEST_7( triangular(Matrix<float,Dynamic,Dynamic,RowMajor>(5, 5)) ); CALL_SUBTEST_7( triangular_square(Matrix<float,Dynamic,Dynamic,RowMajor>(5, 5)) );
CALL_SUBTEST_8( triangular_rect(Matrix<float, 4, 5>()) );
CALL_SUBTEST_9( triangular_rect(Matrix<double, 6, 2>()) );
CALL_SUBTEST_4( triangular_rect(MatrixXcf(4, 10)) );
CALL_SUBTEST_6( triangular_rect(MatrixXcd(11, 3)) );
CALL_SUBTEST_7( triangular_rect(Matrix<float,Dynamic,Dynamic,RowMajor>(7, 6)) );
} }
} }