mirror of
https://gitlab.com/libeigen/eigen.git
synced 2025-05-02 08:44:12 +08:00
Implement complex MatrixPowerTriangular. There are still problems with real one.
This commit is contained in:
Chen-Pang He
parent
209199a13e
commit
332eb36436
@ -163,8 +163,8 @@ template<typename Derived> class MatrixBase
|
||||
template<typename ProductDerived, typename Lhs, typename Rhs>
|
||||
Derived& lazyAssign(const ProductBase<ProductDerived, Lhs,Rhs>& other);
|
||||
|
||||
template<typename ProductDerived, typename Lhs, typename Rhs>
|
||||
Derived& lazyAssign(const MatrixPowerProductBase<ProductDerived, Lhs,Rhs>& other);
|
||||
template<typename MatrixPower, typename Lhs, typename Rhs>
|
||||
Derived& lazyAssign(const MatrixPowerProduct<MatrixPower, Lhs,Rhs>& other);
|
||||
#endif // not EIGEN_PARSED_BY_DOXYGEN
|
||||
|
||||
template<typename OtherDerived>
|
||||
|
||||
@ -271,7 +271,7 @@ template<typename Derived> class MatrixFunctionReturnValue;
|
||||
template<typename Derived> class MatrixSquareRootReturnValue;
|
||||
template<typename Derived> class MatrixLogarithmReturnValue;
|
||||
template<typename Derived> class MatrixPowerReturnValue;
|
||||
template<typename Derived, typename Lhs, typename Rhs> class MatrixPowerProductBase;
|
||||
template<typename Derived, typename Lhs, typename Rhs> class MatrixPowerProduct;
|
||||
|
||||
namespace internal {
|
||||
template <typename Scalar>
|
||||
|
||||
@ -12,7 +12,222 @@
|
||||
|
||||
namespace Eigen {
|
||||
|
||||
template<typename MatrixType> class MatrixPowerEvaluator;
|
||||
/**
|
||||
* \ingroup MatrixFunctions_Module
|
||||
*
|
||||
* \brief Class for computing matrix powers.
|
||||
*
|
||||
* \tparam MatrixType type of the base, expected to be an instantiation
|
||||
* of the Matrix class template.
|
||||
*
|
||||
* This class is capable of computing complex upper triangular matrices raised
|
||||
* to an arbitrary real power.
|
||||
*/
|
||||
template<typename MatrixType>
|
||||
class MatrixPowerTriangular : public MatrixPowerBase<MatrixPowerTriangular<MatrixType>,MatrixType>
|
||||
{
|
||||
public:
|
||||
EIGEN_MATRIX_POWER_PUBLIC_INTERFACE(MatrixPowerTriangular)
|
||||
|
||||
/**
|
||||
* \brief Constructor.
|
||||
*
|
||||
* \param[in] A the base of the matrix power.
|
||||
*
|
||||
* The class stores a reference to A, so it should not be changed
|
||||
* (or destroyed) before evaluation.
|
||||
*/
|
||||
explicit MatrixPowerTriangular(const MatrixType& A) : Base(A,0), m_T(Base::m_A)
|
||||
{ }
|
||||
|
||||
#ifdef EIGEN_PARSED_BY_DOXYGEN
|
||||
/**
|
||||
* \brief Returns the matrix power.
|
||||
*
|
||||
* \param[in] p exponent, a real scalar.
|
||||
* \return The expression \f$ A^p \f$, where A is specified in the
|
||||
* constructor.
|
||||
*/
|
||||
const MatrixPowerBaseReturnValue<MatrixPowerTriangular<MatrixType>,MatrixType> operator()(RealScalar p);
|
||||
#endif
|
||||
|
||||
/**
|
||||
* \brief Compute the matrix power.
|
||||
*
|
||||
* \param[in] p exponent, a real scalar.
|
||||
* \param[out] res \f$ A^p \f$ where A is specified in the
|
||||
* constructor.
|
||||
*/
|
||||
void compute(MatrixType& res, RealScalar p);
|
||||
|
||||
/**
|
||||
* \brief Compute the matrix power multiplied by another matrix.
|
||||
*
|
||||
* \param[in] b a matrix with the same rows as A.
|
||||
* \param[in] p exponent, a real scalar.
|
||||
* \param[out] res \f$ A^p b \f$, where A is specified in the
|
||||
* constructor.
|
||||
*/
|
||||
template<typename Derived, typename ResultType>
|
||||
void compute(const Derived& b, ResultType& res, RealScalar p);
|
||||
|
||||
private:
|
||||
EIGEN_MATRIX_POWER_PROTECTED_MEMBERS(MatrixPowerTriangular)
|
||||
|
||||
const TriangularView<MatrixType,Upper> m_T;
|
||||
|
||||
RealScalar modfAndInit(RealScalar, RealScalar*);
|
||||
|
||||
template<typename Derived, typename ResultType>
|
||||
void apply(const Derived&, ResultType&, bool&);
|
||||
|
||||
template<typename ResultType>
|
||||
void computeIntPower(ResultType&, RealScalar);
|
||||
|
||||
template<typename Derived, typename ResultType>
|
||||
void computeIntPower(const Derived&, ResultType&, RealScalar);
|
||||
|
||||
template<typename ResultType>
|
||||
void computeFracPower(ResultType&, RealScalar);
|
||||
};
|
||||
|
||||
template<typename MatrixType>
|
||||
void MatrixPowerTriangular<MatrixType>::compute(MatrixType& res, RealScalar p)
|
||||
{
|
||||
switch (m_A.cols()) {
|
||||
case 0:
|
||||
break;
|
||||
case 1:
|
||||
res(0,0) = std::pow(m_T.coeff(0,0), p);
|
||||
break;
|
||||
default:
|
||||
RealScalar intpart, x = modfAndInit(p, &intpart);
|
||||
res = m_Id;
|
||||
computeIntPower(res, intpart);
|
||||
computeFracPower(res, x);
|
||||
}
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
template<typename Derived, typename ResultType>
|
||||
void MatrixPowerTriangular<MatrixType>::compute(const Derived& b, ResultType& res, RealScalar p)
|
||||
{
|
||||
switch (m_A.cols()) {
|
||||
case 0:
|
||||
break;
|
||||
case 1:
|
||||
res = std::pow(m_T.coeff(0,0), p) * b;
|
||||
break;
|
||||
default:
|
||||
RealScalar intpart, x = modfAndInit(p, &intpart);
|
||||
computeIntPower(b, res, intpart);
|
||||
computeFracPower(res, x);
|
||||
}
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
typename MatrixPowerTriangular<MatrixType>::Base::RealScalar
|
||||
MatrixPowerTriangular<MatrixType>::modfAndInit(RealScalar x, RealScalar* intpart)
|
||||
{
|
||||
*intpart = std::floor(x);
|
||||
RealScalar res = x - *intpart;
|
||||
|
||||
if (!m_conditionNumber && res) {
|
||||
const RealArray absTdiag = m_A.diagonal().array().abs();
|
||||
m_conditionNumber = absTdiag.maxCoeff() / absTdiag.minCoeff();
|
||||
}
|
||||
|
||||
if (res>RealScalar(0.5) && res>(1-res)*std::pow(m_conditionNumber,res)) {
|
||||
--res;
|
||||
++*intpart;
|
||||
}
|
||||
return res;
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
template<typename Derived, typename ResultType>
|
||||
void MatrixPowerTriangular<MatrixType>::apply(const Derived& b, ResultType& res, bool& init)
|
||||
{
|
||||
if (init)
|
||||
res = m_tmp1.template triangularView<Upper>() * res;
|
||||
else {
|
||||
init = true;
|
||||
res.noalias() = m_tmp1.template triangularView<Upper>() * b;
|
||||
}
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
template<typename ResultType>
|
||||
void MatrixPowerTriangular<MatrixType>::computeIntPower(ResultType& res, RealScalar p)
|
||||
{
|
||||
RealScalar pp = std::abs(p);
|
||||
|
||||
if (p<0) m_tmp1 = m_T.solve(m_Id);
|
||||
else m_tmp1 = m_T;
|
||||
|
||||
while (pp >= 1) {
|
||||
if (std::fmod(pp, 2) >= 1)
|
||||
res = m_tmp1.template triangularView<Upper>() * res;
|
||||
m_tmp1 = m_tmp1.template triangularView<Upper>() * m_tmp1;
|
||||
pp /= 2;
|
||||
}
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
template<typename Derived, typename ResultType>
|
||||
void MatrixPowerTriangular<MatrixType>::computeIntPower(const Derived& b, ResultType& res, RealScalar p)
|
||||
{
|
||||
if (b.cols() >= m_A.cols()) {
|
||||
m_tmp2 = m_Id;
|
||||
computeIntPower(m_tmp2, p);
|
||||
res.noalias() = m_tmp2.template triangularView<Upper>() * b;
|
||||
}
|
||||
else {
|
||||
RealScalar pp = std::abs(p);
|
||||
int squarings, applyings = internal::binary_powering_cost(pp, &squarings);
|
||||
bool init = false;
|
||||
|
||||
if (p==0) {
|
||||
res = b;
|
||||
return;
|
||||
}
|
||||
else if (p>0) {
|
||||
m_tmp1 = m_T;
|
||||
}
|
||||
else if (m_A.cols() > 2 && b.cols()*(pp-applyings) <= m_A.cols()*squarings) {
|
||||
res = m_T.solve(b);
|
||||
for (--pp; pp >= 1; --pp)
|
||||
res = m_T.solve(res);
|
||||
return;
|
||||
}
|
||||
else {
|
||||
m_tmp1 = m_T.solve(m_Id);
|
||||
}
|
||||
|
||||
while (b.cols()*(pp-applyings) > m_A.cols()*squarings) {
|
||||
if (std::fmod(pp, 2) >= 1) {
|
||||
apply(b, res, init);
|
||||
--applyings;
|
||||
}
|
||||
m_tmp1 = m_tmp1.template triangularView<Upper>() * m_tmp1;
|
||||
--squarings;
|
||||
pp /= 2;
|
||||
}
|
||||
for (; pp >= 1; --pp)
|
||||
apply(b, res, init);
|
||||
}
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
template<typename ResultType>
|
||||
void MatrixPowerTriangular<MatrixType>::computeFracPower(ResultType& res, RealScalar p)
|
||||
{
|
||||
if (p) {
|
||||
eigen_assert(m_conditionNumber);
|
||||
MatrixPowerTriangularAtomic<MatrixType>(m_A).compute(m_tmp1, p);
|
||||
res = m_tmp1.template triangularView<Upper>() * res;
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* \ingroup MatrixFunctions_Module
|
||||
@ -44,18 +259,22 @@ class MatrixPower : public MatrixPowerBase<MatrixPower<MatrixType>,MatrixType>
|
||||
*
|
||||
* \param[in] A the base of the matrix power.
|
||||
*
|
||||
* \warning Construct with a matrix, not a matrix expression!
|
||||
* The class stores a reference to A, so it should not be changed
|
||||
* (or destroyed) before evaluation.
|
||||
*/
|
||||
explicit MatrixPower(const MatrixType& A) : Base(A,0)
|
||||
{ }
|
||||
|
||||
#ifdef EIGEN_PARSED_BY_DOXYGEN
|
||||
/**
|
||||
* \brief Return the expression \f$ A^p \f$.
|
||||
* \brief Returns the matrix power.
|
||||
*
|
||||
* \param[in] p exponent, a real scalar.
|
||||
* \return The expression \f$ A^p \f$, where A is specified in the
|
||||
* constructor.
|
||||
*/
|
||||
const MatrixPowerEvaluator<MatrixType> operator()(RealScalar p)
|
||||
{ return MatrixPowerEvaluator<MatrixType>(*this, p); }
|
||||
const MatrixPowerBaseReturnValue<MatrixPower<MatrixType>,MatrixType> operator()(RealScalar p);
|
||||
#endif
|
||||
|
||||
/**
|
||||
* \brief Compute the matrix power.
|
||||
@ -242,31 +461,13 @@ void MatrixPower<MatrixType>::computeFracPower(ResultType& res, RealScalar p)
|
||||
}
|
||||
}
|
||||
|
||||
template<typename Lhs, typename Rhs>
|
||||
class MatrixPowerMatrixProduct : public MatrixPowerProductBase<MatrixPowerMatrixProduct<Lhs,Rhs>,Lhs,Rhs>
|
||||
{
|
||||
public:
|
||||
EIGEN_MATRIX_POWER_PRODUCT_PUBLIC_INTERFACE(MatrixPowerMatrixProduct)
|
||||
namespace internal {
|
||||
|
||||
MatrixPowerMatrixProduct(MatrixPower<Lhs>& pow, const Rhs& b, RealScalar p) :
|
||||
m_pow(pow),
|
||||
m_b(b),
|
||||
m_p(p)
|
||||
{ }
|
||||
template<typename Derived>
|
||||
struct traits<MatrixPowerReturnValue<Derived> >
|
||||
{ typedef typename Derived::PlainObject ReturnType; };
|
||||
|
||||
template<typename ResultType>
|
||||
inline void evalTo(ResultType& res) const
|
||||
{ m_pow.compute(m_b, res, m_p); }
|
||||
|
||||
Index rows() const { return m_pow.rows(); }
|
||||
Index cols() const { return m_b.cols(); }
|
||||
|
||||
private:
|
||||
MatrixPower<Lhs>& m_pow;
|
||||
const Rhs& m_b;
|
||||
const RealScalar m_p;
|
||||
MatrixPowerMatrixProduct& operator=(const MatrixPowerMatrixProduct&);
|
||||
};
|
||||
} // namespace internal
|
||||
|
||||
/**
|
||||
* \ingroup MatrixFunctions_Module
|
||||
@ -316,10 +517,11 @@ class MatrixPowerReturnValue : public ReturnByValue<MatrixPowerReturnValue<Deriv
|
||||
* \param[in] b the matrix (expression) to be applied.
|
||||
*/
|
||||
template<typename OtherDerived>
|
||||
const MatrixPowerMatrixProduct<PlainObject,OtherDerived> operator*(const MatrixBase<OtherDerived>& b) const
|
||||
const MatrixPowerProduct<MatrixPower<PlainObject>,PlainObject,OtherDerived>
|
||||
operator*(const MatrixBase<OtherDerived>& b) const
|
||||
{
|
||||
MatrixPower<PlainObject> Apow(m_A.eval());
|
||||
return MatrixPowerMatrixProduct<PlainObject,OtherDerived>(Apow, b.derived(), m_p);
|
||||
return MatrixPowerProduct<MatrixPower<PlainObject>,PlainObject,OtherDerived>(Apow, b.derived(), m_p);
|
||||
}
|
||||
|
||||
Index rows() const { return m_A.rows(); }
|
||||
@ -331,52 +533,6 @@ class MatrixPowerReturnValue : public ReturnByValue<MatrixPowerReturnValue<Deriv
|
||||
MatrixPowerReturnValue& operator=(const MatrixPowerReturnValue&);
|
||||
};
|
||||
|
||||
template<typename MatrixType>
|
||||
class MatrixPowerEvaluator : public ReturnByValue<MatrixPowerEvaluator<MatrixType> >
|
||||
{
|
||||
public:
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
typedef typename MatrixType::Index Index;
|
||||
|
||||
MatrixPowerEvaluator(MatrixPower<MatrixType>& pow, RealScalar p) : m_pow(pow), m_p(p)
|
||||
{ }
|
||||
|
||||
template<typename ResultType>
|
||||
inline void evalTo(ResultType& res) const
|
||||
{ m_pow.compute(res, m_p); }
|
||||
|
||||
template<typename Derived>
|
||||
const MatrixPowerMatrixProduct<MatrixType,Derived> operator*(const MatrixBase<Derived>& b) const
|
||||
{ return MatrixPowerMatrixProduct<MatrixType,Derived>(m_pow, b.derived(), m_p); }
|
||||
|
||||
Index rows() const { return m_pow.rows(); }
|
||||
Index cols() const { return m_pow.cols(); }
|
||||
|
||||
private:
|
||||
MatrixPower<MatrixType>& m_pow;
|
||||
const RealScalar m_p;
|
||||
MatrixPowerEvaluator& operator=(const MatrixPowerEvaluator&);
|
||||
};
|
||||
|
||||
namespace internal {
|
||||
template<typename Lhs, typename Rhs>
|
||||
struct nested<MatrixPowerMatrixProduct<Lhs,Rhs> >
|
||||
{ typedef typename MatrixPowerMatrixProduct<Lhs,Rhs>::PlainObject const& type; };
|
||||
|
||||
template<typename Derived>
|
||||
struct traits<MatrixPowerReturnValue<Derived> >
|
||||
{ typedef typename Derived::PlainObject ReturnType; };
|
||||
|
||||
template<typename MatrixType>
|
||||
struct traits<MatrixPowerEvaluator<MatrixType> >
|
||||
{ typedef MatrixType ReturnType; };
|
||||
|
||||
template<typename Lhs, typename Rhs>
|
||||
struct traits<MatrixPowerMatrixProduct<Lhs,Rhs> >
|
||||
: traits<MatrixPowerProductBase<MatrixPowerMatrixProduct<Lhs,Rhs>,Lhs,Rhs> >
|
||||
{ };
|
||||
} // namespace internal
|
||||
|
||||
template<typename Derived>
|
||||
const MatrixPowerReturnValue<Derived> MatrixBase<Derived>::pow(RealScalar p) const
|
||||
{ return MatrixPowerReturnValue<Derived>(derived(), p); }
|
||||
|
||||
@ -12,9 +12,171 @@
|
||||
|
||||
namespace Eigen {
|
||||
|
||||
#define EIGEN_MATRIX_POWER_PUBLIC_INTERFACE(Derived) \
|
||||
typedef MatrixPowerBase<Derived, MatrixType> Base; \
|
||||
using Base::RowsAtCompileTime; \
|
||||
using Base::ColsAtCompileTime; \
|
||||
using Base::Options; \
|
||||
using Base::MaxRowsAtCompileTime; \
|
||||
using Base::MaxColsAtCompileTime; \
|
||||
typedef typename Base::Scalar Scalar; \
|
||||
typedef typename Base::RealScalar RealScalar; \
|
||||
typedef typename Base::RealArray RealArray;
|
||||
|
||||
#define EIGEN_MATRIX_POWER_PROTECTED_MEMBERS(Derived) \
|
||||
using Base::m_A; \
|
||||
using Base::m_Id; \
|
||||
using Base::m_tmp1; \
|
||||
using Base::m_tmp2; \
|
||||
using Base::m_conditionNumber;
|
||||
|
||||
template<typename Derived, typename MatrixType>
|
||||
class MatrixPowerBaseReturnValue : public ReturnByValue<MatrixPowerBaseReturnValue<Derived,MatrixType> >
|
||||
{
|
||||
public:
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
typedef typename MatrixType::Index Index;
|
||||
|
||||
MatrixPowerBaseReturnValue(Derived& pow, RealScalar p) : m_pow(pow), m_p(p)
|
||||
{ }
|
||||
|
||||
template<typename ResultType>
|
||||
inline void evalTo(ResultType& res) const
|
||||
{ m_pow.compute(res, m_p); }
|
||||
|
||||
template<typename OtherDerived>
|
||||
const MatrixPowerProduct<Derived,MatrixType,OtherDerived> operator*(const MatrixBase<OtherDerived>& b) const
|
||||
{ return MatrixPowerProduct<Derived,MatrixType,OtherDerived>(m_pow, b.derived(), m_p); }
|
||||
|
||||
Index rows() const { return m_pow.rows(); }
|
||||
Index cols() const { return m_pow.cols(); }
|
||||
|
||||
private:
|
||||
Derived& m_pow;
|
||||
const RealScalar m_p;
|
||||
MatrixPowerBaseReturnValue& operator=(const MatrixPowerBaseReturnValue&);
|
||||
};
|
||||
|
||||
template<typename Derived, typename MatrixType>
|
||||
class MatrixPowerBase
|
||||
{
|
||||
private:
|
||||
Derived& derived() { return *static_cast<Derived*>(this); }
|
||||
|
||||
public:
|
||||
enum {
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
|
||||
Options = MatrixType::Options,
|
||||
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
|
||||
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
|
||||
};
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
typedef typename MatrixType::Index Index;
|
||||
|
||||
explicit MatrixPowerBase(const MatrixType& A, RealScalar cond) :
|
||||
m_A(A),
|
||||
m_Id(MatrixType::Identity(A.rows(),A.cols())),
|
||||
m_conditionNumber(cond)
|
||||
{ eigen_assert(A.rows() == A.cols()); }
|
||||
|
||||
#ifndef EIGEN_PARSED_BY_DOXYGEN
|
||||
const MatrixPowerBaseReturnValue<Derived,MatrixType> operator()(RealScalar p)
|
||||
{ return MatrixPowerBaseReturnValue<Derived,MatrixType>(derived(), p); }
|
||||
#endif
|
||||
|
||||
void compute(MatrixType& res, RealScalar p)
|
||||
{ derived().compute(res,p); }
|
||||
|
||||
template<typename OtherDerived, typename ResultType>
|
||||
void compute(const OtherDerived& b, ResultType& res, RealScalar p)
|
||||
{ derived().compute(b,res,p); }
|
||||
|
||||
Index rows() const { return m_A.rows(); }
|
||||
Index cols() const { return m_A.cols(); }
|
||||
|
||||
protected:
|
||||
typedef Array<RealScalar,RowsAtCompileTime,1,ColMajor,MaxRowsAtCompileTime> RealArray;
|
||||
|
||||
const MatrixType& m_A;
|
||||
const MatrixType m_Id;
|
||||
MatrixType m_tmp1, m_tmp2;
|
||||
RealScalar m_conditionNumber;
|
||||
};
|
||||
|
||||
template<typename Derived, typename Lhs, typename Rhs>
|
||||
class MatrixPowerProduct : public MatrixBase<MatrixPowerProduct<Derived,Lhs,Rhs> >
|
||||
{
|
||||
public:
|
||||
typedef MatrixBase<MatrixPowerProduct<Derived,Lhs,Rhs> > Base;
|
||||
EIGEN_DENSE_PUBLIC_INTERFACE(MatrixPowerProduct)
|
||||
|
||||
MatrixPowerProduct(Derived& pow, const Rhs& b, RealScalar p) :
|
||||
m_pow(pow),
|
||||
m_b(b),
|
||||
m_p(p)
|
||||
{ eigen_assert(pow.cols() == b.rows()); }
|
||||
|
||||
template<typename ResultType>
|
||||
inline void evalTo(ResultType& res) const
|
||||
{ m_pow.compute(m_b, res, m_p); }
|
||||
|
||||
inline Index rows() const { return m_pow.rows(); }
|
||||
inline Index cols() const { return m_b.cols(); }
|
||||
|
||||
private:
|
||||
Derived& m_pow;
|
||||
const Rhs& m_b;
|
||||
const RealScalar m_p;
|
||||
};
|
||||
|
||||
template<typename Derived>
|
||||
template<typename MatrixPower, typename Lhs, typename Rhs>
|
||||
Derived& MatrixBase<Derived>::lazyAssign(const MatrixPowerProduct<MatrixPower,Lhs,Rhs>& other)
|
||||
{
|
||||
other.evalTo(derived());
|
||||
return derived();
|
||||
}
|
||||
|
||||
namespace internal {
|
||||
template<int IsComplex>
|
||||
struct recompose_complex_schur
|
||||
|
||||
template<typename Derived, typename MatrixType>
|
||||
struct traits<MatrixPowerBaseReturnValue<Derived, MatrixType> >
|
||||
{ typedef MatrixType ReturnType; };
|
||||
|
||||
template<typename Derived, typename Lhs, typename Rhs>
|
||||
struct nested<MatrixPowerProduct<Derived,Lhs,Rhs> >
|
||||
{ typedef typename MatrixPowerProduct<Derived,Lhs,Rhs>::PlainObject const& type; };
|
||||
|
||||
template<typename Derived, typename _Lhs, typename _Rhs>
|
||||
struct traits<MatrixPowerProduct<Derived,_Lhs,_Rhs> >
|
||||
{
|
||||
typedef MatrixXpr XprKind;
|
||||
typedef typename remove_all<_Lhs>::type Lhs;
|
||||
typedef typename remove_all<_Rhs>::type Rhs;
|
||||
typedef typename remove_all<MatrixPowerProduct<Derived,_Lhs,_Rhs> >::type PlainObject;
|
||||
typedef typename scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
|
||||
typedef typename promote_storage_type<typename traits<Lhs>::StorageKind,
|
||||
typename traits<Rhs>::StorageKind>::ret StorageKind;
|
||||
typedef typename promote_index_type<typename traits<Lhs>::Index,
|
||||
typename traits<Rhs>::Index>::type Index;
|
||||
|
||||
enum {
|
||||
RowsAtCompileTime = traits<Lhs>::RowsAtCompileTime,
|
||||
ColsAtCompileTime = traits<Rhs>::ColsAtCompileTime,
|
||||
MaxRowsAtCompileTime = traits<Lhs>::MaxRowsAtCompileTime,
|
||||
MaxColsAtCompileTime = traits<Rhs>::MaxColsAtCompileTime,
|
||||
Flags = (MaxRowsAtCompileTime==1 ? RowMajorBit : 0)
|
||||
| EvalBeforeNestingBit | EvalBeforeAssigningBit | NestByRefBit,
|
||||
CoeffReadCost = 0
|
||||
};
|
||||
};
|
||||
|
||||
template<bool IsComplex> struct recompose_complex_schur;
|
||||
|
||||
template<>
|
||||
struct recompose_complex_schur<true>
|
||||
{
|
||||
template<typename ResultType, typename MatrixType>
|
||||
static inline void run(ResultType& res, const MatrixType& T, const MatrixType& U)
|
||||
@ -22,7 +184,7 @@ struct recompose_complex_schur
|
||||
};
|
||||
|
||||
template<>
|
||||
struct recompose_complex_schur<0>
|
||||
struct recompose_complex_schur<false>
|
||||
{
|
||||
template<typename ResultType, typename MatrixType>
|
||||
static inline void run(ResultType& res, const MatrixType& T, const MatrixType& U)
|
||||
@ -109,10 +271,14 @@ inline int matrix_power_get_pade_degree(long double normIminusT)
|
||||
break;
|
||||
return degree;
|
||||
}
|
||||
|
||||
} // namespace internal
|
||||
|
||||
template<typename MatrixType, bool IsComplex=NumTraits<typename MatrixType::RealScalar>::IsComplex>
|
||||
class MatrixPowerTriangularAtomic;
|
||||
|
||||
template<typename MatrixType>
|
||||
class MatrixPowerTriangularAtomic
|
||||
class MatrixPowerTriangularAtomic<MatrixType,true>
|
||||
{
|
||||
private:
|
||||
enum {
|
||||
@ -136,13 +302,13 @@ class MatrixPowerTriangularAtomic
|
||||
};
|
||||
|
||||
template<typename MatrixType>
|
||||
MatrixPowerTriangularAtomic<MatrixType>::MatrixPowerTriangularAtomic(const MatrixType& T) :
|
||||
MatrixPowerTriangularAtomic<MatrixType,true>::MatrixPowerTriangularAtomic(const MatrixType& T) :
|
||||
m_T(T),
|
||||
m_Id(MatrixType::Identity(T.rows(), T.cols()))
|
||||
{ eigen_assert(T.rows() == T.cols()); }
|
||||
|
||||
template<typename MatrixType>
|
||||
void MatrixPowerTriangularAtomic<MatrixType>::compute(MatrixType& res, RealScalar p) const
|
||||
void MatrixPowerTriangularAtomic<MatrixType,true>::compute(MatrixType& res, RealScalar p) const
|
||||
{
|
||||
switch (m_T.rows()) {
|
||||
case 0:
|
||||
@ -159,7 +325,7 @@ void MatrixPowerTriangularAtomic<MatrixType>::compute(MatrixType& res, RealScala
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
void MatrixPowerTriangularAtomic<MatrixType>::computePade(int degree, const MatrixType& IminusT, MatrixType& res,
|
||||
void MatrixPowerTriangularAtomic<MatrixType,true>::computePade(int degree, const MatrixType& IminusT, MatrixType& res,
|
||||
RealScalar p) const
|
||||
{
|
||||
int i = degree<<1;
|
||||
@ -172,7 +338,7 @@ void MatrixPowerTriangularAtomic<MatrixType>::computePade(int degree, const Matr
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
void MatrixPowerTriangularAtomic<MatrixType>::compute2x2(MatrixType& res, RealScalar p) const
|
||||
void MatrixPowerTriangularAtomic<MatrixType,true>::compute2x2(MatrixType& res, RealScalar p) const
|
||||
{
|
||||
using std::abs;
|
||||
using std::pow;
|
||||
@ -198,7 +364,7 @@ void MatrixPowerTriangularAtomic<MatrixType>::compute2x2(MatrixType& res, RealSc
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
void MatrixPowerTriangularAtomic<MatrixType>::computeBig(MatrixType& res, RealScalar p) const
|
||||
void MatrixPowerTriangularAtomic<MatrixType,true>::computeBig(MatrixType& res, RealScalar p) const
|
||||
{
|
||||
const int digits = std::numeric_limits<RealScalar>::digits;
|
||||
const RealScalar maxNormForPade = digits <= 24? 4.3386528e-1f: // sigle precision
|
||||
@ -212,7 +378,7 @@ void MatrixPowerTriangularAtomic<MatrixType>::computeBig(MatrixType& res, RealSc
|
||||
bool hasExtraSquareRoot=false;
|
||||
|
||||
while (true) {
|
||||
IminusT = MatrixType::Identity(m_T.rows(), m_T.cols()) - T;
|
||||
IminusT = m_Id - T;
|
||||
normIminusT = IminusT.cwiseAbs().colwise().sum().maxCoeff();
|
||||
if (normIminusT < maxNormForPade) {
|
||||
degree = internal::matrix_power_get_pade_degree(normIminusT);
|
||||
@ -234,126 +400,6 @@ void MatrixPowerTriangularAtomic<MatrixType>::computeBig(MatrixType& res, RealSc
|
||||
compute2x2(res, p);
|
||||
}
|
||||
|
||||
#define EIGEN_MATRIX_POWER_PUBLIC_INTERFACE(Derived) \
|
||||
typedef MatrixPowerBase<Derived, MatrixType> Base; \
|
||||
using Base::RowsAtCompileTime; \
|
||||
using Base::ColsAtCompileTime; \
|
||||
using Base::Options; \
|
||||
using Base::MaxRowsAtCompileTime; \
|
||||
using Base::MaxColsAtCompileTime; \
|
||||
typedef typename Base::Scalar Scalar; \
|
||||
typedef typename Base::RealScalar RealScalar; \
|
||||
typedef typename Base::RealArray RealArray;
|
||||
|
||||
#define EIGEN_MATRIX_POWER_PROTECTED_MEMBERS(Derived) \
|
||||
using Base::m_A; \
|
||||
using Base::m_Id; \
|
||||
using Base::m_tmp1; \
|
||||
using Base::m_tmp2; \
|
||||
using Base::m_conditionNumber;
|
||||
|
||||
#define EIGEN_MATRIX_POWER_PRODUCT_PUBLIC_INTERFACE(Derived) \
|
||||
typedef MatrixPowerProductBase<Derived, Lhs, Rhs> Base; \
|
||||
EIGEN_DENSE_PUBLIC_INTERFACE(Derived)
|
||||
|
||||
namespace internal {
|
||||
template<typename Derived, typename _Lhs, typename _Rhs>
|
||||
struct traits<MatrixPowerProductBase<Derived,_Lhs,_Rhs> >
|
||||
{
|
||||
typedef MatrixXpr XprKind;
|
||||
typedef typename remove_all<_Lhs>::type Lhs;
|
||||
typedef typename remove_all<_Rhs>::type Rhs;
|
||||
typedef typename remove_all<Derived>::type PlainObject;
|
||||
typedef typename scalar_product_traits<typename Lhs::Scalar, typename Rhs::Scalar>::ReturnType Scalar;
|
||||
typedef typename promote_storage_type<typename traits<Lhs>::StorageKind,
|
||||
typename traits<Rhs>::StorageKind>::ret StorageKind;
|
||||
typedef typename promote_index_type<typename traits<Lhs>::Index,
|
||||
typename traits<Rhs>::Index>::type Index;
|
||||
|
||||
enum {
|
||||
RowsAtCompileTime = traits<Lhs>::RowsAtCompileTime,
|
||||
ColsAtCompileTime = traits<Rhs>::ColsAtCompileTime,
|
||||
MaxRowsAtCompileTime = traits<Lhs>::MaxRowsAtCompileTime,
|
||||
MaxColsAtCompileTime = traits<Rhs>::MaxColsAtCompileTime,
|
||||
Flags = (MaxRowsAtCompileTime==1 ? RowMajorBit : 0)
|
||||
| EvalBeforeNestingBit | EvalBeforeAssigningBit | NestByRefBit,
|
||||
CoeffReadCost = 0
|
||||
};
|
||||
};
|
||||
} // namespace internal
|
||||
|
||||
template<typename Derived, typename MatrixType>
|
||||
class MatrixPowerBase
|
||||
{
|
||||
public:
|
||||
enum {
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
ColsAtCompileTime = MatrixType::ColsAtCompileTime,
|
||||
Options = MatrixType::Options,
|
||||
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
|
||||
MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
|
||||
};
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
typedef typename MatrixType::Index Index;
|
||||
|
||||
explicit MatrixPowerBase(const MatrixType& A, RealScalar cond);
|
||||
|
||||
void compute(MatrixType& res, RealScalar p);
|
||||
|
||||
template<typename OtherDerived, typename ResultType>
|
||||
void compute(const OtherDerived& b, ResultType& res, RealScalar p);
|
||||
|
||||
Index rows() const { return m_A.rows(); }
|
||||
Index cols() const { return m_A.cols(); }
|
||||
|
||||
protected:
|
||||
typedef Array<RealScalar,RowsAtCompileTime,1,ColMajor,MaxRowsAtCompileTime> RealArray;
|
||||
|
||||
const MatrixType& m_A;
|
||||
const MatrixType m_Id;
|
||||
MatrixType m_tmp1, m_tmp2;
|
||||
RealScalar m_conditionNumber;
|
||||
};
|
||||
|
||||
template<typename Derived, typename MatrixType>
|
||||
MatrixPowerBase<Derived,MatrixType>::MatrixPowerBase(const MatrixType& A, RealScalar cond) :
|
||||
m_A(A),
|
||||
m_Id(MatrixType::Identity(A.rows(),A.cols())),
|
||||
m_conditionNumber(cond)
|
||||
{ eigen_assert(A.rows() == A.cols()); }
|
||||
|
||||
template<typename Derived, typename MatrixType>
|
||||
void MatrixPowerBase<Derived,MatrixType>::compute(MatrixType& res, RealScalar p)
|
||||
{ static_cast<Derived*>(this)->compute(res,p); }
|
||||
|
||||
template<typename Derived, typename MatrixType>
|
||||
template<typename OtherDerived, typename ResultType>
|
||||
void MatrixPowerBase<Derived,MatrixType>::compute(const OtherDerived& b, ResultType& res, RealScalar p)
|
||||
{ static_cast<Derived*>(this)->compute(b,res,p); }
|
||||
|
||||
template<typename Derived, typename Lhs, typename Rhs>
|
||||
class MatrixPowerProductBase : public MatrixBase<Derived>
|
||||
{
|
||||
public:
|
||||
typedef MatrixBase<Derived> Base;
|
||||
EIGEN_DENSE_PUBLIC_INTERFACE(MatrixPowerProductBase)
|
||||
|
||||
inline Index rows() const { return derived().rows(); }
|
||||
inline Index cols() const { return derived().cols(); }
|
||||
|
||||
template<typename ResultType>
|
||||
inline void evalTo(ResultType& res) const { derived().evalTo(res); }
|
||||
};
|
||||
|
||||
template<typename Derived>
|
||||
template<typename ProductDerived, typename Lhs, typename Rhs>
|
||||
Derived& MatrixBase<Derived>::lazyAssign(const MatrixPowerProductBase<ProductDerived,Lhs,Rhs>& other)
|
||||
{
|
||||
other.derived().evalTo(derived());
|
||||
return derived();
|
||||
}
|
||||
|
||||
} // namespace Eigen
|
||||
|
||||
#endif // EIGEN_MATRIX_POWER
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user