mirror of
https://gitlab.com/libeigen/eigen.git
synced 2026-04-10 11:34:33 +08:00
Apply clang-format
This commit is contained in:
Tobias Wood
@@ -15,7 +15,8 @@
|
||||
|
||||
namespace Eigen {
|
||||
|
||||
template<typename MatrixType> class MatrixPower;
|
||||
template <typename MatrixType>
|
||||
class MatrixPower;
|
||||
|
||||
/**
|
||||
* \ingroup MatrixFunctions_Module
|
||||
@@ -38,36 +39,35 @@ template<typename MatrixType> class MatrixPower;
|
||||
* template<typename MatrixType>
|
||||
* struct traits<MatrixPower<MatrixType>::ReturnValue>;
|
||||
*/
|
||||
template<typename MatrixType>
|
||||
class MatrixPowerParenthesesReturnValue : public ReturnByValue< MatrixPowerParenthesesReturnValue<MatrixType> >
|
||||
{
|
||||
public:
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
template <typename MatrixType>
|
||||
class MatrixPowerParenthesesReturnValue : public ReturnByValue<MatrixPowerParenthesesReturnValue<MatrixType> > {
|
||||
public:
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
|
||||
/**
|
||||
* \brief Constructor.
|
||||
*
|
||||
* \param[in] pow %MatrixPower storing the base.
|
||||
* \param[in] p scalar, the exponent of the matrix power.
|
||||
*/
|
||||
MatrixPowerParenthesesReturnValue(MatrixPower<MatrixType>& pow, RealScalar p) : m_pow(pow), m_p(p)
|
||||
{ }
|
||||
/**
|
||||
* \brief Constructor.
|
||||
*
|
||||
* \param[in] pow %MatrixPower storing the base.
|
||||
* \param[in] p scalar, the exponent of the matrix power.
|
||||
*/
|
||||
MatrixPowerParenthesesReturnValue(MatrixPower<MatrixType>& pow, RealScalar p) : m_pow(pow), m_p(p) {}
|
||||
|
||||
/**
|
||||
* \brief Compute the matrix power.
|
||||
*
|
||||
* \param[out] result
|
||||
*/
|
||||
template<typename ResultType>
|
||||
inline void evalTo(ResultType& result) const
|
||||
{ m_pow.compute(result, m_p); }
|
||||
/**
|
||||
* \brief Compute the matrix power.
|
||||
*
|
||||
* \param[out] result
|
||||
*/
|
||||
template <typename ResultType>
|
||||
inline void evalTo(ResultType& result) const {
|
||||
m_pow.compute(result, m_p);
|
||||
}
|
||||
|
||||
Index rows() const { return m_pow.rows(); }
|
||||
Index cols() const { return m_pow.cols(); }
|
||||
Index rows() const { return m_pow.rows(); }
|
||||
Index cols() const { return m_pow.cols(); }
|
||||
|
||||
private:
|
||||
MatrixPower<MatrixType>& m_pow;
|
||||
const RealScalar m_p;
|
||||
private:
|
||||
MatrixPower<MatrixType>& m_pow;
|
||||
const RealScalar m_p;
|
||||
};
|
||||
|
||||
/**
|
||||
@@ -85,71 +85,64 @@ class MatrixPowerParenthesesReturnValue : public ReturnByValue< MatrixPowerParen
|
||||
* insist that this be nested into MatrixPower. This class is here to
|
||||
* facilitate future development of triangular matrix functions.
|
||||
*/
|
||||
template<typename MatrixType>
|
||||
class MatrixPowerAtomic : internal::noncopyable
|
||||
{
|
||||
private:
|
||||
enum {
|
||||
RowsAtCompileTime = MatrixType::RowsAtCompileTime,
|
||||
MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime
|
||||
};
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
typedef std::complex<RealScalar> ComplexScalar;
|
||||
typedef Block<MatrixType,Dynamic,Dynamic> ResultType;
|
||||
template <typename MatrixType>
|
||||
class MatrixPowerAtomic : internal::noncopyable {
|
||||
private:
|
||||
enum { RowsAtCompileTime = MatrixType::RowsAtCompileTime, MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime };
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
typedef std::complex<RealScalar> ComplexScalar;
|
||||
typedef Block<MatrixType, Dynamic, Dynamic> ResultType;
|
||||
|
||||
const MatrixType& m_A;
|
||||
RealScalar m_p;
|
||||
const MatrixType& m_A;
|
||||
RealScalar m_p;
|
||||
|
||||
void computePade(int degree, const MatrixType& IminusT, ResultType& res) const;
|
||||
void compute2x2(ResultType& res, RealScalar p) const;
|
||||
void computeBig(ResultType& res) const;
|
||||
static int getPadeDegree(float normIminusT);
|
||||
static int getPadeDegree(double normIminusT);
|
||||
static int getPadeDegree(long double normIminusT);
|
||||
static ComplexScalar computeSuperDiag(const ComplexScalar&, const ComplexScalar&, RealScalar p);
|
||||
static RealScalar computeSuperDiag(RealScalar, RealScalar, RealScalar p);
|
||||
void computePade(int degree, const MatrixType& IminusT, ResultType& res) const;
|
||||
void compute2x2(ResultType& res, RealScalar p) const;
|
||||
void computeBig(ResultType& res) const;
|
||||
static int getPadeDegree(float normIminusT);
|
||||
static int getPadeDegree(double normIminusT);
|
||||
static int getPadeDegree(long double normIminusT);
|
||||
static ComplexScalar computeSuperDiag(const ComplexScalar&, const ComplexScalar&, RealScalar p);
|
||||
static RealScalar computeSuperDiag(RealScalar, RealScalar, RealScalar p);
|
||||
|
||||
public:
|
||||
/**
|
||||
* \brief Constructor.
|
||||
*
|
||||
* \param[in] T the base of the matrix power.
|
||||
* \param[in] p the exponent of the matrix power, should be in
|
||||
* \f$ (-1, 1) \f$.
|
||||
*
|
||||
* The class stores a reference to T, so it should not be changed
|
||||
* (or destroyed) before evaluation. Only the upper triangular
|
||||
* part of T is read.
|
||||
*/
|
||||
MatrixPowerAtomic(const MatrixType& T, RealScalar p);
|
||||
|
||||
/**
|
||||
* \brief Compute the matrix power.
|
||||
*
|
||||
* \param[out] res \f$ A^p \f$ where A and p are specified in the
|
||||
* constructor.
|
||||
*/
|
||||
void compute(ResultType& res) const;
|
||||
public:
|
||||
/**
|
||||
* \brief Constructor.
|
||||
*
|
||||
* \param[in] T the base of the matrix power.
|
||||
* \param[in] p the exponent of the matrix power, should be in
|
||||
* \f$ (-1, 1) \f$.
|
||||
*
|
||||
* The class stores a reference to T, so it should not be changed
|
||||
* (or destroyed) before evaluation. Only the upper triangular
|
||||
* part of T is read.
|
||||
*/
|
||||
MatrixPowerAtomic(const MatrixType& T, RealScalar p);
|
||||
|
||||
/**
|
||||
* \brief Compute the matrix power.
|
||||
*
|
||||
* \param[out] res \f$ A^p \f$ where A and p are specified in the
|
||||
* constructor.
|
||||
*/
|
||||
void compute(ResultType& res) const;
|
||||
};
|
||||
|
||||
template<typename MatrixType>
|
||||
MatrixPowerAtomic<MatrixType>::MatrixPowerAtomic(const MatrixType& T, RealScalar p) :
|
||||
m_A(T), m_p(p)
|
||||
{
|
||||
template <typename MatrixType>
|
||||
MatrixPowerAtomic<MatrixType>::MatrixPowerAtomic(const MatrixType& T, RealScalar p) : m_A(T), m_p(p) {
|
||||
eigen_assert(T.rows() == T.cols());
|
||||
eigen_assert(p > -1 && p < 1);
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
void MatrixPowerAtomic<MatrixType>::compute(ResultType& res) const
|
||||
{
|
||||
template <typename MatrixType>
|
||||
void MatrixPowerAtomic<MatrixType>::compute(ResultType& res) const {
|
||||
using std::pow;
|
||||
switch (m_A.rows()) {
|
||||
case 0:
|
||||
break;
|
||||
case 1:
|
||||
res(0,0) = pow(m_A(0,0), m_p);
|
||||
res(0, 0) = pow(m_A(0, 0), m_p);
|
||||
break;
|
||||
case 2:
|
||||
compute2x2(res, m_p);
|
||||
@@ -159,66 +152,68 @@ void MatrixPowerAtomic<MatrixType>::compute(ResultType& res) const
|
||||
}
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
void MatrixPowerAtomic<MatrixType>::computePade(int degree, const MatrixType& IminusT, ResultType& res) const
|
||||
{
|
||||
int i = 2*degree;
|
||||
res = (m_p-RealScalar(degree)) / RealScalar(2*i-2) * IminusT;
|
||||
template <typename MatrixType>
|
||||
void MatrixPowerAtomic<MatrixType>::computePade(int degree, const MatrixType& IminusT, ResultType& res) const {
|
||||
int i = 2 * degree;
|
||||
res = (m_p - RealScalar(degree)) / RealScalar(2 * i - 2) * IminusT;
|
||||
|
||||
for (--i; i; --i) {
|
||||
res = (MatrixType::Identity(IminusT.rows(), IminusT.cols()) + res).template triangularView<Upper>()
|
||||
.solve((i==1 ? -m_p : i&1 ? (-m_p-RealScalar(i/2))/RealScalar(2*i) : (m_p-RealScalar(i/2))/RealScalar(2*i-2)) * IminusT).eval();
|
||||
res = (MatrixType::Identity(IminusT.rows(), IminusT.cols()) + res)
|
||||
.template triangularView<Upper>()
|
||||
.solve((i == 1 ? -m_p
|
||||
: i & 1 ? (-m_p - RealScalar(i / 2)) / RealScalar(2 * i)
|
||||
: (m_p - RealScalar(i / 2)) / RealScalar(2 * i - 2)) *
|
||||
IminusT)
|
||||
.eval();
|
||||
}
|
||||
res += MatrixType::Identity(IminusT.rows(), IminusT.cols());
|
||||
}
|
||||
|
||||
// This function assumes that res has the correct size (see bug 614)
|
||||
template<typename MatrixType>
|
||||
void MatrixPowerAtomic<MatrixType>::compute2x2(ResultType& res, RealScalar p) const
|
||||
{
|
||||
template <typename MatrixType>
|
||||
void MatrixPowerAtomic<MatrixType>::compute2x2(ResultType& res, RealScalar p) const {
|
||||
using std::abs;
|
||||
using std::pow;
|
||||
res.coeffRef(0,0) = pow(m_A.coeff(0,0), p);
|
||||
res.coeffRef(0, 0) = pow(m_A.coeff(0, 0), p);
|
||||
|
||||
for (Index i=1; i < m_A.cols(); ++i) {
|
||||
res.coeffRef(i,i) = pow(m_A.coeff(i,i), p);
|
||||
if (m_A.coeff(i-1,i-1) == m_A.coeff(i,i))
|
||||
res.coeffRef(i-1,i) = p * pow(m_A.coeff(i,i), p-1);
|
||||
else if (2*abs(m_A.coeff(i-1,i-1)) < abs(m_A.coeff(i,i)) || 2*abs(m_A.coeff(i,i)) < abs(m_A.coeff(i-1,i-1)))
|
||||
res.coeffRef(i-1,i) = (res.coeff(i,i)-res.coeff(i-1,i-1)) / (m_A.coeff(i,i)-m_A.coeff(i-1,i-1));
|
||||
for (Index i = 1; i < m_A.cols(); ++i) {
|
||||
res.coeffRef(i, i) = pow(m_A.coeff(i, i), p);
|
||||
if (m_A.coeff(i - 1, i - 1) == m_A.coeff(i, i))
|
||||
res.coeffRef(i - 1, i) = p * pow(m_A.coeff(i, i), p - 1);
|
||||
else if (2 * abs(m_A.coeff(i - 1, i - 1)) < abs(m_A.coeff(i, i)) ||
|
||||
2 * abs(m_A.coeff(i, i)) < abs(m_A.coeff(i - 1, i - 1)))
|
||||
res.coeffRef(i - 1, i) =
|
||||
(res.coeff(i, i) - res.coeff(i - 1, i - 1)) / (m_A.coeff(i, i) - m_A.coeff(i - 1, i - 1));
|
||||
else
|
||||
res.coeffRef(i-1,i) = computeSuperDiag(m_A.coeff(i,i), m_A.coeff(i-1,i-1), p);
|
||||
res.coeffRef(i-1,i) *= m_A.coeff(i-1,i);
|
||||
res.coeffRef(i - 1, i) = computeSuperDiag(m_A.coeff(i, i), m_A.coeff(i - 1, i - 1), p);
|
||||
res.coeffRef(i - 1, i) *= m_A.coeff(i - 1, i);
|
||||
}
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
void MatrixPowerAtomic<MatrixType>::computeBig(ResultType& res) const
|
||||
{
|
||||
template <typename MatrixType>
|
||||
void MatrixPowerAtomic<MatrixType>::computeBig(ResultType& res) const {
|
||||
using std::ldexp;
|
||||
const int digits = std::numeric_limits<RealScalar>::digits;
|
||||
const RealScalar maxNormForPade = RealScalar(
|
||||
digits <= 24? 4.3386528e-1L // single precision
|
||||
: digits <= 53? 2.789358995219730e-1L // double precision
|
||||
: digits <= 64? 2.4471944416607995472e-1L // extended precision
|
||||
: digits <= 106? 1.1016843812851143391275867258512e-1L // double-double
|
||||
: 9.134603732914548552537150753385375e-2L); // quadruple precision
|
||||
const RealScalar maxNormForPade =
|
||||
RealScalar(digits <= 24 ? 4.3386528e-1L // single precision
|
||||
: digits <= 53 ? 2.789358995219730e-1L // double precision
|
||||
: digits <= 64 ? 2.4471944416607995472e-1L // extended precision
|
||||
: digits <= 106 ? 1.1016843812851143391275867258512e-1L // double-double
|
||||
: 9.134603732914548552537150753385375e-2L); // quadruple precision
|
||||
MatrixType IminusT, sqrtT, T = m_A.template triangularView<Upper>();
|
||||
RealScalar normIminusT;
|
||||
int degree, degree2, numberOfSquareRoots = 0;
|
||||
bool hasExtraSquareRoot = false;
|
||||
|
||||
for (Index i=0; i < m_A.cols(); ++i)
|
||||
eigen_assert(m_A(i,i) != RealScalar(0));
|
||||
for (Index i = 0; i < m_A.cols(); ++i) eigen_assert(m_A(i, i) != RealScalar(0));
|
||||
|
||||
while (true) {
|
||||
IminusT = MatrixType::Identity(m_A.rows(), m_A.cols()) - T;
|
||||
normIminusT = IminusT.cwiseAbs().colwise().sum().maxCoeff();
|
||||
if (normIminusT < maxNormForPade) {
|
||||
degree = getPadeDegree(normIminusT);
|
||||
degree2 = getPadeDegree(normIminusT/2);
|
||||
if (degree - degree2 <= 1 || hasExtraSquareRoot)
|
||||
break;
|
||||
degree2 = getPadeDegree(normIminusT / 2);
|
||||
if (degree - degree2 <= 1 || hasExtraSquareRoot) break;
|
||||
hasExtraSquareRoot = true;
|
||||
}
|
||||
matrix_sqrt_triangular(T, sqrtT);
|
||||
@@ -233,66 +228,70 @@ void MatrixPowerAtomic<MatrixType>::computeBig(ResultType& res) const
|
||||
}
|
||||
compute2x2(res, m_p);
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
inline int MatrixPowerAtomic<MatrixType>::getPadeDegree(float normIminusT)
|
||||
{
|
||||
const float maxNormForPade[] = { 2.8064004e-1f /* degree = 3 */ , 4.3386528e-1f };
|
||||
|
||||
template <typename MatrixType>
|
||||
inline int MatrixPowerAtomic<MatrixType>::getPadeDegree(float normIminusT) {
|
||||
const float maxNormForPade[] = {2.8064004e-1f /* degree = 3 */, 4.3386528e-1f};
|
||||
int degree = 3;
|
||||
for (; degree <= 4; ++degree)
|
||||
if (normIminusT <= maxNormForPade[degree - 3])
|
||||
break;
|
||||
if (normIminusT <= maxNormForPade[degree - 3]) break;
|
||||
return degree;
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
inline int MatrixPowerAtomic<MatrixType>::getPadeDegree(double normIminusT)
|
||||
{
|
||||
const double maxNormForPade[] = { 1.884160592658218e-2 /* degree = 3 */ , 6.038881904059573e-2, 1.239917516308172e-1,
|
||||
1.999045567181744e-1, 2.789358995219730e-1 };
|
||||
template <typename MatrixType>
|
||||
inline int MatrixPowerAtomic<MatrixType>::getPadeDegree(double normIminusT) {
|
||||
const double maxNormForPade[] = {1.884160592658218e-2 /* degree = 3 */, 6.038881904059573e-2, 1.239917516308172e-1,
|
||||
1.999045567181744e-1, 2.789358995219730e-1};
|
||||
int degree = 3;
|
||||
for (; degree <= 7; ++degree)
|
||||
if (normIminusT <= maxNormForPade[degree - 3])
|
||||
break;
|
||||
if (normIminusT <= maxNormForPade[degree - 3]) break;
|
||||
return degree;
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
inline int MatrixPowerAtomic<MatrixType>::getPadeDegree(long double normIminusT)
|
||||
{
|
||||
#if LDBL_MANT_DIG == 53
|
||||
template <typename MatrixType>
|
||||
inline int MatrixPowerAtomic<MatrixType>::getPadeDegree(long double normIminusT) {
|
||||
#if LDBL_MANT_DIG == 53
|
||||
const int maxPadeDegree = 7;
|
||||
const double maxNormForPade[] = { 1.884160592658218e-2L /* degree = 3 */ , 6.038881904059573e-2L, 1.239917516308172e-1L,
|
||||
1.999045567181744e-1L, 2.789358995219730e-1L };
|
||||
const double maxNormForPade[] = {1.884160592658218e-2L /* degree = 3 */, 6.038881904059573e-2L, 1.239917516308172e-1L,
|
||||
1.999045567181744e-1L, 2.789358995219730e-1L};
|
||||
#elif LDBL_MANT_DIG <= 64
|
||||
const int maxPadeDegree = 8;
|
||||
const long double maxNormForPade[] = { 6.3854693117491799460e-3L /* degree = 3 */ , 2.6394893435456973676e-2L,
|
||||
6.4216043030404063729e-2L, 1.1701165502926694307e-1L, 1.7904284231268670284e-1L, 2.4471944416607995472e-1L };
|
||||
const long double maxNormForPade[] = {6.3854693117491799460e-3L /* degree = 3 */,
|
||||
2.6394893435456973676e-2L,
|
||||
6.4216043030404063729e-2L,
|
||||
1.1701165502926694307e-1L,
|
||||
1.7904284231268670284e-1L,
|
||||
2.4471944416607995472e-1L};
|
||||
#elif LDBL_MANT_DIG <= 106
|
||||
const int maxPadeDegree = 10;
|
||||
const double maxNormForPade[] = { 1.0007161601787493236741409687186e-4L /* degree = 3 */ ,
|
||||
1.0007161601787493236741409687186e-3L, 4.7069769360887572939882574746264e-3L, 1.3220386624169159689406653101695e-2L,
|
||||
2.8063482381631737920612944054906e-2L, 4.9625993951953473052385361085058e-2L, 7.7367040706027886224557538328171e-2L,
|
||||
1.1016843812851143391275867258512e-1L };
|
||||
const double maxNormForPade[] = {1.0007161601787493236741409687186e-4L /* degree = 3 */,
|
||||
1.0007161601787493236741409687186e-3L,
|
||||
4.7069769360887572939882574746264e-3L,
|
||||
1.3220386624169159689406653101695e-2L,
|
||||
2.8063482381631737920612944054906e-2L,
|
||||
4.9625993951953473052385361085058e-2L,
|
||||
7.7367040706027886224557538328171e-2L,
|
||||
1.1016843812851143391275867258512e-1L};
|
||||
#else
|
||||
const int maxPadeDegree = 10;
|
||||
const double maxNormForPade[] = { 5.524506147036624377378713555116378e-5L /* degree = 3 */ ,
|
||||
6.640600568157479679823602193345995e-4L, 3.227716520106894279249709728084626e-3L,
|
||||
9.619593944683432960546978734646284e-3L, 2.134595382433742403911124458161147e-2L,
|
||||
3.908166513900489428442993794761185e-2L, 6.266780814639442865832535460550138e-2L,
|
||||
9.134603732914548552537150753385375e-2L };
|
||||
const double maxNormForPade[] = {5.524506147036624377378713555116378e-5L /* degree = 3 */,
|
||||
6.640600568157479679823602193345995e-4L,
|
||||
3.227716520106894279249709728084626e-3L,
|
||||
9.619593944683432960546978734646284e-3L,
|
||||
2.134595382433742403911124458161147e-2L,
|
||||
3.908166513900489428442993794761185e-2L,
|
||||
6.266780814639442865832535460550138e-2L,
|
||||
9.134603732914548552537150753385375e-2L};
|
||||
#endif
|
||||
int degree = 3;
|
||||
for (; degree <= maxPadeDegree; ++degree)
|
||||
if (normIminusT <= static_cast<long double>(maxNormForPade[degree - 3]))
|
||||
break;
|
||||
if (normIminusT <= static_cast<long double>(maxNormForPade[degree - 3])) break;
|
||||
return degree;
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
inline typename MatrixPowerAtomic<MatrixType>::ComplexScalar
|
||||
MatrixPowerAtomic<MatrixType>::computeSuperDiag(const ComplexScalar& curr, const ComplexScalar& prev, RealScalar p)
|
||||
{
|
||||
template <typename MatrixType>
|
||||
inline typename MatrixPowerAtomic<MatrixType>::ComplexScalar MatrixPowerAtomic<MatrixType>::computeSuperDiag(
|
||||
const ComplexScalar& curr, const ComplexScalar& prev, RealScalar p) {
|
||||
using std::ceil;
|
||||
using std::exp;
|
||||
using std::log;
|
||||
@@ -300,20 +299,21 @@ MatrixPowerAtomic<MatrixType>::computeSuperDiag(const ComplexScalar& curr, const
|
||||
|
||||
ComplexScalar logCurr = log(curr);
|
||||
ComplexScalar logPrev = log(prev);
|
||||
RealScalar unwindingNumber = ceil((numext::imag(logCurr - logPrev) - RealScalar(EIGEN_PI)) / RealScalar(2*EIGEN_PI));
|
||||
ComplexScalar w = numext::log1p((curr-prev)/prev)/RealScalar(2) + ComplexScalar(0, RealScalar(EIGEN_PI)*unwindingNumber);
|
||||
RealScalar unwindingNumber =
|
||||
ceil((numext::imag(logCurr - logPrev) - RealScalar(EIGEN_PI)) / RealScalar(2 * EIGEN_PI));
|
||||
ComplexScalar w =
|
||||
numext::log1p((curr - prev) / prev) / RealScalar(2) + ComplexScalar(0, RealScalar(EIGEN_PI) * unwindingNumber);
|
||||
return RealScalar(2) * exp(RealScalar(0.5) * p * (logCurr + logPrev)) * sinh(p * w) / (curr - prev);
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
inline typename MatrixPowerAtomic<MatrixType>::RealScalar
|
||||
MatrixPowerAtomic<MatrixType>::computeSuperDiag(RealScalar curr, RealScalar prev, RealScalar p)
|
||||
{
|
||||
template <typename MatrixType>
|
||||
inline typename MatrixPowerAtomic<MatrixType>::RealScalar MatrixPowerAtomic<MatrixType>::computeSuperDiag(
|
||||
RealScalar curr, RealScalar prev, RealScalar p) {
|
||||
using std::exp;
|
||||
using std::log;
|
||||
using std::sinh;
|
||||
|
||||
RealScalar w = numext::log1p((curr-prev)/prev)/RealScalar(2);
|
||||
RealScalar w = numext::log1p((curr - prev) / prev) / RealScalar(2);
|
||||
return 2 * exp(p * (log(curr) + log(prev)) / 2) * sinh(p * w) / (curr - prev);
|
||||
}
|
||||
|
||||
@@ -336,126 +336,118 @@ MatrixPowerAtomic<MatrixType>::computeSuperDiag(RealScalar curr, RealScalar prev
|
||||
* \include MatrixPower_optimal.cpp
|
||||
* Output: \verbinclude MatrixPower_optimal.out
|
||||
*/
|
||||
template<typename MatrixType>
|
||||
class MatrixPower : internal::noncopyable
|
||||
{
|
||||
private:
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
template <typename MatrixType>
|
||||
class MatrixPower : internal::noncopyable {
|
||||
private:
|
||||
typedef typename MatrixType::Scalar Scalar;
|
||||
typedef typename MatrixType::RealScalar RealScalar;
|
||||
|
||||
public:
|
||||
/**
|
||||
* \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 MatrixPower(const MatrixType& A) :
|
||||
m_A(A),
|
||||
m_conditionNumber(0),
|
||||
m_rank(A.cols()),
|
||||
m_nulls(0)
|
||||
{ eigen_assert(A.rows() == A.cols()); }
|
||||
public:
|
||||
/**
|
||||
* \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 MatrixPower(const MatrixType& A) : m_A(A), m_conditionNumber(0), m_rank(A.cols()), m_nulls(0) {
|
||||
eigen_assert(A.rows() == A.cols());
|
||||
}
|
||||
|
||||
/**
|
||||
* \brief Returns the matrix power.
|
||||
*
|
||||
* \param[in] p exponent, a real scalar.
|
||||
* \return The expression \f$ A^p \f$, where A is specified in the
|
||||
* constructor.
|
||||
*/
|
||||
const MatrixPowerParenthesesReturnValue<MatrixType> operator()(RealScalar p)
|
||||
{ return MatrixPowerParenthesesReturnValue<MatrixType>(*this, p); }
|
||||
/**
|
||||
* \brief Returns the matrix power.
|
||||
*
|
||||
* \param[in] p exponent, a real scalar.
|
||||
* \return The expression \f$ A^p \f$, where A is specified in the
|
||||
* constructor.
|
||||
*/
|
||||
const MatrixPowerParenthesesReturnValue<MatrixType> operator()(RealScalar p) {
|
||||
return MatrixPowerParenthesesReturnValue<MatrixType>(*this, p);
|
||||
}
|
||||
|
||||
/**
|
||||
* \brief Compute the matrix power.
|
||||
*
|
||||
* \param[in] p exponent, a real scalar.
|
||||
* \param[out] res \f$ A^p \f$ where A is specified in the
|
||||
* constructor.
|
||||
*/
|
||||
template<typename ResultType>
|
||||
void compute(ResultType& res, RealScalar p);
|
||||
|
||||
Index rows() const { return m_A.rows(); }
|
||||
Index cols() const { return m_A.cols(); }
|
||||
/**
|
||||
* \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.
|
||||
*/
|
||||
template <typename ResultType>
|
||||
void compute(ResultType& res, RealScalar p);
|
||||
|
||||
private:
|
||||
typedef std::complex<RealScalar> ComplexScalar;
|
||||
typedef Matrix<ComplexScalar, Dynamic, Dynamic, 0,
|
||||
MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime> ComplexMatrix;
|
||||
Index rows() const { return m_A.rows(); }
|
||||
Index cols() const { return m_A.cols(); }
|
||||
|
||||
/** \brief Reference to the base of matrix power. */
|
||||
typename MatrixType::Nested m_A;
|
||||
private:
|
||||
typedef std::complex<RealScalar> ComplexScalar;
|
||||
typedef Matrix<ComplexScalar, Dynamic, Dynamic, 0, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime>
|
||||
ComplexMatrix;
|
||||
|
||||
/** \brief Temporary storage. */
|
||||
MatrixType m_tmp;
|
||||
/** \brief Reference to the base of matrix power. */
|
||||
typename MatrixType::Nested m_A;
|
||||
|
||||
/** \brief Store the result of Schur decomposition. */
|
||||
ComplexMatrix m_T, m_U;
|
||||
|
||||
/** \brief Store fractional power of m_T. */
|
||||
ComplexMatrix m_fT;
|
||||
/** \brief Temporary storage. */
|
||||
MatrixType m_tmp;
|
||||
|
||||
/**
|
||||
* \brief Condition number of m_A.
|
||||
*
|
||||
* It is initialized as 0 to avoid performing unnecessary Schur
|
||||
* decomposition, which is the bottleneck.
|
||||
*/
|
||||
RealScalar m_conditionNumber;
|
||||
/** \brief Store the result of Schur decomposition. */
|
||||
ComplexMatrix m_T, m_U;
|
||||
|
||||
/** \brief Rank of m_A. */
|
||||
Index m_rank;
|
||||
|
||||
/** \brief Rank deficiency of m_A. */
|
||||
Index m_nulls;
|
||||
/** \brief Store fractional power of m_T. */
|
||||
ComplexMatrix m_fT;
|
||||
|
||||
/**
|
||||
* \brief Split p into integral part and fractional part.
|
||||
*
|
||||
* \param[in] p The exponent.
|
||||
* \param[out] p The fractional part ranging in \f$ (-1, 1) \f$.
|
||||
* \param[out] intpart The integral part.
|
||||
*
|
||||
* Only if the fractional part is nonzero, it calls initialize().
|
||||
*/
|
||||
void split(RealScalar& p, RealScalar& intpart);
|
||||
/**
|
||||
* \brief Condition number of m_A.
|
||||
*
|
||||
* It is initialized as 0 to avoid performing unnecessary Schur
|
||||
* decomposition, which is the bottleneck.
|
||||
*/
|
||||
RealScalar m_conditionNumber;
|
||||
|
||||
/** \brief Perform Schur decomposition for fractional power. */
|
||||
void initialize();
|
||||
/** \brief Rank of m_A. */
|
||||
Index m_rank;
|
||||
|
||||
template<typename ResultType>
|
||||
void computeIntPower(ResultType& res, RealScalar p);
|
||||
/** \brief Rank deficiency of m_A. */
|
||||
Index m_nulls;
|
||||
|
||||
template<typename ResultType>
|
||||
void computeFracPower(ResultType& res, RealScalar p);
|
||||
/**
|
||||
* \brief Split p into integral part and fractional part.
|
||||
*
|
||||
* \param[in] p The exponent.
|
||||
* \param[out] p The fractional part ranging in \f$ (-1, 1) \f$.
|
||||
* \param[out] intpart The integral part.
|
||||
*
|
||||
* Only if the fractional part is nonzero, it calls initialize().
|
||||
*/
|
||||
void split(RealScalar& p, RealScalar& intpart);
|
||||
|
||||
template<int Rows, int Cols, int Options, int MaxRows, int MaxCols>
|
||||
static void revertSchur(
|
||||
Matrix<ComplexScalar, Rows, Cols, Options, MaxRows, MaxCols>& res,
|
||||
const ComplexMatrix& T,
|
||||
const ComplexMatrix& U);
|
||||
/** \brief Perform Schur decomposition for fractional power. */
|
||||
void initialize();
|
||||
|
||||
template<int Rows, int Cols, int Options, int MaxRows, int MaxCols>
|
||||
static void revertSchur(
|
||||
Matrix<RealScalar, Rows, Cols, Options, MaxRows, MaxCols>& res,
|
||||
const ComplexMatrix& T,
|
||||
const ComplexMatrix& U);
|
||||
template <typename ResultType>
|
||||
void computeIntPower(ResultType& res, RealScalar p);
|
||||
|
||||
template <typename ResultType>
|
||||
void computeFracPower(ResultType& res, RealScalar p);
|
||||
|
||||
template <int Rows, int Cols, int Options, int MaxRows, int MaxCols>
|
||||
static void revertSchur(Matrix<ComplexScalar, Rows, Cols, Options, MaxRows, MaxCols>& res, const ComplexMatrix& T,
|
||||
const ComplexMatrix& U);
|
||||
|
||||
template <int Rows, int Cols, int Options, int MaxRows, int MaxCols>
|
||||
static void revertSchur(Matrix<RealScalar, Rows, Cols, Options, MaxRows, MaxCols>& res, const ComplexMatrix& T,
|
||||
const ComplexMatrix& U);
|
||||
};
|
||||
|
||||
template<typename MatrixType>
|
||||
template<typename ResultType>
|
||||
void MatrixPower<MatrixType>::compute(ResultType& res, RealScalar p)
|
||||
{
|
||||
template <typename MatrixType>
|
||||
template <typename ResultType>
|
||||
void MatrixPower<MatrixType>::compute(ResultType& res, RealScalar p) {
|
||||
using std::pow;
|
||||
switch (cols()) {
|
||||
case 0:
|
||||
break;
|
||||
case 1:
|
||||
res(0,0) = pow(m_A.coeff(0,0), p);
|
||||
res(0, 0) = pow(m_A.coeff(0, 0), p);
|
||||
break;
|
||||
default:
|
||||
RealScalar intpart;
|
||||
@@ -467,9 +459,8 @@ void MatrixPower<MatrixType>::compute(ResultType& res, RealScalar p)
|
||||
}
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
void MatrixPower<MatrixType>::split(RealScalar& p, RealScalar& intpart)
|
||||
{
|
||||
template <typename MatrixType>
|
||||
void MatrixPower<MatrixType>::split(RealScalar& p, RealScalar& intpart) {
|
||||
using std::floor;
|
||||
using std::pow;
|
||||
|
||||
@@ -478,19 +469,17 @@ void MatrixPower<MatrixType>::split(RealScalar& p, RealScalar& intpart)
|
||||
|
||||
// Perform Schur decomposition if it is not yet performed and the power is
|
||||
// not an integer.
|
||||
if (!m_conditionNumber && p)
|
||||
initialize();
|
||||
if (!m_conditionNumber && p) initialize();
|
||||
|
||||
// Choose the more stable of intpart = floor(p) and intpart = ceil(p).
|
||||
if (p > RealScalar(0.5) && p > (1-p) * pow(m_conditionNumber, p)) {
|
||||
if (p > RealScalar(0.5) && p > (1 - p) * pow(m_conditionNumber, p)) {
|
||||
--p;
|
||||
++intpart;
|
||||
}
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
void MatrixPower<MatrixType>::initialize()
|
||||
{
|
||||
template <typename MatrixType>
|
||||
void MatrixPower<MatrixType>::initialize() {
|
||||
const ComplexSchur<MatrixType> schurOfA(m_A);
|
||||
JacobiRotation<ComplexScalar> rot;
|
||||
ComplexScalar eigenvalue;
|
||||
@@ -501,18 +490,17 @@ void MatrixPower<MatrixType>::initialize()
|
||||
m_conditionNumber = m_T.diagonal().array().abs().maxCoeff() / m_T.diagonal().array().abs().minCoeff();
|
||||
|
||||
// Move zero eigenvalues to the bottom right corner.
|
||||
for (Index i = cols()-1; i>=0; --i) {
|
||||
if (m_rank <= 2)
|
||||
return;
|
||||
if (m_T.coeff(i,i) == RealScalar(0)) {
|
||||
for (Index j=i+1; j < m_rank; ++j) {
|
||||
eigenvalue = m_T.coeff(j,j);
|
||||
rot.makeGivens(m_T.coeff(j-1,j), eigenvalue);
|
||||
m_T.applyOnTheRight(j-1, j, rot);
|
||||
m_T.applyOnTheLeft(j-1, j, rot.adjoint());
|
||||
m_T.coeffRef(j-1,j-1) = eigenvalue;
|
||||
m_T.coeffRef(j,j) = RealScalar(0);
|
||||
m_U.applyOnTheRight(j-1, j, rot);
|
||||
for (Index i = cols() - 1; i >= 0; --i) {
|
||||
if (m_rank <= 2) return;
|
||||
if (m_T.coeff(i, i) == RealScalar(0)) {
|
||||
for (Index j = i + 1; j < m_rank; ++j) {
|
||||
eigenvalue = m_T.coeff(j, j);
|
||||
rot.makeGivens(m_T.coeff(j - 1, j), eigenvalue);
|
||||
m_T.applyOnTheRight(j - 1, j, rot);
|
||||
m_T.applyOnTheLeft(j - 1, j, rot.adjoint());
|
||||
m_T.coeffRef(j - 1, j - 1) = eigenvalue;
|
||||
m_T.coeffRef(j, j) = RealScalar(0);
|
||||
m_U.applyOnTheRight(j - 1, j, rot);
|
||||
}
|
||||
--m_rank;
|
||||
}
|
||||
@@ -520,67 +508,62 @@ void MatrixPower<MatrixType>::initialize()
|
||||
|
||||
m_nulls = rows() - m_rank;
|
||||
if (m_nulls) {
|
||||
eigen_assert(m_T.bottomRightCorner(m_nulls, m_nulls).isZero()
|
||||
&& "Base of matrix power should be invertible or with a semisimple zero eigenvalue.");
|
||||
eigen_assert(m_T.bottomRightCorner(m_nulls, m_nulls).isZero() &&
|
||||
"Base of matrix power should be invertible or with a semisimple zero eigenvalue.");
|
||||
m_fT.bottomRows(m_nulls).fill(RealScalar(0));
|
||||
}
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
template<typename ResultType>
|
||||
void MatrixPower<MatrixType>::computeIntPower(ResultType& res, RealScalar p)
|
||||
{
|
||||
template <typename MatrixType>
|
||||
template <typename ResultType>
|
||||
void MatrixPower<MatrixType>::computeIntPower(ResultType& res, RealScalar p) {
|
||||
using std::abs;
|
||||
using std::fmod;
|
||||
RealScalar pp = abs(p);
|
||||
|
||||
if (p<0)
|
||||
if (p < 0)
|
||||
m_tmp = m_A.inverse();
|
||||
else
|
||||
else
|
||||
m_tmp = m_A;
|
||||
|
||||
while (true) {
|
||||
if (fmod(pp, 2) >= 1)
|
||||
res = m_tmp * res;
|
||||
if (fmod(pp, 2) >= 1) res = m_tmp * res;
|
||||
pp /= 2;
|
||||
if (pp < 1)
|
||||
break;
|
||||
if (pp < 1) break;
|
||||
m_tmp *= m_tmp;
|
||||
}
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
template<typename ResultType>
|
||||
void MatrixPower<MatrixType>::computeFracPower(ResultType& res, RealScalar p)
|
||||
{
|
||||
Block<ComplexMatrix,Dynamic,Dynamic> blockTp(m_fT, 0, 0, m_rank, m_rank);
|
||||
template <typename MatrixType>
|
||||
template <typename ResultType>
|
||||
void MatrixPower<MatrixType>::computeFracPower(ResultType& res, RealScalar p) {
|
||||
Block<ComplexMatrix, Dynamic, Dynamic> blockTp(m_fT, 0, 0, m_rank, m_rank);
|
||||
eigen_assert(m_conditionNumber);
|
||||
eigen_assert(m_rank + m_nulls == rows());
|
||||
|
||||
MatrixPowerAtomic<ComplexMatrix>(m_T.topLeftCorner(m_rank, m_rank), p).compute(blockTp);
|
||||
if (m_nulls) {
|
||||
m_fT.topRightCorner(m_rank, m_nulls) = m_T.topLeftCorner(m_rank, m_rank).template triangularView<Upper>()
|
||||
.solve(blockTp * m_T.topRightCorner(m_rank, m_nulls));
|
||||
m_fT.topRightCorner(m_rank, m_nulls) = m_T.topLeftCorner(m_rank, m_rank)
|
||||
.template triangularView<Upper>()
|
||||
.solve(blockTp * m_T.topRightCorner(m_rank, m_nulls));
|
||||
}
|
||||
revertSchur(m_tmp, m_fT, m_U);
|
||||
res = m_tmp * res;
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
template<int Rows, int Cols, int Options, int MaxRows, int MaxCols>
|
||||
inline void MatrixPower<MatrixType>::revertSchur(
|
||||
Matrix<ComplexScalar, Rows, Cols, Options, MaxRows, MaxCols>& res,
|
||||
const ComplexMatrix& T,
|
||||
const ComplexMatrix& U)
|
||||
{ res.noalias() = U * (T.template triangularView<Upper>() * U.adjoint()); }
|
||||
template <typename MatrixType>
|
||||
template <int Rows, int Cols, int Options, int MaxRows, int MaxCols>
|
||||
inline void MatrixPower<MatrixType>::revertSchur(Matrix<ComplexScalar, Rows, Cols, Options, MaxRows, MaxCols>& res,
|
||||
const ComplexMatrix& T, const ComplexMatrix& U) {
|
||||
res.noalias() = U * (T.template triangularView<Upper>() * U.adjoint());
|
||||
}
|
||||
|
||||
template<typename MatrixType>
|
||||
template<int Rows, int Cols, int Options, int MaxRows, int MaxCols>
|
||||
inline void MatrixPower<MatrixType>::revertSchur(
|
||||
Matrix<RealScalar, Rows, Cols, Options, MaxRows, MaxCols>& res,
|
||||
const ComplexMatrix& T,
|
||||
const ComplexMatrix& U)
|
||||
{ res.noalias() = (U * (T.template triangularView<Upper>() * U.adjoint())).real(); }
|
||||
template <typename MatrixType>
|
||||
template <int Rows, int Cols, int Options, int MaxRows, int MaxCols>
|
||||
inline void MatrixPower<MatrixType>::revertSchur(Matrix<RealScalar, Rows, Cols, Options, MaxRows, MaxCols>& res,
|
||||
const ComplexMatrix& T, const ComplexMatrix& U) {
|
||||
res.noalias() = (U * (T.template triangularView<Upper>() * U.adjoint())).real();
|
||||
}
|
||||
|
||||
/**
|
||||
* \ingroup MatrixFunctions_Module
|
||||
@@ -595,38 +578,37 @@ inline void MatrixPower<MatrixType>::revertSchur(
|
||||
* MatrixBase::pow() and related functions and most of the
|
||||
* time this is the only way it is used.
|
||||
*/
|
||||
template<typename Derived>
|
||||
class MatrixPowerReturnValue : public ReturnByValue< MatrixPowerReturnValue<Derived> >
|
||||
{
|
||||
public:
|
||||
typedef typename Derived::PlainObject PlainObject;
|
||||
typedef typename Derived::RealScalar RealScalar;
|
||||
template <typename Derived>
|
||||
class MatrixPowerReturnValue : public ReturnByValue<MatrixPowerReturnValue<Derived> > {
|
||||
public:
|
||||
typedef typename Derived::PlainObject PlainObject;
|
||||
typedef typename Derived::RealScalar RealScalar;
|
||||
|
||||
/**
|
||||
* \brief Constructor.
|
||||
*
|
||||
* \param[in] A %Matrix (expression), the base of the matrix power.
|
||||
* \param[in] p real scalar, the exponent of the matrix power.
|
||||
*/
|
||||
MatrixPowerReturnValue(const Derived& A, RealScalar p) : m_A(A), m_p(p)
|
||||
{ }
|
||||
/**
|
||||
* \brief Constructor.
|
||||
*
|
||||
* \param[in] A %Matrix (expression), the base of the matrix power.
|
||||
* \param[in] p real scalar, the exponent of the matrix power.
|
||||
*/
|
||||
MatrixPowerReturnValue(const Derived& A, RealScalar p) : m_A(A), m_p(p) {}
|
||||
|
||||
/**
|
||||
* \brief Compute the matrix power.
|
||||
*
|
||||
* \param[out] result \f$ A^p \f$ where \p A and \p p are as in the
|
||||
* constructor.
|
||||
*/
|
||||
template<typename ResultType>
|
||||
inline void evalTo(ResultType& result) const
|
||||
{ MatrixPower<PlainObject>(m_A.eval()).compute(result, m_p); }
|
||||
/**
|
||||
* \brief Compute the matrix power.
|
||||
*
|
||||
* \param[out] result \f$ A^p \f$ where \p A and \p p are as in the
|
||||
* constructor.
|
||||
*/
|
||||
template <typename ResultType>
|
||||
inline void evalTo(ResultType& result) const {
|
||||
MatrixPower<PlainObject>(m_A.eval()).compute(result, m_p);
|
||||
}
|
||||
|
||||
Index rows() const { return m_A.rows(); }
|
||||
Index cols() const { return m_A.cols(); }
|
||||
Index rows() const { return m_A.rows(); }
|
||||
Index cols() const { return m_A.cols(); }
|
||||
|
||||
private:
|
||||
const Derived& m_A;
|
||||
const RealScalar m_p;
|
||||
private:
|
||||
const Derived& m_A;
|
||||
const RealScalar m_p;
|
||||
};
|
||||
|
||||
/**
|
||||
@@ -642,67 +624,71 @@ class MatrixPowerReturnValue : public ReturnByValue< MatrixPowerReturnValue<Deri
|
||||
* MatrixBase::pow() and related functions and most of the
|
||||
* time this is the only way it is used.
|
||||
*/
|
||||
template<typename Derived>
|
||||
class MatrixComplexPowerReturnValue : public ReturnByValue< MatrixComplexPowerReturnValue<Derived> >
|
||||
{
|
||||
public:
|
||||
typedef typename Derived::PlainObject PlainObject;
|
||||
typedef typename std::complex<typename Derived::RealScalar> ComplexScalar;
|
||||
template <typename Derived>
|
||||
class MatrixComplexPowerReturnValue : public ReturnByValue<MatrixComplexPowerReturnValue<Derived> > {
|
||||
public:
|
||||
typedef typename Derived::PlainObject PlainObject;
|
||||
typedef typename std::complex<typename Derived::RealScalar> ComplexScalar;
|
||||
|
||||
/**
|
||||
* \brief Constructor.
|
||||
*
|
||||
* \param[in] A %Matrix (expression), the base of the matrix power.
|
||||
* \param[in] p complex scalar, the exponent of the matrix power.
|
||||
*/
|
||||
MatrixComplexPowerReturnValue(const Derived& A, const ComplexScalar& p) : m_A(A), m_p(p)
|
||||
{ }
|
||||
/**
|
||||
* \brief Constructor.
|
||||
*
|
||||
* \param[in] A %Matrix (expression), the base of the matrix power.
|
||||
* \param[in] p complex scalar, the exponent of the matrix power.
|
||||
*/
|
||||
MatrixComplexPowerReturnValue(const Derived& A, const ComplexScalar& p) : m_A(A), m_p(p) {}
|
||||
|
||||
/**
|
||||
* \brief Compute the matrix power.
|
||||
*
|
||||
* Because \p p is complex, \f$ A^p \f$ is simply evaluated as \f$
|
||||
* \exp(p \log(A)) \f$.
|
||||
*
|
||||
* \param[out] result \f$ A^p \f$ where \p A and \p p are as in the
|
||||
* constructor.
|
||||
*/
|
||||
template<typename ResultType>
|
||||
inline void evalTo(ResultType& result) const
|
||||
{ result = (m_p * m_A.log()).exp(); }
|
||||
/**
|
||||
* \brief Compute the matrix power.
|
||||
*
|
||||
* Because \p p is complex, \f$ A^p \f$ is simply evaluated as \f$
|
||||
* \exp(p \log(A)) \f$.
|
||||
*
|
||||
* \param[out] result \f$ A^p \f$ where \p A and \p p are as in the
|
||||
* constructor.
|
||||
*/
|
||||
template <typename ResultType>
|
||||
inline void evalTo(ResultType& result) const {
|
||||
result = (m_p * m_A.log()).exp();
|
||||
}
|
||||
|
||||
Index rows() const { return m_A.rows(); }
|
||||
Index cols() const { return m_A.cols(); }
|
||||
Index rows() const { return m_A.rows(); }
|
||||
Index cols() const { return m_A.cols(); }
|
||||
|
||||
private:
|
||||
const Derived& m_A;
|
||||
const ComplexScalar m_p;
|
||||
private:
|
||||
const Derived& m_A;
|
||||
const ComplexScalar m_p;
|
||||
};
|
||||
|
||||
namespace internal {
|
||||
|
||||
template<typename MatrixPowerType>
|
||||
struct traits< MatrixPowerParenthesesReturnValue<MatrixPowerType> >
|
||||
{ typedef typename MatrixPowerType::PlainObject ReturnType; };
|
||||
template <typename MatrixPowerType>
|
||||
struct traits<MatrixPowerParenthesesReturnValue<MatrixPowerType> > {
|
||||
typedef typename MatrixPowerType::PlainObject ReturnType;
|
||||
};
|
||||
|
||||
template<typename Derived>
|
||||
struct traits< MatrixPowerReturnValue<Derived> >
|
||||
{ typedef typename Derived::PlainObject ReturnType; };
|
||||
template <typename Derived>
|
||||
struct traits<MatrixPowerReturnValue<Derived> > {
|
||||
typedef typename Derived::PlainObject ReturnType;
|
||||
};
|
||||
|
||||
template<typename Derived>
|
||||
struct traits< MatrixComplexPowerReturnValue<Derived> >
|
||||
{ typedef typename Derived::PlainObject ReturnType; };
|
||||
template <typename Derived>
|
||||
struct traits<MatrixComplexPowerReturnValue<Derived> > {
|
||||
typedef typename Derived::PlainObject ReturnType;
|
||||
};
|
||||
|
||||
} // namespace internal
|
||||
|
||||
template <typename Derived>
|
||||
const MatrixPowerReturnValue<Derived> MatrixBase<Derived>::pow(const RealScalar& p) const {
|
||||
return MatrixPowerReturnValue<Derived>(derived(), p);
|
||||
}
|
||||
|
||||
template<typename Derived>
|
||||
const MatrixPowerReturnValue<Derived> MatrixBase<Derived>::pow(const RealScalar& p) const
|
||||
{ return MatrixPowerReturnValue<Derived>(derived(), p); }
|
||||
template <typename Derived>
|
||||
const MatrixComplexPowerReturnValue<Derived> MatrixBase<Derived>::pow(const std::complex<RealScalar>& p) const {
|
||||
return MatrixComplexPowerReturnValue<Derived>(derived(), p);
|
||||
}
|
||||
|
||||
template<typename Derived>
|
||||
const MatrixComplexPowerReturnValue<Derived> MatrixBase<Derived>::pow(const std::complex<RealScalar>& p) const
|
||||
{ return MatrixComplexPowerReturnValue<Derived>(derived(), p); }
|
||||
} // namespace Eigen
|
||||
|
||||
} // namespace Eigen
|
||||
|
||||
#endif // EIGEN_MATRIX_POWER
|
||||
#endif // EIGEN_MATRIX_POWER
|
||||
|
||||
Reference in New Issue
Block a user