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Comment on private members of MatrixPower.

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This commit is contained in:
Chen-Pang He 2013-07-20 17:58:12 +08:00
parent c587e63631
commit 2320073e41
1 changed files with 42 additions and 7 deletions
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49
unsupported/Eigen/src/MatrixFunctions/MatrixPower.h
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@ -375,20 +375,51 @@ class MatrixPower : internal::noncopyable
typedef Matrix<ComplexScalar, Dynamic, Dynamic, MatrixType::Options,
MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime> ComplexMatrix;
/** \brief Reference to the base of matrix power. */
typename MatrixType::Nested m_A;
MatrixType m_tmp;
ComplexMatrix m_T, m_U, m_fT;
RealScalar m_conditionNumber;
Index m_rank, m_nulls;
void split(RealScalar&, RealScalar&);
/** \brief Temporary storage for computing integral power. */
MatrixType m_tmp;
/** \brief Store the result of Schur decomposition. */
ComplexMatrix m_T, m_U;
/** \brief Store fractional power of m_T. */
ComplexMatrix m_fT;
/**
* \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 Rank of m_A. */
Index m_rank;
/** \brief Rank deficiency of m_A. */
Index m_nulls;
/**
* \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 Perform Schur decomposition for fractional power. */
void initialize();
template<typename ResultType>
void computeIntPower(ResultType&, RealScalar);
void computeIntPower(ResultType& res, RealScalar p);
template<typename ResultType>
void computeFracPower(ResultType&, RealScalar);
void computeFracPower(ResultType& res, RealScalar p);
template<int Rows, int Cols, int Options, int MaxRows, int MaxCols>
static void revertSchur(
@ -427,9 +458,12 @@ void MatrixPower<MatrixType>::split(RealScalar& p, RealScalar& intpart)
intpart = std::floor(p);
p -= intpart;
// Perform Schur decomposition if it is not yet performed and the power is
// not an integer.
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) * std::pow(m_conditionNumber, p)) {
--p;
++intpart;
@ -448,6 +482,7 @@ void MatrixPower<MatrixType>::initialize()
m_U = schurOfA.matrixU();
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;