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Enable saving intermidiate (Schur decomposition) but disable unstable specialization for matrix power-matrix product.

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Chen-Pang He
2012-09-21 23:24:28 +08:00
parent d5d99dd1f0
commit 87afd99433
5 changed files with 463 additions and 555 deletions
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46
unsupported/Eigen/MatrixFunctions
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@@ -211,8 +211,9 @@ documentation of \ref matrixbase_exp "exp()".
\include MatrixLogarithm.cpp
Output: \verbinclude MatrixLogarithm.out
\note \p M has to be a matrix of \c float, \c double, \c long double
\c complex<float>, \c complex<double>, or \c complex<long double> .
\note \p M has to be a matrix of \c float, \c double, <tt>long
double</tt>, \c complex<float>, \c complex<double>, or \c complex<long
double> .
\sa MatrixBase::exp(), MatrixBase::matrixFunction(),
class MatrixLogarithmAtomic, MatrixBase::sqrt().
@@ -234,27 +235,14 @@ where exp denotes the matrix exponential, and log denotes the matrix
logarithm.
The matrix \f$ M \f$ should meet the conditions to be an argument of
matrix logarithm. If \p p is neither an integer nor the real scalar
type of \p M, it is casted into the real scalar type of \p M.
matrix logarithm. If \p p is not of the real scalar type of \p M, it
is casted into the real scalar type of \p M.
This function computes the matrix logarithm using the
Schur-Pad&eacute; algorithm as implemented by MatrixBase::pow().
The exponent is split into integral part and fractional part, where
the fractional part is in the interval \f$ (-1, 1) \f$. The main
diagonal and the first super-diagonal is directly computed.
The actual work is done by the MatrixPower class, which can compute
\f$ M^p v \f$, where \p v is another matrix with the same rows as
\p M. The matrix \p v is set to be the identity matrix by default.
Therefore, the expression <tt>M.pow(p) * v</tt> is specialized for
this. No temporary storage is created for the result. The code below
directly evaluates R-values into L-values without aliasing issue. Do
\b NOT try to \a optimize with noalias(). It won't compile.
\code
v = m.pow(p) * v;
m = m.pow(q);
// v2.noalias() = m.pow(p) * v1; Won't compile!
\endcode
This function computes the matrix power using the Schur-Pad&eacute;
algorithm as implemented by class MatrixPower. The exponent is split
into integral part and fractional part, where the fractional part is
in the interval \f$ (-1, 1) \f$. The main diagonal and the first
super-diagonal is directly computed.
Details of the algorithm can be found in: Nicholas J. Higham and
Lijing Lin, "A Schur-Pad&eacute; algorithm for fractional powers of a
@@ -277,8 +265,18 @@ the z-axis.
\include MatrixPower.cpp
Output: \verbinclude MatrixPower.out
\note \p M has to be a matrix of \c float, \c double, \c long double
\c complex<float>, \c complex<double>, or \c complex<long double> .
MatrixBase::pow() is user-friendly. However, there are some
circumstances under which you should use class MatrixPower directly.
MatrixPower can save the result of Schur decomposition, so it's
better for computing various powers for the same matrix.
Example:
\include MatrixPower_optimal.cpp
Output: \verbinclude MatrixPower_optimal.out
\note \p M has to be a matrix of \c float, \c double, <tt>long
double</tt>, \c complex<float>, \c complex<double>, or \c complex<long
double> .
\sa MatrixBase::exp(), MatrixBase::log(), class MatrixPower.