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merge with default branch

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This commit is contained in:
Gael Guennebaud
2014-09-14 17:34:54 +02:00
parent af9c9f7706 9452eb38f8
commit 749b56f6af
34 changed files with 426 additions and 111 deletions
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21
unsupported/Eigen/MatrixFunctions
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@@ -82,7 +82,9 @@ const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::cos() const
\param[in] M a square matrix.
\returns expression representing \f$ \cos(M) \f$.
This function calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::cos().
This function computes the matrix cosine. Use ArrayBase::cos() for computing the entry-wise cosine.
The implementation calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::cos().
\sa \ref matrixbase_sin "sin()" for an example.
@@ -123,6 +125,9 @@ differential equations: the solution of \f$ y' = My \f$ with the
initial condition \f$ y(0) = y_0 \f$ is given by
\f$ y(t) = \exp(M) y_0 \f$.
The matrix exponential is different from applying the exp function to all the entries in the matrix.
Use ArrayBase::exp() if you want to do the latter.
The cost of the computation is approximately \f$ 20 n^3 \f$ for
matrices of size \f$ n \f$. The number 20 depends weakly on the
norm of the matrix.
@@ -177,6 +182,9 @@ the scalar logarithm, the equation \f$ \exp(X) = M \f$ may have
multiple solutions; this function returns a matrix whose eigenvalues
have imaginary part in the interval \f$ (-\pi,\pi] \f$.
The matrix logarithm is different from applying the log function to all the entries in the matrix.
Use ArrayBase::log() if you want to do the latter.
In the real case, the matrix \f$ M \f$ should be invertible and
it should have no eigenvalues which are real and negative (pairs of
complex conjugate eigenvalues are allowed). In the complex case, it
@@ -232,7 +240,8 @@ const MatrixPowerReturnValue<Derived> MatrixBase<Derived>::pow(RealScalar p) con
The matrix power \f$ M^p \f$ is defined as \f$ \exp(p \log(M)) \f$,
where exp denotes the matrix exponential, and log denotes the matrix
logarithm.
logarithm. This is different from raising all the entries in the matrix
to the p-th power. Use ArrayBase::pow() if you want to do the latter.
If \p p is complex, the scalar type of \p M should be the type of \p
p . \f$ M^p \f$ simply evaluates into \f$ \exp(p \log(M)) \f$.
@@ -391,7 +400,9 @@ const MatrixFunctionReturnValue<Derived> MatrixBase<Derived>::sin() const
\param[in] M a square matrix.
\returns expression representing \f$ \sin(M) \f$.
This function calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::sin().
This function computes the matrix sine. Use ArrayBase::sin() for computing the entry-wise sine.
The implementation calls \ref matrixbase_matrixfunction "matrixFunction()" with StdStemFunctions::sin().
Example: \include MatrixSine.cpp
Output: \verbinclude MatrixSine.out
@@ -428,7 +439,9 @@ const MatrixSquareRootReturnValue<Derived> MatrixBase<Derived>::sqrt() const
The matrix square root of \f$ M \f$ is the matrix \f$ M^{1/2} \f$
whose square is the original matrix; so if \f$ S = M^{1/2} \f$ then
\f$ S^2 = M \f$.
\f$ S^2 = M \f$. This is different from taking the square root of all
the entries in the matrix; use ArrayBase::sqrt() if you want to do the
latter.
In the <b>real case</b>, the matrix \f$ M \f$ should be invertible and
it should have no eigenvalues which are real and negative (pairs of

19
unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h
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@@ -45,18 +45,24 @@ namespace LevenbergMarquardtSpace {
template<typename FunctorType, typename Scalar=double>
class LevenbergMarquardt
{
static Scalar sqrt_epsilon()
{
using std::sqrt;
return sqrt(NumTraits<Scalar>::epsilon());
}
public:
LevenbergMarquardt(FunctorType &_functor)
: functor(_functor) { nfev = njev = iter = 0; fnorm = gnorm = 0.; useExternalScaling=false; }
typedef DenseIndex Index;
struct Parameters {
Parameters()
: factor(Scalar(100.))
, maxfev(400)
, ftol(sqrt_(NumTraits<Scalar>::epsilon()))
, xtol(sqrt_(NumTraits<Scalar>::epsilon()))
, ftol(sqrt_epsilon())
, xtol(sqrt_epsilon())
, gtol(Scalar(0.))
, epsfcn(Scalar(0.)) {}
Scalar factor;
@@ -72,7 +78,7 @@ public:
LevenbergMarquardtSpace::Status lmder1(
FVectorType &x,
const Scalar tol = sqrt_(NumTraits<Scalar>::epsilon())
const Scalar tol = sqrt_epsilon()
);
LevenbergMarquardtSpace::Status minimize(FVectorType &x);
@@ -83,12 +89,12 @@ public:
FunctorType &functor,
FVectorType &x,
Index *nfev,
const Scalar tol = sqrt_(NumTraits<Scalar>::epsilon())
const Scalar tol = sqrt_epsilon()
);
LevenbergMarquardtSpace::Status lmstr1(
FVectorType &x,
const Scalar tol = sqrt_(NumTraits<Scalar>::epsilon())
const Scalar tol = sqrt_epsilon()
);
LevenbergMarquardtSpace::Status minimizeOptimumStorage(FVectorType &x);
@@ -109,7 +115,6 @@ public:
Scalar lm_param(void) { return par; }
private:
static Scalar sqrt_(const Scalar& x) { using std::sqrt; return sqrt(x); }
FunctorType &functor;
Index n;