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[Toon-members] TooN Cholesky.h LU.h SymEigen.h gauss_jordan.h ...
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From: |
Edward Rosten |
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Subject: |
[Toon-members] TooN Cholesky.h LU.h SymEigen.h gauss_jordan.h ... |
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Date: |
Wed, 15 Apr 2009 15:50:36 +0000 |
CVSROOT: /cvsroot/toon
Module name: TooN
Changes by: Edward Rosten <edrosten> 09/04/15 15:50:36
Modified files:
. : Cholesky.h LU.h SymEigen.h gauss_jordan.h
gaussian_elimination.h se3.h so3.h
benchmark : solve_ax_equals_b.cc
doc : documentation.h
optimization : brent.h conjugate_gradient.h golden_section.h
test : cg_test.cc
Added files:
. : Doxyfile
Removed files:
doc : Choleskydoc.h Doxyfile LUdoc.h SymEigendoc.h
se3doc.h so3doc.h
Log message:
Move documentation around.
CVSWeb URLs:
http://cvs.savannah.gnu.org/viewcvs/TooN/Cholesky.h?cvsroot=toon&r1=1.30&r2=1.31
http://cvs.savannah.gnu.org/viewcvs/TooN/LU.h?cvsroot=toon&r1=1.16&r2=1.17
http://cvs.savannah.gnu.org/viewcvs/TooN/SymEigen.h?cvsroot=toon&r1=1.13&r2=1.14
http://cvs.savannah.gnu.org/viewcvs/TooN/gauss_jordan.h?cvsroot=toon&r1=1.4&r2=1.5
http://cvs.savannah.gnu.org/viewcvs/TooN/gaussian_elimination.h?cvsroot=toon&r1=1.5&r2=1.6
http://cvs.savannah.gnu.org/viewcvs/TooN/se3.h?cvsroot=toon&r1=1.21&r2=1.22
http://cvs.savannah.gnu.org/viewcvs/TooN/so3.h?cvsroot=toon&r1=1.31&r2=1.32
http://cvs.savannah.gnu.org/viewcvs/TooN/Doxyfile?cvsroot=toon&rev=1.1
http://cvs.savannah.gnu.org/viewcvs/TooN/benchmark/solve_ax_equals_b.cc?cvsroot=toon&r1=1.6&r2=1.7
http://cvs.savannah.gnu.org/viewcvs/TooN/doc/documentation.h?cvsroot=toon&r1=1.15&r2=1.16
http://cvs.savannah.gnu.org/viewcvs/TooN/doc/Choleskydoc.h?cvsroot=toon&r1=1.2&r2=0
http://cvs.savannah.gnu.org/viewcvs/TooN/doc/Doxyfile?cvsroot=toon&r1=1.5&r2=0
http://cvs.savannah.gnu.org/viewcvs/TooN/doc/LUdoc.h?cvsroot=toon&r1=1.5&r2=0
http://cvs.savannah.gnu.org/viewcvs/TooN/doc/SymEigendoc.h?cvsroot=toon&r1=1.3&r2=0
http://cvs.savannah.gnu.org/viewcvs/TooN/doc/se3doc.h?cvsroot=toon&r1=1.2&r2=0
http://cvs.savannah.gnu.org/viewcvs/TooN/doc/so3doc.h?cvsroot=toon&r1=1.2&r2=0
http://cvs.savannah.gnu.org/viewcvs/TooN/optimization/brent.h?cvsroot=toon&r1=1.3&r2=1.4
http://cvs.savannah.gnu.org/viewcvs/TooN/optimization/conjugate_gradient.h?cvsroot=toon&r1=1.2&r2=1.3
http://cvs.savannah.gnu.org/viewcvs/TooN/optimization/golden_section.h?cvsroot=toon&r1=1.3&r2=1.4
http://cvs.savannah.gnu.org/viewcvs/TooN/test/cg_test.cc?cvsroot=toon&r1=1.1&r2=1.2
Patches:
Index: Cholesky.h
===================================================================
RCS file: /cvsroot/toon/TooN/Cholesky.h,v
retrieving revision 1.30
retrieving revision 1.31
diff -u -b -r1.30 -r1.31
--- Cholesky.h 14 Apr 2009 13:05:02 -0000 1.30
+++ Cholesky.h 15 Apr 2009 15:50:29 -0000 1.31
@@ -36,13 +36,42 @@
namespace TooN {
-/// Cholesky decomposition of a symmetric matrix.
-/// Only the lower half of the matrix is considered
-/// This uses the non-sqrt version of the decomposition
-/// giving symmetric M = L*D*L.T() where the diagonal of L contains ones
-/// @param Size the size of the matrix
-/// @param Cols also the size of the matrix (there to make Cholesky conform to
other decompositions)
-/// @param Precision the precision of the entries in the matrix and its
decomposition
+/**
+Decomposes a positive-semidefinite symmetric matrix A (such as a covariance)
into L*D*L^T, where L is lower-triangular and D is diagonal.
+Also can compute A = S*S^T, with S lower triangular. The LDL^T form is faster
to compute than the class Cholesky decomposition.
+The decomposition can be used to compute A^-1*x, A^-1*M, M*A^-1*M^T, and A^-1
itself, though the latter rarely needs to be explicitly represented.
+Also efficiently computes det(A) and rank(A).
+It can be used as follows:
address@hidden
+// Declare some matrices.
+Matrix<3> A = ...; // we'll pretend it is pos-def
+Matrix<2,3> M;
+Matrix<2> B;
+Vector<3> y = (make_Vector, 2,3,4);
+// create the Cholesky decomposition of A
+Cholesky<3> chol(A);
+// compute x = A^-1 * y
+Vector<3> x = cholA.inverse_times(y);
+// Identical to above
+x = cholA.backsub(y);
+// compute B = M*A^-1*M^T
+B = cholA.transform_inverse(M);
+//compute A^-1
+Matrix<3> Ainv = cholA.get_inverse();
+Matrix<3> C = ... // again, C is pos-def
+//compute the 'square-root' of C
+Matrix<3> L = Cholesky<3>::sqrt(C);
address@hidden
address@hidden gDecomps
+
+Cholesky decomposition of a symmetric matrix.
+Only the lower half of the matrix is considered
+This uses the non-sqrt version of the decomposition
+giving symmetric M = L*D*L.T() where the diagonal of L contains ones
address@hidden Size the size of the matrix
address@hidden Cols also the size of the matrix (there to make Cholesky conform
to other decompositions)
address@hidden Precision the precision of the entries in the matrix and its
decomposition
+**/
template <int Size=Dynamic, int Cols=Size, class Precision=double>
class Cholesky;
@@ -51,6 +80,9 @@
public:
Cholesky(){}
+ /// Construct the Cholesky decomposition of a matrix. This initialises the
class, and
+ /// performs the decomposition immediately.
+ /// Run time is O(N^3)
template<class P2, class B2>
Cholesky(const Matrix<Size, Size, P2, B2>& m)
: my_cholesky(m) {
@@ -61,6 +93,8 @@
Cholesky(int size) : my_cholesky(size,size) {}
+ /// Compute the LDL^T decomposition of another matrix.
+ /// Run time is O(N^3)
template<class P2, class B2> void compute(const Matrix<Size, Size, P2,
B2>& m){
SizeMismatch<Size,Size>::test(m.num_rows(), m.num_cols());
SizeMismatch<Size,Size>::test(m.num_rows(),
my_cholesky.num_rows());
@@ -89,6 +123,8 @@
}
}
+ /// Compute x = A^-1*v
+ /// Run time is O(N^2)
template<int Size2, class P2, class B2>
Vector<Size, Precision> backsub (const Vector<Size2, P2, B2>& v) {
int size=my_cholesky.num_rows();
@@ -122,7 +158,7 @@
return result;
}
-
+ ///@overload
template<int Size2, int C2, class P2, class B2>
Matrix<Size, C2, Precision> backsub (const Matrix<Size2, C2, P2, B2>&
m) {
int size=my_cholesky.num_rows();
@@ -156,6 +192,8 @@
}
+ /// Compute A^-1 and store in M
+ /// Run time is O(N^3)
// easy way to get inverse - could be made more efficient
Matrix<Size,Size,Precision> get_inverse(){
Matrix<Size,Size,Precision>I(Identity(my_cholesky.num_rows()));
Index: LU.h
===================================================================
RCS file: /cvsroot/toon/TooN/LU.h,v
retrieving revision 1.16
retrieving revision 1.17
diff -u -b -r1.16 -r1.17
--- LU.h 10 Apr 2009 05:48:54 -0000 1.16
+++ LU.h 15 Apr 2009 15:50:32 -0000 1.17
@@ -38,17 +38,44 @@
#include <TooN/TooN.h>
namespace TooN {
-
+/**
+Performs %LU decomposition and back substitutes to solve equations.
+The %LU decomposition is the fastest way of solving the equation
+\f$M\underline{x} = \underline{c}\f$m, but it becomes unstable when
+\f$M\f$ is (nearly) singular (in which cases the SymEigen or SVD decompositions
+are better). It decomposes a matrix \f$M\f$ into
+\f[M = L \times U\f]
+where \f$L\f$ is a lower-diagonal matrix with unit diagonal and \f$U\f$ is an
+upper-diagonal matrix. The library only supports the decomposition of square
matrices.
+It can be used as follows to solve the \f$M\underline{x} = \underline{c}\f$
problem as follows:
address@hidden
+// construct M
+double d1[][] = {{1,2,3},{4,5,6},{7,8,10}};
+Matrix<3> M(d1);
+// construct c
+Vector<3> c = 2,3,4;
+// create the LU decomposition of M
+LU<3> luM(M);
+// compute x = M^-1 * c
+Vector<3> x = luM.backsub(c);
address@hidden
+The convention LU<> (=LU<-1>) is used to create an LU decomposition whose size
is
+determined at runtime.
address@hidden gDecomps
+**/
template <int Size=-1, class Precision=double>
class LU {
public:
+ /// Construct the %LU decomposition of a matrix. This initialises the
class, and
+ /// performs the decomposition immediately.
template<int S1, int S2, class Base>
LU(const Matrix<S1,S2,Precision, Base>& m)
:my_lu(m.num_rows(),m.num_cols()),my_IPIV(m.num_rows()){
compute(m);
}
+ /// Perform the %LU decompsition of another matrix.
template<int S1, int S2, class Base>
void compute(const Matrix<S1,S2,Precision,Base>& m){
//check for consistency with Size
@@ -68,6 +95,8 @@
}
}
+ /// Calculate result of multiplying the inverse of M by another matrix.
For a matrix \f$A\f$, this
+ /// calculates \f$M^{-1}A\f$ by back substitution (i.e. without
explictly calculating the inverse).
template <int Rows, int NRHS, class Base>
Matrix<Size,NRHS,Precision> backsub(const Matrix<Rows,NRHS,Precision,Base>&
rhs){
//Check the number of rows is OK.
@@ -95,6 +124,8 @@
return result;
}
+ /// Calculate result of multiplying the inverse of M by a vector. For a
vector \f$b\f$, this
+ /// calculates \f$M^{-1}b\f$ by back substitution (i.e. without
explictly calculating the inverse).
template <int Rows, class Base>
Vector<Size,Precision> backsub(const Vector<Rows,Precision,Base>& rhs){
//Check the number of rows is OK.
@@ -120,6 +151,8 @@
return result;
}
+ /// Calculate inverse of the matrix. This is not usually needed: if you
need the inverse just to
+ /// multiply it by a matrix or a vector, use one of the backsub()
functions, which will be faster.
Matrix<Size,Size,Precision> get_inverse(){
Matrix<Size,Size,Precision> Inverse(my_lu);
int N = my_lu.num_rows();
@@ -134,7 +167,11 @@
return Inverse;
}
- Matrix<Size,Size,Precision>& get_lu(){return my_lu;}
+ /// Returns the L and U matrices. The permutation matrix is not
returned.
+ /// Since L is lower-triangular (with unit diagonal)
+ /// and U is upper-triangular, these are returned conflated into one
matrix, where the
+ /// diagonal and above parts of the matrix are U and the below-diagonal
part, plus a unit diagonal,
+ /// are L.
const Matrix<Size,Size,Precision>& get_lu()const {return my_lu;}
inline int get_sign() const {
@@ -147,6 +184,7 @@
return result;
}
+ /// Calculate the determinant of the matrix
inline Precision determinant() const {
Precision result = get_sign();
for (int i=0; i<my_lu.num_rows(); i++){
@@ -155,6 +193,7 @@
return result;
}
+ /// Get the LAPACK info
int get_info() const { return my_info; }
private:
Index: SymEigen.h
===================================================================
RCS file: /cvsroot/toon/TooN/SymEigen.h,v
retrieving revision 1.13
retrieving revision 1.14
diff -u -b -r1.13 -r1.14
--- SymEigen.h 14 Apr 2009 14:56:11 -0000 1.13
+++ SymEigen.h 15 Apr 2009 15:50:32 -0000 1.14
@@ -94,16 +94,44 @@
}
};
+/**
+Performs eigen decomposition of a matrix.
+Real symmetric (and hence square matrices) can be decomposed into
+\f[M = U \times \Lambda \times U^T\f]
+where \f$U\f$ is an orthogonal matrix (and hence \f$U^T = U^{-1}\f$) whose
columns
+are the eigenvectors of \f$M\f$ and \f$\Lambda\f$ is a diagonal matrix whose
entries
+are the eigenvalues of \f$M\f$. These quantities are often of use directly,
and can
+be obtained as follows:
address@hidden
+// construct M
+double d1[][] = {{1,2,3},{2,5,6},{3,6,7}};
+Matrix<3> M(d1);
+// create the eigen decomposition of M
+SymEigen<3> eigM(M);
+// print the smallest eigenvalue
+cout << eigM.get_evalues()[0] << endl;
+// print the associated eigenvector
+cout << eigM.get_evectors()[0] << endl;
address@hidden
+
+This decomposition is very similar to the SVD (q.v.), and can be used to solve
+equations using backsub() or get_pinv(), with the same treatment of condition
numbers.
+
+SymEigen<> (= SymEigen<-1>) can be used to create an eigen decomposition whose
size is determined at run-time.
address@hidden gDecomps
+**/
template <int Size=Dynamic, typename Precision = double>
class SymEigen {
public:
inline SymEigen(){}
-
+ /// Construct the eigen decomposition of a matrix. This initialises the
class, and
+ /// performs the decomposition immediately.
template<int R, int C, typename B>
inline SymEigen(const Matrix<R, C, Precision, B>& m) :
my_evectors(m.num_rows(), m.num_cols()), my_evalues(m.num_rows()) {
compute(m);
}
+ /// Perform the eigen decomposition of a matrix.
template<int R, int C, typename B>
inline void compute(const Matrix<R,C,Precision,B>& m){
SizeMismatch<R, C>::test(m.num_rows(), m.num_cols());
@@ -111,20 +139,39 @@
ComputeSymEigen<Size>::compute(m, my_evectors, my_evalues);
}
+ /// Calculate result of multiplying the (pseudo-)inverse of M by a
vector.
+ /// For a vector \f$b\f$, this calculates \f$M^{\dagger}b\f$ by back
substitution
+ /// (i.e. without explictly calculating the (pseudo-)inverse).
+ /// See the SVD detailed description for a description of condition
variables.
template <int S, typename P, typename B>
Vector<Size, Precision> backsub(const Vector<S,P,B>& rhs) const {
return (my_evectors.T() *
diagmult(get_inv_diag(symeigen_condition_no),(my_evectors * rhs)));
}
+ /// Calculate result of multiplying the (pseudo-)inverse of M by
another matrix.
+ /// For a matrix \f$A\f$, this calculates \f$M^{\dagger}A\f$ by back
substitution
+ /// (i.e. without explictly calculating the (pseudo-)inverse).
+ /// See the SVD detailed description for a description of condition
variables.
template <int R, int C, typename P, typename B>
Matrix<Size,C, Precision> backsub(const Matrix<R,C,P,B>& rhs) const {
return (my_evectors.T() *
diagmult(get_inv_diag(symeigen_condition_no),(my_evectors * rhs)));
}
+ /// Calculate (pseudo-)inverse of the matrix. This is not usually
needed:
+ /// if you need the inverse just to multiply it by a matrix or a
vector, use
+ /// one of the backsub() functions, which will be faster.
+ /// See the SVD detailed description for a description of the
pseudo-inverse
+ /// and condition variables.
Matrix<Size, Size, Precision> get_pinv(const double
condition=symeigen_condition_no) const {
return my_evectors.T() *
diagmult(get_inv_diag(condition),my_evectors);
}
+ /// Calculates the reciprocals of the eigenvalues of the matrix.
+ /// The vector <code>invdiag</code> lists the eigenvalues in order, from
+ /// the largest (i.e. smallest reciprocal) to the smallest.
+ /// These are also the diagonal values of the matrix \f$Lambda^{-1}\f$.
+ /// Any eigenvalues which are too small are set to zero (see the SVD
+ /// detailed description for a description of the and condition
variables).
Vector<Size, Precision> get_inv_diag(const double condition) const {
Precision max_diag = -my_evalues[0] >
my_evalues[my_evalues.size()-1] ?
-my_evalues[0]:my_evalues[my_evalues.size()-1];
Vector<Size, Precision> invdiag(my_evalues.size());
@@ -138,11 +185,22 @@
return invdiag;
}
+ /// Returns the eigenvectors of the matrix.
+ /// This returns \f$U^T\f$, so that the rows of the matrix are the
eigenvectors,
+ /// which can be extracted using usual Matrix::operator[]() subscript
operator.
+ /// They are returned in order of the size of the corresponding
eigenvalue, i.e.
+ /// the vector with the largest eigenvalue is first.
Matrix<Size,Size,Precision>& get_evectors() {return my_evectors;}
const Matrix<Size,Size,Precision>& get_evectors() const {return
my_evectors;}
+
+
+ /// Returns the eigenvalues of the matrix.
+ /// The eigenvalues are listed in order, from the largest to the
smallest.
+ /// These are also the diagonal values of the matrix \f$\Lambda\f$.
Vector<Size, Precision>& get_evalues() {return my_evalues;}
const Vector<Size, Precision>& get_evalues() const {return my_evalues;}
+ /// Is the matrix positive definite?
bool is_posdef() const {
for (int i = 0; i < my_evalues.size(); ++i) {
if (my_evalues[i] <= 0.0)
@@ -151,6 +209,7 @@
return true;
}
+ /// Is the matrix negative definite?
bool is_negdef() const {
for (int i = 0; i < my_evalues.size(); ++i) {
if (my_evalues[i] >= 0.0)
@@ -159,6 +218,7 @@
return true;
}
+ /// Get the determinant of the matrix
Precision get_determinant () const {
Precision det = 1.0;
for (int i = 0; i < my_evalues.size(); ++i) {
Index: gauss_jordan.h
===================================================================
RCS file: /cvsroot/toon/TooN/gauss_jordan.h,v
retrieving revision 1.4
retrieving revision 1.5
diff -u -b -r1.4 -r1.5
--- gauss_jordan.h 10 Apr 2009 00:44:48 -0000 1.4
+++ gauss_jordan.h 15 Apr 2009 15:50:32 -0000 1.5
@@ -45,6 +45,7 @@
/// partial pivoting.
///
/// @param m The matrix to be reduced.
+/// @ingroup gDecomps
template<int R, int C, class Precision, class Base> void
gauss_jordan(Matrix<R, C, Precision, Base>& m)
{
using std::swap;
Index: gaussian_elimination.h
===================================================================
RCS file: /cvsroot/toon/TooN/gaussian_elimination.h,v
retrieving revision 1.5
retrieving revision 1.6
diff -u -b -r1.5 -r1.6
--- gaussian_elimination.h 10 Apr 2009 00:57:13 -0000 1.5
+++ gaussian_elimination.h 15 Apr 2009 15:50:32 -0000 1.6
@@ -36,6 +36,7 @@
#include <TooN/TooN.h>
namespace TooN {
+ ///@ingroup gLinAlg
template<int N, typename Precision>
inline Vector<N, Precision> gaussian_elimination (Matrix<N,N,Precision>
A, Vector<N, Precision> b) {
using std::swap;
@@ -93,6 +94,7 @@
};
+ ///@ingroup gLinAlg
template<int R1, int C1, int R2, int C2, typename Precision>
inline Matrix<Internal::Size3<R1, C1, R2>::s, C2, Precision>
gaussian_elimination (Matrix<R1,C1,Precision> A, Matrix<R2, C2, Precision> b) {
using std::swap;
Index: se3.h
===================================================================
RCS file: /cvsroot/toon/TooN/se3.h,v
retrieving revision 1.21
retrieving revision 1.22
diff -u -b -r1.21 -r1.22
--- se3.h 14 Apr 2009 12:42:36 -0000 1.21
+++ se3.h 15 Apr 2009 15:50:33 -0000 1.22
@@ -34,9 +34,22 @@
namespace TooN {
+
+/// Represent a three-dimensional Euclidean transformation (a rotation and a
translation).
+/// This can be represented by a \f$3\times\f$4 matrix operating on a
homogeneous co-ordinate,
+/// so that a vector \f$\underline{x}\f$ is transformed to a new location
\f$\underline{x}'\f$
+/// by
+/// \f[\begin{aligned}\underline{x}' &= E\times\underline{x}\\
\begin{bmatrix}x'\\y'\\z'\end{bmatrix} &= \begin{pmatrix}r_{11} & r_{12} &
r_{13} & t_1\\r_{21} & r_{22} & r_{23} & t_2\\r_{31} & r_{32} & r_{33} &
t_3\end{pmatrix}\begin{bmatrix}x\\y\\z\\1\end{bmatrix}\end{aligned}\f]
+///
+/// This transformation is a member of the Special Euclidean Lie group SE3.
These can be parameterised
+/// six numbers (in the space of the Lie Algebra). In this class, the first
three parameters are a
+/// translation vector while the second three are a rotation vector, whose
direction is the axis of rotation
+/// and length the amount of rotation (in radians), as for SO3
+/// @ingroup gTransforms
template <typename Precision = double>
class SE3 {
public:
+ /// Default constructor. Initialises the the rotation to zero (the
identity) and the translation to zero
inline SE3() : my_translation(Zero) {}
template <int S, typename P, typename A>
@@ -44,14 +57,27 @@
template <int S, typename P, typename A>
SE3(const Vector<S, P, A> & v) { *this = exp(v); }
+ /// Returns the rotation part of the transformation as a SO3
inline SO3<Precision>& get_rotation(){return my_rotation;}
+ /// @overload
inline const SO3<Precision>& get_rotation() const {return my_rotation;}
+
+ /// Returns the translation part of the transformation as a Vector
inline Vector<3, Precision>& get_translation() {return my_translation;}
+ /// @overload
inline const Vector<3, Precision>& get_translation() const {return
my_translation;}
+ /// Exponentiate a Vector in the Lie Algebra to generate a new SE3.
+ /// See the Detailed Description for details of this vector.
+ /// @param vect The Vector to exponentiate
template <int S, typename P, typename A>
static inline SE3 exp(const Vector<S, P, A>& vect);
+
+
+ /// Take the logarithm of the matrix, generating the corresponding
vector in the Lie Algebra.
+ /// See the Detailed Description for details of this vector.
static inline Vector<6, Precision> ln(const SE3& se3);
+ /// @overload
inline Vector<6, Precision> ln() const { return SE3::ln(*this); }
inline SE3 inverse() const {
@@ -59,11 +85,16 @@
return SE3(rinv, -(rinv*my_translation));
}
+ /// Right-multiply by another SE3 (concatenate the two transformations)
+ /// @param rhs The multipier
inline SE3& operator *=(const SE3& rhs) {
get_translation() += get_rotation() * rhs.get_translation();
get_rotation() *= rhs.get_rotation();
return *this;
}
+
+ /// Right-multiply by another SE3 (concatenate the two transformations)
+ /// @param rhs The multipier
inline SE3 operator *(const SE3& rhs) const { return
SE3(get_rotation()*rhs.get_rotation(), get_translation() +
get_rotation()*rhs.get_translation()); }
inline SE3& left_multiply_by(const SE3& left) {
@@ -83,15 +114,24 @@
return result;
}
+ /// Transfer a matrix in the Lie Algebra from one
+ /// co-ordinate frame to another. This is the operation such that for a
matrix
+ /// \f$ B \f$,
+ /// \f$ e^{\text{Adj}(v)} = Be^{v}B^{-1} \f$
+ /// @param M The Matrix to transfer
template<int S, typename Accessor>
inline Vector<6, Precision> adjoint(const Vector<S,Precision,
Accessor>& vect)const;
+ /// Transfer covectors between frames (using the transpose of the
inverse of the adjoint)
+ /// so that trinvadjoint(vect1) * adjoint(vect2) = vect1 * vect2
template<int S, typename Accessor>
inline Vector<6, Precision> trinvadjoint(const
Vector<S,Precision,Accessor>& vect)const;
+ ///@overload
template <int R, int C, typename Accessor>
inline Matrix<6,6,Precision> adjoint(const
Matrix<R,C,Precision,Accessor>& M)const;
+ ///@overload
template <int R, int C, typename Accessor>
inline Matrix<6,6,Precision> trinvadjoint(const
Matrix<R,C,Precision,Accessor>& M)const;
@@ -160,7 +200,8 @@
return result;
}
-// operator ostream& <<
+/// Write an SE3 to a stream
+/// @relates SE3
template <typename Precision>
inline std::ostream& operator <<(std::ostream& os, const SE3<Precision>& rhs){
for(int i=0; i<3; i++){
@@ -169,7 +210,9 @@
return os;
}
-// operator istream& >>
+
+/// Reads an SE3 from a stream
+/// @relates SE3
template <typename Precision>
inline std::istream& operator>>(std::istream& is, SE3<Precision>& rhs){
for(int i=0; i<3; i++){
@@ -206,11 +249,15 @@
int size() const { return 4; }
};
+/// Right-multiply by a Vector
+/// @relates SE3
template<int S, typename PV, typename A, typename P> inline
Vector<4, typename Internal::MultiplyType<P,PV>::type> operator*(const SE3<P>
& lhs, const Vector<S,PV,A>& rhs){
return Vector<4, typename
Internal::MultiplyType<P,PV>::type>(Operator<Internal::SE3VMult<S,PV,A,P>
>(lhs,rhs));
}
+/// Right-multiply by a Vector
+/// @relates SE3
template <typename PV, typename A, typename P> inline
Vector<3, typename Internal::MultiplyType<P,PV>::type> operator*(const SE3<P>&
lhs, const Vector<3,PV,A>& rhs){
return lhs.get_translation() + lhs.get_rotation() * rhs;
@@ -243,6 +290,8 @@
int size() const { return 4; }
};
+/// Left-multiply by a Vector
+/// @relates SE3
template<int S, typename PV, typename A, typename P> inline
Vector<4, typename Internal::MultiplyType<P,PV>::type> operator*( const
Vector<S,PV,A>& lhs, const SE3<P> & rhs){
return Vector<4, typename
Internal::MultiplyType<P,PV>::type>(Operator<Internal::VSE3Mult<S,PV,A,P>
>(lhs,rhs));
@@ -275,6 +324,8 @@
int num_rows() const { return 4; }
};
+/// Right-multiply by a Matrix
+/// @relates SE3
template <int R, int Cols, typename PM, typename A, typename P> inline
Matrix<4,Cols, typename Internal::MultiplyType<P,PM>::type> operator*(const
SE3<P> & lhs, const Matrix<R,Cols,PM, A>& rhs){
return Matrix<4,Cols,typename
Internal::MultiplyType<P,PM>::type>(Operator<Internal::SE3MMult<R, Cols, PM, A,
P> >(lhs,rhs));
@@ -307,6 +358,8 @@
int num_rows() const { return lhs.num_rows(); }
};
+/// Left-multiply by a Matrix
+/// @relates SE3
template <int Rows, int C, typename PM, typename A, typename P> inline
Matrix<Rows,4, typename Internal::MultiplyType<PM,P>::type> operator*(const
Matrix<Rows,C,PM, A>& lhs, const SE3<P> & rhs ){
return Matrix<Rows,4,typename
Internal::MultiplyType<PM,P>::type>(Operator<Internal::MSE3Mult<Rows, C, PM, A,
P> >(lhs,rhs));
Index: so3.h
===================================================================
RCS file: /cvsroot/toon/TooN/so3.h,v
retrieving revision 1.31
retrieving revision 1.32
diff -u -b -r1.31 -r1.32
--- so3.h 14 Apr 2009 12:42:36 -0000 1.31
+++ so3.h 15 Apr 2009 15:50:33 -0000 1.32
@@ -41,6 +41,13 @@
template<class Precision> inline std::istream & operator>>(std::istream &,
SO3<Precision> & );
template<class Precision> inline std::istream & operator>>(std::istream &,
SE3<Precision> & );
+/// Class to represent a three-dimensional rotation matrix. Three-dimensional
rotation
+/// matrices are members of the Special Orthogonal Lie group SO3. This group
can be parameterised
+/// three numbers (a vector in the space of the Lie Algebra). In this class,
the three parameters are the
+/// finite rotation vector, i.e. a three-dimensional vector whose direction is
the axis of rotation
+/// and whose length is the angle of rotation in radians. Exponentiating this
vector gives the matrix,
+/// and the logarithm of the matrix gives this vector.
+/// @ingroup gTransforms
template <typename Precision = double>
class SO3 {
public:
@@ -48,6 +55,7 @@
friend std::istream& operator>> <Precision> (std::istream& is,
SE3<Precision> & rhs);
friend class SE3<Precision>;
+ /// Default constructor. Initialises the matrix to the identity (no
rotation)
SO3() : my_matrix(Identity) {}
template <int S, typename P, typename A>
@@ -56,6 +64,8 @@
template <int R, int C, typename P, typename A>
SO3(const Matrix<R,C,P,A>& rhs) { *this = rhs; }
+ /// Assigment operator from a general matrix. This also calls coerce()
+ /// to make sure that the matrix is a valid rotation matrix.
template <int R, int C, typename P, typename A>
SO3& operator=(const Matrix<R,C,P,A> & rhs) {
my_matrix = rhs;
@@ -63,6 +73,7 @@
return *this;
}
+ /// Modifies the matrix to make sure it is a valid rotation matrix.
void coerce() {
my_matrix[0] = unit(my_matrix[0]);
my_matrix[1] -= my_matrix[0] * (my_matrix[0]*my_matrix[1]);
@@ -72,21 +83,33 @@
my_matrix[2] = unit(my_matrix[2]);
}
+ /// Exponentiate a vector in the Lie algebra to generate a new SO3.
+ /// See the Detailed Description for details of this vector.
template<int S, typename A> inline static SO3 exp(const
Vector<S,Precision,A>& vect);
+ /// Take the logarithm of the matrix, generating the corresponding
vector in the Lie Algebra.
+ /// See the Detailed Description for details of this vector.
inline Vector<3, Precision> ln() const;
+ /// Returns the inverse of this matrix (=the transpose, so this is a
fast operation)
SO3 inverse() const { return SO3(*this, Invert()); }
+ /// Right-multiply by another rotation matrix
SO3& operator *=(const SO3& rhs) {
*this = *this * rhs;
return *this;
}
+ /// Right-multiply by another rotation matrix
SO3 operator *(const SO3& rhs) const { return SO3(*this,rhs); }
+ /// Returns the SO3 as a Matrix<3>
const Matrix<3,3, Precision> & get_matrix() const {return my_matrix;}
+ /// Returns the i-th generator. The generators of a Lie group are the
basis
+ /// for the space of the Lie algebra. For %SO3, the generators are
three
+ /// \f$3\times3\f$ matrices representing the three possible (linearised)
+ /// rotations.
inline static Matrix<3,3, Precision> generator(int i){
Matrix<3,3,Precision> result(Zero);
result[(i+1)%3][(i+2)%3] = -1;
@@ -94,7 +117,10 @@
return result;
}
- // adjoint transformation on the Lie algebra
+ /// Transfer a vector in the Lie Algebra from one
+ /// co-ordinate frame to another such that for a matrix
+ /// \f$ M \f$, the adjoint \f$Adj()\f$ obeys
+ /// \f$ e^{\text{Adj}(v)} = Me^{v}M^{-1} \f$
template <int S, typename A>
inline Vector<3, Precision> adjoint(Vector<3, Precision, A> vect) const
{ return *this * vect; }
@@ -106,11 +132,15 @@
Matrix<3,3, Precision> my_matrix;
};
+/// Write an SO3 to a stream
+/// @relates SO3
template <typename Precision>
inline std::ostream& operator<< (std::ostream& os, const SO3<Precision>& rhs){
return os << rhs.get_matrix();
}
+/// Read from SO3 to a stream
+/// @relates SO3
template <typename Precision>
inline std::istream& operator>>(std::istream& is, SO3<Precision>& rhs){
return is >> rhs.my_matrix;
@@ -225,21 +255,29 @@
return result;
}
+/// Right-multiply by a Vector
+/// @relates SO3
template<int S, typename P, typename PV, typename A> inline
Vector<3, typename Internal::MultiplyType<P, PV>::type> operator*(const
SO3<P>& lhs, const Vector<S, PV, A>& rhs){
return lhs.get_matrix() * rhs;
}
+/// Left-multiply by a Vector
+/// @relates SO3
template<int S, typename P, typename PV, typename A> inline
Vector<3, typename Internal::MultiplyType<PV, P>::type> operator*(const
Vector<S, PV, A>& lhs, const SO3<P>& rhs){
return lhs * rhs.get_matrix();
}
+/// Multiply two SO3 matrices
+/// @relates SO3
template<int R, int C, typename P, typename PM, typename A> inline
Matrix<3, C, typename Internal::MultiplyType<P, PM>::type> operator*(const
SO3<P>& lhs, const Matrix<R, C, PM, A>& rhs){
return lhs.get_matrix() * rhs;
}
+/// Multiply two SO3 matrices
+/// @relates SO3
template<int R, int C, typename P, typename PM, typename A> inline
Matrix<R, 3, typename Internal::MultiplyType<PM, P>::type> operator*(const
Matrix<R, C, PM, A>& lhs, const SO3<P>& rhs){
return lhs * rhs.get_matrix();
Index: benchmark/solve_ax_equals_b.cc
===================================================================
RCS file: /cvsroot/toon/TooN/benchmark/solve_ax_equals_b.cc,v
retrieving revision 1.6
retrieving revision 1.7
diff -u -b -r1.6 -r1.7
--- benchmark/solve_ax_equals_b.cc 2 Apr 2009 13:36:24 -0000 1.6
+++ benchmark/solve_ax_equals_b.cc 15 Apr 2009 15:50:33 -0000 1.7
@@ -122,6 +122,7 @@
}
};
+
template<int Size, int Cols, class Solver> void benchmark_ax_eq_b(map<string,
vector<double> >& results)
{
double time=0, t_tmp, start = get_time_of_day(), t_tmp2;
@@ -146,15 +147,7 @@
Solver::template solve<Size, Cols>(a, b, x);
global_sum += (t_tmp2=get_time_of_day())*x[Size-1][Cols-1];
-
time += t_tmp2 - t_tmp;
-
-
-
- for(int r=0; r < Size; r++)
- for(int c=0; c < Cols; c++)
- sum += x[r][c];
-
n++;
}
@@ -187,8 +180,8 @@
static void iter()
{
static const int Lin = Size*2;
- static const int Grow = 2;
- static const int Cols = C + (C<=Lin?0:(C-Lin)*(C-Lin)/Grow);
+ static const int Grow = 1;
+ static const int Cols = C +
(C<=Lin?0:(C-Lin)*(C-Lin)*(C-Lin)/Grow);
map<string, vector<double> > results;
cout << Size << "\t" << Cols << "\t";
@@ -216,7 +209,7 @@
for(unsigned int i=0; i < res.size(); i++)
cout << res[i].second << " " << setprecision(5) <<
setw(10) << res[i].first << " ";
cout << endl;
- ColIter<Size, C+1, (Cols> 0)>::iter();
+ ColIter<Size, C+1, (Cols> Size*1000)>::iter();
}
};
Index: doc/documentation.h
===================================================================
RCS file: /cvsroot/toon/TooN/doc/documentation.h,v
retrieving revision 1.15
retrieving revision 1.16
diff -u -b -r1.15 -r1.16
--- doc/documentation.h 14 Apr 2009 07:12:37 -0000 1.15
+++ doc/documentation.h 15 Apr 2009 15:50:35 -0000 1.16
@@ -25,17 +25,10 @@
The %TooN library is a set of C++ header files which provide basic numerics
facilities:
- @link TooN::Vector address@hidden and @link TooN::Matrix
address@hidden
- - @link gDecomps Matrix address@hidden (@link TooN::LU address@hidden,
- @link TooN::SVD address@hidden, @link TooN::SymEigen symmetric eigen
- decomposition @endlink)
- - @link gOptimize Function address@hidden (@link
- TooN::DownhillSimplex Downhill address@hidden)
- - Some particular types of @link gTransforms transformation
- address@hidden (@link TooN::SO3 address@hidden and @link TooN::SE3
- address@hidden)
- - Solvers for systems of @link gEquations linear address@hidden using
- @link TooN::WLS address@hidden or @link TooN::IRLS
- address@hidden least squares.
+ - @link gDecomps Matrix address@hidden
+ - @link gOptimize Function address@hidden
+ - @link gTransforms Parameterized matrices (eg transformations)@endlink
+ - @link gEquations linear address@hidden
It provides classes for statically- (known at compile time) and dynamically-
(unknown at compile time) sized vectors and matrices and it delegates advanced
@@ -586,5 +579,29 @@
/// @defgroup gEquations Linear equation solvers
/// Classes to solve linear equations.
-/// @defgroup gOptimize Function optimization
-/// Classes to perform function optimization.
+/**
address@hidden gOptimize Function optimization
+
+Classes and functions to perform function optimization.
+
address@hidden gOneDim One dimensional function optimization
+
+The following functions find the minimum of a 1-D function:
+ - golden_section_search()
+ - brent_line_search()
+
address@hidden gMultiDim Multidimensional dimensional function optimization
+
+The following classes perform multidimensional function minimization:
+ - TooN::DownhillSimplex
+ - TooN::ConjugateGradient
+
+The mode of operation is to set up a mutable class, then repeatedly call an
+iterate function. This allows different sub algorithms (such as termination
+conditions) to be substituted in if need be.
+
address@hidden gTooN Main parts of TooN
+
+
address@hidden gInternal TooN internals
+*/
Index: optimization/brent.h
===================================================================
RCS file: /cvsroot/toon/TooN/optimization/brent.h,v
retrieving revision 1.3
retrieving revision 1.4
diff -u -b -r1.3 -r1.4
--- optimization/brent.h 9 Apr 2009 11:07:22 -0000 1.3
+++ optimization/brent.h 15 Apr 2009 15:50:35 -0000 1.4
@@ -25,6 +25,7 @@
/// @param epsilon Minimum bracket width (defaults to machine precision)
/// @return The minima position is returned as the first element of the
vector,
/// and the minimal value as the second element.
+ /// @ingroup gOptimize
template<class Functor, class Precision> Vector<2, Precision>
brent_line_search(Precision a, Precision x, Precision b, Precision fx, const
Functor& func, int maxiterations, Precision tolerance =
sqrt(numeric_limits<Precision>::epsilon()), Precision epsilon =
numeric_limits<Precision>::epsilon())
{
using std::min;
Index: optimization/conjugate_gradient.h
===================================================================
RCS file: /cvsroot/toon/TooN/optimization/conjugate_gradient.h,v
retrieving revision 1.2
retrieving revision 1.3
diff -u -b -r1.2 -r1.3
--- optimization/conjugate_gradient.h 9 Apr 2009 11:14:27 -0000 1.2
+++ optimization/conjugate_gradient.h 15 Apr 2009 15:50:35 -0000 1.3
@@ -10,21 +10,28 @@
///Turn a multidimensional function in to a 1D function by specifying a
- ///point and direction.
+ ///point and direction. A nre function is defined:
+ ////\f[
+ /// g(a) = \Vec{s} + a \Vec{d}
+ ///\f]
+ ///@ingroup gOptimize
template<int Size, typename Precision, typename Func> struct LineSearch
{
- const Vector<Size, Precision>& start, direction;
- const Func& f;
+ const Vector<Size, Precision>& start; ///< \f$\Vec{s}\f$
+ const Vector<Size, Precision>& direction;///< \f$\Vec{d}\f$
- ///@param s Start point.
- ///@param d direction
- ///@param func Function.
+ const Func& f;///< \f$f(\cdotp)\f$
+
+ ///Set up the line search class.
+ ///@param s Start point, \f$\Vec{s}\f$.
+ ///@param d direction, \f$\Vec{d}\f$.
+ ///@param func Function, \f$f(\cdotp)\f$.
LineSearch(const Vector<Size, Precision>& s, const Vector<Size,
Precision>& d, const Func& func)
:start(s),direction(d),f(func)
{}
///@param x Position to evaluate function
- ///@return \f$f(\vec{d} + x\vec{s})\f$
+ ///@return \f$f(\vec{s} + x\vec{d})\f$
Precision operator()(Precision x) const
{
return f(start + x * direction);
@@ -39,6 +46,7 @@
///@param initial_lambda Initial stepsize
///@return <code>m[i][0]</code> contains the values of \f$x\f$ for the
bracket, in increasing order,
/// and <code>m[i][1]</code> contains the corresponding values
of \f$f(x)\f$.
+ ///@ingroup gOptimize
template<typename Precision, typename Func> Matrix<3,2,Precision>
bracket_minimum_forward(Precision a_val, const Func& func, Precision
initial_lambda=1)
{
//Get a, b, c to bracket a minimum along a line
@@ -137,11 +145,16 @@
}
@endcode
+The chances are that you will want to read the documentation for
+ConjugateGradient::ConjugateGradient and ConjugateGradient::iterate.
+
Linesearch is currently performed using golden-section search and conjugate
vector updates are performed using the Polak-Ribiere equations. There many
tunable parameters, and the internals are readily accessible, so alternative
termination conditions etc can easily be substituted. However, ususally these
will not be necessary.
+
address@hidden gOptimize
*/
template<int Size, class Precision=double> struct ConjugateGradient
{
@@ -166,6 +179,10 @@
int iterations; ///< Number of iterations performed
+ ///Initialize the ConjugateGradient class with sensible values.
+ ///@param start Starting point, \e x
+ ///@param func Function \e f to compute \f$f(x)\f$
+ ///@param deriv Function to compute \f$\nabla f(x)\f$
template<class Func, class Deriv> ConjugateGradient(const Vector<Size>&
start, const Func& func, const Deriv& deriv)
: size(start.size()),
g(size),h(size),old_g(size),old_h(size),x(start),old_x(size)
@@ -197,8 +214,8 @@
///Perform a linesearch from the current point (x) along the current
- ///conjugate vector (h). /The linesearch does not make use of
derivatives.
- ///You probably do not want to use /this function. See iterate()
instead.
+ ///conjugate vector (h). The linesearch does not make use of
derivatives.
+ ///You probably do not want to use this function. See iterate() instead.
///This function updates:
/// - x
/// - old_c
Index: optimization/golden_section.h
===================================================================
RCS file: /cvsroot/toon/TooN/optimization/golden_section.h,v
retrieving revision 1.3
retrieving revision 1.4
diff -u -b -r1.3 -r1.4
--- optimization/golden_section.h 14 Apr 2009 12:56:25 -0000 1.3
+++ optimization/golden_section.h 15 Apr 2009 15:50:36 -0000 1.4
@@ -22,6 +22,7 @@
/// @param tolerance Tolerance at which the search should be stopped.
/// @return The minima position is returned as the first element of the
vector,
/// and the minimal value as the second element.
+ /// @ingroup gOptimize
template<class Functor, class Precision> Vector<2, Precision>
golden_section_search(Precision a, Precision b, Precision c, Precision fb,
const Functor& func, int maxiterations, Precision tol =
sqrt(numeric_limits<Precision>::epsilon()))
{
using std::abs;
@@ -100,6 +101,7 @@
/// @param tolerance Tolerance at which the search should be stopped.
/// @return The minima position is returned as the first element of the
vector,
/// and the minimal value as the second element.
+ /// @ingroup gOptimize
template<class Functor, class Precision> Vector<2, Precision>
golden_section_search(Precision a, Precision b, Precision c, const Functor&
func, int maxiterations, Precision tol =
sqrt(numeric_limits<Precision>::epsilon()))
{
return golden_section_search(a, b, c, func(b), func,
maxiterations, tol);
Index: test/cg_test.cc
===================================================================
RCS file: /cvsroot/toon/TooN/test/cg_test.cc,v
retrieving revision 1.1
retrieving revision 1.2
diff -u -b -r1.1 -r1.2
--- test/cg_test.cc 7 Apr 2009 14:33:06 -0000 1.1
+++ test/cg_test.cc 15 Apr 2009 15:50:36 -0000 1.2
@@ -30,11 +30,13 @@
return ret;
}
+int evals=0;
double Spiral(const Vector<2>& v)
{
double x = v[0];
double y = v[1];
+ evals++;
return sin(20.0*sqrt(x*x+y*y)+2.0*atan(y/x))+2.0*x*x+2.0*y*y;
}
@@ -60,5 +62,7 @@
while(cg.iterate(Spiral, SpiralDerivatives))
cout << cg.x << " " << cg.y << endl;
cout << cg.x << " " << cg.y << endl;
+
+ cerr << "Total evaluations: " << evals << endl;
}
Index: Doxyfile
===================================================================
RCS file: Doxyfile
diff -N Doxyfile
--- /dev/null 1 Jan 1970 00:00:00 -0000
+++ Doxyfile 15 Apr 2009 15:50:30 -0000 1.1
@@ -0,0 +1,1118 @@
+# Doxyfile 1.3.6
+
+# This file describes the settings to be used by the documentation system
+# doxygen (www.doxygen.org) for a project
+#
+# All text after a hash (#) is considered a comment and will be ignored
+# The format is:
+# TAG = value [value, ...]
+# For lists items can also be appended using:
+# TAG += value [value, ...]
+# Values that contain spaces should be placed between quotes (" ")
+
+#---------------------------------------------------------------------------
+# Project related configuration options
+#---------------------------------------------------------------------------
+
+# The PROJECT_NAME tag is a single word (or a sequence of words surrounded
+# by quotes) that should identify the project.
+
+PROJECT_NAME = TooN
+
+# The PROJECT_NUMBER tag can be used to enter a project or revision number.
+# This could be handy for archiving the generated documentation or
+# if some version control system is used.
+
+PROJECT_NUMBER = 2.0.0-beta2
+
+# The OUTPUT_DIRECTORY tag is used to specify the (relative or absolute)
+# base path where the generated documentation will be put.
+# If a relative path is entered, it will be relative to the location
+# where doxygen was started. If left blank the current directory will be used.
+
+OUTPUT_DIRECTORY =
+
+# The OUTPUT_LANGUAGE tag is used to specify the language in which all
+# documentation generated by doxygen is written. Doxygen will use this
+# information to generate all constant output in the proper language.
+# The default language is English, other supported languages are:
+# Brazilian, Catalan, Chinese, Chinese-Traditional, Croatian, Czech, Danish,
Dutch,
+# Finnish, French, German, Greek, Hungarian, Italian, Japanese, Japanese-en
+# (Japanese with English messages), Korean, Korean-en, Norwegian, Polish,
Portuguese,
+# Romanian, Russian, Serbian, Slovak, Slovene, Spanish, Swedish, and Ukrainian.
+
+OUTPUT_LANGUAGE = English
+
+# This tag can be used to specify the encoding used in the generated output.
+# The encoding is not always determined by the language that is chosen,
+# but also whether or not the output is meant for Windows or non-Windows
users.
+# In case there is a difference, setting the USE_WINDOWS_ENCODING tag to YES
+# forces the Windows encoding (this is the default for the Windows binary),
+# whereas setting the tag to NO uses a Unix-style encoding (the default for
+# all platforms other than Windows).
+
+#USE_WINDOWS_ENCODING = NO
+
+# If the BRIEF_MEMBER_DESC tag is set to YES (the default) Doxygen will
+# include brief member descriptions after the members that are listed in
+# the file and class documentation (similar to JavaDoc).
+# Set to NO to disable this.
+
+BRIEF_MEMBER_DESC = NO
+
+# If the REPEAT_BRIEF tag is set to YES (the default) Doxygen will prepend
+# the brief description of a member or function before the detailed
description.
+# Note: if both HIDE_UNDOC_MEMBERS and BRIEF_MEMBER_DESC are set to NO, the
+# brief descriptions will be completely suppressed.
+
+REPEAT_BRIEF = YES
+
+# This tag implements a quasi-intelligent brief description abbreviator
+# that is used to form the text in various listings. Each string
+# in this list, if found as the leading text of the brief description, will be
+# stripped from the text and the result after processing the whole list, is
used
+# as the annotated text. Otherwise, the brief description is used as-is. If
left
+# blank, the following values are used ("$name" is automatically replaced with
the
+# name of the entity): "The $name class" "The $name widget" "The $name file"
+# "is" "provides" "specifies" "contains" "represents" "a" "an" "the"
+
+ABBREVIATE_BRIEF =
+
+# If the ALWAYS_DETAILED_SEC and REPEAT_BRIEF tags are both set to YES then
+# Doxygen will generate a detailed section even if there is only a brief
+# description.
+
+ALWAYS_DETAILED_SEC = NO
+
+# If the INLINE_INHERITED_MEMB tag is set to YES, doxygen will show all
inherited
+# members of a class in the documentation of that class as if those members
were
+# ordinary class members. Constructors, destructors and assignment operators
of
+# the base classes will not be shown.
+
+INLINE_INHERITED_MEMB = NO
+
+# If the FULL_PATH_NAMES tag is set to YES then Doxygen will prepend the full
+# path before files name in the file list and in the header files. If set
+# to NO the shortest path that makes the file name unique will be used.
+
+FULL_PATH_NAMES = YES
+
+# If the FULL_PATH_NAMES tag is set to YES then the STRIP_FROM_PATH tag
+# can be used to strip a user-defined part of the path. Stripping is
+# only done if one of the specified strings matches the left-hand part of
+# the path. It is allowed to use relative paths in the argument list.
+# If left blank the directory from which doxygen is run is used as the
+# path to strip.
+
+STRIP_FROM_PATH =
+
+# If the SHORT_NAMES tag is set to YES, doxygen will generate much shorter
+# (but less readable) file names. This can be useful is your file systems
+# doesn't support long names like on DOS, Mac, or CD-ROM.
+
+SHORT_NAMES = NO
+
+# If the JAVADOC_AUTOBRIEF tag is set to YES then Doxygen
+# will interpret the first line (until the first dot) of a JavaDoc-style
+# comment as the brief description. If set to NO, the JavaDoc
+# comments will behave just like the Qt-style comments (thus requiring an
+# explicit @brief command for a brief description.
+
+JAVADOC_AUTOBRIEF = YES
+
+# The MULTILINE_CPP_IS_BRIEF tag can be set to YES to make Doxygen
+# treat a multi-line C++ special comment block (i.e. a block of //! or ///
+# comments) as a brief description. This used to be the default behaviour.
+# The new default is to treat a multi-line C++ comment block as a detailed
+# description. Set this tag to YES if you prefer the old behaviour instead.
+
+MULTILINE_CPP_IS_BRIEF = NO
+
+# If the DETAILS_AT_TOP tag is set to YES then Doxygen
+# will output the detailed description near the top, like JavaDoc.
+# If set to NO, the detailed description appears after the member
+# documentation.
+
+DETAILS_AT_TOP = NO
+
+# If the INHERIT_DOCS tag is set to YES (the default) then an undocumented
+# member inherits the documentation from any documented member that it
+# re-implements.
+
+INHERIT_DOCS = YES
+
+# If member grouping is used in the documentation and the DISTRIBUTE_GROUP_DOC
+# tag is set to YES, then doxygen will reuse the documentation of the first
+# member in the group (if any) for the other members of the group. By default
+# all members of a group must be documented explicitly.
+
+DISTRIBUTE_GROUP_DOC = NO
+
+# The TAB_SIZE tag can be used to set the number of spaces in a tab.
+# Doxygen uses this value to replace tabs by spaces in code fragments.
+
+TAB_SIZE = 4
+
+# This tag can be used to specify a number of aliases that acts
+# as commands in the documentation. An alias has the form "name=value".
+# For example adding "sideeffect=\par Side Effects:\n" will allow you to
+# put the command \sideeffect (or @sideeffect) in the documentation, which
+# will result in a user-defined paragraph with heading "Side Effects:".
+# You can put \n's in the value part of an alias to insert newlines.
+
+ALIASES =
+
+# Set the OPTIMIZE_OUTPUT_FOR_C tag to YES if your project consists of C
sources
+# only. Doxygen will then generate output that is more tailored for C.
+# For instance, some of the names that are used will be different. The list
+# of all members will be omitted, etc.
+
+OPTIMIZE_OUTPUT_FOR_C = NO
+
+# Set the OPTIMIZE_OUTPUT_JAVA tag to YES if your project consists of Java
sources
+# only. Doxygen will then generate output that is more tailored for Java.
+# For instance, namespaces will be presented as packages, qualified scopes
+# will look different, etc.
+
+OPTIMIZE_OUTPUT_JAVA = NO
+
+# Set the SUBGROUPING tag to YES (the default) to allow class member groups of
+# the same type (for instance a group of public functions) to be put as a
+# subgroup of that type (e.g. under the Public Functions section). Set it to
+# NO to prevent subgrouping. Alternatively, this can be done per class using
+# the \nosubgrouping command.
+
+SUBGROUPING = YES
+
+#---------------------------------------------------------------------------
+# Build related configuration options
+#---------------------------------------------------------------------------
+
+# If the EXTRACT_ALL tag is set to YES doxygen will assume all entities in
+# documentation are documented, even if no documentation was available.
+# Private class members and static file members will be hidden unless
+# the EXTRACT_PRIVATE and EXTRACT_STATIC tags are set to YES
+
+EXTRACT_ALL = NO
+
+# If the EXTRACT_PRIVATE tag is set to YES all private members of a class
+# will be included in the documentation.
+
+EXTRACT_PRIVATE = NO
+
+# If the EXTRACT_STATIC tag is set to YES all static members of a file
+# will be included in the documentation.
+
+EXTRACT_STATIC = NO
+
+# If the EXTRACT_LOCAL_CLASSES tag is set to YES classes (and structs)
+# defined locally in source files will be included in the documentation.
+# If set to NO only classes defined in header files are included.
+
+EXTRACT_LOCAL_CLASSES = YES
+
+# If the HIDE_UNDOC_MEMBERS tag is set to YES, Doxygen will hide all
+# undocumented members of documented classes, files or namespaces.
+# If set to NO (the default) these members will be included in the
+# various overviews, but no documentation section is generated.
+# This option has no effect if EXTRACT_ALL is enabled.
+
+HIDE_UNDOC_MEMBERS = NO
+
+# If the HIDE_UNDOC_CLASSES tag is set to YES, Doxygen will hide all
+# undocumented classes that are normally visible in the class hierarchy.
+# If set to NO (the default) these classes will be included in the various
+# overviews. This option has no effect if EXTRACT_ALL is enabled.
+
+HIDE_UNDOC_CLASSES = NO
+
+# If the HIDE_FRIEND_COMPOUNDS tag is set to YES, Doxygen will hide all
+# friend (class|struct|union) declarations.
+# If set to NO (the default) these declarations will be included in the
+# documentation.
+
+HIDE_FRIEND_COMPOUNDS = YES
+
+# If the HIDE_IN_BODY_DOCS tag is set to YES, Doxygen will hide any
+# documentation blocks found inside the body of a function.
+# If set to NO (the default) these blocks will be appended to the
+# function's detailed documentation block.
+
+HIDE_IN_BODY_DOCS = NO
+
+# The INTERNAL_DOCS tag determines if documentation
+# that is typed after a \internal command is included. If the tag is set
+# to NO (the default) then the documentation will be excluded.
+# Set it to YES to include the internal documentation.
+
+INTERNAL_DOCS = NO
+
+# If the CASE_SENSE_NAMES tag is set to NO then Doxygen will only generate
+# file names in lower-case letters. If set to YES upper-case letters are also
+# allowed. This is useful if you have classes or files whose names only differ
+# in case and if your file system supports case sensitive file names. Windows
+# users are advised to set this option to NO.
+
+CASE_SENSE_NAMES = YES
+
+# If the HIDE_SCOPE_NAMES tag is set to NO (the default) then Doxygen
+# will show members with their full class and namespace scopes in the
+# documentation. If set to YES the scope will be hidden.
+
+HIDE_SCOPE_NAMES = NO
+
+# If the SHOW_INCLUDE_FILES tag is set to YES (the default) then Doxygen
+# will put a list of the files that are included by a file in the
documentation
+# of that file.
+
+SHOW_INCLUDE_FILES = YES
+
+# If the INLINE_INFO tag is set to YES (the default) then a tag [inline]
+# is inserted in the documentation for inline members.
+
+INLINE_INFO = NO
+
+# If the SORT_MEMBER_DOCS tag is set to YES (the default) then doxygen
+# will sort the (detailed) documentation of file and class members
+# alphabetically by member name. If set to NO the members will appear in
+# declaration order.
+
+SORT_MEMBER_DOCS = NO
+
+# If the SORT_BRIEF_DOCS tag is set to YES then doxygen will sort the
+# brief documentation of file, namespace and class members alphabetically
+# by member name. If set to NO (the default) the members will appear in
+# declaration order.
+
+SORT_BRIEF_DOCS = NO
+
+# If the SORT_BY_SCOPE_NAME tag is set to YES, the class list will be
+# sorted by fully-qualified names, including namespaces. If set to
+# NO (the default), the class list will be sorted only by class name,
+# not including the namespace part.
+# Note: This option is not very useful if HIDE_SCOPE_NAMES is set to YES.
+# Note: This option applies only to the class list, not to the
+# alphabetical list.
+
+SORT_BY_SCOPE_NAME = NO
+
+# The GENERATE_TODOLIST tag can be used to enable (YES) or
+# disable (NO) the todo list. This list is created by putting \todo
+# commands in the documentation.
+
+GENERATE_TODOLIST = YES
+
+# The GENERATE_TESTLIST tag can be used to enable (YES) or
+# disable (NO) the test list. This list is created by putting \test
+# commands in the documentation.
+
+GENERATE_TESTLIST = YES
+
+# The GENERATE_BUGLIST tag can be used to enable (YES) or
+# disable (NO) the bug list. This list is created by putting \bug
+# commands in the documentation.
+
+GENERATE_BUGLIST = YES
+
+# The GENERATE_DEPRECATEDLIST tag can be used to enable (YES) or
+# disable (NO) the deprecated list. This list is created by putting
+# \deprecated commands in the documentation.
+
+GENERATE_DEPRECATEDLIST= NO
+
+# The ENABLED_SECTIONS tag can be used to enable conditional
+# documentation sections, marked by \if sectionname ... \endif.
+
+ENABLED_SECTIONS = IGNORE
+
+# The MAX_INITIALIZER_LINES tag determines the maximum number of lines
+# the initial value of a variable or define consists of for it to appear in
+# the documentation. If the initializer consists of more lines than specified
+# here it will be hidden. Use a value of 0 to hide initializers completely.
+# The appearance of the initializer of individual variables and defines in the
+# documentation can be controlled using \showinitializer or \hideinitializer
+# command in the documentation regardless of this setting.
+
+MAX_INITIALIZER_LINES = 30
+
+# Set the SHOW_USED_FILES tag to NO to disable the list of files generated
+# at the bottom of the documentation of classes and structs. If set to YES the
+# list will mention the files that were used to generate the documentation.
+
+SHOW_USED_FILES = NO
+
+#---------------------------------------------------------------------------
+# configuration options related to warning and progress messages
+#---------------------------------------------------------------------------
+
+# The QUIET tag can be used to turn on/off the messages that are generated
+# by doxygen. Possible values are YES and NO. If left blank NO is used.
+
+QUIET = NO
+
+# The WARNINGS tag can be used to turn on/off the warning messages that are
+# generated by doxygen. Possible values are YES and NO. If left blank
+# NO is used.
+
+WARNINGS = YES
+
+# If WARN_IF_UNDOCUMENTED is set to YES, then doxygen will generate warnings
+# for undocumented members. If EXTRACT_ALL is set to YES then this flag will
+# automatically be disabled.
+
+WARN_IF_UNDOCUMENTED = YES
+
+# If WARN_IF_DOC_ERROR is set to YES, doxygen will generate warnings for
+# potential errors in the documentation, such as not documenting some
+# parameters in a documented function, or documenting parameters that
+# don't exist or using markup commands wrongly.
+
+WARN_IF_DOC_ERROR = YES
+
+# The WARN_FORMAT tag determines the format of the warning messages that
+# doxygen can produce. The string should contain the $file, $line, and $text
+# tags, which will be replaced by the file and line number from which the
+# warning originated and the warning text.
+
+WARN_FORMAT = "$file:$line: $text"
+
+# The WARN_LOGFILE tag can be used to specify a file to which warning
+# and error messages should be written. If left blank the output is written
+# to stderr.
+
+WARN_LOGFILE =
+
+#---------------------------------------------------------------------------
+# configuration options related to the input files
+#---------------------------------------------------------------------------
+
+# The INPUT tag can be used to specify the files and/or directories that
contain
+# documented source files. You may enter file names like "myfile.cpp" or
+# directories like "/usr/src/myproject". Separate the files or directories
+# with spaces.
+
+INPUT = . doc optimization
+
+# If the value of the INPUT tag contains directories, you can use the
+# FILE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp
+# and *.h) to filter out the source-files in the directories. If left
+# blank the following patterns are tested:
+# *.c *.cc *.cxx *.cpp *.c++ *.java *.ii *.ixx *.ipp *.i++ *.inl *.h *.hh
*.hxx *.hpp
+# *.h++ *.idl *.odl *.cs *.php *.php3 *.inc
+
+FILE_PATTERNS = documentation.h *doc.h *.h
+
+# The RECURSIVE tag can be used to turn specify whether or not subdirectories
+# should be searched for input files as well. Possible values are YES and NO.
+# If left blank NO is used.
+
+RECURSIVE = NO
+
+# The EXCLUDE tag can be used to specify files and/or directories that should
+# excluded from the INPUT source files. This way you can easily exclude a
+# subdirectory from a directory tree whose root is specified with the INPUT
tag.
+
+EXCLUDE = wls_cholesky.h lapack.h
+
+# The EXCLUDE_SYMLINKS tag can be used select whether or not files or
directories
+# that are symbolic links (a Unix filesystem feature) are excluded from the
input.
+
+EXCLUDE_SYMLINKS = NO
+
+# If the value of the INPUT tag contains directories, you can use the
+# EXCLUDE_PATTERNS tag to specify one or more wildcard patterns to exclude
+# certain files from those directories.
+
+EXCLUDE_PATTERNS =
+
+# The EXAMPLE_PATH tag can be used to specify one or more files or
+# directories that contain example code fragments that are included (see
+# the \include command).
+
+EXAMPLE_PATH =
+
+# If the value of the EXAMPLE_PATH tag contains directories, you can use the
+# EXAMPLE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp
+# and *.h) to filter out the source-files in the directories. If left
+# blank all files are included.
+
+EXAMPLE_PATTERNS =
+
+# If the EXAMPLE_RECURSIVE tag is set to YES then subdirectories will be
+# searched for input files to be used with the \include or \dontinclude
+# commands irrespective of the value of the RECURSIVE tag.
+# Possible values are YES and NO. If left blank NO is used.
+
+EXAMPLE_RECURSIVE = NO
+
+# The IMAGE_PATH tag can be used to specify one or more files or
+# directories that contain image that are included in the documentation (see
+# the \image command).
+
+IMAGE_PATH =
+
+# The INPUT_FILTER tag can be used to specify a program that doxygen should
+# invoke to filter for each input file. Doxygen will invoke the filter program
+# by executing (via popen()) the command <filter> <input-file>, where <filter>
+# is the value of the INPUT_FILTER tag, and <input-file> is the name of an
+# input file. Doxygen will then use the output that the filter program writes
+# to standard output.
+
+INPUT_FILTER =
+
+# If the FILTER_SOURCE_FILES tag is set to YES, the input filter (if set using
+# INPUT_FILTER) will be used to filter the input files when producing source
+# files to browse (i.e. when SOURCE_BROWSER is set to YES).
+
+FILTER_SOURCE_FILES = NO
+
+#---------------------------------------------------------------------------
+# configuration options related to source browsing
+#---------------------------------------------------------------------------
+
+# If the SOURCE_BROWSER tag is set to YES then a list of source files will
+# be generated. Documented entities will be cross-referenced with these
sources.
+# Note: To get rid of all source code in the generated output, make sure also
+# VERBATIM_HEADERS is set to NO.
+
+SOURCE_BROWSER = NO
+
+# Setting the INLINE_SOURCES tag to YES will include the body
+# of functions and classes directly in the documentation.
+
+INLINE_SOURCES = NO
+
+# Setting the STRIP_CODE_COMMENTS tag to YES (the default) will instruct
+# doxygen to hide any special comment blocks from generated source code
+# fragments. Normal C and C++ comments will always remain visible.
+
+STRIP_CODE_COMMENTS = YES
+
+# If the REFERENCED_BY_RELATION tag is set to YES (the default)
+# then for each documented function all documented
+# functions referencing it will be listed.
+
+REFERENCED_BY_RELATION = YES
+
+# If the REFERENCES_RELATION tag is set to YES (the default)
+# then for each documented function all documented entities
+# called/used by that function will be listed.
+
+REFERENCES_RELATION = YES
+
+# If the VERBATIM_HEADERS tag is set to YES (the default) then Doxygen
+# will generate a verbatim copy of the header file for each class for
+# which an include is specified. Set to NO to disable this.
+
+VERBATIM_HEADERS = YES
+
+#---------------------------------------------------------------------------
+# configuration options related to the alphabetical class index
+#---------------------------------------------------------------------------
+
+# If the ALPHABETICAL_INDEX tag is set to YES, an alphabetical index
+# of all compounds will be generated. Enable this if the project
+# contains a lot of classes, structs, unions or interfaces.
+
+ALPHABETICAL_INDEX = NO
+
+# If the alphabetical index is enabled (see ALPHABETICAL_INDEX) then
+# the COLS_IN_ALPHA_INDEX tag can be used to specify the number of columns
+# in which this list will be split (can be a number in the range [1..20])
+
+COLS_IN_ALPHA_INDEX = 5
+
+# In case all classes in a project start with a common prefix, all
+# classes will be put under the same header in the alphabetical index.
+# The IGNORE_PREFIX tag can be used to specify one or more prefixes that
+# should be ignored while generating the index headers.
+
+IGNORE_PREFIX =
+
+#---------------------------------------------------------------------------
+# configuration options related to the HTML output
+#---------------------------------------------------------------------------
+
+# If the GENERATE_HTML tag is set to YES (the default) Doxygen will
+# generate HTML output.
+
+GENERATE_HTML = YES
+
+# The HTML_OUTPUT tag is used to specify where the HTML docs will be put.
+# If a relative path is entered the value of OUTPUT_DIRECTORY will be
+# put in front of it. If left blank `html' will be used as the default path.
+
+HTML_OUTPUT = html
+
+# The HTML_FILE_EXTENSION tag can be used to specify the file extension for
+# each generated HTML page (for example: .htm,.php,.asp). If it is left blank
+# doxygen will generate files with .html extension.
+
+HTML_FILE_EXTENSION = .html
+
+# The HTML_HEADER tag can be used to specify a personal HTML header for
+# each generated HTML page. If it is left blank doxygen will generate a
+# standard header.
+
+HTML_HEADER =
+
+# The HTML_FOOTER tag can be used to specify a personal HTML footer for
+# each generated HTML page. If it is left blank doxygen will generate a
+# standard footer.
+
+HTML_FOOTER =
+
+# The HTML_STYLESHEET tag can be used to specify a user-defined cascading
+# style sheet that is used by each HTML page. It can be used to
+# fine-tune the look of the HTML output. If the tag is left blank doxygen
+# will generate a default style sheet. Note that doxygen will try to copy
+# the style sheet file to the HTML output directory, so don't put your own
+# stylesheet in the HTML output directory as well, or it will be erased!
+
+HTML_STYLESHEET =
+
+# If the HTML_ALIGN_MEMBERS tag is set to YES, the members of classes,
+# files or namespaces will be aligned in HTML using tables. If set to
+# NO a bullet list will be used.
+
+HTML_ALIGN_MEMBERS = YES
+
+# If the GENERATE_HTMLHELP tag is set to YES, additional index files
+# will be generated that can be used as input for tools like the
+# Microsoft HTML help workshop to generate a compressed HTML help file (.chm)
+# of the generated HTML documentation.
+
+GENERATE_HTMLHELP = NO
+
+# If the GENERATE_HTMLHELP tag is set to YES, the CHM_FILE tag can
+# be used to specify the file name of the resulting .chm file. You
+# can add a path in front of the file if the result should not be
+# written to the html output directory.
+
+CHM_FILE =
+
+# If the GENERATE_HTMLHELP tag is set to YES, the HHC_LOCATION tag can
+# be used to specify the location (absolute path including file name) of
+# the HTML help compiler (hhc.exe). If non-empty doxygen will try to run
+# the HTML help compiler on the generated index.hhp.
+
+HHC_LOCATION =
+
+# If the GENERATE_HTMLHELP tag is set to YES, the GENERATE_CHI flag
+# controls if a separate .chi index file is generated (YES) or that
+# it should be included in the master .chm file (NO).
+
+GENERATE_CHI = NO
+
+# If the GENERATE_HTMLHELP tag is set to YES, the BINARY_TOC flag
+# controls whether a binary table of contents is generated (YES) or a
+# normal table of contents (NO) in the .chm file.
+
+BINARY_TOC = NO
+
+# The TOC_EXPAND flag can be set to YES to add extra items for group members
+# to the contents of the HTML help documentation and to the tree view.
+
+TOC_EXPAND = NO
+
+# The DISABLE_INDEX tag can be used to turn on/off the condensed index at
+# top of each HTML page. The value NO (the default) enables the index and
+# the value YES disables it.
+
+DISABLE_INDEX = NO
+
+# This tag can be used to set the number of enum values (range [1..20])
+# that doxygen will group on one line in the generated HTML documentation.
+
+ENUM_VALUES_PER_LINE = 4
+
+# If the GENERATE_TREEVIEW tag is set to YES, a side panel will be
+# generated containing a tree-like index structure (just like the one that
+# is generated for HTML Help). For this to work a browser that supports
+# JavaScript, DHTML, CSS and frames is required (for instance Mozilla 1.0+,
+# Netscape 6.0+, Internet explorer 5.0+, or Konqueror). Windows users are
+# probably better off using the HTML help feature.
+
+GENERATE_TREEVIEW = NO
+
+# If the treeview is enabled (see GENERATE_TREEVIEW) then this tag can be
+# used to set the initial width (in pixels) of the frame in which the tree
+# is shown.
+
+TREEVIEW_WIDTH = 250
+
+#---------------------------------------------------------------------------
+# configuration options related to the LaTeX output
+#---------------------------------------------------------------------------
+
+# If the GENERATE_LATEX tag is set to YES (the default) Doxygen will
+# generate Latex output.
+
+GENERATE_LATEX = NO
+
+# The LATEX_OUTPUT tag is used to specify where the LaTeX docs will be put.
+# If a relative path is entered the value of OUTPUT_DIRECTORY will be
+# put in front of it. If left blank `latex' will be used as the default path.
+
+LATEX_OUTPUT = latex
+
+# The LATEX_CMD_NAME tag can be used to specify the LaTeX command name to be
+# invoked. If left blank `latex' will be used as the default command name.
+
+LATEX_CMD_NAME = latex
+
+# The MAKEINDEX_CMD_NAME tag can be used to specify the command name to
+# generate index for LaTeX. If left blank `makeindex' will be used as the
+# default command name.
+
+MAKEINDEX_CMD_NAME = makeindex
+
+# If the COMPACT_LATEX tag is set to YES Doxygen generates more compact
+# LaTeX documents. This may be useful for small projects and may help to
+# save some trees in general.
+
+COMPACT_LATEX = NO
+
+# The PAPER_TYPE tag can be used to set the paper type that is used
+# by the printer. Possible values are: a4, a4wide, letter, legal and
+# executive. If left blank a4wide will be used.
+
+PAPER_TYPE = a4wide
+
+# The EXTRA_PACKAGES tag can be to specify one or more names of LaTeX
+# packages that should be included in the LaTeX output.
+
+EXTRA_PACKAGES = amsmath \
+ amssymb
+
+# The LATEX_HEADER tag can be used to specify a personal LaTeX header for
+# the generated latex document. The header should contain everything until
+# the first chapter. If it is left blank doxygen will generate a
+# standard header. Notice: only use this tag if you know what you are doing!
+
+LATEX_HEADER =
+
+# If the PDF_HYPERLINKS tag is set to YES, the LaTeX that is generated
+# is prepared for conversion to pdf (using ps2pdf). The pdf file will
+# contain links (just like the HTML output) instead of page references
+# This makes the output suitable for online browsing using a pdf viewer.
+
+PDF_HYPERLINKS = NO
+
+# If the USE_PDFLATEX tag is set to YES, pdflatex will be used instead of
+# plain latex in the generated Makefile. Set this option to YES to get a
+# higher quality PDF documentation.
+
+USE_PDFLATEX = NO
+
+# If the LATEX_BATCHMODE tag is set to YES, doxygen will add the \\batchmode.
+# command to the generated LaTeX files. This will instruct LaTeX to keep
+# running if errors occur, instead of asking the user for help.
+# This option is also used when generating formulas in HTML.
+
+LATEX_BATCHMODE = NO
+
+# If LATEX_HIDE_INDICES is set to YES then doxygen will not
+# include the index chapters (such as File Index, Compound Index, etc.)
+# in the output.
+
+LATEX_HIDE_INDICES = NO
+
+#---------------------------------------------------------------------------
+# configuration options related to the RTF output
+#---------------------------------------------------------------------------
+
+# If the GENERATE_RTF tag is set to YES Doxygen will generate RTF output
+# The RTF output is optimized for Word 97 and may not look very pretty with
+# other RTF readers or editors.
+
+GENERATE_RTF = NO
+
+# The RTF_OUTPUT tag is used to specify where the RTF docs will be put.
+# If a relative path is entered the value of OUTPUT_DIRECTORY will be
+# put in front of it. If left blank `rtf' will be used as the default path.
+
+RTF_OUTPUT = rtf
+
+# If the COMPACT_RTF tag is set to YES Doxygen generates more compact
+# RTF documents. This may be useful for small projects and may help to
+# save some trees in general.
+
+COMPACT_RTF = NO
+
+# If the RTF_HYPERLINKS tag is set to YES, the RTF that is generated
+# will contain hyperlink fields. The RTF file will
+# contain links (just like the HTML output) instead of page references.
+# This makes the output suitable for online browsing using WORD or other
+# programs which support those fields.
+# Note: wordpad (write) and others do not support links.
+
+RTF_HYPERLINKS = NO
+
+# Load stylesheet definitions from file. Syntax is similar to doxygen's
+# config file, i.e. a series of assignments. You only have to provide
+# replacements, missing definitions are set to their default value.
+
+RTF_STYLESHEET_FILE =
+
+# Set optional variables used in the generation of an rtf document.
+# Syntax is similar to doxygen's config file.
+
+RTF_EXTENSIONS_FILE =
+
+#---------------------------------------------------------------------------
+# configuration options related to the man page output
+#---------------------------------------------------------------------------
+
+# If the GENERATE_MAN tag is set to YES (the default) Doxygen will
+# generate man pages
+
+GENERATE_MAN = NO
+
+# The MAN_OUTPUT tag is used to specify where the man pages will be put.
+# If a relative path is entered the value of OUTPUT_DIRECTORY will be
+# put in front of it. If left blank `man' will be used as the default path.
+
+MAN_OUTPUT = man
+
+# The MAN_EXTENSION tag determines the extension that is added to
+# the generated man pages (default is the subroutine's section .3)
+
+MAN_EXTENSION = .3
+
+# If the MAN_LINKS tag is set to YES and Doxygen generates man output,
+# then it will generate one additional man file for each entity
+# documented in the real man page(s). These additional files
+# only source the real man page, but without them the man command
+# would be unable to find the correct page. The default is NO.
+
+MAN_LINKS = YES
+
+#---------------------------------------------------------------------------
+# configuration options related to the XML output
+#---------------------------------------------------------------------------
+
+# If the GENERATE_XML tag is set to YES Doxygen will
+# generate an XML file that captures the structure of
+# the code including all documentation.
+
+GENERATE_XML = NO
+
+# The XML_OUTPUT tag is used to specify where the XML pages will be put.
+# If a relative path is entered the value of OUTPUT_DIRECTORY will be
+# put in front of it. If left blank `xml' will be used as the default path.
+
+XML_OUTPUT = xml
+
+# The XML_SCHEMA tag can be used to specify an XML schema,
+# which can be used by a validating XML parser to check the
+# syntax of the XML files.
+
+XML_SCHEMA =
+
+# The XML_DTD tag can be used to specify an XML DTD,
+# which can be used by a validating XML parser to check the
+# syntax of the XML files.
+
+XML_DTD =
+
+# If the XML_PROGRAMLISTING tag is set to YES Doxygen will
+# dump the program listings (including syntax highlighting
+# and cross-referencing information) to the XML output. Note that
+# enabling this will significantly increase the size of the XML output.
+
+XML_PROGRAMLISTING = YES
+
+#---------------------------------------------------------------------------
+# configuration options for the AutoGen Definitions output
+#---------------------------------------------------------------------------
+
+# If the GENERATE_AUTOGEN_DEF tag is set to YES Doxygen will
+# generate an AutoGen Definitions (see autogen.sf.net) file
+# that captures the structure of the code including all
+# documentation. Note that this feature is still experimental
+# and incomplete at the moment.
+
+GENERATE_AUTOGEN_DEF = NO
+
+#---------------------------------------------------------------------------
+# configuration options related to the Perl module output
+#---------------------------------------------------------------------------
+
+# If the GENERATE_PERLMOD tag is set to YES Doxygen will
+# generate a Perl module file that captures the structure of
+# the code including all documentation. Note that this
+# feature is still experimental and incomplete at the
+# moment.
+
+GENERATE_PERLMOD = NO
+
+# If the PERLMOD_LATEX tag is set to YES Doxygen will generate
+# the necessary Makefile rules, Perl scripts and LaTeX code to be able
+# to generate PDF and DVI output from the Perl module output.
+
+PERLMOD_LATEX = NO
+
+# If the PERLMOD_PRETTY tag is set to YES the Perl module output will be
+# nicely formatted so it can be parsed by a human reader. This is useful
+# if you want to understand what is going on. On the other hand, if this
+# tag is set to NO the size of the Perl module output will be much smaller
+# and Perl will parse it just the same.
+
+PERLMOD_PRETTY = YES
+
+# The names of the make variables in the generated doxyrules.make file
+# are prefixed with the string contained in PERLMOD_MAKEVAR_PREFIX.
+# This is useful so different doxyrules.make files included by the same
+# Makefile don't overwrite each other's variables.
+
+PERLMOD_MAKEVAR_PREFIX =
+
+#---------------------------------------------------------------------------
+# Configuration options related to the preprocessor
+#---------------------------------------------------------------------------
+
+# If the ENABLE_PREPROCESSING tag is set to YES (the default) Doxygen will
+# evaluate all C-preprocessor directives found in the sources and include
+# files.
+
+ENABLE_PREPROCESSING = YES
+
+# If the MACRO_EXPANSION tag is set to YES Doxygen will expand all macro
+# names in the source code. If set to NO (the default) only conditional
+# compilation will be performed. Macro expansion can be done in a controlled
+# way by setting EXPAND_ONLY_PREDEF to YES.
+
+MACRO_EXPANSION = NO
+
+# If the EXPAND_ONLY_PREDEF and MACRO_EXPANSION tags are both set to YES
+# then the macro expansion is limited to the macros specified with the
+# PREDEFINED and EXPAND_AS_PREDEFINED tags.
+
+EXPAND_ONLY_PREDEF = NO
+
+# If the SEARCH_INCLUDES tag is set to YES (the default) the includes files
+# in the INCLUDE_PATH (see below) will be search if a #include is found.
+
+SEARCH_INCLUDES = YES
+
+# The INCLUDE_PATH tag can be used to specify one or more directories that
+# contain include files that are not input files but should be processed by
+# the preprocessor.
+
+INCLUDE_PATH =
+
+# You can use the INCLUDE_FILE_PATTERNS tag to specify one or more wildcard
+# patterns (like *.h and *.hpp) to filter out the header-files in the
+# directories. If left blank, the patterns specified with FILE_PATTERNS will
+# be used.
+
+INCLUDE_FILE_PATTERNS =
+
+# The PREDEFINED tag can be used to specify one or more macro names that
+# are defined before the preprocessor is started (similar to the -D option of
+# gcc). The argument of the tag is a list of macros of the form: name
+# or name=definition (no spaces). If the definition and the = are
+# omitted =1 is assumed.
+
+PREDEFINED = DOXYGEN_IGNORE_INTERNAL DOXYGEN_INCLUDE_ONLY_FOR_DOCS
+
+# If the MACRO_EXPANSION and EXPAND_ONLY_PREDEF tags are set to YES then
+# this tag can be used to specify a list of macro names that should be
expanded.
+# The macro definition that is found in the sources will be used.
+# Use the PREDEFINED tag if you want to use a different macro definition.
+
+EXPAND_AS_DEFINED =
+
+# If the SKIP_FUNCTION_MACROS tag is set to YES (the default) then
+# doxygen's preprocessor will remove all function-like macros that are alone
+# on a line, have an all uppercase name, and do not end with a semicolon. Such
+# function macros are typically used for boiler-plate code, and will confuse
the
+# parser if not removed.
+
+SKIP_FUNCTION_MACROS = YES
+
+#---------------------------------------------------------------------------
+# Configuration::additions related to external references
+#---------------------------------------------------------------------------
+
+# The TAGFILES option can be used to specify one or more tagfiles.
+# Optionally an initial location of the external documentation
+# can be added for each tagfile. The format of a tag file without
+# this location is as follows:
+# TAGFILES = file1 file2 ...
+# Adding location for the tag files is done as follows:
+# TAGFILES = file1=loc1 "file2 = loc2" ...
+# where "loc1" and "loc2" can be relative or absolute paths or
+# URLs. If a location is present for each tag, the installdox tool
+# does not have to be run to correct the links.
+# Note that each tag file must have a unique name
+# (where the name does NOT include the path)
+# If a tag file is not located in the directory in which doxygen
+# is run, you must also specify the path to the tagfile here.
+
+TAGFILES =
+
+# When a file name is specified after GENERATE_TAGFILE, doxygen will create
+# a tag file that is based on the input files it reads.
+
+GENERATE_TAGFILE =
+
+# If the ALLEXTERNALS tag is set to YES all external classes will be listed
+# in the class index. If set to NO only the inherited external classes
+# will be listed.
+
+ALLEXTERNALS = NO
+
+# If the EXTERNAL_GROUPS tag is set to YES all external groups will be listed
+# in the modules index. If set to NO, only the current project's groups will
+# be listed.
+
+EXTERNAL_GROUPS = YES
+
+# The PERL_PATH should be the absolute path and name of the perl script
+# interpreter (i.e. the result of `which perl').
+
+PERL_PATH = /usr/bin/perl
+
+#---------------------------------------------------------------------------
+# Configuration options related to the dot tool
+#---------------------------------------------------------------------------
+
+# If the CLASS_DIAGRAMS tag is set to YES (the default) Doxygen will
+# generate a inheritance diagram (in HTML, RTF and LaTeX) for classes with
base or
+# super classes. Setting the tag to NO turns the diagrams off. Note that this
+# option is superseded by the HAVE_DOT option below. This is only a fallback.
It is
+# recommended to install and use dot, since it yields more powerful graphs.
+
+CLASS_DIAGRAMS = YES
+
+# If set to YES, the inheritance and collaboration graphs will hide
+# inheritance and usage relations if the target is undocumented
+# or is not a class.
+
+HIDE_UNDOC_RELATIONS = YES
+
+# If you set the HAVE_DOT tag to YES then doxygen will assume the dot tool is
+# available from the path. This tool is part of Graphviz, a graph
visualization
+# toolkit from AT&T and Lucent Bell Labs. The other options in this section
+# have no effect if this option is set to NO (the default)
+
+HAVE_DOT = NO
+
+# If the CLASS_GRAPH and HAVE_DOT tags are set to YES then doxygen
+# will generate a graph for each documented class showing the direct and
+# indirect inheritance relations. Setting this tag to YES will force the
+# the CLASS_DIAGRAMS tag to NO.
+
+CLASS_GRAPH = YES
+
+# If the COLLABORATION_GRAPH and HAVE_DOT tags are set to YES then doxygen
+# will generate a graph for each documented class showing the direct and
+# indirect implementation dependencies (inheritance, containment, and
+# class references variables) of the class with other documented classes.
+
+COLLABORATION_GRAPH = YES
+
+# If the UML_LOOK tag is set to YES doxygen will generate inheritance and
+# collaboration diagrams in a style similar to the OMG's Unified Modeling
+# Language.
+
+UML_LOOK = YES
+
+# If set to YES, the inheritance and collaboration graphs will show the
+# relations between templates and their instances.
+
+TEMPLATE_RELATIONS = NO
+
+# If the ENABLE_PREPROCESSING, SEARCH_INCLUDES, INCLUDE_GRAPH, and HAVE_DOT
+# tags are set to YES then doxygen will generate a graph for each documented
+# file showing the direct and indirect include dependencies of the file with
+# other documented files.
+
+INCLUDE_GRAPH = YES
+
+# If the ENABLE_PREPROCESSING, SEARCH_INCLUDES, INCLUDED_BY_GRAPH, and
+# HAVE_DOT tags are set to YES then doxygen will generate a graph for each
+# documented header file showing the documented files that directly or
+# indirectly include this file.
+
+INCLUDED_BY_GRAPH = YES
+
+# If the CALL_GRAPH and HAVE_DOT tags are set to YES then doxygen will
+# generate a call dependency graph for every global function or class method.
+# Note that enabling this option will significantly increase the time of a
run.
+# So in most cases it will be better to enable call graphs for selected
+# functions only using the \callgraph command.
+
+CALL_GRAPH = NO
+
+# If the GRAPHICAL_HIERARCHY and HAVE_DOT tags are set to YES then doxygen
+# will graphical hierarchy of all classes instead of a textual one.
+
+GRAPHICAL_HIERARCHY = YES
+
+# The DOT_IMAGE_FORMAT tag can be used to set the image format of the images
+# generated by dot. Possible values are png, jpg, or gif
+# If left blank png will be used.
+
+DOT_IMAGE_FORMAT = png
+
+# The tag DOT_PATH can be used to specify the path where the dot tool can be
+# found. If left blank, it is assumed the dot tool can be found on the path.
+
+DOT_PATH =
+
+# The DOTFILE_DIRS tag can be used to specify one or more directories that
+# contain dot files that are included in the documentation (see the
+# \dotfile command).
+
+DOTFILE_DIRS =
+
+# The MAX_DOT_GRAPH_WIDTH tag can be used to set the maximum allowed width
+# (in pixels) of the graphs generated by dot. If a graph becomes larger than
+# this value, doxygen will try to truncate the graph, so that it fits within
+# the specified constraint. Beware that most browsers cannot cope with very
+# large images.
+
+#MAX_DOT_GRAPH_WIDTH = 1024
+
+# The MAX_DOT_GRAPH_HEIGHT tag can be used to set the maximum allows height
+# (in pixels) of the graphs generated by dot. If a graph becomes larger than
+# this value, doxygen will try to truncate the graph, so that it fits within
+# the specified constraint. Beware that most browsers cannot cope with very
+# large images.
+
+#MAX_DOT_GRAPH_HEIGHT = 1024
+
+# The MAX_DOT_GRAPH_DEPTH tag can be used to set the maximum depth of the
+# graphs generated by dot. A depth value of 3 means that only nodes reachable
+# from the root by following a path via at most 3 edges will be shown. Nodes
that
+# lay further from the root node will be omitted. Note that setting this
option to
+# 1 or 2 may greatly reduce the computation time needed for large code bases.
Also
+# note that a graph may be further truncated if the graph's image dimensions
are
+# not sufficient to fit the graph (see MAX_DOT_GRAPH_WIDTH and
MAX_DOT_GRAPH_HEIGHT).
+# If 0 is used for the depth value (the default), the graph is not
depth-constrained.
+
+MAX_DOT_GRAPH_DEPTH = 0
+
+# If the GENERATE_LEGEND tag is set to YES (the default) Doxygen will
+# generate a legend page explaining the meaning of the various boxes and
+# arrows in the dot generated graphs.
+
+GENERATE_LEGEND = YES
+
+# If the DOT_CLEANUP tag is set to YES (the default) Doxygen will
+# remove the intermediate dot files that are used to generate
+# the various graphs.
+
+DOT_CLEANUP = YES
+
+#---------------------------------------------------------------------------
+# Configuration::additions related to the search engine
+#---------------------------------------------------------------------------
+
+# The SEARCHENGINE tag specifies whether or not a search engine should be
+# used. If set to NO the values of all tags below this one will be ignored.
+
+SEARCHENGINE = NO
Index: doc/Choleskydoc.h
===================================================================
RCS file: doc/Choleskydoc.h
diff -N doc/Choleskydoc.h
--- doc/Choleskydoc.h 6 Mar 2007 22:47:25 -0000 1.2
+++ /dev/null 1 Jan 1970 00:00:00 -0000
@@ -1,174 +0,0 @@
-/*
- Copyright (c) 2005 Paul Smith
-
- Permission is granted to copy, distribute and/or modify this document under
- the terms of the GNU Free Documentation License, Version 1.2 or any later
- version published by the Free Software Foundation; with no Invariant
- Sections, no Front-Cover Texts, and no Back-Cover Texts.
-
- You should have received a copy of the GNU Free Documentation License
- License along with this library; if not, write to the Free Software
- Foundation, Inc.
- 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
-
-*/
-// A proxy version of the Cholesky class,
-// cleaned up to present a comprehensible
-// version of the Cholesky interface
-
-#ifdef DOXYGEN_INCLUDE_ONLY_FOR_DOCS
-
-
-#include <iostream>
-
-#include <TooN/lapack.h>
-
-#include <TooN/TooN.h>
-#include <TooN/helpers.h>
-#include <limits>
-
-/// All classes and functions are within this namespace
-namespace TooN
-{
-/**
address@hidden Cholesky Choleskydoc.h TooN/Cholesky.h
-Decomposes a positive-semidefinite symmetric matrix A (such as a covariance)
into L*D*L^T, where L is lower-triangular and D is diagonal.
-Also can compute A = S*S^T, with S lower triangular. The LDL^T form is faster
to compute than the class Cholesky decomposition.
-The decomposition can be used to compute A^-1*x, A^-1*M, M*A^-1*M^T, and A^-1
itself, though the latter rarely needs to be explicitly represented.
-Also efficiently computes det(A) and rank(A).
-It can be used as follows:
address@hidden
-// Declare some matrices.
-Matrix<3> A = ...; // we'll pretend it is pos-def
-Matrix<2,3> M;
-Matrix<2> B;
-Vector<3> y = (make_Vector, 2,3,4);
-// create the Cholesky decomposition of A
-Cholesky<3> chol(A);
-// compute x = A^-1 * y
-Vector<3> x = cholA.inverse_times(y);
-// Identical to above
-x = cholA.backsub(y);
-// compute B = M*A^-1*M^T
-B = cholA.transform_inverse(M);
-//compute A^-1
-Matrix<3> Ainv = cholA.get_inverse();
-Matrix<3> C = ... // again, C is pos-def
-//compute the 'square-root' of C
-Matrix<3> L = Cholesky<3>::sqrt(C);
address@hidden
address@hidden gDecomps
-**/
-
-template <int N>
-class Cholesky {
-public:
- /// Construct the Cholesky-ish decomposition of a matrix. This initialises
the class, and
- /// performs the decomposition immediately.
- /// Run time is O(N^3)
- template<class Accessor> Cholesky(const FixedMatrix<N,N,Accessor>& m);
-
- /// Compute the LDL^T decomposition of another matrix.
- /// Run time is O(N^3)
- template<class Accessor> void compute(const FixedMatrix<N,N,Accessor>& m);
-
- /// Get the rank of the matrix
- int get_rank() const;
-
- /// Get the determinant
- double get_determinant() const;
-
- /// Get the internal representation of L and D.
- /// L has 1's on the diagonal, so here D is stored in its diagonal.
- /// L is lower triangular; the upper-triangular contents are not
initialized.
- /// Not yet present in Cholesky<-1>
- const Matrix<N>& get_L_D() const { return L; }
-
- /// Compute the lower-triangular 'square-root' L of A, s.t. A = L*L^T
- /// Run time is O(N^3)
- /// Not yet present in Cholesky<-1>
- template <class A1, class A2> static void sqrt(const FixedMatrix<N,N,A1>&
A, FixedMatrix<N,N,A2>& L);
-
- /// Compute the lower-triangular 'square-root' L, of A, s.t. A = L*L^T
- /// Run time is O(N^3)
- /// Not yet present in Cholesky<-1>
- template <class A1> static Matrix<N> sqrt(const FixedMatrix<N,N,A1>& A);
-
- /// Compute the lower-triangular 'square-root' L of the decomposed matrix,
s.t. A = L*L^T
- /// L is stored in M
- /// Not yet present in Cholesky<-1>
- template <class A> void get_sqrt(FixedMatrix<N,N,A>& M) const;
-
- /// Compute the lower-triangular 'square-root' L of the decomposed matrix,
s.t. A = L*L^T
- /// Not yet present in Cholesky<-1>
- Matrix<N> get_sqrt() const;
-
- /// Compute the lower-triangular 'square-root' L of the decomposed matrix,
s.t. A = L*L^T
- /// @deprecated Use get_sqrt, or the static sqrt function
- Matrix<N> get_L() const __attribute__ ((deprecated));
-
- /// Compute the lower-triangular 'square-root' L of the inverse of the
decomposed matrix, s.t. A^-1 = L*L^T
- /// Not yet present in Cholesky<-1>
- template <class A> void get_inv_sqrt(FixedMatrix<N,N,A>& M) const;
-
- /// Compute the Mahalanobis squared magnitude of x, d = x*A^-1*x
- /// Run time is O(N^2)
- /// Not yet present in Cholesky<-1>
- template <class A> double mahalanobis(const FixedVector<N,A>& v) const;
-
- /// Compute J*A^-1*J^T, and store in T using F::eval (for instance, F
might be util::PlusAssign to add the result to T)
- /// Run time is O(MN^2 + NM^2)
- /// Not yet present in Cholesky<-1>
- template <class F, int M, class A1, class A2> void transform_inverse(const
FixedMatrix<M,N,A1>& J, FixedMatrix<M,M,A2>& T) const;
-
- /// Compute J*A^-1*J^T, and store in T
- /// Run time is O(MN^2 + NM^2)
- /// Not yet present in Cholesky<-1>
- template <int M, class A1, class A2> void transform_inverse(const
FixedMatrix<M,N,A1>& J, FixedMatrix<M,M,A2>& T) const;
-
- /// Compute J*A^-1*J^T
- /// Run time is O(MN^2 + NM^2)
- /// Not yet present in Cholesky<-1>
- template <int M, class A> Matrix<M> transform_inverse(const
FixedMatrix<M,N,A>& J) const;
-
- /// Compute x = A^-1*v
- /// Run time is O(N^2)
- /// Not yet present in Cholesky<-1>
- template <class A1, class A2> inline void inverse_times(const
FixedVector<N,A1>& v, FixedVector<N,A2>& x) const;
-
- /// Compute A^-1*v
- /// Run time is O(N^2)
- /// Not yet present in Cholesky<-1>
- template <class Accessor> inline Vector<N> inverse_times(const
FixedVector<N,Accessor>& v) const;
-
- /// Compute x = A^-1*v
- /// Run time is O(N^2)
- template <class Accessor> inline Vector<N> backsub(const
FixedVector<N,Accessor>& v) const;
-
- /// Compute A^-1*B
- /// Run time is O(MN^2)
- /// Not yet present in Cholesky<-1>
- template <class A, int M> inline Matrix<N,M> inverse_times(const
FixedMatrix<N,M,A>& B);
-
- /// Compute A^-1 and store in M
- /// Run time is O(N^3)
- template <class A> void get_inverse(FixedMatrix<N,N,A>& M) const;
-
- /// Compute A^-1
- /// Run time is O(N^3)
- Matrix<N> get_inverse() const;
-
- /// Update the decomposition for A' = A + V*V^T
- /// Run time is O(MN^2), but for small N, it's faster to compute A' and
recompute the decomposition
- /// Not yet present in Cholesky<-1>
- template <int M, class A> void update(const FixedMatrix<N,M,A>& V);
-
- /// Update the decomposition for A' = A + v*v^T
- /// Run time is O(N^2), but for small N, it's faster to compute A' and
recompute the decomposition
- /// Not yet present in Cholesky<-1>
- template <class A> void update(const FixedVector<N,A>& v);
-};
-
-};
-
-#endif
Index: doc/Doxyfile
===================================================================
RCS file: doc/Doxyfile
diff -N doc/Doxyfile
--- doc/Doxyfile 14 Apr 2009 07:12:37 -0000 1.5
+++ /dev/null 1 Jan 1970 00:00:00 -0000
@@ -1,1118 +0,0 @@
-# Doxyfile 1.3.6
-
-# This file describes the settings to be used by the documentation system
-# doxygen (www.doxygen.org) for a project
-#
-# All text after a hash (#) is considered a comment and will be ignored
-# The format is:
-# TAG = value [value, ...]
-# For lists items can also be appended using:
-# TAG += value [value, ...]
-# Values that contain spaces should be placed between quotes (" ")
-
-#---------------------------------------------------------------------------
-# Project related configuration options
-#---------------------------------------------------------------------------
-
-# The PROJECT_NAME tag is a single word (or a sequence of words surrounded
-# by quotes) that should identify the project.
-
-PROJECT_NAME = TooN
-
-# The PROJECT_NUMBER tag can be used to enter a project or revision number.
-# This could be handy for archiving the generated documentation or
-# if some version control system is used.
-
-PROJECT_NUMBER = 2.0.0
-
-# The OUTPUT_DIRECTORY tag is used to specify the (relative or absolute)
-# base path where the generated documentation will be put.
-# If a relative path is entered, it will be relative to the location
-# where doxygen was started. If left blank the current directory will be used.
-
-OUTPUT_DIRECTORY =
-
-# The OUTPUT_LANGUAGE tag is used to specify the language in which all
-# documentation generated by doxygen is written. Doxygen will use this
-# information to generate all constant output in the proper language.
-# The default language is English, other supported languages are:
-# Brazilian, Catalan, Chinese, Chinese-Traditional, Croatian, Czech, Danish,
Dutch,
-# Finnish, French, German, Greek, Hungarian, Italian, Japanese, Japanese-en
-# (Japanese with English messages), Korean, Korean-en, Norwegian, Polish,
Portuguese,
-# Romanian, Russian, Serbian, Slovak, Slovene, Spanish, Swedish, and Ukrainian.
-
-OUTPUT_LANGUAGE = English
-
-# This tag can be used to specify the encoding used in the generated output.
-# The encoding is not always determined by the language that is chosen,
-# but also whether or not the output is meant for Windows or non-Windows
users.
-# In case there is a difference, setting the USE_WINDOWS_ENCODING tag to YES
-# forces the Windows encoding (this is the default for the Windows binary),
-# whereas setting the tag to NO uses a Unix-style encoding (the default for
-# all platforms other than Windows).
-
-USE_WINDOWS_ENCODING = NO
-
-# If the BRIEF_MEMBER_DESC tag is set to YES (the default) Doxygen will
-# include brief member descriptions after the members that are listed in
-# the file and class documentation (similar to JavaDoc).
-# Set to NO to disable this.
-
-BRIEF_MEMBER_DESC = NO
-
-# If the REPEAT_BRIEF tag is set to YES (the default) Doxygen will prepend
-# the brief description of a member or function before the detailed
description.
-# Note: if both HIDE_UNDOC_MEMBERS and BRIEF_MEMBER_DESC are set to NO, the
-# brief descriptions will be completely suppressed.
-
-REPEAT_BRIEF = YES
-
-# This tag implements a quasi-intelligent brief description abbreviator
-# that is used to form the text in various listings. Each string
-# in this list, if found as the leading text of the brief description, will be
-# stripped from the text and the result after processing the whole list, is
used
-# as the annotated text. Otherwise, the brief description is used as-is. If
left
-# blank, the following values are used ("$name" is automatically replaced with
the
-# name of the entity): "The $name class" "The $name widget" "The $name file"
-# "is" "provides" "specifies" "contains" "represents" "a" "an" "the"
-
-ABBREVIATE_BRIEF =
-
-# If the ALWAYS_DETAILED_SEC and REPEAT_BRIEF tags are both set to YES then
-# Doxygen will generate a detailed section even if there is only a brief
-# description.
-
-ALWAYS_DETAILED_SEC = NO
-
-# If the INLINE_INHERITED_MEMB tag is set to YES, doxygen will show all
inherited
-# members of a class in the documentation of that class as if those members
were
-# ordinary class members. Constructors, destructors and assignment operators
of
-# the base classes will not be shown.
-
-INLINE_INHERITED_MEMB = NO
-
-# If the FULL_PATH_NAMES tag is set to YES then Doxygen will prepend the full
-# path before files name in the file list and in the header files. If set
-# to NO the shortest path that makes the file name unique will be used.
-
-FULL_PATH_NAMES = YES
-
-# If the FULL_PATH_NAMES tag is set to YES then the STRIP_FROM_PATH tag
-# can be used to strip a user-defined part of the path. Stripping is
-# only done if one of the specified strings matches the left-hand part of
-# the path. It is allowed to use relative paths in the argument list.
-# If left blank the directory from which doxygen is run is used as the
-# path to strip.
-
-STRIP_FROM_PATH =
-
-# If the SHORT_NAMES tag is set to YES, doxygen will generate much shorter
-# (but less readable) file names. This can be useful is your file systems
-# doesn't support long names like on DOS, Mac, or CD-ROM.
-
-SHORT_NAMES = NO
-
-# If the JAVADOC_AUTOBRIEF tag is set to YES then Doxygen
-# will interpret the first line (until the first dot) of a JavaDoc-style
-# comment as the brief description. If set to NO, the JavaDoc
-# comments will behave just like the Qt-style comments (thus requiring an
-# explicit @brief command for a brief description.
-
-JAVADOC_AUTOBRIEF = YES
-
-# The MULTILINE_CPP_IS_BRIEF tag can be set to YES to make Doxygen
-# treat a multi-line C++ special comment block (i.e. a block of //! or ///
-# comments) as a brief description. This used to be the default behaviour.
-# The new default is to treat a multi-line C++ comment block as a detailed
-# description. Set this tag to YES if you prefer the old behaviour instead.
-
-MULTILINE_CPP_IS_BRIEF = NO
-
-# If the DETAILS_AT_TOP tag is set to YES then Doxygen
-# will output the detailed description near the top, like JavaDoc.
-# If set to NO, the detailed description appears after the member
-# documentation.
-
-DETAILS_AT_TOP = NO
-
-# If the INHERIT_DOCS tag is set to YES (the default) then an undocumented
-# member inherits the documentation from any documented member that it
-# re-implements.
-
-INHERIT_DOCS = YES
-
-# If member grouping is used in the documentation and the DISTRIBUTE_GROUP_DOC
-# tag is set to YES, then doxygen will reuse the documentation of the first
-# member in the group (if any) for the other members of the group. By default
-# all members of a group must be documented explicitly.
-
-DISTRIBUTE_GROUP_DOC = NO
-
-# The TAB_SIZE tag can be used to set the number of spaces in a tab.
-# Doxygen uses this value to replace tabs by spaces in code fragments.
-
-TAB_SIZE = 4
-
-# This tag can be used to specify a number of aliases that acts
-# as commands in the documentation. An alias has the form "name=value".
-# For example adding "sideeffect=\par Side Effects:\n" will allow you to
-# put the command \sideeffect (or @sideeffect) in the documentation, which
-# will result in a user-defined paragraph with heading "Side Effects:".
-# You can put \n's in the value part of an alias to insert newlines.
-
-ALIASES =
-
-# Set the OPTIMIZE_OUTPUT_FOR_C tag to YES if your project consists of C
sources
-# only. Doxygen will then generate output that is more tailored for C.
-# For instance, some of the names that are used will be different. The list
-# of all members will be omitted, etc.
-
-OPTIMIZE_OUTPUT_FOR_C = NO
-
-# Set the OPTIMIZE_OUTPUT_JAVA tag to YES if your project consists of Java
sources
-# only. Doxygen will then generate output that is more tailored for Java.
-# For instance, namespaces will be presented as packages, qualified scopes
-# will look different, etc.
-
-OPTIMIZE_OUTPUT_JAVA = NO
-
-# Set the SUBGROUPING tag to YES (the default) to allow class member groups of
-# the same type (for instance a group of public functions) to be put as a
-# subgroup of that type (e.g. under the Public Functions section). Set it to
-# NO to prevent subgrouping. Alternatively, this can be done per class using
-# the \nosubgrouping command.
-
-SUBGROUPING = YES
-
-#---------------------------------------------------------------------------
-# Build related configuration options
-#---------------------------------------------------------------------------
-
-# If the EXTRACT_ALL tag is set to YES doxygen will assume all entities in
-# documentation are documented, even if no documentation was available.
-# Private class members and static file members will be hidden unless
-# the EXTRACT_PRIVATE and EXTRACT_STATIC tags are set to YES
-
-EXTRACT_ALL = NO
-
-# If the EXTRACT_PRIVATE tag is set to YES all private members of a class
-# will be included in the documentation.
-
-EXTRACT_PRIVATE = NO
-
-# If the EXTRACT_STATIC tag is set to YES all static members of a file
-# will be included in the documentation.
-
-EXTRACT_STATIC = NO
-
-# If the EXTRACT_LOCAL_CLASSES tag is set to YES classes (and structs)
-# defined locally in source files will be included in the documentation.
-# If set to NO only classes defined in header files are included.
-
-EXTRACT_LOCAL_CLASSES = YES
-
-# If the HIDE_UNDOC_MEMBERS tag is set to YES, Doxygen will hide all
-# undocumented members of documented classes, files or namespaces.
-# If set to NO (the default) these members will be included in the
-# various overviews, but no documentation section is generated.
-# This option has no effect if EXTRACT_ALL is enabled.
-
-HIDE_UNDOC_MEMBERS = NO
-
-# If the HIDE_UNDOC_CLASSES tag is set to YES, Doxygen will hide all
-# undocumented classes that are normally visible in the class hierarchy.
-# If set to NO (the default) these classes will be included in the various
-# overviews. This option has no effect if EXTRACT_ALL is enabled.
-
-HIDE_UNDOC_CLASSES = NO
-
-# If the HIDE_FRIEND_COMPOUNDS tag is set to YES, Doxygen will hide all
-# friend (class|struct|union) declarations.
-# If set to NO (the default) these declarations will be included in the
-# documentation.
-
-HIDE_FRIEND_COMPOUNDS = YES
-
-# If the HIDE_IN_BODY_DOCS tag is set to YES, Doxygen will hide any
-# documentation blocks found inside the body of a function.
-# If set to NO (the default) these blocks will be appended to the
-# function's detailed documentation block.
-
-HIDE_IN_BODY_DOCS = NO
-
-# The INTERNAL_DOCS tag determines if documentation
-# that is typed after a \internal command is included. If the tag is set
-# to NO (the default) then the documentation will be excluded.
-# Set it to YES to include the internal documentation.
-
-INTERNAL_DOCS = NO
-
-# If the CASE_SENSE_NAMES tag is set to NO then Doxygen will only generate
-# file names in lower-case letters. If set to YES upper-case letters are also
-# allowed. This is useful if you have classes or files whose names only differ
-# in case and if your file system supports case sensitive file names. Windows
-# users are advised to set this option to NO.
-
-CASE_SENSE_NAMES = YES
-
-# If the HIDE_SCOPE_NAMES tag is set to NO (the default) then Doxygen
-# will show members with their full class and namespace scopes in the
-# documentation. If set to YES the scope will be hidden.
-
-HIDE_SCOPE_NAMES = NO
-
-# If the SHOW_INCLUDE_FILES tag is set to YES (the default) then Doxygen
-# will put a list of the files that are included by a file in the
documentation
-# of that file.
-
-SHOW_INCLUDE_FILES = YES
-
-# If the INLINE_INFO tag is set to YES (the default) then a tag [inline]
-# is inserted in the documentation for inline members.
-
-INLINE_INFO = NO
-
-# If the SORT_MEMBER_DOCS tag is set to YES (the default) then doxygen
-# will sort the (detailed) documentation of file and class members
-# alphabetically by member name. If set to NO the members will appear in
-# declaration order.
-
-SORT_MEMBER_DOCS = NO
-
-# If the SORT_BRIEF_DOCS tag is set to YES then doxygen will sort the
-# brief documentation of file, namespace and class members alphabetically
-# by member name. If set to NO (the default) the members will appear in
-# declaration order.
-
-SORT_BRIEF_DOCS = NO
-
-# If the SORT_BY_SCOPE_NAME tag is set to YES, the class list will be
-# sorted by fully-qualified names, including namespaces. If set to
-# NO (the default), the class list will be sorted only by class name,
-# not including the namespace part.
-# Note: This option is not very useful if HIDE_SCOPE_NAMES is set to YES.
-# Note: This option applies only to the class list, not to the
-# alphabetical list.
-
-SORT_BY_SCOPE_NAME = NO
-
-# The GENERATE_TODOLIST tag can be used to enable (YES) or
-# disable (NO) the todo list. This list is created by putting \todo
-# commands in the documentation.
-
-GENERATE_TODOLIST = YES
-
-# The GENERATE_TESTLIST tag can be used to enable (YES) or
-# disable (NO) the test list. This list is created by putting \test
-# commands in the documentation.
-
-GENERATE_TESTLIST = YES
-
-# The GENERATE_BUGLIST tag can be used to enable (YES) or
-# disable (NO) the bug list. This list is created by putting \bug
-# commands in the documentation.
-
-GENERATE_BUGLIST = YES
-
-# The GENERATE_DEPRECATEDLIST tag can be used to enable (YES) or
-# disable (NO) the deprecated list. This list is created by putting
-# \deprecated commands in the documentation.
-
-GENERATE_DEPRECATEDLIST= NO
-
-# The ENABLED_SECTIONS tag can be used to enable conditional
-# documentation sections, marked by \if sectionname ... \endif.
-
-ENABLED_SECTIONS = IGNORE
-
-# The MAX_INITIALIZER_LINES tag determines the maximum number of lines
-# the initial value of a variable or define consists of for it to appear in
-# the documentation. If the initializer consists of more lines than specified
-# here it will be hidden. Use a value of 0 to hide initializers completely.
-# The appearance of the initializer of individual variables and defines in the
-# documentation can be controlled using \showinitializer or \hideinitializer
-# command in the documentation regardless of this setting.
-
-MAX_INITIALIZER_LINES = 30
-
-# Set the SHOW_USED_FILES tag to NO to disable the list of files generated
-# at the bottom of the documentation of classes and structs. If set to YES the
-# list will mention the files that were used to generate the documentation.
-
-SHOW_USED_FILES = NO
-
-#---------------------------------------------------------------------------
-# configuration options related to warning and progress messages
-#---------------------------------------------------------------------------
-
-# The QUIET tag can be used to turn on/off the messages that are generated
-# by doxygen. Possible values are YES and NO. If left blank NO is used.
-
-QUIET = NO
-
-# The WARNINGS tag can be used to turn on/off the warning messages that are
-# generated by doxygen. Possible values are YES and NO. If left blank
-# NO is used.
-
-WARNINGS = YES
-
-# If WARN_IF_UNDOCUMENTED is set to YES, then doxygen will generate warnings
-# for undocumented members. If EXTRACT_ALL is set to YES then this flag will
-# automatically be disabled.
-
-WARN_IF_UNDOCUMENTED = YES
-
-# If WARN_IF_DOC_ERROR is set to YES, doxygen will generate warnings for
-# potential errors in the documentation, such as not documenting some
-# parameters in a documented function, or documenting parameters that
-# don't exist or using markup commands wrongly.
-
-WARN_IF_DOC_ERROR = YES
-
-# The WARN_FORMAT tag determines the format of the warning messages that
-# doxygen can produce. The string should contain the $file, $line, and $text
-# tags, which will be replaced by the file and line number from which the
-# warning originated and the warning text.
-
-WARN_FORMAT = "$file:$line: $text"
-
-# The WARN_LOGFILE tag can be used to specify a file to which warning
-# and error messages should be written. If left blank the output is written
-# to stderr.
-
-WARN_LOGFILE =
-
-#---------------------------------------------------------------------------
-# configuration options related to the input files
-#---------------------------------------------------------------------------
-
-# The INPUT tag can be used to specify the files and/or directories that
contain
-# documented source files. You may enter file names like "myfile.cpp" or
-# directories like "/usr/src/myproject". Separate the files or directories
-# with spaces.
-
-INPUT = . doc optimization
-
-# If the value of the INPUT tag contains directories, you can use the
-# FILE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp
-# and *.h) to filter out the source-files in the directories. If left
-# blank the following patterns are tested:
-# *.c *.cc *.cxx *.cpp *.c++ *.java *.ii *.ixx *.ipp *.i++ *.inl *.h *.hh
*.hxx *.hpp
-# *.h++ *.idl *.odl *.cs *.php *.php3 *.inc
-
-FILE_PATTERNS = documentation.h *doc.h irls.h wls.h wls_cholesky.h
../optimization/downhill_simplex.h
-
-# The RECURSIVE tag can be used to turn specify whether or not subdirectories
-# should be searched for input files as well. Possible values are YES and NO.
-# If left blank NO is used.
-
-RECURSIVE = NO
-
-# The EXCLUDE tag can be used to specify files and/or directories that should
-# excluded from the INPUT source files. This way you can easily exclude a
-# subdirectory from a directory tree whose root is specified with the INPUT
tag.
-
-EXCLUDE =
-
-# The EXCLUDE_SYMLINKS tag can be used select whether or not files or
directories
-# that are symbolic links (a Unix filesystem feature) are excluded from the
input.
-
-EXCLUDE_SYMLINKS = NO
-
-# If the value of the INPUT tag contains directories, you can use the
-# EXCLUDE_PATTERNS tag to specify one or more wildcard patterns to exclude
-# certain files from those directories.
-
-EXCLUDE_PATTERNS =
-
-# The EXAMPLE_PATH tag can be used to specify one or more files or
-# directories that contain example code fragments that are included (see
-# the \include command).
-
-EXAMPLE_PATH =
-
-# If the value of the EXAMPLE_PATH tag contains directories, you can use the
-# EXAMPLE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp
-# and *.h) to filter out the source-files in the directories. If left
-# blank all files are included.
-
-EXAMPLE_PATTERNS =
-
-# If the EXAMPLE_RECURSIVE tag is set to YES then subdirectories will be
-# searched for input files to be used with the \include or \dontinclude
-# commands irrespective of the value of the RECURSIVE tag.
-# Possible values are YES and NO. If left blank NO is used.
-
-EXAMPLE_RECURSIVE = NO
-
-# The IMAGE_PATH tag can be used to specify one or more files or
-# directories that contain image that are included in the documentation (see
-# the \image command).
-
-IMAGE_PATH =
-
-# The INPUT_FILTER tag can be used to specify a program that doxygen should
-# invoke to filter for each input file. Doxygen will invoke the filter program
-# by executing (via popen()) the command <filter> <input-file>, where <filter>
-# is the value of the INPUT_FILTER tag, and <input-file> is the name of an
-# input file. Doxygen will then use the output that the filter program writes
-# to standard output.
-
-INPUT_FILTER =
-
-# If the FILTER_SOURCE_FILES tag is set to YES, the input filter (if set using
-# INPUT_FILTER) will be used to filter the input files when producing source
-# files to browse (i.e. when SOURCE_BROWSER is set to YES).
-
-FILTER_SOURCE_FILES = NO
-
-#---------------------------------------------------------------------------
-# configuration options related to source browsing
-#---------------------------------------------------------------------------
-
-# If the SOURCE_BROWSER tag is set to YES then a list of source files will
-# be generated. Documented entities will be cross-referenced with these
sources.
-# Note: To get rid of all source code in the generated output, make sure also
-# VERBATIM_HEADERS is set to NO.
-
-SOURCE_BROWSER = NO
-
-# Setting the INLINE_SOURCES tag to YES will include the body
-# of functions and classes directly in the documentation.
-
-INLINE_SOURCES = NO
-
-# Setting the STRIP_CODE_COMMENTS tag to YES (the default) will instruct
-# doxygen to hide any special comment blocks from generated source code
-# fragments. Normal C and C++ comments will always remain visible.
-
-STRIP_CODE_COMMENTS = YES
-
-# If the REFERENCED_BY_RELATION tag is set to YES (the default)
-# then for each documented function all documented
-# functions referencing it will be listed.
-
-REFERENCED_BY_RELATION = YES
-
-# If the REFERENCES_RELATION tag is set to YES (the default)
-# then for each documented function all documented entities
-# called/used by that function will be listed.
-
-REFERENCES_RELATION = YES
-
-# If the VERBATIM_HEADERS tag is set to YES (the default) then Doxygen
-# will generate a verbatim copy of the header file for each class for
-# which an include is specified. Set to NO to disable this.
-
-VERBATIM_HEADERS = YES
-
-#---------------------------------------------------------------------------
-# configuration options related to the alphabetical class index
-#---------------------------------------------------------------------------
-
-# If the ALPHABETICAL_INDEX tag is set to YES, an alphabetical index
-# of all compounds will be generated. Enable this if the project
-# contains a lot of classes, structs, unions or interfaces.
-
-ALPHABETICAL_INDEX = NO
-
-# If the alphabetical index is enabled (see ALPHABETICAL_INDEX) then
-# the COLS_IN_ALPHA_INDEX tag can be used to specify the number of columns
-# in which this list will be split (can be a number in the range [1..20])
-
-COLS_IN_ALPHA_INDEX = 5
-
-# In case all classes in a project start with a common prefix, all
-# classes will be put under the same header in the alphabetical index.
-# The IGNORE_PREFIX tag can be used to specify one or more prefixes that
-# should be ignored while generating the index headers.
-
-IGNORE_PREFIX =
-
-#---------------------------------------------------------------------------
-# configuration options related to the HTML output
-#---------------------------------------------------------------------------
-
-# If the GENERATE_HTML tag is set to YES (the default) Doxygen will
-# generate HTML output.
-
-GENERATE_HTML = YES
-
-# The HTML_OUTPUT tag is used to specify where the HTML docs will be put.
-# If a relative path is entered the value of OUTPUT_DIRECTORY will be
-# put in front of it. If left blank `html' will be used as the default path.
-
-HTML_OUTPUT = html
-
-# The HTML_FILE_EXTENSION tag can be used to specify the file extension for
-# each generated HTML page (for example: .htm,.php,.asp). If it is left blank
-# doxygen will generate files with .html extension.
-
-HTML_FILE_EXTENSION = .html
-
-# The HTML_HEADER tag can be used to specify a personal HTML header for
-# each generated HTML page. If it is left blank doxygen will generate a
-# standard header.
-
-HTML_HEADER =
-
-# The HTML_FOOTER tag can be used to specify a personal HTML footer for
-# each generated HTML page. If it is left blank doxygen will generate a
-# standard footer.
-
-HTML_FOOTER =
-
-# The HTML_STYLESHEET tag can be used to specify a user-defined cascading
-# style sheet that is used by each HTML page. It can be used to
-# fine-tune the look of the HTML output. If the tag is left blank doxygen
-# will generate a default style sheet. Note that doxygen will try to copy
-# the style sheet file to the HTML output directory, so don't put your own
-# stylesheet in the HTML output directory as well, or it will be erased!
-
-HTML_STYLESHEET =
-
-# If the HTML_ALIGN_MEMBERS tag is set to YES, the members of classes,
-# files or namespaces will be aligned in HTML using tables. If set to
-# NO a bullet list will be used.
-
-HTML_ALIGN_MEMBERS = YES
-
-# If the GENERATE_HTMLHELP tag is set to YES, additional index files
-# will be generated that can be used as input for tools like the
-# Microsoft HTML help workshop to generate a compressed HTML help file (.chm)
-# of the generated HTML documentation.
-
-GENERATE_HTMLHELP = NO
-
-# If the GENERATE_HTMLHELP tag is set to YES, the CHM_FILE tag can
-# be used to specify the file name of the resulting .chm file. You
-# can add a path in front of the file if the result should not be
-# written to the html output directory.
-
-CHM_FILE =
-
-# If the GENERATE_HTMLHELP tag is set to YES, the HHC_LOCATION tag can
-# be used to specify the location (absolute path including file name) of
-# the HTML help compiler (hhc.exe). If non-empty doxygen will try to run
-# the HTML help compiler on the generated index.hhp.
-
-HHC_LOCATION =
-
-# If the GENERATE_HTMLHELP tag is set to YES, the GENERATE_CHI flag
-# controls if a separate .chi index file is generated (YES) or that
-# it should be included in the master .chm file (NO).
-
-GENERATE_CHI = NO
-
-# If the GENERATE_HTMLHELP tag is set to YES, the BINARY_TOC flag
-# controls whether a binary table of contents is generated (YES) or a
-# normal table of contents (NO) in the .chm file.
-
-BINARY_TOC = NO
-
-# The TOC_EXPAND flag can be set to YES to add extra items for group members
-# to the contents of the HTML help documentation and to the tree view.
-
-TOC_EXPAND = NO
-
-# The DISABLE_INDEX tag can be used to turn on/off the condensed index at
-# top of each HTML page. The value NO (the default) enables the index and
-# the value YES disables it.
-
-DISABLE_INDEX = NO
-
-# This tag can be used to set the number of enum values (range [1..20])
-# that doxygen will group on one line in the generated HTML documentation.
-
-ENUM_VALUES_PER_LINE = 4
-
-# If the GENERATE_TREEVIEW tag is set to YES, a side panel will be
-# generated containing a tree-like index structure (just like the one that
-# is generated for HTML Help). For this to work a browser that supports
-# JavaScript, DHTML, CSS and frames is required (for instance Mozilla 1.0+,
-# Netscape 6.0+, Internet explorer 5.0+, or Konqueror). Windows users are
-# probably better off using the HTML help feature.
-
-GENERATE_TREEVIEW = NO
-
-# If the treeview is enabled (see GENERATE_TREEVIEW) then this tag can be
-# used to set the initial width (in pixels) of the frame in which the tree
-# is shown.
-
-TREEVIEW_WIDTH = 250
-
-#---------------------------------------------------------------------------
-# configuration options related to the LaTeX output
-#---------------------------------------------------------------------------
-
-# If the GENERATE_LATEX tag is set to YES (the default) Doxygen will
-# generate Latex output.
-
-GENERATE_LATEX = NO
-
-# The LATEX_OUTPUT tag is used to specify where the LaTeX docs will be put.
-# If a relative path is entered the value of OUTPUT_DIRECTORY will be
-# put in front of it. If left blank `latex' will be used as the default path.
-
-LATEX_OUTPUT = latex
-
-# The LATEX_CMD_NAME tag can be used to specify the LaTeX command name to be
-# invoked. If left blank `latex' will be used as the default command name.
-
-LATEX_CMD_NAME = latex
-
-# The MAKEINDEX_CMD_NAME tag can be used to specify the command name to
-# generate index for LaTeX. If left blank `makeindex' will be used as the
-# default command name.
-
-MAKEINDEX_CMD_NAME = makeindex
-
-# If the COMPACT_LATEX tag is set to YES Doxygen generates more compact
-# LaTeX documents. This may be useful for small projects and may help to
-# save some trees in general.
-
-COMPACT_LATEX = NO
-
-# The PAPER_TYPE tag can be used to set the paper type that is used
-# by the printer. Possible values are: a4, a4wide, letter, legal and
-# executive. If left blank a4wide will be used.
-
-PAPER_TYPE = a4wide
-
-# The EXTRA_PACKAGES tag can be to specify one or more names of LaTeX
-# packages that should be included in the LaTeX output.
-
-EXTRA_PACKAGES = amsmath \
- amssymb
-
-# The LATEX_HEADER tag can be used to specify a personal LaTeX header for
-# the generated latex document. The header should contain everything until
-# the first chapter. If it is left blank doxygen will generate a
-# standard header. Notice: only use this tag if you know what you are doing!
-
-LATEX_HEADER =
-
-# If the PDF_HYPERLINKS tag is set to YES, the LaTeX that is generated
-# is prepared for conversion to pdf (using ps2pdf). The pdf file will
-# contain links (just like the HTML output) instead of page references
-# This makes the output suitable for online browsing using a pdf viewer.
-
-PDF_HYPERLINKS = NO
-
-# If the USE_PDFLATEX tag is set to YES, pdflatex will be used instead of
-# plain latex in the generated Makefile. Set this option to YES to get a
-# higher quality PDF documentation.
-
-USE_PDFLATEX = NO
-
-# If the LATEX_BATCHMODE tag is set to YES, doxygen will add the \\batchmode.
-# command to the generated LaTeX files. This will instruct LaTeX to keep
-# running if errors occur, instead of asking the user for help.
-# This option is also used when generating formulas in HTML.
-
-LATEX_BATCHMODE = NO
-
-# If LATEX_HIDE_INDICES is set to YES then doxygen will not
-# include the index chapters (such as File Index, Compound Index, etc.)
-# in the output.
-
-LATEX_HIDE_INDICES = NO
-
-#---------------------------------------------------------------------------
-# configuration options related to the RTF output
-#---------------------------------------------------------------------------
-
-# If the GENERATE_RTF tag is set to YES Doxygen will generate RTF output
-# The RTF output is optimized for Word 97 and may not look very pretty with
-# other RTF readers or editors.
-
-GENERATE_RTF = NO
-
-# The RTF_OUTPUT tag is used to specify where the RTF docs will be put.
-# If a relative path is entered the value of OUTPUT_DIRECTORY will be
-# put in front of it. If left blank `rtf' will be used as the default path.
-
-RTF_OUTPUT = rtf
-
-# If the COMPACT_RTF tag is set to YES Doxygen generates more compact
-# RTF documents. This may be useful for small projects and may help to
-# save some trees in general.
-
-COMPACT_RTF = NO
-
-# If the RTF_HYPERLINKS tag is set to YES, the RTF that is generated
-# will contain hyperlink fields. The RTF file will
-# contain links (just like the HTML output) instead of page references.
-# This makes the output suitable for online browsing using WORD or other
-# programs which support those fields.
-# Note: wordpad (write) and others do not support links.
-
-RTF_HYPERLINKS = NO
-
-# Load stylesheet definitions from file. Syntax is similar to doxygen's
-# config file, i.e. a series of assignments. You only have to provide
-# replacements, missing definitions are set to their default value.
-
-RTF_STYLESHEET_FILE =
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-# If the GENERATE_MAN tag is set to YES (the default) Doxygen will
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-#---------------------------------------------------------------------------
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-GENERATE_XML = NO
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-# The XML_OUTPUT tag is used to specify where the XML pages will be put.
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-# If the GENERATE_AUTOGEN_DEF tag is set to YES Doxygen will
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-# that captures the structure of the code including all
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-# and incomplete at the moment.
-
-GENERATE_AUTOGEN_DEF = NO
-
-#---------------------------------------------------------------------------
-# configuration options related to the Perl module output
-#---------------------------------------------------------------------------
-
-# If the GENERATE_PERLMOD tag is set to YES Doxygen will
-# generate a Perl module file that captures the structure of
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-# feature is still experimental and incomplete at the
-# moment.
-
-GENERATE_PERLMOD = NO
-
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-# The names of the make variables in the generated doxyrules.make file
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-# files.
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-ENABLE_PREPROCESSING = YES
-
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-SEARCH_INCLUDES = YES
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-# The INCLUDE_PATH tag can be used to specify one or more directories that
-# contain include files that are not input files but should be processed by
-# the preprocessor.
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-INCLUDE_PATH =
-
-# You can use the INCLUDE_FILE_PATTERNS tag to specify one or more wildcard
-# patterns (like *.h and *.hpp) to filter out the header-files in the
-# directories. If left blank, the patterns specified with FILE_PATTERNS will
-# be used.
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-# are defined before the preprocessor is started (similar to the -D option of
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-# or name=definition (no spaces). If the definition and the = are
-# omitted =1 is assumed.
-
-PREDEFINED = DOXYGEN_IGNORE_INTERNAL DOXYGEN_INCLUDE_ONLY_FOR_DOCS
-
-# If the MACRO_EXPANSION and EXPAND_ONLY_PREDEF tags are set to YES then
-# this tag can be used to specify a list of macro names that should be
expanded.
-# The macro definition that is found in the sources will be used.
-# Use the PREDEFINED tag if you want to use a different macro definition.
-
-EXPAND_AS_DEFINED =
-
-# If the SKIP_FUNCTION_MACROS tag is set to YES (the default) then
-# doxygen's preprocessor will remove all function-like macros that are alone
-# on a line, have an all uppercase name, and do not end with a semicolon. Such
-# function macros are typically used for boiler-plate code, and will confuse
the
-# parser if not removed.
-
-SKIP_FUNCTION_MACROS = YES
-
-#---------------------------------------------------------------------------
-# Configuration::additions related to external references
-#---------------------------------------------------------------------------
-
-# The TAGFILES option can be used to specify one or more tagfiles.
-# Optionally an initial location of the external documentation
-# can be added for each tagfile. The format of a tag file without
-# this location is as follows:
-# TAGFILES = file1 file2 ...
-# Adding location for the tag files is done as follows:
-# TAGFILES = file1=loc1 "file2 = loc2" ...
-# where "loc1" and "loc2" can be relative or absolute paths or
-# URLs. If a location is present for each tag, the installdox tool
-# does not have to be run to correct the links.
-# Note that each tag file must have a unique name
-# (where the name does NOT include the path)
-# If a tag file is not located in the directory in which doxygen
-# is run, you must also specify the path to the tagfile here.
-
-TAGFILES =
-
-# When a file name is specified after GENERATE_TAGFILE, doxygen will create
-# a tag file that is based on the input files it reads.
-
-GENERATE_TAGFILE =
-
-# If the ALLEXTERNALS tag is set to YES all external classes will be listed
-# in the class index. If set to NO only the inherited external classes
-# will be listed.
-
-ALLEXTERNALS = NO
-
-# If the EXTERNAL_GROUPS tag is set to YES all external groups will be listed
-# in the modules index. If set to NO, only the current project's groups will
-# be listed.
-
-EXTERNAL_GROUPS = YES
-
-# The PERL_PATH should be the absolute path and name of the perl script
-# interpreter (i.e. the result of `which perl').
-
-PERL_PATH = /usr/bin/perl
-
-#---------------------------------------------------------------------------
-# Configuration options related to the dot tool
-#---------------------------------------------------------------------------
-
-# If the CLASS_DIAGRAMS tag is set to YES (the default) Doxygen will
-# generate a inheritance diagram (in HTML, RTF and LaTeX) for classes with
base or
-# super classes. Setting the tag to NO turns the diagrams off. Note that this
-# option is superseded by the HAVE_DOT option below. This is only a fallback.
It is
-# recommended to install and use dot, since it yields more powerful graphs.
-
-CLASS_DIAGRAMS = YES
-
-# If set to YES, the inheritance and collaboration graphs will hide
-# inheritance and usage relations if the target is undocumented
-# or is not a class.
-
-HIDE_UNDOC_RELATIONS = YES
-
-# If you set the HAVE_DOT tag to YES then doxygen will assume the dot tool is
-# available from the path. This tool is part of Graphviz, a graph
visualization
-# toolkit from AT&T and Lucent Bell Labs. The other options in this section
-# have no effect if this option is set to NO (the default)
-
-HAVE_DOT = NO
-
-# If the CLASS_GRAPH and HAVE_DOT tags are set to YES then doxygen
-# will generate a graph for each documented class showing the direct and
-# indirect inheritance relations. Setting this tag to YES will force the
-# the CLASS_DIAGRAMS tag to NO.
-
-CLASS_GRAPH = YES
-
-# If the COLLABORATION_GRAPH and HAVE_DOT tags are set to YES then doxygen
-# will generate a graph for each documented class showing the direct and
-# indirect implementation dependencies (inheritance, containment, and
-# class references variables) of the class with other documented classes.
-
-COLLABORATION_GRAPH = YES
-
-# If the UML_LOOK tag is set to YES doxygen will generate inheritance and
-# collaboration diagrams in a style similar to the OMG's Unified Modeling
-# Language.
-
-UML_LOOK = YES
-
-# If set to YES, the inheritance and collaboration graphs will show the
-# relations between templates and their instances.
-
-TEMPLATE_RELATIONS = NO
-
-# If the ENABLE_PREPROCESSING, SEARCH_INCLUDES, INCLUDE_GRAPH, and HAVE_DOT
-# tags are set to YES then doxygen will generate a graph for each documented
-# file showing the direct and indirect include dependencies of the file with
-# other documented files.
-
-INCLUDE_GRAPH = YES
-
-# If the ENABLE_PREPROCESSING, SEARCH_INCLUDES, INCLUDED_BY_GRAPH, and
-# HAVE_DOT tags are set to YES then doxygen will generate a graph for each
-# documented header file showing the documented files that directly or
-# indirectly include this file.
-
-INCLUDED_BY_GRAPH = YES
-
-# If the CALL_GRAPH and HAVE_DOT tags are set to YES then doxygen will
-# generate a call dependency graph for every global function or class method.
-# Note that enabling this option will significantly increase the time of a
run.
-# So in most cases it will be better to enable call graphs for selected
-# functions only using the \callgraph command.
-
-CALL_GRAPH = NO
-
-# If the GRAPHICAL_HIERARCHY and HAVE_DOT tags are set to YES then doxygen
-# will graphical hierarchy of all classes instead of a textual one.
-
-GRAPHICAL_HIERARCHY = YES
-
-# The DOT_IMAGE_FORMAT tag can be used to set the image format of the images
-# generated by dot. Possible values are png, jpg, or gif
-# If left blank png will be used.
-
-DOT_IMAGE_FORMAT = png
-
-# The tag DOT_PATH can be used to specify the path where the dot tool can be
-# found. If left blank, it is assumed the dot tool can be found on the path.
-
-DOT_PATH =
-
-# The DOTFILE_DIRS tag can be used to specify one or more directories that
-# contain dot files that are included in the documentation (see the
-# \dotfile command).
-
-DOTFILE_DIRS =
-
-# The MAX_DOT_GRAPH_WIDTH tag can be used to set the maximum allowed width
-# (in pixels) of the graphs generated by dot. If a graph becomes larger than
-# this value, doxygen will try to truncate the graph, so that it fits within
-# the specified constraint. Beware that most browsers cannot cope with very
-# large images.
-
-MAX_DOT_GRAPH_WIDTH = 1024
-
-# The MAX_DOT_GRAPH_HEIGHT tag can be used to set the maximum allows height
-# (in pixels) of the graphs generated by dot. If a graph becomes larger than
-# this value, doxygen will try to truncate the graph, so that it fits within
-# the specified constraint. Beware that most browsers cannot cope with very
-# large images.
-
-MAX_DOT_GRAPH_HEIGHT = 1024
-
-# The MAX_DOT_GRAPH_DEPTH tag can be used to set the maximum depth of the
-# graphs generated by dot. A depth value of 3 means that only nodes reachable
-# from the root by following a path via at most 3 edges will be shown. Nodes
that
-# lay further from the root node will be omitted. Note that setting this
option to
-# 1 or 2 may greatly reduce the computation time needed for large code bases.
Also
-# note that a graph may be further truncated if the graph's image dimensions
are
-# not sufficient to fit the graph (see MAX_DOT_GRAPH_WIDTH and
MAX_DOT_GRAPH_HEIGHT).
-# If 0 is used for the depth value (the default), the graph is not
depth-constrained.
-
-MAX_DOT_GRAPH_DEPTH = 0
-
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-# generate a legend page explaining the meaning of the various boxes and
-# arrows in the dot generated graphs.
-
-GENERATE_LEGEND = YES
-
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-# remove the intermediate dot files that are used to generate
-# the various graphs.
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-DOT_CLEANUP = YES
-
-#---------------------------------------------------------------------------
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Index: doc/LUdoc.h
===================================================================
RCS file: doc/LUdoc.h
diff -N doc/LUdoc.h
--- doc/LUdoc.h 11 Mar 2007 21:26:35 -0000 1.5
+++ /dev/null 1 Jan 1970 00:00:00 -0000
@@ -1,94 +0,0 @@
-/*
- Copyright (c) 2005 Paul Smith
-
- Permission is granted to copy, distribute and/or modify this document
under
- the terms of the GNU Free Documentation License, Version 1.2 or any
later
- version published by the Free Software Foundation; with no Invariant
- Sections, no Front-Cover Texts, and no Back-Cover Texts.
-
- You should have received a copy of the GNU Free Documentation License
- License along with this library; if not, write to the Free Software
- Foundation, Inc.
- 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
-
-*/
-// A proxy version of the LU class,
-// cleaned up to present a comprehensible
-// version of the LU interface
-
-#ifdef DOXYGEN_INCLUDE_ONLY_FOR_DOCS
-
-#include <iostream>
-#include <lapack.h>
-#include <TooN/TooN.h>
-
-/// All classes and functions are within this namespace
-namespace TooN
-{
-/**
address@hidden LU LUdoc.h TooN/LU.h
-Performs %LU decomposition and back substitutes to solve equations.
-The %LU decomposition is the fastest way of solving the equation
-\f$M\underline{x} = \underline{c}\f$m, but it becomes unstable when
-\f$M\f$ is (nearly) singular (in which cases the SymEigen or SVD decompositions
-are better). It decomposes a matrix \f$M\f$ into
-\f[M = L \times U\f]
-where \f$L\f$ is a lower-diagonal matrix with unit diagonal and \f$U\f$ is an
-upper-diagonal matrix. The library only supports the decomposition of square
matrices.
-It can be used as follows to solve the \f$M\underline{x} = \underline{c}\f$
problem as follows:
address@hidden
-// construct M
-double d1[][] = {{1,2,3},{4,5,6},{7,8,10}};
-Matrix<3> M(d1);
-// construct c
-Vector<3> c = 2,3,4;
-// create the LU decomposition of M
-LU<3> luM(M);
-// compute x = M^-1 * c
-Vector<3> x = luM.backsub(c);
address@hidden
-The convention LU<> (=LU<-1>) is used to create an LU decomposition whose size
is
-determined at runtime.
address@hidden gDecomps
-**/
-
-template <int Size>
-class LU
-{
-public:
- /// Construct the %LU decomposition of a matrix. This initialises the
class, and
- /// performs the decomposition immediately.
- LU(const Matrix<Size,Size>& M);
-
- /// Perform the %LU decompsition of another matrix.
- void compute(const Matrix<Size,Size>& M);
-
- /// Calculate result of multiplying the inverse of M by another matrix.
For a matrix \f$A\f$, this
- /// calculates \f$M^{-1}A\f$ by back substitution (i.e. without
explictly calculating the inverse).
- template<int Cols>
- Matrix<Size, Cols> backsub(const Matrix<Size, Cols>& rhs);
-
- /// Calculate result of multiplying the inverse of M by a vector. For a
vector \f$b\f$, this
- /// calculates \f$M^{-1}b\f$ by back substitution (i.e. without
explictly calculating the inverse).
- Vector<Size> backsub(const Vector<Size>& rhs);
-
- /// Calculate inverse of the matrix. This is not usually needed: if you
need the inverse just to
- /// multiply it by a matrix or a vector, use one of the backsub()
functions, which will be faster.
- Matrix<Size,Size> get_inverse();
-
- /// Calculate the determinant of the matrix
- double determinant() const;
-
-
- /// Returns the L and U matrices. The permutation matrix is not
returned.
- /// Since L is lower-triangular (with unit diagonal)
- /// and U is upper-triangular, these are returned conflated into one
matrix, where the
- /// diagonal and above parts of the matrix are U and the below-diagonal
part, plus a unit diagonal,
- /// are L.
- Matrix<Size,Size>& get_lu();
-
-};
-
-}
-
-#endif
Index: doc/SymEigendoc.h
===================================================================
RCS file: doc/SymEigendoc.h
diff -N doc/SymEigendoc.h
--- doc/SymEigendoc.h 7 Jul 2006 14:20:06 -0000 1.3
+++ /dev/null 1 Jan 1970 00:00:00 -0000
@@ -1,125 +0,0 @@
-/*
- Copyright (c) 2005 Paul Smith
-
- Permission is granted to copy, distribute and/or modify this document
under
- the terms of the GNU Free Documentation License, Version 1.2 or any
later
- version published by the Free Software Foundation; with no Invariant
- Sections, no Front-Cover Texts, and no Back-Cover Texts.
-
- You should have received a copy of the GNU Free Documentation License
- License along with this library; if not, write to the Free Software
- Foundation, Inc.
- 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
-
-*/
-// A proxy version of the SymEigen class,
-// cleaned up to present a comprehensible
-// version of the SymEigen interface
-
-#ifdef DOXYGEN_INCLUDE_ONLY_FOR_DOCS
-
-#include <iostream>
-#include <lapack.h>
-#include <TooN/toon.h>
-
-/// All classes and functions are within this namespace
-namespace TooN
-{
-
-/**
address@hidden SymEigen SymEigendoc.h TooN/SymEigen.h
-Performs eigen decomposition of a matrix.
-Real symmetric (and hence square matrices) can be decomposed into
-\f[M = U \times \Lambda \times U^T\f]
-where \f$U\f$ is an orthogonal matrix (and hence \f$U^T = U^{-1}\f$) whose
columns
-are the eigenvectors of \f$M\f$ and \f$\Lambda\f$ is a diagonal matrix whose
entries
-are the eigenvalues of \f$M\f$. These quantities are often of use directly,
and can
-be obtained as follows:
address@hidden
-// construct M
-double d1[][] = {{1,2,3},{2,5,6},{3,6,7}};
-Matrix<3> M(d1);
-// create the eigen decomposition of M
-SymEigen<3> eigM(M);
-// print the smallest eigenvalue
-cout << eigM.get_evalues()[0] << endl;
-// print the associated eigenvector
-cout << eigM.get_evectors()[0] << endl;
address@hidden
-
-This decomposition is very similar to the SVD (q.v.), and can be used to solve
-equations using backsub() or get_pinv(), with the same treatment of condition
numbers.
-
-SymEigen<> (= SymEigen<-1>) can be used to create an eigen decomposition whose
size is determined at run-time.
address@hidden gDecomps
-**/
-template <int Size>
-class SymEigen
-{
-public:
- /// Default constructor. Does nothing.
- SymEigen(){}
-
- /// Construct the eigen decomposition of a matrix. This initialises the
class, and
- /// performs the decomposition immediately.
- SymEigen(const Matrix<Size,Size>& M);
-
- /// Perform the eigen decomposition of a matrix.
- void compute(const Matrix<Size,Size>& M);
-
- /// Calculate result of multiplying the (pseudo-)inverse of M by
another matrix.
- /// For a matrix \f$A\f$, this calculates \f$M^{\dagger}A\f$ by back
substitution
- /// (i.e. without explictly calculating the (pseudo-)inverse).
- /// See the SVD detailed description for a description of condition
variables.
- Matrix<Size,RHS> backsub(const Matrix<Size,RHS>& rhs, const double
condition = 1e9);
-
- /// Calculate result of multiplying the (pseudo-)inverse of M by a
vector.
- /// For a vector \f$b\f$, this calculates \f$M^{\dagger}b\f$ by back
substitution
- /// (i.e. without explictly calculating the (pseudo-)inverse).
- /// See the SVD detailed description for a description of condition
variables.
- Vector<Size> backsub(const Vector<Size>& v, const double condition = 1e9);
-
- /// Calculate (pseudo-)inverse of the matrix. This is not usually
needed:
- /// if you need the inverse just to multiply it by a matrix or a
vector, use
- /// one of the backsub() functions, which will be faster.
- /// See the SVD detailed description for a description of the
pseudo-inverse
- /// and condition variables.
- Matrix<Size,Size> get_pinv(const double condition = 1e9);
-
- /// Calculates the reciprocals of the eigenvalues of the matrix.
- /// The vector <code>invdiag</code> lists the eigenvalues in order, from
- /// the largest (i.e. smallest reciprocal) to the smallest.
- /// These are also the diagonal values of the matrix \f$Lambda^{-1}\f$.
- /// Any eigenvalues which are too small are set to zero (see the SVD
- /// detailed description for a description of the and condition
variables).
- void get_inv_diag(Vector<Size>& invdiag, double condition=1e9);
-
- /// Returns the eigenvectors of the matrix.
- /// This returns \f$U^T\f$, so that the rows of the matrix are the
eigenvectors,
- /// which can be extracted using usual Matrix::operator[]() subscript
operator.
- /// They are returned in order of the size of the corresponding
eigenvalue, i.e.
- /// the vector with the largest eigenvalue is first.
- Matrix<Size,Size,RowMajor>& get_evectors() {return my_evectors;}
-
- /// Returns the eigenvectors of the matrix.
- /// This returns \f$U^T\f$, so that the rows of the matrix are the
eigenvectors,
- /// which can be extracted using usual Matrix::operator[]() subscript
operator.
- /// They are returned in order of the size of the corresponding
eigenvalue, i.e.
- /// the vector with the largest eigenvalue is first.
- const Matrix<Size,Size,RowMajor>& get_evectors();
-
- /// Returns the eigenvalues of the matrix.
- /// The eigenvalues are listed in order, from the largest to the
smallest.
- /// These are also the diagonal values of the matrix \f$\Lambda\f$.
- Vector<Size>& get_evalues();
-
- /// Returns the eigenvalues of the matrix.
- /// The eigenvalues are listed in order, from the largest to the
smallest.
- /// These are also the diagonal values of the matrix \f$\Lambda\f$.
- const Vector<Size>& get_evalues() const;
-
-};
-
-}
-
-#endif
Index: doc/se3doc.h
===================================================================
RCS file: doc/se3doc.h
diff -N doc/se3doc.h
--- doc/se3doc.h 9 Jun 2005 09:33:54 -0000 1.2
+++ /dev/null 1 Jan 1970 00:00:00 -0000
@@ -1,140 +0,0 @@
-/*
- Copyright (c) 2005 Paul Smith
-
- Permission is granted to copy, distribute and/or modify this document
under
- the terms of the GNU Free Documentation License, Version 1.2 or any
later
- version published by the Free Software Foundation; with no Invariant
- Sections, no Front-Cover Texts, and no Back-Cover Texts.
-
- You should have received a copy of the GNU Free Documentation License
- License along with this library; if not, write to the Free Software
- Foundation, Inc.
- 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
-
-*/
-// A proxy version of the SE3 class,
-// cleaned up to present a comprehensible
-// version of the SE3 interface
-
-#ifdef DOXYGEN_INCLUDE_ONLY_FOR_DOCS
-
-/// All classes and functions are within this namespace
-namespace TooN
-{
-
-
-/// @class SE3 se3doc.h TooN/SE3.h
-/// Represent a three-dimensional Euclidean transformation (a rotation and a
translation).
-/// This can be represented by a \f$3\times\f$4 matrix operating on a
homogeneous co-ordinate,
-/// so that a vector \f$\underline{x}\f$ is transformed to a new location
\f$\underline{x}'\f$
-/// by
-/// \f[\begin{aligned}\underline{x}' &= E\times\underline{x}\\
\begin{bmatrix}x'\\y'\\z'\end{bmatrix} &= \begin{pmatrix}r_{11} & r_{12} &
r_{13} & t_1\\r_{21} & r_{22} & r_{23} & t_2\\r_{31} & r_{32} & r_{33} &
t_3\end{pmatrix}\begin{bmatrix}x\\y\\z\\1\end{bmatrix}\end{aligned}\f]
-///
-/// This transformation is a member of the Special Euclidean Lie group SE3.
These can be parameterised
-/// six numbers (in the space of the Lie Algebra). In this class, the first
three parameters are a
-/// translation vector while the second three are a rotation vector, whose
direction is the axis of rotation
-/// and length the amount of rotation (in radians), as for SO3
-/// @ingroup gTransforms
-class SE3 {
- friend SE3 operator*(const SO3& lhs, const SE3& rhs);
- friend std::istream& operator>> (std::istream& is, SE3& rhs);
-public:
- /// Default constructor. Initialises the the rotation to zero (the
identity) and the translation to zero
- SE3();
-
- /// Returns the rotation part of the transformation as a SO3
- SO3& get_rotation(){return my_rotation;}
- /// @overload
- const SO3& get_rotation() const {return my_rotation;}
- /// Returns the translation part of the transformation as a Vector
- Vector<3>& get_translation() {return my_translation;}
- /// @overload
- const Vector<3>& get_translation() const {return my_translation;}
-
- /// Exponentiate a Vector in the Lie Algebra to generate a new SE3.
- /// See the Detailed Description for details of this vector.
- /// @param vect The Vector to exponentiate
- static SE3 exp(const Vector<6>& vect);
- /// Take the logarithm of the matrix, generating the corresponding vector in
the Lie Algebra.
- /// See the Detailed Description for details of this vector.
- Vector<6> ln() const;
-
- /// Returns a SE3 representing the inverse transformation.
- /// An SE3 is \f$ \left[R|t \right] \f$ (where \f$R\f$ is a rotation matrix
and
- /// \f$t\f$ the translation), so the inverse is \f$\left[R^T|-R^Tt\right]\f$
- SE3 inverse() const;
-
- /// Right-multiply by another SE3 (concatenate the two transformations)
- /// @param rhs The multipier
- SE3& operator *=(const SE3& rhs);
- /// Right-multiply by another SE3 (concatenate the two transformations)
- /// @param rhs The multipier
- SE3 operator *(const SE3& rhs) const;
-
- /// Returns the i-th generator multiplied by a vector.
- /// The generators of a Lie group are the basis for the space of the Lie
algebra.
- /// For %SE3, the generators are six \f$4\times4\f$ matrices representing
- /// the six possible (linearised) degrees of freedom. These matrices are
usally sparse,
- /// and are usually obtained to immediately multiply them by a vector, so
- /// this function provides a fast way of doing this operation.
- /// @param i The required generator
- /// @param pos The vector to multuiply by the generator
- static Vector<4> generator_field(int i, Vector<4> pos);
-
- /// Transfer a vector in the Lie Algebra from one
- /// co-ordinate frame to another. This is the operation such that for a
matrix
- /// \f$ B \f$,
- /// \f$ e^{\text{Adj}(v)} = Be^{v}B^{-1} \f$
- /// @param v The Vector to transfer
- inline void adjoint(Vector<6>& v)const;
-
- /// Transfer a matrix in the Lie Algebra from one
- /// co-ordinate frame to another. This is the operation such that for a
matrix
- /// \f$ B \f$,
- /// \f$ e^{\text{Adj}(v)} = Be^{v}B^{-1} \f$
- /// @param M The Matrix to transfer
- inline void adjoint(Matrix<6,6>& M)const;
-
- /// Transfer covectors between frames (using the transpose of the inverse of
the adjoint)
- /// so that trinvadjoint(vect1) * adjoint(vect2) = vect1 * vect2
- inline void trinvadjoint(Vector<6>& v)const;
-
- ///@overload
- inline void trinvadjoint(Matrix<6,6>& M)const;
-};
-
-
-/// Left-multiply an SE3 by an SO3
-/// @relates SE3
-SE3 operator*(const SO3& lhs, const SE3& rhs);
-
-/// Write an SE3 to a stream
-/// @relates SE3
-std::ostream& operator <<(std::ostream& os, const SE3& rhs);
-
-/// Reads an SE3 from a stream
-/// @relates SE3
-std::istream& operator>>(std::istream& is, SE3& rhs);
-
-/// Right-multiply by a Vector
-/// @relates SE3
-Vector<4> operator*(const SE3& lhs, const Vector<4>& rhs);
-
-
-/// Left-multiply by a Vector
-/// @relates SE3
-Vector<4> operator*(const Vector<4>& lhs, const SE3& rhs);
-
-/// Right-multiply by a Matrix
-/// @relates SE3
-template <int RHS>
-Matrix<4,RHS> operator*(const SE3& lhs, const Matrix<4,RHS>& rhs);
-
-/// Left-multiply by a Matrix
-/// @relates SE3
-template <int LHS>
-Matrix<LHS,4> operator*(const Matrix<LHS,4>& lhs, const SE3& rhs);
-
-}
-
-#endif
Index: doc/so3doc.h
===================================================================
RCS file: doc/so3doc.h
diff -N doc/so3doc.h
--- doc/so3doc.h 9 Jun 2005 09:33:54 -0000 1.2
+++ /dev/null 1 Jan 1970 00:00:00 -0000
@@ -1,120 +0,0 @@
-/*
- Copyright (c) 2005 Paul Smith
-
- Permission is granted to copy, distribute and/or modify this document
under
- the terms of the GNU Free Documentation License, Version 1.2 or any
later
- version published by the Free Software Foundation; with no Invariant
- Sections, no Front-Cover Texts, and no Back-Cover Texts.
-
- You should have received a copy of the GNU Free Documentation License
- License along with this library; if not, write to the Free Software
- Foundation, Inc.
- 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
-
-*/
-// A proxy version of the SO3 class,
-// cleaned up to present a comprehensible
-// version of the SO3 interface
-
-#ifdef DOXYGEN_INCLUDE_ONLY_FOR_DOCS
-
-/// All classes and functions are within this namespace
-namespace TooN
-{
-
-/// @class SO3 so3doc.h TooN/SO3.h
-/// Class to represent a three-dimensional rotation matrix. Three-dimensional
rotation
-/// matrices are members of the Special Orthogonal Lie group SO3. This group
can be parameterised
-/// three numbers (a vector in the space of the Lie Algebra). In this class,
the three parameters are the
-/// finite rotation vector, i.e. a three-dimensional vector whose direction is
the axis of rotation
-/// and whose length is the angle of rotation in radians. Exponentiating this
vector gives the matrix,
-/// and the logarithm of the matrix gives this vector.
-/// @ingroup gTransforms
-class SO3 {
-public:
- friend inline std::istream& operator>>(std::istream& is, SO3& rhs);
- friend inline std::istream& operator>>(std::istream& is, SE3& rhs);
- /// Default constructor. Initialises the matrix to the identity (no rotation)
- SO3();
-
- /// Assignment operator.
- SO3& operator=(const SO3& rhs);
-
- /// Assigment operator from a general matrix. This also calls coerce()
- /// to make sure that the matrix is a valid rotation matrix.
- SO3& operator=(const Matrix<3>& rhs);
-
- /// Modifies the matrix to make sure it is a valid rotation matrix.
- void coerce();
-
- /// Exponentiate a vector in the Lie algebra to generate a new SO3.
- /// See the Detailed Description for details of this vector.
- inline static SO3 exp(const Vector<3>& vect);
-
- /// Exponentiate a vector in the Lie algebra to generate a new SO3.
- /// See the Detailed Description for details of this vector.
- static SO3 exp(const double* vect);
-
- /// Take the logarithm of the matrix, generating the corresponding vector in
the Lie Algebra.
- /// See the Detailed Description for details of this vector.
- Vector<3> ln() const;
-
- /// Individual member access. Access is row major i.e. <code>[4]</code> will
give the 2,1 element.
- double operator[](int i);
-
- /// Returns the inverse of this matrix (=the transpose, so this is a fast
operation)
- SO3 inverse() const;
-
- /// Right-multiply by another rotation matrix
- SO3& operator *=(const SO3& rhs);
-
- /// Right-multiply by another rotation matrix
- SO3 operator *(const SO3& rhs) const;
-
- /// Returns the SO3 as a Matrix<3>
- const Matrix<3>& get_matrix()const {return my_matrix;}
-
- /// Returns the i-th generator multiplied by a vector.
- /// The generators of a Lie group are the basis for the space of the Lie
algebra.
- /// For %SO3, the generators are three \f$3\times3\f$ matrices representing
- /// the three possible (linearised) rotations. These matrices are usally
sparse,
- /// and are usually obtained to immediately multiply them by a vector, so
- /// this function provides a fast way of doing this operation.
- static Vector<3> generator_field(int i, Vector<3> pos);
-
- /// Transfer a vector in the Lie Algebra from one
- /// co-ordinate frame to another such that for a matrix
- /// \f$ M \f$, the adjoint \f$Adj()\f$ obeys
- /// \f$ e^{\text{Adj}(v)} = Me^{v}M^{-1} \f$
- Vector<3> adjoint(Vector<3> v) const ;
-
- private:
- Matrix<3> my_matrix;
-};
-
-/// Write an SO3 to a stream
-/// @relates SO3
-inline std::ostream& operator<< (std::ostream& os, const SO3& rhs);
-
-/// Read from SO3 to a stream
-/// @relates SO3
-inline std::istream& operator>>(std::istream& is, SO3& rhs);
-
-
-/// Right-multiply by a Vector
-/// @relates SO3
-Vector<3> operator*(const SO3& lhs, const Vector<3>& rhs);
-
-/// Left-multiply by a Vector
-/// @relates SO3
-Vector<3> operator*(const Vector<3>& lhs, const SO3& rhs);
-
-/// Multiply two SO3 matrices
-/// @relates SO3
-template <int LHS>
-Matrix<LHS,3> operator*(Matrix<LHS,3>& lhs, const SO3& rhs);
-
-
-}
-
-#endif
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