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/*
* Matrix, MatrixView, ConstMatrixView classes wrap the gsl matrix routines;
* "views" mimic the semantic of C++ references: any operation performed
* on a "view" is actually performed on the "viewed object"
*
* Authors:
* Marco Cecchetti <mrcekets at gmail.com>
*
* Copyright 2008 authors
*
* This library is free software; you can redistribute it and/or
* modify it either under the terms of the GNU Lesser General Public
* License version 2.1 as published by the Free Software Foundation
* (the "LGPL") or, at your option, under the terms of the Mozilla
* Public License Version 1.1 (the "MPL"). If you do not alter this
* notice, a recipient may use your version of this file under either
* the MPL or the LGPL.
*
* You should have received a copy of the LGPL along with this library
* in the file COPYING-LGPL-2.1; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
* You should have received a copy of the MPL along with this library
* in the file COPYING-MPL-1.1
*
* The contents of this file are subject to the Mozilla Public License
* Version 1.1 (the "License"); you may not use this file except in
* compliance with the License. You may obtain a copy of the License at
* http://www.mozilla.org/MPL/
*
* This software is distributed on an "AS IS" basis, WITHOUT WARRANTY
* OF ANY KIND, either express or implied. See the LGPL or the MPL for
* the specific language governing rights and limitations.
*/
#include <2geom/numeric/matrix.h>
#include <2geom/numeric/vector.h>
namespace Geom { namespace NL {
Vector operator*( detail::BaseMatrixImpl const& A,
detail::BaseVectorImpl const& v )
{
assert(A.columns() == v.size());
Vector result(A.rows(), 0.0);
for (size_t i = 0; i < A.rows(); ++i)
for (size_t j = 0; j < A.columns(); ++j)
result[i] += A(i,j) * v[j];
return result;
}
Matrix operator*( detail::BaseMatrixImpl const& A,
detail::BaseMatrixImpl const& B )
{
assert(A.columns() == B.rows());
Matrix C(A.rows(), B.columns(), 0.0);
for (size_t i = 0; i < C.rows(); ++i)
for (size_t j = 0; j < C.columns(); ++j)
for (size_t k = 0; k < A.columns(); ++k)
C(i,j) += A(i,k) * B(k, j);
return C;
}
Matrix pseudo_inverse(detail::BaseMatrixImpl const& A)
{
Matrix U(A);
Matrix V(A.columns(), A.columns());
Vector s(A.columns());
gsl_vector* work = gsl_vector_alloc(A.columns());
gsl_linalg_SV_decomp( U.get_gsl_matrix(),
V.get_gsl_matrix(),
s.get_gsl_vector(),
work );
Matrix P(A.columns(), A.rows(), 0.0);
int sz = s.size();
while ( sz-- > 0 && s[sz] == 0 ) {}
++sz;
if (sz == 0) return P;
VectorView sv(s, sz);
for (size_t i = 0; i < sv.size(); ++i)
{
VectorView v = V.column_view(i);
v.scale(1/sv[i]);
for (size_t h = 0; h < P.rows(); ++h)
for (size_t k = 0; k < P.columns(); ++k)
P(h,k) += V(h,i) * U(k,i);
}
return P;
}
double trace (detail::BaseMatrixImpl const& A)
{
if (A.rows() != A.columns())
{
THROW_RANGEERROR ("NL::Matrix: computing trace: "
"rows() != columns()");
}
double t = 0;
for (size_t i = 0; i < A.rows(); ++i)
{
t += A(i,i);
}
return t;
}
double det (detail::BaseMatrixImpl const& A)
{
if (A.rows() != A.columns())
{
THROW_RANGEERROR ("NL::Matrix: computing determinant: "
"rows() != columns()");
}
Matrix LU(A);
int s;
gsl_permutation * p = gsl_permutation_alloc(LU.rows());
gsl_linalg_LU_decomp (LU.get_gsl_matrix(), p, &s);
double t = 1;
for (size_t i = 0; i < LU.rows(); ++i)
{
t *= LU(i,i);
}
gsl_permutation_free(p);
return t;
}
} } // end namespaces
/*
Local Variables:
mode:c++
c-file-style:"stroustrup"
c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
indent-tabs-mode:nil
fill-column:99
End:
*/
// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :
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