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/*
//
// Copyright 1997-2009 Torsten Rohlfing
//
// Copyright 2004-2013 SRI International
//
// This file is part of the Computational Morphometry Toolkit.
//
// http://www.nitrc.org/projects/cmtk/
//
// The Computational Morphometry Toolkit is free software: you can
// redistribute it and/or modify it under the terms of the GNU General Public
// License as published by the Free Software Foundation, either version 3 of
// the License, or (at your option) any later version.
//
// The Computational Morphometry Toolkit is distributed in the hope that it
// will be useful, but WITHOUT ANY WARRANTY; without even the implied
// warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License along
// with the Computational Morphometry Toolkit. If not, see
// <http://www.gnu.org/licenses/>.
//
// $Revision: 5436 $
//
// $LastChangedDate: 2018-12-10 19:01:20 -0800 (Mon, 10 Dec 2018) $
//
// $LastChangedBy: torstenrohlfing $
//
*/
#include <Base/cmtkMathUtil.h>
#include <Base/cmtkMatrix.h>
#include <System/cmtkConsole.h>
#include "Numerics/sevd.h"
#include "Numerics/spddet.h"
#include "Numerics/svd.h"
#include <math.h>
#include <algorithm>
#include <vector>
namespace
cmtk
{
void
MathUtil::SVD( Matrix2D<double>& U, std::vector<double>& W, Matrix2D<double>& V )
{
const size_t m = U.NumberOfRows();
const size_t n = U.NumberOfColumns();
W.resize( n );
V.Resize( n, n );
ap::real_2d_array apA;
apA.setbounds(0, m-1, 0, n-1);
for (size_t j = 0; j < n; j++)
for (size_t i = 0; i < m; i++)
apA(i,j) = U[i][j];
ap::real_1d_array w;
ap::real_2d_array u;
ap::real_2d_array vt;
rmatrixsvd( apA, m, n,
true /* U needed */,
true /* V needed */,
2 /*max-level memory usage */,
w, u, vt);
/* Put u in U */
for (size_t j = 0; j < n; j++)
for (size_t i = 0; i < m; i++)
U[i][j] = u(i,j);
/* Put w in W */
for (size_t i = 0; i < n; i++)
W[i] = w(i);
/* Un-transpose vt and put it in V */
for (size_t j = 0; j < n; j++)
for (size_t i = 0; i < n; i++)
V[i][j] = vt(j,i);
}
/** TODO: move this someplace more logical than the linear-algebra module
*/
void
MathUtil::SVDLinearRegression( const Matrix2D<double>& U, const std::vector<double>& W, const Matrix2D<double>& V, const std::vector<double>& b, std::vector<double>& lm_params )
{
const size_t m = U.NumberOfRows();
const size_t n = U.NumberOfColumns();
lm_params.resize( n );
// From alglib linear regression:
// Take the inverses of the singular values, setting the inverse
// to 0 if the sv is close to 0 (tolerance controlled by epstol)
double epstol = 1000;
ap::real_1d_array svi;
svi.setbounds( 0, n-1 );
for( size_t i = 0; i < n; i++ )
if( W[i] > epstol*ap::machineepsilon * W[0] )
svi(i) = 1 / W[i];
else
svi(i) = 0;
// Calculate linear model parameters following Heath, Ch. 3.6
// (Scientific Computing: An Introductory Survey, 2nd Ed., 2002)
for ( size_t i = 0; i < n; i++ )
lm_params[i] = 0.0;
for ( size_t i = 0; i < n; i++ )
{
double ut_times_b = 0.0;
for ( size_t j = 0; j < m; j++ )
ut_times_b += U[j][i] * b[j];
ut_times_b *= svi(i);
for ( size_t j = 0; j < n; j++ )
lm_params[j] += ut_times_b * V[j][i];
}
}
/////////////////////////////////////////////////////////////////////
// HELPERS
/////////////////////////////////////////////////////////////////////
template<class T>
T
MathUtil::CholeskyDeterminant
(const Matrix2D<T>& matrix, int n)
{
ap::real_2d_array apMatrix;
apMatrix.setbounds(0, n-1, 0, n-1);
for (int j = 0; j < n; j++)
for (int i = 0; i < n; i++)
apMatrix(i,j) = (double)(1.0 * matrix[i][j]);
spdmatrixcholesky( apMatrix, n, false );
T determinant = (T) spdmatrixcholeskydet( apMatrix, n );
return determinant;
}
template double MathUtil::CholeskyDeterminant<double>(const Matrix2D<double>& matrix, int n);
template float MathUtil::CholeskyDeterminant<float>(const Matrix2D<float>& matrix, int n);
} // namespace cmtk
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