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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2006-2007 Benoit Jacob <jacob@math.jussieu.fr>
//
// Eigen 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 2 or (at your option) any later version.
//
// Eigen 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 Eigen; if not, write to the Free Software Foundation, Inc., 51
// Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
//
// As a special exception, if other files instantiate templates or use macros
// or inline functions from this file, or you compile this file and link it
// with other works to produce a work based on this file, this file does not
// by itself cause the resulting work to be covered by the GNU General Public
// License. This exception does not invalidate any other reasons why a work
// based on this file might be covered by the GNU General Public License.
#include "main.h"
#include "../src/regression.h"
template< typename T,
int Size,
typename VectorType,
typename BigVecType >
void makeNoisyCohyperplanarPoints( int numPoints,
VectorType * points,
BigVecType * coeffs,
T noiseAmplitude )
{
int i, j;
// pick a random hyperplane, store the coefficients of its equation
coeffs->resize( Size + 1 );
for( j = 0; j < Size + 1; j++ )
{
(*coeffs)(j) = static_cast<T>(0);
while( std::abs( (*coeffs)(j) ) < 0.5 ) pickRandom((*coeffs)(j));
}
// now pick numPoints random points on this hyperplane
for( i = 0; i < numPoints; i++ )
{
VectorType cur_point(Size);
do
{
// make cur_point a random vector
for( j = 0; j < Size; j++ )
pickRandom( cur_point(j) );
cur_point.normalize();
// project cur_point onto the hyperplane
T x = static_cast<T>(0);
for( j = 0; j < Size; j++ )
x -= (*coeffs)(j) * cur_point(j);
cur_point *= (*coeffs)(Size) / x;
} while( std::abs(cur_point.norm()) < 0.5
|| std::abs(cur_point.norm()) > 2.0 );
points[i] = cur_point;
}
// add some noise to these points
for( i = 0; i < numPoints; i++ )
{
for( j = 0; j < Size; j++ )
{
T someNoise;
pickRandom( someNoise );
points[i](j) += someNoise * noiseAmplitude;
}
}
}
template< typename T,
typename VectorType,
typename BigVecType,
typename MatrixType >
void helper_checkComputeFittingHyperplane( int numPoints,
const VectorType * points,
const BigVecType * coeffs,
T allowedError )
{
int size = points[0].size();
BigVecType result( size + 1 );
computeFittingHyperplane_internal< T, VectorType,
BigVecType, MatrixType >
( numPoints, points, & result );
result /= result( size );
result *= (*coeffs)( size );
T error = (result - *coeffs).norm() / coeffs->norm();
QVERIFY( std::abs(error) < std::abs(allowedError) );
}
void MainTest::checkRegression()
{
for( int repeat = 0; repeat < REPEAT; repeat++ )
{
Vector2f points2f [1000];
Vector3f coeffs3f;
makeNoisyCohyperplanarPoints< float, 2, Vector2f, Vector3f >
( 1000, points2f, &coeffs3f, 0.01 );
helper_checkComputeFittingHyperplane
< float, Vector2f, Vector3f, Matrix2f >
( 10, points2f, &coeffs3f, 0.05 );
helper_checkComputeFittingHyperplane
< float, Vector2f, Vector3f, Matrix2f >
( 100, points2f, &coeffs3f, 0.01 );
helper_checkComputeFittingHyperplane
< float, Vector2f, Vector3f, Matrix2f >
( 1000, points2f, &coeffs3f, 0.002 );
Vector4d points4d [1000];
Vector<double, 5> coeffs5d;
makeNoisyCohyperplanarPoints< double, 4, Vector4d, Vector<double,5> >
( 1000, points4d, &coeffs5d, 0.01 );
helper_checkComputeFittingHyperplane
< double, Vector4d, Vector<double, 5>, Matrix4d >
( 10, points4d, &coeffs5d, 0.05 );
helper_checkComputeFittingHyperplane
< double, Vector4d, Vector<double, 5>, Matrix4d >
( 100, points4d, &coeffs5d, 0.01 );
helper_checkComputeFittingHyperplane
< double, Vector4d, Vector<double, 5>, Matrix4d >
( 1000, points4d, &coeffs5d, 0.002 );
VectorXcd points8cd [1000];
VectorXcd coeffs9cd;
makeNoisyCohyperplanarPoints< complex<double>, 8, VectorXcd, VectorXcd >
( 1000, points8cd, &coeffs9cd, 0.01 );
helper_checkComputeFittingHyperplane
< complex<double>, VectorXcd, VectorXcd, MatrixXcd >
( 10, points8cd, &coeffs9cd, 0.35 );
helper_checkComputeFittingHyperplane
< complex<double>, VectorXcd, VectorXcd, MatrixXcd >
( 100, points8cd, &coeffs9cd, 0.025 );
helper_checkComputeFittingHyperplane
< complex<double>, VectorXcd, VectorXcd, MatrixXcd >
( 1000, points8cd, &coeffs9cd, 0.006 );
VectorXd points20d [1000];
VectorXd coeffs21d;
makeNoisyCohyperplanarPoints< double, 20, VectorXd, VectorXd >
( 1000, points20d, &coeffs21d, 0.01 );
helper_checkComputeFittingHyperplane
< double, VectorXd, VectorXd, MatrixXd >
( 100, points20d, &coeffs21d, 0.1 );
helper_checkComputeFittingHyperplane
< double, VectorXd, VectorXd, MatrixXd >
( 1000, points20d, &coeffs21d, 0.015 );
}
}
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