PCA_unittest.cc

/*
 * This software is distributed under BSD 3-clause license (see LICENSE file).
 *
 * Authors: Parijat Mazumdar, Heiko Strathmann
 */

#include <gtest/gtest.h>
#include <shogun/mathematics/Math.h>
#include <shogun/features/DenseFeatures.h>
#include <shogun/lib/SGMatrix.h>
#include <shogun/lib/SGVector.h>
#include <shogun/mathematics/linalg/LinalgNamespace.h>

#include <shogun/preprocessor/PCA.h>

using namespace shogun;

/** Check eigenvector equality
 * This expects that the input vectors are normalised
 *
 * @param a first vector
 * @param b second vector
 * @return 1.0 if the eigen vectors are pointing to the same director, -1.0
 * if pointing to the opposite direction.
 */
template <class T>
inline T check_eigenvector_eq(
    const SGVector<T>& a, const SGVector<T>& b, float64_t epsilon = 10E-8)
{
	T sign = linalg::dot(a, b);
	EXPECT_NEAR(1.0, CMath::abs(sign), epsilon);
	return (sign < 0.0) ? -1.0 : 1.0;
}

TEST(PCA, PCA_N_greater_D_EVD)
{
	SGMatrix<float64_t> data(3,5);
	data(0,0)=2.908008030729362;
	data(0,1)=-1.058180257987362;
	data(0,2)=1.098424617888623;
	data(0,3)=-2.051816299911149;
	data(0,4)=-1.577057022799202;
	data(1,0)=0.825218894228491;
	data(1,1)=-0.468615581100624;
	data(1,2)=-0.277871932787639;
	data(1,3)=-0.353849997774433;
	data(1,4)=0.507974650905946;
	data(2,0)=1.378971977916614;
	data(2,1)=-0.272469409250187;
	data(2,2)=0.701541458163284;
	data(2,3)=-0.823586525156853;
	data(2,4)=0.281984063670556;

	CDenseFeatures<float64_t>* features=new CDenseFeatures<float64_t>(data);
	CPCA* pca=new CPCA(EVD);
	pca->set_target_dim(3);
	pca->fit(features);

	SGMatrix<float64_t> transmat=pca->get_transformation_matrix();
	SGMatrix<float64_t> finalmat=pca->apply_to_feature_matrix(features);
	SGVector<float64_t> eigvec=pca->get_eigenvalues();

	float64_t epsilon = 0.00000000000001;

	// comparing outputs against MATLAB 'princomp' implementation
	EXPECT_NEAR(0.041855883987175,eigvec[0],epsilon);
	EXPECT_NEAR(0.291219269837891,eigvec[1],epsilon);
	EXPECT_NEAR(5.077526030285309,eigvec[2],epsilon);

	SGMatrix<float64_t> evs(3,3);
	evs(0,0)=0.238820512479407;
	evs(0,1)=-0.304406370622002;
	evs(0,2)=0.922117955764778;
	evs(1,0)=0.502124514814308;
	evs(1,1)=0.851501730295596;
	evs(1,2)=0.151048915673366;
	evs(2,0)=-0.831165287076865;
	evs(2,1)=0.426944451689378;
	evs(2,2)=0.356205980761254;

	auto s0 = check_eigenvector_eq(evs.get_column(0), transmat.get_column(0), epsilon);
	auto s1 = check_eigenvector_eq(evs.get_column(1), transmat.get_column(1), epsilon);
	auto s2 = check_eigenvector_eq(evs.get_column(2), transmat.get_column(2), epsilon);

	EXPECT_NEAR(0.182350122017013, s0*finalmat(0,0),epsilon);
	EXPECT_NEAR(-0.041902251203685, s0*finalmat(0,1),epsilon);
	EXPECT_NEAR(-0.240647729898028, s0*finalmat(0,2),epsilon);
	EXPECT_NEAR(0.236493108746648, s0*finalmat(0,3),epsilon);
	EXPECT_NEAR(-0.136293249661948, s0*finalmat(0,4),epsilon);
	EXPECT_NEAR(0.216971008375464, s1*finalmat(1,0),epsilon);
	EXPECT_NEAR(-0.382472041452699, s1*finalmat(1,1),epsilon);
	EXPECT_NEAR(-0.460689222275080, s1*finalmat(1,2),epsilon);
	EXPECT_NEAR(-0.217576202298234, s1*finalmat(1,3),epsilon);
	EXPECT_NEAR(0.843766457650550, s1*finalmat(1,4),epsilon);
	EXPECT_NEAR(3.325638119909419, s2*finalmat(2,0),epsilon);
	EXPECT_NEAR(-1.115340910605008, s2*finalmat(2,1),epsilon);
	EXPECT_NEAR(1.249063286478502, s2*finalmat(2,2),epsilon);
	EXPECT_NEAR(-2.210566542225781, s2*finalmat(2,3),epsilon);
	EXPECT_NEAR(-1.248793953557132, s2*finalmat(2,4),epsilon);

	SG_UNREF(pca);
	SG_UNREF(features);
}

TEST(PCA, PCA_N_equals_D_EVD)
{
	SGMatrix<float64_t> data(3,3);
	data(0,0)=2.908008030729362;
	data(0,1)=-1.058180257987362;
	data(0,2)=1.098424617888623;
	data(1,0)=0.825218894228491;
	data(1,1)=-0.468615581100624;
	data(1,2)=-0.277871932787639;
	data(2,0)=1.378971977916614;
	data(2,1)=-0.272469409250187;
	data(2,2)=0.701541458163284;

	CDenseFeatures<float64_t>* features=new CDenseFeatures<float64_t>(data);
	CPCA* pca=new CPCA(EVD);
	pca->set_target_dim(3);
	pca->fit(features);

	SGMatrix<float64_t> transmat=pca->get_transformation_matrix();
	SGMatrix<float64_t> finalmat=pca->apply_to_feature_matrix(features);
	SGVector<float64_t> eigvec=pca->get_eigenvalues();

	float64_t epsilon = 0.00000001;

	// comparing outputs against MATLAB 'princomp' implementation
	EXPECT_NEAR(0.0,eigvec[0],epsilon);
	EXPECT_NEAR(0.084750433,eigvec[1],epsilon);
	EXPECT_NEAR(5.03495863,eigvec[2],epsilon);

	SGMatrix<float64_t> evs(3,3);
	evs(0,0)=0.41770275;
	evs(0,1)=0.20781429;
	evs(0,2)=0.88449852;
	evs(1,0)=-0.13328384;
	evs(1,1)=-0.94894524;
	evs(1,2)=0.28589918;
	evs(2,0)=-0.8987546;
	evs(2,1)=0.23731023;
	evs(2,2)=0.36867875;

	auto s0 = check_eigenvector_eq(evs.get_column(0), transmat.get_column(0));
	auto s1 = check_eigenvector_eq(evs.get_column(1), transmat.get_column(1));
	auto s2 = check_eigenvector_eq(evs.get_column(2), transmat.get_column(2));

	EXPECT_NEAR(0.0, s0*finalmat(0,0),epsilon);
	EXPECT_NEAR(0.0, s0*finalmat(0,1),epsilon);
	EXPECT_NEAR(0.0, s0*finalmat(0,2),epsilon);
	EXPECT_NEAR(-0.173865951, s1*finalmat(1,0),epsilon);
	EXPECT_NEAR(-0.162222411, s1*finalmat(1,1),epsilon);
	EXPECT_NEAR(0.336088362, s1*finalmat(1,2),epsilon);
	EXPECT_NEAR(2.21751537, s2*finalmat(2,0),epsilon);
	EXPECT_NEAR(-2.26932988, s2*finalmat(2,1),epsilon);
	EXPECT_NEAR(0.0518145101, s2*finalmat(2,2),epsilon);

	SG_UNREF(pca);
	SG_UNREF(features);
}

TEST(PCA, PCA_N_less_D_EVD)
{
	SGMatrix<float64_t> data(5,3);
	data(0,0)=0.033479882244451;
	data(0,1)=0.022889792751630;
	data(0,2)=-0.979206305167302;
	data(1,0)=-1.333677943428106;
	data(1,1)=-0.261995434966092;
	data(1,2)=-1.156401655664002;
	data(2,0)=1.127492278341590;
	data(2,1)=-1.750212368446790;
	data(2,2)=-0.533557109315987;
	data(3,0)=0.350179410603312;
	data(3,1)=-0.285650971595330;
	data(3,2)=-2.002635735883060;
	data(4,0)=-0.299066030332982;
	data(4,1)=-0.831366511567624;
	data(4,2)=0.964229422631627;

	CDenseFeatures<float64_t>* features=new CDenseFeatures<float64_t>(data);
	CPCA* pca=new CPCA(EVD);
	pca->set_target_dim(2);
	pca->fit(features);

	SGMatrix<float64_t> transmat=pca->get_transformation_matrix();
	SGMatrix<float64_t> finalmat=pca->apply_to_feature_matrix(features);
	SGVector<float64_t> eigvec=pca->get_eigenvalues();

	float64_t epsilon = 1E-13;

	// comparing outputs against MATLAB 'princomp' implementation
	EXPECT_NEAR(0,eigvec[0],epsilon);
	EXPECT_NEAR(2.327794822241147,std::abs(eigvec[1]),epsilon);
	EXPECT_NEAR(2.759160840481412,std::abs(eigvec[2]),epsilon);

	SGMatrix<float64_t> evs(5,2);
	evs(0,0) = 0.258049566055304;
	evs(0,1) = 0.257746561935451;
	evs(1,0) = 0.349092719192590;
	evs(1,1) = -0.129544636386834;
	evs(2,0) = -0.630860251575450;
	evs(2,1) = 0.648487498866225;
	evs(3,0) = 0.374280965623520;
	evs(3,1) = 0.647067522254220;
	evs(4,0) = -0.522947221638548;
	evs(4,1) = -0.278482463454826;

	auto s0 = check_eigenvector_eq(evs.get_column(0), transmat.get_column(0), epsilon);
	auto s1 = check_eigenvector_eq(evs.get_column(1), transmat.get_column(1), epsilon);

	EXPECT_NEAR(-0.511467003751085, s0*finalmat(0,0),epsilon);
	EXPECT_NEAR(1.715732114990145, s0*finalmat(0,1),epsilon);
	EXPECT_NEAR(-1.204265111239059, s0*finalmat(0,2),epsilon);
	EXPECT_NEAR(1.835430614937060, s1*finalmat(1,0),epsilon);
	EXPECT_NEAR(-0.435473994643473, s1*finalmat(1,1),epsilon);
	EXPECT_NEAR(-1.39995662029358, s1*finalmat(1,2),epsilon);

	SG_UNREF(pca);
	SG_UNREF(features);
}

TEST(PCA, PCA_N_greater_D_SVD)
{
	SGMatrix<float64_t> data(3,5);
	data(0,0)=2.908008030729362;
	data(0,1)=-1.058180257987362;
	data(0,2)=1.098424617888623;
	data(0,3)=-2.051816299911149;
	data(0,4)=-1.577057022799202;
	data(1,0)=0.825218894228491;
	data(1,1)=-0.468615581100624;
	data(1,2)=-0.277871932787639;
	data(1,3)=-0.353849997774433;
	data(1,4)=0.507974650905946;
	data(2,0)=1.378971977916614;
	data(2,1)=-0.272469409250187;
	data(2,2)=0.701541458163284;
	data(2,3)=-0.823586525156853;
	data(2,4)=0.281984063670556;

	CDenseFeatures<float64_t>* features=new CDenseFeatures<float64_t>(data);
	CPCA* pca=new CPCA(SVD);
	pca->set_target_dim(3);
	pca->fit(features);

	SGMatrix<float64_t> transmat=pca->get_transformation_matrix();
	SGMatrix<float64_t> finalmat=pca->apply_to_feature_matrix(features);
	SGVector<float64_t> eigvec=pca->get_eigenvalues();

	float64_t epsilon = 0.0000000000001;

	// comparing outputs against BRMLtoolbox MATLAB
	// http://web4.cs.ucl.ac.uk/staff/D.Barber/pmwiki/pmwiki.php?n=Brml.Software
	EXPECT_NEAR(0.041855883987175,eigvec[2],epsilon);
	EXPECT_NEAR(0.291219269837891,eigvec[1],epsilon);
	EXPECT_NEAR(5.077526030285309,eigvec[0],epsilon);

	EXPECT_NEAR(-0.238820512479407,transmat(0,2),epsilon);
	EXPECT_NEAR(-0.304406370622002,transmat(0,1),epsilon);
	EXPECT_NEAR(0.922117955764778,transmat(0,0),epsilon);
	EXPECT_NEAR(-0.502124514814308,transmat(1,2),epsilon);
	EXPECT_NEAR(0.851501730295596,transmat(1,1),epsilon);
	EXPECT_NEAR(0.151048915673366,transmat(1,0),epsilon);
	EXPECT_NEAR(0.831165287076865,transmat(2,2),epsilon);
	EXPECT_NEAR(0.426944451689378,transmat(2,1),epsilon);
	EXPECT_NEAR(0.356205980761254,transmat(2,0),epsilon);

	EXPECT_NEAR(-0.182350122017013,finalmat(2,0),epsilon);
	EXPECT_NEAR(0.041902251203685,finalmat(2,1),epsilon);
	EXPECT_NEAR(0.240647729898028,finalmat(2,2),epsilon);
	EXPECT_NEAR(-0.236493108746648,finalmat(2,3),epsilon);
	EXPECT_NEAR(0.136293249661948,finalmat(2,4),epsilon);
	EXPECT_NEAR(0.216971008375464,finalmat(1,0),epsilon);
	EXPECT_NEAR(-0.382472041452699,finalmat(1,1),epsilon);
	EXPECT_NEAR(-0.460689222275080,finalmat(1,2),epsilon);
	EXPECT_NEAR(-0.217576202298234,finalmat(1,3),epsilon);
	EXPECT_NEAR(0.843766457650550,finalmat(1,4),epsilon);
	EXPECT_NEAR(3.325638119909419,finalmat(0,0),epsilon);
	EXPECT_NEAR(-1.115340910605008,finalmat(0,1),epsilon);
	EXPECT_NEAR(1.249063286478502,finalmat(0,2),epsilon);
	EXPECT_NEAR(-2.210566542225781,finalmat(0,3),epsilon);
	EXPECT_NEAR(-1.248793953557132,finalmat(0,4),epsilon);

	SG_UNREF(pca);
	SG_UNREF(features);
}

TEST(PCA, PCA_N_equals_D_SVD)
{
	SGMatrix<float64_t> data(3,3);
	data(0,0)=2.908008030729362;
	data(0,1)=-1.058180257987362;
	data(0,2)=1.098424617888623;
	data(1,0)=0.825218894228491;
	data(1,1)=-0.468615581100624;
	data(1,2)=-0.277871932787639;
	data(2,0)=1.378971977916614;
	data(2,1)=-0.272469409250187;
	data(2,2)=0.701541458163284;

	CDenseFeatures<float64_t>* features=new CDenseFeatures<float64_t>(data);
	CPCA* pca=new CPCA(SVD);
	pca->set_target_dim(3);
	pca->fit(features);

	SGMatrix<float64_t> transmat=pca->get_transformation_matrix();
	SGMatrix<float64_t> finalmat=pca->apply_to_feature_matrix(features);
	SGVector<float64_t> eigvec=pca->get_eigenvalues();

	float64_t epsilon = 0.00000001;

	// comparing outputs against MATLAB 'princomp' implementation
	EXPECT_NEAR(5.03495863,eigvec[0],epsilon);
	EXPECT_NEAR(0.084750433,eigvec[1],epsilon);
	EXPECT_NEAR(0.0,eigvec[2],epsilon);

	EXPECT_NEAR(-0.41770275,transmat(0,2),epsilon);
	EXPECT_NEAR(-0.20781429,transmat(0,1),epsilon);
	EXPECT_NEAR(0.88449852,transmat(0,0),epsilon);
	EXPECT_NEAR(0.13328384,transmat(1,2),epsilon);
	EXPECT_NEAR(0.94894524,transmat(1,1),epsilon);
	EXPECT_NEAR(0.28589918,transmat(1,0),epsilon);
	EXPECT_NEAR(0.8987546,transmat(2,2),epsilon);
	EXPECT_NEAR(-0.23731023,transmat(2,1),epsilon);
	EXPECT_NEAR(0.36867875,transmat(2,0),epsilon);

	EXPECT_NEAR(0.0,finalmat(2,0),epsilon);
	EXPECT_NEAR(0.0,finalmat(2,1),epsilon);
	EXPECT_NEAR(0.0,finalmat(2,2),epsilon);
	EXPECT_NEAR(0.173865951,finalmat(1,0),epsilon);
	EXPECT_NEAR(0.162222411,finalmat(1,1),epsilon);
	EXPECT_NEAR(-0.336088362,finalmat(1,2),epsilon);
	EXPECT_NEAR(2.21751537,finalmat(0,0),epsilon);
	EXPECT_NEAR(-2.26932988,finalmat(0,1),epsilon);
	EXPECT_NEAR(0.0518145101,finalmat(0,2),epsilon);

	SG_UNREF(pca);
	SG_UNREF(features);
}

TEST(PCA, PCA_N_less_D_SVD)
{
	SGMatrix<float64_t> data(5,3);
	data(0,0)=0.033479882244451;
	data(0,1)=0.022889792751630;
	data(0,2)=-0.979206305167302;
	data(1,0)=-1.333677943428106;
	data(1,1)=-0.261995434966092;
	data(1,2)=-1.156401655664002;
	data(2,0)=1.127492278341590;
	data(2,1)=-1.750212368446790;
	data(2,2)=-0.533557109315987;
	data(3,0)=0.350179410603312;
	data(3,1)=-0.285650971595330;
	data(3,2)=-2.002635735883060;
	data(4,0)=-0.299066030332982;
	data(4,1)=-0.831366511567624;
	data(4,2)=0.964229422631627;

	CDenseFeatures<float64_t>* features=new CDenseFeatures<float64_t>(data);
	CPCA* pca=new CPCA(SVD);
	pca->set_target_dim(2);
	pca->fit(features);

	SGMatrix<float64_t> transmat=pca->get_transformation_matrix();
	SGMatrix<float64_t> finalmat=pca->apply_to_feature_matrix(features);
	SGVector<float64_t> eigvec=pca->get_eigenvalues();

	float64_t epsilon = 0.0000000000001;

	// comparing outputs against BRMLtoolbox MATLAB
	// http://web4.cs.ucl.ac.uk/staff/D.Barber/pmwiki/pmwiki.php?n=Brml.Software
	EXPECT_NEAR(0,eigvec[2],epsilon);
	EXPECT_NEAR(2.327794822241147,eigvec[1],epsilon);
	EXPECT_NEAR(2.759160840481412,eigvec[0],epsilon);

	EXPECT_NEAR(-0.258049566055304,transmat(0,1),epsilon);
	EXPECT_NEAR(-0.257746561935451,transmat(0,0),epsilon);
	EXPECT_NEAR(-0.349092719192590,transmat(1,1),epsilon);
	EXPECT_NEAR(0.129544636386834,transmat(1,0),epsilon);
	EXPECT_NEAR(0.630860251575450,transmat(2,1),epsilon);
	EXPECT_NEAR(-0.648487498866225,transmat(2,0),epsilon);
	EXPECT_NEAR(-0.374280965623520,transmat(3,1),epsilon);
	EXPECT_NEAR(-0.647067522254220,transmat(3,0),epsilon);
	EXPECT_NEAR(0.522947221638548,transmat(4,1),epsilon);
	EXPECT_NEAR(0.278482463454826,transmat(4,0),epsilon);

	EXPECT_NEAR(0.511467003751085,finalmat(1,0),epsilon);
	EXPECT_NEAR(-1.715732114990145,finalmat(1,1),epsilon);
	EXPECT_NEAR(1.204265111239059,finalmat(1,2),epsilon);
	EXPECT_NEAR(-1.835430614937060,finalmat(0,0),epsilon);
	EXPECT_NEAR(0.435473994643473,finalmat(0,1),epsilon);
	EXPECT_NEAR(1.39995662029358,finalmat(0,2),epsilon);

	SG_UNREF(pca);
	SG_UNREF(features);
}

TEST(PCA, PCA_MEM_IN_PLACE)
{
	SGMatrix<float64_t> data(3,3);
	data(0,0)=2.908008030729362;
	data(0,1)=-1.058180257987362;
	data(0,2)=1.098424617888623;
	data(1,0)=0.825218894228491;
	data(1,1)=-0.468615581100624;
	data(1,2)=-0.277871932787639;
	data(2,0)=1.378971977916614;
	data(2,1)=-0.272469409250187;
	data(2,2)=0.701541458163284;

	CDenseFeatures<float64_t>* features=new CDenseFeatures<float64_t>(data);
	CPCA* pca=new CPCA(AUTO,false,MEM_IN_PLACE);
	pca->set_target_dim(3);
	pca->fit(features);

	SGMatrix<float64_t> transmat=pca->get_transformation_matrix();
	SGMatrix<float64_t> finalmat=pca->apply_to_feature_matrix(features);
	SGVector<float64_t> eigvec=pca->get_eigenvalues();

	float64_t epsilon = 0.00000001;

	// comparing outputs against MATLAB 'princomp' implementation
	EXPECT_NEAR(5.03495863,eigvec[0],epsilon);
	EXPECT_NEAR(0.084750433,eigvec[1],epsilon);
	EXPECT_NEAR(0.0,eigvec[2],epsilon);

	EXPECT_NEAR(-0.41770275,transmat(0,2),epsilon);
	EXPECT_NEAR(-0.20781429,transmat(0,1),epsilon);
	EXPECT_NEAR(0.88449852,transmat(0,0),epsilon);
	EXPECT_NEAR(0.13328384,transmat(1,2),epsilon);
	EXPECT_NEAR(0.94894524,transmat(1,1),epsilon);
	EXPECT_NEAR(0.28589918,transmat(1,0),epsilon);
	EXPECT_NEAR(0.8987546,transmat(2,2),epsilon);
	EXPECT_NEAR(-0.23731023,transmat(2,1),epsilon);
	EXPECT_NEAR(0.36867875,transmat(2,0),epsilon);

	EXPECT_NEAR(0.0,finalmat(2,0),epsilon);
	EXPECT_NEAR(0.0,finalmat(2,1),epsilon);
	EXPECT_NEAR(0.0,finalmat(2,2),epsilon);
	EXPECT_NEAR(0.173865951,finalmat(1,0),epsilon);
	EXPECT_NEAR(0.162222411,finalmat(1,1),epsilon);
	EXPECT_NEAR(-0.336088362,finalmat(1,2),epsilon);
	EXPECT_NEAR(2.21751537,finalmat(0,0),epsilon);
	EXPECT_NEAR(-2.26932988,finalmat(0,1),epsilon);
	EXPECT_NEAR(0.0518145101,finalmat(0,2),epsilon);

	SG_UNREF(pca);
	SG_UNREF(features);
}

TEST(PCA, PCA_apply_to_feature_vector_methodTest)
{
	SGMatrix<float64_t> data(5,3);
	data(0,0)=0.033479882244451;
	data(0,1)=0.022889792751630;
	data(0,2)=-0.979206305167302;
	data(1,0)=-1.333677943428106;
	data(1,1)=-0.261995434966092;
	data(1,2)=-1.156401655664002;
	data(2,0)=1.127492278341590;
	data(2,1)=-1.750212368446790;
	data(2,2)=-0.533557109315987;
	data(3,0)=0.350179410603312;
	data(3,1)=-0.285650971595330;
	data(3,2)=-2.002635735883060;
	data(4,0)=-0.299066030332982;
	data(4,1)=-0.831366511567624;
	data(4,2)=0.964229422631627;

	SGVector<float64_t> inputVector(5);
	inputVector[0] = 0.033479882244451;
	inputVector[1] = -1.333677943428106;
	inputVector[2] = 1.127492278341590;
	inputVector[3] = 0.350179410603312;
	inputVector[4] = -0.299066030332982;

	CDenseFeatures<float64_t>* features=new CDenseFeatures<float64_t>(data);
	CPCA* pca=new CPCA(SVD);
	pca->set_target_dim(2);
	pca->fit(features);

	SGVector<float64_t> finalVector=pca->apply_to_feature_vector(inputVector);

	// comparing outputs against BRMLtoolbox MATLAB
	// http://web4.cs.ucl.ac.uk/staff/D.Barber/pmwiki/pmwiki.php?n=Brml.Software
	EXPECT_NEAR(-1.835430614937060, finalVector[0], 1e-13);
	EXPECT_NEAR(0.511467003751085, finalVector[1], 1e-13);

	SG_UNREF(pca);
	SG_UNREF(features);
}

TEST(PCA, PCA_WHITEN_SVD)
{
	SGMatrix<float64_t> data(5,3);
	data(0,0)=0.033479882244451;
	data(0,1)=0.022889792751630;
	data(0,2)=-0.979206305167302;
	data(1,0)=-1.333677943428106;
	data(1,1)=-0.261995434966092;
	data(1,2)=-1.156401655664002;
	data(2,0)=1.127492278341590;
	data(2,1)=-1.750212368446790;
	data(2,2)=-0.533557109315987;
	data(3,0)=0.350179410603312;
	data(3,1)=-0.285650971595330;
	data(3,2)=-2.002635735883060;
	data(4,0)=-0.299066030332982;
	data(4,1)=-0.831366511567624;
	data(4,2)=0.964229422631627;

	CDenseFeatures<float64_t>* features=new CDenseFeatures<float64_t>(data);
	CPCA* pca=new CPCA(SVD,true);
	pca->set_target_dim(3);
	pca->fit(features);

	SGMatrix<float64_t> transmat=pca->get_transformation_matrix();
	SGMatrix<float64_t> finalmat=pca->apply_to_feature_matrix(features);
	SGVector<float64_t> eigvec=pca->get_eigenvalues();

	SGMatrix<float64_t> covariance_mat=finalmat.matrix_multiply(finalmat,finalmat,false,true);
	float64_t epsilon = 0.0000001;

	// eigen vector
	EXPECT_NEAR(0,eigvec[2],epsilon);
	EXPECT_NEAR(2.327794822241147,eigvec[1],epsilon);
	EXPECT_NEAR(2.759160840481412,eigvec[0],epsilon);

	// transformation matrix
	EXPECT_NEAR(-0.10972090328509905,transmat(0,0),epsilon);
	EXPECT_NEAR(-0.119595760920349875,transmat(0,1),epsilon);
	EXPECT_NEAR(0.0,transmat(0,2),epsilon);
	EXPECT_NEAR(0.0551462429348085689,transmat(1,0),epsilon);
	EXPECT_NEAR(-0.161790659142760002,transmat(1,1),epsilon);
	EXPECT_NEAR(0.0,transmat(1,2),epsilon);
	EXPECT_NEAR(-0.276056579030211358,transmat(2,0),epsilon);
	EXPECT_NEAR(0.2923787587590716,transmat(2,1),epsilon);
	EXPECT_NEAR(0.0,transmat(2,2),epsilon);
	EXPECT_NEAR(-0.275452104947822463,transmat(3,0),epsilon);
	EXPECT_NEAR(-0.173464414476695611,transmat(3,1),epsilon);
	EXPECT_NEAR(0.0,transmat(3,2),epsilon);
	EXPECT_NEAR(0.118548031096433193,transmat(4,0),epsilon);
	EXPECT_NEAR(0.242365340306910926,transmat(4,1),epsilon);
	EXPECT_NEAR(0.0,transmat(4,2),epsilon);

	// final matrix
	EXPECT_NEAR(-0.781329936957440241,finalmat(0,0),epsilon);
	EXPECT_NEAR(0.185378224604300035,finalmat(0,1),epsilon);
	EXPECT_NEAR(0.595951712353140373,finalmat(0,2),epsilon);
	EXPECT_NEAR(0.237044713673916413,finalmat(1,0),epsilon);
	EXPECT_NEAR(-0.79517393097939526,finalmat(1,1),epsilon);
	EXPECT_NEAR(0.55812921730547882,finalmat(1,2),epsilon);
	EXPECT_NEAR(0.0,finalmat(2,0),epsilon);
	EXPECT_NEAR(0.0,finalmat(2,1),epsilon);
	EXPECT_NEAR(0.0,finalmat(2,2),epsilon);

	// covariance matrix
	EXPECT_NEAR(1.0,covariance_mat(0,0),epsilon);
	EXPECT_NEAR(0.0,covariance_mat(0,1),epsilon);
	EXPECT_NEAR(0.0,covariance_mat(0,2),epsilon);
	EXPECT_NEAR(0.0,covariance_mat(1,0),epsilon);
	EXPECT_NEAR(1.0,covariance_mat(1,1),epsilon);
	EXPECT_NEAR(0.0,covariance_mat(1,2),epsilon);
	EXPECT_NEAR(0.0,covariance_mat(2,0),epsilon);
	EXPECT_NEAR(0.0,covariance_mat(2,1),epsilon);
	EXPECT_NEAR(0.0,covariance_mat(2,2),epsilon);

	SG_UNREF(pca);
	SG_UNREF(features);
}

TEST(PCA, PCA_WHITEN_EVD)
{
	SGMatrix<float64_t> data(5,3);
	data(0,0)=0.033479882244451;
	data(0,1)=0.022889792751630;
	data(0,2)=-0.979206305167302;
	data(1,0)=-1.333677943428106;
	data(1,1)=-0.261995434966092;
	data(1,2)=-1.156401655664002;
	data(2,0)=1.127492278341590;
	data(2,1)=-1.750212368446790;
	data(2,2)=-0.533557109315987;
	data(3,0)=0.350179410603312;
	data(3,1)=-0.285650971595330;
	data(3,2)=-2.002635735883060;
	data(4,0)=-0.299066030332982;
	data(4,1)=-0.831366511567624;
	data(4,2)=0.964229422631627;

	CDenseFeatures<float64_t>* features=new CDenseFeatures<float64_t>(data);
	CPCA* pca=new CPCA(EVD,true);
	pca->set_target_dim(3);
	pca->fit(features);

	SGMatrix<float64_t> finalmat=pca->apply_to_feature_matrix(features);

	SGMatrix<float64_t> covariance_mat=finalmat.matrix_multiply(finalmat,finalmat,false,true);

	float64_t epsilon = 0.0000001;

	EXPECT_NEAR(0.0,covariance_mat(0,0),epsilon);
	EXPECT_NEAR(0.0,covariance_mat(0,1),epsilon);
	EXPECT_NEAR(0.0,covariance_mat(0,2),epsilon);
	EXPECT_NEAR(0.0,covariance_mat(1,0),epsilon);
	EXPECT_NEAR(1.0,covariance_mat(1,1),epsilon);
	EXPECT_NEAR(0.0,covariance_mat(1,2),epsilon);
	EXPECT_NEAR(0.0,covariance_mat(2,0),epsilon);
	EXPECT_NEAR(0.0,covariance_mat(2,1),epsilon);
	EXPECT_NEAR(1.0,covariance_mat(2,2),epsilon);

	SG_UNREF(pca);
	SG_UNREF(features);
}