Major bugfix for nonlinear GenSVM

Nonlinear GenSVM depends on the eigendecomposition of the
kernel matrix. Mathematically, the Sigma vector in the code
should contain the square root of the eigenvalues. Taking
the square root was however neglected, which resulted in
poor performance of nonlinear GenSVM. This is now fixed,
which means that the performance of nonlinear GenSVM will
be much better.

1 files changed, 104 insertions, 79 deletions

diff --git a/tests/src/test_gensvm_kernel.c b/tests/src/test_gensvm_kernel.c
index cf1d4db..b075bc5 100644
--- a/tests/src/test_gensvm_kernel.c
+++ b/tests/src/test_gensvm_kernel.c
@@ -326,245 +326,269 @@ char *test_kernel_preprocess_kernel()
 	mu_assert(data->r == 7, "Incorrect data->r");
 
 	double eps = 1e-14;
+
+	mu_assert(fabs(matrix_get(data->Sigma, 1, 0, 0) -
+				2.7638223432435374) < eps,
+			"Incorrect data->Sigma at 0, 0");
+	mu_assert(fabs(matrix_get(data->Sigma, 1, 1, 0) -
+				0.8989108618424078) < eps,
+			"Incorrect data->Sigma at 1, 0");
+	mu_assert(fabs(matrix_get(data->Sigma, 1, 2, 0) -
+				0.8492992522024180) < eps,
+			"Incorrect data->Sigma at 2, 0");
+	mu_assert(fabs(matrix_get(data->Sigma, 1, 3, 0) -
+				0.6551312398422764) < eps,
+			"Incorrect data->Sigma at 3, 0");
+	mu_assert(fabs(matrix_get(data->Sigma, 1, 4, 0) -
+				0.4151267289513675) < eps,
+			"Incorrect data->Sigma at 4, 0");
+	mu_assert(fabs(matrix_get(data->Sigma, 1, 5, 0) -
+				0.3219015071458272) < eps,
+			"Incorrect data->Sigma at 5, 0");
+	mu_assert(fabs(matrix_get(data->Sigma, 1, 6, 0) -
+				0.2206142024294812) < eps,
+			"Incorrect data->Sigma at 6, 0");
+
+
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 0, 0)) -
 				fabs(1.0000000000000000)) < eps,
 			"Incorrect data->Z at 0, 0");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 0, 1)) -
-				fabs(2.4632837902141640)) < eps,
+				fabs(0.8912598149573278)) < eps,
 			"Incorrect data->Z at 0, 1");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 0, 2)) -
-				fabs(-0.3037489220604925)) < eps,
+				fabs(-0.3379077225053534)) < eps,
 			"Incorrect data->Z at 0, 2");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 0, 3)) -
-				fabs(-0.0061287029147240)) < eps,
+				fabs(-0.0072161878146390)) < eps,
 			"Incorrect data->Z at 0, 3");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 0, 4)) -
-				fabs(0.1822712619914593)) < eps,
+				fabs(0.2782209897902920)) < eps,
 			"Incorrect data->Z at 0, 4");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 0, 5)) -
-				fabs(0.0252737053303148)) < eps,
+				fabs(0.0608819032061786)) < eps,
 			"Incorrect data->Z at 0, 5");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 0, 6)) -
-				fabs(-0.0078753266252524)) < eps,
+				fabs(-0.0244650194249782)) < eps,
 			"Incorrect data->Z at 0, 6");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 0, 7)) -
-				fabs(-0.0012800124996018)) < eps,
+				fabs(-0.0058020403287988)) < eps,
 			"Incorrect data->Z at 0, 7");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 1, 0)) -
 				fabs(1.0000000000000000)) < eps,
 			"Incorrect data->Z at 1, 0");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 1, 1)) -
-				fabs(2.2923640983040641)) < eps,
+				fabs(0.8294180354638190)) < eps,
 			"Incorrect data->Z at 1, 1");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 1, 2)) -
-				fabs(-0.3048037728463330)) < eps,
+				fabs(-0.3390811990207864)) < eps,
 			"Incorrect data->Z at 1, 2");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 1, 3)) -
-				fabs(-0.2586192720897897)) < eps,
+				fabs(-0.3045090071834334)) < eps,
 			"Incorrect data->Z at 1, 3");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 1, 4)) -
-				fabs(0.1747912247100736)) < eps,
+				fabs(0.2668033732480146)) < eps,
 			"Incorrect data->Z at 1, 4");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 1, 5)) -
-				fabs(-0.0623497873850738)) < eps,
+				fabs(-0.1501945864641692)) < eps,
 			"Incorrect data->Z at 1, 5");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 1, 6)) -
-				fabs(-0.0199493291395259)) < eps,
+				fabs(-0.0619733946461100)) < eps,
 			"Incorrect data->Z at 1, 6");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 1, 7)) -
-				fabs(0.0068540206892510)) < eps,
+				fabs(0.0310679032164383)) < eps,
 			"Incorrect data->Z at 1, 7");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 2, 0)) -
 				fabs(1.0000000000000000)) < eps,
 			"Incorrect data->Z at 2, 0");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 2, 1)) -
-				fabs(2.4167201742337761)) < eps,
+				fabs(0.8744122718819858)) < eps,
 			"Incorrect data->Z at 2, 1");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 2, 2)) -
-				fabs(-0.1499385272847361)) < eps,
+				fabs(-0.1668002175181436)) < eps,
 			"Incorrect data->Z at 2, 2");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 2, 3)) -
-				fabs(-0.1781619658696836)) < eps,
+				fabs(-0.2097752534311912)) < eps,
 			"Incorrect data->Z at 2, 3");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 2, 4)) -
-				fabs(-0.2363293887681946)) < eps,
+				fabs(-0.3607359478462531)) < eps,
 			"Incorrect data->Z at 2, 4");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 2, 5)) -
-				fabs(-0.0362117307160720)) < eps,
+				fabs(-0.0872305447725448)) < eps,
 			"Incorrect data->Z at 2, 5");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 2, 6)) -
-				fabs(0.0366137533260933)) < eps,
+				fabs(0.1137420997209145)) < eps,
 			"Incorrect data->Z at 2, 6");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 2, 7)) -
-				fabs(0.0227049982868101)) < eps,
+				fabs(0.1029172103916005)) < eps,
 			"Incorrect data->Z at 2, 7");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 3, 0)) -
 				fabs(1.0000000000000000)) < eps,
 			"Incorrect data->Z at 3, 0");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 3, 1)) -
-				fabs(2.3339314848494390)) < eps,
+				fabs(0.8444578540132961)) < eps,
 			"Incorrect data->Z at 3, 1");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 3, 2)) -
-				fabs(0.4067278927345656)) < eps,
+				fabs(0.4524674358711562)) < eps,
 			"Incorrect data->Z at 3, 2");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 3, 3)) -
-				fabs(0.0198947146890620)) < eps,
+				fabs(0.0234248583611390)) < eps,
 			"Incorrect data->Z at 3, 3");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 3, 4)) -
-				fabs(0.1187106614859180)) < eps,
+				fabs(0.1812013445038858)) < eps,
 			"Incorrect data->Z at 3, 4");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 3, 5)) -
-				fabs(0.0734848412140159)) < eps,
+				fabs(0.1770178504276099)) < eps,
 			"Incorrect data->Z at 3, 5");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 3, 6)) -
-				fabs(-0.0166955533210990)) < eps,
+				fabs(-0.0518654089852882)) < eps,
 			"Incorrect data->Z at 3, 6");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 3, 7)) -
-				fabs(0.0229112619510384)) < eps,
+				fabs(0.1038521622757349)) < eps,
 			"Incorrect data->Z at 3, 7");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 4, 0)) -
 				fabs(1.0000000000000000)) < eps,
 			"Incorrect data->Z at 4, 0");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 4, 1)) -
-				fabs(2.5061509421266424)) < eps,
+				fabs(0.9067699116960968)) < eps,
 			"Incorrect data->Z at 4, 1");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 4, 2)) -
-				fabs(0.0574469229922174)) < eps,
+				fabs(0.0639072520210456)) < eps,
 			"Incorrect data->Z at 4, 2");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 4, 3)) -
-				fabs(-0.2858649955147738)) < eps,
+				fabs(-0.3365892466918618)) < eps,
 			"Incorrect data->Z at 4, 3");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 4, 4)) -
-				fabs(-0.0995031375002134)) < eps,
+				fabs(-0.1518827548571320)) < eps,
 			"Incorrect data->Z at 4, 4");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 4, 5)) -
-				fabs(0.0223790101651578)) < eps,
+				fabs(0.0539088634973914)) < eps,
 			"Incorrect data->Z at 4, 5");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 4, 6)) -
-				fabs(-0.0355571480867735)) < eps,
+				fabs(-0.1104597129788070)) < eps,
 			"Incorrect data->Z at 4, 6");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 4, 7)) -
-				fabs(-0.0219026472149696)) < eps,
+				fabs(-0.0992803136596373)) < eps,
 			"Incorrect data->Z at 4, 7");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 5, 0)) -
 				fabs(1.0000000000000000)) < eps,
 			"Incorrect data->Z at 5, 0");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 5, 1)) -
-				fabs(2.4482858151168982)) < eps,
+				fabs(0.8858332812534048)) < eps,
 			"Incorrect data->Z at 5, 1");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 5, 2)) -
-				fabs(-0.0670998214520230)) < eps,
+				fabs(-0.0746456899124524)) < eps,
 			"Incorrect data->Z at 5, 2");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 5, 3)) -
-				fabs(0.3147064295566219)) < eps,
+				fabs(0.3705483417541217)) < eps,
 			"Incorrect data->Z at 5, 3");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 5, 4)) -
-				fabs(0.1070535630418465)) < eps,
+				fabs(0.1634078128645188)) < eps,
 			"Incorrect data->Z at 5, 4");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 5, 5)) -
-				fabs(-0.0052824396955993)) < eps,
+				fabs(-0.0127248845405431)) < eps,
 			"Incorrect data->Z at 5, 5");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 5, 6)) -
-				fabs(0.0614363461130733)) < eps,
+				fabs(0.1908544842110400)) < eps,
 			"Incorrect data->Z at 5, 6");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 5, 7)) -
-				fabs(-0.0075355247061472)) < eps,
+				fabs(-0.0341570244488496)) < eps,
 			"Incorrect data->Z at 5, 7");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 6, 0)) -
 				fabs(1.0000000000000000)) < eps,
 			"Incorrect data->Z at 6, 0");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 6, 1)) -
-				fabs(2.3638928644404329)) < eps,
+				fabs(0.8552984131629242)) < eps,
 			"Incorrect data->Z at 6, 1");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 6, 2)) -
-				fabs(0.3482541374011597)) < eps,
+				fabs(0.3874178766595150)) < eps,
 			"Incorrect data->Z at 6, 2");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 6, 3)) -
-				fabs(-0.2422541976251498)) < eps,
+				fabs(-0.2852400929318269)) < eps,
 			"Incorrect data->Z at 6, 3");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 6, 4)) -
-				fabs(0.0251886519764033)) < eps,
+				fabs(0.0384482534865339)) < eps,
 			"Incorrect data->Z at 6, 4");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 6, 5)) -
-				fabs(-0.0079397861684362)) < eps,
+				fabs(-0.0191261742853618)) < eps,
 			"Incorrect data->Z at 6, 5");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 6, 6)) -
-				fabs(0.0424975213407462)) < eps,
+				fabs(0.1320202620905840)) < eps,
 			"Incorrect data->Z at 6, 6");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 6, 7)) -
-				fabs(-0.0204279932276333)) < eps,
+				fabs(-0.0925960024453241)) < eps,
 			"Incorrect data->Z at 6, 7");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 7, 0)) -
 				fabs(1.0000000000000000)) < eps,
 			"Incorrect data->Z at 7, 0");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 7, 1)) -
-				fabs(2.3607306299135344)) < eps,
+				fabs(0.8541542605604135)) < eps,
 			"Incorrect data->Z at 7, 1");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 7, 2)) -
-				fabs(-0.0220102589508912)) < eps,
+				fabs(-0.0244854744615944)) < eps,
 			"Incorrect data->Z at 7, 2");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 7, 3)) -
-				fabs(0.3913398731540265)) < eps,
+				fabs(0.4607797217991149)) < eps,
 			"Incorrect data->Z at 7, 3");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 7, 4)) -
-				fabs(-0.0941469673695446)) < eps,
+				fabs(-0.1437070340168947)) < eps,
 			"Incorrect data->Z at 7, 4");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 7, 5)) -
-				fabs(-0.0477595489009114)) < eps,
+				fabs(-0.1150481180085769)) < eps,
 			"Incorrect data->Z at 7, 5");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 7, 6)) -
-				fabs(-0.0367688438245860)) < eps,
+				fabs(-0.1142238946024231)) < eps,
 			"Incorrect data->Z at 7, 6");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 7, 7)) -
-				fabs(-0.0133498576642393)) < eps,
+				fabs(-0.0605122313850435)) < eps,
 			"Incorrect data->Z at 7, 7");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 8, 0)) -
 				fabs(1.0000000000000000)) < eps,
 			"Incorrect data->Z at 8, 0");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 8, 1)) -
-				fabs(2.5023932475093376)) < eps,
+				fabs(0.9054103110595034)) < eps,
 			"Incorrect data->Z at 8, 1");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 8, 2)) -
-				fabs(0.2929602950386334)) < eps,
+				fabs(0.3259058350214859)) < eps,
 			"Incorrect data->Z at 8, 2");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 8, 3)) -
-				fabs(0.1371647327912284)) < eps,
+				fabs(0.1615034187720415)) < eps,
 			"Incorrect data->Z at 8, 3");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 8, 4)) -
-				fabs(-0.0270505649533715)) < eps,
+				fabs(-0.0412902992687150)) < eps,
 			"Incorrect data->Z at 8, 4");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 8, 5)) -
-				fabs(-0.0685258491091892)) < eps,
+				fabs(-0.1650721197410958)) < eps,
 			"Incorrect data->Z at 8, 5");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 8, 6)) -
-				fabs(-0.0213385621647371)) < eps,
+				fabs(-0.0662891030052566)) < eps,
 			"Incorrect data->Z at 8, 6");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 8, 7)) -
-				fabs(0.0121305554343051)) < eps,
+				fabs(0.0549853785509707)) < eps,
 			"Incorrect data->Z at 8, 7");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 9, 0)) -
 				fabs(1.0000000000000000)) < eps,
 			"Incorrect data->Z at 9, 0");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 9, 1)) -
-				fabs(2.4579608302226870)) < eps,
+				fabs(0.8893338735144964)) < eps,
 			"Incorrect data->Z at 9, 1");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 9, 2)) -
-				fabs(-0.2538863526247282)) < eps,
+				fabs(-0.2824377403832496)) < eps,
 			"Incorrect data->Z at 9, 2");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 9, 3)) -
-				fabs(0.0991005899665861)) < eps,
+				fabs(0.1166851256604740)) < eps,
 			"Incorrect data->Z at 9, 3");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 9, 4)) -
-				fabs(-0.1374781282330359)) < eps,
+				fabs(-0.2098482256259584)) < eps,
 			"Incorrect data->Z at 9, 4");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 9, 5)) -
-				fabs(0.1043628273525485)) < eps,
+				fabs(0.2513999221784036)) < eps,
 			"Incorrect data->Z at 9, 5");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 9, 6)) -
-				fabs(-0.0024213407513349)) < eps,
+				fabs(-0.0075219925896089)) < eps,
 			"Incorrect data->Z at 9, 6");
 	mu_assert(fabs(fabs(matrix_get(data->Z, data->r+1, 9, 7)) -
-				fabs(0.0007673936590348)) < eps,
+				fabs(0.0034784417801946)) < eps,
 			"Incorrect data->Z at 9, 7");
 
 	mu_assert(fabs(matrix_get(data->RAW, data->m+1, 0, 0) -
@@ -748,9 +772,9 @@ char *test_kernel_preprocess_kernel()
 				0.1028774221216107) < eps,
 			"Incorrect data->RAW at 9, 5");
 
-	// end test code //
 
 
+	// end test code //
 
 	gensvm_free_model(model);
 	gensvm_free_data(data);
@@ -2317,7 +2341,7 @@ char *test_kernel_eigendecomp()
 
 	mu_assert(r == 7, "Incorrect number of eigenvalues kept");
 
-	// Note: to overcome sign variability in the eigenvectors, we take the 
+	// Note: to overcome sign variability in the eigenvectors, we take the
 	// absolute value of the elements of P and the expected outcome.
 
 	mu_assert(fabs(fabs(matrix_get(P, r, 0, 0)) -
@@ -2532,19 +2556,20 @@ char *test_kernel_eigendecomp()
 			"Incorrect P at 9, 6");
 
 	eps = 1e-13;
-	mu_assert(fabs(Sigma[0] - 22.9663721202447704) < eps,
+
+	mu_assert(fabs(Sigma[0] - 4.7923242920575353) < eps,
 			"Incorrect Sigma at 0");
-	mu_assert(fabs(Sigma[1] - 2.2569857335186856) < eps,
+	mu_assert(fabs(Sigma[1] - 1.5023267732150303) < eps,
 			"Incorrect Sigma at 1");
-	mu_assert(fabs(Sigma[2] - 1.4177404640754938) < eps,
+	mu_assert(fabs(Sigma[2] - 1.1906890711161726) < eps,
 			"Incorrect Sigma at 2");
-	mu_assert(fabs(Sigma[3] - 1.0075496644459232) < eps,
+	mu_assert(fabs(Sigma[3] - 1.0037677343120393) < eps,
 			"Incorrect Sigma at 3");
-	mu_assert(fabs(Sigma[4] - 0.7919296491505164) < eps,
+	mu_assert(fabs(Sigma[4] - 0.8899042921295091) < eps,
 			"Incorrect Sigma at 4");
-	mu_assert(fabs(Sigma[5] - 0.6808726728950240) < eps,
+	mu_assert(fabs(Sigma[5] - 0.8251500911319253) < eps,
 			"Incorrect Sigma at 5");
-	mu_assert(fabs(Sigma[6] - 0.2909718164349679) < eps,
+	mu_assert(fabs(Sigma[6] - 0.5394180349552358) < eps,
 			"Incorrect Sigma at 6");
 
 	// end test code //