Set PartialPivLU decomposition as the default policy and relaxed the …

…unit tests accordingly

This makes the learning process a lot faster.
If compiled with -fopenmp (gcc/clang) or /openmp (VS), it will additionally run in parallel.

include/superviseddescent/regressors.hpp

@@ -295,7 +295,7 @@ class ColPivHouseholderQRSolver
  * Works with multi-dimensional label data. In that case, the coefficients for
  * each label will be learned independently.
  */
-template<class Solver = ColPivHouseholderQRSolver>
+template<class Solver = PartialPivLUSolver>
 class LinearRegressor : public Regressor
 {
 

test/test_LinearRegressorND.cpp

@@ -181,7 +181,7 @@ TEST(LinearRegressor, NDimManyExamplesNDimYRegularisation) {
 	bool isInvertible = lr.learn(data, labels);
 	EXPECT_EQ(true, isInvertible);
 	EXPECT_FLOAT_EQ(0.282755911f, lr.x.at<float>(0, 0)) << "Expected the learned x_0_0 to be different"; // Every col is a learned regressor for a label
-	EXPECT_FLOAT_EQ(0.0360795595f, lr.x.at<float>(1, 0)) << "Expected the learned x_1_0 to be different";
+	EXPECT_NEAR(0.03607957f, lr.x.at<float>(1, 0), 0.00000002) << "Expected the learned x_1_0 to be different";
 	EXPECT_FLOAT_EQ(0.291039944f, lr.x.at<float>(2, 0)) << "Expected the learned x_2_0 to be different";
 	EXPECT_NEAR(-0.0989616f, lr.x.at<float>(0, 1), 0.0000001) << "Expected the learned x_0_1 to be different";
 	EXPECT_FLOAT_EQ(0.330635577f, lr.x.at<float>(1, 1)) << "Expected the learned x_1_1 to be different";
@@ -235,7 +235,7 @@ TEST(LinearRegressor, NDimManyExamplesNDimYBiasRegularisation) {
 	bool isInvertible = lr.learn(data, labels);
 	EXPECT_EQ(true, isInvertible);
 	EXPECT_NEAR(0.2814246f, lr.x.at<float>(0, 0), 0.0000002) << "Expected the learned x_0_0 to be different"; // Every col is a learned regressor for a label
-	EXPECT_FLOAT_EQ(0.0331765190f, lr.x.at<float>(1, 0)) << "Expected the learned x_1_0 to be different";
+	EXPECT_NEAR(0.03317654f, lr.x.at<float>(1, 0), 00000003) << "Expected the learned x_1_0 to be different";
 	EXPECT_FLOAT_EQ(0.289116770f, lr.x.at<float>(2, 0)) << "Expected the learned x_2_0 to be different";
 	EXPECT_FLOAT_EQ(0.0320090912f, lr.x.at<float>(3, 0)) << "Expected the learned x_3_0 to be different";
 	EXPECT_NEAR(-0.1005448f, lr.x.at<float>(0, 1), 0.0000001) << "Expected the learned x_0_1 to be different";

test/test_SupervisedDescentOptimiser.cpp

@@ -133,7 +133,7 @@ TEST(SupervisedDescentOptimiser, SinConvergenceCascade) {
 	// Make sure the training converges, i.e. the residual is correct on the training data:
 	Mat predictions = sdo.test(x0, y_tr, h);
 	double trainingResidual = normalisedLeastSquaresResidual(predictions, x_tr);
-	EXPECT_NEAR(0.040279395, trainingResidual, 0.000000001);
+	EXPECT_NEAR(0.040279395, trainingResidual, 0.00000008);
 
 	// Test the trained model:
 	// Test data with finer resolution:
@@ -153,7 +153,7 @@ TEST(SupervisedDescentOptimiser, SinConvergenceCascade) {
 
 	predictions = sdo.test(x0_ts, y_ts, h);
 	double testResidual = normalisedLeastSquaresResidual(predictions, x_ts_gt);
-	ASSERT_NEAR(0.026156775, testResidual, 0.000000004);
+	ASSERT_NEAR(0.026156775, testResidual, 0.00000005);
 }
 
 TEST(SupervisedDescentOptimiser, XCubeConvergence) {
@@ -420,7 +420,7 @@ TEST(SupervisedDescentOptimiser, ExpConvergence) {
 
 	predictions = sdo.test(x0_ts, y_ts, h);
 	double testResidual = normalisedLeastSquaresResidual(predictions, x_ts_gt);
-	ASSERT_NEAR(0.1924569501, testResidual, 0.0000000005);
+	ASSERT_NEAR(0.1924569501, testResidual, 0.000000006);
 }
 
 TEST(SupervisedDescentOptimiser, ExpConvergenceCascade) {