multiples lad with integration data

doc/cookbook/source/examples/multiclass_classifier/linear_discriminant_analysis.rst

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+============================
+Linear Discriminant Analysis
+============================
+
+This cookbook page introduces the application of
+`linear discriminant analysis <http://shogun.ml/cookbook/latest/examples/binary_classifier/lda.html>`_
+to multi-class classifications.
+
+-------
+Example
+-------
+
+Imagine we have files with training and test data. We create CDenseFeatures (here 64 bit floats aka RealFeatures) and :sgclass:`CMulticlassLabels` as
+
+.. sgexample:: linear_discriminant_analysis.sg:create_features
+
+We create an instance of the :sgclass:`CMCLDA` classifier with feature matrix and label list.
+:sgclass:`CMCLDA` also has two default parameters, to set tolerance used in training and mark whether to store the within class covariances.
+
+.. sgexample:: linear_discriminant_analysis.sg:create_instance
+
+Then we train and apply it to the test data, which here gives :sgclass:`CMulticlassLabels`.
+
+.. sgexample:: linear_discriminant_analysis.sg:train_and_apply
+
+We can extract the mean vector of one class.
+If we enabled storing covariance when creating instances, we can also extract the covariance matrix:
+
+.. sgexample:: linear_discriminant_analysis.sg:extract_mean_and_cov
+
+We can evaluate test performance via e.g. :sgclass:`CMulticlassAccuracy`.
+
+.. sgexample:: linear_discriminant_analysis.sg:evaluate_accuracy
+
+----------
+References
+----------
+
+:wiki:`Linear_discriminant_analysis`
+
+:wiki:`Linear_discriminant_analysis#Multiclass_LDA`

examples/meta/src/multiclass_classifier/linear_discriminant_analysis.sg

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+CSVFile f_feats_train("../../data/classifier_4class_2d_linear_features_train.dat")
+CSVFile f_feats_test("../../data/classifier_4class_2d_linear_features_test.dat")
+CSVFile f_labels_train("../../data/classifier_4class_2d_linear_labels_train.dat")
+CSVFile f_labels_test("../../data/classifier_4class_2d_linear_labels_test.dat")
+
+#![create_features]
+RealFeatures features_train(f_feats_train)
+RealFeatures features_test(f_feats_test)
+MulticlassLabels labels_train(f_labels_train)
+MulticlassLabels labels_test(f_labels_test)
+#![create_features]
+
+#![create_instance]
+MCLDA mc_lda(features_train, labels_train, 0.0001, True)
+#![create_instance]
+
+#![train_and_apply]
+mc_lda.train()
+MulticlassLabels labels_predict = mc_lda.apply_multiclass(features_test)
+#![train_and_apply]
+
+#![extract_mean_and_cov]
+int classlabel = 1
+RealVector m = mc_lda.get_mean(classlabel)
+RealMatrix c = mc_lda.get_cov()
+#![extract_mean_and_cov]
+
+#![evaluate_accuracy]
+MulticlassAccuracy evals()
+real accuracy = evals.evaluate(labels_predict, labels_test)
+#![evaluate_accuracy]
+
+# additional integration testing variables
+RealVector output = labels_predict.get_labels()