/*
 *  RapidMiner
 *
 *  Copyright (C) 2001-2014 by RapidMiner and the contributors
 *
 *  Complete list of developers available at our web site:
 *
 *       http://rapidminer.com
 *
 *  This program is free software: you can redistribute it and/or modify
 *  it under the terms of the GNU Affero General Public License as published by
 *  the Free Software Foundation, either version 3 of the License, or
 *  (at your option) any later version.
 *
 *  This program 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 Affero General Public License for more details.
 *
 *  You should have received a copy of the GNU Affero General Public License
 *  along with this program.  If not, see http://www.gnu.org/licenses/.
 */
package com.rapidminer.operator.learner.functions.linear;

import java.util.LinkedList;
import java.util.List;

import com.rapidminer.example.ExampleSet;
import com.rapidminer.parameter.ParameterType;
import com.rapidminer.parameter.ParameterTypeDouble;
import com.rapidminer.parameter.UndefinedParameterError;
import com.rapidminer.tools.math.FDistribution;

/**
 * This implements an attribute selection method for linear regression that is based on
 * a T-Test. It will filter out all attributes whose coefficient is not significantly different
 * from 0.
 * 
 * @author Sebastian Land, Ingo Mierswa
 *
 */
public class TTestLinearRegressionMethod implements LinearRegressionMethod {

    public static final String PARAMETER_SIGNIFICANCE_LEVEL = "alpha";

    @Override
    public LinearRegressionResult applyMethod(LinearRegression regression, boolean useBias, double ridge, ExampleSet exampleSet, boolean[] isUsedAttribute, int numberOfExamples, int numberOfUsedAttributes, double[] means, double labelMean, double[] standardDeviations, double labelStandardDeviation, double[] coefficientsOnFullData, double errorOnFullData) throws UndefinedParameterError {
        double alpha = regression.getParameterAsDouble(PARAMETER_SIGNIFICANCE_LEVEL);

        LinearRegressionResult result = filterByPValue(regression, useBias, ridge, exampleSet, isUsedAttribute, means, labelMean, standardDeviations, labelStandardDeviation, coefficientsOnFullData, alpha);
        return result;
    }

    /**
     * This method filters the selected attributes depending on their p-value in respect to the significance niveau alpha.
     */
    protected LinearRegressionResult filterByPValue(LinearRegression regression, boolean useBias, double ridge, ExampleSet exampleSet, boolean[] isUsedAttribute, double[] means, double labelMean, double[] standardDeviations, double labelStandardDeviation, double[] coefficientsOnFullData, double alpha) throws UndefinedParameterError {
        FDistribution fdistribution = new FDistribution(1, exampleSet.size() - coefficientsOnFullData.length);

        double generalCorrelation = regression.getCorrelation(exampleSet, isUsedAttribute, coefficientsOnFullData, useBias);
        generalCorrelation *= generalCorrelation;

        int index = 0;
        for (int i = 0; i < isUsedAttribute.length; i++) {
            if (isUsedAttribute[i]) {
                double coefficient = coefficientsOnFullData[index];
                double probability = getPValue(coefficient, i, regression, useBias, ridge, exampleSet, isUsedAttribute, standardDeviations, labelStandardDeviation, fdistribution, generalCorrelation);
                if ((probability < 0 ? 1.0d : Math.max(0.0d, 1.0d - probability)) > alpha) {
                    isUsedAttribute[i] = false;
                }
                index++;
            }
        }

        LinearRegressionResult result = new LinearRegressionResult();
        result.isUsedAttribute = isUsedAttribute;
        result.coefficients = regression.performRegression(exampleSet, isUsedAttribute, means, labelMean, ridge);
        result.error = regression.getSquaredError(exampleSet, isUsedAttribute, result.coefficients, useBias);
        return result;
    }

    /**
     * Returns the PValue of the attributeIndex-th attribute that expresses the probability that
     * the coefficient is only random.
     */
    protected double getPValue(double coefficient, int attributeIndex, LinearRegression regression, boolean useBias, double ridge, ExampleSet exampleSet, boolean[] isUsedAttribute, double[] standardDeviations, double labelStandardDeviation, FDistribution fdistribution, double generalCorrelation) throws UndefinedParameterError {
        double tolerance = regression.getTolerance(exampleSet, isUsedAttribute, attributeIndex, ridge, useBias);
        double standardError = Math.sqrt((1.0d - generalCorrelation) / (tolerance * (exampleSet.size() - exampleSet.getAttributes().size() - 1.0d))) * labelStandardDeviation / standardDeviations[attributeIndex];

        // calculating other statistics
        double tStatistics = coefficient / standardError;
        double probability = fdistribution.getProbabilityForValue(tStatistics * tStatistics);
        return probability;
    }

    @Override
    public List<ParameterType> getParameterTypes() {
        LinkedList<ParameterType> types = new LinkedList<ParameterType>();
        types.add(new ParameterTypeDouble(PARAMETER_SIGNIFICANCE_LEVEL, "This is the significance level of the t-test.", 0, 1, 0.05));
        return types;
    }

}