///////////////////////////////////////////////////////////////////////////////
// For information as to what this class does, see the Javadoc, below.       //
// Copyright (C) 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006,       //
// 2007, 2008, 2009, 2010, 2014, 2015 by Peter Spirtes, Richard Scheines, Joseph   //
// Ramsey, and Clark Glymour.                                                //
//                                                                           //
// This program is free software; you can redistribute it and/or modify      //
// it under the terms of the GNU General Public License as published by      //
// the Free Software Foundation; either version 2 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 General Public License for more details.                              //
//                                                                           //
// You should have received a copy of the GNU General Public License         //
// along with this program; if not, write to the Free Software               //
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA //
///////////////////////////////////////////////////////////////////////////////

package edu.cmu.tetrad.search;

import cern.colt.matrix.DoubleMatrix1D;
import cern.colt.matrix.DoubleMatrix2D;
import cern.colt.matrix.impl.DenseDoubleMatrix2D;
import cern.colt.matrix.linalg.Algebra;
import cern.jet.math.Functions;
import edu.cmu.tetrad.data.DataSet;
import edu.cmu.tetrad.data.GeneralAndersonDarlingTest;
import edu.cmu.tetrad.data.ICovarianceMatrix;
import edu.cmu.tetrad.graph.Node;
import edu.cmu.tetrad.regression.RegressionDataset;
import edu.cmu.tetrad.regression.RegressionResult;
import edu.cmu.tetrad.util.*;
import org.apache.commons.math3.distribution.NormalDistribution;
import org.apache.commons.math3.distribution.RealDistribution;

import java.text.NumberFormat;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;

import static java.lang.Math.tanh;

/**
 * Checks independence of X _||_ Y | Z for variables X and Y and list Z of variables. Partial correlations are
 * calculated using generalized inverses, so linearly dependent variables do not throw exceptions. Must supply a
 * continuous data set; don't know how to do this with covariance or correlation matrices.
 *
 * @author Joseph Ramsey
 * @author Frank Wimberly adapted IndTestCramerT for Fisher's Z
 */
public final class IndTestRegressionAD implements IndependenceTest {

    /**
     * The correlation matrix.
     */
    private final DoubleMatrix2D data;

    /**
     * The variables of the correlation matrix, in order. (Unmodifiable list.)
     */
    private final List<Node> variables;

    /**
     * The significance level of the independence tests.
     */
    private double alpha;

    /**
     * The cutoff value for 'alpha' area in the two tails of the partial correlation distribution function.
     */
    private double thresh = Double.NaN;

    /**
     * The last calculated partial correlation, needed to calculate relative strength.
     */
    private double storedR = 0.;

    /**
     * The value of the Fisher's Z statistic associated with the las calculated partial correlation.
     */
    private double fishersZ;

    /**
     * The standard number formatter for Tetrad.
     */
    private static NumberFormat nf = NumberFormatUtil.getInstance().getNumberFormat();
    private DataSet dataSet;
    private double pvalue = Double.NaN;
    private boolean verbose = false;

    //==========================CONSTRUCTORS=============================//

    /**
     * Constructs a new Independence test which checks independence facts based on the correlation matrix implied by the
     * given data set (must be continuous). The given significance level is used.
     *
     * @param dataSet A data set containing only continuous columns.
     * @param alpha   The alpha level of the test.
     */
    public IndTestRegressionAD(DataSet dataSet, double alpha) {
        this.dataSet = dataSet;
        this.data = new DenseDoubleMatrix2D(dataSet.getDoubleData().toArray());
        this.variables = Collections.unmodifiableList(dataSet.getVariables());
        setAlpha(alpha);
    }

    //==========================PUBLIC METHODS=============================//

    /**
     * Creates a new IndTestCramerT instance for a subset of the variables.
     */
    public IndependenceTest indTestSubset(List vars) {
        throw new UnsupportedOperationException();
    }

    /**
     * Determines whether variable x is independent of variable y given a list of conditioning variables z.
     *
     * @param xVar  the one variable being compared.
     * @param yVar  the second variable being compared.
     * @param zList the list of conditioning variables.
     * @return true iff x _||_ y | z.
     * @throws RuntimeException if a matrix singularity is encountered.
     */
    public boolean isIndependent(Node xVar, Node yVar, List<Node> zList) {
        if (zList == null) {
            throw new NullPointerException();
        }

        for (Node node : zList) {
            if (node == null) {
                throw new NullPointerException();
            }
        }

        TetradVector v1, v2;

        try {
            List<Node> regressors = new ArrayList<>();
            regressors.add(dataSet.getVariable(yVar.getName()));

            for (Node zVar : zList) {
                regressors.add(dataSet.getVariable(zVar.getName()));
            }

            RegressionDataset regression = new RegressionDataset(dataSet);
            RegressionResult result = regression.regress(xVar, regressors);
            v1 = result.getResiduals();

            v2 = regression.getResidualsWithoutFirstRegressor();

//            regressors.remove(dataSet.getVariable(yVar.getNode()));
//            regression = new RegressionDataset(dataSet);
//            result = regression.regress(xVar, regressors);
//            v2 = result.getResiduals();
        } catch (Exception e) {
            throw e;
        }

        List<Double> d1 = new ArrayList<>();
        for (int i = 0; i < v1.size(); i++) d1.add(v1.get(i));

        List<Double> d2 = new ArrayList<>();
        double[] f2 = new double[v2.size()];
        for (int i = 0; i < v2.size(); i++) {
            d2.add(v2.get(i));
            f2[i] = v2.get(i);
        }

        double sd = StatUtils.sd(f2);

//        RealDistribution c2 = new EmpiricalCdf(d2);
        RealDistribution c2 = new NormalDistribution(0, sd);

        GeneralAndersonDarlingTest test = new GeneralAndersonDarlingTest(d1, c2);
        double aSquaredStar = test.getASquaredStar();
        System.out.println("A squared star = " + aSquaredStar + " p = " + test.getP());
        double p = test.getP();
        double aa2 = 1 - tanh(aSquaredStar);
        boolean independent = p > alpha;

        this.pvalue = aa2;

        if (verbose) {
            if (independent) {
                TetradLogger.getInstance().log("independencies", SearchLogUtils.independenceFactMsg(xVar, yVar, zList, 0.));
            } else {
                TetradLogger.getInstance().log("dependencies", SearchLogUtils.dependenceFactMsg(xVar, yVar, zList, 0.));
            }
        }

        return independent;
    }

    public boolean isIndependent(Node x, Node y, Node... z) {
        List<Node> zList = Arrays.asList(z);
        return isIndependent(x, y, zList);
    }

    public boolean isDependent(Node x, Node y, List<Node> z) {
        return !isIndependent(x, y, z);
    }

    public boolean isDependent(Node x, Node y, Node... z) {
        List<Node> zList = Arrays.asList(z);
        return isDependent(x, y, zList);
    }

    /**
     * @return the probability associated with the most recently computed independence test.
     */
    public double getPValue() {
        return this.pvalue;
    }

    /**
     * Sets the significance level at which independence judgments should be made.  Affects the cutoff for partial
     * correlations to be considered statistically equal to zero.
     */
    public void setAlpha(double alpha) {
        if (alpha < 0.0 || alpha > 1.0) {
            throw new IllegalArgumentException("Significance out of range.");
        }

        this.alpha = alpha;
    }

    /**
     * Gets the getModel significance level.
     */
    public double getAlpha() {
        return this.alpha;
    }

    /**
     * @return the list of variables over which this independence checker is capable of determinine independence
     * relations-- that is, all the variables in the given graph or the given data set.
     */
    public List<Node> getVariables() {
        return this.variables;
    }

    /**
     * @return the variable with the given name.
     */
    public Node getVariable(String name) {
        for (int i = 0; i < getVariables().size(); i++) {
            Node variable = getVariables().get(i);

            if (variable.getName().equals(name)) {
                return variable;
            }
        }

        return null;
    }

    /**
     * @return the list of variable varNames.
     */
    public List<String> getVariableNames() {
        List<Node> variables = getVariables();
        List<String> variableNames = new ArrayList<>();

        for (Node variable : variables) {
            variableNames.add(variable.getName());
        }

        return variableNames;
    }

    public String toString() {
        return "Linear Regression Test, alpha = " + nf.format(getAlpha());
    }

    //==========================PRIVATE METHODS============================//

//    /**
//     * Return the p-value of the last calculated independence fact.
//     *
//     * @return this p-value.  When accessed through the IndependenceChecker
//     *         interface, this p-value should only be considered to be a
//     *         relative strength.
//     */
//    private double getRelativeStrength() {
//
//        // precondition:  pdf is the most recently used partial
//        // correlation distribution function, and storedR is the most
//        // recently calculated partial correlation.
//        return 2.0 * Integrator.getArea(npdf, Math.abs(storedR), 9.0, 100);
//    }

//    /**
//     * Computes that value x such that P(abs(N(0,1) > x) < alpha.  Note that
//     * this is a two sided test of the null hypothesis that the Fisher's Z
//     * value, which is distributed as N(0,1) is not equal to 0.0.
//     */
//    private double cutoffGaussian() {
//        npdf = new NormalPdf();
//        final double upperBound = 9.0;
//        final double delta = 0.001;
//        //        double alpha = this.alpha/2.0;    //Two sided test
//        return CutoffFinder.getCutoff(npdf, upperBound, alpha, delta);
//    }

//    private int sampleSize() {
//        return data.rows();
//    }

    public boolean determines(List<Node> zList, Node xVar) {
        if (zList == null) {
            throw new NullPointerException();
        }

        for (Node node : zList) {
            if (node == null) {
                throw new NullPointerException();
            }
        }

        int size = zList.size();
        int[] zCols = new int[size];

        int xIndex = getVariables().indexOf(xVar);

        for (int i = 0; i < zList.size(); i++) {
            zCols[i] = getVariables().indexOf(zList.get(i));
        }

        int[] zRows = new int[data.rows()];
        for (int i = 0; i < data.rows(); i++) {
            zRows[i] = i;
        }

        DoubleMatrix2D Z = data.viewSelection(zRows, zCols);
        DoubleMatrix1D x = data.viewColumn(xIndex);
        DoubleMatrix2D Zt = new Algebra().transpose(Z);
        DoubleMatrix2D ZtZ = new Algebra().mult(Zt, Z);
        DoubleMatrix2D G = new DenseDoubleMatrix2D(new TetradMatrix(ZtZ.toArray()).inverse().toArray());

        // Bug in Colt? Need to make a copy before multiplying to avoid
        // a ClassCastException.
        DoubleMatrix2D Zt2 = Zt.like();
        Zt2.assign(Zt);
        DoubleMatrix2D GZt = new Algebra().mult(G, Zt2);

        DoubleMatrix1D b_x = new Algebra().mult(GZt, x);

        DoubleMatrix1D xPred = new Algebra().mult(Z, b_x);

        DoubleMatrix1D xRes = xPred.copy().assign(x, Functions.minus);

        double SSE = xRes.aggregate(Functions.plus, Functions.square);
        boolean determined = SSE < 0.0001;

        if (determined) {
            StringBuilder sb = new StringBuilder();
            sb.append("Determination found: ").append(xVar).append(
                    " is determined by {");

            for (int i = 0; i < zList.size(); i++) {
                sb.append(zList.get(i));

                if (i < zList.size() - 1) {
                    sb.append(", ");
                }
            }

            sb.append("}");

            TetradLogger.getInstance().log("independencies", sb.toString());
        }

        return determined;
    }

    public DataSet getData() {
        return dataSet;
    }

    @Override
    public ICovarianceMatrix getCov() {
        return null;
    }

    @Override
    public List<DataSet> getDataSets() {
        return null;
    }

    @Override
    public int getSampleSize() {
        return 0;
    }

    @Override
    public List<TetradMatrix> getCovMatrices() {
        return null;
    }

    @Override
    public double getScore() {
        return getPValue();
    }

    public boolean isVerbose() {
        return verbose;
    }

    public void setVerbose(boolean verbose) {
        this.verbose = verbose;
    }
}




