///////////////////////////////////////////////////////////////////////////////
// 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, 2022 by Peter Spirtes, Richard        //
// Scheines, Joseph Ramsey, and Clark Glymour.                               //
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package edu.cmu.tetrad.util;


import org.apache.commons.math3.special.Gamma;
import org.apache.commons.math3.util.FastMath;

/**
 * Frequency function of partial correlation r(12|34...k), assuming that the
 * true partial correlation is equal to zero.  Uses the equation (29.13.4) from
 * Cramer's _Mathematical Methods of Statistics_.
 *
 * @author josephramsey
 */
public class PartialCorrelationPdf implements Function, TetradSerializable {
    static final long serialVersionUID = 23L;

    /**
     * Number of data points in the sample.
     *
     * @serial
     */
    private final int n;

    /**
     * Number of compared variables--that is, 2 + (#conditioning variables).
     *
     * @serial
     */
    private final int k;

    /**
     * The aggregate value of the constant expression in the distribution
     * function for zero partial correlation.
     *
     * @serial
     */
    private double constant = Double.NaN;

    /**
     * The power to which the variable expression is raised in the distribution
     * function for zero partial correlation.
     *
     * @serial
     */
    private final double outsideExp;

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

    /**
     * Constructs a new zero partial correlation distribution function with the
     * given values for n and k.
     *
     * @param n sample size
     * @param k the number of variables being compared.
     */
    public PartialCorrelationPdf(int n, int k) {
        this.n = n;
        this.k = k;
        /*
      The ratio of the two gamma expressions in the distribution function for
      zero partial correlation.

      */
        double gammaRatio = gammaRatio(n, k);
        this.constant = (1 / FastMath.pow(FastMath.PI, 0.5)) * gammaRatio;
        this.outsideExp = (double) (n - k - 2) / 2.0;
    }

    /**
     * Generates a simple exemplar of this class to test serialization.
     *
     * @return the examplar.
     */
    @SuppressWarnings("UnusedDeclaration")
    public static PartialCorrelationPdf serializableInstance() {
        return new PartialCorrelationPdf(5, 2);
    }

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

    /**
     * Calculates the value of the function at the given domain point.
     *
     * @param x the domain point.
     * @return the value of the function at x.
     */
    public double valueAt(double x) {
        return this.constant * FastMath.pow(1 - x * x, this.outsideExp);
    }

    /**
     * Calculates the ratio of gamma values in the distribution equation.
     *
     * @param n sample size
     * @param k the number of variables being compared.
     * @return this ratio.
     */
    private double gammaRatio(int n, int k) {
        double top = (n - k + 1) / 2.0;
        double bottom = (n - k) / 2.0;
        double lngamma = Gamma.logGamma(top) - Gamma.logGamma(bottom);
        return FastMath.exp(lngamma);
    }

    /**
     * @return a description of the function.
     */
    public String toString() {
        return "Zero partial correlation distribution with n = " + getN() +
                " and k = " + getK() + "\n\n";
    }

    private int getN() {
        return this.n;
    }

    /**
     * @return Ibid.
     */
    public int getK() {
        return this.k;
    }
}





