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/*
 * Copyright (c) "Neo4j"
 * Neo4j Sweden AB [http://neo4j.com]
 *
 * This file is part of Neo4j.
 *
 * Neo4j 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 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 General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see .
 */
package org.neo4j.gds.similarity.knn.metrics;

/**
 * Here we compute Pearson correlation coefficient and turn that into a metric.
 *
 * We use the formula from https://en.wikipedia.org/wiki/Pearson_correlation_coefficient#For_a_sample for the Pearson
 * computation.
 *
 * If input arrays are of different length we ignore the longer tail.
 *
 * In the end we turn Pearson's r into a metric moving it to the range 0..1
 */
public final class Pearson {
    private Pearson() {}

    public static double floatMetric(float[] a, float[] b) {
        int n = Math.min(a.length, b.length);

        // compute sample means
        double sumA = 0d;
        double sumB = 0d;
        for (int i = 0; i < n; i++) {
            sumA += a[i];
            sumB += b[i];
        }
        double meanA = sumA / n;
        double meanB = sumB / n;

        // compute sums
        double sumOfProductOfADeltaBDelta = 0d;
        double sumOfADeltaSquared = 0d;
        double sumOfBDeltaSquared = 0d;
        for (int i = 0; i < n; i++) {
            double aDelta = a[i] - meanA;
            double bDelta = b[i] - meanB;

            sumOfProductOfADeltaBDelta += aDelta * bDelta;
            sumOfADeltaSquared += aDelta * aDelta;
            sumOfBDeltaSquared += bDelta * bDelta;
        }

        // final formula
        double r = sumOfProductOfADeltaBDelta/ (Math.sqrt(sumOfADeltaSquared * sumOfBDeltaSquared));

        // now turn it into a metric; Pearson's r is in the range -1..1 and we want to land it in 0..1
        return (r+1)/ 2;
    }

    public static double doubleMetric(double[] a, double[] b) {
        int n = Math.min(a.length, b.length);

        // compute sample means
        double sumA = 0d;
        double sumB = 0d;
        for (int i = 0; i < n; i++) {
            sumA += a[i];
            sumB += b[i];
        }
        double meanA = sumA / n;
        double meanB = sumB / n;

        // compute sums
        double sumOfProductOfADeltaBDelta = 0d;
        double sumOfADeltaSquared = 0d;
        double sumOfBDeltaSquared = 0d;
        for (int i = 0; i < n; i++) {
            double aDelta = a[i] - meanA;
            double bDelta = b[i] - meanB;

            sumOfProductOfADeltaBDelta += aDelta * bDelta;
            sumOfADeltaSquared += aDelta * aDelta;
            sumOfBDeltaSquared += bDelta * bDelta;
        }

        // final formula
        double r = sumOfProductOfADeltaBDelta/ (Math.sqrt(sumOfADeltaSquared * sumOfBDeltaSquared));

        // now turn it into a metric; Pearson's r is in the range -1..1 and we want to land it in 0..1
        return (r+1)/ 2;
    }
}