Java Code Examples for org.apache.commons.math3.util.CombinatoricsUtils#combinationsIterator()

/**
 * Computes \(P(D_{n,m} > d)\) if {@code strict} is {@code true}; otherwise \(P(D_{n,m} \ge
 * d)\), where \(D_{n,m}\) is the 2-sample Kolmogorov-Smirnov statistic. See
 * {@link #kolmogorovSmirnovStatistic(double[], double[])} for the definition of \(D_{n,m}\).
 * <p>
 * The returned probability is exact, obtained by enumerating all partitions of {@code m + n}
 * into {@code m} and {@code n} sets, computing \(D_{n,m}\) for each partition and counting the
 * number of partitions that yield \(D_{n,m}\) values exceeding (resp. greater than or equal to)
 * {@code d}.
 * </p>
 * <p>
 * <strong>USAGE NOTE</strong>: Since this method enumerates all combinations in \({m+n} \choose
 * {n}\), it is very slow if called for large {@code m, n}. For this reason,
 * {@link #kolmogorovSmirnovTest(double[], double[])} uses this only for {@code m * n < }
 * {@value #SMALL_SAMPLE_PRODUCT}.
 * </p>
 *
 * @param d D-statistic value
 * @param n first sample size
 * @param m second sample size
 * @param strict whether or not the probability to compute is expressed as a strict inequality
 * @return probability that a randomly selected m-n partition of m + n generates \(D_{n,m}\)
 *         greater than (resp. greater than or equal to) {@code d}
 */
public double exactP(double d, int n, int m, boolean strict) {
    Iterator<int[]> combinationsIterator = CombinatoricsUtils.combinationsIterator(n + m, n);
    long tail = 0;
    final double[] nSet = new double[n];
    final double[] mSet = new double[m];
    while (combinationsIterator.hasNext()) {
        // Generate an n-set
        final int[] nSetI = combinationsIterator.next();
        // Copy the n-set to nSet and its complement to mSet
        int j = 0;
        int k = 0;
        for (int i = 0; i < n + m; i++) {
            if (j < n && nSetI[j] == i) {
                nSet[j++] = i;
            } else {
                mSet[k++] = i;
            }
        }
        final double curD = kolmogorovSmirnovStatistic(nSet, mSet);
        if (curD > d) {
            tail++;
        } else if (curD == d && !strict) {
            tail++;
        }
    }
    return (double) tail / (double) CombinatoricsUtils.binomialCoefficient(n + m, n);
}
 

/**
 * Computes \(P(D_{n,m} > d)\) if {@code strict} is {@code true}; otherwise \(P(D_{n,m} \ge
 * d)\), where \(D_{n,m}\) is the 2-sample Kolmogorov-Smirnov statistic. See
 * {@link #kolmogorovSmirnovStatistic(double[], double[])} for the definition of \(D_{n,m}\).
 * <p>
 * The returned probability is exact, obtained by enumerating all partitions of {@code m + n}
 * into {@code m} and {@code n} sets, computing \(D_{n,m}\) for each partition and counting the
 * number of partitions that yield \(D_{n,m}\) values exceeding (resp. greater than or equal to)
 * {@code d}.
 * </p>
 * <p>
 * <strong>USAGE NOTE</strong>: Since this method enumerates all combinations in \({m+n} \choose
 * {n}\), it is very slow if called for large {@code m, n}. For this reason,
 * {@link #kolmogorovSmirnovTest(double[], double[])} uses this only for {@code m * n < }
 * {@value #SMALL_SAMPLE_PRODUCT}.
 * </p>
 *
 * @param d D-statistic value
 * @param n first sample size
 * @param m second sample size
 * @param strict whether or not the probability to compute is expressed as a strict inequality
 * @return probability that a randomly selected m-n partition of m + n generates \(D_{n,m}\)
 *         greater than (resp. greater than or equal to) {@code d}
 */
public double exactP(double d, int n, int m, boolean strict) {
    Iterator<int[]> combinationsIterator = CombinatoricsUtils.combinationsIterator(n + m, n);
    long tail = 0;
    final double[] nSet = new double[n];
    final double[] mSet = new double[m];
    while (combinationsIterator.hasNext()) {
        // Generate an n-set
        final int[] nSetI = combinationsIterator.next();
        // Copy the n-set to nSet and its complement to mSet
        int j = 0;
        int k = 0;
        for (int i = 0; i < n + m; i++) {
            if (j < n && nSetI[j] == i) {
                nSet[j++] = i;
            } else {
                mSet[k++] = i;
            }
        }
        final double curD = kolmogorovSmirnovStatistic(nSet, mSet);
        if (curD > d) {
            tail++;
        } else if (curD == d && !strict) {
            tail++;
        }
    }
    return (double) tail / (double) CombinatoricsUtils.binomialCoefficient(n + m, n);
}
 

/** 
 * Print all combinations of r elements from a set
 * @param n - number of elements in set
 * @param r - number of elements in selection
 */
public static void generate(int n, int r) {
    Iterator<int[]> iterator = CombinatoricsUtils.combinationsIterator(n, r);
    while (iterator.hasNext()) {
        final int[] combination = iterator.next();
        System.out.println(Arrays.toString(combination));
    }
}