durbins.c

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#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "local_proto.h"


/* could probably use some cleanup/optimization */
double *durbins_exact(double *x, int n)
{
    static double y[2];
    double *xcopy, sumx = 0.0, sumx2 = 0.0, s2, *b, *c, *g, *z, sqrt2;
    int i, j;

    if ((b = (double *)malloc(n * sizeof(double))) == NULL) {
        fprintf(stderr, "Memory error in durbins_exact\n");
        exit(EXIT_FAILURE);
    }
    if ((c = (double *)malloc((n + 1) * sizeof(double))) == NULL) {
        fprintf(stderr, "Memory error in durbins_exact\n");
        exit(EXIT_FAILURE);
    }
    if ((g = (double *)malloc((n + 1) * sizeof(double))) == NULL) {
        fprintf(stderr, "Memory error in durbins_exact\n");
        exit(EXIT_FAILURE);
    }
    if ((z = (double *)malloc(n * sizeof(double))) == NULL) {
        fprintf(stderr, "Memory error in durbins_exact\n");
        exit(EXIT_FAILURE);
    }
    if ((xcopy = (double *)malloc(n * sizeof(double))) == NULL) {
        fprintf(stderr, "Memory error in durbins_exact\n");
        exit(EXIT_FAILURE);
    }

    sqrt2 = sqrt((double)2.0);
    for (i = 0; i < n; ++i) {
        xcopy[i] = x[i];
        sumx += x[i];
        sumx2 += x[i] * x[i];
    }

    s2 = sqrt((sumx2 - sumx * sumx / n) / (n - 1));
    for (i = 0; i < n; ++i) {
        xcopy[i] = (xcopy[i] - sumx / n) / s2;
        b[i] = 0.5 + normp(xcopy[i] / sqrt2) / 2.0;
    }

    qsort(b, n, sizeof(double), dcmp);

    for (i = 1; i < n; ++i)
        c[i] = b[i] - b[i - 1];

    c[0] = b[0];
    c[n] = 1 - b[n - 1];

    qsort(c, n + 1, sizeof(double), dcmp);

    for (j = 1; j <= n; ++j)
        g[j] = (n + 1 - j) * (c[j] - c[j - 1]);

    g[0] = (n + 1) * c[0];
    g[n] = c[n] - c[n - 1];

    for (i = 0; i < n; ++i) {
        z[i] = 0.0;
        for (j = 0; j <= i; ++j)
            z[i] += g[j];

        z[i] = (i + 1.0) / n - z[i];
    }

    qsort(z, n, sizeof(double), dcmp);

    y[0] = z[n - 1];
    y[1] = sqrt((double)n) * z[n - 1];

#ifdef NOISY
    fprintf(stdout, "  TEST7  DRB(N) =%10.4f\n", y[0]);
#endif /* NOISY */

    free(b);
    free(c);
    free(g);
    free(xcopy);
    free(z);

    return y;
}