class.c

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/* functions to classify sorted arrays of doubles and fill a vector of classbreaks */

#include <grass/glocale.h>
#include <grass/arraystats.h>

double class_apply_algorithm(char *algo, double *data, int nrec, int *nbreaks,
                             double *classbreaks)
{
    double finfo = 0.0;

    if (G_strcasecmp(algo, "int") == 0)
        finfo = class_interval(data, nrec, *nbreaks, classbreaks);
    else if (G_strcasecmp(algo, "std") == 0)
        finfo = class_stdev(data, nrec, *nbreaks, classbreaks);
    else if (G_strcasecmp(algo, "qua") == 0)
        finfo = class_quant(data, nrec, *nbreaks, classbreaks);
    else if (G_strcasecmp(algo, "equ") == 0)
        finfo = class_equiprob(data, nrec, nbreaks, classbreaks);
    else if (G_strcasecmp(algo, "dis") == 0)
            /*  finfo = class_discont(data, nrec, *nbreaks, classbreaks); disabled because of bugs */
        G_fatal_error(_("Discont algorithm currently not available because of bugs"));
    else
        G_fatal_error(_("%s: Unknown algorithm"), algo);

    if (finfo == 0)
        G_fatal_error(_("%s: Error in classification algorithm"), algo);

    return finfo;
}

int class_interval(double *data, int count, int nbreaks, double *classbreaks)
{
    double min, max;
    double step;
    int i = 0;

    min = data[0];
    max = data[count - 1];

    step = (max - min) / (nbreaks + 1);

    for (i = 0; i < nbreaks; i++)
        classbreaks[i] = min + (step * (i + 1));

    return (1);
}

double class_stdev(double *data, int count, int nbreaks, double *classbreaks)
{
    struct GASTATS stats;
    int i;
    int nbclass;
    double scale = 1.0;

    basic_stats(data, count, &stats);

    nbclass = nbreaks + 1;

    if (nbclass % 2 == 1) {     /* number of classes is uneven so we center middle class on mean */

        /* find appropriate fraction of stdev for step */
        i = 1;
        while (i) {
            if (((stats.mean + stats.stdev * scale / 2) +
                 (stats.stdev * scale * (nbclass / 2 - 1)) > stats.max) ||
                ((stats.mean - stats.stdev * scale / 2) -
                 (stats.stdev * scale * (nbclass / 2 - 1)) < stats.min))
                scale = scale / 2;
            else
                i = 0;
        }

        /* classbreaks below the mean */
        for (i = 0; i < nbreaks / 2; i++)
            classbreaks[i] =
                (stats.mean - stats.stdev * scale / 2) -
                stats.stdev * scale * (nbreaks / 2 - (i + 1));
        /* classbreaks above the mean */
        for (i = i; i < nbreaks; i++)
            classbreaks[i] =
                (stats.mean + stats.stdev * scale / 2) +
                stats.stdev * scale * (i - nbreaks / 2);

    }
    else {                      /* number of classes is even so mean is a classbreak */

        /* decide whether to use 1*stdev or 0.5*stdev as step */
        i = 1;
        while (i) {
            if (((stats.mean) + (stats.stdev * scale * (nbclass / 2 - 1)) >
                 stats.max) ||
                ((stats.mean) - (stats.stdev * scale * (nbclass / 2 - 1)) <
                 stats.min))
                scale = scale / 2;
            else
                i = 0;
        }

        /* classbreaks below the mean and on the mean */
        for (i = 0; i <= nbreaks / 2; i++)
            classbreaks[i] =
                stats.mean - stats.stdev * scale * (nbreaks / 2 - i);
        /* classbreaks above the mean */
        for (i = i; i < nbreaks; i++)
            classbreaks[i] =
                stats.mean + stats.stdev * scale * (i - nbreaks / 2);
    }

    return (scale);
}

int class_quant(double *data, int count, int nbreaks, double *classbreaks)
{
    int i, step;

    step = count / (nbreaks + 1);

    for (i = 0; i < nbreaks; i++)
        classbreaks[i] = data[step * (i + 1)];

    return (1);
}


int class_equiprob(double *data, int count, int *nbreaks, double *classbreaks)
{
    int i, j;
    double *lequi;              /*Vector of scale factors for probabilities of the normal distribution */
    struct GASTATS stats;
    int nbclass;

    nbclass = *nbreaks + 1;

    lequi = G_malloc(*nbreaks * sizeof(double));

    /*The following values come from the normal distribution and 
     * will be used as: 
     * classbreak[i] = (lequi[i] * stdev) + mean;
     */

    if (nbclass < 3) {
        lequi[0] = 0;
    }
    else if (nbclass == 3) {
        lequi[0] = -0.43076;
        lequi[1] = 0.43076;
    }
    else if (nbclass == 4) {
        lequi[0] = -0.6745;
        lequi[1] = 0;
        lequi[2] = 0.6745;
    }
    else if (nbclass == 5) {
        lequi[0] = -0.8416;
        lequi[1] = -0.2533;
        lequi[2] = 0.2533;
        lequi[3] = 0.8416;
    }
    else if (nbclass == 6) {
        lequi[0] = -0.9676;
        lequi[1] = -0.43076;
        lequi[2] = 0;
        lequi[3] = 0.43076;
        lequi[4] = 0.9676;
    }
    else if (nbclass == 7) {
        lequi[0] = -1.068;
        lequi[1] = -0.566;
        lequi[2] = -0.18;
        lequi[3] = 0.18;
        lequi[4] = 0.566;
        lequi[5] = 1.068;
    }
    else if (nbclass == 8) {
        lequi[0] = -1.1507;
        lequi[1] = -0.6745;
        lequi[2] = -0.3187;
        lequi[3] = 0;
        lequi[4] = 0.3187;
        lequi[5] = 0.6745;
        lequi[6] = 1.1507;
    }
    else if (nbclass == 9) {
        lequi[0] = -1.2208;
        lequi[1] = -0.7648;
        lequi[2] = -0.4385;
        lequi[3] = -0.1397;
        lequi[4] = 0.1397;
        lequi[5] = 0.4385;
        lequi[6] = 0.7648;
        lequi[7] = 1.2208;
    }
    else if (nbclass == 10) {
        lequi[0] = -1.28155;
        lequi[1] = -0.84162;
        lequi[2] = -0.5244;
        lequi[3] = -0.25335;
        lequi[4] = 0;
        lequi[5] = 0.25335;
        lequi[6] = 0.5244;
        lequi[7] = 0.84162;
        lequi[8] = 1.28155;
    }
    else {
        G_fatal_error
            ("Equiprobable classbreaks currently limited to 10 classes");
    }

    basic_stats(data, count, &stats);

    /*check if any of the classbreaks would fall outside of the range min-max */
    j = 0;
    for (i = 0; i < *nbreaks; i++) {
        if ((lequi[i] * stats.stdev + stats.mean) >= stats.min &&
            (lequi[i] * stats.stdev) + stats.mean <= stats.max) {
            j++;
        }
    }

    if (j < (*nbreaks)) {
        G_warning(_("There are classbreaks outside the range min-max. Number of classes reduced to %i, but using probabilities for %i classes."),
                  j + 1, *nbreaks + 1);
        G_realloc(classbreaks, j * sizeof(double));
        for (i = 0; i < j; i++)
            classbreaks[i] = 0;
    }

    j = 0;
    for (i = 0; i < *nbreaks; i++) {
        if ((lequi[i] * stats.stdev + stats.mean) >= stats.min &&
            (lequi[i] * stats.stdev) + stats.mean <= stats.max) {
            classbreaks[j] = lequi[i] * stats.stdev + stats.mean;
            j++;
        }
    }

    *nbreaks = j;

    G_free(lequi);
    return (1);
}

/* FixMe: there seems to a problem with array overflow, probably due to the fact that the code was ported from fortran which has 1-based arrays*/
double class_discont(double *data, int count, int nbreaks,
                     double *classbreaks)
{
    int *num, nbclass;
    double *no, *zz, *nz, *xn, *co;
    double *x;                  //Vecteur des observations standardisées
    int i, j, k;
    double min = 0, max = 0, rangemax = 0;
    int n = 0;
    double rangemin = 0, xlim = 0;
    double dmax = 0.0, d2 = 0.0, dd = 0.0, p = 0.0;
    int nf = 0, nmax = 0;
    double *abc;
    int nd = 0;
    double den = 0, d = 0;
    int im = 0, ji = 0;
    int tmp = 0;
    int nff = 0, jj = 0, no1 = 0, no2 = 0;
    double f = 0, xt1 = 0, xt2 = 0, chi2 = 1000.0, xnj_1 = 0, xj_1 = 0;


    /*get the number of values */
    n = count;

    nbclass = nbreaks + 1;

    num = G_malloc((nbclass + 1) * sizeof(int));
    no = G_malloc((nbclass + 1) * sizeof(double));
    zz = G_malloc((nbclass + 1) * sizeof(double));
    nz = G_malloc(3 * sizeof(double));
    xn = G_malloc((n + 1) * sizeof(double));
    co = G_malloc((nbclass + 1) * sizeof(double));

    /* We copy the array of values to x, in order to be able to standardize it */
    x = G_malloc((n + 1) * sizeof(double));
    x[0] = n;
    xn[0] = 0;

    min = data[0];
    max = data[count - 1];
    for (i = 1; i <= n; i++)
        x[i] = data[i - 1];

    rangemax = max - min;
    rangemin = rangemax;

    for (i = 2; i <= n; i++) {
        if (x[i] != x[i - 1] && x[i] - x[i - 1] < rangemin)
            rangemin = x[i] - x[i - 1]; /* rangemin = minimal distance */
    }

    /* STANDARDIZATION 
     * and creation of the number vector (xn) */

    for (i = 1; i <= n; i++) {
        x[i] = (x[i] - min) / rangemax;
        xn[i] = i / (double)n;
    }
    xlim = rangemin / rangemax;
    rangemin = rangemin / 2.0;

    /* Searching for the limits */
    num[1] = n;
    abc = G_malloc(3 * sizeof(double));

    /*     Loop through possible solutions */
    for (i = 1; i <= nbclass; i++) {
        nmax = 0;
        dmax = 0.0;
        d2 = 0.0;
        nf = 0;                 /*End number */

        /*           Loop through classes */
        for (j = 1; j <= i; j++) {
            nd = nf;            /*Start number */
            nf = num[j];
            co[j] = 10e37;
            eqdrt(x, xn, nd, nf, abc);
            den = sqrt(pow(abc[1], 2) + 1.0);
            nd++;
            /*              Loop through observations */
            for (k = nd; k <= nf; k++) {
                if (abc[2] == 0.0)
                    d = fabs((-1.0 * abc[1] * x[k]) + xn[k] - abc[0]) / den;
                else
                    d = fabs(x[k] - abc[2]);
                d2 += pow(d, 2);
                if (x[k] - x[nd] < xlim)
                    continue;
                if (x[nf] - x[k] < xlim)
                    continue;
                if (d <= dmax)
                    continue;
                dmax = d;
                nmax = k;
            }
            nd--;               /* A VERIFIER! */
            if (x[nf] != x[nd]) {
                if (nd != 0)
                    co[j] = (xn[nf] - xn[nd]) / (x[nf] - x[nd]);
                else
                    co[j] = (xn[nf]) / (x[nf]); /* A VERIFIER! */
            }
        }
        if (i == 1)
            dd = d2;
        p = d2 / dd;
        for (j = 1; j <= i; j++) {
            no[j] = num[j];
            zz[j] = x[num[j]] * rangemax + min;
            if (j == i)
                continue;
            if (co[j] > co[j + 1]) {
                zz[j] = zz[j] + rangemin;
                continue;
            }
            zz[j] = zz[j] - rangemin;
            no[j] = no[j] - 1;
        }
        im = i - 1;
        if (im != 0.0) {
            for (j = 1; j <= im; j++) {
                ji = i + 1 - j;
                no[ji] -= no[ji - 1];
            }
        }
        if (nmax == 0) {
            break;
        }
        nff = i + 2;
        tmp = 0;
        for (j = 1; j <= i; j++) {
            jj = nff - j;
            if (num[jj - 1] < nmax) {
                num[jj] = nmax;
                tmp = 1;
                break;
            }
            num[jj] = num[jj - 1];
        }
        if (tmp == 0) {
            num[1] = nmax;
            jj = 1;
        }
        if (jj == 1) {
            xnj_1 = 0;
            xj_1 = 0;
        }
        else {
            xnj_1 = xn[num[jj - 1]];
            xj_1 = x[num[jj - 1]];
        }
        no1 = (xn[num[jj]] - xnj_1) * n;
        no2 = (xn[num[jj + 1]] - xn[num[jj]]) * n;
        f = (xn[num[jj + 1]] - xnj_1) / (x[num[jj + 1]] - xj_1);
        f *= n;
        xt1 = (x[num[jj]] - xj_1) * f;
        xt2 = (x[num[jj + 1]] - x[num[jj]]) * f;
        if (xt2 == 0) {
            xt2 = rangemin / 2.0 / rangemax * f;
            xt1 -= xt2;
        }
        else if (xt1 * xt2 == 0) {
            xt1 = rangemin / 2.0 / rangemax * f;
            xt2 -= xt1;
        }

        /* calculate chi-square to indicate statistical significance of new class, i.e. how probable would it be that the new class could be the result of purely random choice */
        if (chi2 > pow((double)((no1 - no2) - (xt1 - xt2)), 2) / (xt1 + xt2))
            chi2 = pow((double)((no1 - no2) - (xt1 - xt2)), 2) / (xt1 + xt2);

    }

    /*  Fill up classbreaks of i <=nbclass classes */
    for (j = 0; j <= (i - 1); j++)
        classbreaks[j] = zz[j + 1];

    return (chi2);
}

int class_frequencies(double *data, int count, int nbreaks,
                      double *classbreaks, int *frequencies)
{
    int i, j;
    double min, max;

    min = data[0];
    max = data[count - 1];
    /* count cases in all classes, except for last class */
    i = 0;
    for (j = 0; j < nbreaks; j++) {
        while (data[i] <= classbreaks[j]) {
            frequencies[j]++;
            i++;
        }
    }

    /*Now count cases in last class */
    for (i = i; i < count; i++) {
        frequencies[nbreaks]++;
    }

    return (1);
}