classapp.c

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/*====================================================================*
 -  Copyright (C) 2001 Leptonica.  All rights reserved.
 -
 -  Redistribution and use in source and binary forms, with or without
 -  modification, are permitted provided that the following conditions
 -  are met:
 -  1. Redistributions of source code must retain the above copyright
 -     notice, this list of conditions and the following disclaimer.
 -  2. Redistributions in binary form must reproduce the above
 -     copyright notice, this list of conditions and the following
 -     disclaimer in the documentation and/or other materials
 -     provided with the distribution.
 -
 -  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 -  ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 -  LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
 -  A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL ANY
 -  CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
 -  EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
 -  PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
 -  PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
 -  OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
 -  NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 -  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 *====================================================================*/

#include <string.h>
#include "allheaders.h"

static const l_int32 L_BUF_SIZE = 512;        
static const l_int32 JB_WORDS_MIN_WIDTH = 5;  
static const l_int32 JB_WORDS_MIN_HEIGHT = 3; 
    /* Static comparison functions */
static l_int32 testLineAlignmentX(NUMA *na1, NUMA *na2, l_int32 shiftx,
                                  l_int32 delx, l_int32 nperline);
static l_int32 countAlignedMatches(NUMA *nai1, NUMA *nai2, NUMA *nasx,
                                   NUMA *nasy, l_int32 n1, l_int32 n2,
                                   l_int32 delx, l_int32 dely,
                                   l_int32 nreq, l_int32 *psame,
                                   l_int32 debugflag);
static void printRowIndices(l_int32 *index1, l_int32 n1,
                            l_int32 *index2, l_int32 n2);


/*------------------------------------------------------------------*
 *          Top-level jb2 correlation and rank-hausdorff            *
 *------------------------------------------------------------------*/
l_int32
jbCorrelation(const char  *dirin,
              l_float32    thresh,
              l_float32    weight,
              l_int32      components,
              const char  *rootname,
              l_int32      firstpage,
              l_int32      npages,
              l_int32      renderflag)
{
char        filename[L_BUF_SIZE];
l_int32     nfiles, i, numpages;
JBDATA     *data;
JBCLASSER  *classer;
PIX        *pix;
PIXA       *pixa;
SARRAY     *safiles;

    PROCNAME("jbCorrelation");

    if (!dirin)
        return ERROR_INT("dirin not defined", procName, 1);
    if (!rootname)
        return ERROR_INT("rootname not defined", procName, 1);
    if (components != JB_CONN_COMPS && components != JB_CHARACTERS &&
        components != JB_WORDS)
        return ERROR_INT("components invalid", procName, 1);

    safiles = getSortedPathnamesInDirectory(dirin, NULL, firstpage, npages);
    nfiles = sarrayGetCount(safiles);

        /* Classify components */
    classer = jbCorrelationInit(components, 0, 0, thresh, weight);
    jbAddPages(classer, safiles);

        /* Save data */
    data = jbDataSave(classer);
    jbDataWrite(rootname, data);

        /* Optionally, render pages using class templates */
    if (renderflag) {
        pixa = jbDataRender(data, FALSE);
        numpages = pixaGetCount(pixa);
        if (numpages != nfiles)
            fprintf(stderr, "numpages = %d, nfiles = %d, not equal!\n",
                    numpages, nfiles);
        for (i = 0; i < numpages; i++) {
            pix = pixaGetPix(pixa, i, L_CLONE);
            snprintf(filename, L_BUF_SIZE, "%s.%04d", rootname, i);
            fprintf(stderr, "filename: %s\n", filename);
            pixWrite(filename, pix, IFF_PNG);
            pixDestroy(&pix);
        }
        pixaDestroy(&pixa);
    }

    sarrayDestroy(&safiles);
    jbClasserDestroy(&classer);
    jbDataDestroy(&data);
    return 0;
}


l_int32
jbRankHaus(const char  *dirin,
           l_int32      size,
           l_float32    rank,
           l_int32      components,
           const char  *rootname,
           l_int32      firstpage,
           l_int32      npages,
           l_int32      renderflag)
{
char        filename[L_BUF_SIZE];
l_int32     nfiles, i, numpages;
JBDATA     *data;
JBCLASSER  *classer;
PIX        *pix;
PIXA       *pixa;
SARRAY     *safiles;

    PROCNAME("jbRankHaus");

    if (!dirin)
        return ERROR_INT("dirin not defined", procName, 1);
    if (!rootname)
        return ERROR_INT("rootname not defined", procName, 1);
    if (components != JB_CONN_COMPS && components != JB_CHARACTERS &&
        components != JB_WORDS)
        return ERROR_INT("components invalid", procName, 1);

    safiles = getSortedPathnamesInDirectory(dirin, NULL, firstpage, npages);
    nfiles = sarrayGetCount(safiles);

        /* Classify components */
    classer = jbRankHausInit(components, 0, 0, size, rank);
    jbAddPages(classer, safiles);

        /* Save data */
    data = jbDataSave(classer);
    jbDataWrite(rootname, data);

        /* Optionally, render pages using class templates */
    if (renderflag) {
        pixa = jbDataRender(data, FALSE);
        numpages = pixaGetCount(pixa);
        if (numpages != nfiles)
            fprintf(stderr, "numpages = %d, nfiles = %d, not equal!\n",
                    numpages, nfiles);
        for (i = 0; i < numpages; i++) {
            pix = pixaGetPix(pixa, i, L_CLONE);
            snprintf(filename, L_BUF_SIZE, "%s.%04d", rootname, i);
            fprintf(stderr, "filename: %s\n", filename);
            pixWrite(filename, pix, IFF_PNG);
            pixDestroy(&pix);
        }
        pixaDestroy(&pixa);
    }

    sarrayDestroy(&safiles);
    jbClasserDestroy(&classer);
    jbDataDestroy(&data);
    return 0;
}



/*------------------------------------------------------------------*
 *           Extract and classify words in textline order           *
 *------------------------------------------------------------------*/
JBCLASSER *
jbWordsInTextlines(const char  *dirin,
                   l_int32      reduction,
                   l_int32      maxwidth,
                   l_int32      maxheight,
                   l_float32    thresh,
                   l_float32    weight,
                   NUMA       **pnatl,
                   l_int32      firstpage,
                   l_int32      npages)
{
char       *fname;
l_int32     nfiles, i, w, h;
BOXA       *boxa;
JBCLASSER  *classer;
NUMA       *nai, *natl;
PIX        *pix1, *pix2;
PIXA       *pixa;
SARRAY     *safiles;

    PROCNAME("jbWordsInTextlines");

    if (!pnatl)
        return (JBCLASSER *)ERROR_PTR("&natl not defined", procName, NULL);
    *pnatl = NULL;
    if (!dirin)
        return (JBCLASSER *)ERROR_PTR("dirin not defined", procName, NULL);
    if (reduction != 1 && reduction != 2)
        return (JBCLASSER *)ERROR_PTR("reduction not in {1,2}", procName, NULL);

    safiles = getSortedPathnamesInDirectory(dirin, NULL, firstpage, npages);
    nfiles = sarrayGetCount(safiles);

        /* Classify components */
    classer = jbCorrelationInit(JB_WORDS, maxwidth, maxheight, thresh, weight);
    classer->safiles = sarrayCopy(safiles);
    natl = numaCreate(0);
    *pnatl = natl;
    for (i = 0; i < nfiles; i++) {
        fname = sarrayGetString(safiles, i, L_NOCOPY);
        if ((pix1 = pixRead(fname)) == NULL) {
            L_WARNING("image file %d not read\n", procName, i);
            continue;
        }
        if (reduction == 1)
            pix2 = pixClone(pix1);
        else  /* reduction == 2 */
            pix2 = pixReduceRankBinaryCascade(pix1, 1, 0, 0, 0);
        pixGetWordsInTextlines(pix2, JB_WORDS_MIN_WIDTH,
                               JB_WORDS_MIN_HEIGHT, maxwidth, maxheight,
                               &boxa, &pixa, &nai);
        pixGetDimensions(pix2, &w, &h, NULL);
        classer->w = w;
        classer->h = h;
        jbAddPageComponents(classer, pix2, boxa, pixa);
        numaJoin(natl, nai, 0, -1);
        pixDestroy(&pix1);
        pixDestroy(&pix2);
        numaDestroy(&nai);
        boxaDestroy(&boxa);
        pixaDestroy(&pixa);
    }

    sarrayDestroy(&safiles);
    return classer;
}


l_int32
pixGetWordsInTextlines(PIX     *pixs,
                       l_int32  minwidth,
                       l_int32  minheight,
                       l_int32  maxwidth,
                       l_int32  maxheight,
                       BOXA   **pboxad,
                       PIXA   **ppixad,
                       NUMA   **pnai)
{
BOXA    *boxa1, *boxad;
BOXAA   *baa;
NUMA    *nai;
NUMAA   *naa;
PIXA    *pixa1, *pixad;
PIXAA   *paa;

    PROCNAME("pixGetWordsInTextlines");

    if (!pboxad || !ppixad || !pnai)
        return ERROR_INT("&boxad, &pixad, &nai not all defined", procName, 1);
    *pboxad = NULL;
    *ppixad = NULL;
    *pnai = NULL;
    if (!pixs)
        return ERROR_INT("pixs not defined", procName, 1);

        /* Get the bounding boxes of the words from the word mask. */
    pixWordBoxesByDilation(pixs, minwidth, minheight, maxwidth, maxheight,
                           &boxa1, NULL, NULL);

        /* Generate a pixa of the word images */
    pixa1 = pixaCreateFromBoxa(pixs, boxa1, NULL);  /* mask over each word */

        /* Sort the bounding boxes of these words by line.  We use the
         * index mapping to allow identical sorting of the pixa. */
    baa = boxaSort2d(boxa1, &naa, -1, -1, 4);
    paa = pixaSort2dByIndex(pixa1, naa, L_CLONE);

        /* Flatten the word paa */
    pixad = pixaaFlattenToPixa(paa, &nai, L_CLONE);
    boxad = pixaGetBoxa(pixad, L_COPY);

    *pnai = nai;
    *pboxad = boxad;
    *ppixad = pixad;

    pixaDestroy(&pixa1);
    boxaDestroy(&boxa1);
    boxaaDestroy(&baa);
    pixaaDestroy(&paa);
    numaaDestroy(&naa);
    return 0;
}


l_int32
pixGetWordBoxesInTextlines(PIX     *pixs,
                           l_int32  minwidth,
                           l_int32  minheight,
                           l_int32  maxwidth,
                           l_int32  maxheight,
                           BOXA   **pboxad,
                           NUMA   **pnai)
{
BOXA    *boxa1;
BOXAA   *baa;
NUMA    *nai;

    PROCNAME("pixGetWordBoxesInTextlines");

    if (pnai) *pnai = NULL;
    if (!pboxad)
        return ERROR_INT("&boxad and &nai not both defined", procName, 1);
    *pboxad = NULL;
    if (!pixs)
        return ERROR_INT("pixs not defined", procName, 1);

        /* Get the bounding boxes of the words from the word mask. */
    pixWordBoxesByDilation(pixs, minwidth, minheight, maxwidth, maxheight,
                           &boxa1, NULL, NULL);

        /* 2D sort the bounding boxes of these words. */
    baa = boxaSort2d(boxa1, NULL, 3, -5, 5);

        /* Flatten the boxaa, saving the boxa index for each box */
    *pboxad = boxaaFlattenToBoxa(baa, &nai, L_CLONE);

    if (pnai)
        *pnai = nai;
    else
        numaDestroy(&nai);
    boxaDestroy(&boxa1);
    boxaaDestroy(&baa);
    return 0;
}


/*------------------------------------------------------------------*
 *           Use word bounding boxes to compare page images         *
 *------------------------------------------------------------------*/
NUMAA *
boxaExtractSortedPattern(BOXA  *boxa,
                         NUMA  *na)
{
l_int32  index, nbox, row, prevrow, x, y, w, h;
BOX     *box;
NUMA    *nad;
NUMAA   *naa;

    PROCNAME("boxaExtractSortedPattern");

    if (!boxa)
        return (NUMAA *)ERROR_PTR("boxa not defined", procName, NULL);
    if (!na)
        return (NUMAA *)ERROR_PTR("na not defined", procName, NULL);

    naa = numaaCreate(0);
    nbox = boxaGetCount(boxa);
    if (nbox == 0)
        return naa;

    prevrow = -1;
    for (index = 0; index < nbox; index++) {
        box = boxaGetBox(boxa, index, L_CLONE);
        numaGetIValue(na, index, &row);
        if (row > prevrow) {
            if (index > 0)
                numaaAddNuma(naa, nad, L_INSERT);
            nad = numaCreate(0);
            prevrow = row;
            boxGetGeometry(box, NULL, &y, NULL, &h);
            numaAddNumber(nad, y + h / 2);
        }
        boxGetGeometry(box, &x, NULL, &w, NULL);
        numaAddNumber(nad, x);
        numaAddNumber(nad, x + w - 1);
        boxDestroy(&box);
    }
    numaaAddNuma(naa, nad, L_INSERT);

    return naa;
}


l_int32
numaaCompareImagesByBoxes(NUMAA    *naa1,
                          NUMAA    *naa2,
                          l_int32   nperline,
                          l_int32   nreq,
                          l_int32   maxshiftx,
                          l_int32   maxshifty,
                          l_int32   delx,
                          l_int32   dely,
                          l_int32  *psame,
                          l_int32   debugflag)
{
l_int32   n1, n2, i, j, nbox, y1, y2, xl1, xl2;
l_int32   shiftx, shifty, match;
l_int32  *line1, *line2;  /* indicator for sufficient boxes in a line */
l_int32  *yloc1, *yloc2;  /* arrays of y value for first box in a line */
l_int32  *xleft1, *xleft2;  /* arrays of x value for left side of first box */
NUMA     *na1, *na2, *nai1, *nai2, *nasx, *nasy;

    PROCNAME("numaaCompareImagesByBoxes");

    if (!psame)
        return ERROR_INT("&same not defined", procName, 1);
    *psame = 0;
    if (!naa1)
        return ERROR_INT("naa1 not defined", procName, 1);
    if (!naa2)
        return ERROR_INT("naa2 not defined", procName, 1);
    if (nperline < 1)
        return ERROR_INT("nperline < 1", procName, 1);
    if (nreq < 1)
        return ERROR_INT("nreq < 1", procName, 1);

    n1 = numaaGetCount(naa1);
    n2 = numaaGetCount(naa2);
    if (n1 < nreq || n2 < nreq)
        return 0;

        /* Find the lines in naa1 and naa2 with sufficient boxes.
         * Also, find the y-values for each of the lines, and the
         * LH x-values of the first box in each line. */
    line1 = (l_int32 *)LEPT_CALLOC(n1, sizeof(l_int32));
    line2 = (l_int32 *)LEPT_CALLOC(n2, sizeof(l_int32));
    yloc1 = (l_int32 *)LEPT_CALLOC(n1, sizeof(l_int32));
    yloc2 = (l_int32 *)LEPT_CALLOC(n2, sizeof(l_int32));
    xleft1 = (l_int32 *)LEPT_CALLOC(n1, sizeof(l_int32));
    xleft2 = (l_int32 *)LEPT_CALLOC(n2, sizeof(l_int32));
    if (!line1 || !line2 || !yloc1 || !yloc2 || !xleft1 || !xleft2)
        return ERROR_INT("callof failure for an array", procName, 1);
    for (i = 0; i < n1; i++) {
        na1 = numaaGetNuma(naa1, i, L_CLONE);
        numaGetIValue(na1, 0, yloc1 + i);
        numaGetIValue(na1, 1, xleft1 + i);
        nbox = (numaGetCount(na1) - 1) / 2;
        if (nbox >= nperline)
            line1[i] = 1;
        numaDestroy(&na1);
    }
    for (i = 0; i < n2; i++) {
        na2 = numaaGetNuma(naa2, i, L_CLONE);
        numaGetIValue(na2, 0, yloc2 + i);
        numaGetIValue(na2, 1, xleft2 + i);
        nbox = (numaGetCount(na2) - 1) / 2;
        if (nbox >= nperline)
            line2[i] = 1;
        numaDestroy(&na2);
    }

        /* Enumerate all possible line matches.  A 'possible' line
         * match is one where the x and y shifts for the first box
         * in each line are within the maxshiftx and maxshifty
         * constraints, and the left and right sides of the remaining
         * (nperline - 1) successive boxes are within delx of each other.
         * The result is a set of four numas giving parameters of
         * each set of matching lines. */
    nai1 = numaCreate(0);  /* line index 1 of match */
    nai2 = numaCreate(0);  /* line index 2 of match */
    nasx = numaCreate(0);  /* shiftx for match */
    nasy = numaCreate(0);  /* shifty for match */
    for (i = 0; i < n1; i++) {
        if (line1[i] == 0) continue;
        y1 = yloc1[i];
        xl1 = xleft1[i];
        na1 = numaaGetNuma(naa1, i, L_CLONE);
        for (j = 0; j < n2; j++) {
            if (line2[j] == 0) continue;
            y2 = yloc2[j];
            if (L_ABS(y1 - y2) > maxshifty) continue;
            xl2 = xleft2[j];
            if (L_ABS(xl1 - xl2) > maxshiftx) continue;
            shiftx = xl1 - xl2;  /* shift to add to x2 values */
            shifty = y1 - y2;  /* shift to add to y2 values */
            na2 = numaaGetNuma(naa2, j, L_CLONE);

                /* Now check if 'nperline' boxes in the two lines match */
            match = testLineAlignmentX(na1, na2, shiftx, delx, nperline);
            if (match) {
                numaAddNumber(nai1, i);
                numaAddNumber(nai2, j);
                numaAddNumber(nasx, shiftx);
                numaAddNumber(nasy, shifty);
            }
            numaDestroy(&na2);
        }
        numaDestroy(&na1);
    }

        /* Determine if there are a sufficient number of mutually
         * aligned matches.  Mutually aligned matches place an additional
         * constraint on the 'possible' matches, where the relative
         * shifts must not exceed the (delx, dely) distances. */
    countAlignedMatches(nai1, nai2, nasx, nasy, n1, n2, delx, dely,
                        nreq, psame, debugflag);

    LEPT_FREE(line1);
    LEPT_FREE(line2);
    LEPT_FREE(yloc1);
    LEPT_FREE(yloc2);
    LEPT_FREE(xleft1);
    LEPT_FREE(xleft2);
    numaDestroy(&nai1);
    numaDestroy(&nai2);
    numaDestroy(&nasx);
    numaDestroy(&nasy);
    return 0;
}


static l_int32
testLineAlignmentX(NUMA    *na1,
                   NUMA    *na2,
                   l_int32  shiftx,
                   l_int32  delx,
                   l_int32  nperline)
{
l_int32  i, xl1, xr1, xl2, xr2, diffl, diffr;

    PROCNAME("testLineAlignmentX");

    if (!na1)
        return ERROR_INT("na1 not defined", procName, 1);
    if (!na2)
        return ERROR_INT("na2 not defined", procName, 1);

    for (i = 0; i < nperline; i++) {
        numaGetIValue(na1, i + 1, &xl1);
        numaGetIValue(na1, i + 2, &xr1);
        numaGetIValue(na2, i + 1, &xl2);
        numaGetIValue(na2, i + 2, &xr2);
        diffl = L_ABS(xl1 - xl2 - shiftx);
        diffr = L_ABS(xr1 - xr2 - shiftx);
        if (diffl > delx || diffr > delx)
            return 0;
    }

    return 1;
}


/*
 *  countAlignedMatches()
 *      Input:  nai1, nai2 (numas of row pairs for matches)
 *              nasx, nasy (numas of x and y shifts for the matches)
 *              n1, n2 (number of rows in images 1 and 2)
 *              delx, dely (allowed difference in shifts of the match,
 *                          compared to the reference match)
 *              nreq (number of required aligned matches)
 *              &same (<return> 1 if %nreq row matches are found; 0 otherwise)
 *      Return: 0 if OK, 1 on error
 *
 *  Notes:
 *      (1) This takes 4 input arrays giving parameters of all the
 *          line matches.  It looks for the maximum set of aligned
 *          matches (matches with approximately the same overall shifts)
 *          that do not use rows from either image more than once.
 */
static l_int32
countAlignedMatches(NUMA     *nai1,
                    NUMA     *nai2,
                    NUMA     *nasx,
                    NUMA     *nasy,
                    l_int32   n1,
                    l_int32   n2,
                    l_int32   delx,
                    l_int32   dely,
                    l_int32   nreq,
                    l_int32  *psame,
                    l_int32   debugflag)
{
l_int32   i, j, nm, shiftx, shifty, nmatch, diffx, diffy;
l_int32  *ia1, *ia2, *iasx, *iasy, *index1, *index2;

    PROCNAME("countAlignedMatches");

    if (!nai1 || !nai2 || !nasx || !nasy)
        return ERROR_INT("4 input numas not defined", procName, 1);
    if (!psame)
        return ERROR_INT("&same not defined", procName, 1);
    *psame = 0;

        /* Check for sufficient aligned matches, doing a double iteration
         * over the set of raw matches.  The row index arrays
         * are used to verify that the same rows in either image
         * are not used in more than one match.  Whenever there
         * is a match that is properly aligned, those rows are
         * marked in the index arrays.  */
    nm = numaGetCount(nai1);  /* number of matches */
    if (nm < nreq)
        return 0;

    ia1 = numaGetIArray(nai1);
    ia2 = numaGetIArray(nai2);
    iasx = numaGetIArray(nasx);
    iasy = numaGetIArray(nasy);
    index1 = (l_int32 *)LEPT_CALLOC(n1, sizeof(l_int32));  /* watch rows */
    index2 = (l_int32 *)LEPT_CALLOC(n2, sizeof(l_int32));
    if (!index1 || !index2)
        return ERROR_INT("calloc fail for array", procName, 1);
    for (i = 0; i < nm; i++) {
        if (*psame == 1)
            break;

            /* Reset row index arrays */
        memset(index1, 0, 4 * n1);
        memset(index2, 0, 4 * n2);
        nmatch = 1;
        index1[ia1[i]] = nmatch;  /* mark these rows as taken */
        index2[ia2[i]] = nmatch;
        shiftx = iasx[i];  /* reference shift between two rows */
        shifty = iasy[i];  /* ditto */
        if (nreq == 1) {
            *psame = 1;
            break;
        }
        for (j = 0; j < nm; j++) {
            if (j == i) continue;
                /* Rows must both be different from any previously seen */
            if (index1[ia1[j]] > 0 || index2[ia2[j]] > 0) continue;
                /* Check the shift for this match */
            diffx = L_ABS(shiftx - iasx[j]);
            diffy = L_ABS(shifty - iasy[j]);
            if (diffx > delx || diffy > dely) continue;
                /* We have a match */
            nmatch++;
            index1[ia1[j]] = nmatch;  /* mark the rows */
            index2[ia2[j]] = nmatch;
            if (nmatch >= nreq) {
                *psame = 1;
                if (debugflag)
                    printRowIndices(index1, n1, index2, n2);
                break;
            }
        }
    }

    LEPT_FREE(ia1);
    LEPT_FREE(ia2);
    LEPT_FREE(iasx);
    LEPT_FREE(iasy);
    LEPT_FREE(index1);
    LEPT_FREE(index2);
    return 0;
}


static void
printRowIndices(l_int32  *index1,
                l_int32   n1,
                l_int32  *index2,
                l_int32   n2)
{
l_int32  i;

    fprintf(stderr, "Index1: ");
    for (i = 0; i < n1; i++) {
        if (i && (i % 20 == 0))
            fprintf(stderr, "\n        ");
        fprintf(stderr, "%3d", index1[i]);
    }
    fprintf(stderr, "\n");

    fprintf(stderr, "Index2: ");
    for (i = 0; i < n2; i++) {
        if (i && (i % 20 == 0))
            fprintf(stderr, "\n        ");
        fprintf(stderr, "%3d", index2[i]);
    }
    fprintf(stderr, "\n");
    return;
}