Vol error

Hello,
When I used command :shutdown. show one error message:
/usr/sbin/vold[499]:problem unmounting vol: No such file or directory.
but I checked / directory, found /vol directory everything is fine.
Somebody can help me.
thanks.

A harmless error message, I'd say. Ignore it...

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    minx = 0.5((1-PADDING)*polymaxx(1PADDING)polyminx);
    maxy = 0.5(polymaxypolyminy(maxx-minx)ly/lx);
    miny = 0.5(polymaxy+polyminy-(maxx-minx)ly/lx);
    else
    maxy = 0.5((1PADDING)*polymaxy(1-PADDING)polyminy);
    miny = 0.5((1-PADDING)*polymaxy(1PADDING)polyminy);
    maxx = 0.5(polymaxxpolyminx(maxy-miny)lx/ly);
    minx = 0.5(polymaxx+polyminx-(maxy-miny)lx/ly);
    // Uncomment the next lines for interactive choice of boundary conditions.
    /* printf("For the %i polygon(s) under consideration:\n",npoly);
    printf("minimum x = %f\tmaximum x = %f\n",polyminx,polymaxx);
    printf("minimum y = %f\tmaximum y = %f\n",polyminy,polymaxy);
    while (!bnd_ok)
    printf("Type in your choice of boundaries.\nminx = ");
    scanf("%f",&minx);
    printf("maxx = ");
    scanf("%f",&maxx);
    printf("miny = ");
    scanf("%f",&miny);
    printf("maxy = ");
    scanf("%f",&maxy);
    if (minx>polyminx || maxx<polymaxx || miny>polyminy || maxy<polymaxy)
    printf("Invalid choice, does not enclose the polygon(s).\n");
    else bnd_ok = TRUE;
    // Function to read polygon corners. The first and last vertex of each polygon
    // must be identical.
    void readcorn(FILE *infile)
    char line[LINELENGTH];
    float xcoord,ycoord;
    int i,id,polyctr=0;
    polygonid = (int)malloc(npolysizeof(int));
    xstepsize = (maxx-minx)/lx;
    ystepsize = (maxy-miny)/ly;
    if (fabs((xstepsize/ystepsize)-1)>1e-3)
    fprintf(stderr,"WARNING: Area elements are not square: %f : %f\n",
    xstepsize,ystepsize);
    readline(line,infile);
    sscanf(line,"%i",&id);
    polygonid[polyctr] = id;
    i = 0;
    while (!readline(line,infile))
    if (line[0] != 'E')
    sscanf(line,"%f %f",&xcoord,&ycoord);
    polycorn[polyctr].x = (xcoord-minx)/xstepsize;
    polycorn[polyctr][i++].y = (ycoord-miny)/ystepsize;
    else
    // Is first and last vertex the same?
    if (fabs(polycorn[polyctr][0].x-
    polycorn[polyctr][npolycorn[polyctr]-1].x)+
    fabs(polycorn[polyctr][0].y-
    polycorn[polyctr][npolycorn[polyctr]-1].y)>1e-12)
    fprintf(stderr,
    "ERROR: %i-th polygon does not close upon itself.\n",
    polyctr+1);
    fprintf(stderr,"Identifier %i, first point %f %f.\n",
    polygonid[polyctr],polycorn[polyctr][0].x*xstepsize+minx,
    polycorn[polyctr][0].y*ystepsize+miny);
    exit(1);
    readline(line,infile);
    sscanf(line,"%i",&id);
    i = 0;
    polyctr++;
    if (polyctr<npoly) polygonid[polyctr] = id;
    polyminx = (polyminx-minx)/xstepsize;
    polyminy = (polyminy-miny)/ystepsize;
    polymaxx = (polymaxx-minx)/xstepsize;
    polymaxy = (polymaxy-miny)/ystepsize;
    // Function to make regions from polygons.
    void makeregion(void)
    BOOLEAN repeat;
    int i,lastid,minid,polyctr,ptctr,regctr;
    // Count the number of regions.
    nregion = 0;
    maxid = minid = polygonid[0];
    for (polyctr=0; polyctr<npoly; polyctr++)
    if (polygonid[polyctr] == -99999) continue;
    if (polygonid[polyctr]>maxid || polygonid[polyctr]<minid) nregion++;
    else
    repeat = FALSE;
    for (i=0; i<polyctr; i++)
    if (polygonid[polyctr]==polygonid)
    repeat = TRUE;
    break;
    if (!repeat) nregion++;
    if (polygonid[polyctr]>maxid) maxid = polygonid[polyctr];
    if (polygonid[polyctr]<minid) minid = polygonid[polyctr];
    if (minid < 0)
    fprintf(stderr,
    "ERROR: Negative region identifier %i.\n",minid);
    exit(1);
    // Match region identifiers.
    regionid = (int)malloc(nregionsizeof(int));
    nregion = 0;
    maxid = minid = polygonid[0];
    for (polyctr=0; polyctr<npoly; polyctr++)
    if (polygonid[polyctr] == -99999) continue;
    if (polygonid[polyctr]>maxid || polygonid[polyctr]<minid)
    regionid[nregion++] = polygonid[polyctr];
    else
    repeat = FALSE;
    for (i=0; i<polyctr; i++)
    if (polygonid[polyctr]==polygonid)
    repeat = TRUE;
    break;
    if (!repeat) regionid[nregion++] = polygonid[polyctr];
    if (polygonid[polyctr]>maxid) maxid = polygonid[polyctr];
    if (polygonid[polyctr]<minid) minid = polygonid[polyctr];
    regionidinv = (int)malloc((maxid+1)sizeof(int));
    // Negative number for unused identifiers.
    for (i=0; i<=maxid; i++) regionidinv = -1;
    for (regctr=0; regctr<nregion; regctr++)
    regionidinv[regionid[regctr]] = regctr;
    // Which polygons contribute to which regions?
    npolyinreg = (int*)calloc(nregion,sizeof(int));
    polyinreg = (int*)malloc(nregion*sizeof(int));
    lastid = polygonid[0];
    for (polyctr=0; polyctr<npoly; polyctr++)
    if (polygonid[polyctr] != -99999)
    npolyinreg[regionidinv[polygonid[polyctr]]]++;
    lastid = polygonid[polyctr];
    else npolyinreg[regionidinv[lastid]]++;
    for (regctr=0; regctr<nregion; regctr++)
    polyinreg[regctr] = (int)malloc(npolyinreg[regctr]sizeof(int));
    for (regctr=0; regctr<nregion; regctr++) npolyinreg[regctr] = 0;
    lastid = polygonid[0];
    for (polyctr=0; polyctr<npoly; polyctr++)
    if (polygonid[polyctr] != -99999)
    polyinreg[regionidinv[polygonid[polyctr]]]
    [npolyinreg[regionidinv[polygonid[polyctr]]]++] = polyctr;
    lastid = polygonid[polyctr];
    else polyinreg[regionidinv[lastid]][npolyinreg[regionidinv[lastid]]++]
    = polyctr;
    // Make regions from polygons. Start and end each polygon at (0,0).
    nregcorn = (int*)calloc(nregion,sizeof(int));
    regcorn = (POINT*)malloc(nregion*sizeof(POINT));
    for (regctr=0; regctr<nregion; regctr++)
    for (i=0; i<npolyinreg[regctr]; i++)
    nregcorn[regctr] += npolycorn[polyinreg[regctr]]+1;
    nregcorn[regctr]++;
    for (regctr=0; regctr<nregion; regctr++)
    regcorn[regctr] = (POINT)malloc(nregcorn[regctr]sizeof(POINT));
    ptctr = 0;
    regcorn[regctr][ptctr].x = regcorn[regctr][ptctr++].y = 0.0;
    for (polyctr=0; polyctr<npolyinreg[regctr]; polyctr++)
    for (i=0; i<npolycorn[polyinreg[regctr][polyctr]]; i++)
    regcorn[regctr][ptctr++] = polycorn[polyinreg[regctr][polyctr]];
    regcorn[regctr][ptctr].x = regcorn[regctr][ptctr++].y = 0.0;
    // Function to prepare a map in postscript standard letter format.
    void pspicture(FILE *outfile)
    char line[LINELENGTH];
    float addx,addy,b,conv,g,r;
    int ptctr,regctr;
    if (11*lx > 8.5*ly)
    conv = (float)8.5*72/lx;
    addx = 0;
    addy = 1136-8.5*36ly/lx;
    else
    conv = (float)11*72/ly;
    addx = 8.536-11*36lx/ly;
    addy = 0;
    fprintf(outfile,"0.5 setlinewidth\n");
    for (regctr=0; regctr<nregion; regctr++)
    fprintf(outfile,"newpath\n");
    fprintf(outfile,"%f %f moveto\n",
    regcorn[regctr][1].x*conv+addx,
    regcorn[regctr][1].y*conv+addy);
    for (ptctr=2; ptctr<nregcorn[regctr]; ptctr++)
    if (fabs(regcorn[regctr][ptctr].x)+
    fabs(regcorn[regctr][ptctr].y)>1e-12)
    fprintf(outfile,"%f %f lineto\n",
    regcorn[regctr][ptctr].x*conv+addx,
    regcorn[regctr][ptctr].y*conv+addy);
    else
    fprintf(outfile,"closepath\n");
    if (ptctr<nregcorn[regctr]-1)
    ptctr++;
    fprintf(outfile,"%f %f moveto\n",
    regcorn[regctr][ptctr].x*conv+addx,
    regcorn[regctr][ptctr].y*conv+addy);
    // Determine colors for map (without better knowledge I will do it
    // arbitrarily).
    if (regctr%3 == 0)
    r = (float)regctr/nregion;
    g = 1-(float)regctr/nregion;
    b = fabs(1-2*(float)regctr/nregion);
    else if (regctr%3 == 1)
    b = (float)regctr/nregion;
    r = 1-(float)regctr/nregion;
    g = fabs(1-2*(float)regctr/nregion);
    else
    g = (float)regctr/nregion;
    b = 1-(float)regctr/nregion;
    r = fabs(1-2*(float)regctr/nregion);
    fprintf(outfile,"%f %f %f setrgbcolor\ngsave\nfill\n",r,g,b);
    fprintf(outfile,"grestore\n0 setgray stroke\n");
    fprintf(outfile,"showpage\n");
    // Function to find the bounding box for each polygon.
    void bboxes(void)
    int i,j;
    float maxx, minx, maxy, miny;
    bbmaxx = (float)malloc(npolysizeof(float));
    bbmaxy = (float)malloc(npolysizeof(float));
    bbminx = (float)malloc(npolysizeof(float));
    bbminy = (float)malloc(npolysizeof(float));
    for (i = 0; i < npoly; i++)
    maxx = polycorn[0].x;
    maxy = polycorn[0].y;
    minx = maxx;
    miny = maxy;
    for (j = 0; j < npolycorn; j++)
    if (polycorn[j].x > maxx) maxx = polycorn[j].x;
    if (polycorn[j].x < minx) minx = polycorn[j].x;
    if (polycorn[j].y < miny) miny = polycorn[j].y;
    if (polycorn[j].y > maxy) maxy = polycorn[j].y;
    bbmaxx=maxx;
    bbmaxy=maxy;
    bbminx=minx;
    bbminy=miny;
    void interior(void)
    int i,inhowmanyregions,inregion[2],j,k,l,m,n,regctr;
    // Initialize within[][]. -1 means outside all regions.
    for (i=0; i<=lx; i++) for (j=0; j<=ly; j++) within[j] = -1;
    // Fill within[][].
    for (i=0; i<nregion; i++) for (j=0; j<npolyinreg; j++)
    for (k=0, n=npolycorn[polyinreg[j]]-1;
    k<npolycorn[polyinreg[j]]; n=k++)
    for (l=(int)ceil(MIN(polycorn[polyinreg[j]][k-1].y,
    polycorn[polyinreg[j]][k].y));
    l<MAX(polycorn[polyinreg[j]][k-1].y,
    polycorn[polyinreg[j]][k].y); l++)
    for (m=(int)floor(bbminx[polyinreg[j]]);
    m<(polycorn[polyinreg[j]][n].x-
    polycorn[polyinreg[j]][k].x)*
    (l-polycorn[polyinreg[j]][k].y)/
    (polycorn[polyinreg[j]][n].y-
    polycorn[polyinreg[j]][k].y)+
    polycorn[polyinreg[j]][k].x;
    m++)
    within[m][l] = i-within[m][l]-1;
    // Function to determine polygon area. This is needed to determine the average
    // population.
    // The problem in short is to find the area of a polygon whose vertices are
    // given. Recall Stokes' theorem in 3d for a vector field v:
    // integral[around closed curve dA]v(x,y,z).ds =
    // integral[over area A]curl(v).dA.
    // Now let v(x,y,z) = (0,Q(x,y),0) and dA = (0,0,dx*dy). Then
    // integral[around closed curve dA]Q(x,y)dy = integral[over area A]dQ/dxdxdy.
    // If Q = x:
    // A = integral[over area A]dx*dy = integral[around closed curve dA]x dy.
    // For every edge from (x,y) to (x[i1],y[i1]) there is a
    // parametrization
    // (x(t),y(t)) = ((1-t)xtx[i+1],(1-t)y+ty[i1]), 0<t<1
    // so that the path integral along this edge is
    // int[from 0 to 1]{(1-t)xt*x[i+1]}(y[i1]-y)dt =
    // 0.5(y[i1]-y)(x+x[i1]).
    // Summing over all edges yields:
    // Area = 0.5*[(x[0]+x[1])(y[1]-y[0]) + (x[1]+x[2])(y[2]-y[1]) + ...
    // ...(x[n-1]+x[n])(y[n]-y[n-1])+(x[n]x[0])(y[0]-y[n])]
    // ArcGIS treats a clockwise direction as positive, so there is a minus sign.
    double regionarea(int ncrns,POINT *polygon)
    double area=0;
    int i;
    for (i=0; i<ncrns-1; i++)
    area -=
    0.5(polygon.xpolygon[i+1].x)(polygon[i1].y-polygon.y);
    return area -= 0.5(polygon[ncrns-1].x+polygon[0].x)
    (polygon[0].y-polygon[ncrns-1].y);
    // Function to digitize density.
    void digdens(void)
    char line[LINELENGTH];
    double area,avgdens,*cases,dens,minpop=INFTY,ncases,totarea=0.0,totpop=0.0;
    FILE* infile;
    int i,id,ii,inhowmanyregions,inregion[2],j,jj,regctr;
    if ((infile=fopen(CENSUSFILE))==NULL)
    fprintf(stderr,"ERROR: Cannot find CENSUSFILE.\n");
    exit(1);
    // Find the minimum positive number of cases.
    while (!readline(line,infile))
    sscanf(line,"%i %lf",&id,&ncases);
    if (ncases<minpop && ncases>1e-12) minpop = ncases;
    fclose(infile);
    // Store the number of cases in an array.
    cases = (double)malloc(nregionsizeof(double));
    for (i=0; i<nregion; i++) cases = -1.0;
    infile = fopen(CENSUSFILE);
    while (!readline(line,infile))
    sscanf(line,"%i %lf",&id,&ncases);
    if (id>maxid || regionidinv[id]<0)
    fprintf(stderr,"ERROR: Identifier %i in CENSUSFILE does not\n",id);
    fprintf(stderr,"match any identifier in generate file.\n");
    exit(1);
    if (ncases>1e-12) totpop += (cases[regionidinv[id]] = ncases);
    else totpop += (cases[regionidinv[id]] = MINPOPFAC*minpop);
    for (regctr=0; regctr<nregion; regctr++) if (cases[regctr] < 0.0)
    fprintf(stderr,"ERROR: No density for region %i?\n",regionid[regctr]);
    fprintf(stderr,"cases = %f\n",cases[regctr]);
    exit(1);
    fclose(infile);
    // Calculate regions' areas, total area to be mapped, regional and average
    // densities.
    area = (double)malloc(nregionsizeof(double));
    for (regctr=0; regctr<nregion; regctr++)
    totarea += (area[regctr] = regionarea(nregcorn[regctr],regcorn[regctr]));
    dens = (double)malloc(nregionsizeof(double));
    for (regctr=0; regctr<nregion; regctr++)
    dens[regctr] = cases[regctr]/area[regctr];
    avgdens = totpop/totarea;
    // Digitize density.
    for (i=0; i<=lx; i++) for (j=0; j<=ly; j++) rho_0[j] = 0; // Initialize.
    printf("digitizing density ...\n");
    for (i=0; i<lx; i++) for (j=0; j<ly; j++)
    if (within[j]==-1) rho_0[j] = avgdens;
    else rho_0[j] = dens[within[j]];
    // Fill the edges correctly.
    rho_0[0][0] += rho_0[0][ly] + rho_0[lx][0] + rho_0[lx][ly];
    for (i=1; i<lx; i++) rho_0[0] += rho_0[ly];
    for (j=1; j<ly; j++) rho_0[0][j] += rho_0[lx][j];
    for (i=0; i<lx; i++) rho_0[ly] = rho_0[0];
    for (j=0; j<=ly; j++) rho_0[lx][j] = rho_0[0][j];
    // Replace rho_0 by Fourier transform
    coscosft(rho_0,1,1);
    free(area);
    free(cases);
    for (i=0; i<npoly; i++) free(polycorn);
    free(polycorn);
    for (i=0; i<nregion; i++) free(regcorn);
    free(regcorn);
    free(dens);
    free(npolycorn);
    free(nregcorn);
    free(polygonid);
    free(regionid);
    free(regionidinv);
    free(bbmaxx);
    free(bbmaxy);
    free(bbminx);
    free(bbminy);
    for (i=0; i<nregion; i++) free(polyinreg);
    free(polyinreg);
    free(npolyinreg);
    // Function to replace data[1...2*nn] by its discrete Fourier transform, if
    // isign is input as 1; or replaces data[1...2*nn] by nn times its inverse
    // discrete Fourier transform, if isign is input as -1. data is a complex array
    // of length nn or, equivalently, a real array of length 2*nn. nn MUST be an
    // integer power of 2 (this is not checked for!).
    // From "Numerical Recipes in C".
    void four1(float data[],unsigned long nn,int isign)
    double theta,wi,wpi,wpr,wr,wtemp;
    float tempi,tempr;
    unsigned long i,istep,j,m,mmax,n;
    n=nn<<1;
    j=1;
    for (i=1; i<n; i+=2)
    if (j>i)
    // This is the bit-reversal section of the routine.
    SWAP(data[j],data);
    SWAP(data[j1],data[i1]); // Exchange the two complex numbers.
    m=n>>1;
    while (m>=2 && j>m)
    j -= m;
    m>>=1;
    j += m;
    // Here begins the Danielson-Lanczos section of the routine.
    mmax=2;
    while (n>mmax) // Outer loop executed log_2 nn times.
    istep = mmax<<1;
    // Initialize the trigonometric recurrence.
    theta = isign*(6.28318530717959/mmax);
    wtemp = sin(0.5*theta);
    wpr = -2.0wtempwtemp;
    wpi = sin(theta);
    wr = 1.0;
    wi = 0.0;
    for (m=1; m<mmax; m+=2) // Here are the two nested inner loops.
    for (i=m; i<=n; i+=istep)
    j=i+mmax; // This is the Danielson-Lanczos formula
    tempr=wrdata[j]-widata[j+1];
    tempi=wrdata[j1]widata[j];
    data[j]=data-tempr;
    data[j1]=data[i1]-tempi;
    data += tempr;
    data[i+1] += tempi;
    wr = (wtemp=wr)wpr-wiwpi+wr; // Trigonometric recurrence.
    wi = wiwprwtempwpiwi;
    mmax=istep;
    // Function to calculate the Fourier Transform of a set of n real-valued data
    // points. It replaces this data (which is stored in array data[1...n]) by the
    // positive frequency half of its complex Fourier Transform. The real-valued
    // first and last components of the complex transform are returned as elements
    // data[1] and data[2] respectively. n must be a power of 2. This routine also
    // calculates the inverse transform of a complex data array if it is the
    // transform of real data. (Result in this case must be multiplied by 2/n).
    // From "Numerical Recipes in C".
    void realft(float data[],unsigned long n,int isign)
    double theta,wi,wpi,wpr,wr,wtemp;
    float c1=0.5,c2,h1i,h1r,h2i,h2r;
    unsigned long i,i1,i2,i3,i4,np3;
    theta = 3.141592653589793/(double) (n>>1); // Initialize the recurrence
    if (isign == 1)
    c2 = -0.5;
    four1(data,n>>1,1); // The forward transform is here.
    else // Otherwise set up for an inverse transform.
    c2 = 0.5;
    theta = -theta;
    wtemp = sin(0.5*theta);
    wpr = -2.0wtempwtemp;
    wpi = sin(theta);
    wr = 1.0+wpr;
    wi = wpi;
    np3 = n+3;
    for (i=2; i<=(n>>2); i++) // Case i=1 done separately below.
    i4 = 1(i3=np3-(i2=1+(i1=ii-1)));
    // The two separate transforms are separated out of data.
    h1r = c1*(data[i1]+data[i3]);
    h1i = c1*(data[i2]-data[i4]);
    h2r = -c2*(data[i2]+data[i4]);
    h2i = c2*(data[i1]-data[i3]);
    // Here they are recombined to form the true transform of the original
    // data.
    data[i1] = h1r+wrh2r-wih2i;
    data[i2] = h1iwrh2iwih2r;
    data[i3] = h1r-wrh2r+wih2i;
    data[i4] = -h1iwrh2iwih2r;
    wr = (wtemp=wr)wpr-wiwpi+wr; // The recurrence.
    wi = wiwprwtempwpiwi;
    if (isign == 1)
    data[1] = (h1r=data[1])+data[2]; // Squeeze the first and last data
    // together to get them all within the original array.
    data[2] = h1r-data[2];
    else
    data[1] = c1*((h1r=data[1])+data[2]);
    data[2] = c1*(h1r-data[2]);
    // This is the inverse transform for the case isign = -1.
    four1(data,n>>1,-1);
    // Function to calculate the cosine transform of a set z[0...n] of real-valued
    // data points. The transformed data replace the original data in array z. n
    // must be a power of 2. For forward transform set isign=1, for back transform
    // isign = -1. (Note: The factor 2/n has been taken care of.)
    // From "Numerical Recipes in C".
    void cosft(float z[],unsigned long n,int isign)
    double theta,wi=0.0,wpi,wpr,wr=1.0,wtemp;
    float *a,sum,y1,y2;
    int j,n2;
    // Numerical Recipes starts counting at 1 which is rather confusing. I will
    // count from 0.
    a = (float)malloc((n+2)sizeof(float));
    for (j=1; j<=n+1; j++) a[j] = z[j-1];
    // Here is the Numerical Recipes code.
    theta=PI/n; //Initialize the recurrence.
    wtemp = sin(0.5*theta);
    wpr = -2.0wtempwtemp;
    wpi = sin(theta);
    sum = 0.5*(a[1]-a[n+1]);
    a[1] = 0.5*(a[1]a[n1]);
    n2 = n+2;
    for (j=2; j<=(n>>1); j++)
    wr = (wtemp=wr)wpr-wiwpi+wr;
    wi = wiwprwtempwpiwi;
    y1 = 0.5*(a[j]+a[n2-j]);
    y2 = (a[j]-a[n2-j]);
    a[j] = y1-wi*y2;
    a[n2-j] = y1+wi*y2;
    sum += wr*y2;
    realft(a,n,1);
    a[n+1] = a[2];
    a[2] = sum;
    for (j=4; j<=n; j+=2)
    sum += a[j];
    a[j] = sum;
    // Finally I revert to my counting method.
    if (isign == 1) for (j=1; j<=n+1; j++) z[j-1] = a[j];
    else if (isign == -1) for (j=1; j<=n+1; j++) z[j-1] = 2.0*a[j]/n;
    free(a);
    // Function to calculate the sine transform of a set of n real-valued data
    // points stored in array z[0..n]. The number n must be a power of 2. On exit
    // z is replaced by its transform. For forward transform set isign=1, for back
    // transform isign = -1.
    void sinft(float z[],unsigned long n,int isign)
    double theta,wi=0.0,wpi,wpr,wr=1.0,wtemp;
    float *a,sum,y1,y2;
    int j;
    unsigned long n2=n+2;
    // See my comment about Numerical Recipe's counting above. Note that the last
    // component plays a completely passive role and does not need to be stored.
    a = (float*) malloc((n+1)*sizeof(float));
    for (j=1; j<=n; j++) a[j] = z[j-1];
    // Here is the Numerical Recipes code.
    theta = PI/(double)n; // Initialize the recurrence.
    wtemp = sin(0.5*theta);
    wpr = -2.0wtempwtemp;
    wpi = sin(theta);
    a[1] = 0.0;
    for (j=2; j<=(n>>1)+1; j++)
    // Calculate the sine for the auxiliary array.
    wr = (wtemp=wr)wpr-wiwpi+wr;
    // The cosine is needed to continue the recurrence.
    wi = wiwprwtempwpiwi;
    // Construct the auxiliary array.
    y1 = wi*(a[j]+a[n2-j]);
    y2 = 0.5*(a[j]-a[n2-j]);
    // Terms j and N-j are related.
    a[j] = y1+y2;
    a[n2-j] = y1-y2;
    // Transform the auxiliary array.
    realft(a,n,1);
    // Initialize the sum used for odd terms below.
    a[1] *= 0.5;
    sum = a[2] = 0.0;
    // Even terms determined directly. Odd terms determined by running sum.
    for (j=1; j<=n-1; j+=2)
    sum += a[j];
    a[j] = a[j+1];
    a[j+1] = sum;
    // Change the indices.
    if (isign == 1) for (j=1; j<=n; j++) z[j-1] = a[j];
    else if (isign == -1) for (j=1; j<=n; j++) z[j-1] = 2.0*a[j]/n;
    z[n] = 0.0;
    free(a);
    // Function to calculate a two-dimensional cosine Fourier transform. Forward/
    // backward transform in x: isign1 = +/-1, in y: isign2 = +/-1.
    void coscosft(float **y,int isign1,int isign2)
    float temp[lx+1];
    unsigned long i,j;
    for (i=0; i<=lx; i++)
    cosft(y,ly,isign2);
    for (j=0; j<=ly; j++)
    for (i=0; i<=lx; i++) temp=y[j];
    cosft(temp,lx,isign1);
    for (i=0; i<=lx; i++) y[j]=temp;
    // Function to calculate a cosine Fourier transform in x and a sine transform
    // in y. Forward/backward transform in x: isign1 = +/-1, in y: isign2 = +/-1.
    void cossinft(float **y,int isign1,int isign2)
    float temp[lx+1];
    unsigned long i,j;
    for (i=0; i<=lx; i++)
    sinft(y,ly,isign2);
    for (j=0; j<=ly; j++)
    for (i=0; i<=lx; i++) temp=y[j];
    cosft(temp,lx,isign1);
    for (i=0; i<=lx; i++) y[j]=temp;
    // Function to calculate a sine Fourier transform in x and a cosine transform
    // in y. Forward/backward transform in x: isign1 = +/-1, in y: isign2 = +/-1.
    void sincosft(float **y,int isign1,int isign2)
    float temp[lx+1];
    unsigned long i,j;
    for (i=0; i<=lx; i++)
    cosft(y,ly,isign2);
    for (j=0; j<=ly; j++)
    for (i=0; i<=lx; i++) temp=y[j];
    sinft(temp,lx,isign1);
    for (i=0; i<=lx; i++) y[j]=temp;
    // Function to allocate a float matrix with subscript range
    // m[nrl..nrh][ncl..nch]. From "Numerical Recipes in C".
    float **dmatrix(long nrl,long nrh,long ncl,long nch)
    long i, nrow=nrh-nrl1,ncol=nch-ncl1;
    float **m;
    /* allocate pointers to rows */
    m=(float **) malloc((unsigned int)((nrow+NR_END)sizeof(float)));
    if (!m)
    fprintf(stderr,"allocation failure 1 in matrix()\n");
    exit(1);
    m += NR_END;
    m -= nrl;
    /* allocate rows and set pointers to them */
    m[nrl]=(float *) malloc((unsigned int)((nrowncol+NR_END)sizeof(float)));
    if (!m[nrl])
    fprintf(stderr,"allocation failure 2 in matrix()\n");
    exit(1);
    m[nrl] += NR_END;
    m[nrl] -= ncl;
    for(i=nrl1;i<=nrh;i+) m=m[i-1]+ncol;
    /* return pointer to array of pointers to rows */
    return m;
    // Function to allocate a float 3tensor with range
    // t[nrl..nrh][ncl..nch][ndl..ndh]. From "Numerical Recipes in C".
    float *d3tensor(long nrl, long nrh, long ncl, long nch, long ndl, long ndh)
    long i,j,nrow=nrh-nrl1,ncol=nch-ncl+1,ndep=ndh-ndl1;
    float *t;
    /* allocate pointers to pointers to rows */
    t=(float *) malloc((sizet)((nrow+NREND)sizeof(float*)));
    if (!t)
    fprintf(stderr,"allocation failure 1 in f3tensor()\n");
    exit(1);
    t += NR_END;
    t -= nrl;
    /* allocate pointers to rows and set pointers to them */
    t[nrl]=(float **) malloc((sizet)((nrowncol+NREND)*sizeof(float)));
    if (!t[nrl])
    fprintf(stderr,"allocation failure 2 in f3tensor()\n");
    exit(1);
    t[nrl] += NR_END;
    t[nrl] -= ncl;
    /* allocate rows and set pointers to them */
    t[nrl][ncl]=(float *) malloc((sizet)((nrowncol*ndep+NREND)sizeof(float)));
    if (!t[nrl][ncl])
    fprintf(stderr,"allocation failure 3 in f3tensor()\n");
    exit(1);
    t[nrl][ncl] += NR_END;
    t[nrl][ncl] -= ndl;
    for(j=ncl1;j<=nch;j+) t[nrl][j]=t[nrl][j-1]+ndep;
    for(i=nrl1;i<=nrh;i+) {
    t=t[i-1]+ncol;
    t[ncl]=t[i-1][ncl]+ncol*ndep;
    for(j=ncl1;j<=nch;j+) t[j]=t[j-1]+ndep;
    /* return pointer to array of pointers to rows */
    return t;
    void free_matrix(float **m,long nrl,long nrh,long ncl,long nch)
    free((char*) (m[nrl]+ncl-1));
    free((char*) (m+nrl-1));
    void free_f3tensor(float *t,long nrl,long nrh,long ncl,long nch,long ndl,
    long ndh)
    free((char*) (t[nrl][ncl]+ndl-1));
    free((char*) (t[nrl]+ncl-1));
    free((char*) (t+nrl-1));
    // Function to replace data by its ndim-dimensional discrete Fourier transform,
    // if isign is input as 1. nn[1..ndim] is an integer array containing the
    // lengths of each dimension (number of complex values), which MUST be all
    // powers of 2. data is a real array of length twice the product of these
    // lengths, in which the data are stored as in a multidimensional complex
    // array: real and imaginary parts of each element are in consecutive
    // locations, and the rightmost index of the array increases most rapidly as
    // one proceeds along data. For a two-dimensional array, this is equivalent to
    // storing the arrays by rows. If isign is input as -1, data is replaced by its
    // inverse transform times the product of the lengths of all dimensions.
    void fourn(float data[],unsigned long nn[],int ndim,int isign)
    int idim;
    unsigned long i1,i2,i3,i2rev,i3rev,ip1,ip2,ip3,ifp1,ifp2;
    unsigned long ibit,k1,k2,n,nprev,nrem,ntot;
    double tempi,tempr;
    float theta,wi,wpi,wpr,wr,wtemp;
    for (ntot=1, idim=1; idim<=ndim; idim++)
    ntot *= nn[idim];
    nprev = 1;
    for (idim=ndim; idim>=1; idim--)
    n = nn[idim];
    nrem = ntot/(n*nprev);
    ip1=nprev << 1;
    ip2 = ip1*n;
    ip3 = ip2*nrem;
    i2rev = 1;
    for (i2=1; i2<=ip2; i2+=ip1)
    if (i2 < i2rev)
    for (i1=i2; i1<=i2+ip1-2; i1+=2)
    for (i3=i1; i3<=ip3; i3+=ip2)
    i3rev = i2rev+i3-i2;
    SWAP(data[i3],data[i3rev]);
    SWAP(data[i31],data[i3rev1]);
    ibit = ip2>>1;
    while (ibit>=ip1 && i2rev>ibit)
    i2rev -= ibit;
    ibit >>= 1;
    i2rev += ibit;
    ifp1 = ip1;
    while (ifp1 < ip2)
    ifp2 = ifp1 << 1;
    theta = 2isignPI/(ifp2/ip1);
    wtemp = sin(0.5*theta);
    wpr = -2.0wtempwtemp;
    wpi = sin(theta);
    wr = 1.0;
    wi = 0.0;
    for (i3=1; i3<=ifp1; i3+=ip1)
    for (i1=i3; i1<=i3+ip1-2; i1+=2)
    for (i2=i1; i2<=ip3; i2+=ifp2)
    k1 = i2;
    k2 = k1+ifp1;
    tempr = (float)wrdata[k2]-(float)widata[k2+1];
    tempi = (float)wrdata[k21](float)widata[k2];
    data[k2] = data[k1]-tempr;
    data[k2+1] = data[k1+1]-tempi;
    data[k1] += tempr;
    data[k1+1] += tempi;
    wr = (wtemp=wr)wpr-wiwpi+wr;
    wi = wiwprwtempwpiwi;
    ifp1 = ifp2;
    nprev *= n;
    // Function to calculate a three-dimensional Fourier transform of
    // data[1..nn1][1..nn2][1..nn3] (where nn1=1 for the case of a logically two-
    // dimensional array). This routine returns (for isign=1) the complex fast
    // Fourier transform as two complex arrays: On output, data contains the zero
    // and positive frequency values of the third frequency component, while
    // speq[1..nn1][1..2*nn2] contains the Nyquist critical frequency values of the
    // third frequency component. First (and second) frequency components are
    // stored for zero, positive, and negative frequencies, in standard wrap-around
    // order. See Numerical Recipes for description of how complex values are
    // arranged. For isign=-1, the inverse transform (times nn1nn2nn3/2 as a
    // constant multiplicative factor) is performed, with output data (viewed as
    // real array) deriving from input data (viewed as complex) and speq. For
    // inverse transforms on data not generated first by a forward transform, make
    // sure the complex input data array satisfies property 12.5.2 from NR. The
    // dimensions nn1, nn2, nn3 must always be integer powers of 2.
    void rlft3(float *data,float **speq,unsigned long nn1,unsigned long nn2,
    unsigned long nn3,int isign)
    double theta,wi,wpi,wpr,wr,wtemp;
    float c1,c2,h1r,h1i,h2r,h2i;
    unsigned long i1,i2,i3,j1,j2,j3,nn[4],ii3;
    if (1+&data[nn1][nn2][nn3]-&data[1][1][1] != nn1nn2nn3)
    fprintf(stderr,
    "rlft3: problem with dimensions or contiguity of data array\n");
    exit(1);
    c1 = 0.5;
    c2 = -0.5*isign;
    theta = 2isign(PI/nn3);
    wtemp = sin(0.5*theta);
    wpr = -2.0wtempwtemp;
    wpi = sin(theta);
    nn[1] = nn1;
    nn[2] = nn2;
    nn[3] = nn3 >> 1;
    // Case of forward transform. Here is where most all of the compute time is
    // spent. Extend data periodically into speq.
    if (isign == 1)
    fourn(&data[1][1][1]-1,nn,3,isign);
    for (i1=1; i1<=nn1; i1++)
    for (i2=1, j2=0; i2<=nn2; i2++)
    speq[i1][++j2] = data[i1][i2][1];
    speq[i1][++j2] = data[i1][i2][2];
    for (i1=1; i1<=nn1; i1++)
    // Zero frequency is its own reflection; otherwise locate corresponding
    // negative frequency in wrap-around order.
    j1 = (i1 != 1 ? nn1-i1+2 : 1);
    // Initialize trigonometric recurrence.
    wr = 1.0;
    wi = 0.0;
    for (ii3=1, i3=1; i3<=(nn3>>2)+1; i3+,ii3=2)
    for (i2=1; i2<=nn2; i2++)
    if (i3 == 1)
    j2 = (i2 != 1 ? ((nn2-i2)<<1)+3 : 1);
    h1r = c1*(data[i1][i2][1]+speq[j1][j2]);
    h1i = c1*(data[i1][i2][2]-speq[j1][j2+1]);
    h2i = c2*(data[i1][i2][1]-speq[j1][j2]);
    h2r = -c2*(data[i1][i2][2]speq[j1][j21]);
    data[i1][i2][1] = h1r+h2r;
    data[i1][i2][2] = h1i+h2i;
    speq[j1][j2] = h1r-h2r;
    speq[j1][j2+1] = h2i-h1i;
    else
    j2 = (i2 != 1 ? nn2-i2+2 : 1);
    j3 = nn3+3-(i3<<1);
    h1r = c1*(data[i1][i2][ii3]+data[j1][j2][j3]);
    h1i = c1*(data[i1][i2][ii31]-data[j1][j2][j31]);
    h2i = c2*(data[i1][i2][ii3]-data[j1][j2][j3]);
    h2r = -c2*(data[i1][i2][ii31]+data[j1][j2][j31]);
    data[i1][i2][ii3] = h1r+wrh2r-wih2i;
    data[i1][i2][ii3+1] = h1iwrh2iwih2r;
    data[j1][j2][j3] = h1r-wrh2r+wih2i;
    data[j1][j2][j3+1] = -h1iwrh2iwih2r;
    // Do the recurrence.
    wr = (wtemp=wr)wpr-wiwpi+wr;
    wi = wiwprwtempwpiwi;
    // Case of reverse transform.
    if (isign == -1)
    fourn(&data[1][1][1]-1,nn,3,isign);
    // Function to perform Gaussian blur.
    void gaussianblur(void)
    float **blur,***conv,***pop,**speqblur,**speqconv,*speqpop;
    int i,j,p,q;
    blur = d3tensor(1,1,1,lx,1,ly);
    conv = d3tensor(1,1,1,lx,1,ly);
    pop = d3tensor(1,1,1,lx,1,ly);
    speqblur = dmatrix(1,1,1,2*lx);
    speqconv = dmatrix(1,1,1,2*lx);
    speqpop = dmatrix(1,1,1,2*lx);
    // Fill population and convolution matrix.
    for (i=1; i<=lx; i++) for (j=1; j<=ly; j++)
    if (i > lx/2) p = i-1-lx;
    else p = i-1;
    if (j > ly/2) q = j-1-ly;
    else q = j-1;
    pop[1][j] = rho_0[i-1][j-1];
    conv[1][j] = 0.5*
    (erf((p+0.5)/(sqrt(2.0)(SIGMApow(SIGMAFAC,nblurs))))-
    erf((p-0.5)/(sqrt(2.0)(SIGMA*pow(SIGMAFAC,nblurs)))))
    (erf((q+0.5)/(sqrt(2.0)(SIGMApow(SIGMAFAC,nblurs))))-
    erf((q-0.5)/(sqrt(2.0)(SIGMA*pow(SIGMAFAC,nblurs)))))/(lxly);
    // Fourier transform.
    rlft3(pop,speqpop,1,lx,ly,1);
    rlft3(conv,speqconv,1,lx,ly,1);
    // Multiply pointwise.
    for (i=1; i<=lx; i++)
    for (j=1; j<=ly/2; j++)
    blur[1][2*j-1] =
    pop[1][2j-1]*conv[1][2j-1]-
    pop[1][2j]*conv[1][2j];
    blur[1][2*j] =
    pop[1][2j]*conv[1][2j-1]+
    pop[1][2j-1]*conv[1][2j];
    for (i=1; i<=lx; i++)
    speqblur[1][2*i-1] =
    speqpop[1][2i-1]*speqconv[1][2i-1]-
    speqpop[1][2i]*speqconv[1][2i];
    speqblur[1][2*i] =
    speqpop[1][2i]*speqconv[1][2i-1]+
    speqpop[1][2i-1]*speqconv[1][2i];
    // Backtransform.
    rlft3(blur,speqblur,1,lx,ly,-1);
    // Write to rho_0.
    for (i=1; i<=lx; i++) for (j=1; j<=ly; j++) rho_0[i-1][j-1] = blur[1][j];
    free_f3tensor(blur,1,1,1,lx,1,ly);
    free_f3tensor(conv,1,1,1,lx,1,ly);
    free_f3tensor(pop,1,1,1,lx,1,ly);
    free_matrix(speqblur,1,1,1,2*lx);
    free_matrix(speqconv,1,1,1,2*lx);
    free_matrix(speqpop,1,1,1,2*lx);
    // Function to initialize rho_0. The original density is blurred with width
    // SIGMA*pow(SIGMAFAC,nblurs).
    void initcond(void)
    float maxpop;
    int i,j;
    // Reconstruct population density.
    coscosft(rho_0,-1,-1);
    // There must not be negative densities.
    for (i=0; i<lx; i++) for (j=0; j<ly; j++) if (rho_0[j]<-1e10)
    fprintf(stderr,"ERROR: Negative density in DENSITYFILE.\n");
    exit(1);
    // Perform Gaussian blur.
    printf("Gaussian blur ...\n");
    gaussianblur();
    // Find the mimimum density. If it is very small suggest an increase in
    // SIGMA.
    minpop = rho_0[0][0];
    maxpop = rho_0[0][0];
    for (i=0; i<lx; i++) for (j=0; j<ly; j++) if (rho_0[j]<minpop)
    minpop = rho_0[j];
    for (i=0; i<lx; i++) for (j=0; j<ly; j++) if (rho_0[j]>maxpop)
    maxpop = rho_0[j];
    if (0<minpop && minpop<1e-8*maxpop)
    fprintf(stderr,"Minimimum population very small (%f). Integrator\n",
    minpop);
    fprintf(stderr,
    "will probably converge very slowly. You can speed up the\n");
    fprintf(stderr,"process by increasing SIGMA to a value > %f.\n",
    SIGMA*pow(SIGMAFAC,nblurs));
    // Replace rho_0 by cosine Fourier transform in both variables.
    coscosft(rho_0,1,1);
    // Function to calculate the velocity field
    void calcv(float t)
    int j,k;
    // Fill rho with Fourier coefficients.
    for (j=0; j<=lx; j++) for (k=0; k<=ly; k++)
    rho[j][k] = exp(-((PIj/lx)*(PI*j/lx)+(PI*k/ly)*(PI*k/ly))*t)rho_0[j][k];
    // Calculate the Fourier coefficients for the partial derivative of rho.
    // Store temporary results in arrays gridvx, gridvy.
    for (j=0; j<=lx; j++) for (k=0; k<=ly; k++)
    gridvx[j][k] = -(PIj/lx)rho[j][k];
    gridvy[j][k] = -(PIk/ly)rho[j][k];
    // Replace rho by cosine Fourier backtransform in both variables.
    coscosft(rho,-1,-1);
    // Replace vx by sine Fourier backtransform in the first and cosine Fourier
    // backtransform in the second variable.
    sincosft(gridvx,-1,-1);
    // Replace vy by cosine Fourier backtransform in the first and sine Fourier
    // backtransform in the second variable.
    cossinft(gridvy,-1,-1);
    // Calculate the velocity field.
    for (j=0; j<=lx; j++) for (k=0; k<=ly; k++)
    gridvx[j][k] = -gridvx[j][k]/rho[j][k];
    gridvy[j][k] = -gridvy[j][k]/rho[j][k];
    // Function to bilinearly interpolate a two-dimensional array. For higher
    // accuracy one could consider higher order interpolation schemes.
    float intpol(float **arr,float x,float y)
    int gaussx,gaussy;
    float deltax,deltay;
    // Decompose x and y into an integer part and a decimal.
    gaussx = (int)x;
    gaussy = (int)y;
    deltax = x-gaussx;
    deltay = y-gaussy;
    // Interpolate.
    if (gaussx==lx && gaussy==ly)
    return arr[gaussx][gaussy];
    if (gaussx==lx)
    return (1-deltay)arr[gaussx][gaussy]deltayarr[gaussx][gaussy1];
    if (gaussy==ly)
    return (1-deltax)arr[gaussx][gaussy]deltaxarr[gaussx1][gaussy];
    return (1-deltax)(1-deltay)arr[gaussx][gaussy]+
    (1-deltax)deltayarr[gaussx][gaussy1]
    deltax(1-deltay)arr[gaussx1][gaussy]
    deltaxdeltayarr[gaussx1][gaussy1];
    // Function to find the root of the system of equations
    // xappr-0.5h*v_x(t+h,xappr,yappr)-x[j][k]-0.5*hvx[j][k]=0,
    // yappr-0.5h*v_y(t+h,xappr,yappr)-y[j][k]-0.5*hvy[j][k]=0
    // with Newton-Raphson. Returns TRUE after sufficient convergence.
    BOOLEAN newt2(float h,float *xappr,float xguess,float *yappr,float yguess,
    int j,int k)
    float deltax,deltay,dfxdx,dfxdy,dfydx,dfydy,fx,fy;
    int gaussx,gaussxplus,gaussy,gaussyplus,i;
    // Initial guess.
    *xappr = xguess;
    *yappr = yguess;
    for (i=1; i<=IMAX; i++)
    // fx, fy are the left-hand sides of the two equations. Find
    // v_x(t+h,xappr,yappr), v_y(t+h,xappr,yappr) by interpolation.
    fx = xappr-0.5*h*intpol(gridvx,*xappr,*yappr)-x[j][k]-0.5*hvx[j][k];
    fy = yappr-0.5*h*intpol(gridvy,*xappr,*yappr)-y[j][k]-0.5*hvy[j][k];
    // Linearly approximate the partial derivatives of fx, fy with a finite
    // difference method. More elaborate techniques are possible, but this
    // quick and dirty method appears to work reasonably for our purpose.
    gaussx = (int)(*xappr);
    gaussy = (int)(*yappr);
    if (gaussx == lx) gaussxplus = 0;
    else gaussxplus = gaussx+1;
    if (gaussy == ly) gaussyplus = 0;
    else gaussyplus = gaussy+1;
    deltax = x[j][k] - gaussx;
    deltay = y[j][k] - gaussy;
    dfxdx = 1 - 0.5h
    ((1-deltay)*(gridvx[gaussxplus][gaussy]-gridvx[gaussx][gaussy])+
    deltay*(gridvx[gaussxplus][gaussyplus]-gridvx[gaussx][gaussyplus]));
    dfxdy = -0.5h
    ((1-deltax)*(gridvx[gaussx][gaussyplus]-gridvx[gaussx][gaussy])+
    deltax*(gridvx[gaussxplus][gaussyplus]-gridvx[gaussxplus][gaussy]));
    dfydx = -0.5h
    ((1-deltay)*(gridvy[gaussxplus][gaussy]-gridvy[gaussx][gaussy])+
    deltay*(gridvy[gaussxplus][gaussyplus]-gridvy[gaussx][gaussyplus]));
    dfydy = 1 - 0.5h
    ((1-deltax)*(gridvy[gaussx][gaussyplus]-gridvy[gaussx][gaussy])+
    deltax*(gridvy[gaussxplus][gaussyplus]-gridvy[gaussxplus][gaussy]));
    // If the current approximation is (xappr,yappr) for the zero of
    // (fx(x,y),fy(x,y)) and J is the Jacobian, then we can approximate (in
    // vector notation) for |delta|<<1:
    // f((xappr,yappr)+delta) = f(xappr,yappr)+J*delta.
    // Setting f((xappr,yappr)+delta)=0 we obtain a set of linear equations
    // for the correction delta which moves f closer to zero, namely
    // J*delta = -f.
    // The improved approximation is then x = xappr+delta.
    // The process will be iterated until convergence is reached.
    if ((fx*fx + fy*fy) < TOLF) return TRUE;
    deltax = (fy*dfxdy - fxdfydy)/(dfxdxdfydy - dfxdy*dfydx);
    deltay = (fx*dfydx - fydfxdx)/(dfxdxdfydy - dfxdy*dfydx);
    if ((deltax*deltax + deltay*deltay) < TOLX) return TRUE;
    *xappr += deltax;
    *yappr += deltay;
    //printf("deltax %f, deltay %f\n",deltax,deltay);
    fprintf(stderr,"newt2 failed, increasing sigma to %f.\n",
    SIGMA*pow(SIGMAFAC,nblurs));
    return FALSE;
    // Function to integrate the nonlinear Volterra equation. Returns TRUE after
    // the displacement field converged, after MAXINTSTEPS integration steps, or
    // if the time exceeds TIMELIMIT.
    BOOLEAN nonlinvoltra(void)
    BOOLEAN stepsize_ok;
    #ifdef DISPLFILE
    FILE *displfile = fopen(DISPLFILE);
    #endif
    float h,maxchange=INFTY,t,vxplus,vyplus,xguess,yguess;
    int i,j,k;
    do
    initcond();
    nblurs++;
    if (minpop<0.0)
    fprintf(stderr,
    "Minimum population negative, will increase sigma to %f\n",
    SIGMA*pow(SIGMAFAC,nblurs));
    while (minpop<0.0);
    h = HINITIAL;
    t = 0; // Start at time t=0.
    // (x[j][k],y[j][k]) is the position for the element that was at position
    // (j,k) at time t=0.
    for (j=0; j<=lx; j++) for (k=0; k<=ly; k++)
    x[j][k] = j;
    y[j][k] = k;
    calcv(0.0);
    // (gridvx[j][k],gridvy[j][k]) is the velocity at position (j,k).
    // (vx[j][k],vy[j][k]) is the velocity at position (x[j][k],y[j][k]).
    // At t=0 they are of course identical.
    for (j=0; j<=lx; j++) for (k=0; k<=ly; k++)
    vx[j][k] = gridvx[j][k];
    vy[j][k] = gridvy[j][k];
    i = 1; // i counts the integration steps.
    // Here is the integrator.
    do
    stepsize_ok = TRUE;
    calcv(t+h);
    for (j=0; j<=lx; j++) for (k=0; k<=ly; k++)
    // First take a naive integration step. The velocity at time t+h for
    // the element [j][k] is approximately
    // v(th,x[j][k]+hvx[j][k],y[j][k]hvy[j][k]).
    // The components, call them vxplus and vyplus, are interpolated from
    // gridvx and gridvy.
    vxplus = intpol(gridvx,x[j][k]hvx[j][k],y[j][k]hvy[j][k]);
    vyplus = intpol(gridvy,x[j][k]hvx[j][k],y[j][k]hvy[j][k]);
    // Based on (vx[j][k],vy[j][k]) and (vxplus,vyplus) we expect the
    // new position at time t+h to be:
    xguess = x[j][k] + 0.5h(vx[j][k]+vxplus);
    yguess = y[j][k] + 0.5h(vy[j][k]+vyplus);
    // Then we make a better approximation by solving the two nonlinear
    // equations:
    // xappr[j][k]-0.5hv_x(t+h,xappr[j][k],yappr[j][k])-
    // x[j][k]-0.5hvx[j][k]=0,
    // yappr[j][k]-0.5hv_y(t+h,xappr[j][k],yappr[j][k])-
    // y[j][k]-0.5hvy[j][k]=0
    // with Newton-Raphson and (xguess,yguess) as initial guess.
    // If newt2 fails to converge, exit nonlinvoltra.
    if (!newt2(h,&xappr[j][k],xguess,&yappr[j][k],yguess,j,k))
    return FALSE;
    // If the integration step was too large reduce the step size.
    if ((xguess-xappr[j][k])*(xguess-xappr[j][k])+
    (yguess-yappr[j][k])*(yguess-yappr[j][k]) > TOLINT)
    if (h<MINH)
    fprintf(stderr,
    "Time step below %f, increasing SIGMA to %f\n",
    h,SIGMA*pow(SIGMAFAC,nblurs));
    nblurs++;
    return FALSE;
    h /= 10;
    stepsize_ok = FALSE;
    break;
    if (!stepsize_ok) continue;
    else
    t += h;
    maxchange = 0.0; // Monitor the maximum change in positions.
    for (j=0; j<=lx; j++) for (k=0; k<=ly; k++)
    if ((x[j][k]-xappr[j][k])*(x[j][k]-xappr[j][k])+
    (y[j][k]-yappr[j][k])*(y[j][k]-yappr[j][k]) > maxchange)
    maxchange =
    (x[j][k]-xappr[j][k])*(x[j][k]-xappr[j][k])+
    (y[j][k]-yappr[j][k])*(y[j][k]-yappr[j][k]);
    x[j][k] = xappr[j][k];
    y[j][k] = yappr[j][k];
    vx[j][k] = intpol(gridvx,xappr[j][k],yappr[j][k]);
    vy[j][k] = intpol(gridvy,xappr[j][k],yappr[j][k]);
    h *= 1.2; // Make the next integration step larger.
    if (i%10==0) printf("time %f\n",t);
    i++;
    } while (i<MAXINTSTEPS && t<TIMELIMIT && maxchange>CONVERGENCE);
    if (maxchange>CONVERGENCE)
    fprintf(stderr,
    "WARNING: Insufficient convergence within %i steps, time %f.\n",
    MAXINTSTEPS,TIMELIMIT);
    #ifdef DISPLFILE
    // Write displacement field to file.
    fprintf(displfile,"time %f\nminx %f\nmaxx %f\nminy %f\nmaxy %f\n",
    t,minx,maxx,miny,maxy);
    fprintf(displfile,"sigma %f\n",SIGMA*pow(SIGMAFAC,nblurs-1));
    fprintf(displfile,"background %f\nlx\nly\n\n",0,lx,ly);
    for (j=0; j<=lx; j++) for (k=0; k<=ly; k++)
    fprintf(displfile,"j %i, k %i, x %f, y %f\n",j,k,x[j][k],y[j][k]);
    fclose(displfile);
    #endif
    return TRUE;
    // Function to transform points according to displacement field.
    POINT transf(POINT p)
    float deltax,deltay,den,t,u;
    int gaussx,gaussy;
    POINT a,b,c,d,ptr;
    p.x = (p.x-minx)*lx/(maxx-minx);
    p.y = (p.y-miny)*ly/(maxy-miny);
    gaussx = (int)p.x;
    gaussy = (int)p.y;
    if (gaussx<0 || gaussx>lx || gaussy<0 || gaussy>ly)
    fprintf(stderr,"ERROR: Coordinate limits exceeded in transf.\n");
    exit(1);
    deltax = p.x - gaussx;
    deltay = p.y - gaussy;
    // The transformed point is the intersection of the lines:
    // (I) connecting
    // (1-deltax)(x,y[gaussx][gaussy])deltax(x,y[gaussx1][gaussy])
    // and
    // (1-deltax)(x,y[gaussx][gaussy1])+deltax(x,y[gaussx+1][gaussy1])
    // (II) connecting
    // (1-deltay)(x,y[gaussx][gaussy])deltay(x,y[gaussx][gaussy1])
    // and
    // (1-deltay)(x,y[gaussx1][gaussy])+deltay(x,y[gaussx+1][gaussy1]).
    // Call these four points a, b, c and d.
    a.x = (1-deltax)*x[gaussx][gaussy] + deltax*x[gaussx+1][gaussy];
    a.y = (1-deltax)*y[gaussx][gaussy] + deltax*y[gaussx+1][gaussy];
    b.x = (1-deltax)*x[gaussx][gaussy+1] + deltax*x[gaussx1][gaussy1];
    b.y = (1-deltax)*y[gaussx][gaussy+1] + deltax*y[gaussx1][gaussy1];
    c.x = (1-deltay)*x[gaussx][gaussy] + deltay*x[gaussx][gaussy+1];
    c.y = (1-deltay)*y[gaussx][gaussy] + deltay*y[gaussx][gaussy+1];
    d.x = (1-deltay)*x[gaussx+1][gaussy] + deltay*x[gaussx1][gaussy1];
    d.y = (1-deltay)*y[gaussx+1][gaussy] + deltay*y[gaussx1][gaussy1];
    // Solve the vector equation a+t(b-a) = c+u(d-c) for the scalars t, u.
    if (fabs(den=(b.x-a.x)(c.y-d.y)+(a.y-b.y)(c.x-d.x))<1e-12)
    fprintf(stderr,"ERROR: Transformed area element has parallel edges.\n");
    exit(1);
    t = ((c.x-a.x)(c.y-d.y)+(a.y-c.y)(c.x-d.x))/den;
    u = ((b.x-a.x)(c.y-a.y)+(a.y-b.y)(c.x-a.x))/den;
    if (t<-1e-3|| t>1+1e-3 || u<-1e-3 || u>1+1e-3)
    fprintf(stderr,"WARNING: Transformed area element non-convex.\n");
    ptr.x = (1-(a.x+t(b.x-a.x))/lx)minx + ((a.x+t(b.x-a.x))/lx)maxx;
    ptr.y = (1-(a.y+t(b.y-a.y))/ly)miny + ((a.y+t(b.y-a.y))/ly)maxy;
    return ptr;
    // Function to read spatial features from user-specified file and map to
    // cartogram.
    void cartogram(void)
    char id[LINELENGTH],line[LINELENGTH];
    FILE infile,outfile;
    float xcoord,ycoord;
    POINT p;
    infile = fopen(MAPGENFILE);
    outfile = fopen(CARTGENFILE,"w");
    while (!readline(line,infile))
    if (sscanf(line,"%s %f %f",&id,&xcoord,&ycoord)==3)
    p.x = xcoord;
    p.y = ycoord;
    p = transf(p);
    fprintf(outfile,"%s %f %f\n",id,p.x,p.y);
    else if (sscanf(line,"%f %f",&xcoord,&ycoord)==2)
    p.x = xcoord;
    p.y = ycoord;
    p = transf(p);
    fprintf(outfile,"%f %f\n",p.x,p.y);
    else
    sscanf(line,"%s",&id);
    fprintf(outfile,"%s\n",id);
    fclose(infile);
    fclose(outfile);
    main(void)
    BOOLEAN n;
    char c;
    FILE genfile,psfile = fopen(MAP2PS);
    float oldlx,oldly,oldmaxx,oldmaxy,oldminx,oldminy,totarea;
    int i,polyctr,regctr;
    // Read the polygon coordinates.
    if ((genfile = fopen(MAPGENFILE)) == NULL)
    fprintf(stderr,"ERROR: Cannot find MAPGENFILE\n");
    exit(1);
    countpoly(genfile);
    fclose(genfile);
    genfile = fopen(MAPGENFILE);
    countcorn(genfile);
    fclose(genfile);
    genfile = fopen(MAPGENFILE);
    readcorn(genfile);
    fclose(genfile);
    makeregion();
    printf("%i polygon(s), %i region(s)\n",npoly,nregion);
    printf("lx=%i, ly=%i\n",lx,ly);
    // Calculate total area.
    //totarea = 0.0;
    //for (regctr=0; regctr<nregion; regctr++)
    // printf("region %i has area %f, contains %i polygons\n",regionid[regctr],
    // regionarea(nregcorn[regctr],regcorn[regctr]),npolyinreg[regctr]);
    // totarea += regionarea(nregcorn[regctr],regcorn[regctr]);
    //printf("totarea = %f\n",totarea);
    // Make map.
    pspicture(psfile);
    fclose(psfile);
    // Allocate memory for arrays.
    gridvx = (float*)malloc((lx+1)*sizeof(float));
    gridvy = (float*)malloc((lx+1)*sizeof(float));
    rho = (float*)malloc((lx+1)*sizeof(float));
    rho_0 = (float*)malloc((lx+1)*sizeof(float));
    vx = (float*)malloc((lx+1)*sizeof(float));
    vy = (float*)malloc((lx+1)*sizeof(float));
    x = (float*)malloc((lx+1)*sizeof(float));
    xappr = (float*)malloc((lx+1)*sizeof(float));
    y = (float*)malloc((lx+1)*sizeof(float));
    yappr = (float*)malloc((lx+1)*sizeof(float));
    within = (int*)malloc((lx+1)*sizeof(int));
    for (i=0; i<=lx; i++)
    gridvx = (float)malloc((ly+1)sizeof(float));
    gridvy = (float)malloc((ly+1)sizeof(float));
    rho = (float)malloc((ly+1)sizeof(float));
    rho_0 = (float)malloc((ly+1)sizeof(float));
    vx = (float)malloc((ly+1)sizeof(float));
    vy = (float)malloc((ly+1)sizeof(float));
    x = (float)malloc((ly+1)sizeof(float));
    xappr = (float)malloc((ly+1)sizeof(float));
    y = (float)malloc((ly+1)sizeof(float));
    yappr = (float)malloc((ly+1)sizeof(float));
    within = (int)malloc((ly+1)sizeof(int));
    // Digitize the density.
    bboxes();
    interior();
    digdens();
    // Solve the diffusion equation.
    do n = nonlinvoltra(); while (!n);
    // Print cartogram generate file.
    cartogram();
    // Read the transformed polygon coordinates.
    oldlx = lx;
    oldly = ly;
    oldmaxx = maxx;
    oldmaxy = maxy;
    oldminx = minx;
    oldminy = miny;
    genfile = fopen(CARTGENFILE,"r");
    countpoly(genfile);
    fclose(genfile);
    genfile = fopen(CARTGENFILE,"r");
    countcorn(genfile);
    fclose(genfile);
    lx = oldlx;
    ly = oldly;
    maxx = oldmaxx;
    maxy = oldmaxy;
    minx = oldminx;
    miny = oldminy;
    genfile = fopen(CARTGENFILE,"r");
    readcorn(genfile);
    fclose(genfile);
    makeregion();
    // Make cartogram
    psfile = fopen(CART2PS);
    pspicture(psfile);
    fclose(psfile);
    The part of the code where the bus error occurs is this:
    void interior(void)
    int i,inhowmanyregions,inregion[2],j,k,l,m,n,regctr;
    // Initialize within[][]. -1 means outside all regions.
    for (i=0; i<=lx; i++) for (j=0; j<=ly; j++) within[j] = -1;
    // Fill within[][].
    for (i=0; i<nregion; i++) for (j=0; j<npolyinreg; j++)
    for (k=0, n=npolycorn[polyinreg[j]]-1;
    k<npolycorn[polyinreg[j]]; n=k++)
    for (l=(int)ceil(MIN(polycorn[polyinreg[j]][k-1].y,
    polycorn[polyinreg[j]][k].y));
    l<MAX(polycorn[polyinreg[j]][k-1].y,
    polycorn[polyinreg[j]][k].y); l++)
    for (m=(int)floor(bbminx[polyinreg[j]]);
    m<(polycorn[polyinreg[j]][n].x-
    polycorn[polyinreg[j]][k].x)*
    (l-polycorn[polyinreg[j]][k].y)/
    (polycorn[polyinreg[j]][n].y-
    polycorn[polyinreg[j]][k].y)+
    polycorn[polyinreg[j]][k].x;
    m++)
    within[m][l] = i-within[m][l]-1;
    I really have no idea what is going on. Can anyone help?
    Thanks,
    mooseguy

    orangekay wrote:
    That is absolutely unreadable.
    I agree completely. How about also providing a link to a set of input files so that we could actually run the code ourselves? Otherwise, there is no chance to debug the source code, it is just a mess.
    You might have better luck with an older version of the file. To quote the comments:
    // Modified on March 31, 2005. Initialized maxchange in nonlinvoltra() as
    // INFTY. Replaced crnmbr() by a similar, but faster routine interior().
    // Many thanks to Stuart Anderson for pointing out this shortcut.
    I suspect that the "interior" function is just plain incorrect. It doesn't matter if it runs on some other OS. Something about it is wrong and the code is so cryptic that it can't be deciphered.

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    15:45:02
    15:45:02
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    1+0 records out
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    1/12/14 8:26:57.284 AM com.apple.backupd[1456]: Ejected Time Machine disk image: /Volumes/Data/Macintosh.sparsebundle
    1/12/14 8:26:57.000 AM kernel[0]: AFP_VFS afpfs_unmount: /Volumes/Data, flags 0, pid 1500
    1/12/14 8:26:57.000 AM kernel[0]: ASP_TCP Disconnect: triggering reconnect by bumping reconnTrigger from curr value 0 on so 0xffffff8054511530
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    I decided, based on various clues from Pondini's page, that the hard drive in my Time Capsule was failing.  I started a full backup on my second Time Capsule and am currenly only using the original as an internet router.

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