source: branches/lib/GDE/TREEPUZZLE/src/util.c

/*
 * util.c
 *
 *
 * Part of TREE-PUZZLE 5.0 (June 2000)
 *
 * (c) 1999-2000 by Heiko A. Schmidt, Korbinian Strimmer,
 *                  M. Vingron, and Arndt von Haeseler
 * (c) 1995-1999 by Korbinian Strimmer and Arndt von Haeseler
 *
 * All parts of the source except where indicated are distributed under
 * the GNU public licence.  See http://www.opensource.org for details.
 */


#include "util.h"

#define STDOUT     stdout
#ifndef PARALLEL             /* because printf() runs significantly faster */
                             /* than fprintf(stdout) on an Apple McIntosh  */
                             /* (HS) */
#       define FPRINTF    printf
#       define STDOUTFILE
#else
#       define FPRINTF    fprintf
#       define STDOUTFILE STDOUT,
        extern int PP_NumProcs;
        extern int PP_Myid;
        long int PP_randn;
        long int PP_rand;
#endif


/*
 * memory allocation error handler
 */

void maerror(const char *message)
{
        FPRINTF(STDOUTFILE "\n\n\nUnable to proceed (lack of memory: %s)\n\n", message);
        FPRINTF(STDOUTFILE "Hint for Macintosh users:\n");
        FPRINTF(STDOUTFILE "Use the <Get Info> command of the Finder to increase the memory partition!\n\n");
        exit(1);
}


/*
 * memory allocate double vectors, matrices, and cubes
 */

dvector new_dvector(int n)
{
        dvector v;

        v = (dvector) malloc((unsigned) (n * sizeof(double)));
        if (v == NULL) maerror("step 1 in new_dvector");

        return v;
}

dmatrix new_dmatrix(int nrow, int ncol)
{
        int i;
        dmatrix m;

        m = (dmatrix) malloc((unsigned) (nrow * sizeof(dvector)));
        if (m == NULL) maerror("step 1 in in new_dmatrix");

        *m = (dvector) malloc((unsigned) (nrow * ncol * sizeof(double)));
        if (*m == NULL) maerror("step 2 in in new_dmatrix");

        for (i = 1; i < nrow; i++) m[i] = m[i-1] + ncol;

        return m;
}

dcube new_dcube(int ntri, int nrow, int ncol)
{
        int i, j;
        dcube c;

        c = (dcube) malloc((unsigned) (ntri * sizeof(dmatrix)));
        if (c == NULL) maerror("step 1 in in new_dcube");

        *c = (dmatrix) malloc((unsigned) (ntri * nrow * sizeof(dvector)));
        if (*c == NULL) maerror("step 2 in in new_dcube");

        **c = (dvector) malloc((unsigned) (ntri * nrow * ncol * sizeof(double)));
        if (**c == NULL) maerror("step 3 in in new_dcube");

        for (j = 1; j < nrow; j++) c[0][j] = c[0][j-1] + ncol;

        for (i = 1; i < ntri; i++) {
                c[i] = c[i-1] + nrow;
                c[i][0] = c[i-1][0] + nrow * ncol;
                for (j = 1; j < nrow; j++) c[i][j] = c[i][j-1] + ncol;
        }

        return c;
}

void free_dvector(dvector v)
{
        free((double *) v);
}

void free_dmatrix(dmatrix m)
{
        free((double *) *m);
        free((double *) m);
}

void free_dcube(dcube c)
{
        free((double *) **c);
        free((double *) *c);
        free((double *) c);
}


/*
 * memory allocate char vectors, matrices, and cubes
 */

cvector new_cvector(int n)
{
        cvector v;

        v = (cvector) malloc((unsigned)n * sizeof(char));
        if (v == NULL) maerror("step1 in new_cvector");

        return v;
}

cmatrix new_cmatrix(int nrow, int ncol)
{
        int i;
        cmatrix m;

        m = (cmatrix) malloc((unsigned) (nrow * sizeof(cvector)));
        if (m == NULL) maerror("step 1 in new_cmatrix");

        *m = (cvector) malloc((unsigned) (nrow * ncol * sizeof(char)));
        if (*m == NULL) maerror("step 2 in new_cmatrix");

        for (i = 1; i < nrow; i++) m[i] = m[i-1] + ncol;

        return m;
}

ccube new_ccube(int ntri, int nrow, int ncol)
{
        int i, j;
        ccube c;

        c = (ccube) malloc((unsigned) (ntri * sizeof(cmatrix)));
        if (c == NULL) maerror("step 1 in new_ccube");

        *c = (cmatrix) malloc((unsigned) (ntri * nrow * sizeof(cvector)));
        if (*c == NULL) maerror("step 2 in new_ccube");

        **c = (cvector) malloc((unsigned) (ntri * nrow * ncol * sizeof(char)));
        if (**c == NULL) maerror("step 3 in new_ccube");

        for (j = 1; j < nrow; j++) c[0][j] = c[0][j-1] + ncol;

        for (i = 1; i < ntri; i++) {
                c[i] = c[i-1] + nrow;
                c[i][0] = c[i-1][0] + nrow * ncol;
                for (j = 1; j < nrow; j++) c[i][j] = c[i][j-1] + ncol;
        }

        return c;
}

void free_cvector(cvector v)
{
        free((char *) v);
}

void free_cmatrix(cmatrix m)
{
        free((char *) *m);
        free((char *) m);
}

void free_ccube(ccube c)
{
        free((char *) **c);
        free((char *) *c);
        free((char *) c);
}


/*
 * memory allocate int vectors, matrices, and cubes
 */

ivector new_ivector(int n)
{
        ivector v;

        v = (ivector) malloc((unsigned) (n * sizeof(int)));
        if (v == NULL) maerror("step 1 in new_ivector");

        return v;
}

imatrix new_imatrix(int nrow, int ncol)
{
        int i;
        imatrix m;

        m = (imatrix) malloc((unsigned) (nrow * sizeof(ivector)));
        if (m == NULL) maerror("step 1 in new_imatrix");

        *m = (ivector) malloc((unsigned) (nrow * ncol * sizeof(int)));
        if (*m == NULL) maerror("step 2 in new_imatrix");

        for (i = 1; i < nrow; i++) m[i] = m[i-1] + ncol;

        return m;
}

icube new_icube(int ntri, int nrow, int ncol)
{
        int i, j;
        icube c;

        c = (icube) malloc((unsigned) (ntri * sizeof(imatrix)));
        if (c == NULL) maerror("step 1 in new_icube");

        *c = (imatrix) malloc((unsigned) (ntri * nrow * sizeof(ivector)));
        if (*c == NULL) maerror("step 2 in new_icube");

        **c = (ivector) malloc((unsigned) (ntri * nrow * ncol * sizeof(int)));
        if (**c == NULL) maerror("step 3 in new_icube");

        for (j = 1; j < nrow; j++) c[0][j] = c[0][j-1] + ncol;

        for (i = 1; i < ntri; i++) {
                c[i] = c[i-1] + nrow;
                c[i][0] = c[i-1][0] + nrow * ncol;
                for (j = 1; j < nrow; j++) c[i][j] = c[i][j-1] + ncol;
        }

        return c;
}

void free_ivector(ivector v)
{
        free((int *) v);
}

void free_imatrix(imatrix m)
{
        free((int *) *m);
        free((int *) m);
}

void free_icube(icube c)
{
        free((int *) **c);
        free((int *) *c);
        free((int *) c);
}


/*
 * memory allocate uli vectors, matrices, and cubes
 */

ulivector new_ulivector(int n)
{
        ulivector v;

        v = (ulivector) malloc((unsigned) (n * sizeof(uli)));
        if (v == NULL) maerror("step 1 in new_ulivector");

        return v;
}

ulimatrix new_ulimatrix(int nrow, int ncol)
{
        int i;
        ulimatrix m;

        m = (ulimatrix) malloc((unsigned) (nrow * sizeof(ulivector)));
        if (m == NULL) maerror("step 1 in new_ulimatrix");

        *m = (ulivector) malloc((unsigned) (nrow * ncol * sizeof(uli)));
        if (*m == NULL) maerror("step 2 in new_ulimatrix");

        for (i = 1; i < nrow; i++) m[i] = m[i-1] + ncol;

        return m;
}

ulicube new_ulicube(int ntri, int nrow, int ncol)
{
        int i, j;
        ulicube c;

        c = (ulicube) malloc((unsigned) (ntri * sizeof(ulimatrix)));
        if (c == NULL) maerror("step 1 in new_ulicube");

        *c = (ulimatrix) malloc((unsigned) (ntri * nrow * sizeof(ulivector)));
        if (*c == NULL) maerror("step 2 in new_ulicube");

        **c = (ulivector) malloc((unsigned) (ntri * nrow * ncol * sizeof(uli)));
        if (**c == NULL) maerror("step 3 in new_ulicube");

        for (j = 1; j < nrow; j++) c[0][j] = c[0][j-1] + ncol;

        for (i = 1; i < ntri; i++) {
                c[i] = c[i-1] + nrow;
                c[i][0] = c[i-1][0] + nrow * ncol;
                for (j = 1; j < nrow; j++) c[i][j] = c[i][j-1] + ncol;
        }

        return c;
}

void free_ulivector(ulivector v)
{
        free((uli *) v);
}

void free_ulimatrix(ulimatrix m)
{
        free((uli *) *m);
        free((uli *) m);
}

void free_ulicube(ulicube c)
{
        free((uli *) **c);
        free((uli *) *c);
        free((uli *) c);
}


/******************************************************************************/
/* random numbers generator  (Numerical recipes)                              */
/******************************************************************************/

/* definitions */
#define IM1 2147483563
#define IM2 2147483399
#define AM (1.0/IM1)
#define IMM1 (IM1-1)
#define IA1 40014
#define IA2 40692
#define IQ1 53668
#define IQ2 52774
#define IR1 12211
#define IR2 3791
#define NTAB 32
#define NDIV (1+IMM1/NTAB)
#define EPS 1.2e-7
#define RNMX (1.0-EPS)

/* variable */
long idum;

double randomunitinterval()
/* Long period (> 2e18) random number generator. Returns a uniform random
   deviate between 0.0 and 1.0 (exclusive of endpoint values).

   Source:
   Press et al., "Numerical recipes in C", Cambridge University Press, 1992
   (chapter 7 "Random numbers", ran2 random number generator) */
{
        int j;
        long k;
        static long idum2=123456789;
        static long iy=0;
        static long iv[NTAB];
        double temp;

        if (idum <= 0) {
                if (-(idum) < 1)
                        idum=1;
                else
                        idum=-(idum);
                idum2=(idum);
                for (j=NTAB+7;j>=0;j--) {
                        k=(idum)/IQ1;
                        idum=IA1*(idum-k*IQ1)-k*IR1;
                        if (idum < 0)
                                idum += IM1;
                        if (j < NTAB)
                                iv[j] = idum;
                }
                iy=iv[0];
        }
        k=(idum)/IQ1;
        idum=IA1*(idum-k*IQ1)-k*IR1;
        if (idum < 0)
                idum += IM1;
        k=idum2/IQ2;
        idum2=IA2*(idum2-k*IQ2)-k*IR2;
        if (idum2 < 0)
                idum2 += IM2;
        j=iy/NDIV;
        iy=iv[j]-idum2;
        iv[j] = idum;
        if (iy < 1)
                iy += IMM1;
        if ((temp=AM*iy) > RNMX)
                return RNMX;
        else
                return temp;
}

#undef IM1
#undef IM2
#undef AM
#undef IMM1
#undef IA1
#undef IA2
#undef IQ1
#undef IQ2
#undef IR1
#undef IR2
#undef NTAB
#undef NDIV
#undef EPS
#undef RNMX

int initrandom(int seed)
{
   srand((unsigned) time(NULL));
   if (seed < 0)
        seed = rand();
   idum=-(long) seed;
#  ifdef PARALLEL
        {
        int n;
        for (n=0; n<PP_Myid; n++)
                (void) randomunitinterval();
#       ifdef PVERBOSE1
           fprintf(stderr, "(%2d) !!! random seed set to %d, %dx drawn !!!\n", PP_Myid, seed, n);
#       endif
        }
#  else
#       ifdef PVERBOSE1
           fprintf(stderr, "!!! random seed set to %d !!!\n", seed);
#       endif
#  endif
   return (seed);
}  /* initrandom */


/* returns a random integer in the range [0; n - 1] */
int randominteger(int n)
{
        int t;
#  ifndef FIXEDINTRAND
#       ifndef PARALLEL
                t = (int) floor(randomunitinterval()*n);
                return t;
#       else
                int m;
                for (m=1; m<PP_NumProcs; m++)
                        (void) randomunitinterval();
                PP_randn+=(m-1); PP_rand++;
                return (int) floor(randomunitinterval()*n);
#       endif
#  else
        fprintf(stderr, "!!! fixed \"random\" integers for testing purposes !!!\n");
        return (int)0;
#  endif /* FIXEDINTRAND */
}

/* Draw s numbers from the set 0,1,2,..,t-1 and put them
   into slist (every number can be drawn only one time) */
void chooser(int t, int s, ivector slist)
{
        int i, j, k, l;
        ivector isfree;

        isfree = new_ivector(t);
        for (i = 0; i < t; i++) isfree[i] = TRUE;
        for (i = 0; i < s; i++) {
                /* random integer in the range [0, t-1-i] */
                j = randominteger(t-i);
                k = -1;
                l = -1;
                do {
                        k++;
                        if (isfree[k] == TRUE) l++;
                } while ( l != j);
                slist[i] = k;
                isfree[k] = FALSE;
        }
        free_ivector(isfree);
}

/* a realloc function that works also on non-ANSI compilers */
void *myrealloc(void *p, size_t s)
{
        if (p == NULL) return malloc(s);
        else return realloc(p, s);
}

/* safer variant of gets */
/* Reads characters from stdin until a newline character or EOF
   is received.  The newline is not made part of the string.
   If an error occurs a null string \0 is returned */
cvector mygets()
{
        int c, n;
        cvector str;

        str = new_cvector(100);

        n = 0;
        c = getchar();
        while (c != '\n' && c != '\r' && n < 99 && c != EOF && !ferror(stdin))
        {
                str[n] = (char) c;
                c = getchar();
                n++;
        }
        if (c == EOF || ferror(stdin))
        {
                str[0] = '\0';
        }
        else
        {
                str[n] = '\0';
        }

        return str;
}



/******************************************************************************/
/* minimization of a function by Brents method (Numerical Recipes)            */
/******************************************************************************/

double brent(double, double, double, double (*f )(double ), double, double *, double *, double, double, double);


#define ITMAX 100
#define CGOLD 0.3819660
#define GOLD 1.618034
#define GLIMIT 100.0
#define TINY 1.0e-20
#define ZEPS 1.0e-10
#define SHFT(a,b,c,d) (a)=(b);(b)=(c);(c)=(d);
#define SIGN(a,b) ((b) >= 0.0 ? fabs(a) : -fabs(a))

/* Brents method in one dimension */
double brent(double ax, double bx, double cx, double (*f)(double), double tol,
        double *foptx, double *f2optx, double fax, double fbx, double fcx)
{
        int iter;
        double a,b,d=0,etemp,fu,fv,fw,fx,p,q,r,tol1,tol2,u,v,w,x,xm;
        double xw,wv,vx;
        double e=0.0;

        a=(ax < cx ? ax : cx);
        b=(ax > cx ? ax : cx);
        x=bx;
        fx=fbx;
        if (fax < fcx) {
                w=ax;
                fw=fax;
                v=cx;
                fv=fcx;
        } else {
                w=cx;
                fw=fcx;
                v=ax;
                fv=fax;
        }
        for (iter=1;iter<=ITMAX;iter++) {
                xm=0.5*(a+b);
                tol2=2.0*(tol1=tol*fabs(x)+ZEPS);
                if (fabs(x-xm) <= (tol2-0.5*(b-a))) {
                        *foptx = fx;
                        xw = x-w;
                        wv = w-v;
                        vx = v-x;
                        *f2optx = 2.0*(fv*xw + fx*wv + fw*vx)/
                                (v*v*xw + x*x*wv + w*w*vx);
                        return x;
                }
                if (fabs(e) > tol1) {
                        r=(x-w)*(fx-fv);
                        q=(x-v)*(fx-fw);
                        p=(x-v)*q-(x-w)*r;
                        q=2.0*(q-r);
                        if (q > 0.0) p = -p;
                        q=fabs(q);
                        etemp=e;
                        e=d;
                        if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))
                                d=CGOLD*(e=(x >= xm ? a-x : b-x));
                        else {
                                d=p/q;
                                u=x+d;
                                if (u-a < tol2 || b-u < tol2)
                                        d=SIGN(tol1,xm-x);
                        }
                } else {
                        d=CGOLD*(e=(x >= xm ? a-x : b-x));
                }
                u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));
                fu=(*f)(u);
                if (fu <= fx) {
                        if (u >= x) a=x; else b=x;
                        SHFT(v,w,x,u)
                        SHFT(fv,fw,fx,fu)
                } else {
                        if (u < x) a=u; else b=u;
                        if (fu <= fw || w == x) {
                                v=w;
                                w=u;
                                fv=fw;
                                fw=fu;
                        } else if (fu <= fv || v == x || v == w) {
                                v=u;
                                fv=fu;
                        }
                }
        }
        *foptx = fx;
        xw = x-w;
        wv = w-v;
        vx = v-x;
        *f2optx = 2.0*(fv*xw + fx*wv + fw*vx)/
                (v*v*xw + x*x*wv + w*w*vx);
        return x;
}
#undef ITMAX
#undef CGOLD
#undef ZEPS
#undef SHFT
#undef SIGN
#undef GOLD
#undef GLIMIT
#undef TINY

/* one-dimensional minimization - as input a lower and an upper limit and a trial
  value for the minimum is needed: xmin < xguess < xmax
  the function and a fractional tolerance has to be specified
  onedimenmin returns the optimal x value and the value of the function
  and its second derivative at this point
  */
double onedimenmin(double xmin, double xguess, double xmax, double (*f)(double),
        double tol, double *fx, double *f2x)
{
        double eps, optx, ax, bx, cx, fa, fb, fc;

        /* first attempt to bracketize minimum */
        eps = xguess*tol*50.0;
        ax = xguess - eps;
        if (ax < xmin) ax = xmin;
        bx = xguess;
        cx = xguess + eps;
        if (cx > xmax) cx = xmax;

        /* check if this works */
        fa = (*f)(ax);
        fb = (*f)(bx);
        fc = (*f)(cx);

        /* if it works use these borders else be conservative */
        if ((fa < fb) || (fc < fb)) {
                if (ax != xmin) fa = (*f)(xmin);
                if (cx != xmax) fc = (*f)(xmax);
                optx = brent(xmin, xguess, xmax, f, tol, fx, f2x, fa, fb, fc);
        } else
                optx = brent(ax, bx, cx, f, tol, fx, f2x, fa, fb, fc);

        return optx; /* return optimal x */
}

/* two-dimensional minimization with borders and calculations of standard errors */
/* we optimize along basis vectors - not very optimal but it seems to work well */
void twodimenmin(double tol,
        int active1, double min1, double *x1, double max1, double (*func1)(double), double *err1,
        int active2, double min2, double *x2, double max2, double (*func2)(double), double *err2)
{
        int it, nump, change;
        double x1old, x2old;
        double fx, f2x;

        it = 0;
        nump = 0;

        /* count number of parameters */
        if (active1) nump++;
        if (active2) nump++;

        do { /* repeat until nothing changes any more */
                it++;
                change = FALSE;

                /* optimize first variable */
                if (active1) {

                        if ((*x1) <= min1) (*x1) = min1 + 0.2*(max1-min1);
                        if ((*x1) >= max1) (*x1) = max1 - 0.2*(max1-min1);
                        x1old = (*x1);
                        (*x1) = onedimenmin(min1, (*x1), max1, func1, tol, &fx, &f2x);
                        if ((*x1) < min1) (*x1) = min1;
                        if ((*x1) > max1) (*x1) = max1;
                        /* same tolerance as 1D minimization */
                        if (fabs((*x1) - x1old) > 3.3*tol) change = TRUE;

                        /* standard error */
                        f2x = fabs(f2x);
                        if (1.0/(max1*max1) < f2x) (*err1) = sqrt(1.0/f2x);
                        else (*err1) = max1;

                }

                /* optimize second variable */
                if (active2) {

                        if ((*x2) <= min2) (*x2) = min2 + 0.2*(max2-min2);
                        if ((*x2) >= max2) (*x2) = max2 - 0.2*(max2-min2);
                        x2old = (*x2);
                        (*x2) = onedimenmin(min2, (*x2), max2, func2, tol, &fx, &f2x);
                        if ((*x2) < min2) (*x2) = min2;
                        if ((*x2) > max2) (*x2) = max2;
                        /* same tolerance as 1D minimization */
                        if (fabs((*x2) - x2old) > 3.3*tol) change = TRUE;

                        /* standard error */
                        f2x = fabs(f2x);
                        if (1.0/(max2*max2) < f2x) (*err2) = sqrt(1.0/f2x);
                        else (*err2) = max2;

                }

                if (nump == 1) return;

        } while (it != MAXITS && change);

        return;
}