text: // From: Numerical Recipes: The Art of Scientific Computing by William Press
  //   Saul Teukolsky, William  Vetterling, Brian Flannery
  // The contents of this file are in the public domain. Thanks to the authors.
  
  /* CAUTION: This is the ANSI C (only) version of the Numerical Recipes
     utility file nrutil.c.  Do not confuse this file with the same-named
     file nrutil.c that is supplied in the 'misc' subdirectory.
     *That* file is the one from the book, and contains both ANSI and
     traditional K&R versions, along with #ifdef macros to select the
     correct version.  *This* file contains only ANSI C.               */
  
  #include <stdio.h>
  #include <stddef.h>
  #include <stdlib.h>
  #define NR_END 1
  #define FREE_ARG char*
  
  void nrerror(char error_text[])
  /* Numerical Recipes standard error handler */
  {
    fprintf(stderr,"Numerical Recipes run-time error...\n");
    fprintf(stderr,"%s\n",error_text);
    fprintf(stderr,"...now exiting to system...\n");
    exit(1);
  }
  
  float *vector(long nl, long nh)
  /* allocate a float vector with subscript range v[nl..nh] */
  {
    float *v;
  
    v=(float *)malloc((size_t) ((nh-nl+1+NR_END)*sizeof(float)));
    if (!v) nrerror("allocation failure in vector()");
    return v-nl+NR_END;
  }
  
  int *ivector(long nl, long nh)
  /* allocate an int vector with subscript range v[nl..nh] */
  {
    int *v;
  
    v=(int *)malloc((size_t) ((nh-nl+1+NR_END)*sizeof(int)));
    if (!v) nrerror("allocation failure in ivector()");
    return v-nl+NR_END;
  }
  
  char *cvector(long nl, long nh)
  /* allocate an char vector with subscript range v[nl..nh] */
  {
    char *v;
  
    v=(char *)malloc((size_t) ((nh-nl+1+NR_END)*sizeof(char)));
    if (!v) nrerror("allocation failure in cvector()");
    return v-nl+NR_END;
  }
  
  // cam new:
  
  char **cmatrix(long nrl, long nrh, long ncl, long nch)
  /* allocate a character matrix with subscript range m[nrl..nrh][ncl..nch] */
  
  {
    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;
    char **m;
  
    /* allocate pointers to rows */
    m=(char **) malloc((size_t)((nrow+NR_END)*sizeof(char*)));
    if (!m) nrerror("allocation failure 1 in cmatrix()");
    m += NR_END;
    m -= nrl;
  
    /* allocate rows and set pointers to them */
    m[nrl]=(char *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(char)));
    if (!m[nrl]) nrerror("allocation failure 2 in cmatrix()");
    m[nrl] += NR_END;
    m[nrl] -= ncl;
  
    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;
  
    /* return pointer to array of pointers to rows */
    return m;
  }
  
  
  //
  
  unsigned long *lvector(long nl, long nh)
  /* allocate an unsigned long vector with subscript range v[nl..nh] */
  {
    unsigned long *v;
  
    v=(unsigned long *)malloc((size_t) ((nh-nl+1+NR_END)*sizeof(long)));
    if (!v) nrerror("allocation failure in lvector()");
    return v-nl+NR_END;
  }
  
  double *dvector(long nl, long nh)
  /* allocate a double vector with subscript range v[nl..nh] */
  {
    double *v;
  
    v=(double *)malloc((size_t) ((nh-nl+1+NR_END)*sizeof(double)));
    if (!v) nrerror("allocation failure in dvector()");
    return v-nl+NR_END;
  }
  
  float **matrix(long nrl, long nrh, long ncl, long nch)
  /* allocate a float matrix with subscript range m[nrl..nrh][ncl..nch] */
  {
    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;
    float **m;
  
    /* allocate pointers to rows */
    m=(float **) malloc((size_t)((nrow+NR_END)*sizeof(float*)));
    if (!m) nrerror("allocation failure 1 in matrix()");
    m += NR_END;
    m -= nrl;
  
    /* allocate rows and set pointers to them */
    m[nrl]=(float *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(float)));
    if (!m[nrl]) nrerror("allocation failure 2 in matrix()");
    m[nrl] += NR_END;
    m[nrl] -= ncl;
  
    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;
  
    /* return pointer to array of pointers to rows */
    return m;
  }
  
  double **dmatrix(long nrl, long nrh, long ncl, long nch)
  /* allocate a double matrix with subscript range m[nrl..nrh][ncl..nch] */
  {
    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;
    double **m;
  
    /* allocate pointers to rows */
    m=(double **) malloc((size_t)((nrow+NR_END)*sizeof(double*)));
    if (!m) nrerror("allocation failure 1 in dmatrix()");
    m += NR_END;
    m -= nrl;
  
    /* allocate rows and set pointers to them */
    m[nrl]=(double *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double)));
    if (!m[nrl]) nrerror("allocation failure 2 in dmatrix()");
    m[nrl] += NR_END;
    m[nrl] -= ncl;
  
    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;
  
    /* return pointer to array of pointers to rows */
    return m;
  }
  
  int **imatrix(long nrl, long nrh, long ncl, long nch)
  /* allocate a int matrix with subscript range m[nrl..nrh][ncl..nch] */
  {
    long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;
    int **m;
  
    /* allocate pointers to rows */
    m=(int **) malloc((size_t)((nrow+NR_END)*sizeof(int*)));
    if (!m) nrerror("allocation failure 1 in imatrix()");
    m += NR_END;
    m -= nrl;
  
  
    /* allocate rows and set pointers to them */
    m[nrl]=(int *) malloc((size_t)((nrow*ncol+NR_END)*sizeof(int)));
    if (!m[nrl]) nrerror("allocation failure 2 in imatrix()");
    m[nrl] += NR_END;
    m[nrl] -= ncl;
  
    for(i=nrl+1;i<=nrh;i++) m[i]=m[i-1]+ncol;
  
    /* return pointer to array of pointers to rows */
    return m;
  }
  
  float **submatrix(float **a, long oldrl, long oldrh, long oldcl, long oldch,
                    long newrl, long newcl)
  /* point a submatrix [newrl..][newcl..] to a[oldrl..oldrh][oldcl..oldch] */
  {
    long i,j,nrow=oldrh-oldrl+1,ncol=oldcl-newcl;
    float **m;
  
    /* allocate array of pointers to rows */
    m=(float **) malloc((size_t) ((nrow+NR_END)*sizeof(float*)));
    if (!m) nrerror("allocation failure in submatrix()");
    m += NR_END;
    m -= newrl;
  
    /* set pointers to rows */
    for(i=oldrl,j=newrl;i<=oldrh;i++,j++) m[j]=a[i]+ncol;
  
    /* return pointer to array of pointers to rows */
    return m;
  }
  
  float **convert_matrix(float *a, long nrl, long nrh, long ncl, long nch)
  /* allocate a float matrix m[nrl..nrh][ncl..nch] that points to the matrix
     declared in the standard C manner as a[nrow][ncol], where nrow=nrh-nrl+1
     and ncol=nch-ncl+1. The routine should be called with the address
     &a[0][0] as the first argument. */
  {
    long i,j,nrow=nrh-nrl+1,ncol=nch-ncl+1;
    float **m;
  
    /* allocate pointers to rows */
    m=(float **) malloc((size_t) ((nrow+NR_END)*sizeof(float*)));
    if (!m) nrerror("allocation failure in convert_matrix()");
    m += NR_END;
    m -= nrl;
  
    /* set pointers to rows */
    m[nrl]=a-ncl;
    for(i=1,j=nrl+1;i<nrow;i++,j++) m[j]=m[j-1]+ncol;
    /* return pointer to array of pointers to rows */
    return m;
  }
  
  float ***f3tensor(long nrl, long nrh, long ncl, long nch, long ndl, long ndh)
  /* allocate a float 3tensor with range t[nrl..nrh][ncl..nch][ndl..ndh] */
  {
    long i,j,nrow=nrh-nrl+1,ncol=nch-ncl+1,ndep=ndh-ndl+1;
    float ***t;
  
    /* allocate pointers to pointers to rows */
    t=(float ***) malloc((size_t)((nrow+NR_END)*sizeof(float**)));
    if (!t) nrerror("allocation failure 1 in f3tensor()");
    t += NR_END;
    t -= nrl;
  
    /* allocate pointers to rows and set pointers to them */
    t[nrl]=(float **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(float*)));
    if (!t[nrl]) nrerror("allocation failure 2 in f3tensor()");
    t[nrl] += NR_END;
    t[nrl] -= ncl;
  
    /* allocate rows and set pointers to them */
    t[nrl][ncl]=(float *) malloc((size_t)((nrow*ncol*ndep+NR_END)*sizeof(float)));
    if (!t[nrl][ncl]) nrerror("allocation failure 3 in f3tensor()");
    t[nrl][ncl] += NR_END;
    t[nrl][ncl] -= ndl;
  
    for(j=ncl+1;j<=nch;j++) t[nrl][j]=t[nrl][j-1]+ndep;
    for(i=nrl+1;i<=nrh;i++) {
      t[i]=t[i-1]+ncol;
      t[i][ncl]=t[i-1][ncl]+ncol*ndep;
      for(j=ncl+1;j<=nch;j++) t[i][j]=t[i][j-1]+ndep;
    }
  
    /* return pointer to array of pointers to rows */
    return t;
  }
  
  double ***d3tensor(long nrl, long nrh, long ncl, long nch, long ndl, long ndh)
  /* allocate a double 3tensor with range t[nrl..nrh][ncl..nch][ndl..ndh] */
  {
    long i,j,nrow=nrh-nrl+1,ncol=nch-ncl+1,ndep=ndh-ndl+1;
    double ***t;
  
    /* allocate pointers to pointers to rows */
    t=(double ***) malloc((size_t)((nrow+NR_END)*sizeof(double**)));
    if (!t) nrerror("allocation failure 1 in d3tensor()");
    t += NR_END;
    t -= nrl;
  
    /* allocate pointers to rows and set pointers to them */
    t[nrl]=(double **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(double*)));
    if (!t[nrl]) nrerror("allocation failure 2 in d3tensor()");
    t[nrl] += NR_END;
    t[nrl] -= ncl;
  
    /* allocate rows and set pointers to them */
    t[nrl][ncl]=(double *) malloc((size_t)((nrow*ncol*ndep+NR_END)*sizeof(double)));
    if (!t[nrl][ncl]) nrerror("allocation failure 3 in d3tensor()");
    t[nrl][ncl] += NR_END;
    t[nrl][ncl] -= ndl;
  
    for(j=ncl+1;j<=nch;j++) t[nrl][j]=t[nrl][j-1]+ndep;
    for(i=nrl+1;i<=nrh;i++) {
      t[i]=t[i-1]+ncol;
      t[i][ncl]=t[i-1][ncl]+ncol*ndep;
      for(j=ncl+1;j<=nch;j++) t[i][j]=t[i][j-1]+ndep;
    }
  
    /* return pointer to array of pointers to rows */
    return t;
  }
  
  // cam added:
  char ***c3d(long nrl, long nrh, long ncl, long nch, long ndl, long ndh)
  /* allocate a char 3tensor with range t[nrl..nrh][ncl..nch][ndl..ndh] */
  {
    long i,j,nrow=nrh-nrl+1,ncol=nch-ncl+1,ndep=ndh-ndl+1;
    char ***t;
  
    /* allocate pointers to pointers to rows */
    t=(char ***) malloc((size_t)((nrow+NR_END)*sizeof(char**)));
    if (!t) nrerror("allocation failure 1 in c3d()");
    t += NR_END;
    t -= nrl;
  
    /* allocate pointers to rows and set pointers to them */
    t[nrl]=(char **) malloc((size_t)((nrow*ncol+NR_END)*sizeof(char*)));
    if (!t[nrl]) nrerror("allocation failure 2 in c3d()");
    t[nrl] += NR_END;
    t[nrl] -= ncl;
  
    /* allocate rows and set pointers to them */
    t[nrl][ncl]=(char *) malloc((size_t)((nrow*ncol*ndep+NR_END)*sizeof(char)));
    if (!t[nrl][ncl]) nrerror("allocation failure 3 in c3d()");
    t[nrl][ncl] += NR_END;
    t[nrl][ncl] -= ndl;
  
    for(j=ncl+1;j<=nch;j++) t[nrl][j]=t[nrl][j-1]+ndep;
    for(i=nrl+1;i<=nrh;i++) {
      t[i]=t[i-1]+ncol;
      t[i][ncl]=t[i-1][ncl]+ncol*ndep;
      for(j=ncl+1;j<=nch;j++) t[i][j]=t[i][j-1]+ndep;
    }
  
    /* return pointer to array of pointers to rows */
    return t;
  }
  
  
  void free_vector(float *v, long nl, long nh)
  /* free a float vector allocated with vector() */
  {
    free((FREE_ARG) (v+nl-NR_END));
  }
  
  void free_ivector(int *v, long nl, long nh)
  /* free an int vector allocated with ivector() */
  {
    free((FREE_ARG) (v+nl-NR_END));
  }
  
  void free_cvector(char *v, long nl, long nh)
  /* free an char vector allocated with cvector() */
  {
    free((FREE_ARG) (v+nl-NR_END));
  }
  
  void free_lvector(unsigned long *v, long nl, long nh)
  /* free an unsigned long vector allocated with lvector() */
  {
    free((FREE_ARG) (v+nl-NR_END));
  }
  
  void free_dvector(double *v, long nl, long nh)
  /* free a double vector allocated with dvector() */
  {
    free((FREE_ARG) (v+nl-NR_END));
  }
  
  void free_matrix(float **m, long nrl, long nrh, long ncl, long nch)
  /* free a float matrix allocated by matrix() */
  {
    free((FREE_ARG) (m[nrl]+ncl-NR_END));
    free((FREE_ARG) (m+nrl-NR_END));
  }
  
  void free_cmatrix(char **m, long nrl, long nrh, long ncl, long nch)
  /* free a character matrix allocated by matrix() */
  {
    free((FREE_ARG) (m[nrl]+ncl-NR_END));
    free((FREE_ARG) (m+nrl-NR_END));
  }
  
  void free_dmatrix(double **m, long nrl, long nrh, long ncl, long nch)
  /* free a double matrix allocated by dmatrix() */
  {
    free((FREE_ARG) (m[nrl]+ncl-NR_END));
    free((FREE_ARG) (m+nrl-NR_END));
  }
  
  void free_imatrix(int **m, long nrl, long nrh, long ncl, long nch)
  /* free an int matrix allocated by imatrix() */
  {
    free((FREE_ARG) (m[nrl]+ncl-NR_END));
    free((FREE_ARG) (m+nrl-NR_END));
  }
  
  void free_submatrix(float **b, long nrl, long nrh, long ncl, long nch)
  /* free a submatrix allocated by submatrix() */
  {
    free((FREE_ARG) (b+nrl-NR_END));
  }
  
  void free_convert_matrix(float **b, long nrl, long nrh, long ncl, long nch)
  /* free a matrix allocated by convert_matrix() */
  {
    free((FREE_ARG) (b+nrl-NR_END));
  }
  
  void free_f3tensor(float ***t, long nrl, long nrh, long ncl, long nch,
                     long ndl, long ndh)
  /* free a float f3tensor allocated by f3tensor() */
  {
    free((FREE_ARG) (t[nrl][ncl]+ndl-NR_END));
    free((FREE_ARG) (t[nrl]+ncl-NR_END));
    free((FREE_ARG) (t+nrl-NR_END));
  }
  
  void free_d3tensor(double ***t, long nrl, long nrh, long ncl, long nch,
                     long ndl, long ndh)
  /* free a double d3tensor allocated by f3tensor() */
  {
    free((FREE_ARG) (t[nrl][ncl]+ndl-NR_END));
    free((FREE_ARG) (t[nrl]+ncl-NR_END));
    free((FREE_ARG) (t+nrl-NR_END));
  }
  
  void free_c3d(char ***t, long nrl, long nrh, long ncl, long nch,\
                long ndl, long ndh)
  /* free a float f3tensor allocated by f3tensor() */
  {
    free((FREE_ARG) (t[nrl][ncl]+ndl-NR_END));
    free((FREE_ARG) (t[nrl]+ncl-NR_END));
    free((FREE_ARG) (t+nrl-NR_END));
  }
  
  