Style for handling matrices in C

[Alan Myrvold]

There's been another (well deserved) round of bashing 
in comp.lang.c for the way "Numerical Recipes" dynamically 
allocates matrices.

It is kinda too bad that they picked such an ugly (and illegal)
way to handle matrices and vectors. I have their book (in FORTRAN) 
and find it a nice readable introduction to many numerical 
methods. Had they chosen a reasonable style, it might have become
commonplace.

So my question is, what C style SHOULD become commonplace for
allocating matrices :

1) Encapsulate size and data into a struct :
   typedef struct { int row,col; double **x; } matrix;

2) Allocate a matrix as a vector and do arithmetic in subscript
   calculations (like Fortran, but the C compiler probably
   won't optimize the loops as well as Fortran).
 
   typedef double *matrix;
   x = malloc(row*col*sizeof(double));
   x[j*row+i] = 3.0;

3) K&R style 2-d matrices -- number of rows required to free matrix
   typedef double **matrix;

   matrix mat_alloc(row,col)
   int row,col;
   {
      matrix x;

      x = (double **) malloc(row*sizeof(double *));
      for (i = 0; i < row; i++) 
          x[i] = (double *) malloc(col*sizeof(double));
      return x;
   }

   void free_mat(x,row) 
   matrix x;
   int row;
   {
      for (i = row-1; i >= 0; i--) free(x[i]);
      free(x);
   }

4) 2-d matrices -- number of rows NOT required to free matrix
   typedef double **matrix;

   matrix mat_alloc(row,col)
   int row,col;
   {
      matrix x;

      x = (double **) malloc((row+1)*sizeof(double *));
      for (i = 0; i < row; i++) 
          x[i] = (double *) malloc(col*sizeof(double));
      x[row] = NULL;
      return x;
   }

   void free_mat(x) 
   matrix x;
   {
      matrix y;

      for (y = x; *y; y++) free(*y);
      free(x);
   }

5) Are there any other styles commonly used for 
   non-sparse matrices in C ???

---
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