mod2dense.c

/* MOD2DENSE.C - Procedures for handling dense mod2 matrices. */

/* Copyright (c) 1995-2012 by Radford M. Neal.
 *
 * Permission is granted for anyone to copy, use, modify, and distribute
 * these programs and accompanying documents for any purpose, provided
 * this copyright notice is retained and prominently displayed, and note
 * is made of any changes made to these programs.  These programs and
 * documents are distributed without any warranty, express or implied.
 * As the programs were written for research purposes only, they have not
 * been tested to the degree that would be advisable in any important
 * application.  All use of these programs is entirely at the user's own
 * risk.
 */


/* NOTE:  See mod2dense.html for documentation on these procedures. */


#include <stdlib.h>
#include <stdio.h>
#include <math.h>

#include "alloc.h"
#include "intio.h"
#include "mod2dense.h"


/* ALLOCATE SPACE FOR A DENSE MOD2 MATRIX. */

mod2dense *mod2dense_allocate 
( int n_rows, 		/* Number of rows in matrix */
  int n_cols		/* Number of columns in matrix */
)
{
  mod2dense *m;
  int j;

  if (n_rows<=0 || n_cols<=0)
  { fprintf(stderr,"mod2dense_allocate: Invalid number of rows or columns\n");
    exit(1);
  }

  m = chk_alloc (1, sizeof *m);

  m->n_rows = n_rows;
  m->n_cols = n_cols;

  m->n_words = (n_rows+mod2_wordsize-1) >> mod2_wordsize_shift;

  m->col = chk_alloc (m->n_cols, sizeof *m->col);

  m->bits = chk_alloc(m->n_words*m->n_cols, sizeof *m->bits);

  for (j = 0; j<m->n_cols; j++)
  { m->col[j] = m->bits + j*m->n_words;
  }

  return m;
}


/* FREE SPACE OCCUPIED BY A DENSE MOD2 MATRIX. */

void mod2dense_free
( mod2dense *m		/* Matrix to free */
)
{ free(m->bits);
  free(m->col);
  free(m);
}


/* CLEAR A DENSE MOD2 MATRIX. */

void mod2dense_clear
( mod2dense *r
)
{
  int k, j;

  for (j = 0; j<mod2dense_cols(r); j++)
  { for (k = 0; k<r->n_words; k++)
    { r->col[j][k] = 0;
    }
  }

}


/* COPY A DENSE MOD2 MATRIX. */

void mod2dense_copy
( mod2dense *m,		/* Matrix to copy */
  mod2dense *r		/* Place to store copy of matrix */
)
{ 
  int k, j;

  if (mod2dense_rows(m)>mod2dense_rows(r) 
   || mod2dense_cols(m)>mod2dense_cols(r))
  { fprintf(stderr,"mod2dense_copy: Destination matrix is too small\n");
    exit(1);
  }

  for (j = 0; j<mod2dense_cols(m); j++)
  { for (k = 0; k<m->n_words; k++)
    { r->col[j][k] = m->col[j][k];
    }
    for ( ; k<r->n_words; k++)
    { r->col[j][k] = 0;
    }
  }

  for ( ; j<mod2dense_cols(r); j++)
  { for (k = 0; k<r->n_words; k++)
    { r->col[j][k] = 0;
    }
  }
}


/* COPY ROWS OF A DENSE MOD2 MATRIX. */

void mod2dense_copyrows
( mod2dense *m,		/* Matrix to copy */
  mod2dense *r,		/* Place to store copy of matrix */
  int *rows		/* Indexes of rows to copy, from 0 */
)
{ 
  int i, j;

  if (mod2dense_cols(m)>mod2dense_cols(r))
  { fprintf(stderr,
      "mod2dense_copyrows: Destination matrix has fewer columns than source\n");
    exit(1);
  }

  mod2dense_clear(r);

  for (i = 0; i<mod2dense_rows(r); i++)
  { if (rows[i]<0 || rows[i]>=mod2dense_rows(m))
    { fprintf(stderr,"mod2dense_copyrows: Row index out of range\n");
      exit(1);
    }
    for (j = 0; j<mod2dense_cols(m); j++)
    { mod2dense_set(r,i,j,mod2dense_get(m,rows[i],j));
    }
  }
}


/* COPY COLUMNS OF A DENSE MOD2 MATRIX. */

void mod2dense_copycols
( mod2dense *m,		/* Matrix to copy */
  mod2dense *r,		/* Place to store copy of matrix */
  int *cols		/* Indexes of columns to copy, from 0 */
)
{ 
  int k, j;

  if (mod2dense_rows(m)>mod2dense_rows(r))
  { fprintf(stderr,
      "mod2dense_copycols: Destination matrix has fewer rows than source\n");
    exit(1);
  }

  for (j = 0; j<mod2dense_cols(r); j++)
  { if (cols[j]<0 || cols[j]>=mod2dense_cols(m))
    { fprintf(stderr,"mod2dense_copycols: Column index out of range\n");
      exit(1);
    }
    for (k = 0; k<m->n_words; k++)
    { r->col[j][k] = m->col[cols[j]][k];
    }
    for ( ; k<r->n_words; k++)
    { r->col[j][k] = 0;
    }
  }
}


/* PRINT A DENSE MOD2 MATRIX IN HUMAN-READABLE FORM. */

void mod2dense_print     
( FILE *f,
  mod2dense *m
)
{ 
  int i, j;

  for (i = 0; i<mod2dense_rows(m); i++)
  { for (j = 0; j<mod2dense_cols(m); j++)
    { fprintf(f," %d",mod2dense_get(m,i,j));
    }
    fprintf(f,"\n");
  }
}


/* WRITE A DENSE MOD2 MATRIX TO A FILE IN MACHINE-READABLE FORM.

   Data is written using intio_write, so that it will be readable on a machine
   with a different byte-ordering.  At present, this assumes that the words 
   used to pack bits into are no longer than 32 bits. */

int mod2dense_write     
( FILE *f, 
  mod2dense *m
)
{ 
  int j, k;

  intio_write(f,m->n_rows);
  if (ferror(f)) return 0;

  intio_write(f,m->n_cols);
  if (ferror(f)) return 0;

  for (j = 0; j<mod2dense_cols(m); j++)
  {
    for (k = 0; k<m->n_words; k++)
    { intio_write(f,m->col[j][k]);
      if (ferror(f)) return 0;
    }
  }

  return 1;
}


/* READ A DENSE MOD2 MATRIX STORED IN MACHINE-READABLE FORM FROM A FILE. */

mod2dense *mod2dense_read  
( FILE *f
)
{ 
  int n_rows, n_cols;
  mod2dense *m;
  int j, k;
  
  n_rows = intio_read(f);
  if (feof(f) || ferror(f) || n_rows<=0) return 0;

  n_cols = intio_read(f);
  if (feof(f) || ferror(f) || n_cols<=0) return 0;

  m = mod2dense_allocate(n_rows,n_cols);

  for (j = 0; j<mod2dense_cols(m); j++)
  {
    for (k = 0; k<m->n_words; k++)
    { m->col[j][k] = intio_read(f);
      if (feof(f) || ferror(f)) 
      { mod2dense_free(m);
        return 0;
      }
    }
  }

  return m;
}


/* GET AN ELEMENT FROM A DENSE MOD2 MATRIX. */

int mod2dense_get  
( mod2dense *m, 	/* Matrix to get element from */
  int row,		/* Row of element (starting with zero) */
  int col		/* Column of element (starting with zero) */
)
{
  if (row<0 || row>=mod2dense_rows(m) || col<0 || col>=mod2dense_cols(m))
  { fprintf(stderr,"mod2dense_get: row or column index out of bounds\n");
    exit(1);
  }

  return mod2_getbit (m->col[col][row>>mod2_wordsize_shift], 
                      row&mod2_wordsize_mask);
}


/* SET AN ELEMENT IN A DENSE MOD2 MATRIX. */

void mod2dense_set 
( mod2dense *m, 	/* Matrix to modify element of */
  int row,		/* Row of element (starting with zero) */
  int col,		/* Column of element (starting with zero) */
  int value		/* New value of element (0 or 1) */
)
{ 
  mod2word *w;

  if (row<0 || row>=mod2dense_rows(m) || col<0 || col>=mod2dense_cols(m))
  { fprintf(stderr,"mod2dense_set: row or column index out of bounds\n");
    exit(1);
  }

  w = &m->col[col][row>>mod2_wordsize_shift];

  *w = value ? mod2_setbit1(*w,row&mod2_wordsize_mask) 
             : mod2_setbit0(*w,row&mod2_wordsize_mask);
}


/* FLIP AN ELEMENT OF A DENSE MOD2 MATRIX. */

int mod2dense_flip  
( mod2dense *m, 	/* Matrix to flip element in */
  int row,		/* Row of element (starting with zero) */
  int col		/* Column of element (starting with zero) */
)
{
  mod2word *w;
  int b;

  if (row<0 || row>=mod2dense_rows(m) || col<0 || col>=mod2dense_cols(m))
  { fprintf(stderr,"mod2dense_flip: row or column index out of bounds\n");
    exit(1);
  }

  b = 1 ^ mod2_getbit (m->col[col][row>>mod2_wordsize_shift], 
                       row&mod2_wordsize_mask);

  w = &m->col[col][row>>mod2_wordsize_shift];

  *w = b ? mod2_setbit1(*w,row&mod2_wordsize_mask) 
         : mod2_setbit0(*w,row&mod2_wordsize_mask);

  return b;
}


/* COMPUTE THE TRANSPOSE OF A DENSE MOD2 MATRIX. */

void mod2dense_transpose
( mod2dense *m,		/* Matrix to compute transpose of (left unchanged) */
  mod2dense *r		/* Result of transpose operation */
)
{
  mod2word w, v, *p;
  int k1, j1, i2, j2;

  if (mod2dense_rows(m)!=mod2dense_cols(r) 
   || mod2dense_cols(m)!=mod2dense_rows(r))
  { fprintf(stderr,
     "mod2dense_transpose: Matrices have incompatible dimensions\n");
    exit(1);
  }

  if (r==m)
  { fprintf(stderr, 
     "mod2dense_transpose: Result matrix is the same as the operand\n");
    exit(1);
  }

  mod2dense_clear(r);

  for (j1 = 0; j1<mod2dense_cols(m); j1++)
  { 
    i2 = j1 >> mod2_wordsize_shift;
    v = 1 << (j1 & mod2_wordsize_mask);

    p = m->col[j1];
    k1 = 0;

    for (j2 = 0; j2<mod2dense_cols(r); j2++)
    { if (k1==0)
      { w = *p++;
        k1 = mod2_wordsize;
      }
      if (w&1)
      { r->col[j2][i2] |= v;
      }
      w >>= 1;     
      k1 -= 1;
    }
  }
}


/* ADD TWO DENSE MOD2 MATRICES. */

void mod2dense_add
( mod2dense *m1,	/* Left operand of add */
  mod2dense *m2,	/* Right operand of add */
  mod2dense *r		/* Place to store result of add */
)
{
  int j, k;

  if (mod2dense_rows(m1)!=mod2dense_rows(r) 
   || mod2dense_cols(m1)!=mod2dense_cols(r) 
   || mod2dense_rows(m2)!=mod2dense_rows(r)
   || mod2dense_cols(m2)!=mod2dense_cols(r))
  { fprintf(stderr,"mod2dense_add: Matrices have different dimensions\n");
    exit(1);
  }

  for (j = 0; j<mod2dense_cols(r); j++)
  { for (k = 0; k<r->n_words; k++)
    { r->col[j][k] = m1->col[j][k] ^ m2->col[j][k];
    }
  }
}


/* MULTIPLY TWO DENSE MOD2 MATRICES. 

   The algorithm used runs faster if the second matrix (right operand of the
   multiply) is sparse, but it is also appropriate for dense matrices.  This
   procedure could be speeded up a bit by replacing the call of mod2dense_get
   with in-line code that avoids division, but this doesn't seem worthwhile
   at the moment. 
*/

void mod2dense_multiply 
( mod2dense *m1, 	/* Left operand of multiply */
  mod2dense *m2,	/* Right operand of multiply */
  mod2dense *r		/* Place to store result of multiply */
)
{
  int i, j, k;

  if (mod2dense_cols(m1)!=mod2dense_rows(m2) 
   || mod2dense_rows(m1)!=mod2dense_rows(r) 
   || mod2dense_cols(m2)!=mod2dense_cols(r))
  { fprintf(stderr,
     "mod2dense_multiply: Matrices have incompatible dimensions\n");
    exit(1);
  }

  if (r==m1 || r==m2)
  { fprintf(stderr,
      "mod2dense_multiply: Result matrix is the same as one of the operands\n");
    exit(1);
  }

  mod2dense_clear(r);

  for (j = 0; j<mod2dense_cols(r); j++)
  { for (i = 0; i<mod2dense_rows(m2); i++)
    { if (mod2dense_get(m2,i,j))
      { for (k = 0; k<r->n_words; k++)
        { r->col[j][k] ^= m1->col[i][k];
        }
      }
    }
  }
}


/* SEE WHETHER TWO DENSE MOD2 MATRICES ARE EQUAL. */

int mod2dense_equal
( mod2dense *m1,
  mod2dense *m2
)
{
  int k, j, w;
  mod2word m;

  if (mod2dense_rows(m1)!=mod2dense_rows(m2) 
   || mod2dense_cols(m1)!=mod2dense_cols(m2))
  { fprintf(stderr,"mod2dense_equal: Matrices have different dimensions\n");
    exit(1);
  }

  w = m1->n_words;

  /* Form a mask that has 1s in the lower bit positions corresponding to
     bits that contain information in the last word of a matrix column. */

  m = (1 << (mod2_wordsize - (w*mod2_wordsize-m1->n_rows))) - 1;
  
  for (j = 0; j<mod2dense_cols(m1); j++)
  {
    for (k = 0; k<w-1; k++)
    { if (m1->col[j][k] != m2->col[j][k]) return 0;
    }

    if ((m1->col[j][k]&m) != (m2->col[j][k]&m)) return 0;
  }

  return 1;
}


/* INVERT A DENSE MOD2 MATRIX. */

int mod2dense_invert 
( mod2dense *m,		/* The matrix to find the inverse of (destroyed) */
  mod2dense *r		/* Place to store the inverse */
)
{
  mod2word *s, *t;
  int i, j, k, n, w, k0, b0;

  if (mod2dense_rows(m)!=mod2dense_cols(m))
  { fprintf(stderr,"mod2dense_invert: Matrix to invert is not square\n");
    exit(1);
  }

  if (r==m)
  { fprintf(stderr, 
      "mod2dense_invert: Result matrix is the same as the operand\n");
    exit(1);
  }

  n = mod2dense_rows(m);
  w = m->n_words;

  if (mod2dense_rows(r)!=n || mod2dense_cols(r)!=n)
  { fprintf(stderr,
     "mod2dense_invert: Matrix to receive inverse has wrong dimensions\n");
    exit(1);
  }

  mod2dense_clear(r);
  for (i = 0; i<n; i++) 
  { mod2dense_set(r,i,i,1);
  }

  for (i = 0; i<n; i++)
  { 
    k0 = i >> mod2_wordsize_shift;
    b0 = i & mod2_wordsize_mask;

    for (j = i; j<n; j++) 
    { if (mod2_getbit(m->col[j][k0],b0)) break;
    }

    if (j==n) return 0;

    if (j!=i)
    {
      t = m->col[i];
      m->col[i] = m->col[j];
      m->col[j] = t;

      t = r->col[i];
      r->col[i] = r->col[j];
      r->col[j] = t;
    }

    for (j = 0; j<n; j++)
    { if (j!=i && mod2_getbit(m->col[j][k0],b0))
      { s = m->col[j];
        t = m->col[i];
        for (k = k0; k<w; k++) s[k] ^= t[k];
        s = r->col[j];
        t = r->col[i];
        for (k = 0; k<w; k++) s[k] ^= t[k];
      }
    }
  }

  return 1;
}


/* INVERT A DENSE MOD2 MATRIX WITH ROWS & COLUMNS SELECTED FROM BIGGER MATRIX.*/

int mod2dense_invert_selected
( mod2dense *m,		/* Matrix from which to pick a submatrix to invert */
  mod2dense *r,		/* Place to store the inverse */
  int *rows,		/* Set to indexes of rows used and not used */
  int *cols		/* Set to indexes of columns used and not used */
)
{
  mod2word *s, *t;
  int i, j, k, n, n2, w, k0, b0, c, R;

  if (r==m)
  { fprintf(stderr, 
      "mod2dense_invert_selected2: Result matrix is the same as the operand\n");
    exit(1);
  }

  n = mod2dense_rows(m);
  w = m->n_words;

  n2 = mod2dense_cols(m);

  if (mod2dense_rows(r)!=n || mod2dense_cols(r)!=n2)
  { fprintf(stderr,
"mod2dense_invert_selected2: Matrix to receive inverse has wrong dimensions\n");
    exit(1);
  }

  mod2dense_clear(r);

  for (i = 0; i<n; i++)
  { rows[i] = i;
  }

  for (j = 0; j<n2; j++)
  { cols[j] = j;
  }

  R = 0;
  i = 0;

  for (;;)
  { 
    while (i<n-R)
    {
      k0 = rows[i] >> mod2_wordsize_shift;
      b0 = rows[i] & mod2_wordsize_mask;

      for (j = i; j<n2; j++) 
      { if (mod2_getbit(m->col[cols[j]][k0],b0)) break;
      }

      if (j<n2) break;

      R += 1;
      c = rows[i];
      rows[i] = rows[n-R];
      rows[n-R] = c;

    }

    if (i==n-R) break;

    c = cols[j];
    cols[j] = cols[i];
    cols[i] = c;

    mod2dense_set(r,rows[i],c,1);

    for (j = 0; j<n2; j++)
    { if (j!=c && mod2_getbit(m->col[j][k0],b0))
      { s = m->col[j];
        t = m->col[c];
        for (k = 0; k<w; k++) s[k] ^= t[k];
        s = r->col[j];
        t = r->col[c];
        for (k = 0; k<w; k++) s[k] ^= t[k];
      }
    }

    i += 1;
  }

  for (j = n-R; j<n; j++)
  { s = r->col[cols[j]];
    for (k = 0; k<w; k++) s[k] = 0;
  }

  return R;
}


/* FORCIBLY INVERT A DENSE MOD2 MATRIX. */

int mod2dense_forcibly_invert 
( mod2dense *m, 	/* The matrix to find the inverse of (destroyed) */
  mod2dense *r,		/* Place to store the inverse */
  int *a_row,		/* Place to store row indexes of altered elements */
  int *a_col		/* Place to store column indexes of altered elements */
)
{
  mod2word *s, *t;
  int i, j, k, n, w, k0, b0;
  int u, c;

  if (mod2dense_rows(m)!=mod2dense_cols(m))
  { fprintf(stderr,
      "mod2dense_forcibly_invert: Matrix to invert is not square\n");
    exit(1);
  }

  if (r==m)
  { fprintf(stderr, 
      "mod2dense_forcibly_invert: Result matrix is the same as the operand\n");
    exit(1);
  }

  n = mod2dense_rows(m);
  w = m->n_words;

  if (mod2dense_rows(r)!=n || mod2dense_cols(r)!=n)
  { fprintf(stderr,
 "mod2dense_forcibly_invert: Matrix to receive inverse has wrong dimensions\n");
    exit(1);
  }

  mod2dense_clear(r);
  for (i = 0; i<n; i++) 
  { mod2dense_set(r,i,i,1);
  }

  for (i = 0; i<n; i++)
  { a_row[i] = -1;
    a_col[i] = i;
  }

  for (i = 0; i<n; i++)
  { 
    k0 = i >> mod2_wordsize_shift;
    b0 = i & mod2_wordsize_mask;

    for (j = i; j<n; j++) 
    { if (mod2_getbit(m->col[j][k0],b0)) break;
    }

    if (j==n)
    { j = i;
      mod2dense_set(m,i,j,1);
      a_row[i] = i;
    }

    if (j!=i)
    { 
      t = m->col[i];
      m->col[i] = m->col[j];
      m->col[j] = t;

      t = r->col[i];
      r->col[i] = r->col[j];
      r->col[j] = t;

      u = a_col[i];
      a_col[i] = a_col[j];
      a_col[j] = u;
    }

    for (j = 0; j<n; j++)
    { if (j!=i && mod2_getbit(m->col[j][k0],b0))
      { s = m->col[j];
        t = m->col[i];
        for (k = k0; k<w; k++) s[k] ^= t[k];
        s = r->col[j];
        t = r->col[i];
        for (k = 0; k<w; k++) s[k] ^= t[k];
      }
    }
  }

  c = 0;
  for (i = 0; i<n; i++)
  { if (a_row[i]!=-1)
    { a_row[c] = a_row[i];
      a_col[c] = a_col[i];
      c += 1;
    }
  }

  return c;
}