xref: /petsc/src/mat/impls/aij/seq/bas/spbas.c (revision 6322f4bdd5f893e0305d79cc40d8f509f3e1c464)

#include "petsc.h"
#include "../src/mat/impls/aij/seq/aij.h"
#include "spbas.h"


/*
  spbas_memory_requirement:
    Calculate the number of bytes needed to store tha matrix
*/
#undef __FUNCT__
#define __FUNCT__ "spbas_memory_requirement"
long int spbas_memory_requirement( spbas_matrix matrix)
{
   long int memreq = 6 * sizeof(PetscInt)         + /* nrows, ncols, nnz, n_alloc_icol,
						       n_alloc_val, col_idx_type */
     sizeof(PetscTruth)                 + /* block_data */
     sizeof(PetscScalar**)        + /* values */
     sizeof(PetscScalar*)         + /* alloc_val */
     2 * sizeof(int**)            + /* icols, icols0 */
     2 * sizeof(PetscInt*)             + /* row_nnz, alloc_icol */
     matrix.nrows * sizeof(PetscInt)   + /* row_nnz[*] */
     matrix.nrows * sizeof(PetscInt*);   /* icols[*] */

   /* icol0[*] */
   if (matrix.col_idx_type == SPBAS_OFFSET_ARRAY)
      { memreq += matrix.nrows * sizeof(PetscInt); }

   /* icols[*][*] */
   if (matrix.block_data)
      { memreq += matrix.n_alloc_icol * sizeof(PetscInt); }
   else
      { memreq += matrix.nnz * sizeof(PetscInt); }

   if (matrix.values)
   {
     memreq += matrix.nrows * sizeof(PetscScalar*); /* values[*] */
     /* values[*][*] */
       if (matrix.block_data)
          { memreq += matrix.n_alloc_val  * sizeof(PetscScalar); }
       else
          { memreq += matrix.nnz * sizeof(PetscScalar); }
   }

   return memreq;
}

/*
  spbas_allocate_pattern:
    allocate the pattern arrays row_nnz, icols and optionally values
*/
#undef __FUNCT__
#define __FUNCT__ "spbas_allocate_pattern"
PetscErrorCode spbas_allocate_pattern( spbas_matrix * result, PetscTruth do_values)
{
   PetscErrorCode ierr;
   PetscInt nrows = result->nrows;
   PetscInt col_idx_type = result->col_idx_type;

   PetscFunctionBegin;
   /* Allocate sparseness pattern */
   ierr = PetscMalloc(nrows*sizeof(PetscInt),&result->row_nnz);CHKERRQ(ierr);
   ierr = PetscMalloc(nrows*sizeof(PetscInt*),&result->icols);CHKERRQ(ierr);

   /* If offsets are given wrt an array, create array */
   if (col_idx_type == SPBAS_OFFSET_ARRAY)
   {
      ierr = PetscMalloc(nrows*sizeof(PetscInt),&result->icol0);CHKERRQ(ierr);
   }
   else
   {
      result->icol0 = PETSC_NULL;
   }

   /* If values are given, allocate values array */
   if (do_values)
   {
      ierr = PetscMalloc(nrows*sizeof(PetscScalar*),&result->values);CHKERRQ(ierr);
   }
   else
   {
      result->values = PETSC_NULL;
   }

   PetscFunctionReturn(0);
}

/*
spbas_allocate_data:
   in case of block_data:
       Allocate the data arrays alloc_icol and optionally alloc_val,
       set appropriate pointers from icols and values;
   in case of !block_data:
       Allocate the arrays icols[i] and optionally values[i]
*/
#undef __FUNCT__
#define __FUNCT__ "spbas_allocate_data"
PetscErrorCode spbas_allocate_data( spbas_matrix * result)
{
   PetscInt i;
   PetscInt nnz   = result->nnz;
   PetscInt nrows = result->nrows;
   PetscInt r_nnz;
   PetscErrorCode ierr;
   PetscTruth do_values = (result->values != PETSC_NULL) ? PETSC_TRUE : PETSC_FALSE;
   PetscTruth block_data = result->block_data;

   PetscFunctionBegin;
   if (block_data)
   {
     /* Allocate the column number array and point to it */
      result->n_alloc_icol = nnz;
      ierr = PetscMalloc(nnz*sizeof(PetscInt), &result->alloc_icol);CHKERRQ(ierr);
      result->icols[0]= result->alloc_icol;
      for (i=1; i<nrows; i++)
      {
          result->icols[i] = result->icols[i-1] + result->row_nnz[i-1];
      }

      /* Allocate the value array and point to it */
      if (do_values)
      {
         result->n_alloc_val= nnz;
         ierr = PetscMalloc(nnz*sizeof(PetscScalar), &result->alloc_val);CHKERRQ(ierr);
         result->values[0]= result->alloc_val;
         for (i=1; i<nrows; i++)
         {
             result->values[i] = result->values[i-1] + result->row_nnz[i-1];
         }
      }
   }
   else
   {
      for (i=0; i<nrows; i++)
      {
         r_nnz = result->row_nnz[i];
         ierr = PetscMalloc(r_nnz*sizeof(PetscInt), &result->icols[i]);CHKERRQ(ierr);
      }
      if (do_values)
      {
         for (i=0; i<nrows; i++)
         {
            r_nnz = result->row_nnz[i];
            ierr = PetscMalloc(r_nnz*sizeof(PetscScalar),
                               &result->values[i]);CHKERRQ(ierr);
         }
      }
   }

   PetscFunctionReturn(0);
}

/*
  spbas_row_order_icol
     determine if row i1 should come
       + before row i2 in the sorted rows (return -1),
       + after (return 1)
       + is identical (return 0).
*/
#undef __FUNCT__
#define __FUNCT__ "spbas_row_order_icol"
int spbas_row_order_icol(PetscInt i1, PetscInt i2, PetscInt *irow_in, PetscInt *icol_in,PetscInt col_idx_type)
{
   PetscInt j;
   PetscInt nnz1 = irow_in[i1+1] - irow_in[i1];
   PetscInt nnz2 = irow_in[i2+1] - irow_in[i2];

   PetscInt * icol1 = &icol_in[irow_in[i1]];
   PetscInt * icol2 = &icol_in[irow_in[i2]];

   if (nnz1<nnz2) {return -1;}
   if (nnz1>nnz2) {return 1;}

   if (col_idx_type == SPBAS_COLUMN_NUMBERS)
   {
      for (j=0; j<nnz1; j++)
      {
         if (icol1[j]< icol2[j]) {return -1;}
         if (icol1[j]> icol2[j]) {return 1;}
      }
   }
   else if (col_idx_type == SPBAS_DIAGONAL_OFFSETS)
   {
      for (j=0; j<nnz1; j++)
      {
         if (icol1[j]-i1< icol2[j]-i2) {return -1;}
         if (icol1[j]-i1> icol2[j]-i2) {return 1;}
      }
   }
   else if (col_idx_type == SPBAS_OFFSET_ARRAY)
   {
      for (j=1; j<nnz1; j++)
      {
         if (icol1[j]-icol1[0] < icol2[j]-icol2[0]) {return -1;}
         if (icol1[j]-icol1[0] > icol2[j]-icol2[0]) {return 1;}
      }
   }
   return 0;
}

/*
  spbas_mergesort_icols:
    return a sorting of the rows in which identical sparseness patterns are
    next to each other
*/
#undef __FUNCT__
#define __FUNCT__ "spbas_mergesort_icols"
PetscErrorCode spbas_mergesort_icols( PetscInt nrows, PetscInt * irow_in, PetscInt * icol_in,PetscInt col_idx_type, PetscInt *isort)
{
   PetscErrorCode ierr;
   PetscInt istep;       /* Chunk-sizes of already sorted parts of arrays */

   PetscInt i, i1, i2;   /* Loop counters for (partly) sorted arrays */

   PetscInt istart, i1end, i2end; /* start of newly sorted array part, end of both  parts */

   PetscInt *ialloc;     /* Allocated arrays */
   PetscInt *iswap;      /* auxiliary pointers for swapping */
   PetscInt *ihlp1;      /* Pointers to new version of arrays, */
   PetscInt *ihlp2;      /* Pointers to previous version of arrays, */

   PetscFunctionBegin;

   ierr = PetscMalloc(nrows*sizeof(PetscInt),&ialloc);CHKERRQ(ierr);

   ihlp1 = ialloc;
   ihlp2 = isort;

   /* Sorted array chunks are first 1 long, and increase until they are the complete array */
   for (istep=1; istep<nrows; istep*=2)
   {
     /*
       Combine sorted parts
            istart:istart+istep-1 and istart+istep-1:istart+2*istep-1
       of ihlp2 and vhlp2

       into one sorted part
            istart:istart+2*istep-1
       of ihlp1 and vhlp1
     */
      for (istart=0; istart<nrows; istart+=2*istep)
      {

	/* Set counters and bound array part endings */
         i1=istart;        i1end = i1+istep;  if (i1end>nrows) {i1end=nrows;}
         i2=istart+istep;  i2end = i2+istep;  if (i2end>nrows) {i2end=nrows;}

         /* Merge the two array parts */
         for (i=istart; i<i2end; i++)
         {
            if (i1<i1end && i2<i2end &&
                spbas_row_order_icol( ihlp2[i1], ihlp2[i2],
                             irow_in, icol_in, col_idx_type) < 0)
            {
                ihlp1[i] = ihlp2[i1];
                i1++;
            }
            else if (i2<i2end )
            {
                ihlp1[i] = ihlp2[i2];
                i2++;
            }
            else
            {
                ihlp1[i] = ihlp2[i1];
                i1++;
            }
         }
      }

      /* Swap the two array sets */
      iswap = ihlp2; ihlp2 = ihlp1; ihlp1 = iswap;
   }

   /* Copy one more time in case the sorted arrays are the temporary ones */
   if (ihlp2 != isort)
   {
      for (i=0; i<nrows; i++) { isort[i] = ihlp2[i]; }
   }

   ierr = PetscFree(ialloc);CHKERRQ(ierr);
   PetscFunctionReturn(0);
}



/*
  spbas_compress_pattern:
     calculate a compressed sparseness pattern for a sparseness pattern
     given in compressed row storage. The compressed sparseness pattern may
     require (much) less memory.
*/
#undef __FUNCT__
#define __FUNCT__ "spbas_compress_pattern"
PetscErrorCode spbas_compress_pattern(PetscInt *irow_in, PetscInt *icol_in, PetscInt nrows, PetscInt ncols,
				      PetscInt col_idx_type, spbas_matrix *B,PetscReal *mem_reduction)
{
   PetscInt nnz = irow_in[nrows];
   long int mem_orig = (nrows + nnz) * sizeof(PetscInt);
   long int mem_compressed;
   PetscErrorCode ierr;
   PetscInt *isort;
   PetscInt *icols;
   PetscInt row_nnz;
   PetscInt *ipoint;
   PetscTruth *used;
   PetscInt ptr;
   PetscInt i,j;

   const PetscTruth no_values = PETSC_FALSE;

   PetscFunctionBegin;

   /* Allocate the structure of the new matrix */
   B->nrows = nrows;
   B->ncols = ncols;
   B->nnz   = nnz;
   B->col_idx_type= col_idx_type;
   B->block_data = PETSC_TRUE;
   ierr = spbas_allocate_pattern( B, no_values);CHKERRQ(ierr);

   /* When using an offset array, set it */
   if (col_idx_type==SPBAS_OFFSET_ARRAY)
   {
      for (i=0; i<nrows; i++) {B->icol0[i] = icol_in[irow_in[i]];}
   }

   /* Allocate the ordering for the rows */
   ierr = PetscMalloc(nrows*sizeof(PetscInt),&isort);CHKERRQ(ierr);
   ierr = PetscMalloc(nrows*sizeof(PetscInt),&ipoint);CHKERRQ(ierr);
   ierr = PetscMalloc(nrows*sizeof(PetscTruth),&used);CHKERRQ(ierr);

   /*  Initialize the sorting */
   memset((void*) used, 0, nrows*sizeof(PetscTruth));
   for (i = 0; i<nrows; i++)
   {
      B->row_nnz[i] = irow_in[i+1]-irow_in[i];
      isort[i] = i;
      ipoint[i]= i;
   }

   /* Sort the rows so that identical columns will be next to each other */
   ierr = spbas_mergesort_icols( nrows, irow_in, icol_in, col_idx_type, isort);CHKERRQ(ierr);
   ierr = PetscInfo(PETSC_NULL,"Rows have been sorted for patterns\n");CHKERRQ(ierr);

   /* Replace identical rows with the first one in the list */
   for (i=1; i<nrows; i++)
   {
      if (spbas_row_order_icol(isort[i-1], isort[i],
                      irow_in, icol_in, col_idx_type) == 0)
      {
         ipoint[isort[i]] = ipoint[isort[i-1]];
      }
   }

   /* Collect the rows which are used*/
   for (i=0; i<nrows; i++) {used[ipoint[i]] = PETSC_TRUE;}

   /* Calculate needed memory */
   B->n_alloc_icol = 0;
   for (i=0; i<nrows; i++)
   {
      if (used[i]) {B->n_alloc_icol += B->row_nnz[i];}
   }

   ierr = PetscMalloc(B->n_alloc_icol*sizeof(PetscInt),&B->alloc_icol);CHKERRQ(ierr);

   /* Fill in the diagonal offsets for the rows which store their own data */
   ptr = 0;
   for (i=0; i<B->nrows; i++)
   {
      if (used[i])
      {
         B->icols[i] = &B->alloc_icol[ptr];
         icols = &icol_in[irow_in[i]];
         row_nnz = B->row_nnz[i];
         if (col_idx_type == SPBAS_COLUMN_NUMBERS)
         {
            for (j=0; j<row_nnz; j++)
            {
               B->icols[i][j] = icols[j];
            }
         }
         else if (col_idx_type == SPBAS_DIAGONAL_OFFSETS)
         {
            for (j=0; j<row_nnz; j++)
            {
               B->icols[i][j] = icols[j]-i;
            }
         }
         else if (col_idx_type == SPBAS_OFFSET_ARRAY)
         {
            for (j=0; j<row_nnz; j++)
            {
               B->icols[i][j] = icols[j]-icols[0];
            }
         }
         ptr += B->row_nnz[i];
      }
   }

   /* Point to the right places for all data */
   for (i=0; i<nrows; i++)
   {
      B->icols[i] = B->icols[ipoint[i]];
   }
   ierr = PetscInfo(PETSC_NULL,"Row patterns have been compressed\n");CHKERRQ(ierr);
   ierr = PetscInfo1(PETSC_NULL,"         (%G nonzeros per row)\n",  (PetscReal) nnz / (PetscReal) nrows);CHKERRQ(ierr);

   ierr=PetscFree(isort);CHKERRQ(ierr);
   ierr=PetscFree(used);CHKERRQ(ierr);
   ierr=PetscFree(ipoint);CHKERRQ(ierr);

   mem_compressed = spbas_memory_requirement( *B );
   *mem_reduction = 100.0 * (PetscReal)(mem_orig-mem_compressed)/
                            (PetscReal) mem_orig;
   PetscFunctionReturn(0);
}

/*
   spbas_incomplete_cholesky
       Incomplete Cholesky decomposition
*/
#include "spbas_cholesky.h"

/*
  spbas_delete : de-allocate the arrays owned by this matrix
*/
#undef __FUNCT__
#define __FUNCT__ "spbas_delete"
PetscErrorCode spbas_delete(spbas_matrix matrix)
{
   PetscInt       i;
   PetscErrorCode ierr;

   PetscFunctionBegin;
   if (matrix.block_data) {
      ierr=PetscFree(matrix.alloc_icol);CHKERRQ(ierr)
      if (matrix.values){ierr=PetscFree(matrix.alloc_val);CHKERRQ(ierr);}
   } else  {
     for (i=0; i<matrix.nrows; i++) { ierr=PetscFree(matrix.icols[i]);CHKERRQ(ierr);}
     ierr = PetscFree(matrix.icols);CHKERRQ(ierr);
     if (matrix.values) {
         for (i=0; i<matrix.nrows; i++) { ierr=PetscFree(matrix.values[i]);CHKERRQ(ierr);}
      }
   }

   ierr=PetscFree(matrix.row_nnz);CHKERRQ(ierr);
   ierr=PetscFree(matrix.icols);CHKERRQ(ierr);
   if (matrix.col_idx_type == SPBAS_OFFSET_ARRAY) {ierr=PetscFree(matrix.icol0);CHKERRQ(ierr);}
   if (matrix.values)  {ierr=PetscFree(matrix.values);CHKERRQ(ierr);}
   PetscFunctionReturn(0);
}

/*
spbas_matrix_to_crs:
   Convert an spbas_matrix to compessed row storage
*/
#undef __FUNCT__
#define __FUNCT__ "spbas_matrix_to_crs"
PetscErrorCode spbas_matrix_to_crs(spbas_matrix matrix_A,MatScalar **val_out, PetscInt **irow_out, PetscInt **icol_out)
{
   PetscInt       nrows = matrix_A.nrows;
   PetscInt       nnz   = matrix_A.nnz;
   PetscInt       i,j,r_nnz,i0;
   PetscInt       *irow;
   PetscInt       *icol;
   PetscInt       *icol_A;
   MatScalar      *val;
   PetscScalar    *val_A;
   PetscInt       col_idx_type = matrix_A.col_idx_type;
   PetscTruth     do_values = matrix_A.values ? PETSC_TRUE : PETSC_FALSE;
   PetscErrorCode ierr;

   PetscFunctionBegin;
   ierr = PetscMalloc( sizeof(PetscInt) * (nrows+1), &irow);CHKERRQ(ierr);
   ierr = PetscMalloc( sizeof(PetscInt) * nnz, &icol);CHKERRQ(ierr);
   *icol_out = icol;
   *irow_out=irow;
   if (do_values)  {
      ierr = PetscMalloc( sizeof(MatScalar) * nnz, &val);CHKERRQ(ierr);
      *val_out = val; *icol_out = icol; *irow_out=irow;
   }

   irow[0]=0;
   for (i=0; i<nrows; i++) {
      r_nnz = matrix_A.row_nnz[i];
      i0 = irow[i];
      irow[i+1] = i0 + r_nnz;
      icol_A = matrix_A.icols[i];

      if (do_values) {
          val_A = matrix_A.values[i];
          for (j=0; j<r_nnz; j++) {
             icol[i0+j] = icol_A[j];
             val[i0+j]  = val_A[j];
          }
      } else {
          for (j=0; j<r_nnz; j++) { icol[i0+j] = icol_A[j]; }
      }

      if (col_idx_type == SPBAS_DIAGONAL_OFFSETS) {
         for (j=0; j<r_nnz; j++) { icol[i0+j] += i; }
      }
      else if (col_idx_type == SPBAS_OFFSET_ARRAY) {
         i0 = matrix_A.icol0[i];
         for (j=0; j<r_nnz; j++) { icol[i0+j] += i0; }
      }
   }
   PetscFunctionReturn(0);
}


/*
    spbas_transpose
       return the transpose of a matrix
*/
#undef __FUNCT__
#define __FUNCT__ "spbas_transpose"
PetscErrorCode spbas_transpose( spbas_matrix in_matrix, spbas_matrix * result)
{
   PetscInt       col_idx_type = in_matrix.col_idx_type;
   PetscInt       nnz   = in_matrix.nnz;
   PetscInt       ncols = in_matrix.nrows;
   PetscInt       nrows = in_matrix.ncols;
   PetscInt       i,j,k;
   PetscInt       r_nnz;
   PetscInt       *irow;
   PetscInt       icol0;
   PetscScalar    * val;
   PetscErrorCode ierr;
   PetscFunctionBegin;

   /* Copy input values */
   result->nrows        = nrows;
   result->ncols        = ncols;
   result->nnz          = nnz;
   result->col_idx_type = SPBAS_COLUMN_NUMBERS;
   result->block_data   = PETSC_TRUE;

   /* Allocate sparseness pattern */
   ierr =  spbas_allocate_pattern(result, in_matrix.values ? PETSC_TRUE : PETSC_FALSE);CHKERRQ(ierr);

   /*  Count the number of nonzeros in each row */
   for (i = 0; i<nrows; i++) { result->row_nnz[i] = 0; }

   for (i=0; i<ncols; i++) {
      r_nnz = in_matrix.row_nnz[i];
      irow  = in_matrix.icols[i];
      if (col_idx_type == SPBAS_COLUMN_NUMBERS)  {
         for (j=0; j<r_nnz; j++) { result->row_nnz[irow[j]]++; }
      } else if (col_idx_type == SPBAS_DIAGONAL_OFFSETS)  {
         for (j=0; j<r_nnz; j++) { result->row_nnz[i+irow[j]]++; }
      } else if (col_idx_type == SPBAS_OFFSET_ARRAY) {
         icol0=in_matrix.icol0[i];
         for (j=0; j<r_nnz; j++) { result->row_nnz[icol0+irow[j]]++; }
      }
   }

   /* Set the pointers to the data */
   ierr = spbas_allocate_data(result);CHKERRQ(ierr);

   /* Reset the number of nonzeros in each row */
   for (i = 0; i<nrows; i++) { result->row_nnz[i] = 0; }

   /* Fill the data arrays */
   if (in_matrix.values) {
      for (i=0; i<ncols; i++) {
         r_nnz = in_matrix.row_nnz[i];
         irow  = in_matrix.icols[i];
         val   = in_matrix.values[i];

         if      (col_idx_type == SPBAS_COLUMN_NUMBERS)   {icol0=0;}
         else if (col_idx_type == SPBAS_DIAGONAL_OFFSETS) {icol0=i;}
         else if (col_idx_type == SPBAS_OFFSET_ARRAY)
                 {icol0=in_matrix.icol0[i];}
         for (j=0; j<r_nnz; j++)  {
            k = icol0 + irow[j];
            result->icols[k][result->row_nnz[k]]  = i;
            result->values[k][result->row_nnz[k]] = val[j];
            result->row_nnz[k]++;
         }
      }
   }  else {
      for (i=0; i<ncols; i++) {
         r_nnz = in_matrix.row_nnz[i];
         irow  = in_matrix.icols[i];

         if      (col_idx_type == SPBAS_COLUMN_NUMBERS)   {icol0=0;}
         else if (col_idx_type == SPBAS_DIAGONAL_OFFSETS) {icol0=i;}
         else if (col_idx_type == SPBAS_OFFSET_ARRAY)     {icol0=in_matrix.icol0[i];}

         for (j=0; j<r_nnz; j++) {
            k = icol0 + irow[j];
            result->icols[k][result->row_nnz[k]]  = i;
            result->row_nnz[k]++;
         }
      }
   }
   PetscFunctionReturn(0);
}

/*
   spbas_mergesort

      mergesort for an array of intergers and an array of associated
      reals

      on output, icol[0..nnz-1] is increasing;
                  val[0..nnz-1] has undergone the same permutation as icol

      NB: val may be PETSC_NULL: in that case, only the integers are sorted

*/
#undef __FUNCT__
#define __FUNCT__ "spbas_mergesort"
PetscErrorCode spbas_mergesort(PetscInt nnz, PetscInt *icol, PetscScalar *val)
{
  PetscInt       istep;       /* Chunk-sizes of already sorted parts of arrays */
  PetscInt       i, i1, i2;   /* Loop counters for (partly) sorted arrays */
  PetscInt       istart, i1end, i2end; /* start of newly sorted array part, end of both parts */
  PetscInt       *ialloc;     /* Allocated arrays */
  PetscScalar    *valloc=PETSC_NULL;
  PetscInt       *iswap;      /* auxiliary pointers for swapping */
  PetscScalar    *vswap;
  PetscInt       *ihlp1;      /* Pointers to new version of arrays, */
  PetscScalar    *vhlp1=PETSC_NULL;  /* (arrays under construction) */
  PetscInt       *ihlp2;      /* Pointers to previous version of arrays, */
  PetscScalar    *vhlp2=PETSC_NULL;
  PetscErrorCode ierr;

   ierr = PetscMalloc(nnz*sizeof(PetscInt),&ialloc);CHKERRQ(ierr);
   ihlp1 = ialloc;
   ihlp2 = icol;

   if (val) {
      ierr = PetscMalloc(nnz*sizeof(PetscScalar),&valloc);CHKERRQ(ierr);
      vhlp1 = valloc;
      vhlp2 = val;
   }


   /* Sorted array chunks are first 1 long, and increase until they are the complete array */
   for (istep=1; istep<nnz; istep*=2) {
     /*
       Combine sorted parts
            istart:istart+istep-1 and istart+istep-1:istart+2*istep-1
       of ihlp2 and vhlp2

       into one sorted part
            istart:istart+2*istep-1
       of ihlp1 and vhlp1
     */
      for (istart=0; istart<nnz; istart+=2*istep) {

	/* Set counters and bound array part endings */
         i1=istart;        i1end = i1+istep;  if (i1end>nnz) {i1end=nnz;}
         i2=istart+istep;  i2end = i2+istep;  if (i2end>nnz) {i2end=nnz;}

         /* Merge the two array parts */
         if (val) {
            for (i=istart; i<i2end; i++) {
               if (i1<i1end && i2<i2end && ihlp2[i1] < ihlp2[i2]) {
                   ihlp1[i] = ihlp2[i1];
                   vhlp1[i] = vhlp2[i1];
                   i1++;
               } else if (i2<i2end ){
                   ihlp1[i] = ihlp2[i2];
                   vhlp1[i] = vhlp2[i2];
                   i2++;
               } else {
                   ihlp1[i] = ihlp2[i1];
                   vhlp1[i] = vhlp2[i1];
                   i1++;
               }
            }
         } else {
            for (i=istart; i<i2end; i++) {
               if (i1<i1end && i2<i2end && ihlp2[i1] < ihlp2[i2]) {
                   ihlp1[i] = ihlp2[i1];
                   i1++;
               } else if (i2<i2end ) {
                   ihlp1[i] = ihlp2[i2];
                   i2++;
               } else {
                   ihlp1[i] = ihlp2[i1];
                   i1++;
               }
            }
         }
      }

      /* Swap the two array sets */
      iswap = ihlp2; ihlp2 = ihlp1; ihlp1 = iswap;
      vswap = vhlp2; vhlp2 = vhlp1; vhlp1 = vswap;
   }

   /* Copy one more time in case the sorted arrays are the temporary ones */
   if (ihlp2 != icol) {
      for (i=0; i<nnz; i++) { icol[i] = ihlp2[i]; }
      if (val) {
         for (i=0; i<nnz; i++) { val[i] = vhlp2[i]; }
      }
   }

   ierr = PetscFree(ialloc);CHKERRQ(ierr);
   if(val){ierr = PetscFree(valloc);CHKERRQ(ierr);}
   PetscFunctionReturn(0);
}

/*
  spbas_apply_reordering_rows:
    apply the given reordering to the rows:  matrix_A = matrix_A(perm,:);
*/
#undef __FUNCT__
#define __FUNCT__ "spbas_apply_reordering_rows"
PetscErrorCode spbas_apply_reordering_rows(spbas_matrix *matrix_A, const PetscInt *permutation)
{
   PetscInt       i,j,ip;
   PetscInt       nrows=matrix_A->nrows;
   PetscInt       * row_nnz;
   PetscInt       **icols;
   PetscTruth     do_values = matrix_A->values ? PETSC_TRUE : PETSC_FALSE;
   PetscScalar    **vals=PETSC_NULL;
   PetscErrorCode ierr;

   PetscFunctionBegin;
   if (matrix_A->col_idx_type != SPBAS_DIAGONAL_OFFSETS) SETERRQ( PETSC_ERR_SUP_SYS,"must have diagonal offsets in pattern\n");

   if (do_values)  {
     ierr = PetscMalloc( sizeof(PetscScalar*)*nrows, &vals);CHKERRQ(ierr);
   }
   ierr = PetscMalloc( sizeof(PetscInt)*nrows, &row_nnz);CHKERRQ(ierr);
   ierr = PetscMalloc( sizeof(PetscInt*)*nrows, &icols);CHKERRQ(ierr);

   for (i=0; i<nrows;i++) {
      ip = permutation[i];
      if (do_values) {vals[i]    = matrix_A->values[ip];}
      icols[i]   = matrix_A->icols[ip];
      row_nnz[i] = matrix_A->row_nnz[ip];
      for (j=0; j<row_nnz[i]; j++) { icols[i][j] += ip-i; }
   }

   if (do_values){ ierr = PetscFree(matrix_A->values);CHKERRQ(ierr);}
   ierr = PetscFree(matrix_A->icols);CHKERRQ(ierr);
   ierr = PetscFree(matrix_A->row_nnz);CHKERRQ(ierr);

   if (do_values) { matrix_A->values  = vals; }
   matrix_A->icols   = icols;
   matrix_A->row_nnz = row_nnz;

   PetscFunctionReturn(0);
}


/*
  spbas_apply_reordering_cols:
    apply the given reordering to the columns:  matrix_A(:,perm) = matrix_A;
*/
#undef __FUNCT__
#define __FUNCT__ "spbas_apply_reordering_cols"
PetscErrorCode spbas_apply_reordering_cols( spbas_matrix *matrix_A,const PetscInt *permutation)
{
   PetscInt    i,j;
   PetscInt    nrows=matrix_A->nrows;
   PetscInt    row_nnz;
   PetscInt    *icols;
   PetscTruth  do_values = matrix_A->values ? PETSC_TRUE : PETSC_FALSE;
   PetscScalar *vals=PETSC_NULL;
   PetscErrorCode ierr;

   PetscFunctionBegin;
   if (matrix_A->col_idx_type != SPBAS_DIAGONAL_OFFSETS) SETERRQ( PETSC_ERR_SUP_SYS, "must have diagonal offsets in pattern\n");

   for (i=0; i<nrows;i++) {
      icols   = matrix_A->icols[i];
      row_nnz = matrix_A->row_nnz[i];
      if (do_values) { vals = matrix_A->values[i]; }

      for (j=0; j<row_nnz; j++)  {
         icols[j] = permutation[i+icols[j]]-i;
      }
      ierr = spbas_mergesort(row_nnz, icols, vals);CHKERRQ(ierr);
   }
   PetscFunctionReturn(0);
}

/*
  spbas_apply_reordering:
    apply the given reordering:  matrix_A(perm,perm) = matrix_A;
*/
#undef __FUNCT__
#define __FUNCT__ "spbas_apply_reordering"
PetscErrorCode spbas_apply_reordering( spbas_matrix *matrix_A, const PetscInt *permutation, const PetscInt * inv_perm)
{
   PetscErrorCode ierr;
   PetscFunctionBegin;
   ierr = spbas_apply_reordering_rows( matrix_A, inv_perm);CHKERRQ(ierr);
   ierr = spbas_apply_reordering_cols( matrix_A, permutation);CHKERRQ(ierr);
   PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "spbas_pattern_only"
PetscErrorCode spbas_pattern_only(PetscInt nrows, PetscInt ncols, PetscInt *ai, PetscInt *aj, spbas_matrix * result)
{
   spbas_matrix   retval;
   PetscInt       i, j, i0, r_nnz;
   PetscErrorCode ierr;

   PetscFunctionBegin;

   /* Copy input values */
   retval.nrows = nrows;
   retval.ncols = ncols;
   retval.nnz   = ai[nrows];

   retval.block_data   = PETSC_TRUE;
   retval.col_idx_type = SPBAS_DIAGONAL_OFFSETS;

   /* Allocate output matrix */
   ierr =  spbas_allocate_pattern(&retval, PETSC_FALSE);CHKERRQ(ierr);
   for (i=0; i<nrows; i++)  {retval.row_nnz[i] = ai[i+1]-ai[i];}
   ierr =  spbas_allocate_data(&retval);CHKERRQ(ierr);
   /* Copy the structure */
   for (i = 0; i<retval.nrows; i++)  {
      i0 = ai[i];
      r_nnz = ai[i+1]-i0;

      for (j=0; j<r_nnz; j++) {
         retval.icols[i][j]  = aj[i0+j]-i;
      }
   }
   *result = retval;
   PetscFunctionReturn(0);
}


/*
   spbas_mark_row_power:
      Mark the columns in row 'row' which are nonzero in
          matrix^2log(marker).
*/
#undef __FUNCT__
#define __FUNCT__ "spbas_mark_row_power"
PetscErrorCode spbas_mark_row_power(
				    PetscInt *iwork,             /* marker-vector */
				    PetscInt row,                /* row for which the columns are marked */
				    spbas_matrix * in_matrix, /* matrix for which the power is being  calculated */
				    PetscInt marker,             /* marker-value: 2^power */
				    PetscInt minmrk,            /* lower bound for marked points */
				    PetscInt maxmrk)            /* upper bound for marked points */
{
   PetscErrorCode ierr;
   PetscInt       i,j, nnz;

   PetscFunctionBegin;
   nnz = in_matrix->row_nnz[row];

   /* For higher powers, call this function recursively */
   if (marker>1) {
      for (i=0; i<nnz;i++) {
         j = row + in_matrix->icols[row][i];
         if (minmrk<=j && j<maxmrk && iwork[j] < marker ) {
            ierr =  spbas_mark_row_power( iwork, row + in_matrix->icols[row][i],in_matrix, marker/2,minmrk,maxmrk);CHKERRQ(ierr);
            iwork[j] |= marker;
         }
      }
   } else  {
     /*  Mark the columns reached */
      for (i=0; i<nnz;i++)  {
         j = row + in_matrix->icols[row][i];
         if (minmrk<=j && j<maxmrk) { iwork[j] |= 1; }
      }
   }
   PetscFunctionReturn(0);
}


/*
   spbas_power
      Calculate sparseness patterns for incomplete Cholesky decompositions
      of a given order: (almost) all nonzeros of the matrix^(order+1) which
      are inside the band width are found and stored in the output sparseness
      pattern.
*/
#undef __FUNCT__
#define __FUNCT__ "spbas_power"
PetscErrorCode spbas_power (spbas_matrix in_matrix,PetscInt power, spbas_matrix * result)
{
   spbas_matrix   retval;
   PetscInt       nrows = in_matrix.nrows;
   PetscInt       ncols = in_matrix.ncols;
   PetscInt       i, j, kend;
   PetscInt       nnz, inz;
   PetscInt       *iwork;
   PetscInt       marker;
   PetscInt       maxmrk=0;
   PetscErrorCode ierr;

   PetscFunctionBegin;
   if (in_matrix.col_idx_type != SPBAS_DIAGONAL_OFFSETS) SETERRQ( PETSC_ERR_SUP_SYS,"must have diagonal offsets in pattern\n");
   if (ncols != nrows) SETERRQ( PETSC_ERR_ARG_INCOMP, "Dimension error\n");
   if (in_matrix.values) SETERRQ( PETSC_ERR_ARG_INCOMP, "Input array must be sparseness pattern (no values)");
   if (power<=0) SETERRQ( PETSC_ERR_SUP_SYS, "Power must be 1 or up");

   /* Copy input values*/
   retval.nrows = ncols;
   retval.ncols = nrows;
   retval.nnz   = 0;
   retval.col_idx_type = SPBAS_DIAGONAL_OFFSETS;
   retval.block_data = PETSC_FALSE;

   /* Allocate sparseness pattern */
   ierr =  spbas_allocate_pattern(&retval, in_matrix.values ? PETSC_TRUE : PETSC_FALSE);CHKERRQ(ierr);

   /* Allocate marker array */
   ierr = PetscMalloc(nrows * sizeof(PetscInt), &iwork);CHKERRQ(ierr);

   /* Erase the pattern for this row */
   memset( (void *) iwork, 0, retval.nrows*sizeof(PetscInt));

   /* Calculate marker values */
   marker = 1; for (i=1; i<power; i++) {marker*=2;}

   for (i=0; i<nrows; i++)  {
     /* Calculate the pattern for each row */

      nnz    = in_matrix.row_nnz[i];
      kend   = i+in_matrix.icols[i][nnz-1];
      if (maxmrk<=kend) {maxmrk=kend+1;}
      ierr =  spbas_mark_row_power( iwork, i, &in_matrix, marker, i, maxmrk);CHKERRQ(ierr);

      /* Count the columns*/
      nnz = 0;
      for (j=i; j<maxmrk; j++) {nnz+= (iwork[j]!=0);}

      /* Allocate the column indices */
      retval.row_nnz[i] = nnz;
      ierr = PetscMalloc(nnz*sizeof(PetscInt),&retval.icols[i]);CHKERRQ(ierr);

      /* Administrate the column indices */
      inz = 0;
      for (j=i; j<maxmrk; j++) {
         if (iwork[j])  {
            retval.icols[i][inz] = j-i;
            inz++;
            iwork[j]=0;
         }
      }
      retval.nnz += nnz;
   };
   ierr = PetscFree(iwork);CHKERRQ(ierr);
   *result = retval;
   PetscFunctionReturn(0);
}



/*
   spbas_keep_upper:
      remove the lower part of the matrix: keep the upper part
*/
#undef __FUNCT__
#define __FUNCT__ "spbas_keep_upper"
PetscErrorCode spbas_keep_upper( spbas_matrix * inout_matrix)
{
   PetscInt i, j;
   PetscInt jstart;

   PetscFunctionBegin;
   if (inout_matrix->block_data) SETERRQ( PETSC_ERR_SUP_SYS, "Not yet for block data matrices\n");
   for (i=0; i<inout_matrix->nrows; i++)  {
       for (jstart=0; (jstart<inout_matrix->row_nnz[i]) && (inout_matrix->icols[i][jstart]<0); jstart++){}
       if (jstart>0) {
          for (j=0; j<inout_matrix->row_nnz[i]-jstart; j++) {
             inout_matrix->icols[i][j] =  inout_matrix->icols[i][j+jstart];
          }

          if (inout_matrix->values) {
             for (j=0; j<inout_matrix->row_nnz[i]-jstart; j++) {
                inout_matrix->values[i][j] = inout_matrix->values[i][j+jstart];
             }
          }

          inout_matrix->row_nnz[i] -= jstart;

          inout_matrix->icols[i] = (PetscInt*) realloc((void*) inout_matrix->icols[i], inout_matrix->row_nnz[i]*sizeof(PetscInt));

          if (inout_matrix->values) {
             inout_matrix->values[i] = (PetscScalar*) realloc((void*) inout_matrix->values[i], inout_matrix->row_nnz[i]*sizeof(PetscScalar));
          }
          inout_matrix->nnz -= jstart;
       }
   }
   PetscFunctionReturn(0);
}