xref: /petsc/src/mat/impls/aij/seq/bas/spbas.c (revision 9767453c85a88b60d52ea72032faaafc609f88f5)

#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)
{


   // Requirement for
   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 = NULL;
   }

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

   // Create arrays
   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]; }
   }

   // Remove help arrays
   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);
   printf("Rows have been sorted for patterns\n");

   // 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]];
   }
   printf("Row patterns have been compressed\n");
   printf("         (%6.2f nonzeros per row)\n",  (PetscReal) nnz / (PetscReal) nrows);


   // Clean up
   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]++;
         }
      }
   }

   // Set return value
   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 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=NULL;
   PetscInt *iswap;      // auxiliary pointers for swapping
   PetscScalar *vswap;
   PetscInt *ihlp1;      // Pointers to new version of arrays,
   PetscScalar *vhlp1=NULL;  // (arrays under construction)
   PetscInt *ihlp2;      // Pointers to previous version of arrays,
   PetscScalar *vhlp2=NULL;
   PetscErrorCode ierr;

   // Create arrays
   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]; }
      }
   }

   // Remove help arrays
   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=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=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;
      }
   }

   // Set return value
   *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);
}