#include <petsc/private/matimpl.h> /*I  "petscmat.h"  I*/

/*@
  MatComputeBandwidth - Calculate the full bandwidth of the matrix, meaning the width 2k+1 where k diagonals on either side are sufficient to contain all the matrix nonzeros.

  Collective

  Input Parameters:
+ A        - The `Mat`
- fraction - An optional percentage of the Frobenius norm of the matrix that the bandwidth should enclose

  Output Parameter:
. bw - The matrix bandwidth

  Level: beginner

.seealso: `DMPlexCreate()`, `DMPlexSetConeSize()`, `DMPlexSetChart()`
@*/
PetscErrorCode MatComputeBandwidth(Mat A, PetscReal fraction, PetscInt *bw)
{
  PetscInt lbw[2] = {0, 0}, gbw[2];
  PetscInt rStart, rEnd, r;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(A, MAT_CLASSID, 1);
  PetscValidLogicalCollectiveReal(A, fraction, 2);
  PetscAssertPointer(bw, 3);
  PetscCheck(!(fraction > 0.0) || !(fraction < 1.0), PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "We do not yet support a fractional bandwidth");
  PetscCall(MatGetOwnershipRange(A, &rStart, &rEnd));
  for (r = rStart; r < rEnd; ++r) {
    const PetscInt *cols;
    PetscInt        ncols;

    PetscCall(MatGetRow(A, r, &ncols, &cols, NULL));
    if (ncols) {
      lbw[0] = PetscMax(lbw[0], r - cols[0]);
      lbw[1] = PetscMax(lbw[1], cols[ncols - 1] - r);
    }
    PetscCall(MatRestoreRow(A, r, &ncols, &cols, NULL));
  }
  PetscCallMPI(MPIU_Allreduce(lbw, gbw, 2, MPIU_INT, MPI_MAX, PetscObjectComm((PetscObject)A)));
  *bw = 2 * PetscMax(gbw[0], gbw[1]) + 1;
  PetscFunctionReturn(PETSC_SUCCESS);
}