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

PetscErrorCode MatMult_Centering(Mat A, Vec xx, Vec yy) {
  PetscScalar       *y;
  const PetscScalar *x;
  PetscScalar        sum, mean;
  PetscInt           i, m = A->rmap->n, size;

  PetscFunctionBegin;
  PetscCall(VecSum(xx, &sum));
  PetscCall(VecGetSize(xx, &size));
  mean = sum / (PetscScalar)size;
  PetscCall(VecGetArrayRead(xx, &x));
  PetscCall(VecGetArray(yy, &y));
  for (i = 0; i < m; i++) { y[i] = x[i] - mean; }
  PetscCall(VecRestoreArrayRead(xx, &x));
  PetscCall(VecRestoreArray(yy, &y));
  PetscFunctionReturn(0);
}

/*@
   MatCreateCentering - Creates a new matrix object that implements the (symmetric and idempotent) centering matrix, I - (1/N) * ones*ones'

   Collective on Mat

   Input Parameters:
+  comm - MPI communicator
.  n - number of local rows (or PETSC_DECIDE to have calculated if N is given)
           This value should be the same as the local size used in creating the
           y vector for the matrix-vector product y = Ax.
-  N - number of global rows (or PETSC_DETERMINE to have calculated if n is given)

   Output Parameter:
.  C - the matrix

   Notes:
   The entries of the matrix C are not explicitly stored. Instead, the new matrix
   object is a shell that simply performs the action of the centering matrix, i.e.,
   multiplying C*x subtracts the mean of the vector x from each of its elements.
   This is useful for preserving sparsity when mean-centering the columns of a
   matrix is required. For instance, to perform principal components analysis with
   a matrix A, the composite matrix C*A can be passed to a partial SVD solver.

   Level: intermediate

.seealso: `MatCreateLRC()`, `MatCreateComposite()`
@*/
PetscErrorCode MatCreateCentering(MPI_Comm comm, PetscInt n, PetscInt N, Mat *C) {
  PetscMPIInt size;

  PetscFunctionBegin;
  PetscCall(MatCreate(comm, C));
  PetscCall(MatSetSizes(*C, n, n, N, N));
  PetscCallMPI(MPI_Comm_size(comm, &size));
  PetscCall(PetscObjectChangeTypeName((PetscObject)*C, MATCENTERING));

  (*C)->ops->mult                   = MatMult_Centering;
  (*C)->assembled                   = PETSC_TRUE;
  (*C)->preallocated                = PETSC_TRUE;
  (*C)->symmetric                   = PETSC_BOOL3_TRUE;
  (*C)->symmetry_eternal            = PETSC_TRUE;
  (*C)->structural_symmetry_eternal = PETSC_TRUE;
  PetscCall(MatSetUp(*C));
  PetscFunctionReturn(0);
}