Actual source code: centering.c


  2: #include <petsc/private/matimpl.h>

  4: PetscErrorCode MatMult_Centering(Mat A, Vec xx, Vec yy)
  5: {
  6:   PetscScalar       *y;
  7:   const PetscScalar *x;
  8:   PetscScalar        sum, mean;
  9:   PetscInt           i, m = A->rmap->n, size;

 11:   VecSum(xx, &sum);
 12:   VecGetSize(xx, &size);
 13:   mean = sum / (PetscScalar)size;
 14:   VecGetArrayRead(xx, &x);
 15:   VecGetArray(yy, &y);
 16:   for (i = 0; i < m; i++) y[i] = x[i] - mean;
 17:   VecRestoreArrayRead(xx, &x);
 18:   VecRestoreArray(yy, &y);
 19:   return 0;
 20: }

 22: /*@
 23:    MatCreateCentering - Creates a new matrix object that implements the (symmetric and idempotent) centering matrix, I - (1/N) * ones*ones'

 25:    Collective

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

 34:    Output Parameter:
 35: .  C - the matrix

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

 45:    Level: intermediate

 47: .seealso: `MatCreateLRC()`, `MatCreateComposite()`
 48: @*/
 49: PetscErrorCode MatCreateCentering(MPI_Comm comm, PetscInt n, PetscInt N, Mat *C)
 50: {
 51:   PetscMPIInt size;

 53:   MatCreate(comm, C);
 54:   MatSetSizes(*C, n, n, N, N);
 55:   MPI_Comm_size(comm, &size);
 56:   PetscObjectChangeTypeName((PetscObject)*C, MATCENTERING);

 58:   (*C)->ops->mult                   = MatMult_Centering;
 59:   (*C)->assembled                   = PETSC_TRUE;
 60:   (*C)->preallocated                = PETSC_TRUE;
 61:   (*C)->symmetric                   = PETSC_BOOL3_TRUE;
 62:   (*C)->symmetry_eternal            = PETSC_TRUE;
 63:   (*C)->structural_symmetry_eternal = PETSC_TRUE;
 64:   MatSetUp(*C);
 65:   return 0;
 66: }