MatCreateCentering#

Creates a new matrix object that implements the (symmetric and idempotent) centering matrix, \( I - (1/N) * 1^T * 1\)

Synopsis#

#include "petscmat.h" 
PetscErrorCode MatCreateCentering(MPI_Comm comm, PetscInt n, PetscInt N, Mat *C)

Collective

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

Location#

src/mat/impls/centering/centering.c

Index of all Mat routines
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Index of all manual pages