Sparse Matrices

Implements sparse matrices data structures as dedicated CSR matrices sparse_matrix_csr. Each instance of sparse_matrix_csr corresponds to a rank-1 array of a tuple of dynamically reallocated arrays, sparse_row_csr: one array store the columns indices and one array store the values of the non-zero elements of a given matrix.

This structure guarantees \(O(1)\) access. If MPI parallelization is enabled the structure includes an automatic rows split balanced among the different threads and a further subdivision of the columns/values in local and non-local blocks.

Note

A more modern, object oriented, class for sparse matrices is available in SciFortran

Description

This class defines a data structure to efficiently store sparse matrices into dedicated CSR matrices, featuring support to MPI parallel storage, so that each matrix is spread across the threads.

Quick access

Types:

sparse_row_csr, sparse_matrix_csr

Routines:

sp_dump_matrix(), sp_init_matrix(), sp_insert_element(), sp_set_mpi_matrix()

Used modules

External modules

Types

type  ed_sparse_matrix/sparse_row_csr

The sparse row data structure containing the non-zero elements on any given row of sparse matrix.

Type fields:

  • size [integer] – the current size of the row, corresponding to number of non-zero elements

  • dvals (•) [real, allocatable] – rank-1 array for double precision values

  • cvals (•) [complex, allocatable] – rank-1 array for double complex values

  • cols (•) [integer, allocatable] – rank-1 array for column indices

type  ed_sparse_matrix/sparse_matrix_csr

The sparse matrix data structure realized as an allocatable array of of sparse_row_csr types.

Type fields:

  • row (•) [sparse_row_csr, pointer] – the array of sparse_row_csr

  • nrow [integer] – the total number of rows

  • ncol [integer] – the total number of columns

  • status [logical] – Allocation status

  • loc (•) [sparse_row_csr, pointer] – the array of sparse_row_csr for the diagonal blocks

  • istart [integer] – starting index for the MPI decomposition of the sparse matrix

  • iend [integer] – ending index for the MPI decomposition of the sparse matrix

  • ishift [integer] – integer shift index for the MPI decomposition of the sparse matrix

  • mpi [logical]

Subroutines and functions

interface  ed_sparse_matrix/sp_init_matrix(sparse, n, mpicomm[, n1])

Initialization of the sparse_matrix_csr via memory allocation. An empty matrix is returned

Parameters:

  • sparse [sparse_matrix_csr, inout] – sparse matrix to be initialized

  • n [integer] – Number of rows

  • mpicomm [integer] – MPI global communicator

Options:

n1 [integer] – Number of columns [Optional]. If not present N1=N

interface  ed_sparse_matrix/sp_insert_element(sparse, value, i, j, mpicomm)

Matrix element insertion at a given row and columns. If an active MPI communicator is passed as input the element is stored in the matrix chunk of the corresponding thread. Double precision and double complex values are supported.

Parameters:

  • sparse [sparse_matrix_csr, inout]

  • value [real/complex, in] – matrix value to be inserted

  • i [integer, in] – row index of the matrix value to be inserted

  • j [integer, in] – column index of the matrix value to be inserted

  • mpicomm [integer] – MPI global communicator

interface  ed_sparse_matrix/sp_dump_matrix(sparse, matrix, mpicomm)

Dump the sparse_matrix_csr into a dense matrix.

Parameters:

  • sparse [sparse_matrix_csr, in] – sparse matrix to dump

  • matrix (•, •) [real/complex, inout] – dense matrix having the same type of the sparse one

  • mpicomm [integer] – MPI global communicator

interface  ed_sparse_matrix/sp_set_mpi_matrix(mpicomm, sparse, istart, iend, ishift)

Set up the MPI parameters in the sparse_matrix_csr for automatic spread of the values across the threads

Parameters:

  • mpicomm [integer] – MPI global communicator

  • sparse [sparse_matrix_csr, inout]

  • istart [integer] – starting index for the MPI decomposition of the sparse matrix

  • iend [integer] – ending index for the MPI decomposition of the sparse matrix

  • ishift [integer] – shift index for the MPI decomposition of the sparse matrix