library.sparse Submodule

Module Summary

Interfaces for the NAG Mark 27.1 sparse Chapter.

sparse - Large Scale Linear Systems

This module provides functions for the solution of large sparse systems of simultaneous linear equations. These include iterative methods for real nonsymmetric and symmetric, complex non-Hermitian and Hermitian linear systems and direct methods for general real linear systems. Further direct methods are currently available in submodule matop and submodule linsys.

Functionality Index

Basic functions for complex Hermitian linear systems

diagnostic function: complex_herm_basic_diag()

reverse communication CG or SYMMLQ solver function: complex_herm_basic_solver()

setup function: complex_herm_basic_setup()

Basic functions for complex non-Hermitian linear systems

diagnostic function: complex_gen_basic_diag()

reverse communication RGMRES, CGS, Bi-CGSTAB or TFQMR solver function: complex_gen_basic_solver()

setup function: complex_gen_basic_setup()

Basic functions for real nonsymmetric linear systems

diagnostic function: real_gen_basic_diag()

reverse communication RGMRES, CGS, Bi-CGSTAB or TFQMR solver function: real_gen_basic_solver()

setup function: real_gen_basic_setup()

Basic functions for real symmetric linear systems

diagnostic function: real_symm_basic_diag()

reverse communication CG or SYMMLQ solver: real_symm_basic_solver()

setup function: real_symm_basic_setup()

Black Box functions for complex Hermitian linear systems

CG or SYMMLQ solver

with incomplete Cholesky preconditioning: complex_herm_solve_ilu()

with no preconditioning, Jacobi or SSOR preconditioning: complex_herm_solve_jacssor()

Black Box functions for complex non-Hermitian linear systems

RGMRES, CGS, Bi-CGSTAB or TFQMR solver

with block Jacobi or additive Schwarz preconditioning: complex_gen_solve_bdilu()

with incomplete preconditioning: complex_gen_solve_ilu()

with no preconditioning, Jacobi, or SSOR preconditioning: complex_gen_solve_jacssor()

Black Box functions for real nonsymmetric linear systems

RGMRES, CGS, Bi-CGSTAB or TFQMR solver

with block Jacobi or additive Schwarz preconditioning: real_gen_solve_bdilu()

with incomplete preconditioning: real_gen_solve_ilu()

with no preconditioning, Jacobi, or SSOR preconditioning: real_gen_solve_jacssor()

Black Box functions for real symmetric linear systems

CG or SYMMLQ solver

with incomplete Cholesky preconditioning: real_symm_solve_ichol()

with no preconditioning, Jacobi, or SSOR preconditioning: real_symm_solve_jacssor()

Direct methods for real sparse nonsymmetric linear systems in CCS format

apply iterative refinement to the solution and compute error estimates, after factorizing the matrix of coefficients: direct_real_gen_refine()

condition number estimation, after factorizing the matrix of coefficients: direct_real_gen_cond()

factorization

solution of simultaneous linear equations, after factorizing the matrix of coefficients: direct_real_gen_solve()

utility

compute a norm or the element of largest absolute value: direct_real_gen_norm()

matrix-matrix multiplier: direct_real_gen_matmul()

Utility function for complex Hermitian linear systems

incomplete Cholesky factorization: complex_herm_precon_ichol()

matrix-vector multiplier for complex Hermitian matrices in SCS format: complex_herm_matvec()

solver for linear systems involving preconditioning matrix from complex_herm_precon_ichol(): complex_herm_precon_ilu_solve()

solver for linear systems involving SSOR preconditioning matrix: complex_herm_precon_ssor_solve()

sort function for complex Hermitian matrices in SCS format: complex_herm_sort()

Utility function for complex linear systems

solver for linear systems involving iterated Jacobi method: complex_gen_precon_jacobi()

Utility function for complex non-Hermitian linear systems

incomplete factorization: complex_gen_precon_ilu()

incomplete factorization of local or overlapping diagonal blocks: complex_gen_precon_bdilu()

matrix-vector multiplier for complex non-Hermitian matrices in CS format: complex_gen_matvec()

solver for linear systems involving preconditioning matrix from complex_gen_precon_ilu(): complex_gen_precon_ilu_solve()

solver for linear systems involving SSOR preconditioning matrix: complex_gen_precon_ssor_solve()

sort function for complex non-Hermitian matrices in CS format: complex_gen_sort()

Utility function for real linear systems

solver for linear systems involving iterated Jacobi method: real_gen_precon_jacobi()

Utility function for real nonsymmetric linear systems

incomplete factorization: real_gen_precon_ilu()

incomplete factorization of local or overlapping diagonal blocks: real_gen_precon_bdilu()

matrix-vector multiplier for real nonsymmetric matrices in CS format: real_gen_matvec()

solver for linear systems involving preconditioning matrix from real_gen_precon_ilu(): real_gen_precon_ilu_solve()

solver for linear systems involving SSOR preconditioning matrix: real_gen_precon_ssor_solve()

sort function for real nonsymmetric matrices in CS format: real_gen_sort()

sort function for real rectangular matrices in CS or CCS format: real_rect_sort()

Utility function for real symmetric linear systems

incomplete Cholesky factorization: real_symm_precon_ichol()

matrix-vector multiplier for real symmetric matrices in SCS format: real_symm_matvec()

solver for linear systems involving preconditioning matrix from real_symm_precon_ichol(): real_symm_precon_ichol_solve()

solver for linear systems involving SSOR preconditioning matrix: real_symm_precon_ssor_solve()

sort function for real symmetric matrices in SCS format: real_symm_sort()

Utility function for real symmetric linear systems, compute bandwidth-reducing reverse Cuthill–McKee permutation: sym_rcm()

For full information please refer to the NAG Library document

https://www.nag.com/numeric/nl/nagdoc_27.1/flhtml/f11/f11intro.html