SPARSE-SKYLINE-SOLVERS(3DXML) — Subroutines
Digital
Name
skyline-solvers − A library of sparse linear solvers (direct)
Description
The sparse skyline solvers are a part of the Digital Extended Math Library (DXML). The sparse skyline solver library includes a set of routines for the direct solution of a sparse linear system of equations with the matrix stored using the skyline storage scheme. Routines are provided for the following functions:
•LDU factorization - This includes options for the evaluation of the determinant, evaluation of the inertia, partial factorization and statistics on the matrix. No pivoting is done, though options are provided for handling small pivots.
•Solve - This includes multiple right hand sides and the solution of either A ∗ x = b or A^T ∗ x = b.
•Norm evaluation - This includes the 1-norm, the infinity-norm, the Frobenius norm and the maximum absolute value of the matrix.
•Condition number estimation - This includes estimates of the 1-norm and infinity-norm condition number.
•Iterative refinement - This includes the component-wise relative backward error and the estimated forward error bound for each solution vector.
•Simple driver
•Expert driver
This functionality is provided for each of the following storage schemes:
For Symmetric matrices:
•Profile-in storage mode
•Diagonal-out storage mode
For Unsymmetric matrices:
•Profile-in storage mode
•Diagonal-out storage mode
•Structurally symmetric profile-in storage mode
These solvers are available in real, double precision only.
The following routines are provided. The Subprogram Name is the name of the manual page containing documentation on the subprogram.
| Subprogram Name | Meaning |
| dsskyn | Obtains, in double precision arithmetic, the 1-norm, the infinity-norm, the Frobenius norm, or the maximum absolute value of a symmetric matrix stored in either the profile-in or the diagonal-out skyline storage mode. |
| dsskyf | Obtains, in double precision arithmetic, the U tranpose ∗ D ∗ U factorization of a symmetric matrix stored in either the profile-in or the diagonal-out skyline storage mode. |
| dsskys | Obtains, in double precision arithmetic, the solution to the system A ∗ X = B, where A has been factored using the routine DSSKYF. |
| dsskyc | Obtains, in double precision arithmetic, the reciprocal of the estimate of the condition number of a symmetric matrix stored in either the profile-in or the diagonal-out skyline storage mode. |
| dsskyr | Obtains, in double precision arithmetic, an improvement to the solution via iterative refinement, the component-wise relative backward error and the estimated forward error bounds for the solution vector. The symmetric matrix is stored in either the profile-in or the diagonal-out skyline storage mode. |
| dsskyd | Obtains, in double precision arithmetic, the U transpose ∗ D ∗ U factorization of the matrix A, followed by the solution of the system A ∗ X = B, where the symmetric matrix A is stored in either the profile-in or the diagonal-out skyline storage mode. |
| dsskyx | Obtains, in double precision arithmetic, the U transpose ∗ D ∗ U factorization and the condition number estimate of the matrix A. If the matrix is non-singular, the solution of the system A ∗ X = B is obtained, followed by iterative refinement and the calculation of the component-wise relative backward error and the estimated forward error bounds for the solution vector. The symmetric matrix A is stored in either the profile-in or the diagonal-out skyline storage mode. |
| duskyn | Obtains, in double precision arithmetic, the 1-norm, the infinity-norm, the Frobenius norm or the maximum absolute value of an unsymmetric matrix stored in either the profile-in, the diagonal-out or the structurally symmetric profile-in skyline storage mode. |
| duskyf | Obtains, in double precision arithmetic, the LDU factorization of an unsymmetric matrix stored in either the profile-in, the diagonal-out or the structurally symmetric profile-in skyline storage mode. |
| duskys | Obtains, in double precision arithmetic, the solution to the system A ∗ X = B or (A transpose) ∗ X = B, where A has been factored using the routine DUSKYF. |
| duskyc | Obtains, in double precision arithmetic, the reciprocal of the estimate of the condition number of an unsymmetric matrix stored in either the profile-in, the diagonal-out or the structurally symmetric profile-in skyline storage mode. Either the 1-norm or the infinity-norm can be used. |
| duskyr | Obtains, in double precision arithmetic, an improvement to the solution via iterative refinement, the component-wise relative backward error and the estimated forward error bounds for the solution vector. The unsymmetric matrix is stored in either the profile-in, the diagonal-out or the structurally symmetric profile-in skyline storage mode. |
| duskyd | Obtains, in double precision arithmetic, the LDU factorization of the matrix A, followed by the solution of the system A ∗ X = B or (A transpose) ∗ X = B, where the unsymmetric matrix A is stored in either the profile-in, the diagonal-out or the structurally symmetric profile-in skyline storage mode. |
| duskyx | Obtains, in double precision arithmetic, the LDU factorization and the condition number estimate of the matrix A. If the matrix is non-singular, the solution of the system A ∗ X = B or (A transpose) ∗ X = B is obtained, followed by iterative refinement and the calculation of the component-wise relative backward error and the estimated forward error bounds for the solution vector. The unsymmetric matrix A is stored in either the profile-in, the diagonal-out or the structurally symmetric profile-in skyline storage mode. |