CXML
skyline-solvers
A library of sparse linear solvers (direct)
Description
The sparse skyline solvers are a part of the Compaq Extended Math Library
(CXML). 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.
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