Developer Reference

  • 2020.2
  • 07/15/2020
  • Public Content
Contents

?sysvxx

Uses extra precise iterative refinement to compute the solution to the system of linear equations with a symmetric indefinite coefficient matrix A applying the diagonal pivoting factorization.

Syntax

call ssysvxx
(
fact
,
uplo
,
n
,
nrhs
,
a
,
lda
,
af
,
ldaf
,
ipiv
,
equed
,
s
,
b
,
ldb
,
x
,
ldx
,
rcond
,
rpvgrw
,
berr
,
n_err_bnds
,
err_bnds_norm
,
err_bnds_comp
,
nparams
,
params
,
work
,
iwork
,
info
)
call dsysvxx
(
fact
,
uplo
,
n
,
nrhs
,
a
,
lda
,
af
,
ldaf
,
ipiv
,
equed
,
s
,
b
,
ldb
,
x
,
ldx
,
rcond
,
rpvgrw
,
berr
,
n_err_bnds
,
err_bnds_norm
,
err_bnds_comp
,
nparams
,
params
,
work
,
iwork
,
info
)
call csysvxx
(
fact
,
uplo
,
n
,
nrhs
,
a
,
lda
,
af
,
ldaf
,
ipiv
,
equed
,
s
,
b
,
ldb
,
x
,
ldx
,
rcond
,
rpvgrw
,
berr
,
n_err_bnds
,
err_bnds_norm
,
err_bnds_comp
,
nparams
,
params
,
work
,
rwork
,
info
)
call zsysvxx
(
fact
,
uplo
,
n
,
nrhs
,
a
,
lda
,
af
,
ldaf
,
ipiv
,
equed
,
s
,
b
,
ldb
,
x
,
ldx
,
rcond
,
rpvgrw
,
berr
,
n_err_bnds
,
err_bnds_norm
,
err_bnds_comp
,
nparams
,
,
work
,
rwork
,
info
)
Include Files
  • mkl.fi
    ,
    lapack.f90
Description
The routine uses the diagonal pivoting factorization to compute the solution to a real or complex system of linear equations
A*X
=
B
, where
A
is an
n
-by-
n
real symmetric/Hermitian matrix, the columns of matrix
B
are individual right-hand sides, and the columns of
X
are the corresponding solutions.
Both normwise and maximum componentwise error bounds are also provided on request. The routine returns a solution with a small guaranteed error (
O(eps)
, where
eps
is the working machine precision) unless the matrix is very ill-conditioned, in which case a warning is returned. Relevant condition numbers are also calculated and returned.
The routine accepts user-provided factorizations and equilibration factors; see definitions of the
fact
and
equed
options. Solving with refinement and using a factorization from a previous call of the routine also produces a solution with
O(eps)
errors or warnings but that may not be true for general user-provided factorizations and equilibration factors if they differ from what the routine would itself produce.
The routine
?sysvxx
performs the following steps: