Developer Reference

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

?hesvx

Uses the diagonal pivoting factorization to compute the solution to the complex system of linear equations with a Hermitian coefficient matrix A, and provides error bounds on the solution.

Syntax

call chesvx
(
fact
,
uplo
,
n
,
nrhs
,
a
,
lda
,
af
,
ldaf
,
ipiv
,
b
,
ldb
,
x
,
ldx
,
rcond
,
ferr
,
berr
,
work
,
lwork
,
rwork
,
info
)
call zhesvx
(
fact
,
uplo
,
n
,
nrhs
,
a
,
lda
,
af
,
ldaf
,
ipiv
,
b
,
ldb
,
x
,
ldx
,
rcond
,
ferr
,
berr
,
work
,
lwork
,
rwork
,
info
)
call hesvx
(
a
,
b
,
x
[
,
uplo
]
[
,
af
]
[
,
ipiv
]
[
,
fact
]
[
,
ferr
]
[
,
berr
]
[
,
rcond
]
[
,
info
]
)
Include Files
  • mkl.fi
    ,
    lapack.f90
Description
The routine uses the diagonal pivoting factorization to compute the solution to a complex system of linear equations
A*X
=
B
, where
A
is an
n
-by-
n
Hermitian matrix, the columns of matrix
B
are individual right-hand sides, and the columns of
X
are the corresponding solutions.
Error bounds on the solution and a condition estimate are also provided.
The routine
?hesvx
performs the following steps:
  1. If
    fact
    =
    'N'
    , the diagonal pivoting method is used to factor the matrix
    A
    . The form of the factorization is
    A
    =
    U*D*U
    H
    or
    A =
    L*D*L
    H
    , where
    U
    (or
    L
    ) is a product of permutation and unit upper (lower) triangular matrices, and
    D
    is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
  2. If some
    d
    i
    ,
    i
    = 0, so that
    D
    is exactly singular, then the routine returns with
    info
    =
    i
    . Otherwise, the factored form of
    A
    is used to estimate the condition number of the matrix
    A
    . If the reciprocal of the condition number is less than machine precision,
    info
    =
    n
    +1
    is returned as a warning, but the routine still goes on to solve for
    X
    and compute error bounds as described below.
  3. The system of equations is solved for
    X
    using the factored form of
    A
    .
  4. Iterative refinement is applied to improve the computed solution matrix and calculate error bounds and backward error estimates for it.
Input Parameters
fact
CHARACTER*1
.
Must be
'F'
or
'N'
.
Specifies whether or not the factored form of the matrix
A
has been supplied on entry.
If
fact
=
'F'
: on entry,
af
and
ipiv
contain the factored form of
A
. Arrays
a
,
af
, and
ipiv
are not modified.
If
fact
=
'N'
, the matrix
A
is copied to
af
and factored.
uplo
CHARACTER*1
.
Must be
'U'
or
'L'
.
Indicates whether the upper or lower triangular part of
A
is stored and how
A
is factored:
If
uplo
=
'U'
, the array
a
stores the upper triangular part of the Hermitian matrix
A
, and