## Developer Reference

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

# ?hecon_rook

Estimates the reciprocal of the condition number of a Hermitian matrix using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges).

## Syntax

Include Files
• mkl.fi
,
lapack.f90
Description
The routine estimates the reciprocal of the condition number of a Hermitian matrix
A
using the factorization
A
=
U
*
D
*
U
H
or
A
=
L
*
D
*
L
H
computed by hetrf_rook.
An estimate is obtained for norm(
A
-1
), and the reciprocal of the condition number is computed as
rcond
= 1/(
anorm
*norm(
A
-1
)).
Input Parameters
uplo
CHARACTER*1
.
Must be
'U'
or
'L'
.
Indicates how the input matrix
A
has been factored:
If
uplo
=
'U'
, the array
a
stores the upper triangular factor
U
of the factorization
A
=
U*D*U
H
.
If
uplo
=
'L'
, the array
a
stores the lower triangular factor
L
of the factorization
A
=
L*D*L
H
.
n
INTEGER
.
The order of matrix
A
;
n
0.
a
,
work
COMPLEX
for
checon_rook
COMPLEX*16
for
zhecon_rook
.
Arrays:
a
(
lda
,
n
)
,
work
(*)
.
The array
a
contains the factored matrix
A
, as returned by
?hetrf_rook
.
The second dimension of
a
must be at least
max(1,
n
)
.
The array
work
is a workspace for the routine. The dimension of
work
must be at least
max(1, 2*
n
)
.
lda
INTEGER
.
a
;
lda
max(1,
n
)
.
ipiv
INTEGER
.
Array, size at least
max(1,
n
)
.
The array
ipiv
, as returned by hetrf_rook.
anorm
REAL
for
checon_rook
DOUBLE PRECISION
for
zhecon_rook
.
The 1-norm of the original matrix
A
(see
Description
).
Output Parameters
rcond
REAL
for
checon_rook
DOUBLE PRECISION
for
zhecon_rook
.
The reciprocal of the condition number of the matrix
A
, computed as
rcond
= 1/(