Developer Reference

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

?pocon

Estimates the reciprocal of the condition number of a symmetric (Hermitian) positive-definite matrix.

Syntax

call spocon
(
uplo
,
n
,
a
,
lda
,
anorm
,
rcond
,
work
,
iwork
,
info
)
call dpocon
(
uplo
,
n
,
a
,
lda
,
anorm
,
rcond
,
work
,
iwork
,
info
)
call cpocon
(
uplo
,
n
,
a
,
lda
,
anorm
,
rcond
,
work
,
rwork
,
info
)
call zpocon
(
uplo
,
n
,
a
,
lda
,
anorm
,
rcond
,
work
,
rwork
,
info
)
call pocon
(
a
,
anorm
,
rcond
[
,
uplo
]
[
,
info
]
)
Include Files
  • mkl.fi
    ,
    lapack.f90
Description
The routine estimates the reciprocal of the condition number of a symmetric (Hermitian) positive-definite matrix
A
:
κ
1
(
A
) = ||
A
||
1
||
A
-1
||
1
(since
A
is symmetric or Hermitian,
κ
(
A
) =
κ
1
(
A
)
).
An estimate is obtained for
||
A
-1
||
, and the reciprocal of the condition number is computed as
rcond
= 1 / (||
A
|| ||
A
-1
||)
.
Before calling this routine:
  • compute
    anorm
    (either
    ||
    A
    ||
    1
    = max
    j
    Σ
    i
    |
    a
    i
    j
    |
    or
    ||
    A
    ||
    = max
    i
    Σ
    j
    |
    a
    i
    j
    |)
  • call
    ?potrf
    to compute the Cholesky factorization of
    A
    .
Input Parameters
n
INTEGER
.
The order of the matrix
A
;
n
0.
a
,
work
REAL
for
spocon
DOUBLE PRECISION
for
dpocon
COMPLEX
for
cpocon
DOUBLE COMPLEX
for
zpocon
.
Arrays:
a
(
lda
,*)
,
work
(*)
.
The array
a
contains the factored matrix
A
, as returned by
?potrf
.
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, 3*
n
)
for real flavors and
max(1, 2*