Developer Reference

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

?spcon

Estimates the reciprocal of the condition number of a packed symmetric matrix.

Syntax

call sspcon
(
uplo
,
n
,
ap
,
ipiv
,
anorm
,
rcond
,
work
,
iwork
,
info
)
call dspcon
(
uplo
,
n
,
ap
,
ipiv
,
anorm
,
rcond
,
work
,
iwork
,
info
)
call cspcon
(
uplo
,
n
,
ap
,
ipiv
,
anorm
,
rcond
,
work
,
info
)
call zspcon
(
uplo
,
n
,
ap
,
ipiv
,
anorm
,
rcond
,
work
,
info
)
call spcon
(
ap
,
ipiv
,
anorm
,
rcond
[
,
uplo
]
[
,
info
]
)
Include Files
  • mkl.fi
    ,
    lapack.f90
Description
The routine estimates the reciprocal of the condition number of a packed symmetric matrix
A
:
κ
1
(
A
) = ||
A
||
1
||
A
-1
||
1
(since
A
is symmetric,
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
    ?sptrf
    to compute the factorization of
    A
    .
Input Parameters
uplo
CHARACTER*1
.
Must be
'U'
or
'L'
.
Indicates how the input matrix
A
has been factored:
If
uplo
=
'U'
, the array
ap
stores the packed upper triangular factor
U
of the factorization
A
=
U*D*U
T
.