Contents

# p?gecon

Estimates the reciprocal of the condition number of a general distributed matrix in either the 1-norm or the infinity-norm.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?gecon
function
estimates the reciprocal of the condition number of a general distributed real/complex matrix sub(
A
) =
A
(
ia
:
ia
+
n
-1,
ja
:
ja
+
n
-1) in either the 1-norm or infinity-norm, using the
LU
factorization computed by
p?getrf
.
An estimate is obtained for ||(sub(
A
))
-1
||
, and the reciprocal of the condition number is computed as
Input Parameters
norm
(global) Must be
'1'
or
'O'
or
'I'
.
Specifies whether the 1-norm condition number or the infinity-norm condition number is required.
If
norm
=
'1'
or
'O'
, then the 1-norm is used;
If
norm
=
'I'
, then the infinity-norm is used.
n
(global) The order of the distributed matrix sub(
A
)
(
n
0)
.
a
(local)
Pointer into the local memory to an array of size
lld_a
*
LOCc
(
ja
+
n
-1)
.
The array
a
contains the local pieces of the factors
L
and
U
from the factorization sub(
A
) =
P
*L*
U
; the unit diagonal elements of
L
are not stored.
ia
,
ja
(global) The row and column indices in the global matrix
A
indicating the first row and the first column of the matrix sub(
A
), respectively.
desca
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
A
.
anorm
(global)
If
norm
=
'1'
or
'O'
, the 1-norm of the original distributed matrix sub(
A
);
If
norm
=
'I'
, the infinity-norm of the original distributed matrix sub(
A
).
work
(local)
The array
work
of size
lwork
is a workspace array.
lwork
(local or global) The size of the array
work
.
For real flavors:
lwork
must be at least
lwork
2*
LOCr
(
n
+mod(
ia
-1,
mb_a
))+
2*
LOCc
(
n
+mod(
ja
-1,
nb_a
))+
max(2, max(
nb_a
*max(1, iceil(
NPROW
-1,
NPCOL
))
,
LOCc
(
n
+mod(
ja
-1,
nb_a
)) +
nb_a
*max(1, iceil(
NPCOL
-1,
NPROW
))))
.
For complex flavors:
lwork
must be at least
lwork
2*
LOCr
(
n
+mod(
ia
-1,
mb_a
))+
max(2, max(
nb_a
*iceil(
NPROW
-1,
NPCOL
)
,
LOCc
(
n
+mod(
ja
-1,
nb_a
))+
nb_a
*iceil(
NPCOL
-1,
NPROW
)))
.
LOCr
and
LOCc
values can be computed using the ScaLAPACK tool function
numroc
;
NPROW
and
NPCOL
can be determined by calling the
function
blacs_gridinfo
.
iceil(
x
,
y
)
is the ceiling of
x
/
y
, and
mod(
x
,
y
)
is the integer remainder of
x
/
y
.
iwork
(local) Workspace array of size
liwork
. Used in real flavors only.
liwork
(local or global) The size of the array
iwork
; used in real flavors only. Must be at least
liwork
LOCr
(
n
+mod(
ia
-1,
mb_a
))
.
rwork
(local)
Workspace array of size
lrwork
. Used in complex flavors only.
lrwork
(local or global) The size of the array
rwork
; used in complex flavors only. Must be at least
lrwork
max(1, 2*
LOCc
(
n
+mod(
ja
-1,
nb_a
)))
.
Output Parameters
rcond
(global)
The reciprocal of the condition number of the distributed matrix sub(
A
). See Description.
work
[0]
On exit,
work
[0]
contains the minimum value of
lwork
required for optimum performance.
iwork
[0]
On exit,
iwork
[0]
contains the minimum value of
liwork
required for optimum performance (for real flavors).
rwork
[0]
On exit,
rwork
[0]
contains the minimum value of
lrwork
required for optimum performance (for complex flavors).
info
(global) If
info
=0
, the execution is successful.
info
< 0:
If the
i
-th argument is an array and the
j-
th entry
, indexed
j
- 1,
info
= -(
i
*100+
j
); if the
i-
th argument is a scalar and had an illegal value, then
info
=
-i
.

#### Product and Performance Information

1

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804