Contents

# p?pocon

Estimates the reciprocal of the condition number (in the 1 - norm) of a symmetric / Hermitian positive-definite distributed matrix.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?pocon
function
estimates the reciprocal of the condition number (in the 1 - norm) of a real symmetric or complex Hermitian positive definite distributed matrix sub(
A
) =
A
(
ia
:
ia
+
n
-1,
ja
:
ja
+
n
-1), using the Cholesky factorization sub(
A
) =
U
H
*U
or sub(
A
) =
L*L
H
computed by
p?potrf
.
An estimate is obtained for ||(sub(
A
))
-1
||
, and the reciprocal of the condition number is computed as Input Parameters
uplo
(global) Must be
'U'
or
'L'
.
Specifies whether the factor stored in sub(
A
) is upper or lower triangular.
If
uplo
=
'U'
, sub(
A
) stores the upper triangular factor
U
of the Cholesky factorization sub(
A
) =
U
H
*U
.
If
uplo
=
'L'
, sub(
A
) stores the lower triangular factor
L
of the Cholesky factorization sub(
A
) =
L*L
H
.
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
or
U
from the Cholesky factorization sub(
A
) =
U
H
*U
, or sub(
A
) =
L*L
H
, as computed by
p?potrf
.
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)
The 1-norm of the symmetric/Hermitian 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
*iceil(
NPROW
-1,
NPCOL
)
,
LOCc
(
n
+mod(
ja
-1,
nb_a
))+
nb_a
*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
*max(1,iceil(
NPROW
-1,
NPCOL
))
,
LOCc
(
n
+mod(
ja
-1,
nb_a
))+
nb_a
*max(1,iceil(
NPCOL
-1,
NPROW
))))
.
If
lwork
= -1, then
lwork
is a global input and a workspace query is assumed. The routine only calculates the minimum and optimal size for all work arrays. Each value is returned in the first entry of the corresponding work array, and no error message is issued by
pxerbla
.
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
))
.
If
liwork
= -1, then
liwork
is a global input and a workspace query is assumed. The routine only calculates the minimum and optimal size for all work arrays. Each value is returned in the first entry of the corresponding work array, and no error message is issued by
pxerbla
.
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
2*
LOCc
(
n
+mod(
ja
-1,
nb_a
))
.
If
lrwork
= -1, then
lrwork
is a global input and a workspace query is assumed. The routine only calculates the minimum and optimal size for all work arrays. Each value is returned in the first entry of the corresponding work array, and no error message is issued by
pxerbla
.
Output Parameters
rcond
(global)
The reciprocal of the condition number of the distributed matrix sub(
A
).
work

On exit,
work

contains the minimum value of
lwork
required for optimum performance.
iwork

On exit,
iwork

contains the minimum value of
liwork
required for optimum performance (for real flavors).
rwork

On exit,
rwork

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