## Developer Reference

• 0.10
• 10/21/2020
• Public Content
Contents

# p?trcon

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

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?trcon
function
estimates the reciprocal of the condition number of a triangular distributed matrix sub(
A
) =
A
(
ia
:
ia
+
n
-1,
ja
:
ja
+
n
-1), in either the 1-norm or the infinity-norm.
The norm of sub(
A
) is computed and an estimate is obtained for ||(sub(
A
))
-1
||
, then 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.
uplo
(global) Must be
'U'
or
'L'
.
If
uplo
=
'U'
, sub(
A
) is upper triangular. If
uplo
=
'L'
, sub(
A
) is lower triangular.
diag
(global) Must be
'N'
or
'U'
.
If
diag
=
'N'
, sub(
A
) is non-unit triangular. If
diag
=
'U'
, sub(
A
) is unit triangular.
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 triangular distributed matrix sub(
A
).
If
uplo
=
'U'
n
-by-
n
upper triangular part of this distributed matrix contains the upper triangular matrix, and its strictly lower triangular part is not referenced.
If
uplo
=
'L'
n
-by-
n
lower triangular part of this distributed matrix contains the lower triangular matrix, and its strictly upper triangular part is not referenced.
If
diag
=
'U'
, the diagonal elements of sub(
A
) are also not referenced and are assumed to be 1.
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
.
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
))+
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
)))
.
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
LOCc
(
n
+mod(
ja
-1,
nb_a
))
.
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