Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
Contents

p?pocon

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

Syntax

void
pspocon
(
char
*uplo
,
MKL_INT
*n
,
float
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
float
*anorm
,
float
*rcond
,
float
*work
,
MKL_INT
*lwork
,
MKL_INT
*iwork
,
MKL_INT
*liwork
,
MKL_INT
*info
);
void
pdpocon
(
char
*uplo
,
MKL_INT
*n
,
double
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
double
*anorm
,
double
*rcond
,
double
*work
,
MKL_INT
*lwork
,
MKL_INT
*iwork
,
MKL_INT
*liwork
,
MKL_INT
*info
);
void
pcpocon
(
char
*uplo
,
MKL_INT
*n
,
MKL_Complex8
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
float
*anorm
,
float
*rcond
,
MKL_Complex8
*work
,
MKL_INT
*lwork
,
float
*rwork
,
MKL_INT
*lrwork
,
MKL_INT
*info
);
void
pzpocon
(
char
*uplo
,
MKL_INT
*n
,
MKL_Complex16
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
double
*anorm
,
double
*rcond
,
MKL_Complex16
*work
,
MKL_INT
*lwork
,
double
*rwork
,
MKL_INT
*lrwork
,
MKL_INT
*info
);
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
Equation
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
[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,
 had an illegal value, then
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

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.