Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
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

void
psgecon
(
char
*norm
,
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
pdgecon
(
char
*norm
,
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
pcgecon
(
char
*norm
,
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
pzgecon
(
char
*norm
,
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?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
Equation
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,
 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.