Contents

# p?syr2k

Performs a rank-2k update of a symmetric distributed matrix.

## Syntax

Include Files
• mkl_pblas.h
Description
The
p?syr2k
routines perform a distributed matrix-matrix operation defined as
`sub(C):=alpha*sub(A)*sub(B)'+alpha*sub(B)*sub(A)'+ beta*sub(C),`
or
`sub(C):=alpha*sub(A)'*sub(B) +alpha*sub(B)'*sub(A) + beta*sub(C),`
where:
alpha
and
beta
are scalars,
sub(
C
)
is an
n
-by-
n
symmetric distributed matrix,
sub(
C
)=C(
ic
:
ic
+
n
-1,
jc
:
jc
+
n
-1)
.
sub(
A
)
is a distributed matrix,
sub(
A
)=
A
(
ia
:
ia
+
n
-1,
ja
:
ja
+
k
-1)
, if
trans
=
'N'
or
'n'
, and
sub(
A
)=
A
(
ia
:
ia
+
k
-1,
ja
:
ja
+
n
-1)
otherwise.
sub(
B
)
is a distributed matrix,
sub(
B
)=
B
(
ib
:
ib
+
n
-1,
jb
:
jb
+
k
-1)
, if
trans
=
'N'
or
'n'
, and
sub(
B
)=
B
(
ib
:
ib
+
k
-1,
jb
:
jb
+
n
-1)
otherwise.
Input Parameters
uplo
(global) Specifies whether the upper or lower triangular part of the symmetric distributed matrix
sub(
C
)
is used:
If
uplo
=
'U'
or
'u'
, then the upper triangular part of the
sub(
C
)
is used.
If
uplo
=
'L'
or
'l'
, then the low triangular part of the
sub(
C
)
is used.
trans
(global) Specifies the operation:
if
trans
=
'N'
or
'n'
, then
sub(
C
) :=
alpha
*sub(
A
)*sub(
B
)' +
alpha
*sub(
B
)*sub(
A
)' +
beta
*sub(
C
)
;
if
trans
=
'T'
or
't'
, then
sub(
C
) :=
alpha
*sub(
B
)'*sub(
A
) +
alpha
*sub(
A
)'*sub(
B
) +
beta
*sub(
C
)
.
n
(global) Specifies the order of the distributed matrix
sub(
C
)
,
n
0.
k
(global) On entry with
trans
=
'N'
or
'n'
,
k
specifies the number of columns of the distributed matrices
sub(
A
)
and
sub(
B
)
, and on entry with
trans
=
'T'
or
't'
,
k
specifies the number of rows of the distributed matrices
sub(
A
)
and
sub(
B
)
,
k
0.
alpha
(global)
Specifies the scalar
alpha
.
a
(local)
Array, size
(
lld_a
,
kla
)
, where
kla
is
LOCq(
ja
+
k
-1)
when
trans
=
'N'
or
'n'
, and is
LOCq(
ja
+
n
-1)
otherwise. Before entry with
trans
=
'N'
or
'n'
, this array contains the local pieces of the distributed matrix
sub(
A
)
.
ia
,
ja
(global) The row and column indices in the distributed matrix
A
indicating the first row and the first column of the submatrix
sub(
A
)
, respectively.
desca
(global and local) array of dimension 9. The array descriptor of the distributed matrix
A
.
b
(local)
Array, size
(
lld_b
,
klb
)
, where
klb
is
LOCq(
jb
+
k
-1)
when
trans
=
'N'
or
'n'
, and is
LOCq(
jb
+
n
-1)
otherwise. Before entry with
trans
=
'N'
or
'n'
, this array contains the local pieces of the distributed matrix
sub(
B
)
.
ib
,
jb
(global) The row and column indices in the distributed matrix
B
indicating the first row and the first column of the submatrix
sub(
B
)
, respectively.
descb
(global and local) array of dimension 9. The array descriptor of the distributed matrix
B
.
beta
(global)
Specifies the scalar
beta
.
c
(local)
Array, size
(
lld_c
, LOCq(
jc
+
n
-1))
.
Before entry with
uplo
=
'U'
or
'u'
, this array contains
n
-by-
n
upper triangular part of the symmetric distributed matrix
sub(
C
)
and its strictly lower triangular part is not referenced.
Before entry with
uplo
=
'L'
or
'l'
, this array contains
n
-by-
n
lower triangular part of the symmetric distributed matrix
sub(
C
)
and its strictly upper triangular part is not referenced.
ic
,
jc
(global) The row and column indices in the distributed matrix
C
indicating the first row and the first column of the submatrix
sub(
C
)
, respectively.
descc
(global and local) array of dimension 9. The array descriptor of the distributed matrix
C
.
Output Parameters
c
With
uplo
=
'U'
or
'u'
, the upper triangular part of
sub(
C
)
is overwritten by the upper triangular part of the updated distributed matrix.
With
uplo
=
'L'
or
'l'
, the lower triangular part of
sub(
C
)
is overwritten by the upper triangular part of the updated distributed matrix.

#### Product and Performance Information

1

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Notice revision #20110804