Contents

# p?lapiv

Applies a permutation matrix to a general distributed matrix, resulting in row or column pivoting.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?lapiv
function
applies either
P
(permutation matrix indicated by
ipiv
) or inv(
P
) to a general
m
-by-
n
distributed matrix sub
(
A
) =
A
(
ia
:
ia
+
m
-1
,
ja
:
ja
+
n
-1)
, resulting in row or column pivoting. The pivot vector may be distributed across a process row or a column. The pivot vector should be aligned with the distributed matrix
A
. This
function
will transpose the pivot vector, if necessary.
For example, if the row pivots should be applied to the columns of sub(
A
), pass
rowcol
=
'C'
and
pivroc
=
'C'
.
Input Parameters
direc
(global)
Specifies in which order the permutation is applied:
=
'F'
(Forward): Applies pivots forward from top of matrix. Computes
P
*sub(
A
)
.
=
'B'
(Backward): Applies pivots backward from bottom of matrix. Computes
inv(
P
)*sub(
A
)
.
rowcol
(global)
Specifies if the rows or columns are to be permuted:
=
'R'
: Rows will be permuted,
=
'C'
: Columns will be permuted.
pivroc
(global)
Specifies whether
ipiv
is distributed over a process row or column:
=
'R'
:
ipiv
is distributed over a process row,
=
'C'
:
ipiv
is distributed over a process column.
m
(global)
The number of rows in the distributed matrix sub(
A
). When
m
= 0
,
p?lapiv
is set to zero.
m
0
.
n
(global)
The number of columns in the distributed matrix sub(
A
). When
n
= 0
,
p?lapiv
is set to zero.
n
0.
a
(local).
Pointer into the local memory to an array of size
lld_a
*
LOCc
(
ja
+
n
-1)
containing the local pieces of the distributed matrix sub(
A
).
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.
ipiv
(local)
Array of size
lipiv
;
when
rowcol
=
'R'
or
'r'
:
lipiv
LOCr
(
ia
+
m
-1) +
mb_a
if
pivroc
=
'C'
or
'c'
,
lipiv
LOCc
(
m
+
mod
(
jp
-1,
nb_p
))
if
pivroc
=
'R'
or
'r'
, and,
when
rowcol
=
'C'
or
'c'
:
lipiv
LOCr
(
n
+
mod
(
ip
-1,
mb_p
))
if
pivroc
=
'C'
or
'c'
,
lipiv
LOCc
(
ja
+
n
-1) +
nb_a
if
pivroc
=
'R'
or
'r'
.
This array contains the pivoting information.
ipiv(i)
is the global row (column), local row (column)
i
was swapped with. When
rowcol
=
'R'
or
'r'
and
pivroc
=
'C'
or
'c'
, or
rowcol
=
'C'
or
'c'
and
pivroc
=
'R'
or
'r'
, the last piece of this array of size
mb_a
(resp.
nb_a
) is used as workspace. In those cases, this array is tied to the distributed matrix
A
.
ip
,
jp
(global) The row and column indices in the global matrix
P
indicating the first row and the first column of the matrix sub(
P
), respectively.
descip
(global and local) array of size
dlen_
. The array descriptor for the distributed vector
ipiv
.
iwork
(local).
Array of size
ldw
, where
ldw
is equal to the workspace necessary for transposition, and the storage of the transposed
ipiv
:
Let
lcm
be the least common multiple of
nprow
and
npcol
.
```if( *rowcol == 'r' &&  *pivroc == 'r') {
if( nprow == npcol) {
ldw = LOCr( n_p + (*jp-1)%nb_p ) + nb_p;
} else {
ldw = LOCr( n_p + (*jp-1)%nb_p )+
nb_p * ceil( ceil(LOCc(n_p)/nb_p) / (lcm/npcol) );
}
} else if( *rowcol == 'c' &&  *pivroc == 'c') {
if( nprow == npcol ) {
ldw = LOCc( m_p + (*ip-1)%mb_p ) + mb_p;
} else {
ldw = LOCc( m_p + (*ip-1)%mb_p ) +
mb_p *ceil(ceil(LOCr(m_p)/mb_p) / (lcm/nprow) );
}
} else {
// iwork is not referenced.```
Output Parameters
a
(local).
On exit, the local pieces of the permuted distributed submatrix.

#### 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