Contents

# p?unmr3

Applies an orthogonal distributed matrix to a general
m
-by-
n
distributed matrix.

## Syntax

Include Files
• mkl_scalapack.h
Description
p?unmr3
overwrites the general complex
m
-by-
n
distributed matrix sub(
C
) =
C
(
ic
:
ic
+
m
-1,
jc
:
jc
+
n
-1) with

side
= 'L'
side
= 'R'
trans
= 'N':
Q
* sub(
C
)         sub(
C
) *
Q
trans
= 'C':
Q
H
* sub(
C
)       sub(
C
) *
Q
H
where
Q
is a complex unitary distributed matrix defined as the product of
k
elementary reflectors
Q = H(1)' H(2)' . . . H(
k
)'
as returned by
p?tzrzf
.
Q
is of order
m
if
side
= 'L' and of order
n
if
side
= 'R'.
Input Parameters
side
(global)
= 'L': apply
Q
or
Q
H
from the Left;
= 'R': apply
Q
or
Q
H
from the Right.
trans
(global)
= 'N': No transpose, apply
Q
;
= 'C': Conjugate transpose, apply
Q
H
.
m
(global)
The number of rows to be operated on i.e the number of rows of the distributed submatrix sub(
C
).
m
>= 0.
n
(global)
The number of columns to be operated on i.e the number of columns of the distributed submatrix sub(
C
).
n
>= 0.
k
(global)
The number of elementary reflectors whose product defines the matrix
Q
.
If
side
= 'L',
m
>=
k
>= 0, if
side
= 'R',
n
>=
k
>= 0.
l
(global)
The columns of the distributed submatrix
sub( A )
containing the meaningful part of the Householder reflectors.
If
side
= 'L',
m
>=
l
>= 0, if
side
= 'R',
n
>=
l
>= 0.
a
(local)
Pointer into the local memory to an array of size
lld_a
*
LOCc
(
ja
+
m
-1)
if
side
='L', and
lld_a
*
LOCc
(
ja
+
n
-1)
if
side
='R', where
lld_a
>= MAX(1,LOCr(
ia
+
k
-1));
On entry, the i-th row must contain the vector which defines the elementary reflector H(i),
ia
<= i <=
ia
+
k
-1, as returned by
p?tzrzf
in the
k
rows of its distributed matrix argument
A
(
ia
:
ia
+
k
-1,
ja
:*).
A
(
ia
:
ia
+
k
-1,
ja
:*) is modified by the routine but restored on exit.
ia
(global)
The row index in the global array
a
indicating the first row of
sub( A )
.
ja
(global)
The column index in the global array
a
indicating the first column of
sub( A )
.
desca
(global and local)
Array of size
dlen_
.
The array descriptor for the distributed matrix
A
.
tau
(local)
Array, size LOCc(
ia
+
k
-1).
This array contains the scalar factors
tau
(i) of the elementary reflectors H(i) as returned by
p?tzrzf
.
tau
is tied to the distributed matrix
A
.
c
(local)
Pointer into the local memory to an array of size
lld_c
*
LOCc
(
jc
+
n
-1)
.
On entry, the local pieces of the distributed matrix sub(
C
).
ic
(global)
The row index in the global array
c
indicating the first row of sub(
C
).
jc
(global)
The column index in the global array
c
indicating the first column of sub(
C
).
descc
(global and local)
Array of size
dlen_
.
The array descriptor for the distributed matrix
C
.
work
(local)
Array, size (
lwork
)
On exit,
work
(1) returns the minimal and optimal
lwork
.
lwork
(local or global)
The size of the array
work
.
lwork
is local input and must be at least
If
side
= 'L',
lwork
>= MpC0 + MAX( MAX( 1, NqC0 ),
numroc
(
numroc
(
m
+IROFFC,
mb_a
,0,0,NPROW ),
mb_a
,0,0,LCMP ) );
if
side
= 'R',
lwork
>= NqC0 + MAX( 1, MpC0 );
where LCMP = LCM / NPROW with LCM = ICLM( NPROW, NPCOL ),
IROFFC = MOD(
ic
-1, MB_C ), ICOFFC = MOD(
jc
-1,
nb_c
),
ICROW =
indxg2p
(
ic
, MB_C, MYROW,
rsrc_c
, NPROW ),
ICCOL =
indxg2p
(
jc
,
nb_c
, MYCOL,
csrc_c
, NPCOL ),
MpC0 =
numroc
(
m
+IROFFC, MB_C, MYROW, ICROW, NPROW ),
NqC0 =
numroc
(
n
+ICOFFC,
nb_c
, MYCOL, ICCOL, NPCOL ),
ilcm
,
indxg2p
, and
numroc
are ScaLAPACK tool functions;
MYROW, MYCOL, NPROW and NPCOL can be determined by calling the subroutine
blacs_gridinfo
.
If
lwork
= -1, then
lwork
is global input and a workspace query is assumed; the routine only calculates the minimum and optimal size for all work arrays. Each of these values is returned in the first entry of the corresponding work array, and no error message is issued by
pxerbla
.
Output Parameters
c
On exit, sub(
C
) is overwritten by
Q
*sub(
C
) or
Q
'*sub(
C
) or sub(
C
)*
Q
' or sub(
C
)*
Q
.
work
(local)
Array, size (
lwork
)
On exit,
work
[0]
returns the minimal and optimal
lwork
.
info
(local)
= 0: successful exit
< 0: If the
i
-th argument is an array and the
j
-th entry 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
.
Application Notes
Alignment requirements
The distributed submatrices
A
(
ia
:*,
ja
:*) and
C
(
ic
:
ic
+
m
-1,
jc
:
jc
+
n
-1) must verify some alignment properties, namely the following expressions should be true:
If
side
= 'L', (
nb_a
= MB_C and ICOFFA = IROFFC )
If
side
= 'R', (
nb_a
=
nb_c
and ICOFFA = ICOFFC and IACOL = ICCOL )

#### Product and Performance Information

1

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Notice revision #20110804