Contents

p?unmtr

Multiplies a general matrix by the unitary transformation matrix from a reduction to tridiagonal form determined by
p?hetrd
.

Syntax

Include Files
• mkl_scalapack.h
Description
This
function
overwrites the general complex distributed
m
-by-
n
matrix sub(
C
) =
C
(
:
+
m
-1,
:
+
n
-1) with
 side ='L' side ='R' trans = 'N': Q*sub(C) sub(C)*Q trans = 'C': QH*sub(C) sub(C)*QH
where
Q
is a complex unitary distributed matrix of order
nq
, with
nq
=
m
if
side
=
'L'
and
nq
=
n
if
side
=
'R'
.
Q
is defined as the product of
nq
-1 elementary reflectors, as returned by
p?hetrd
.
If
uplo
=
'U'
,
Q
=
H
(
nq
-1)...
H
(2)
H
(1);
If
uplo
=
'L'
,
Q
=
H
(1)
H
(2)...
H
(
nq
-1).
Input Parameters
side
(global)
=
'L'
:
Q
or
Q
H
is applied from the left.
=
'R'
:
Q
or
Q
H
is applied from the right.
trans
(global)
=
'N'
, no transpose,
Q
is applied.
=
'C'
, conjugate transpose,
Q
H
is applied.
uplo
(global)
=
'U'
: Upper triangle of
A
(
ia
:*,
ja
:*)
contains elementary reflectors from
p?hetrd
;
=
'L'
: Lower triangle of
A
(
ia
:*,
ja
:*)
contains elementary reflectors from
p?hetrd
m
(global) The number of rows in the distributed matrix sub(
C
)
(
m
0)
.
n
(global) The number of columns in the distributed matrix sub(
C
)
(
n
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'
.
Contains the vectors which define the elementary reflectors, as returned by
p?hetrd
.
If
side
=
'L'
,
lld_a
max
(1,
LOCr
(
ia
+
m
-1))
;
If
side
=
'R'
,
lld_a
max
(1,
LOCr
(
ia
+
n
-1))
.
ia
,
ja
(global) The row and column indices in the global matrix
A
indicating the first row and the first column of the submatrix
A
, respectively.
desca
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
A
.
tau
(local)
Array of size of
ltau
where
If
side
=
'L'
and
uplo
=
'U'
,
ltau
=
LOCc
(
m_a
)
,
if
side
=
'L'
and
uplo
=
'L'
,
ltau
=
LOCc
(
ja
+
m
-2)
,
if
side
=
'R'
and
uplo
=
'U'
,
ltau
=
LOCc
(
n_a
)
,
if
side
=
'R'
and
uplo
=
'L'
,
ltau
=
LOCc
(
ja
+
n
-2)
.
tau
[
i
]
must contain the scalar factor of the elementary reflector
H
(
i
+1)
, as returned by
p?hetrd
(0 ≤
i
<
ltau
)
.
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)
. Contains the local pieces of the distributed matrix sub (
C
).
ic
,
jc
(global) The row and column indices in the global matrix
C
indicating the first row and the first column of the submatrix
C
, respectively.
descc
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
C
.
work
(local)
Workspace array of size
lwork
.
lwork
(local or global) size of
work
, must be at least:
If
uplo
=
'U'
,
iaa
=
ia
;
jaa
=
ja
+1,
icc
=
ic
;
jcc
=
jc
;
else
uplo
=
'L'
,
iaa
=
ia
+1,
jaa
=
ja
;
If
side
=
'L'
,
icc
=
ic
+1;
jcc
=
jc
;
else
icc
=
ic
;
jcc
=
jc
+1
;
end if
end if
If
side
=
'L'
,
mi
=
m
-1;
ni
=
n
lwork
max
((
nb_a
*(
nb_a
-1))/2, (
nqc
0 +
mpc
0)*
nb_a
) +
nb_a
*
nb_a
else
If
side
=
'R'
,
mi
=
m
;
mi
=
n
-1
;
lwork
max
((
nb_a
*(
nb_a
-1))/2, (
nqc
0 +
max
(
npa
0+
numroc
(
numroc
(
ni
+
icoffc
,
nb_a
, 0, 0,
NPCOL
),
nb_a
, 0, 0,
lcmq
),
mpc
0))*
nb_a
) +
nb_a
*
nb_a
end if
where
lcmq
=
lcm
/
NPCOL
with
lcm
=
ilcm
(
NPROW
,
NPCOL
)
,
iroffa
=
mod
(
iaa
-1,
mb_a
)
,
icoffa
=
mod
(
jaa
-1,
nb_a
)
,
iarow
=
indxg2p
(
iaa
,
mb_a
,
MYROW
,
rsrc_a
,
NPROW
)
,
npa
0 =
numroc
(
ni
+
iroffa
,
mb_a
,
MYROW
,
iarow
,
NPROW
),
iroffc
=
mod
(
icc
-1,
mb_c
)
,
icoffc
=
mod
(
jcc
-1,
nb_c
)
,
icrow
=
indxg2p
(
icc
,
mb_c
,
MYROW
,
rsrc_c
,
NPROW
)
,
iccol
=
indxg2p
(
jcc
,
nb_c
,
MYCOL
,
csrc_c
,
NPCOL
)
,
mpc
0 =
numroc
(
mi
+
iroffc
,
mb_c
,
MYROW
,
icrow
,
NPROW
)
,
nqc
0 =
numroc
(
ni
+
icoffc
,
nb_c
,
MYCOL
,
iccol
,
NPCOL
)
,
mod(
x
,
y
)
is the integer remainder of
x
/
y
.
ilcm
,
indxg2p
and
numroc
are ScaLAPACK tool functions;
MYROW
,
MYCOL
,
NPROW
and
NPCOL
can be determined by calling the
function
blacs_gridinfo
. If
lwork
= -1
, then
lwork
is global input and a workspace query is assumed; the
function
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
Overwritten by the product
Q
*sub(
C
), or
Q'
*sub(
C
), or sub(
C
)*
Q',
or sub(
C
)*
Q
.
work
[0]
On exit
work
[0]
contains the minimum value of
lwork
required for optimum performance.
info
(global)
= 0
: the execution is successful.
< 0
: if the
i
-th argument is an array and the
j-
th entry
, indexed
j
- 1,
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.