Developer Reference

Contents

p?unmbr

Multiplies a general matrix by one of the unitary transformation matrices from a reduction to bidiagonal form determined by
p?gebrd
.

Syntax

void
pcunmbr
(
char
*vect
,
char
*side
,
char
*trans
,
MKL_INT
*m
,
MKL_INT
*n
,
MKL_INT
*k
,
MKL_Complex8
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_Complex8
*tau
,
MKL_Complex8
*c
,
MKL_INT
*ic
,
MKL_INT
*jc
,
MKL_INT
*descc
,
MKL_Complex8
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pzunmbr
(
char
*vect
,
char
*side
,
char
*trans
,
MKL_INT
*m
,
MKL_INT
*n
,
MKL_INT
*k
,
MKL_Complex16
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_Complex16
*tau
,
MKL_Complex16
*c
,
MKL_INT
*ic
,
MKL_INT
*jc
,
MKL_INT
*descc
,
MKL_Complex16
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
Include Files
  • mkl_scalapack.h
Description
If
vect
= 'Q'
, the
p?unmbr
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'
:
Q
H
*sub(
C
)
sub(
C
)*
Q
H
If
vect
= 'P'
, the
function
overwrites sub(
C
) with
side
=
'L'
side
=
'R'
trans
=
'N'
:
P
*sub(
C
)
sub(
C
)*
P
trans
=
'C'
:
P
H
*sub(
C
)
sub(
C
)*
P
H
Here
Q
and
P
H
are the unitary distributed matrices determined by
p?gebrd
when reducing a complex distributed matrix
A
(
ia
:*,
ja
:*) to bidiagonal form:
A
(
ia
:*,
ja
:*) =
Q
*
B
*
P
H
.
Q
and
P
H
are defined as products of elementary reflectors
H
(
i
) and
G
(
i
) respectively.
Let
nq
=
m
if
side
=
'L'
and
nq
=
n
if
side
=
'R'
. Therefore
nq
is the order of the unitary matrix
Q
or
P
H
that is applied.
If
vect
=
'Q'
,
A
(
ia
:*,
ja
:*) is assumed to have been an
nq
-by-
k
matrix:
If
nq
k
,
Q
=
H
(1)
H
(2)...
H
(
k
);
If
nq
<
k
,
Q
=
H
(1)
H
(2)...
H
(
nq
-1).
If
vect
=
'P'
,
A
(
ia
:*,
ja
:*) is assumed to have been a
k
-by-
nq
matrix:
If
k
<
nq
,
P
=
G
(1)
G
(2)...
G
(
k
);
If
k
nq
,
P
=
G
(1)
G
(2)...
G
(
nq
-1).
Input Parameters
vect
(global)
If
vect
=
'Q'
, then
Q
or
Q
H
is applied.
If
vect
=
'P'
, then
P
or
P
H
is applied.
side
(global)
If
side
=
'L'
, then
Q
or
Q
H
,
P
or
P
H
is applied from the left.
If
side
=
'R'
, then
Q
or
Q
H
,
P
or
P
H
is applied from the right.
trans
(global)
If
trans
=
'N'
, no transpose,
Q
or
P
is applied.
If
trans
=
'C'
, conjugate transpose,
Q
H
or
P
H
is applied.
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
.
k
(global)
If
vect
=
'Q'
, the number of columns in the original distributed matrix reduced by
p?gebrd
;
If
vect
=
'P'
, the number of rows in the original distributed matrix reduced by
p?gebrd
.
Constraints:
k
0.
a
(local)
Pointer into the local memory to an array of size
lld_a
*
LOCc
(
ja
+
min
(
nq
,
k
)-1)
if
vect
=
'Q'
, and
lld_a
*
LOCc
(
ja
+
nq
-1)
if
vect
=
'P'
.
nq
=
m
if
side
=
'L'
, and
nq
=
n
otherwise.
The vectors that define the elementary reflectors
H
(
i
) and
G
(
i
), whose products determine the matrices
Q
and
P
, as returned by
p?gebrd
.
If
vect
=
'Q'
,
lld_a
max
(1,
LOCr
(
ia
+
nq
-1))
;
If
vect
=
'P'
,
lld_a
max
(1,
LOCr
(
ia
+
min
(
nq
,
k
)-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
LOCc
(
ja
+
min
(
nq
,
k
)-1)
, if
vect
=
'Q'
, and
LOCr
(
ia
+
min
(
nq
,
k
)-1)
, if
vect
=
'P'
.
tau
[
i
]
must contain the scalar factor of the elementary reflector
H
(
i
+1)
or
G
(
i
+1)
, which determines
Q
or
P
, as returned by
p?gebrd
in its array argument
tauq
or
taup
.
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
side
=
'L'
nq
=
m
;
if
((
vect
=
'Q'
and
nq
k
)
or
(
vect
is not equal to
'Q'
and
nq
>
k
))
,
iaa
=
ia
;
jaa
=
ja
;
mi
=
m
;
ni
=
n
;
icc
=
ic
;
jcc
=
jc
;
else
iaa
=
ia
+1;
jaa
=
ja
;
mi
=
m
-1;
ni
=
n
;
icc
=
ic
+1;
jcc
=
jc
;
end if
else
If
side
=
'R'
,
nq
=
n
;
if ((
vect
=
'Q'
and
nq
k
) or (
vect
is not equal to
'Q'
and
nq
k
))
,
iaa
=
ia
;
jaa
=
ja
;
mi
=
m
;
ni
=
n
;
icc
=
ic
;
jcc
=
jc
;
else
iaa
=
ia
;
jaa
=
ja
+1
;
mi
=
m
;
ni
=
n
-1
;
icc
=
ic
;
jcc
=
jc
+1
;
end if
end if
If
vect
=
'Q'
,
If
side
=
'L'
,
lwork
max
((
nb_a
*(
nb_a
-1))/2, (
nqc
0+
mpc
0)*
nb_a
) +
nb_a
*
nb_a
else if
side
=
'R'
,
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
else if
vect
is not equal to
'Q'
,
if
side
=
'L'
,
lwork
max
((
mb_a
*(
mb_a
-1))/2, (
mpc
0 +
max
(
mqa
0+
numroc
(
numroc
(
mi
+
iroffc
,
mb_a
, 0, 0,
NPROW
),
mb_a
, 0, 0,
lcmp
),
nqc
0))*
mb_a
) +
mb_a
*
mb_a
else if
side
=
'R'
,
lwork
max
((
mb_a
*(
mb_a
-1))/2, (
mpc
0 +
nqc
0)*
mb_a
) +
mb_a
*
mb_a
end if
end if
where
lcmp
=
lcm
/
NPROW
,
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
)
,
iacol
=
indxg2p
(
jaa
,
nb_a
,
MYCOL
,
csrc_a
,
NPCOL
)
,
mqa
0 =
numroc
(
mi
+
icoffa
,
nb_a
,
MYCOL
,
iacol
,
NPCOL
),
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
.
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
On exit, if
vect
=
'Q'
, sub(
C
) is overwritten by
Q
*sub(
C
), or
Q'
*sub(
C
), or sub(
C
)*
Q'
, or sub(
C
)*
Q
; if
vect
=
'P'
, sub(
C
) is overwritten by
P
*sub(
C
), or
P'
*sub(
C
), or sub(
C
)*
P,
or sub(
C
)*
P'
.
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,
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

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