Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

p?ormbr

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

Syntax

void
psormbr
(
char
*vect
,
char
*side
,
char
*trans
,
MKL_INT
*m
,
MKL_INT
*n
,
MKL_INT
*k
,
float
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
float
*tau
,
float
*c
,
MKL_INT
*ic
,
MKL_INT
*jc
,
MKL_INT
*descc
,
float
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pdormbr
(
char
*vect
,
char
*side
,
char
*trans
,
MKL_INT
*m
,
MKL_INT
*n
,
MKL_INT
*k
,
double
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
double
*tau
,
double
*c
,
MKL_INT
*ic
,
MKL_INT
*jc
,
MKL_INT
*descc
,
double
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
Include Files
  • mkl_scalapack.h
Description
If
vect
 = '
Q
', the
p?ormbr
function
overwrites the general real distributed
m
-by-
n
 matrix sub(
C
) =
C
(
iс
:
iс
+
m
-1,
jс
:
jс
+
n
-1) with
side
 =
'L'
side
 =
'R'
trans
 =
'N'
:
Q
 sub(
C
)
sub(
C
)
Q
trans
 =
'T'
:
Q
T
 sub(
C
)
sub(
C
)
Q
T
If
vect
 = 'P', the
function
overwrites sub(
C
) with
side
 =
'L'
side
 =
'R'
trans
 =
'N'
:
P
 sub(
C
)
sub(
C
)
P
trans
 =
'T'
:
P
T
 sub(
C
)
sub(
C
)
P
T
Here
Q
 and
P
T
 are the orthogonal distributed matrices determined by
p?gebrd
 when reducing a real distributed matrix
A
(
ia
:*,
ja
:*) to bidiagonal form:
A
(
ia
:*,
ja
:*) =
Q
*
B
*
P
T
.
Q
 and
P
T
 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 orthogonal matrix
Q
 or
P
T
 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
T
 is applied.
If
vect
 =
'P'
, then
P
 or
P
T
 is applied.
side
(global)
If
side
 =
'L'
, then
Q
 or
Q
T
,
P
 or
P
T
 is applied from the left.
If
side
 =
'R'
, then
Q
 or
Q
T
,
P
 or
P
T
 is applied from the right.
trans
(global)
If
trans
 =
'N'
, no transpose,
Q
 or
P
 is applied.
If
trans
 =
'T'
, then
Q
T
 or
P
T
 is applied.
m
(global) The number of rows in the distributed matrix sub (
C
).
n
(global) The number of columns in the distributed matrix sub (
C
).
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
pdgebrd
 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
+