Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
Contents

p?unmql

Multiplies a general matrix by the unitary matrix
Q
 of the
QL
 factorization formed by
p?geqlf
.

Syntax

void
pcunmql
(
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
pzunmql
(
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
This
function
overwrites the general complex
m
-by-
n
 distributed 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
 =
'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
(
k
)' ...
H
(2)'
H
(1)'
as returned by
p?geqlf
.
Q
 is of order
m
 if
side
 =
'L'
 and of order
n
 if
side
 =
'R'
.
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.
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) The number of elementary reflectors whose product defines the matrix
Q
. Constraints:
If
side
 =
'L'
,
m
≥
k
≥0
If
side
 =
'R'
,
n
≥
k
≥0
.
a
(local)
Pointer into the local memory to an array of size
lld_a
*
LOCc
(
ja
+
k
-1)
. The
j
-th column
of the matrix stored in
a
must contain the vector that defines the elementary reflector
H
(
j
),
ja
≤
j
≤
ja
+
k
-1, as returned by
p?geqlf
 in the
k
 columns of its distributed matrix argument
A
(
ia
:*,
ja
:
ja
+
k
-1).
A
(
ia
:*,
ja
:
ja
+
k
-1) is modified by the
function
but restored on exit.
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
LOCc
(
ia
+
n
-1)
.
Contains the scalar factor
tau
[
j
]
 of elementary reflectors
H
(
j
+1)
 as returned by
p?geqlf
(0 ≤
j
 <
LOCc
(
ia
+
n
-1)
)
.
tau
 is tied to the distributed matrix
A
.
c
(local)
Pointer into the local memory to an array of local size
lld_c
*
LOCc
(
jc
+
n
-1)
.
Contains the local pieces of the distributed matrix sub(
C
) to be factored.
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 of
lwork
.
lwork
(local or global) size of
work
, must be at least:
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
(
n
+
icoffc
,
nb_a
, 0, 0,
NPCOL
),
nb_a
, 0, 0,
lcmq
),
mpc
0))*
nb_a
) +
nb_a
*nb_a
end if
where
lcmp
 =
lcm
/
NPCOL
 with
lcm
 =
ilcm
 (
NPROW
,
NPCOL
)
,
iroffa
 =
mod
(
ia
-1,
mb_a
)
,
icoffa
 =
mod
(
ja
-1,
nb_a
)
,
iarow
 =
indxg2p
(
ia
,
mb_a
,
MYROW
,
rsrc_a
,
NPROW
)
,
npa
0 =
numroc
 (
n
 +
iroffa
,
mb_a
,
MYROW
,
iarow
,
NPROW
)
,
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
)
,
mpc
0 =
numroc
(
m
+
iroffc
,
mb_c
,
MYROW
,
icrow
,
NPROW
)
,
nqc
0 =
numroc
(
n
+
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
.
mod(
x
,
y
)
 is the integer remainder of
x
/
y
.
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,
 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

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.