Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

p?unmhr

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

Syntax

void
pcunmhr
(
char
*side
,
char
*trans
,
MKL_INT
*m
,
MKL_INT
*n
,
MKL_INT
*ilo
,
MKL_INT
*ihi
,
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
pzunmhr
(
char
*side
,
char
*trans
,
MKL_INT
*m
,
MKL_INT
*n
,
MKL_INT
*ilo
,
MKL_INT
*ihi
,
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 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
 =
'H'
:
Q
H
*sub(
C
)
sub(
C
)*
Q
H
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
ihi
-
ilo
 elementary reflectors, as returned by
p?gehrd
.
Q
 =
H
(
ilo
)
H
(
ilo
+1)...
H
(
ihi
-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.
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)
.
ilo
,
ihi
(global)
These must be the same parameters
ilo
 and
ihi
, respectively, as supplied to
p?gehrd
.
Q
 is equal to the unit matrix except in the distributed submatrix
Q
(
ia
+
ilo
:
ia
+
ihi
-1,
ja
+
ilo
:
ja
+
ihi
-1).
If
side
='L'
, then
1≤
ilo
≤
ihi
≤max(1,
m
)
.
If
side
 =
'R'
, then
1≤
ilo
≤
ihi
≤max(1,
n
)
ilo
 and
ihi
 are relative indexes.
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?gehrd
.
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
+
m
-2)
, if
side
 =
'L'
, and
LOCc
(
ja
+
n
-2)
 if
side
 =
'R'
.
tau
[
j
]
 contains the scalar factor of the elementary reflector
H
(
j
+1)
 as returned by
p?gehrd
(0 ≤
j
 < size(
tau
))
.
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 with size
lwork
.
lwork
(local or global)
The size of the array
work
.
lwork
must be at least
iaa
 =
ia
 +
ilo
;
jaa
 =
ja
+
ilo
-1;
If
side
 =
'L'
,
mi
 =
ihi
-
ilo
;
ni
 =
n
;
icc
 =
ic
 +
ilo
;
jcc
 =
jc
;
lwork
 ≥
max
((
nb_a
*(
nb_a
-1))/2, (
nqc
0+
mpc
0)*
nb_a
) +
nb_a
*
nb_a
else if
side
 =
'R'
,
mi
 =
m
;
ni
 =
ihi
-
ilo
;
icc
 =
ic
;
jcc
 =
jc
 +
ilo
;
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
C
 is overwritten by
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.