Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 0.10
  • 10/21/2020
  • Public Content
Contents

p?ormtr

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

Syntax

void
psormtr
(
char
*side
,
char
*uplo
,
char
*trans
,
MKL_INT
*m
,
MKL_INT
*n
,
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
pdormtr
(
char
*side
,
char
*uplo
,
char
*trans
,
MKL_INT
*m
,
MKL_INT
*n
,
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
This
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
where
Q
 is a real orthogonal 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
 elementary reflectors, as returned by
p?sytrd
.
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
T
 is applied from the left.
=
'R'
:
Q
 or
Q
T
 is applied from the right.
trans
(global)
=
'N'
, no transpose,
Q
 is applied.
=
'T'
, transpose,
Q
T
 is applied.
uplo
(global)
=
'U'
: Upper triangle of
A
(
ia
:*,
ja
:*)
 contains elementary reflectors from
p?sytrd
;
=
'L'
: Lower triangle of
A
(
ia
:*,
ja
:*)
 contains elementary reflectors from
p?sytrd
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 that define the elementary reflectors, as returned by
p?sytrd
.
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?sytrd
(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,
 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
.