Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

p?orm2r/p?unm2r

Multiplies a general matrix by the orthogonal/unitary matrix from a QR factorization determined by
p?geqrf
 (unblocked algorithm).

Syntax

void
psorm2r
(
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
pdorm2r
(
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
);
void
pcunm2r
(
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
pzunm2r
(
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
The
p?orm2r/p?unm2r
function
overwrites the general real/complex
m
-by-
n
 distributed matrix sub
(
C
)=
C
(
ic
:
ic
+
m
-1
, jc
:
jc
+
n
-1)
 with
Q
*sub(
C
) if
side
 =
'L'
 and
trans
 =
'N'
, or
Q
T
*sub(
C
) /
Q
H
*sub(
C
)
 if
side
 =
'L'
 and
trans
 =
'T'
 (for real flavors) or
trans
 =
'C'
 (for complex flavors), or
sub(
C
)*
Q
 if
side
 =
'R
' and
trans
 =
'N'
, or
sub(
C
)*
Q
T
 / sub(
C
)*
Q
H
 if
side
 =
'R'
 and
trans
 =
'T'
 (for real flavors) or
trans
 =
'C'
 (for complex flavors).
where
Q
 is a real orthogonal or complex unitary matrix defined as the product of
k
 elementary reflectors
Q = H(
k
)*...*
H
(2)*
H
(1)
 as returned by
p?geqrf
 .
Q
 is of order
m
 if
side
 =
'L'
 and of order
n
 if
side
 =
'R'
.
Input Parameters
side
(global)
=
'L'
: apply
Q
 or
Q
T
 for real flavors (
Q
H
 for complex flavors) from the left,
=
'R'
: apply
Q
 or
Q
T
 for real flavors (
Q
H
 for complex flavors) from the right.
trans
(global)
=
'N'
: apply
Q
 (no transpose)
=
'T'
: apply
Q
T
 (transpose, for real flavors)
=
'C'
: apply
Q
H
 (conjugate transpose, for complex flavors)
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
.
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)
.
On entry, 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?geqrf
 in the
k
 columns of its distributed matrix argument
A
(
ia
:*,
ja
:
ja
+
k
-1)
. The argument
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
(global)
The row index in the global matrix
A
 indicating the first row of sub(
A
).
ja
(global)
The column index in the global matrix
A
 indicating the first column of sub(
A
).
desca
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
A
.
tau
(local)
Array of size
LOCc
(
ja
+
k
-1)
.
tau
[
j
]
 contains the scalar factor of the elementary reflector
H
(
j
+1),
j
 = 0, 1, ...,
LOCc
(
ja
+
k
-1)
-1
, as returned by
p?geqrf
. This array 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)
.
On entry, the local pieces of the distributed matrix sub (
C
).
ic
(global)
The row index in the global matrix
C
 indicating the first row of sub(
C
).
jc
(global)
The column index in the global matrix
C
 indicating the first column of sub(
C
).
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)
The size of the array
work
.
lwork
 is local input and must be at least
if
side
 =
'L'
,
lwork
≥
mpc
0 + max(1,
nqc
0)
,
if
side
 =
'R'
,
lwork
≥
nqc
0 + max(max(1,
mpc
0),
numroc
(
numroc
(
n
+
icoffc
,
nb_a
, 0, 0,
npcol
),
nb_a
, 0, 0,
lcmq
))
,
where
lcmq
 =
lcm
/
npcol
 ,
lcm
 =
iclm
(
nprow
,
npcol
)
,
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
)
,
Mqc0
 =
numroc
(
m
+
icoffc
,
nb_c
,
mycol
,
icrow
,
nprow
)
,
Npc0
 =
numroc
(
n
+
iroffc
,
mb_c
,
myrow
,
iccol
,
npcol
)
,
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
On exit,
c
 is overwritten by
Q
*sub(
C
), or
Q
T
*sub(
C
)/
Q
H
*sub(
C
), or sub(
C
)*
Q
, or sub(
C
)*
Q
T
 / sub(
C
)*
Q
H
work
On exit,
work
[0]
 returns the minimal and optimal
lwork
.
info
(local)
= 0
: successful exit
< 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
.
The distributed submatrices
A
(
ia
:*,
ja
:*)
 and
C
(
ic
:
ic
+
m
-1
,
jc
:
jc
+
n
-1)
 must verify some alignment properties, namely the following expressions should be true:
If
side
 =
'L'
,
(
mb_a
 ==
mb_c
) && (
iroffa
 ==
iroffc
) && (
iarow
 ==
icrow
)
.
If
side
 =
'R'
,
(
mb_a
 ==
nb_c
) && (
iroffa
 ==
iroffc
)
.
</