Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

p?gerq2

Computes an RQ factorization of a general rectangular matrix (unblocked algorithm).

Syntax

void
psgerq2
(
MKL_INT
*m
,
MKL_INT
*n
,
float
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
float
*tau
,
float
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pdgerq2
(
MKL_INT
*m
,
MKL_INT
*n
,
double
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
double
*tau
,
double
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pcgerq2
(
MKL_INT
*m
,
MKL_INT
*n
,
MKL_Complex8
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_Complex8
*tau
,
MKL_Complex8
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pzgerq2
(
MKL_INT
*m
,
MKL_INT
*n
,
MKL_Complex16
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_Complex16
*tau
,
MKL_Complex16
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
Include Files
  • mkl_scalapack.h
Description
The
p?gerq2
function
computes an
RQ
 factorization of a real/complex distributed
m
-by-
n
 matrix
sub(
A
) =
A
(
ia
:
ia
+
m
-1
,
ja
:
ja
+
n
-1) =
R
*
Q
.
Input Parameters
m
(global) The number of rows in the distributed matrix sub(
A
).
(
m
≥0)
.
n
(global) The number of columns in the distributed matrix sub(
A
).
(
n
≥0)
.
a
(local).
Pointer into the local memory to an array of size
lld_a
 *
LOC
c
(
ja
+
n
-1)
.
On entry, this array contains the local pieces of the
m
-by-
n
 distributed matrix sub(
A
) which is to be factored.
ia
,
ja
(global) The row and column indices in the global matrix
A
indicating the first row and the first column of sub(
A
), respectively.
desca
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix A.
work
(local).
This is a workspace array of size
lwork
.
lwork
(local or global)
The size of the array
work
.
lwork
 is local input and must be at least
lwork
≥
nq
0 + max(1,
mp
0)
, where
iroff
 =
mod
(
ia
-1,
mb_a
),
icoff
 = mod(
ja
-1,
nb_a
)
,
iarow
 =
indxg2p
(
ia
,
mb_a
,
myrow
,
rsrc_a
,
nprow
)
,
iacol
 =
indxg2p
(
ja
,
nb_a
,
mycol
,
csrc_a
,
npcol
),
mp
0 =
numroc
(
m
+
iroff
,
mb_a
,
myrow
,
iarow
,
nprow
)
,
nq
0 =
numroc
(
n
+
icoff
,
nb_a
,
mycol
,
iacol
,
npcol
)
,
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
a
(local).
On exit,
if
m
 ≤
n
, the upper triangle of
A
(
ia+m-n:ia+m-1
,
ja:ja+n-1
) contains the
m
-by-
m
 upper triangular matrix
R
;
if
m
≥
n
, the elements on and above the (
m-n
)-th subdiagonal contain the
m
-by-
n
 upper trapezoidal matrix
R
; the remaining elements, with the array
tau
, represent the orthogonal/ unitary matrix
Q
 as a product of elementary reflectors
(see
Application Notes
 below)
.
tau
(local).
Array of size
LOCr
(
ia
+
m
 -1). This array contains the scalar factors of the elementary reflectors.
tau
 is tied to the distributed matrix
A
.
work
On exit,
work
[0]
 returns the minimal and optimal
lwork
.
info
(local)
If
info
 = 0, the execution is successful.
if
info
 < 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
.
Application Notes
The matrix
Q
 is represented as a product of elementary reflectors
Q
 =
H
(
ia
)*
H
(
ia
+1)*...*
H
(
ia
+
k
-1)
 for real flavors,
Q
 = (
H
(
ia
))
H
*(
H
(
ia
+1))
H
...*(
H
(
ia
+
k
-1))
H
 for complex flavors,
where
k
 = min(
m
,
n
)
.
Each
H
(
i
)
 has the form
H
(
i
) =
I
 -
tau
*
v
*
v'
,
where
tau
 is a real/complex scalar, and
v
 is a real/complex vector with
v
(
n-k
+
i
+1:
n
) = 0
 and
v
(
n
-
k
+
i
) = 1
;
v
(1:
n
-
k
+
i
-1)
 for real flavors or
conjg
(
v
(1:
n
-
k
+
i
-1))
 for complex flavors is stored on exit in
A
(
ia
+
m-k
+
i
-1,
ja
:
ja
+
n-k
+
i
-2)
, and
tau
 in
tau
[
ia
+
m-k
+
i
-2]
.

Product and Performance Information

1

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