Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

p?geqpf

Computes the
QR
 factorization of a general m-by-n matrix with pivoting.

Syntax

void
psgeqpf
(
MKL_INT
*m
,
MKL_INT
*n
,
float
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_INT
*ipiv
,
float
*tau
,
float
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pdgeqpf
(
MKL_INT
*m
,
MKL_INT
*n
,
double
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_INT
*ipiv
,
double
*tau
,
double
*work
,
MKL_INT
*lwork
,
MKL_INT
*info
);
void
pcgeqpf
(
MKL_INT
*m
,
MKL_INT
*n
,
MKL_Complex8
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_INT
*ipiv
,
MKL_Complex8
*tau
,
MKL_Complex8
*work
,
MKL_INT
*lwork
,
float
*rwork
,
MKL_INT
*lrwork
,
MKL_INT
*info
);
void
pzgeqpf
(
MKL_INT
*m
,
MKL_INT
*n
,
MKL_Complex16
*a
,
MKL_INT
*ia
,
MKL_INT
*ja
,
MKL_INT
*desca
,
MKL_INT
*ipiv
,
MKL_Complex16
*tau
,
MKL_Complex16
*work
,
MKL_INT
*lwork
,
double
*rwork
,
MKL_INT
*lrwork
,
MKL_INT
*info
);
Include Files
  • mkl_scalapack.h
Description
The
p?geqpf
function
forms the
QR
 factorization with column pivoting of a general
m
-by-
n
 distributed matrix sub(
A
)=
A
(
ia
:
ia
+
m
-1,
ja
:
ja
+
n
-1) as
sub(
A
)*
P
=
Q
*
R
.
Input Parameters
m
(global) The number of rows in the matrix sub(
A
)
(
m
≥
 0)
.
n
(global) The number of columns in the matrix sub(
A
)
(
n
≥
 0)
.
a
(local)
Pointer into the local memory to an array of local size
lld_a
*
LOCc
(
ja
+
n
-1)
.
Contains the local pieces of the distributed matrix sub(
A
) 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 the submatrix
A
(
ia
:
ia
+
m
-1,
ja
:
ja
+
n
-1), respectively.
desca
(global and local) array of size
dlen_
. The array descriptor for the distributed matrix
A
.
work
(local).
Workspace array of size
lwork
.
lwork
(local or global) size of
work
, must be at least
For real flavors:
lwork
≥
max
(3,
mp
0+
nq
0) +
LOCc
 (
ja
+
n
-
1
) +
nq
0
.
For complex flavors:
lwork
≥
max
(3,
mp
0+
nq
0)
 .
Here
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
)
,
LOCc
 (
ja
+
n
-
1
) =
numroc
(
ja
+
n
-
1
,
nb_a
,
MYCOL
,
csrc_a
,
NPCOL
)
, and
numroc
,
indxg2p
 are ScaLAPACK tool functions.
You can determine
MYROW
,
MYCOL
,
NPROW
 and
NPCOL
 by calling the
blacs_gridinfo
function
.
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.
rwork
(local).
Workspace array of size
lrwork
 (complex flavors only).
lrwork
(local or global) size of
rwork
 (complex flavors only). The value of
lrwork
 must be at least
lwork
≥
LOCc
 (
ja
+
n
-
1
) +
nq
0
 .
Here
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
)
,
LOCc
 (
ja
+
n
-
1
) =
numroc
(
ja
+
n
-
1
,
nb_a
,
MYCOL
,
csrc_a
,
NPCOL
)
, and
numroc
,
indxg2p
 are ScaLAPACK tool functions.
You can determine
MYROW
,
MYCOL
,
NPROW
 and
NPCOL
 by calling the
blacs_gridinfo
function
.
If
lrwork
 = -1
, then
lrwork
 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
The elements on and above the diagonal of sub(
A
)contain the min(
m
,
n
)-by-
n
 upper trapezoidal matrix
R
 (
R
 is upper triangular if
m
≥
n
); the elements below the diagonal, with the array
tau
, represent the orthogonal/unitary matrix
Q
 as a product of elementary reflectors
(see
Application Notes
 below)
.
ipiv
(local) Array of size
LOCc
(
ja
+
n
-1)
.
ipiv
[
i
] =
k
, the local (
i
+1)-th
 column of sub(
A
)*
P
 was the global
k
-th column of sub(
A
)
(0 ≤
i
 <
LOCc
(
ja
+
n
-1)
.
ipiv
 is tied to the distributed matrix
A
.
tau
(local)
Array of size
LOCc
(
ja
+min(
m
,
n
)-1)
.
Contains the scalar factor
tau
 of elementary reflectors.
tau
 is tied to the distributed matrix
A
.
work
[0]
On exit,
work
[0]
 contains the minimum value of
lwork
 required for optimum performance.
rwork
[0]
On exit,
rwork
[0]
 contains the minimum value of
lrwork
 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
.
Application Notes
The matrix
Q
 is represented as a product of elementary reflectors
Q
 =
H
(1)*
H
(2)*...*
H
(
k
)
where
k
 = min(
m
,
n
).
Each
H
(
i
) has the form
H
 =
I
 -
tau
*
v
*
v'
where
tau
 is a real/complex scalar, and
v
 is a real/complex vector with
v
(1:
i
-1) = 0 and
v
(
i
) = 1;
v
(
i
+
1
:
m
) is stored on exit in
A
(
ia
+
i
:
ia
+m-1,
ja
+
i
-1).
The matrix
P
 is represented in
ipiv
 as follows: if
ipiv
[
j
]=
i
 then the (
j
+1)-th column of
P
 is the
i
-th
canonical unit vector
(0 ≤
j
 <
LOCc
(
ja
+
n
-1)
.

Product and Performance Information

1

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