Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

?orgqr

Generates the real orthogonal matrix Q of the QR factorization formed by
?geqrf
.

Syntax

lapack_int
LAPACKE_sorgqr
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
lapack_int
k
,
float
*
a
,
lapack_int
lda
,
const
float
*
tau
);
lapack_int
LAPACKE_dorgqr
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
lapack_int
k
,
double
*
a
,
lapack_int
lda
,
const
double
*
tau
);
Include Files
  • mkl.h
Description
The routine generates the whole or part of
m
-by-
m
 orthogonal matrix
Q
 of the
QR
 factorization formed by the routine
?geqrf
or geqpf. Use this routine after a call to
sgeqrf
/
dgeqrf
 or
sgeqpf
/
dgeqpf
.
Usually
Q
 is determined from the
QR
 factorization of an
m
 by
p
 matrix
A
 with
m
≥
p
. To compute the whole matrix
Q
, use: 
 LAPACKE_?orgqr(matrix_layout, m, m, p, a, lda, tau)
To compute the leading
p
 columns of
Q
 (which form an orthonormal basis in the space spanned by the columns of
A
): 
 LAPACKE_?orgqr(matrix_layout, m, p, p, a, lda)
To compute the matrix
Q
k
 of the
QR
 factorization of leading
k
 columns of the matrix
A
: 
 LAPACKE_?orgqr(matrix_layout, m, m, k, a, lda, tau)
To compute the leading
k
 columns of
Q
k
 (which form an orthonormal basis in the space spanned by leading
k
 columns of the matrix
A
): 
 LAPACKE_?orgqr(matrix_layout, m, k, k, a, lda, tau)
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
m
The order of the orthogonal matrix
Q
 (
m
≥
 0
).
n
The number of columns of
Q
 to be computed
(0
≤
n
≤
m
).
k
The number of elementary reflectors whose product defines the matrix
Q
 (0
≤
k
≤
n
).
a
,
tau
Arrays:
a
 and
tau
 are the arrays returned by
sgeqrf
 /
dgeqrf
 or
sgeqpf
 /
dgeqpf
.
The size of
a
 is max(1,
lda
*
n
) for column major layout and max(1,
lda
*
m
) for row major layout .
The size of
tau
 must be at least max(1,
k
).
lda
The leading dimension of
a
; at least max(1,
m
)
for column major layout and max(1,
n
) for row major layout
.
Output Parameters
a
Overwritten by
n
 leading columns of the
m
-by-
m
 orthogonal matrix
Q
.
Return Values
This function returns a value
info
.
If
info
=0
, the execution is successful.
If
info
 =
-i
, the
i
-th parameter had an illegal value.
Application Notes
The computed
Q
 differs from an exactly orthogonal matrix by a matrix
E
 such that
||
E
||
2
 =
O
(
ε
)|*|
A
||
2
 where
ε
 is the machine precision.
The total number of floating-point operations is approximately
4*
m
*
n
*
k
 - 2*(
m
 +
n
)*
k
2
 + (4/3)*
k
3
.
If
n
 =
k
, the number is approximately
(2/3)*
n
2
*(3
m
 -
n
)
.
The complex counterpart of this routine is ungqr.

Product and Performance Information

1

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