Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 0.9
  • 09/09/2020
  • 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

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804