Contents

# ?orglq

Generates the real orthogonal matrix Q of the LQ factorization formed by
?gelqf
.

## Syntax

Include Files
• mkl.h
Description
The routine generates the whole or part of
n
-by-
n
orthogonal matrix
Q
of the
LQ
factorization formed by the routines gelqf. Use this routine after a call to
sgelqf
/
dgelqf
.
Usually
Q
is determined from the
LQ
factorization of an
p
-by-
n
matrix
A
with
n
p
. To compute the whole matrix
Q
, use:
`info = LAPACKE_?orglq(matrix_layout, n, n, p, a, lda, tau)`
p
rows of
Q
, which form an orthonormal basis in the space spanned by the rows of
A
, use:
`info = LAPACKE_?orglq(matrix_layout, p, n, p, a, lda, tau)`
To compute the matrix
Q
k
of the
LQ
k
rows of
A
, use:
`info = LAPACKE_?orglq(matrix_layout, n, n, k, a, lda, tau)`
k
rows of
Q
k
, which form an orthonormal basis in the space spanned by the leading
k
rows of
A
, use:
`info = LAPACKE_?orgqr(matrix_layout, k, n, 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 number of rows of
Q
to be computed
(
0
m
n
).
n
The order of the orthogonal matrix
Q
(
n
m
).
k
The number of elementary reflectors whose product defines the matrix
Q
(
0
k
m
).
a
,
tau
Arrays:
a
(size max(1,
lda
*
n
) for column major layout and max(1,
lda
*
m
) for row major layout)
and
tau
are the arrays returned by
sgelqf
/
dgelqf
.
The size of
tau
must be at least max(1,
k
).
lda
a
; at least max(1,
m
)
for column major layout and max(1,
n
) for row major layout
.
Output Parameters
a
Overwritten by
m
n
-by-
n
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
m
=
k
, the number is approximately
(2/3)*
m
2
*(3
n
-
m
)
.
The complex counterpart of this routine is unglq.

#### 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