Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

?orglq

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

Syntax

lapack_int
LAPACKE_sorglq
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
lapack_int
k
,
float
*
a
,
lapack_int
lda
,
const
float
*
tau
);
lapack_int
LAPACKE_dorglq
(
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
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)
To compute the leading
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
 factorization of the leading
k
 rows of
A
, use: 
info = LAPACKE_?orglq(matrix_layout, n, n, k, a, lda, tau)
To compute the leading
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
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
m
 leading rows of the
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

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