Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

?orgbr

Generates the real orthogonal matrix
Q
 or
P
T
 determined by
?gebrd
.

Syntax

lapack_int
LAPACKE_sorgbr
(
int
matrix_layout
,
char
vect
,
lapack_int
m
,
lapack_int
n
,
lapack_int
k
,
float
*
a
,
lapack_int
lda
,
const
float
*
tau
);
lapack_int
LAPACKE_dorgbr
(
int
matrix_layout
,
char
vect
,
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 the orthogonal matrices
Q
 and
P
T
 formed by the routines
gebrd
. Use this routine after a call to
sgebrd
/
dgebrd
. All valid combinations of arguments are described in
Input parameters
. In most cases you need the following:
To compute the whole
m
-by-
m
 matrix
Q
: 
LAPACKE_?orgbr(matrix_layout, 'Q', m, m, n, a, lda, tau )
(note that the array
a
 must have at least
m
 columns).
To form the
n
 leading columns of
Q
 if
m
 >
n
: 
LAPACKE_?orgbr(matrix_layout, 'Q', m, n, n, a, lda, tau )
To compute the whole
n
-by-
n
 matrix
P
T
: 
LAPACKE_?orgbr(matrix_layout, 'P', n, n, m, a, lda, tau )
(note that the array
a
 must have at least
n
 rows).
To form the
m
 leading rows of
P
T
 if
m
 <
n
: 
LAPACKE_?orgbr(matrix_layout, 'P', m, n, m, a, lda, tau )
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
vect
Must be
'Q'
 or
'P'
.
If
vect
 =
'Q'
, the routine generates the matrix
Q
.
If
vect
 =
'P'
, the routine generates the matrix
P
T
.
m, n
The number of rows (
m
) and columns (
n
) in the matrix
Q
 or
P
T
 to be returned (
m
≥
 0
,
n
≥
 0
).
If
vect
 =
'Q'
,
m
 ≥
n
 ≥ min(
m
,
k
)
.
If
vect
 =
'P'
,
n
 ≥
m
 ≥ min(
n
,
k
)
.
k
If
vect
 =
'Q'
, the number of columns in the original
m
-by-
k
 matrix reduced by gebrd.
If
vect
 =
'P'
, the number of rows in the original
k
-by-
n
 matrix reduced by gebrd.
a
Array, size at least
lda
*
n
 for column major layout and
lda
*
m
 for row major layout.
 The vectors which define the elementary reflectors, as returned by gebrd.
lda
The leading dimension of the array
a
.
lda
 ≥ max(
1
,
m
)
for column major layout and at least max(1,
n
) for row major layout
 .
tau
Array, size
min (
m
,
k
) if
vect
 =
'Q'
,
min (
n
,
k
) if
vect
 =
'P'
. Scalar factor of the elementary reflector
H
(
i
) or
G
(
i
), which determines
Q
 and
P
T
 as returned by
gebrd
 in the array
tauq
 or
taup
.
Output Parameters
a
Overwritten by the orthogonal matrix
Q
 or
P
T
 (or the leading rows or columns thereof) as specified by
vect
,
m
, and
n
.
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 matrix
Q
 differs from an exactly orthogonal matrix by a matrix
E
 such that
||
E
||
2
 =
O
(
ε
)
.
The approximate numbers of floating-point operations for the cases listed in
Description
 are as follows:
To form the whole of
Q
:
(4/3)*
n
*(3
m
2
 - 3
m
*
n
 +
n
2
)
 if
m
 >
n
;
(4/3)*
m
3
 if
m
≤
n
.
To form the
n
 leading columns of
Q
 when
m
 >
n
:
(2/3)*
n
2
*(3
m
 -
n
)
 if
m
 >
n
.
To form the whole of
P
T
:
(4/3)*
n
3
 if
m
≥
n
;
(4/3)*
m
*(3
n
2
 - 3
m
*
n
 +
m
2
)
 if
m
 <
n
.
To form the
m
 leading columns of
P
T
 when
m
 <
n
:
(2/3)*
n
2
*(3
m
 -
n
)
 if
m
 >
n
.
The complex counterpart of this routine is ungbr.

Product and Performance Information

1

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