Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 0.9
  • 09/09/2020
  • Public Content
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

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