Developer Reference

  • 0.9
  • 09/09/2020
  • Public Content
Contents

?opgtr

Generates the real orthogonal matrix Q determined by
?sptrd
.

Syntax

lapack_int
LAPACKE_sopgtr
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
const
float
*
ap
,
const
float
*
tau
,
float
*
q
,
lapack_int
ldq
);
lapack_int
LAPACKE_dopgtr
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
const
double
*
ap
,
const
double
*
tau
,
double
*
q
,
lapack_int
ldq
);
Include Files
  • mkl.h
Description
The routine explicitly generates the
n
-by-
n
orthogonal matrix
Q
formed by sptrd when reducing a packed real symmetric matrix
A
to tridiagonal form:
A
=
Q*T*Q
T
. Use this routine after a call to
?sptrd
.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
uplo
Must be
'U'
or
'L'
. Use the same
uplo
as supplied to
?sptrd
.
n
The order of the matrix
Q
(
n
0
).
ap
,
tau
Arrays
ap
and
tau
, as returned by
?sptrd
.
The size of
ap
must be at least max(1,
n
(
n
+1)/2).
The size of
tau
must be at least max(1,
n
-1).
ldq
The leading dimension of the output array
q
; at least max(1,
n
).
Output Parameters
q
Array, size
(size max(1,
ldq
*
n
))
.
Contains the computed 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 matrix
Q
differs from an exactly orthogonal matrix by a matrix
E
such that
||
E
||
2
=
O
(
ε
)
, where
ε
is the machine precision.
The approximate number of floating-point operations is
(4/3)
n
3
.
The complex counterpart of this routine is upgtr.

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