Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

?orgtr

Generates the real orthogonal matrix Q determined by
?sytrd
.

Syntax

lapack_int
LAPACKE_sorgtr
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
float
*
a
,
lapack_int
lda
,
const
float
*
tau
);
lapack_int
LAPACKE_dorgtr
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
double
*
a
,
lapack_int
lda
,
const
double
*
tau
);
Include Files
  • mkl.h
Description
The routine explicitly generates the
n
-by-
n
 orthogonal matrix
Q
 formed by
?sytrd
 when reducing a real symmetric matrix
A
 to tridiagonal form:
A
 =
Q*T*Q
T
. Use this routine after a call to
?sytrd
.
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
?sytrd
.
n
The order of the matrix
Q
 (
n
≥
 0
).
a
,
tau
Arrays:
a
(size max(1,
lda
*
n
))
 is the array
a
 as returned by
?sytrd
.
tau
 is the array
tau
 as returned by
?sytrd
.
The size of
tau
 must be at least max(1,
n
-1).
lda
The leading dimension of
a
; at least max(1,
n
).
Output Parameters
a
Overwritten by the 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 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 ungtr.

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