Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

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