Developer Reference

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

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