Developer Reference

Contents

?orghr

Generates the real orthogonal matrix Q determined by
?gehrd
.

Syntax

lapack_int
LAPACKE_sorghr
(
int
matrix_layout
,
lapack_int
n
,
lapack_int
ilo
,
lapack_int
ihi
,
float
*
a
,
lapack_int
lda
,
const
float
*
tau
);
lapack_int
LAPACKE_dorghr
(
int
matrix_layout
,
lapack_int
n
,
lapack_int
ilo
,
lapack_int
ihi
,
double
*
a
,
lapack_int
lda
,
const
double
*
tau
);
Include Files
  • mkl.h
Description
The routine explicitly generates the orthogonal matrix
Q
that has been determined by a preceding call to
sgehrd
/
dgehrd
. (The routine
?gehrd
reduces a real general matrix
A
to upper Hessenberg form
H
by an orthogonal similarity transformation,
A
=
Q*H*Q
T
, and represents the matrix
Q
as a product of
ihi
-
ilo
elementary reflectors. Here
ilo
and
ihi
are values determined by
sgebal
/
dgebal
when balancing the matrix; if the matrix has not been balanced,
ilo
= 1
and
ihi
=
n
.)
The matrix
Q
generated by
?orghr
has the structure:
Equation
where
Q
22
occupies rows and columns
ilo
to
ihi
.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
n
The order of the matrix
Q
(
n
0
).
ilo
,
ihi
These must be the same parameters
ilo
and
ihi
, respectively, as supplied to
?gehrd
. (If
n
> 0
, then
1
ilo
ihi
n
; if
n
=
0
,
ilo
= 1
and
ihi
= 0
.)
a
,
tau
Arrays:
a
(size max(1,
lda
*
n
))
contains details of the vectors which define the elementary reflectors, as returned by
?gehrd
.
tau
contains further details of the elementary reflectors, as returned by
?gehrd
.
The dimension 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
n
-by-
n
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 the exact result 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)(
ihi
-
ilo
)
3
.
The complex counterpart of this routine is unghr.

Product and Performance Information

1

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