Contents

# ?unghr

Generates the complex unitary matrix Q determined by
?gehrd
.

## Syntax

Include Files
• mkl.h
Description
The routine is intended to be used following a call to
cgehrd
/
zgehrd
, which reduces a complex matrix
A
to upper Hessenberg form
H
by a unitary similarity transformation:
A
=
Q*H*Q
H
.
?gehrd
represents the matrix
Q
as a product of
ihi
-
ilo
elementary reflectors. Here
ilo
and
ihi
are values determined by
cgebal
/
zgebal
when balancing the matrix; if the matrix has not been balanced,
ilo
= 1
and
ihi
=
n
.
Use the routine unghr to generate
Q
explicitly as a square matrix. The matrix
Q
has the structure: 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, then
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
a
; at least max(1,
n
).
Output Parameters
a
Overwritten by the
n
-by-
n
unitary 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 real floating-point operations is
(16/3)(
ihi
-
ilo
)
3
.
The real counterpart of this routine is orghr.

#### Product and Performance Information

1

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