Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

?unghr

Generates the complex unitary matrix Q determined by
?gehrd
.

Syntax

lapack_int
LAPACKE_cunghr
(
int
matrix_layout
,
lapack_int
n
,
lapack_int
ilo
,
lapack_int
ihi
,
lapack_complex_float
*
a
,
lapack_int
lda
,
const
lapack_complex_float
*
tau
);
lapack_int
LAPACKE_zunghr
(
int
matrix_layout
,
lapack_int
n
,
lapack_int
ilo
,
lapack_int
ihi
,
lapack_complex_double
*
a
,
lapack_int
lda
,
const
lapack_complex_double
*
tau
);
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:
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, 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
The leading dimension of
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.