Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
Contents

?unmhr

Multiplies an arbitrary complex matrix C by the complex unitary matrix Q determined by
?gehrd
.

Syntax

lapack_int
LAPACKE_cunmhr
(
int
matrix_layout
,
char
side
,
char
trans
,
lapack_int
m
,
lapack_int
n
,
lapack_int
ilo
,
lapack_int
ihi
,
const
lapack_complex_float
*
a
,
lapack_int
lda
,
const
lapack_complex_float
*
tau
,
lapack_complex_float
*
c
,
lapack_int
ldc
);
lapack_int
LAPACKE_zunmhr
(
int
matrix_layout
,
char
side
,
char
trans
,
lapack_int
m
,
lapack_int
n
,
lapack_int
ilo
,
lapack_int
ihi
,
const
lapack_complex_double
*
a
,
lapack_int
lda
,
const
lapack_complex_double
*
tau
,
lapack_complex_double
*
c
,
lapack_int
ldc
);
Include Files
  • mkl.h
Description
The routine multiplies a matrix
C
 by the unitary matrix
Q
 that has been determined by a preceding call to
cgehrd
/
zgehrd
. (The routine
?gehrd
 reduces a real general matrix
A
 to upper Hessenberg form
H
 by an orthogonal similarity transformation,
A
 =
Q*H*Q
H
, and 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
.)
With
?unmhr
, you can form one of the matrix products
Q*C
,
Q
H
*C
,
C*Q
, or
C*Q
H
, overwriting the result on
C
 (which may be any complex rectangular matrix). A common application of this routine is to transform a matrix
V
 of eigenvectors of
H
 to the matrix
QV
 of eigenvectors of
A
.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
side
Must be
'L'
 or
'R'
.
If
side
 =
'L'
, then the routine forms
Q*C
 or
Q
H
*C
.
If
side
 =
'R'
, then the routine forms
C*Q
 or
C*Q
H
.
trans
Must be
'N'
 or
'C'
.
If
trans
 =
'N'
, then
Q
 is applied to
C
.
If
trans
 =
'T'
, then
Q
H
 is applied to
C
.
m
The number of rows in
C
 (
m
≥
 0
).
n
The number of columns in
C
 (
n
≥
 0
).
ilo
,
ihi
These must be the same parameters
ilo
 and
ihi
, respectively, as supplied to
?gehrd
 .
If
m
 > 0
 and
side
 =
'L'
, then
1
≤
ilo
≤
ihi
≤
m
.
If
m
 = 0
 and
side
 =
'L'
, then
ilo
 = 1
 and
ihi
 = 0
.
If
n
 > 0
 and
side
 =
'R'
, then
1
≤
ilo
≤
ihi
≤
n
.
If
n
 = 0
 and
side
 =
'R'
, then
ilo
 =1
 and
ihi
 = 0
.
a
,
tau
,
c
Arrays:
a
(size max(1,
lda
*
n
) for
side
='R' and size max(1,
lda
*
m
) for
side
='L')
 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,
m
-1)
if
side
 =
'L'
 and at least max (1,
n
-1) if
side
 =
'R'
.
c
(size max(1,
ldc
*
n
) for column major layout and max(1,
ldc
*
m
 for row major layout)
 contains the
m
-by-
n
 matrix
C
.
lda
The leading dimension of
a
; at least max(1,
m
) if
side
 =
'L'
 and at least max (1,
n
) if
side
 =
'R'
.
ldc
The leading dimension of
c
; at least max(1,
m
)
for column major layout and at least max(1,
n
) for row major layout
.
Output Parameters
c
C
 is overwritten by
Q*C
, or
Q
H
*
C,
 or
C*Q
H
, or
C*Q
 as specified by
side
 and
trans
.
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
)*||
C
||
2
, where
ε
 is the machine precision.
The approximate number of floating-point operations is
8
n
(
ihi
-
ilo
)
2
 if
side
 =
'L'
;
8
m
(
ihi
-
ilo
)
2
 if
side
 =
'R'
.
The real counterpart of this routine is ormhr.

Product and Performance Information

1

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