Developer Reference

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

?larfg

Generates an elementary reflector (Householder matrix).

Syntax

lapack_int
LAPACKE_slarfg
(
lapack_int
n
,
float
*
alpha
,
float
*
x
,
lapack_int
incx
,
float
*
tau
);
lapack_int
LAPACKE_dlarfg
(
lapack_int
n
,
double
*
alpha
,
double
*
x
,
lapack_int
incx
,
double
*
tau
);
lapack_int
LAPACKE_clarfg
(
lapack_int
n
,
lapack_complex_float
*
alpha
,
lapack_complex_float
*
x
,
lapack_int
incx
,
lapack_complex_float
*
tau
);
lapack_int
LAPACKE_zlarfg
(
lapack_int
n
,
lapack_complex_double
*
alpha
,
lapack_complex_double
*
x
,
lapack_int
incx
,
lapack_complex_double
*
tau
);
Include Files
  • mkl.h
Description
The routine
?larfg
generates a real/complex elementary reflector
H
of order
n
, such that
for real flavors and
Equation for complex flavors,
where
alpha
and
beta
are scalars (with
beta
real for all flavors), and
x
is an (
n
-1)-element real/complex vector.
H
is represented in the form
for real flavors and
Equation for complex flavors,
where
tau
is a real/complex scalar and v is a real/complex (
n
-1)-element vector, respectively. Note that for
clarfg
/
zlarfg
,
H
is not Hermitian.
If the elements of
x
are all zero (and, for complex flavors,
alpha
is real), then
tau
= 0
and
H
is taken to be the unit matrix.
Otherwise,
1 ≤
tau
≤ 2
(for real flavors), or
1 ≤ Re(
tau
) ≤ 2
and
abs(
tau
-1) ≤ 1
(for complex flavors).
Input Parameters
A
<datatype>
placeholder, if present, is used for the C interface data types in the C interface section above. See C Interface Conventions for the C interface principal conventions and type definitions.
n
The order of the elementary reflector.
alpha
x
Array, size (1+(
n
-2)*abs(
incx
)).
On entry, the vector
x
.
incx
The increment between elements of
x
.
incx
> 0
.
Output Parameters
alpha
On exit, it is overwritten with the value
beta
.
x
On exit, it is overwritten with the vector
v
.
tau
Return Values
This function returns a value
info
.
If
info
= 0
, the execution is successful.
If
info
= -2
,
alpha
is NaN
If
info
= -3
, array
x
contains NaN components.

Product and Performance Information

1

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