Developer Reference

  • 0.9
  • 09/09/2020
  • 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

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804