Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 7/13/2023
Public

A newer version of this document is available. Customers should click here to go to the newest version.

Document Table of Contents

?larfg

Generates an elementary reflector (Householder matrix).

Syntax

call slarfg( n, alpha, x, incx, tau )

call dlarfg( n, alpha, x, incx, tau )

call clarfg( n, alpha, x, incx, tau )

call zlarfg( n, alpha, x, incx, tau )

Include Files

  • mkl.fi

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

The data types are given for the Fortran interface.

n

INTEGER. The order of the elementary reflector.

alpha

REAL for slarfg

DOUBLE PRECISION for dlarfg

COMPLEX for clarfg

DOUBLE COMPLEX for zlarfg On entry, the value alpha.

x

REAL for slarfg

DOUBLE PRECISION for dlarfg

COMPLEX for clarfg

DOUBLE COMPLEX for zlarfg

Array, size (1+(n-2)*abs(incx)).

On entry, the vector x.

incx

INTEGER.

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

REAL for slarfg

DOUBLE PRECISION for dlarfg

COMPLEX for clarfg

DOUBLE COMPLEX for zlarfg The value tau.