# ?larfgp

Generates an elementary reflector (Householder matrix) with non-negative beta .

## Syntax

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

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

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

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

## Include Files

• Fortran: mkl.fi
• C: mkl.h

## Description

The routine ?larfgp generates a real/complex elementary reflector H of order n, such that

for real flavors and

for complex flavors,

where alpha and beta are scalars (with beta real and non-negative for all flavors), and x is an (n-1)-element real/complex vector. H is represented in the form

for real flavors and

for complex flavors,

where tau is a real/complex scalar and v is a real/complex (n-1)-element vector. Note that for c/zlarfgp, 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

n

INTEGER. The order of the elementary reflector.

alpha

REAL for slarfgp

DOUBLE PRECISION for dlarfgp

COMPLEX for clarfgp

DOUBLE COMPLEX for zlarfgp

On entry, the value alpha.

x

REAL for s

DOUBLE PRECISION for dlarfgp

COMPLEX for clarfgp

DOUBLE COMPLEX for zlarfgp

Array, DIMENSION (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 slarfgp

DOUBLE PRECISION for dlarfgp

COMPLEX for clarfgp

DOUBLE COMPLEX for zlarfgp

The value tau.