?larfp

Syntax

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

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

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

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

Include Files

• mkl.fi

Description

The ?larfp routines generate a real or complex elementary reflector H of order n, such that

H * (alpha) = (beta),
    (  x  )   ( 0  )

and H'*H =I for real flavors, conjg(H)'*H =I for complex flavors.

Here

alpha and beta are scalars, beta is real and non-negative,

x is (n-1)-element vector.

H is represented in the form

H = I - tau*( 1 )* (1  v'),
            ( v )

where tau is scalar, and v is (n-1)-element vector .

For real flavors if the elements of x are all zero, then tau = 0 and H is taken to be the unit matrix. Otherwise 1 ≤tau≤ 2.

For complex flavors if the elements of x are all zero and alpha is real, then tau = 0 and H is taken to be the unit matrix. Otherwise 1 ≤ real(tau) ≤ 2, and abs (tau-1≤ 1.

Input Parameters

n

INTEGER. Specifies the order of the elementary reflector.

alpha

REAL for slarfp

DOUBLE PRECISION for dlarfp

COMPLEX for clarfp

DOUBLE COMPLEX for zlarfp

Specifies the scalar alpha.

x

REAL for slarfp

DOUBLE PRECISION for dlarfp

COMPLEX for clarfp

DOUBLE COMPLEX for zlarfp

Array, DIMENSION at least (1 + (n - 1)*abs(incx)). It contains the vector x.

incx

INTEGER. Specifies the increment for the elements of x.

The value of incx must not be zero.

Output Parameters

alpha

Overwritten by the value beta.

y

Overwritten by the vector v.

tau

REAL for slarfp

DOUBLE PRECISION for dlarfp

COMPLEX for clarfp

DOUBLE COMPLEX for zlarfp

Contains the scalar tau.