?larfx

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

Version

Public

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?larfx

Applies an elementary reflector to a general rectangular matrix, with loop unrolling when the reflector has order less than or equal to 10.

Syntax

call slarfx( side, m, n, v, tau, c, ldc, work )

call dlarfx( side, m, n, v, tau, c, ldc, work )

call clarfx( side, m, n, v, tau, c, ldc, work )

call zlarfx( side, m, n, v, tau, c, ldc, work )

Include Files

mkl.fi

Description

The routine ?larfx applies a real/complex elementary reflector H to a real/complex m-by-n matrix C, from either the left or the right.

H is represented in the following forms:

H = I - tau*v*v^T, where tau is a real scalar and v is a real vector.
H = I - tau*v*v^H, where tau is a complex scalar and v is a complex vector.

If tau = 0, then H is taken to be the unit matrix.

Input Parameters

The data types are given for the Fortran interface.

side

CHARACTER*1.

If side = 'L': form H*C

If side = 'R': form C*H.

m

INTEGER. The number of rows of the matrix C.

n

INTEGER. The number of columns of the matrix C.

v

REAL for slarfx

DOUBLE PRECISION for dlarfx

COMPLEX for clarfx

DOUBLE COMPLEX for zlarfx

Array, size

(m) if side = 'L' or

(n) if side = 'R'.

The vector v in the representation of H.

tau

REAL for slarfx

DOUBLE PRECISION for dlarfx

COMPLEX for clarfx

DOUBLE COMPLEX for zlarfx

The value tau in the representation of H.

c

REAL for slarfx

DOUBLE PRECISION for dlarfx

COMPLEX for clarfx

DOUBLE COMPLEX for zlarfx

Array, size ldc by n. On entry, the m-by-n matrix C.

ldc

INTEGER. The leading dimension of the array c. lda≥ (1,m).

work

REAL for slarfx

DOUBLE PRECISION for dlarfx

COMPLEX for clarfx

DOUBLE COMPLEX for zlarfx

Workspace array, size

(n) if side = 'L' or

(m) if side = 'R'.

work is not referenced if H has order < 11.

Output Parameters

c: On exit, C is overwritten by the matrix H*C if side = 'L', or C*H if side = 'R'.

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?larfx