?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

The FORTRAN 77 interfaces are specified in the mkl_lapack.fi include file (to be used in Fortran programs) and in the mkl_lapack.h include file (to be used in C programs).

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 form

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

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

Input Parameters

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

COMPLEX*16 for zlarfx

Array, DIMENSION

(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

COMPLEX*16 for zlarfx

The value tau in the representation of H.

c

REAL for slarfx

DOUBLE PRECISION for dlarfx

COMPLEX for clarfx

COMPLEX*16 for zlarfx

Array, DIMENSION (ldc,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

COMPLEX*16 for zlarfx

Workspace array, DIMENSION

(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'.