?larf

Applies an elementary reflector to a general rectangular matrix.

Syntax

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

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

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

call zlarf( side, m, n, v, incv, 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 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. For clarf/zlarf, to apply H' (the conjugate transpose of H), supply conjg(tau) instead of tau.

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 slarf

DOUBLE PRECISION for dlarf

COMPLEX for clarf

COMPLEX*16 for zlarf

Array, DIMENSION

(1 + (m-1)*abs(incv)) if side = 'L' or

(1 + (n-1)*abs(incv)) if side = 'R'. The vector v in the representation of H. v is not used if tau = 0.

incv

INTEGER. The increment between elements of v.

incv ≠ 0.

tau

REAL for slarf

DOUBLE PRECISION for dlarf

COMPLEX for clarf

COMPLEX*16 for zlarf

The value tau in the representation of H.

c

REAL for slarf

DOUBLE PRECISION for dlarf

COMPLEX for clarf

COMPLEX*16 for zlarf

Array, DIMENSION (ldc,n).

On entry, the m-by-n matrix C.

ldc

INTEGER. The leading dimension of the array c.

ldc ≥ max(1,m).

work

REAL for slarf

DOUBLE PRECISION for dlarf

COMPLEX for clarf

COMPLEX*16 for zlarf

Workspace array, DIMENSION

(n) if side = 'L' or

(m) if side = 'R'.

Output Parameters

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