?larfb

Applies a block reflector or its transpose/conjugate-transpose to a general rectangular matrix.

Syntax

call slarfb( side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork )

call dlarfb( side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork )

call clarfb( side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork )

call zlarfb( side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork )

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 ?larfb applies a complex block reflector H or its transpose H' to a complex m-by-n matrix C from either left or right.

Input Parameters

side

CHARACTER*1.

If side = 'L': apply H or H' from the left

If side = 'R': apply H or H' from the right

trans

CHARACTER*1.

If trans = 'N': apply H (No transpose)

If trans = 'C': apply H' (Conjugate transpose)

direct

CHARACTER*1.

Indicates how H is formed from a product of elementary reflectors

If direct = 'F': H = H(1)*H(2)*. . . *H(k) (forward)

If direct = 'B': H = H(k)* . . . H(2)*H(1) (backward)

storev

CHARACTER*1.

Indicates how the vectors which define the elementary reflectors are stored:

If storev = 'C': Column-wise

If storev = 'R': Row-wise

m

INTEGER. The number of rows of the matrix C.

n

INTEGER. The number of columns of the matrix C.

k

INTEGER. The order of the matrix T (equal to the number of elementary reflectors whose product defines the block reflector).

v

REAL for slarfb

DOUBLE PRECISION for dlarfb

COMPLEX for clarfb

COMPLEX*16 for zlarfb

Array, DIMENSION

(ldv, k) if storev = 'C'

(ldv, m) if storev = 'R' and side = 'L'

(ldv, n) if storev = 'R' and side = 'R'

The matrix v.

ldv

INTEGER. The leading dimension of the array v.

If storev = 'C' and side = 'L', ldv ≥ max(1,m);

if storev = 'C' and side = 'R', ldv ≥ max(1,n);

if storev = 'R', ldv ≥ k.

t

REAL for slarfb

DOUBLE PRECISION for dlarfb

COMPLEX for clarfb

COMPLEX*16 for zlarfb

Array, DIMENSION (ldt,k).

Contains the triangular k-by-k matrix T in the representation of the block reflector.

LDT

INTEGER. The leading dimension of the array t.

ldt ≥ k.

c

REAL for slarfb

DOUBLE PRECISION for dlarfb

COMPLEX for clarfb

COMPLEX*16 for zlarfb

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 slarfb

DOUBLE PRECISION for dlarfb

COMPLEX for clarfb

COMPLEX*16 for zlarfb

Workspace array, DIMENSION (ldwork, k).

ldwork

INTEGER. The leading dimension of the array work.

If side = 'L', ldwork ≥ max(1, n);

if side = 'R', ldwork ≥ max(1, m).

Output Parameters

c: On exit, c is overwritten by H*C, or H'*C, or C*H, or C*H'.