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clarfb.f(3) LAPACK clarfb.f(3)

NAME

clarfb.f

SYNOPSIS

Functions/Subroutines


subroutine clarfb (SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
CLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.

Function/Subroutine Documentation

subroutine clarfb (character SIDE, character TRANS, character DIRECT, character STOREV, integer M, integer N, integer K, complex, dimension( ldv, * ) V, integer LDV, complex, dimension( ldt, * ) T, integer LDT, complex, dimension( ldc, * ) C, integer LDC, complex, dimension( ldwork, * ) WORK, integer LDWORK)

CLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.

Purpose:


CLARFB applies a complex block reflector H or its transpose H**H to a
complex M-by-N matrix C, from either the left or the right.

Parameters:

SIDE


SIDE is CHARACTER*1
= 'L': apply H or H**H from the Left
= 'R': apply H or H**H from the Right

TRANS


TRANS is CHARACTER*1
= 'N': apply H (No transpose)
= 'C': apply H**H (Conjugate transpose)

DIRECT


DIRECT is CHARACTER*1
Indicates how H is formed from a product of elementary
reflectors
= 'F': H = H(1) H(2) . . . H(k) (Forward)
= 'B': H = H(k) . . . H(2) H(1) (Backward)

STOREV


STOREV is CHARACTER*1
Indicates how the vectors which define the elementary
reflectors are stored:
= 'C': Columnwise
= 'R': Rowwise

M


M is INTEGER
The number of rows of the matrix C.

N


N is INTEGER
The number of columns of the matrix C.

K


K is INTEGER
The order of the matrix T (= the number of elementary
reflectors whose product defines the block reflector).

V


V is COMPLEX 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. See Further Details.

LDV


LDV is 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


T is COMPLEX array, dimension (LDT,K)
The triangular K-by-K matrix T in the representation of the
block reflector.

LDT


LDT is INTEGER
The leading dimension of the array T. LDT >= K.

C


C is COMPLEX array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.

LDC


LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).

WORK


WORK is COMPLEX array, dimension (LDWORK,K)

LDWORK


LDWORK is INTEGER
The leading dimension of the array WORK.
If SIDE = 'L', LDWORK >= max(1,N);
if SIDE = 'R', LDWORK >= max(1,M).

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

June 2013

Further Details:


The shape of the matrix V and the storage of the vectors which define
the H(i) is best illustrated by the following example with n = 5 and
k = 3. The elements equal to 1 are not stored; the corresponding
array elements are modified but restored on exit. The rest of the
array is not used.
DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':
V = ( 1 ) V = ( 1 v1 v1 v1 v1 )
( v1 1 ) ( 1 v2 v2 v2 )
( v1 v2 1 ) ( 1 v3 v3 )
( v1 v2 v3 )
( v1 v2 v3 )
DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
V = ( v1 v2 v3 ) V = ( v1 v1 1 )
( v1 v2 v3 ) ( v2 v2 v2 1 )
( 1 v2 v3 ) ( v3 v3 v3 v3 1 )
( 1 v3 )
( 1 )

Definition at line 197 of file clarfb.f.

Author

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