clarfb.f man page

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 (characterSIDE, characterTRANS, characterDIRECT, characterSTOREV, integerM, integerN, integerK, complex, dimension( ldv, * )V, integerLDV, complex, dimension( ldt, * )T, integerLDT, complex, dimension( ldc, * )C, integerLDC, complex, dimension( ldwork, * )WORK, integerLDWORK)

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 195 of file clarfb.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

clarfb(3) is an alias of clarfb.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK