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dlarfb-f(3)

dlarfb.f –

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

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

DLARFB applies a block reflector or its transpose to a general rectangular matrix.

Purpose:

 DLARFB applies a real block reflector H or its transpose H**T to a
 real m by n matrix C, from either the left or the right.

 

Parameters:

SIDE

 SIDE is CHARACTER*1
 = 'L': apply H or H**T from the Left
 = 'R': apply H or H**T from the Right

TRANS

 TRANS is CHARACTER*1
 = 'N': apply H (No transpose)
 = 'T': apply H**T (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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDC,N)
 On entry, the m by n matrix C.
 On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.

LDC

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

WORK

 WORK is DOUBLE PRECISION 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:

September 2012

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 dlarfb.f.

Author

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