ZLARFB
Purpose
ZLARFB 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.
complex M-by-N matrix C, from either the left or the right.
Arguments
| SIDE |
(input) CHARACTER*1
= 'L': apply H or H**H from the Left
= 'R': apply H or H**H from the Right |
| TRANS |
(input) CHARACTER*1
= 'N': apply H (No transpose)
= 'C': apply H**H (Conjugate transpose) |
| DIRECT |
(input) 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 |
(input) CHARACTER*1
Indicates how the vectors which define the elementary
reflectors are stored: = 'C': Columnwise = 'R': Rowwise |
| M |
(input) INTEGER
The number of rows of the matrix C.
|
| N |
(input) INTEGER
The number of columns of the matrix C.
|
| K |
(input) INTEGER
The order of the matrix T (= the number of elementary
reflectors whose product defines the block reflector). |
| V |
(input) COMPLEX*16 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 |
(input) 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 |
(input) COMPLEX*16 array, dimension (LDT,K)
The triangular K-by-K matrix T in the representation of the
block reflector. |
| LDT |
(input) INTEGER
The leading dimension of the array T. LDT >= K.
|
| C |
(input/output) COMPLEX*16 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 |
(input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
|
| WORK |
(workspace) COMPLEX*16 array, dimension (LDWORK,K)
|
| LDWORK |
(input) INTEGER
The leading dimension of the array WORK.
If SIDE = 'L', LDWORK >= max(1,N); if SIDE = 'R', LDWORK >= max(1,M). |
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 )
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 )