table of contents
other versions
- wheezy 3.4.1+dfsg-1+deb70u1
 - jessie 3.5.0-4
 - jessie-backports 3.7.0-1~bpo8+1
 - testing 3.7.0-2
 - unstable 3.7.0-2
 
| clarft.f(3) | LAPACK | clarft.f(3) | 
NAME¶
clarft.f -SYNOPSIS¶
Functions/Subroutines¶
subroutine clarft (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
Function/Subroutine Documentation¶
subroutine clarft (characterDIRECT, characterSTOREV, integerN, integerK, complex, dimension( ldv, * )V, integerLDV, complex, dimension( * )TAU, complex, dimension( ldt, * )T, integerLDT)¶
CLARFT Purpose: CLARFT forms the triangular factor T of a complex block reflector H
 of order n, which is defined as a product of k elementary reflectors.
 If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;
 If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.
 If STOREV = 'C', the vector which defines the elementary reflector
 H(i) is stored in the i-th column of the array V, and
    H  =  I - V * T * V**H
 If STOREV = 'R', the vector which defines the elementary reflector
 H(i) is stored in the i-th row of the array V, and
    H  =  I - V**H * T * V
DIRECT
 
STOREV
 
N
 
K
 
V
 
LDV
 
TAU
 
T
 
LDT
 
Author:
          DIRECT is CHARACTER*1
          Specifies the order in which the elementary reflectors are
          multiplied to form the block reflector:
          = 'F': H = H(1) H(2) . . . H(k) (Forward)
          = 'B': H = H(k) . . . H(2) H(1) (Backward)
          STOREV is CHARACTER*1
          Specifies how the vectors which define the elementary
          reflectors are stored (see also Further Details):
          = 'C': columnwise
          = 'R': rowwise
          N is INTEGER
          The order of the block reflector H. N >= 0.
          K is INTEGER
          The order of the triangular factor T (= the number of
          elementary reflectors). K >= 1.
          V is COMPLEX array, dimension
                               (LDV,K) if STOREV = 'C'
                               (LDV,N) if STOREV = 'R'
          The matrix V. See further details.
          LDV is INTEGER
          The leading dimension of the array V.
          If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
          TAU is COMPLEX array, dimension (K)
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i).
          T is COMPLEX array, dimension (LDT,K)
          The k by k triangular factor T of the block reflector.
          If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
          lower triangular. The rest of the array is not used.
          LDT is INTEGER
          The leading dimension of the array T. LDT >= K.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
April 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.
  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 )
Author¶
Generated automatically by Doxygen for LAPACK from the source code.| Sun May 26 2013 | Version 3.4.1 |