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dlarft.f File Reference

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Functions/Subroutines

subroutine dlarft (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
 DLARFT forms the triangular factor T of a block reflector H = I - vtvH More...
 

Function/Subroutine Documentation

subroutine dlarft ( character  DIRECT,
character  STOREV,
integer  N,
integer  K,
double precision, dimension( ldv, * )  V,
integer  LDV,
double precision, dimension( * )  TAU,
double precision, dimension( ldt, * )  T,
integer  LDT 
)

DLARFT forms the triangular factor T of a block reflector H = I - vtvH

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Purpose:
 DLARFT forms the triangular factor T of a real 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**T

 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**T * T * V
Parameters
[in]DIRECT
          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)
[in]STOREV
          STOREV is CHARACTER*1
          Specifies how the vectors which define the elementary
          reflectors are stored (see also Further Details):
          = 'C': columnwise
          = 'R': rowwise
[in]N
          N is INTEGER
          The order of the block reflector H. N >= 0.
[in]K
          K is INTEGER
          The order of the triangular factor T (= the number of
          elementary reflectors). K >= 1.
[in]V
          V is DOUBLE PRECISION array, dimension
                               (LDV,K) if STOREV = 'C'
                               (LDV,N) if STOREV = 'R'
          The matrix V. See further details.
[in]LDV
          LDV is INTEGER
          The leading dimension of the array V.
          If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
[in]TAU
          TAU is DOUBLE PRECISION array, dimension (K)
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i).
[out]T
          T is DOUBLE PRECISION 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.
[in]LDT
          LDT is INTEGER
          The leading dimension of the array T. LDT >= K.
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.

  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 164 of file dlarft.f.

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