zlarft.f man page

zlarft.f —

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine zlarft (characterDIRECT, characterSTOREV, integerN, integerK, complex*16, dimension( ldv, * )V, integerLDV, complex*16, dimension( * )TAU, complex*16, dimension( ldt, * )T, integerLDT)

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

Purpose:

 ZLARFT 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
Parameters:

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)

STOREV

          STOREV is CHARACTER*1
          Specifies how the vectors which define the elementary
          reflectors are stored (see also Further Details):
          = 'C': columnwise
          = 'R': rowwise

N

          N is INTEGER
          The order of the block reflector H. N >= 0.

K

          K is INTEGER
          The order of the triangular factor T (= the number of
          elementary reflectors). K >= 1.

V

          V is COMPLEX*16 array, dimension
                               (LDV,K) if STOREV = 'C'
                               (LDV,N) if STOREV = 'R'
          The matrix V. See further details.

LDV

          LDV is INTEGER
          The leading dimension of the array V.
          If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.

TAU

          TAU is COMPLEX*16 array, dimension (K)
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i).

T

          T is COMPLEX*16 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

          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 zlarft.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

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

Sat Nov 16 2013 Version 3.4.2 LAPACK