clarft.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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NAME

clarft.f  

SYNOPSIS


 

Functions/Subroutines


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

Function/Subroutine Documentation

 

subroutine clarft (character DIRECT, character STOREV, integer N, integer K, complex, dimension( ldv, * ) V, integer LDV, complex, dimension( * ) TAU, complex, dimension( ldt, * ) T, integer LDT)

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

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


 

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


T

          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

          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:

December 2016

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 165 of file clarft.f.  

Author

Generated automatically by Doxygen for LAPACK from the source code.


 

Index

NAME
SYNOPSIS
Functions/Subroutines
Function/Subroutine Documentation
subroutine clarft (character DIRECT, character STOREV, integer N, integer K, complex, dimension( ldv, * ) V, integer LDV, complex, dimension( * ) TAU, complex, dimension( ldt, * ) T, integer LDT)
Author
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