clarzt.f File Reference

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Functions/Subroutines
subroutine	clarzt (DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT)
	CLARZT forms the triangular factor T of a block reflector H = I - vtvH.

---

Function/Subroutine Documentation

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

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

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Purpose:

 CLARZT 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

 Currently, only STOREV = 'R' and DIRECT = 'B' are supported.

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, not supported yet) = '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 (not supported yet) = '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,out]	V	V is COMPLEX 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 COMPLEX array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i).
[out]	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.
[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

Contributors:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

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_____
         ( v1 v2 v3 )                        /            \
         ( v1 v2 v3 )                      ( v1 v1 v1 v1 v1 . . . . 1 )
     V = ( v1 v2 v3 )                      ( v2 v2 v2 v2 v2 . . . 1   )
         ( v1 v2 v3 )                      ( v3 v3 v3 v3 v3 . . 1     )
         ( v1 v2 v3 )
            .  .  .
            .  .  .
            1  .  .
               1  .
                  1

  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':

                                                        ______V_____
            1                                          /            \
            .  1                           ( 1 . . . . v1 v1 v1 v1 v1 )
            .  .  1                        ( . 1 . . . v2 v2 v2 v2 v2 )
            .  .  .                        ( . . 1 . . v3 v3 v3 v3 v3 )
            .  .  .
         ( v1 v2 v3 )
         ( v1 v2 v3 )
     V = ( v1 v2 v3 )
         ( v1 v2 v3 )
         ( v1 v2 v3 )

Definition at line 186 of file clarzt.f.

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