clarzt.f man page

clarzt.f —

Synopsis

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

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

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:

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)

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

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:

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.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

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

Sat Nov 16 2013 Version 3.4.2 LAPACK