DLARZT 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


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

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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (K)


          TAU(i) must contain the scalar factor of the elementary


          reflector H(i).

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.

LDT

          LDT is INTEGER


          The leading dimension of the array T. LDT >= K.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016

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

  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 )