slarzt (l) - Linux Manuals

slarzt: forms the triangular factor T of a real block reflector H of order > n, which is defined as a product of k elementary reflectors

Command to display slarzt manual in Linux: $ man l slarzt

NAME

SLARZT - forms the triangular factor T of a real block reflector H of order > n, which is defined as a product of k elementary reflectors

SYNOPSIS

SUBROUTINE SLARZT(: DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
: CHARACTER DIRECT, STOREV
: INTEGER K, LDT, LDV, N
: REAL T( LDT, * ), TAU( * ), V( LDV, * )

PURPOSE

SLARZT 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 = aqFaq, H = H(1) H(2) . . . H(k) and T is upper triangular; If DIRECT = aqBaq, H = H(k) . . . H(2) H(1) and T is lower triangular. If STOREV = aqCaq, 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 * Vaq
If STOREV = aqRaq, the vector which defines the elementary reflector H(i) is stored in the i-th row of the array V, and

H = I - Vaq * T * V
Currently, only STOREV = aqRaq and DIRECT = aqBaq are supported.

ARGUMENTS

DIRECT (input) CHARACTER*1: Specifies the order in which the elementary reflectors are multiplied to form the block reflector:
= aqFaq: H = H(1) H(2) . . . H(k) (Forward, not supported yet)
= aqBaq: H = H(k) . . . H(2) H(1) (Backward)
STOREV (input) CHARACTER*1: Specifies how the vectors which define the elementary reflectors are stored (see also Further Details):
= aqRaq: rowwise
N (input) INTEGER: The order of the block reflector H. N >= 0.
K (input) INTEGER: The order of the triangular factor T (= the number of elementary reflectors). K >= 1.
V (input/output) REAL array, dimension: (LDV,K) if STOREV = aqCaq (LDV,N) if STOREV = aqRaq The matrix V. See further details.
LDV (input) INTEGER: The leading dimension of the array V. If STOREV = aqCaq, LDV >= max(1,N); if STOREV = aqRaq, LDV >= K.
TAU (input) REAL array, dimension (K): TAU(i) must contain the scalar factor of the elementary reflector H(i).
T (output) REAL array, dimension (LDT,K): The k by k triangular factor T of the block reflector. If DIRECT = aqFaq, T is upper triangular; if DIRECT = aqBaq, T is lower triangular. The rest of the array is not used.
LDT (input) INTEGER: The leading dimension of the array T. LDT >= K.

FURTHER DETAILS

Based on contributions by

  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 = aqFaq and STOREV = aqCaq: DIRECT = aqFaq and STOREV = aqRaq:
                                      ______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 = aqBaq and STOREV = aqCaq: DIRECT = aqBaq and STOREV = aqRaq:
                                                ______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 )