1SLARFT(1) LAPACK auxiliary routine (version 3.2) SLARFT(1)
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6 SLARFT - forms the triangular factor T of a real block reflector H of
7 order n, which is defined as a product of k elementary reflectors
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10 SUBROUTINE SLARFT( DIRECT, STOREV, N, K, V, LDV, TAU, T, LDT )
11 IMPLICIT NONE
13 CHARACTER DIRECT, STOREV
15 INTEGER K, LDT, LDV, N
17 REAL T( LDT, * ), TAU( * ), V( LDV, * )
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21 SLARFT forms the triangular factor T of a real block reflector H of
22 order n, which is defined as a product of k elementary reflectors. If
23 DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular; If
24 DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular. If
25 STOREV = 'C', the vector which defines the elementary reflector H(i) is
26 stored in the i-th column of the array V, and
27 H = I - V * T * V'
28 If STOREV = 'R', the vector which defines the elementary reflector H(i)
29 is stored in the i-th row of the array V, and
30 H = I - V' * T * V
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33 DIRECT (input) CHARACTER*1
34 Specifies the order in which the elementary reflectors are mul‐
35 tiplied to form the block reflector:
36 = 'F': H = H(1) H(2) . . . H(k) (Forward)
37 = 'B': H = H(k) . . . H(2) H(1) (Backward)
38 STOREV (input) CHARACTER*1
40 Specifies how the vectors which define the elementary reflec‐
41 tors are stored (see also Further Details):
42 = 'R': rowwise
43 N (input) INTEGER
45 The order of the block reflector H. N >= 0.
46 K (input) INTEGER
48 The order of the triangular factor T (= the number of elemen‐
49 tary reflectors). K >= 1.
50 V (input/output) REAL array, dimension
52 (LDV,K) if STOREV = 'C' (LDV,N) if STOREV = 'R' The matrix V.
53 See further details.
54 LDV (input) INTEGER
56 The leading dimension of the array V. If STOREV = 'C', LDV >=
57 max(1,N); if STOREV = 'R', LDV >= K.
58 TAU (input) REAL array, dimension (K)
60 TAU(i) must contain the scalar factor of the elementary reflec‐
61 tor H(i).
62 T (output) REAL array, dimension (LDT,K)
64 The k by k triangular factor T of the block reflector. If
65 DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
66 lower triangular. The rest of the array is not used.
67 LDT (input) INTEGER
69 The leading dimension of the array T. LDT >= K.
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72 The shape of the matrix V and the storage of the vectors which define
73 the H(i) is best illustrated by the following example with n = 5 and k
74 = 3. The elements equal to 1 are not stored; the corresponding array
75 elements are modified but restored on exit. The rest of the array is
76 not used.
77 DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':
78 V = ( 1 ) V = ( 1 v1 v1 v1 v1 )
79 ( v1 1 ) ( 1 v2 v2 v2 )
80 ( v1 v2 1 ) ( 1 v3 v3 )
81 ( v1 v2 v3 )
82 ( v1 v2 v3 )
83 DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
84 V = ( v1 v2 v3 ) V = ( v1 v1 1 )
85 ( v1 v2 v3 ) ( v2 v2 v2 1 )
86 ( 1 v2 v3 ) ( v3 v3 v3 v3 1 )
87 ( 1 v3 )
88 ( 1 )
89 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008 SLARFT(1)