1DORMRZ(1) LAPACK routine (version 3.1.1) DORMRZ(1)
2
6 DORMRZ - the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R'
7 TRANS = 'N'
8
10 SUBROUTINE DORMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK,
11 LWORK, INFO )
12 CHARACTER SIDE, TRANS
14 INTEGER INFO, K, L, LDA, LDC, LWORK, M, N
16 DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK(
18 * )
19
21 DORMRZ overwrites the general real M-by-N matrix C with TRANS = 'T':
22 Q**T * C C * Q**T
23 where Q is a real orthogonal matrix defined as the product of k elemen‐
25 tary reflectors
26 Q = H(1) H(2) . . . H(k)
28 as returned by DTZRZF. Q is of order M if SIDE = 'L' and of order N if
30 SIDE = 'R'.
31
34 SIDE (input) CHARACTER*1
35 = 'L': apply Q or Q**T from the Left;
36 = 'R': apply Q or Q**T from the Right.
37 TRANS (input) CHARACTER*1
39 = 'N': No transpose, apply Q;
40 = 'T': Transpose, apply Q**T.
41 M (input) INTEGER
43 The number of rows of the matrix C. M >= 0.
44 N (input) INTEGER
46 The number of columns of the matrix C. N >= 0.
47 K (input) INTEGER
49 The number of elementary reflectors whose product defines the
50 matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >=
51 0.
52 L (input) INTEGER
54 The number of columns of the matrix A containing the meaningful
55 part of the Householder reflectors. If SIDE = 'L', M >= L >=
56 0, if SIDE = 'R', N >= L >= 0.
57 A (input) DOUBLE PRECISION array, dimension
59 (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' The i-th row must
60 contain the vector which defines the elementary reflector H(i),
61 for i = 1,2,...,k, as returned by DTZRZF in the last k rows of
62 its array argument A. A is modified by the routine but
63 restored on exit.
64 LDA (input) INTEGER
66 The leading dimension of the array A. LDA >= max(1,K).
67 TAU (input) DOUBLE PRECISION array, dimension (K)
69 TAU(i) must contain the scalar factor of the elementary reflec‐
70 tor H(i), as returned by DTZRZF.
71 C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
73 On entry, the M-by-N matrix C. On exit, C is overwritten by
74 Q*C or Q**H*C or C*Q**H or C*Q.
75 LDC (input) INTEGER
77 The leading dimension of the array C. LDC >= max(1,M).
78 WORK (workspace/output) DOUBLE PRECISION array, dimension
80 (MAX(1,LWORK))
81 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
82 LWORK (input) INTEGER
84 The dimension of the array WORK. If SIDE = 'L', LWORK >=
85 max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum per‐
86 formance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE
87 = 'R', where NB is the optimal blocksize.
88 If LWORK = -1, then a workspace query is assumed; the routine
90 only calculates the optimal size of the WORK array, returns
91 this value as the first entry of the WORK array, and no error
92 message related to LWORK is issued by XERBLA.
93 INFO (output) INTEGER
95 = 0: successful exit
96 < 0: if INFO = -i, the i-th argument had an illegal value
97
99 Based on contributions by
100 A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
101 LAPACK routine (version 3.1.1) February 2007 DORMRZ(1)