1SORMRZ(1) LAPACK routine (version 3.2) SORMRZ(1)
2
6 SORMRZ - overwrites the general real M-by-N matrix C with SIDE = 'L'
7 SIDE = 'R' TRANS = 'N'
8
10 SUBROUTINE SORMRZ( 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 REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
18
20 SORMRZ overwrites the general real M-by-N matrix C with TRANS = 'T':
21 Q**T * C C * Q**T
22 where Q is a real orthogonal matrix defined as the product of k elemen‐
23 tary reflectors
24 Q = H(1) H(2) . . . H(k)
25 as returned by STZRZF. Q is of order M if SIDE = 'L' and of order N if
26 SIDE = 'R'.
27
29 SIDE (input) CHARACTER*1
30 = 'L': apply Q or Q**T from the Left;
31 = 'R': apply Q or Q**T from the Right.
32 TRANS (input) CHARACTER*1
34 = 'N': No transpose, apply Q;
35 = 'T': Transpose, apply Q**T.
36 M (input) INTEGER
38 The number of rows of the matrix C. M >= 0.
39 N (input) INTEGER
41 The number of columns of the matrix C. N >= 0.
42 K (input) INTEGER
44 The number of elementary reflectors whose product defines the
45 matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >=
46 0.
47 L (input) INTEGER
49 The number of columns of the matrix A containing the meaningful
50 part of the Householder reflectors. If SIDE = 'L', M >= L >=
51 0, if SIDE = 'R', N >= L >= 0.
52 A (input) REAL array, dimension
54 (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' The i-th row must
55 contain the vector which defines the elementary reflector H(i),
56 for i = 1,2,...,k, as returned by STZRZF in the last k rows of
57 its array argument A. A is modified by the routine but
58 restored on exit.
59 LDA (input) INTEGER
61 The leading dimension of the array A. LDA >= max(1,K).
62 TAU (input) REAL array, dimension (K)
64 TAU(i) must contain the scalar factor of the elementary reflec‐
65 tor H(i), as returned by STZRZF.
66 C (input/output) REAL array, dimension (LDC,N)
68 On entry, the M-by-N matrix C. On exit, C is overwritten by
69 Q*C or Q**H*C or C*Q**H or C*Q.
70 LDC (input) INTEGER
72 The leading dimension of the array C. LDC >= max(1,M).
73 WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
75 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
76 LWORK (input) INTEGER
78 The dimension of the array WORK. If SIDE = 'L', LWORK >=
79 max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum per‐
80 formance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE
81 = 'R', where NB is the optimal blocksize. If LWORK = -1, then
82 a workspace query is assumed; the routine only calculates the
83 optimal size of the WORK array, returns this value as the first
84 entry of the WORK array, and no error message related to LWORK
85 is issued by XERBLA.
86 INFO (output) INTEGER
88 = 0: successful exit
89 < 0: if INFO = -i, the i-th argument had an illegal value
90
92 Based on contributions by
93 A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
94 LAPACK routine (version 3.2) November 2008 SORMRZ(1)