1SORMBR(1) LAPACK routine (version 3.2) SORMBR(1)
2
6 SORMBR - VECT = 'Q', SORMBR overwrites the general real M-by-N matrix C
7 with SIDE = 'L' SIDE = 'R' TRANS = 'N'
8
10 SUBROUTINE SORMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
11 WORK, LWORK, INFO )
12 CHARACTER SIDE, TRANS, VECT
14 INTEGER INFO, K, LDA, LDC, LWORK, M, N
16 REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
18
20 If VECT = 'Q', SORMBR overwrites the general real M-by-N matrix C with
21 SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C
22 C * Q TRANS = 'T': Q**T * C C * Q**T
23 If VECT = 'P', SORMBR overwrites the general real M-by-N matrix C with
24 SIDE = 'L' SIDE = 'R'
25 TRANS = 'N': P * C C * P
26 TRANS = 'T': P**T * C C * P**T
27 Here Q and P**T are the orthogonal matrices determined by SGEBRD when
28 reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and
29 P**T are defined as products of elementary reflectors H(i) and G(i)
30 respectively.
31 Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the order
32 of the orthogonal matrix Q or P**T that is applied. If VECT = 'Q', A
33 is assumed to have been an NQ-by-K matrix: if nq >= k, Q = H(1) H(2) .
34 . . H(k);
35 if nq < k, Q = H(1) H(2) . . . H(nq-1).
36 If VECT = 'P', A is assumed to have been a K-by-NQ matrix: if k < nq, P
37 = G(1) G(2) . . . G(k);
38 if k >= nq, P = G(1) G(2) . . . G(nq-1).
39
41 VECT (input) CHARACTER*1
42 = 'Q': apply Q or Q**T;
43 = 'P': apply P or P**T.
44 SIDE (input) CHARACTER*1
46 = 'L': apply Q, Q**T, P or P**T from the Left;
47 = 'R': apply Q, Q**T, P or P**T from the Right.
48 TRANS (input) CHARACTER*1
50 = 'N': No transpose, apply Q or P;
51 = 'T': Transpose, apply Q**T or P**T.
52 M (input) INTEGER
54 The number of rows of the matrix C. M >= 0.
55 N (input) INTEGER
57 The number of columns of the matrix C. N >= 0.
58 K (input) INTEGER
60 If VECT = 'Q', the number of columns in the original matrix
61 reduced by SGEBRD. If VECT = 'P', the number of rows in the
62 original matrix reduced by SGEBRD. K >= 0.
63 A (input) REAL array, dimension
65 (LDA,min(nq,K)) if VECT = 'Q' (LDA,nq) if VECT = 'P' The
66 vectors which define the elementary reflectors H(i) and G(i),
67 whose products determine the matrices Q and P, as returned by
68 SGEBRD.
69 LDA (input) INTEGER
71 The leading dimension of the array A. If VECT = 'Q', LDA >=
72 max(1,nq); if VECT = 'P', LDA >= max(1,min(nq,K)).
73 TAU (input) REAL array, dimension (min(nq,K))
75 TAU(i) must contain the scalar factor of the elementary reflec‐
76 tor H(i) or G(i) which determines Q or P, as returned by SGEBRD
77 in the array argument TAUQ or TAUP.
78 C (input/output) REAL array, dimension (LDC,N)
80 On entry, the M-by-N matrix C. On exit, C is overwritten by
81 Q*C or Q**T*C or C*Q**T or C*Q or P*C or P**T*C or C*P or
82 C*P**T.
83 LDC (input) INTEGER
85 The leading dimension of the array C. LDC >= max(1,M).
86 WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
88 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
89 LWORK (input) INTEGER
91 The dimension of the array WORK. If SIDE = 'L', LWORK >=
92 max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum per‐
93 formance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE
94 = 'R', where NB is the optimal blocksize. If LWORK = -1, then
95 a workspace query is assumed; the routine only calculates the
96 optimal size of the WORK array, returns this value as the first
97 entry of the WORK array, and no error message related to LWORK
98 is issued by XERBLA.
99 INFO (output) INTEGER
101 = 0: successful exit
102 < 0: if INFO = -i, the i-th argument had an illegal value
103 LAPACK routine (version 3.2) November 2008 SORMBR(1)