1SORMBR(1) LAPACK routine (version 3.1) SORMBR(1)
2
6 SORMBR - = 'Q', SORMBR overwrites the general real M-by-N matrix C with
7 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
25 SIDE = 'L' SIDE = 'R'
26 TRANS = 'N': P * C C * P
27 TRANS = 'T': P**T * C C * P**T
28 Here Q and P**T are the orthogonal matrices determined by SGEBRD when
30 reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and
31 P**T are defined as products of elementary reflectors H(i) and G(i)
32 respectively.
33 Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the order
35 of the orthogonal matrix Q or P**T that is applied.
36 If VECT = 'Q', A is assumed to have been an NQ-by-K matrix: if nq >= k,
38 Q = H(1) H(2) . . . H(k);
39 if nq < k, Q = H(1) H(2) . . . H(nq-1).
40 If VECT = 'P', A is assumed to have been a K-by-NQ matrix: if k < nq, P
42 = G(1) G(2) . . . G(k);
43 if k >= nq, P = G(1) G(2) . . . G(nq-1).
44
47 VECT (input) CHARACTER*1
48 = 'Q': apply Q or Q**T;
49 = 'P': apply P or P**T.
50 SIDE (input) CHARACTER*1
52 = 'L': apply Q, Q**T, P or P**T from the Left;
53 = 'R': apply Q, Q**T, P or P**T from the Right.
54 TRANS (input) CHARACTER*1
56 = 'N': No transpose, apply Q or P;
57 = 'T': Transpose, apply Q**T or P**T.
58 M (input) INTEGER
60 The number of rows of the matrix C. M >= 0.
61 N (input) INTEGER
63 The number of columns of the matrix C. N >= 0.
64 K (input) INTEGER
66 If VECT = 'Q', the number of columns in the original matrix
67 reduced by SGEBRD. If VECT = 'P', the number of rows in the
68 original matrix reduced by SGEBRD. K >= 0.
69 A (input) REAL array, dimension
71 (LDA,min(nq,K)) if VECT = 'Q' (LDA,nq) if VECT = 'P' The
72 vectors which define the elementary reflectors H(i) and G(i),
73 whose products determine the matrices Q and P, as returned by
74 SGEBRD.
75 LDA (input) INTEGER
77 The leading dimension of the array A. If VECT = 'Q', LDA >=
78 max(1,nq); if VECT = 'P', LDA >= max(1,min(nq,K)).
79 TAU (input) REAL array, dimension (min(nq,K))
81 TAU(i) must contain the scalar factor of the elementary reflec‐
82 tor H(i) or G(i) which determines Q or P, as returned by SGEBRD
83 in the array argument TAUQ or TAUP.
84 C (input/output) REAL array, dimension (LDC,N)
86 On entry, the M-by-N matrix C. On exit, C is overwritten by
87 Q*C or Q**T*C or C*Q**T or C*Q or P*C or P**T*C or C*P or
88 C*P**T.
89 LDC (input) INTEGER
91 The leading dimension of the array C. LDC >= max(1,M).
92 WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
94 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
95 LWORK (input) INTEGER
97 The dimension of the array WORK. If SIDE = 'L', LWORK >=
98 max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum per‐
99 formance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE
100 = 'R', where NB is the optimal blocksize.
101 If LWORK = -1, then a workspace query is assumed; the routine
103 only calculates the optimal size of the WORK array, returns
104 this value as the first entry of the WORK array, and no error
105 message related to LWORK is issued by XERBLA.
106 INFO (output) INTEGER
108 = 0: successful exit
109 < 0: if INFO = -i, the i-th argument had an illegal value
110 LAPACK routine (version 3.1) November 2006 SORMBR(1)