1DORMBR(1) LAPACK routine (version 3.2) DORMBR(1)
2
6 DORMBR - VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C
7 with SIDE = 'L' SIDE = 'R' TRANS = 'N'
8
10 SUBROUTINE DORMBR( 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 DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK(
18 * )
19
21 If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C with
22 SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C
23 C * Q TRANS = 'T': Q**T * C C * Q**T
24 If VECT = 'P', DORMBR 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 DGEBRD when
29 reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and
30 P**T are defined as products of elementary reflectors H(i) and G(i)
31 respectively.
32 Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the order
33 of the orthogonal matrix Q or P**T that is applied. If VECT = 'Q', A
34 is assumed to have been an NQ-by-K matrix: if nq >= k, Q = H(1) H(2) .
35 . . H(k);
36 if nq < k, Q = H(1) H(2) . . . H(nq-1).
37 If VECT = 'P', A is assumed to have been a K-by-NQ matrix: if k < nq, P
38 = G(1) G(2) . . . G(k);
39 if k >= nq, P = G(1) G(2) . . . G(nq-1).
40
42 VECT (input) CHARACTER*1
43 = 'Q': apply Q or Q**T;
44 = 'P': apply P or P**T.
45 SIDE (input) CHARACTER*1
47 = 'L': apply Q, Q**T, P or P**T from the Left;
48 = 'R': apply Q, Q**T, P or P**T from the Right.
49 TRANS (input) CHARACTER*1
51 = 'N': No transpose, apply Q or P;
52 = 'T': Transpose, apply Q**T or P**T.
53 M (input) INTEGER
55 The number of rows of the matrix C. M >= 0.
56 N (input) INTEGER
58 The number of columns of the matrix C. N >= 0.
59 K (input) INTEGER
61 If VECT = 'Q', the number of columns in the original matrix
62 reduced by DGEBRD. If VECT = 'P', the number of rows in the
63 original matrix reduced by DGEBRD. K >= 0.
64 A (input) DOUBLE PRECISION array, dimension
66 (LDA,min(nq,K)) if VECT = 'Q' (LDA,nq) if VECT = 'P' The
67 vectors which define the elementary reflectors H(i) and G(i),
68 whose products determine the matrices Q and P, as returned by
69 DGEBRD.
70 LDA (input) INTEGER
72 The leading dimension of the array A. If VECT = 'Q', LDA >=
73 max(1,nq); if VECT = 'P', LDA >= max(1,min(nq,K)).
74 TAU (input) DOUBLE PRECISION array, dimension (min(nq,K))
76 TAU(i) must contain the scalar factor of the elementary reflec‐
77 tor H(i) or G(i) which determines Q or P, as returned by DGEBRD
78 in the array argument TAUQ or TAUP.
79 C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
81 On entry, the M-by-N matrix C. On exit, C is overwritten by
82 Q*C or Q**T*C or C*Q**T or C*Q or P*C or P**T*C or C*P or
83 C*P**T.
84 LDC (input) INTEGER
86 The leading dimension of the array C. LDC >= max(1,M).
87 WORK (workspace/output) DOUBLE PRECISION array, dimension
89 (MAX(1,LWORK))
90 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
91 LWORK (input) INTEGER
93 The dimension of the array WORK. If SIDE = 'L', LWORK >=
94 max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum per‐
95 formance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE
96 = 'R', where NB is the optimal blocksize. If LWORK = -1, then
97 a workspace query is assumed; the routine only calculates the
98 optimal size of the WORK array, returns this value as the first
99 entry of the WORK array, and no error message related to LWORK
100 is issued by XERBLA.
101 INFO (output) INTEGER
103 = 0: successful exit
104 < 0: if INFO = -i, the i-th argument had an illegal value
105 LAPACK routine (version 3.2) November 2008 DORMBR(1)