1DORMBR(1) LAPACK routine (version 3.1) DORMBR(1)
2
6 DORMBR - = 'Q', DORMBR overwrites the general real M-by-N matrix C with
7 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
26 SIDE = 'L' SIDE = 'R'
27 TRANS = 'N': P * C C * P
28 TRANS = 'T': P**T * C C * P**T
29 Here Q and P**T are the orthogonal matrices determined by DGEBRD when
31 reducing a real matrix A to bidiagonal form: A = Q * B * P**T. Q and
32 P**T are defined as products of elementary reflectors H(i) and G(i)
33 respectively.
34 Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the order
36 of the orthogonal matrix Q or P**T that is applied.
37 If VECT = 'Q', A is assumed to have been an NQ-by-K matrix: if nq >= k,
39 Q = H(1) H(2) . . . H(k);
40 if nq < k, Q = H(1) H(2) . . . H(nq-1).
41 If VECT = 'P', A is assumed to have been a K-by-NQ matrix: if k < nq, P
43 = G(1) G(2) . . . G(k);
44 if k >= nq, P = G(1) G(2) . . . G(nq-1).
45
48 VECT (input) CHARACTER*1
49 = 'Q': apply Q or Q**T;
50 = 'P': apply P or P**T.
51 SIDE (input) CHARACTER*1
53 = 'L': apply Q, Q**T, P or P**T from the Left;
54 = 'R': apply Q, Q**T, P or P**T from the Right.
55 TRANS (input) CHARACTER*1
57 = 'N': No transpose, apply Q or P;
58 = 'T': Transpose, apply Q**T or P**T.
59 M (input) INTEGER
61 The number of rows of the matrix C. M >= 0.
62 N (input) INTEGER
64 The number of columns of the matrix C. N >= 0.
65 K (input) INTEGER
67 If VECT = 'Q', the number of columns in the original matrix
68 reduced by DGEBRD. If VECT = 'P', the number of rows in the
69 original matrix reduced by DGEBRD. K >= 0.
70 A (input) DOUBLE PRECISION array, dimension
72 (LDA,min(nq,K)) if VECT = 'Q' (LDA,nq) if VECT = 'P' The
73 vectors which define the elementary reflectors H(i) and G(i),
74 whose products determine the matrices Q and P, as returned by
75 DGEBRD.
76 LDA (input) INTEGER
78 The leading dimension of the array A. If VECT = 'Q', LDA >=
79 max(1,nq); if VECT = 'P', LDA >= max(1,min(nq,K)).
80 TAU (input) DOUBLE PRECISION array, dimension (min(nq,K))
82 TAU(i) must contain the scalar factor of the elementary reflec‐
83 tor H(i) or G(i) which determines Q or P, as returned by DGEBRD
84 in the array argument TAUQ or TAUP.
85 C (input/output) DOUBLE PRECISION array, dimension (LDC,N)
87 On entry, the M-by-N matrix C. On exit, C is overwritten by
88 Q*C or Q**T*C or C*Q**T or C*Q or P*C or P**T*C or C*P or
89 C*P**T.
90 LDC (input) INTEGER
92 The leading dimension of the array C. LDC >= max(1,M).
93 WORK (workspace/output) DOUBLE PRECISION array, dimension
95 (MAX(1,LWORK))
96 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
97 LWORK (input) INTEGER
99 The dimension of the array WORK. If SIDE = 'L', LWORK >=
100 max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum per‐
101 formance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE
102 = 'R', where NB is the optimal blocksize.
103 If LWORK = -1, then a workspace query is assumed; the routine
105 only calculates the optimal size of the WORK array, returns
106 this value as the first entry of the WORK array, and no error
107 message related to LWORK is issued by XERBLA.
108 INFO (output) INTEGER
110 = 0: successful exit
111 < 0: if INFO = -i, the i-th argument had an illegal value
112 LAPACK routine (version 3.1) November 2006 DORMBR(1)