1DORGBR(1) LAPACK routine (version 3.1) DORGBR(1)
2
6 DORGBR - one of the real orthogonal matrices Q or P**T determined by
7 DGEBRD when reducing a real matrix A to bidiagonal form
8
10 SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
11 CHARACTER VECT
13 INTEGER INFO, K, LDA, LWORK, M, N
15 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
17
19 DORGBR generates one of the real orthogonal matrices Q or P**T deter‐
20 mined by DGEBRD when reducing a real matrix A to bidiagonal form: A = Q
21 * B * P**T. Q and P**T are defined as products of elementary reflec‐
22 tors H(i) or G(i) respectively.
23 If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q is of
25 order M:
26 if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n col‐
27 umns of Q, where m >= n >= k;
28 if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an M-by-M
29 matrix.
30 If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T is
32 of order N:
33 if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m
34 rows of P**T, where n >= m >= k;
35 if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as an
36 N-by-N matrix.
37
40 VECT (input) CHARACTER*1
41 Specifies whether the matrix Q or the matrix P**T is required,
42 as defined in the transformation applied by DGEBRD:
43 = 'Q': generate Q;
44 = 'P': generate P**T.
45 M (input) INTEGER
47 The number of rows of the matrix Q or P**T to be returned. M
48 >= 0.
49 N (input) INTEGER
51 The number of columns of the matrix Q or P**T to be returned.
52 N >= 0. If VECT = 'Q', M >= N >= min(M,K); if VECT = 'P', N >=
53 M >= min(N,K).
54 K (input) INTEGER
56 If VECT = 'Q', the number of columns in the original M-by-K
57 matrix reduced by DGEBRD. If VECT = 'P', the number of rows in
58 the original K-by-N matrix reduced by DGEBRD. K >= 0.
59 A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
61 On entry, the vectors which define the elementary reflectors,
62 as returned by DGEBRD. On exit, the M-by-N matrix Q or P**T.
63 LDA (input) INTEGER
65 The leading dimension of the array A. LDA >= max(1,M).
66 TAU (input) DOUBLE PRECISION array, dimension
68 (min(M,K)) if VECT = 'Q' (min(N,K)) if VECT = 'P' TAU(i) must
69 contain the scalar factor of the elementary reflector H(i) or
70 G(i), which determines Q or P**T, as returned by DGEBRD in its
71 array argument TAUQ or TAUP.
72 WORK (workspace/output) DOUBLE PRECISION array, dimension
74 (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. LWORK >= max(1,min(M,N)). For
79 optimum performance LWORK >= min(M,N)*NB, where NB is the opti‐
80 mal blocksize.
81 If LWORK = -1, then a workspace query is assumed; the routine
83 only calculates the optimal size of the WORK array, returns
84 this value as the first entry of the WORK array, and no error
85 message related to LWORK 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 LAPACK routine (version 3.1) November 2006 DORGBR(1)