1DORGBR(1) LAPACK routine (version 3.2) DORGBR(1)
2
6 DORGBR - generates one of the real orthogonal matrices Q or P**T deter‐
7 mined by 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
24 order M:
25 if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n col‐
26 umns of Q, where m >= n >= k;
27 if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an M-by-M
28 matrix.
29 If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T is
30 of order N:
31 if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m
32 rows of P**T, where n >= m >= k;
33 if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as an
34 N-by-N matrix.
35
37 VECT (input) CHARACTER*1
38 Specifies whether the matrix Q or the matrix P**T is required,
39 as defined in the transformation applied by DGEBRD:
40 = 'Q': generate Q;
41 = 'P': generate P**T.
42 M (input) INTEGER
44 The number of rows of the matrix Q or P**T to be returned. M
45 >= 0.
46 N (input) INTEGER
48 The number of columns of the matrix Q or P**T to be returned.
49 N >= 0. If VECT = 'Q', M >= N >= min(M,K); if VECT = 'P', N >=
50 M >= min(N,K).
51 K (input) INTEGER
53 If VECT = 'Q', the number of columns in the original M-by-K
54 matrix reduced by DGEBRD. If VECT = 'P', the number of rows in
55 the original K-by-N matrix reduced by DGEBRD. K >= 0.
56 A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
58 On entry, the vectors which define the elementary reflectors,
59 as returned by DGEBRD. On exit, the M-by-N matrix Q or P**T.
60 LDA (input) INTEGER
62 The leading dimension of the array A. LDA >= max(1,M).
63 TAU (input) DOUBLE PRECISION array, dimension
65 (min(M,K)) if VECT = 'Q' (min(N,K)) if VECT = 'P' TAU(i) must
66 contain the scalar factor of the elementary reflector H(i) or
67 G(i), which determines Q or P**T, as returned by DGEBRD in its
68 array argument TAUQ or TAUP.
69 WORK (workspace/output) DOUBLE PRECISION array, dimension
71 (MAX(1,LWORK))
72 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
73 LWORK (input) INTEGER
75 The dimension of the array WORK. LWORK >= max(1,min(M,N)). For
76 optimum performance LWORK >= min(M,N)*NB, where NB is the opti‐
77 mal blocksize. If LWORK = -1, then a workspace query is
78 assumed; the routine only calculates the optimal size of the
79 WORK array, returns this value as the first entry of the WORK
80 array, and no error message related to LWORK is issued by
81 XERBLA.
82 INFO (output) INTEGER
84 = 0: successful exit
85 < 0: if INFO = -i, the i-th argument had an illegal value
86 LAPACK routine (version 3.2) November 2008 DORGBR(1)