1SORGBR(1) LAPACK routine (version 3.2) SORGBR(1)
2
6 SORGBR - generates one of the real orthogonal matrices Q or P**T deter‐
7 mined by SGEBRD when reducing a real matrix A to bidiagonal form
8
10 SUBROUTINE SORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
11 CHARACTER VECT
13 INTEGER INFO, K, LDA, LWORK, M, N
15 REAL A( LDA, * ), TAU( * ), WORK( * )
17
19 SORGBR generates one of the real orthogonal matrices Q or P**T deter‐
20 mined by SGEBRD 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 SORGBR 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 SORGBR 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 SORGBR 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 SORGBR 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 SGEBRD:
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 SGEBRD. If VECT = 'P', the number of rows in
55 the original K-by-N matrix reduced by SGEBRD. K >= 0.
56 A (input/output) REAL array, dimension (LDA,N)
58 On entry, the vectors which define the elementary reflectors,
59 as returned by SGEBRD. 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) REAL 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 SGEBRD in its
68 array argument TAUQ or TAUP.
69 WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
71 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
72 LWORK (input) INTEGER
74 The dimension of the array WORK. LWORK >= max(1,min(M,N)). For
75 optimum performance LWORK >= min(M,N)*NB, where NB is the opti‐
76 mal blocksize. If LWORK = -1, then a workspace query is
77 assumed; the routine only calculates the optimal size of the
78 WORK array, returns this value as the first entry of the WORK
79 array, and no error message related to LWORK is issued by
80 XERBLA.
81 INFO (output) INTEGER
83 = 0: successful exit
84 < 0: if INFO = -i, the i-th argument had an illegal value
85 LAPACK routine (version 3.2) November 2008 SORGBR(1)