1ZUNGBR(1) LAPACK routine (version 3.2) ZUNGBR(1)
2
6 ZUNGBR - generates one of the complex unitary matrices Q or P**H deter‐
7 mined by ZGEBRD when reducing a complex matrix A to bidiagonal form
8
10 SUBROUTINE ZUNGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
11 CHARACTER VECT
13 INTEGER INFO, K, LDA, LWORK, M, N
15 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
17
19 ZUNGBR generates one of the complex unitary matrices Q or P**H deter‐
20 mined by ZGEBRD when reducing a complex matrix A to bidiagonal form: A
21 = Q * B * P**H. Q and P**H are defined as products of elementary
22 reflectors 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 ZUNGBR 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 ZUNGBR 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**H is
30 of order N:
31 if k < n, P**H = G(k) . . . G(2) G(1) and ZUNGBR returns the first m
32 rows of P**H, where n >= m >= k;
33 if k >= n, P**H = G(n-1) . . . G(2) G(1) and ZUNGBR returns P**H as an
34 N-by-N matrix.
35
37 VECT (input) CHARACTER*1
38 Specifies whether the matrix Q or the matrix P**H is required,
39 as defined in the transformation applied by ZGEBRD:
40 = 'Q': generate Q;
41 = 'P': generate P**H.
42 M (input) INTEGER
44 The number of rows of the matrix Q or P**H to be returned. M
45 >= 0.
46 N (input) INTEGER
48 The number of columns of the matrix Q or P**H 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 ZGEBRD. If VECT = 'P', the number of rows in
55 the original K-by-N matrix reduced by ZGEBRD. K >= 0.
56 A (input/output) COMPLEX*16 array, dimension (LDA,N)
58 On entry, the vectors which define the elementary reflectors,
59 as returned by ZGEBRD. On exit, the M-by-N matrix Q or P**H.
60 LDA (input) INTEGER
62 The leading dimension of the array A. LDA >= M.
63 TAU (input) COMPLEX*16 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**H, as returned by ZGEBRD in its
68 array argument TAUQ or TAUP.
69 WORK (workspace/output) COMPLEX*16 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 ZUNGBR(1)