1CUNGBR(1) LAPACK routine (version 3.2) CUNGBR(1)
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6 CUNGBR - generates one of the complex unitary matrices Q or P**H deter‐
7 mined by CGEBRD when reducing a complex matrix A to bidiagonal form
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10 SUBROUTINE CUNGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
11 CHARACTER VECT
13 INTEGER INFO, K, LDA, LWORK, M, N
15 COMPLEX A( LDA, * ), TAU( * ), WORK( * )
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19 CUNGBR generates one of the complex unitary matrices Q or P**H deter‐
20 mined by CGEBRD 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 CUNGBR 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 CUNGBR 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 CUNGBR 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 CUNGBR returns P**H as an
34 N-by-N matrix.
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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 CGEBRD:
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 CGEBRD. If VECT = 'P', the number of rows in
55 the original K-by-N matrix reduced by CGEBRD. K >= 0.
56 A (input/output) COMPLEX array, dimension (LDA,N)
58 On entry, the vectors which define the elementary reflectors,
59 as returned by CGEBRD. 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 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 CGEBRD in its
68 array argument TAUQ or TAUP.
69 WORK (workspace/output) COMPLEX 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 CUNGBR(1)