1ZUNMBR(1) LAPACK routine (version 3.2) ZUNMBR(1)
2
6 ZUNMBR - VECT = 'Q', ZUNMBR overwrites the general complex M-by-N
7 matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'
8
10 SUBROUTINE ZUNMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
11 WORK, LWORK, INFO )
12 CHARACTER SIDE, TRANS, VECT
14 INTEGER INFO, K, LDA, LDC, LWORK, M, N
16 COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
18
20 If VECT = 'Q', ZUNMBR overwrites the general complex M-by-N matrix C
21 with
22 SIDE = 'L' SIDE = 'R' TRANS = 'N': Q * C
23 C * Q TRANS = 'C': Q**H * C C * Q**H
24 If VECT = 'P', ZUNMBR overwrites the general complex M-by-N matrix C
25 with
26 SIDE = 'L' SIDE = 'R'
27 TRANS = 'N': P * C C * P
28 TRANS = 'C': P**H * C C * P**H
29 Here Q and P**H are the unitary matrices determined by ZGEBRD when
30 reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q and
31 P**H are defined as products of elementary reflectors H(i) and G(i)
32 respectively.
33 Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the order
34 of the unitary matrix Q or P**H that is applied.
35 If VECT = 'Q', A is assumed to have been an NQ-by-K matrix: if nq >= k,
36 Q = H(1) H(2) . . . H(k);
37 if nq < k, Q = H(1) H(2) . . . H(nq-1).
38 If VECT = 'P', A is assumed to have been a K-by-NQ matrix: if k < nq, P
39 = G(1) G(2) . . . G(k);
40 if k >= nq, P = G(1) G(2) . . . G(nq-1).
41
43 VECT (input) CHARACTER*1
44 = 'Q': apply Q or Q**H;
45 = 'P': apply P or P**H.
46 SIDE (input) CHARACTER*1
48 = 'L': apply Q, Q**H, P or P**H from the Left;
49 = 'R': apply Q, Q**H, P or P**H from the Right.
50 TRANS (input) CHARACTER*1
52 = 'N': No transpose, apply Q or P;
53 = 'C': Conjugate transpose, apply Q**H or P**H.
54 M (input) INTEGER
56 The number of rows of the matrix C. M >= 0.
57 N (input) INTEGER
59 The number of columns of the matrix C. N >= 0.
60 K (input) INTEGER
62 If VECT = 'Q', the number of columns in the original matrix
63 reduced by ZGEBRD. If VECT = 'P', the number of rows in the
64 original matrix reduced by ZGEBRD. K >= 0.
65 A (input) COMPLEX*16 array, dimension
67 (LDA,min(nq,K)) if VECT = 'Q' (LDA,nq) if VECT = 'P' The
68 vectors which define the elementary reflectors H(i) and G(i),
69 whose products determine the matrices Q and P, as returned by
70 ZGEBRD.
71 LDA (input) INTEGER
73 The leading dimension of the array A. If VECT = 'Q', LDA >=
74 max(1,nq); if VECT = 'P', LDA >= max(1,min(nq,K)).
75 TAU (input) COMPLEX*16 array, dimension (min(nq,K))
77 TAU(i) must contain the scalar factor of the elementary reflec‐
78 tor H(i) or G(i) which determines Q or P, as returned by ZGEBRD
79 in the array argument TAUQ or TAUP.
80 C (input/output) COMPLEX*16 array, dimension (LDC,N)
82 On entry, the M-by-N matrix C. On exit, C is overwritten by
83 Q*C or Q**H*C or C*Q**H or C*Q or P*C or P**H*C or C*P or
84 C*P**H.
85 LDC (input) INTEGER
87 The leading dimension of the array C. LDC >= max(1,M).
88 WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
90 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
91 LWORK (input) INTEGER
93 The dimension of the array WORK. If SIDE = 'L', LWORK >=
94 max(1,N); if SIDE = 'R', LWORK >= max(1,M); if N = 0 or M = 0,
95 LWORK >= 1. For optimum performance LWORK >= max(1,N*NB) if
96 SIDE = 'L', and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is
97 the optimal blocksize. (NB = 0 if M = 0 or N = 0.) If LWORK =
98 -1, then a workspace query is assumed; the routine only calcu‐
99 lates the optimal size of the WORK array, returns this value as
100 the first entry of the WORK array, and no error message related
101 to LWORK is issued by XERBLA.
102 INFO (output) INTEGER
104 = 0: successful exit
105 < 0: if INFO = -i, the i-th argument had an illegal value
106 LAPACK routine (version 3.2) November 2008 ZUNMBR(1)