1ZUNMRZ(1) LAPACK routine (version 3.2) ZUNMRZ(1)
2
6 ZUNMRZ - overwrites the general complex M-by-N matrix C with SIDE =
7 'L' SIDE = 'R' TRANS = 'N'
8
10 SUBROUTINE ZUNMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK,
11 LWORK, INFO )
12 CHARACTER SIDE, TRANS
14 INTEGER INFO, K, L, LDA, LDC, LWORK, M, N
16 COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
18
20 ZUNMRZ overwrites the general complex M-by-N matrix C with TRANS = 'C':
21 Q**H * C C * Q**H
22 where Q is a complex unitary matrix defined as the product of k elemen‐
23 tary reflectors
24 Q = H(1) H(2) . . . H(k)
25 as returned by ZTZRZF. Q is of order M if SIDE = 'L' and of order N if
26 SIDE = 'R'.
27
29 SIDE (input) CHARACTER*1
30 = 'L': apply Q or Q**H from the Left;
31 = 'R': apply Q or Q**H from the Right.
32 TRANS (input) CHARACTER*1
34 = 'N': No transpose, apply Q;
35 = 'C': Conjugate transpose, apply Q**H.
36 M (input) INTEGER
38 The number of rows of the matrix C. M >= 0.
39 N (input) INTEGER
41 The number of columns of the matrix C. N >= 0.
42 K (input) INTEGER
44 The number of elementary reflectors whose product defines the
45 matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >=
46 0.
47 L (input) INTEGER
49 The number of columns of the matrix A containing the meaningful
50 part of the Householder reflectors. If SIDE = 'L', M >= L >=
51 0, if SIDE = 'R', N >= L >= 0.
52 A (input) COMPLEX*16 array, dimension
54 (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' The i-th row must
55 contain the vector which defines the elementary reflector H(i),
56 for i = 1,2,...,k, as returned by ZTZRZF in the last k rows of
57 its array argument A. A is modified by the routine but
58 restored on exit.
59 LDA (input) INTEGER
61 The leading dimension of the array A. LDA >= max(1,K).
62 TAU (input) COMPLEX*16 array, dimension (K)
64 TAU(i) must contain the scalar factor of the elementary reflec‐
65 tor H(i), as returned by ZTZRZF.
66 C (input/output) COMPLEX*16 array, dimension (LDC,N)
68 On entry, the M-by-N matrix C. On exit, C is overwritten by
69 Q*C or Q**H*C or C*Q**H or C*Q.
70 LDC (input) INTEGER
72 The leading dimension of the array C. LDC >= max(1,M).
73 WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
75 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
76 LWORK (input) INTEGER
78 The dimension of the array WORK. If SIDE = 'L', LWORK >=
79 max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum per‐
80 formance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE
81 = 'R', where NB is the optimal blocksize. If LWORK = -1, then
82 a workspace query is assumed; the routine only calculates the
83 optimal size of the WORK array, returns this value as the first
84 entry of the WORK array, and no error message related to LWORK
85 is issued by XERBLA.
86 INFO (output) INTEGER
88 = 0: successful exit
89 < 0: if INFO = -i, the i-th argument had an illegal value
90
92 Based on contributions by
93 A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
94 LAPACK routine (version 3.2) November 2008 ZUNMRZ(1)