1ZUNMRZ(1) LAPACK routine (version 3.1.1) ZUNMRZ(1)
2
6 ZUNMRZ - the general complex M-by-N matrix C with SIDE = 'L' SIDE =
7 '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‐
24 tary reflectors
25 Q = H(1) H(2) . . . H(k)
27 as returned by ZTZRZF. Q is of order M if SIDE = 'L' and of order N if
29 SIDE = 'R'.
30
33 SIDE (input) CHARACTER*1
34 = 'L': apply Q or Q**H from the Left;
35 = 'R': apply Q or Q**H from the Right.
36 TRANS (input) CHARACTER*1
38 = 'N': No transpose, apply Q;
39 = 'C': Conjugate transpose, apply Q**H.
40 M (input) INTEGER
42 The number of rows of the matrix C. M >= 0.
43 N (input) INTEGER
45 The number of columns of the matrix C. N >= 0.
46 K (input) INTEGER
48 The number of elementary reflectors whose product defines the
49 matrix Q. If SIDE = 'L', M >= K >= 0; if SIDE = 'R', N >= K >=
50 0.
51 L (input) INTEGER
53 The number of columns of the matrix A containing the meaningful
54 part of the Householder reflectors. If SIDE = 'L', M >= L >=
55 0, if SIDE = 'R', N >= L >= 0.
56 A (input) COMPLEX*16 array, dimension
58 (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' The i-th row must
59 contain the vector which defines the elementary reflector H(i),
60 for i = 1,2,...,k, as returned by ZTZRZF in the last k rows of
61 its array argument A. A is modified by the routine but
62 restored on exit.
63 LDA (input) INTEGER
65 The leading dimension of the array A. LDA >= max(1,K).
66 TAU (input) COMPLEX*16 array, dimension (K)
68 TAU(i) must contain the scalar factor of the elementary reflec‐
69 tor H(i), as returned by ZTZRZF.
70 C (input/output) COMPLEX*16 array, dimension (LDC,N)
72 On entry, the M-by-N matrix C. On exit, C is overwritten by
73 Q*C or Q**H*C or C*Q**H or C*Q.
74 LDC (input) INTEGER
76 The leading dimension of the array C. LDC >= max(1,M).
77 WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
79 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
80 LWORK (input) INTEGER
82 The dimension of the array WORK. If SIDE = 'L', LWORK >=
83 max(1,N); if SIDE = 'R', LWORK >= max(1,M). For optimum per‐
84 formance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE
85 = 'R', where NB is the optimal blocksize.
86 If LWORK = -1, then a workspace query is assumed; the routine
88 only calculates the optimal size of the WORK array, returns
89 this value as the first entry of the WORK array, and no error
90 message related to LWORK is issued by XERBLA.
91 INFO (output) INTEGER
93 = 0: successful exit
94 < 0: if INFO = -i, the i-th argument had an illegal value
95
97 Based on contributions by
98 A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
99 LAPACK routine (version 3.1.1) February 2007 ZUNMRZ(1)