1CUNMRQ(1)                LAPACK routine (version 3.1)                CUNMRQ(1)
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NAME

6       CUNMRQ  -  the general complex M-by-N matrix C with   SIDE = 'L' SIDE =
7       'R' TRANS = 'N'
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SYNOPSIS

10       SUBROUTINE CUNMRQ( SIDE, TRANS, M, N, K, A, LDA,  TAU,  C,  LDC,  WORK,
11                          LWORK, INFO )
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13           CHARACTER      SIDE, TRANS
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15           INTEGER        INFO, K, LDA, LDC, LWORK, M, N
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17           COMPLEX        A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
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PURPOSE

20       CUNMRQ overwrites the general complex M-by-N matrix C with TRANS = 'C':
21       Q**H * C       C * Q**H
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23       where Q is a complex unitary matrix defined as the product of k elemen‐
24       tary reflectors
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26             Q = H(1)' H(2)' . . . H(k)'
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28       as  returned by CGERQF. Q is of order M if SIDE = 'L' and of order N if
29       SIDE = 'R'.
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ARGUMENTS

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.
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37       TRANS   (input) CHARACTER*1
38               = 'N':  No transpose, apply Q;
39               = 'C':  Transpose, apply Q**H.
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41       M       (input) INTEGER
42               The number of rows of the matrix C. M >= 0.
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44       N       (input) INTEGER
45               The number of columns of the matrix C. N >= 0.
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47       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.
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52       A       (input) COMPLEX array, dimension
53               (LDA,M) if SIDE = 'L', (LDA,N) if SIDE = 'R' The i-th row  must
54               contain the vector which defines the elementary reflector H(i),
55               for i = 1,2,...,k, as returned by CGERQF in the last k rows  of
56               its  array  argument  A.   A  is  modified  by  the routine but
57               restored on exit.
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59       LDA     (input) INTEGER
60               The leading dimension of the array A. LDA >= max(1,K).
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62       TAU     (input) COMPLEX array, dimension (K)
63               TAU(i) must contain the scalar factor of the elementary reflec‐
64               tor H(i), as returned by CGERQF.
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66       C       (input/output) COMPLEX array, dimension (LDC,N)
67               On  entry,  the  M-by-N matrix C.  On exit, C is overwritten by
68               Q*C or Q**H*C or C*Q**H or C*Q.
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70       LDC     (input) INTEGER
71               The leading dimension of the array C. LDC >= max(1,M).
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73       WORK    (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
74               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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76       LWORK   (input) INTEGER
77               The dimension of the array WORK.   If  SIDE  =  'L',  LWORK  >=
78               max(1,N);  if  SIDE = 'R', LWORK >= max(1,M).  For optimum per‐
79               formance LWORK >= N*NB if SIDE = 'L', and LWORK >= M*NB if SIDE
80               = 'R', where NB is the optimal blocksize.
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82               If  LWORK  = -1, then a workspace query is assumed; the routine
83               only calculates the optimal size of  the  WORK  array,  returns
84               this  value  as the first entry of the WORK array, and no error
85               message related to LWORK is issued by XERBLA.
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87       INFO    (output) INTEGER
88               = 0:  successful exit
89               < 0:  if INFO = -i, the i-th argument had an illegal value
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93 LAPACK routine (version 3.1)    November 2006                       CUNMRQ(1)
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