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

6       ZLARZ  - a complex elementary reflector H to a complex M-by-N matrix C,
7       from either the left or the right
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SYNOPSIS

10       SUBROUTINE ZLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
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12           CHARACTER     SIDE
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14           INTEGER       INCV, L, LDC, M, N
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16           COMPLEX*16    TAU
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18           COMPLEX*16    C( LDC, * ), V( * ), WORK( * )
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PURPOSE

21       ZLARZ applies a complex elementary reflector  H  to  a  complex  M-by-N
22       matrix  C,  from  either the left or the right. H is represented in the
23       form
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25             H = I - tau * v * v'
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27       where tau is a complex scalar and v is a complex vector.
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29       If tau = 0, then H is taken to be the unit matrix.
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31       To apply H' (the conjugate transpose of H), supply  conjg(tau)  instead
32       tau.
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34       H is a product of k elementary reflectors as returned by ZTZRZF.
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ARGUMENTS

38       SIDE    (input) CHARACTER*1
39               = 'L': form  H * C
40               = 'R': form  C * H
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42       M       (input) INTEGER
43               The number of rows of the matrix C.
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45       N       (input) INTEGER
46               The number of columns of the matrix C.
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48       L       (input) INTEGER
49               The number of entries of the vector V containing the meaningful
50               part of the Householder vectors.  If SIDE = 'L', M >= L  >=  0,
51               if SIDE = 'R', N >= L >= 0.
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53       V       (input) COMPLEX*16 array, dimension (1+(L-1)*abs(INCV))
54               The  vector v in the representation of H as returned by ZTZRZF.
55               V is not used if TAU = 0.
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57       INCV    (input) INTEGER
58               The increment between elements of v. INCV <> 0.
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60       TAU     (input) COMPLEX*16
61               The value tau in the representation of H.
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63       C       (input/output) COMPLEX*16 array, dimension (LDC,N)
64               On entry, the M-by-N matrix C.  On exit, C  is  overwritten  by
65               the matrix H * C if SIDE = 'L', or C * H if SIDE = 'R'.
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67       LDC     (input) INTEGER
68               The leading dimension of the array C. LDC >= max(1,M).
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70       WORK    (workspace) COMPLEX*16 array, dimension
71               (N) if SIDE = 'L' or (M) if SIDE = 'R'
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FURTHER DETAILS

74       Based on contributions by
75         A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
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80 LAPACK routine (version 3.1)    November 2006                        ZLARZ(1)