1ZUNGRQ(1)                LAPACK routine (version 3.2)                ZUNGRQ(1)
2
3
4

NAME

6       ZUNGRQ - generates an M-by-N complex matrix Q with orthonormal rows,
7

SYNOPSIS

9       SUBROUTINE ZUNGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
10
11           INTEGER        INFO, K, LDA, LWORK, M, N
12
13           COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )
14

PURPOSE

16       ZUNGRQ  generates  an  M-by-N  complex  matrix Q with orthonormal rows,
17       which is defined as the last M  rows  of  a  product  of  K  elementary
18       reflectors of order N
19             Q  =  H(1)' H(2)' . . . H(k)'
20       as returned by ZGERQF.
21

ARGUMENTS

23       M       (input) INTEGER
24               The number of rows of the matrix Q. M >= 0.
25
26       N       (input) INTEGER
27               The number of columns of the matrix Q. N >= M.
28
29       K       (input) INTEGER
30               The  number  of elementary reflectors whose product defines the
31               matrix Q. M >= K >= 0.
32
33       A       (input/output) COMPLEX*16 array, dimension (LDA,N)
34               On entry, the (m-k+i)-th row  must  contain  the  vector  which
35               defines  the  elementary  reflector H(i), for i = 1,2,...,k, as
36               returned by ZGERQF in the last k rows of its array argument  A.
37               On exit, the M-by-N matrix Q.
38
39       LDA     (input) INTEGER
40               The first dimension of the array A. LDA >= max(1,M).
41
42       TAU     (input) COMPLEX*16 array, dimension (K)
43               TAU(i) must contain the scalar factor of the elementary reflec‐
44               tor H(i), as returned by ZGERQF.
45
46       WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
47               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
48
49       LWORK   (input) INTEGER
50               The dimension of the array WORK. LWORK >= max(1,M).  For  opti‐
51               mum  performance  LWORK >= M*NB, where NB is the optimal block‐
52               size.  If LWORK = -1, then a workspace query  is  assumed;  the
53               routine  only  calculates  the  optimal size of the WORK array,
54               returns this value as the first entry of the WORK array, and no
55               error message related to LWORK is issued by XERBLA.
56
57       INFO    (output) INTEGER
58               = 0:  successful exit
59               < 0:  if INFO = -i, the i-th argument has an illegal value
60
61
62
63 LAPACK routine (version 3.2)    November 2008                       ZUNGRQ(1)