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

6       ZGEQRF - a QR factorization of a complex M-by-N matrix A
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SYNOPSIS

9       SUBROUTINE ZGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
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11           INTEGER        INFO, LDA, LWORK, M, N
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13           COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )
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PURPOSE

16       ZGEQRF  computes a QR factorization of a complex M-by-N matrix A: A = Q
17       * R.
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ARGUMENTS

21       M       (input) INTEGER
22               The number of rows of the matrix A.  M >= 0.
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24       N       (input) INTEGER
25               The number of columns of the matrix A.  N >= 0.
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27       A       (input/output) COMPLEX*16 array, dimension (LDA,N)
28               On entry, the M-by-N matrix A.  On exit, the  elements  on  and
29               above the diagonal of the array contain the min(M,N)-by-N upper
30               trapezoidal matrix R (R is upper triangular if  m  >=  n);  the
31               elements  below the diagonal, with the array TAU, represent the
32               unitary matrix Q as a product of min(m,n) elementary reflectors
33               (see Further Details).
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35       LDA     (input) INTEGER
36               The leading dimension of the array A.  LDA >= max(1,M).
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38       TAU     (output) COMPLEX*16 array, dimension (min(M,N))
39               The  scalar  factors  of the elementary reflectors (see Further
40               Details).
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42       WORK    (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
43               On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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45       LWORK   (input) INTEGER
46               The dimension of the array WORK.  LWORK >= max(1,N).  For opti‐
47               mum  performance  LWORK >= N*NB, where NB is the optimal block‐
48               size.
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50               If LWORK = -1, then a workspace query is assumed;  the  routine
51               only  calculates  the  optimal  size of the WORK array, returns
52               this value as the first entry of the WORK array, and  no  error
53               message related to LWORK is issued by XERBLA.
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55       INFO    (output) INTEGER
56               = 0:  successful exit
57               < 0:  if INFO = -i, the i-th argument had an illegal value
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FURTHER DETAILS

60       The matrix Q is represented as a product of elementary reflectors
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62          Q = H(1) H(2) . . . H(k), where k = min(m,n).
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64       Each H(i) has the form
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66          H(i) = I - tau * v * v'
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68       where  tau is a complex scalar, and v is a complex vector with v(1:i-1)
69       = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau  in
70       TAU(i).
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75 LAPACK routine (version 3.1)    November 2006                       ZGEQRF(1)