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

6       ZGETRF - an LU factorization of a general M-by-N matrix A using partial
7       pivoting with row interchanges
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SYNOPSIS

10       SUBROUTINE ZGETRF( M, N, A, LDA, IPIV, INFO )
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12           INTEGER        INFO, LDA, M, N
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14           INTEGER        IPIV( * )
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16           COMPLEX*16     A( LDA, * )
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PURPOSE

19       ZGETRF computes an LU factorization of a general M-by-N matrix A  using
20       partial pivoting with row interchanges.
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22       The factorization has the form
23          A = P * L * U
24       where P is a permutation matrix, L is lower triangular with unit diago‐
25       nal elements (lower trapezoidal if m > n), and U  is  upper  triangular
26       (upper trapezoidal if m < n).
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28       This is the right-looking Level 3 BLAS version of the algorithm.
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ARGUMENTS

32       M       (input) INTEGER
33               The number of rows of the matrix A.  M >= 0.
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35       N       (input) INTEGER
36               The number of columns of the matrix A.  N >= 0.
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38       A       (input/output) COMPLEX*16 array, dimension (LDA,N)
39               On  entry, the M-by-N matrix to be factored.  On exit, the fac‐
40               tors L and U from the factorization A = P*L*U; the unit  diago‐
41               nal elements of L are not stored.
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43       LDA     (input) INTEGER
44               The leading dimension of the array A.  LDA >= max(1,M).
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46       IPIV    (output) INTEGER array, dimension (min(M,N))
47               The  pivot indices; for 1 <= i <= min(M,N), row i of the matrix
48               was interchanged with row IPIV(i).
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50       INFO    (output) INTEGER
51               = 0:  successful exit
52               < 0:  if INFO = -i, the i-th argument had an illegal value
53               > 0:  if INFO = i, U(i,i) is exactly  zero.  The  factorization
54               has  been  completed, but the factor U is exactly singular, and
55               division by zero will occur if it is used to solve a system  of
56               equations.
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60 LAPACK routine (version 3.1)    November 2006                       ZGETRF(1)
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