1ZGETC2(1)           LAPACK auxiliary routine (version 3.2)           ZGETC2(1)
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NAME

6       ZGETC2  - computes an LU factorization, using complete pivoting, of the
7       n-by-n matrix A
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SYNOPSIS

10       SUBROUTINE ZGETC2( N, A, LDA, IPIV, JPIV, INFO )
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12           INTEGER        INFO, LDA, N
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14           INTEGER        IPIV( * ), JPIV( * )
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16           COMPLEX*16     A( LDA, * )
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PURPOSE

19       ZGETC2 computes an LU factorization, using complete pivoting, of the n-
20       by-n  matrix A. The factorization has the form A = P * L * U * Q, where
21       P and Q are permutation matrices, L is lower triangular with unit diag‐
22       onal elements and U is upper triangular.
23       This is a level 1 BLAS version of the algorithm.
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ARGUMENTS

26       N       (input) INTEGER
27               The order of the matrix A. N >= 0.
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29       A       (input/output) COMPLEX*16 array, dimension (LDA, N)
30               On  entry, the n-by-n matrix to be factored.  On exit, the fac‐
31               tors L and U from the factorization A = P*L*U*Q; the unit diag‐
32               onal  elements  of  L are not stored.  If U(k, k) appears to be
33               less than SMIN, U(k, k) is given the value of  SMIN,  giving  a
34               nonsingular perturbed system.
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36       LDA     (input) INTEGER
37               The leading dimension of the array A.  LDA >= max(1, N).
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39       IPIV    (output) INTEGER array, dimension (N).
40               The  pivot  indices;  for  1 <= i <= N, row i of the matrix has
41               been interchanged with row IPIV(i).
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43       JPIV    (output) INTEGER array, dimension (N).
44               The pivot indices; for 1 <= j <= N, column j of the matrix  has
45               been interchanged with column JPIV(j).
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47       INFO    (output) INTEGER
48               = 0: successful exit
49               >  0: if INFO = k, U(k, k) is likely to produce overflow if one
50               tries to solve for x in Ax = b. So U is perturbed to avoid  the
51               overflow.
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FURTHER DETAILS

54       Based on contributions by
55          Bo Kagstrom and Peter Poromaa, Department of Computing Science,
56          Umea University, S-901 87 Umea, Sweden.
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60 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       ZGETC2(1)