1ZGTTRF(1)                LAPACK routine (version 3.2)                ZGTTRF(1)
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NAME

6       ZGTTRF - computes an LU factorization of a complex tridiagonal matrix A
7       using elimination with partial pivoting and row interchanges
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SYNOPSIS

10       SUBROUTINE ZGTTRF( N, DL, D, DU, DU2, IPIV, INFO )
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12           INTEGER        INFO, N
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14           INTEGER        IPIV( * )
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16           COMPLEX*16     D( * ), DL( * ), DU( * ), DU2( * )
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PURPOSE

19       ZGTTRF computes an LU factorization of a complex tridiagonal  matrix  A
20       using elimination with partial pivoting and row interchanges.  The fac‐
21       torization has the form
22          A = L * U
23       where L is a product of permutation and unit lower bidiagonal  matrices
24       and  U  is upper triangular with nonzeros in only the main diagonal and
25       first two superdiagonals.
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ARGUMENTS

28       N       (input) INTEGER
29               The order of the matrix A.
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31       DL      (input/output) COMPLEX*16 array, dimension (N-1)
32               On entry, DL must contain the (n-1) sub-diagonal elements of A.
33               On exit, DL is overwritten by the (n-1) multipliers that define
34               the matrix L from the LU factorization of A.
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36       D       (input/output) COMPLEX*16 array, dimension (N)
37               On entry, D must contain the diagonal elements of A.  On  exit,
38               D is overwritten by the n diagonal elements of the upper trian‐
39               gular matrix U from the LU factorization of A.
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41       DU      (input/output) COMPLEX*16 array, dimension (N-1)
42               On entry, DU must contain the (n-1) super-diagonal elements  of
43               A.   On  exit,  DU  is overwritten by the (n-1) elements of the
44               first super-diagonal of U.
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46       DU2     (output) COMPLEX*16 array, dimension (N-2)
47               On exit, DU2 is overwritten by the (n-2) elements of the second
48               super-diagonal of U.
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50       IPIV    (output) INTEGER array, dimension (N)
51               The  pivot  indices;  for  1 <= i <= n, row i of the matrix was
52               interchanged with row IPIV(i).  IPIV(i) will always be either i
53               or  i+1;  IPIV(i)  =  i  indicates  a  row  interchange was not
54               required.
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56       INFO    (output) INTEGER
57               = 0:  successful exit
58               < 0:  if INFO = -k, the k-th argument had an illegal value
59               > 0:  if INFO = k, U(k,k) is exactly  zero.  The  factorization
60               has  been  completed, but the factor U is exactly singular, and
61               division by zero will occur if it is used to solve a system  of
62               equations.
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66 LAPACK routine (version 3.2)    November 2008                       ZGTTRF(1)
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