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

6       ZGTCON  - the reciprocal of the condition number of a complex tridiago‐
7       nal matrix A using the LU factorization as computed by ZGTTRF
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SYNOPSIS

10       SUBROUTINE ZGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM,  RCOND,  WORK,
11                          INFO )
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13           CHARACTER      NORM
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15           INTEGER        INFO, N
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17           DOUBLE         PRECISION ANORM, RCOND
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19           INTEGER        IPIV( * )
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21           COMPLEX*16     D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
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PURPOSE

24       ZGTCON  estimates  the  reciprocal of the condition number of a complex
25       tridiagonal matrix A using the LU factorization as computed by ZGTTRF.
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27       An estimate is obtained for norm(inv(A)), and  the  reciprocal  of  the
28       condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
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ARGUMENTS

32       NORM    (input) CHARACTER*1
33               Specifies  whether the 1-norm condition number or the infinity-
34               norm condition number is required:
35               = '1' or 'O':  1-norm;
36               = 'I':         Infinity-norm.
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38       N       (input) INTEGER
39               The order of the matrix A.  N >= 0.
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41       DL      (input) COMPLEX*16 array, dimension (N-1)
42               The (n-1) multipliers that define the matrix L from the LU fac‐
43               torization of A as computed by ZGTTRF.
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45       D       (input) COMPLEX*16 array, dimension (N)
46               The  n  diagonal elements of the upper triangular matrix U from
47               the LU factorization of A.
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49       DU      (input) COMPLEX*16 array, dimension (N-1)
50               The (n-1) elements of the first superdiagonal of U.
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52       DU2     (input) COMPLEX*16 array, dimension (N-2)
53               The (n-2) elements of the second superdiagonal of U.
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55       IPIV    (input) INTEGER array, dimension (N)
56               The pivot indices; for 1 <= i <= n, row i  of  the  matrix  was
57               interchanged with row IPIV(i).  IPIV(i) will always be either i
58               or i+1; IPIV(i)  =  i  indicates  a  row  interchange  was  not
59               required.
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61       ANORM   (input) DOUBLE PRECISION
62               If  NORM = '1' or 'O', the 1-norm of the original matrix A.  If
63               NORM = 'I', the infinity-norm of the original matrix A.
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65       RCOND   (output) DOUBLE PRECISION
66               The reciprocal of the condition number of the  matrix  A,  com‐
67               puted  as  RCOND = 1/(ANORM * AINVNM), where AINVNM is an esti‐
68               mate of the 1-norm of inv(A) computed in this routine.
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70       WORK    (workspace) COMPLEX*16 array, dimension (2*N)
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72       INFO    (output) INTEGER
73               = 0:  successful exit
74               < 0:  if INFO = -i, the i-th argument had an illegal value
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78 LAPACK routine (version 3.1)    November 2006                       ZGTCON(1)
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