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

6       CGTCON  - estimates the reciprocal of the condition number of a complex
7       tridiagonal matrix A using the LU factorization as computed by CGTTRF
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SYNOPSIS

10       SUBROUTINE CGTCON( 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           REAL           ANORM, RCOND
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19           INTEGER        IPIV( * )
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21           COMPLEX        D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
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PURPOSE

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

30       NORM    (input) CHARACTER*1
31               Specifies whether the 1-norm condition number or the  infinity-
32               norm condition number is required:
33               = '1' or 'O':  1-norm;
34               = 'I':         Infinity-norm.
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36       N       (input) INTEGER
37               The order of the matrix A.  N >= 0.
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39       DL      (input) COMPLEX array, dimension (N-1)
40               The (n-1) multipliers that define the matrix L from the LU fac‐
41               torization of A as computed by CGTTRF.
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43       D       (input) COMPLEX array, dimension (N)
44               The n diagonal elements of the upper triangular matrix  U  from
45               the LU factorization of A.
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47       DU      (input) COMPLEX array, dimension (N-1)
48               The (n-1) elements of the first superdiagonal of U.
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50       DU2     (input) COMPLEX array, dimension (N-2)
51               The (n-2) elements of the second superdiagonal of U.
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53       IPIV    (input) INTEGER array, dimension (N)
54               The  pivot  indices;  for  1 <= i <= n, row i of the matrix was
55               interchanged with row IPIV(i).  IPIV(i) will always be either i
56               or  i+1;  IPIV(i)  =  i  indicates  a  row  interchange was not
57               required.
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59       ANORM   (input) REAL
60               If NORM = '1' or 'O', the 1-norm of the original matrix A.   If
61               NORM = 'I', the infinity-norm of the original matrix A.
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63       RCOND   (output) REAL
64               The  reciprocal  of  the condition number of the matrix A, com‐
65               puted as RCOND = 1/(ANORM * AINVNM), where AINVNM is  an  esti‐
66               mate of the 1-norm of inv(A) computed in this routine.
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68       WORK    (workspace) COMPLEX array, dimension (2*N)
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70       INFO    (output) INTEGER
71               = 0:  successful exit
72               < 0:  if INFO = -i, the i-th argument had an illegal value
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76 LAPACK routine (version 3.2)    November 2008                       CGTCON(1)
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