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

6       DGTCON  -  estimates  the  reciprocal of the condition number of a real
7       tridiagonal matrix A using the LU factorization as computed by DGTTRF
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SYNOPSIS

10       SUBROUTINE DGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM,  RCOND,  WORK,
11                          IWORK, 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( * ), IWORK( * )
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21           DOUBLE         PRECISION  D( * ), DL( * ), DU( * ), DU2( * ), WORK(
22                          * )
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PURPOSE

25       DGTCON estimates the reciprocal of  the  condition  number  of  a  real
26       tridiagonal  matrix A using the LU factorization as computed by DGTTRF.
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

31       NORM    (input) CHARACTER*1
32               Specifies  whether the 1-norm condition number or the infinity-
33               norm condition number is required:
34               = '1' or 'O':  1-norm;
35               = 'I':         Infinity-norm.
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37       N       (input) INTEGER
38               The order of the matrix A.  N >= 0.
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40       DL      (input) DOUBLE PRECISION array, dimension (N-1)
41               The (n-1) multipliers that define the matrix L from the LU fac‐
42               torization of A as computed by DGTTRF.
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44       D       (input) DOUBLE PRECISION array, dimension (N)
45               The  n  diagonal elements of the upper triangular matrix U from
46               the LU factorization of A.
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48       DU      (input) DOUBLE PRECISION array, dimension (N-1)
49               The (n-1) elements of the first superdiagonal of U.
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51       DU2     (input) DOUBLE PRECISION array, dimension (N-2)
52               The (n-2) elements of the second superdiagonal of U.
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54       IPIV    (input) INTEGER array, dimension (N)
55               The pivot indices; for 1 <= i <= n, row i  of  the  matrix  was
56               interchanged with row IPIV(i).  IPIV(i) will always be either i
57               or i+1; IPIV(i)  =  i  indicates  a  row  interchange  was  not
58               required.
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60       ANORM   (input) DOUBLE PRECISION
61               If  NORM = '1' or 'O', the 1-norm of the original matrix A.  If
62               NORM = 'I', the infinity-norm of the original matrix A.
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64       RCOND   (output) DOUBLE PRECISION
65               The reciprocal of the condition number of the  matrix  A,  com‐
66               puted  as  RCOND = 1/(ANORM * AINVNM), where AINVNM is an esti‐
67               mate of the 1-norm of inv(A) computed in this routine.
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69       WORK    (workspace) DOUBLE PRECISION array, dimension (2*N)
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71       IWORK   (workspace) INTEGER array, dimension (N)
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73       INFO    (output) INTEGER
74               = 0:  successful exit
75               < 0:  if INFO = -i, the i-th argument had an illegal value
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79 LAPACK routine (version 3.2)    November 2008                       DGTCON(1)
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