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

6       DGTCON  -  the reciprocal of the condition number of a real tridiagonal
7       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.
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28       An  estimate  is  obtained  for norm(inv(A)), and the reciprocal of the
29       condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
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ARGUMENTS

33       NORM    (input) CHARACTER*1
34               Specifies whether the 1-norm condition number or the  infinity-
35               norm condition number is required:
36               = '1' or 'O':  1-norm;
37               = 'I':         Infinity-norm.
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39       N       (input) INTEGER
40               The order of the matrix A.  N >= 0.
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42       DL      (input) DOUBLE PRECISION array, dimension (N-1)
43               The (n-1) multipliers that define the matrix L from the LU fac‐
44               torization of A as computed by DGTTRF.
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46       D       (input) DOUBLE PRECISION array, dimension (N)
47               The n diagonal elements of the upper triangular matrix  U  from
48               the LU factorization of A.
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50       DU      (input) DOUBLE PRECISION array, dimension (N-1)
51               The (n-1) elements of the first superdiagonal of U.
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53       DU2     (input) DOUBLE PRECISION array, dimension (N-2)
54               The (n-2) elements of the second superdiagonal of U.
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56       IPIV    (input) INTEGER array, dimension (N)
57               The  pivot  indices;  for  1 <= i <= n, row i of the matrix was
58               interchanged with row IPIV(i).  IPIV(i) will always be either i
59               or  i+1;  IPIV(i)  =  i  indicates  a  row  interchange was not
60               required.
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62       ANORM   (input) DOUBLE PRECISION
63               If NORM = '1' or 'O', the 1-norm of the original matrix A.   If
64               NORM = 'I', the infinity-norm of the original matrix A.
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66       RCOND   (output) DOUBLE PRECISION
67               The  reciprocal  of  the condition number of the matrix A, com‐
68               puted as RCOND = 1/(ANORM * AINVNM), where AINVNM is  an  esti‐
69               mate of the 1-norm of inv(A) computed in this routine.
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71       WORK    (workspace) DOUBLE PRECISION array, dimension (2*N)
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73       IWORK   (workspace) INTEGER array, dimension (N)
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75       INFO    (output) INTEGER
76               = 0:  successful exit
77               < 0:  if INFO = -i, the i-th argument had an illegal value
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81 LAPACK routine (version 3.1)    November 2006                       DGTCON(1)
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