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

6       DPTCON  -  computes  the  reciprocal  of  the  condition number (in the
7       1-norm) of a real symmetric positive definite tridiagonal matrix  using
8       the factorization A = L*D*L**T or A = U**T*D*U computed by DPTTRF
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SYNOPSIS

11       SUBROUTINE DPTCON( N, D, E, ANORM, RCOND, WORK, INFO )
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13           INTEGER        INFO, N
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15           DOUBLE         PRECISION ANORM, RCOND
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17           DOUBLE         PRECISION D( * ), E( * ), WORK( * )
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PURPOSE

20       DPTCON  computes the reciprocal of the condition number (in the 1-norm)
21       of a real symmetric positive definite tridiagonal matrix using the fac‐
22       torization   A   =  L*D*L**T  or  A  =  U**T*D*U  computed  by  DPTTRF.
23       Norm(inv(A)) is computed by a direct method, and the reciprocal of  the
24       condition number is computed as
25                    RCOND = 1 / (ANORM * norm(inv(A))).
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ARGUMENTS

28       N       (input) INTEGER
29               The order of the matrix A.  N >= 0.
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31       D       (input) DOUBLE PRECISION array, dimension (N)
32               The  n diagonal elements of the diagonal matrix D from the fac‐
33               torization of A, as computed by DPTTRF.
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35       E       (input) DOUBLE PRECISION array, dimension (N-1)
36               The (n-1) off-diagonal elements of the unit bidiagonal factor U
37               or L from the factorization of A,  as computed by DPTTRF.
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39       ANORM   (input) DOUBLE PRECISION
40               The 1-norm of the original matrix A.
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42       RCOND   (output) DOUBLE PRECISION
43               The  reciprocal  of  the condition number of the matrix A, com‐
44               puted as RCOND = 1/(ANORM * AINVNM), where AINVNM is the 1-norm
45               of inv(A) computed in this routine.
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47       WORK    (workspace) DOUBLE PRECISION array, dimension (N)
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49       INFO    (output) INTEGER
50               = 0:  successful exit
51               < 0:  if INFO = -i, the i-th argument had an illegal value
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FURTHER DETAILS

54       The  method  used  is described in Nicholas J. Higham, "Efficient Algo‐
55       rithms for Computing the Condition Number  of  a  Tridiagonal  Matrix",
56       SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.
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60 LAPACK routine (version 3.2)    November 2008                       DPTCON(1)
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