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

6       DPTCON  -  the  reciprocal of the condition number (in the 1-norm) of a
7       real symmetric positive definite tridiagonal matrix using  the  factor‐
8       ization 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.
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24       Norm(inv(A))  is computed by a direct method, and the reciprocal of the
25       condition number is computed as
26                    RCOND = 1 / (ANORM * norm(inv(A))).
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ARGUMENTS

30       N       (input) INTEGER
31               The order of the matrix A.  N >= 0.
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33       D       (input) DOUBLE PRECISION array, dimension (N)
34               The n diagonal elements of the diagonal matrix D from the  fac‐
35               torization of A, as computed by DPTTRF.
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37       E       (input) DOUBLE PRECISION array, dimension (N-1)
38               The (n-1) off-diagonal elements of the unit bidiagonal factor U
39               or L from the factorization of A,  as computed by DPTTRF.
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41       ANORM   (input) DOUBLE PRECISION
42               The 1-norm of the original matrix A.
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44       RCOND   (output) DOUBLE PRECISION
45               The reciprocal of the condition number of the  matrix  A,  com‐
46               puted as RCOND = 1/(ANORM * AINVNM), where AINVNM is the 1-norm
47               of inv(A) computed in this routine.
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49       WORK    (workspace) DOUBLE PRECISION array, dimension (N)
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51       INFO    (output) INTEGER
52               = 0:  successful exit
53               < 0:  if INFO = -i, the i-th argument had an illegal value
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FURTHER DETAILS

56       The method used is described in Nicholas J.  Higham,  "Efficient  Algo‐
57       rithms  for  Computing  the  Condition Number of a Tridiagonal Matrix",
58       SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.
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63 LAPACK routine (version 3.1)    November 2006                       DPTCON(1)
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