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

6       ZPTCON  -  computes  the  reciprocal  of  the  condition number (in the
7       1-norm) of a complex Hermitian  positive  definite  tridiagonal  matrix
8       using the factorization A = L*D*L**H or A = U**H*D*U computed by ZPTTRF
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SYNOPSIS

11       SUBROUTINE ZPTCON( N, D, E, ANORM, RCOND, RWORK, 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( * ), RWORK( * )
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19           COMPLEX*16     E( * )
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PURPOSE

22       ZPTCON  computes the reciprocal of the condition number (in the 1-norm)
23       of a complex Hermitian positive definite tridiagonal matrix  using  the
24       factorization  A  =  L*D*L**H  or  A  =  U**H*D*U  computed  by ZPTTRF.
25       Norm(inv(A)) is computed by a direct method, and the reciprocal of  the
26       condition number is computed as
27                        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 ZPTTRF.
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37       E       (input) COMPLEX*16 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 ZPTTRF.
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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       RWORK   (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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62 LAPACK routine (version 3.2)    November 2008                       ZPTCON(1)
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