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

6       ZPTCON  -  the  reciprocal of the condition number (in the 1-norm) of a
7       complex Hermitian positive definite tridiagonal matrix using  the  fac‐
8       torization 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.
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26       Norm(inv(A))  is computed by a direct method, and the reciprocal of the
27       condition number is computed as
28                        RCOND = 1 / (ANORM * norm(inv(A))).
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ARGUMENTS

32       N       (input) INTEGER
33               The order of the matrix A.  N >= 0.
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35       D       (input) DOUBLE PRECISION array, dimension (N)
36               The n diagonal elements of the diagonal matrix D from the  fac‐
37               torization of A, as computed by ZPTTRF.
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39       E       (input) COMPLEX*16 array, dimension (N-1)
40               The (n-1) off-diagonal elements of the unit bidiagonal factor U
41               or L from the factorization of A, as computed by ZPTTRF.
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43       ANORM   (input) DOUBLE PRECISION
44               The 1-norm of the original matrix A.
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46       RCOND   (output) DOUBLE PRECISION
47               The reciprocal of the condition number of the  matrix  A,  com‐
48               puted as RCOND = 1/(ANORM * AINVNM), where AINVNM is the 1-norm
49               of inv(A) computed in this routine.
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51       RWORK   (workspace) DOUBLE PRECISION array, dimension (N)
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53       INFO    (output) INTEGER
54               = 0:  successful exit
55               < 0:  if INFO = -i, the i-th argument had an illegal value
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FURTHER DETAILS

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