cptcon man page on Scientific

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```CPTCON(1)		 LAPACK routine (version 3.2)		     CPTCON(1)

NAME
CPTCON  -  computes  the	 reciprocal  of	 the  condition number (in the
1-norm) of a complex Hermitian  positive	 definite  tridiagonal	matrix
using the factorization A = L*D*L**H or A = U**H*D*U computed by CPTTRF

SYNOPSIS
SUBROUTINE CPTCON( N, D, E, ANORM, RCOND, RWORK, INFO )

INTEGER	  INFO, N

REAL		  ANORM, RCOND

REAL		  D( * ), RWORK( * )

COMPLEX	  E( * )

PURPOSE
CPTCON  computes the reciprocal of the condition number (in the 1-norm)
of a complex Hermitian positive definite tridiagonal matrix  using  the
factorization  A	 =  L*D*L**H  or  A  =	U**H*D*U  computed  by CPTTRF.
Norm(inv(A)) is computed by a direct method, and the reciprocal of  the
condition number is computed as
RCOND = 1 / (ANORM * norm(inv(A))).

ARGUMENTS
N       (input) INTEGER
The order of the matrix A.  N >= 0.

D       (input) REAL array, dimension (N)
The  n diagonal elements of the diagonal matrix D from the fac‐
torization of A, as computed by CPTTRF.

E       (input) COMPLEX array, dimension (N-1)
The (n-1) off-diagonal elements of the unit bidiagonal factor U
or L from the factorization of A, as computed by CPTTRF.

ANORM   (input) REAL
The 1-norm of the original matrix A.

RCOND   (output) REAL
The  reciprocal	of  the condition number of the matrix A, com‐
puted as RCOND = 1/(ANORM * AINVNM), where AINVNM is the 1-norm
of inv(A) computed in this routine.

RWORK   (workspace) REAL array, dimension (N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

FURTHER DETAILS
The  method  used  is described in Nicholas J. Higham, "Efficient Algo‐
rithms for Computing the Condition Number  of  a	 Tridiagonal  Matrix",
SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986.

LAPACK routine (version 3.2)	 November 2008			     CPTCON(1)
```
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