ctpcon man page on Scientific

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CTPCON(1)		 LAPACK routine (version 3.2)		     CTPCON(1)

NAME
       CTPCON  -  estimates the reciprocal of the condition number of a packed
       triangular matrix A, in either the 1-norm or the infinity-norm

SYNOPSIS
       SUBROUTINE CTPCON( NORM, UPLO, DIAG, N, AP, RCOND, WORK, RWORK, INFO )

	   CHARACTER	  DIAG, NORM, UPLO

	   INTEGER	  INFO, N

	   REAL		  RCOND

	   REAL		  RWORK( * )

	   COMPLEX	  AP( * ), WORK( * )

PURPOSE
       CTPCON estimates the reciprocal of the condition	 number	 of  a	packed
       triangular  matrix  A,  in either the 1-norm or the infinity-norm.  The
       norm of A is computed and an estimate  is  obtained  for	 norm(inv(A)),
       then the reciprocal of the condition number is computed as
	  RCOND = 1 / ( norm(A) * norm(inv(A)) ).

ARGUMENTS
       NORM    (input) CHARACTER*1
	       Specifies  whether the 1-norm condition number or the infinity-
	       norm condition number is required:
	       = '1' or 'O':  1-norm;
	       = 'I':	      Infinity-norm.

       UPLO    (input) CHARACTER*1
	       = 'U':  A is upper triangular;
	       = 'L':  A is lower triangular.

       DIAG    (input) CHARACTER*1
	       = 'N':  A is non-unit triangular;
	       = 'U':  A is unit triangular.

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

       AP      (input) COMPLEX array, dimension (N*(N+1)/2)
	       The upper or lower triangular matrix A, packed columnwise in  a
	       linear  array.	The j-th column of A is stored in the array AP
	       as follows: if UPLO = 'U',  AP(i	 +  (j-1)*j/2)	=  A(i,j)  for
	       1<=i<=j;	 if  UPLO  =  'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for
	       j<=i<=n.	 If DIAG = 'U', the diagonal elements  of  A  are  not
	       referenced and are assumed to be 1.

       RCOND   (output) REAL
	       The  reciprocal	of  the condition number of the matrix A, com‐
	       puted as RCOND = 1/(norm(A) * norm(inv(A))).

       WORK    (workspace) COMPLEX array, dimension (2*N)

       RWORK   (workspace) REAL array, dimension (N)

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

 LAPACK routine (version 3.2)	 November 2008			     CTPCON(1)
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