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# ztpcon

```
NAME
ZTPCON - estimate the reciprocal of the condition number of
a packed triangular matrix A, in either the 1-norm or the
infinity-norm

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

CHARACTER      DIAG, NORM, UPLO

INTEGER        INFO, N

DOUBLE         PRECISION RCOND

DOUBLE         PRECISION RWORK( * )

COMPLEX*16     AP( * ), WORK( * )

PURPOSE
ZTPCON 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*16 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) DOUBLE PRECISION
The reciprocal of the condition number of the matrix
A, computed as RCOND = 1/(norm(A) * norm(inv(A))).

WORK    (workspace) COMPLEX*16 array, dimension (2*N)

RWORK   (workspace) DOUBLE PRECISION array, dimension (N)

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