ZTPCON(3) estimates 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