ctrcon(3)

NAME

CTRCON - estimate the reciprocal of the condition number

of a triangular matrix A, in either the 1-norm or the infinity

norm

SYNOPSIS

SUBROUTINE CTRCON( NORM, UPLO, DIAG,  N,  A,  LDA,  RCOND,
WORK, RWORK, INFO )
    CHARACTER      DIAG, NORM, UPLO
    INTEGER        INFO, LDA, N
    REAL           RCOND
    REAL           RWORK( * )
    COMPLEX        A( LDA, * ), WORK( * )

PURPOSE

CTRCON estimates the reciprocal of the condition number of

a 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 com

puted 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.

A (input) COMPLEX array, dimension (LDA,N)

The triangular matrix A. If UPLO = 'U', the lead

ing N-by-N upper triangular part of the array A contains the up

per triangular matrix, and the strictly lower triangular part of

A is not referenced. If UPLO = 'L', the leading N-by-N lower

triangular part of the array A contains the lower triangular ma

trix, and the strictly upper triangular part of A is not refer

enced. If DIAG = 'U', the diagonal elements of A are also not

referenced and are assumed to be 1.

LDA (input) INTEGER

The leading dimension of the array A. LDA >=

max(1,N).

RCOND (output) REAL

The reciprocal of the condition number of the ma

trix A, computed 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 ille

gal value

LAPACK version 3.0 15 June 2000

CTRCON(3)