CTRCON(3f)

NAME
CTRCON - 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 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.

A       (input) COMPLEX array, dimension (LDA,N)
    The triangular matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper 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 matrix, and the strictly upper triangular part of A is not referenced. 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 matrix 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 illegal value