man ztrcon (Fonctions bibliothèques) - estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm

NAME

ZTRCON - estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm

SYNOPSIS

SUBROUTINE ZTRCON(
NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK, RWORK, INFO )
CHARACTER DIAG, NORM, UPLO
INTEGER INFO, LDA, N
DOUBLE PRECISION RCOND
DOUBLE PRECISION RWORK( * )
COMPLEX*16 A( LDA, * ), WORK( * )

PURPOSE

ZTRCON 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*16 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) 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