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 infin
ity-norm. The norm of A is computed and an estimate is
obtained for norm(inv(A)), then the reciprocal of the con
dition 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 lead
ing 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 refer
enced. If UPLO = 'L', the leading N-by-N lower
triangular part of the array A contains the lower
triangular matrix, and the strictly upper
'U', the diagonal elements of A are also not ref
erenced 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 ille
gal value
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