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# ctrcon

```
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
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
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