Provided by: liblapack-doc_3.3.1-1_all #### NAME

```       LAPACK-3  -  estimates 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

LAPACK routine (version 3.2)               April 2011                            ZTRCON(3lapack)
```