# ?gerbr

Tests regularity of an interval matrix by Ris-Beeck and Rex-Rohn criteria.

## Syntax

call sigerbr( n, a, lda, sr, reg, info )

call digerbr( n, a, lda, sr, reg, info )

## Description

The routine ?gerbr checks whether a general interval square matrix A is regular or singular by using a combination of Ris-Beeck spectral criterion and Rex-Rohn test.

## Input Parameters

n

  INTEGER. The order of the matrix A (`n ≥ 0`).

a

  REAL for sigerbr.

  DOUBLE PRECISION for digerbr.

  Array: DIMENSION (lda,*).

  Contains the matrix A.

  The second dimension of a must be at least max(1, n).

lda

  INTEGER. The first dimension of a, `lda ≥ max(1, n)`.

## Output Parameters

sr

  REAL for sigerbr.

  DOUBLE PRECISION for digerbr.

  An upper estimate of the spectral radius of the matrix (`inv(|(mid A))| · rad A`).

  This is an additional information about the matrix A, which is crucial for the so-called strong regularity of A.

reg

  INTEGER. Displays the results of the singularity test.

  If `reg ≥ 0`, then A is regular.

  If `reg < 0`, then A is singular.

  If reg = 0, then the result is undetermined, that is, the test was not sufficiently sensitive to detect whether the matrix A is regular or singular.

info

  INTEGER.

  If `info = 0`, the execution is successful.

  If `info = i ≥ 0`, the execution is not successful.

  If `info = -i`, the i-th parameter has an illegal value.

## Application Notes

The test implemented in the routine ?gerbr is rather crude, and in critical cases further investigation of the matrix A is recommended. However, the routine may help to determine (by comparing the value of sr with 1) whether an interval matrix is strongly regular or not.

Parent topic: Routines for Checking Properties of Interval Matrices