NAME

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

SYNOPSIS

SUBROUTINE DTRCON(
NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK, IWORK, INFO )

CHARACTER DIAG, NORM, UPLO

INTEGER INFO, LDA, N

DOUBLE PRECISION RCOND

INTEGER IWORK( ∗ )

DOUBLE PRECISION A( LDA, ∗ ), WORK( ∗ )

PURPOSE

DTRCON 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (3∗N)

IWORK   (workspace) INTEGER array, dimension (N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

  —  LAPACK version 2.0  —  08 October 1994