---
name: "dtrcon"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/dtrcon/3lapack"
---

# dtrcon(3lapack)

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

## NAME

DTRCON - estimates 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