CTRCON(1) LAPACK routine (version 3.2) CTRCON(1)[top]NAMECTRCON - estimates the reciprocal of the condition number of a triangu‐ lar matrix A, in either the 1-norm or the infinity-normSYNOPSISSUBROUTINE 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( * )PURPOSECTRCON 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 recip‐ rocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ).ARGUMENTSNORM (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 trian‐ gular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower trian‐ gular 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 refer‐ enced 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, com‐ puted 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 =, the i-th argument had an illegal value LAPACK routine (version 3.2) November 2008 CTRCON(1)-i

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