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ZTRCON(l)) ZTRCON(l)NAMEZTRCON - estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-normSYNOPSISSUBROUTINE 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( * )PURPOSEZTRCON 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)) ).ARGUMENTSNORM (input) CHARACTER*1 Specifies whether the 1-norm condition number or the infinity-norm condition num- ber 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 trian- gular 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 ele- ments 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 =, the i-th argument had an illegal value-iLAPACK version 3.015 June 2000 ZTRCON(l)

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