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ZTBCON(l)) ZTBCON(l)NAMEZTBCON - estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-normSYNOPSISSUBROUTINE ZTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB, RCOND, WORK, RWORK, INFO ) CHARACTER DIAG, NORM, UPLO INTEGER INFO, KD, LDAB, N DOUBLE PRECISION RCOND DOUBLE PRECISION RWORK( * ) COMPLEX*16 AB( LDAB, * ), WORK( * )PURPOSEZTBCON estimates the reciprocal of the condition number of a triangular band 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. KD (input) INTEGER The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0. AB (input) COMPLEX*16 array, dimension (LDAB,N) The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as fol- lows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). If DIAG = 'U', the diagonal ele- ments of A are not referenced and are assumed to be 1. LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KD+1. 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 ZTBCON(l)

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