Zgbcon Zgbtrf Zgbtrs Zgecon Zgetrf Zgetri Zgetrs Zgtcon Zgttrf Zgttrs Zspcon Zsptrf Zsptri Zsptrs Zsycon Zsytrf Zsytri Zsytrs

Zgtcon() Sub Zgtcon ( Norm As  String, N As  Long, Dl() As  Complex, D() As  Complex, Du() As  Complex, Du2() As  Complex, IPiv() As  Long, ANorm As  Double, RCond As  Double, Info As  Long  ) Condition number of a complex tridiagonal matrix Purpose This routine estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by Zgttrf. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCond = 1 / (norm(A) * norm(inv(A))). Parameters [in] Norm Specifies whether the 1-norm condition number or the infinity-norm condition number is required. = "1" or "O": 1-norm = "I": Infinity-norm [in] N Order of the matrix A. (N >= 0) (If N = 0, returns RCond = 1) [in] Dl() Array Dl(LDl - 1) (LDl >= N - 1) N-1 multipliers that define the matrix L from the LU factorization of A as computed by Zgttrf. [in] D() Array D(LD - 1) (LD >= N) N diagonal elements of the upper triangular matrix U from the LU factorization of A. [in] Du() Array Du(LDu - 1) (LDu >= N - 1) N-1 elements of the first super-diagonal of U. [in] Du2() Array Du2(LDu2 - 1) (LDu2 >= N - 2) N-2 elements of the second super-diagonal of U. [in] IPiv() Array IPiv(LIPiv - 1) (LIPiv >= N) Pivot indices; for 1 <= i <= N, row i of the matrix was interchanged with row IPiv(i-1). IPiv(i-1) will always be either i or i+1; IPiv(i-1) = i indicates a row interchange was not required. [in] ANorm Norm = "1" or "O": The 1-norm of the original matrix A (ANorm >= 0) Norm = "I": The infinity-norm of the original matrix A (ANorm >= 0) [out] RCond The reciprocal of the condition number of the matrix A, computed as RCond = 1/(ANorm * Ainvnm), where Ainvnm is an estimate of the 1-norm of inv(A) computed in this routine. [out] Info = 0: Successful exit. = -1: The argument Norm had an illegal value. (Norm <> "1", "O" nor "I") = -2: The argument N had an illegal value. (N < 0) = -3: The argument Dl() is invalid. = -4: The argument D() is invalid. = -5: The argument Du() is invalid. = -6: The argument Du2() is invalid. = -7: The argument IPiv() is invalid. = -8: The argument ANorm had an illegal value. (ANorm < 0) Reference LAPACK Example Program See example of Zgtsv.