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

Zgbcon() Sub Zgbcon ( Norm As  String, N As  Long, Kl As  Long, Ku As  Long, Ab() As  Complex, IPiv() As  Long, ANorm As  Double, RCond As  Double, Info As  Long  ) Condition number of a complex band matrix Purpose This routine estimates the reciprocal of the condition number of a complex band matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by Zgbtrf. 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] Kl Number of subdiagonals within the band of A (Kl >= 0) [in] Ku Number of superdiagonals within the band of A (Ku >= 0) [in] Ab() Array Ab(LAb1 - 1, LAb2 - 1) (LAb1 >= 2*Kl+Ku+1, LAb2 >= N) Details of the LU factorization of the band matrix A, as computed by Zgbtrf. U is stored as an upper triangular band matrix with Kl+Ku superdiagonals in rows 1 to Kl+Ku+1, and the multipliers used during the factorization are stored in rows Kl+Ku+2 to 2*Kl+Ku+1 [in] IPiv() Array IPiv(LIPiv - 1) (LIPiv >= N) Pivot indices from Dgbtrf; for 1 <= i <= n, row i of the matrix was interchanged with row IPiv(i-1). [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/(norm(A) * norm(inv(A))). [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 Kl had an illegal value. (Kl < 0) = -4: The argument Ku had an illegal value. (Ku < 0) = -5: The argument Ab() is invalid. = -6: The argument IPiv() is invalid. = -7: The argument ANorm had an illegal value. (ANorm < 0) Reference LAPACK Example Program See example of Zgbsv.