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

Zgbtrs() Sub Zgbtrs ( Trans As  String, N As  Long, Kl As  Long, Ku As  Long, Ab() As  Complex, IPiv() As  Long, B() As  Complex, Info As  Long, Optional Nrhs As  Long = 1  ) Solution to LU factorized system of linear equations AX = B, ATX = B or AHX = B for a complex band matrix Purpose This routine solves a system of linear equations A * X = B, A^T * X = B or A^H * X = B with a complex band matrix A using the LU factorization computed by Zgbtrf. Parameters [in] Trans Specifies the form of the system of equations: = "N": A * X = B. (no transpose) = "T": A^T * X = B. (transpose) = "C": A^H * X = B. (conjugate transpose) [in] N Number of linear equations, i.e., order of the matrix A. (N >= 0) (If N = 0, returns without computation) [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 Zgbtrf; for 1 <= i <= n, row i of the matrix was interchanged with row IPiv(i-1). [in,out] B() Array B(LB1 - 1, LB2 - 1) (LB1 >= max(1, N), LB2 >= Nrhs) (2D array) or B(LB - 1) (LB >= max(1, N), Nrhs = 1) (1D array) [in] N x Nrhs matrix of right hand side matrix B. [out] If Info = 0, the N x Nrhs solution matrix X. [out] Info = 0: Successful exit. = -1: The argument Trans had an illegal value. (Trans <> "N", "T" nor "C") = -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 B() is invalid. = -9: The argument Nrhs had an illegal value. (Nrhs < 0) [in] Nrhs (Optional) Number of right hand sides, i.e., number of columns of the matrix B. (Nrhs >= 0) (If Nrhs = 0, returns without computation) (default = 1) Reference LAPACK Example Program See example of Zgbtrf.