Ztbcon Ztbtrs Ztpcon Ztptri Ztptrs Ztrcon Ztrtri Ztrtrs

Ztbtrs() Sub Ztbtrs ( Uplo As  String, Trans As  String, Diag As  String, N As  Long, Kd As  Long, Ab() As  Complex, B() As  Complex, Info As  Long, Optional Nrhs As  Long = 1  ) Solution to system of linear equations AX = B, ATX = B or AHX = B for a complex triangular band matrix Purpose This routine solves a triangular system of the form A * X = B, A^T * X = B or A^H * X = B where A is a triangular band matrix of order n and B is an n x nrhs matrix. A check is made to verify that A is nonsingular. Parameters [in] Uplo = "U": A is upper triangular. = "L": A is lower triangular. [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] Diag = "N": A is non-unit triangular. = "U": A is unit triangular. (Diagonal elements of Ab() are not referenced and are assumed to be 1) [in] N Order of the matrix A. (N >= 0) (If N = 0, returns without computation) [in] Kd Number of super-diagonals or sub-diagonals of the triangular band matrix A. (Kd >= 0) [in] Ab() Array Ab(LAb1 - 1, LAb2 - 1) (LAb1 >= Kd + 1, LAb2 >= N) N x N triangular band matrix A in Kd+1 x N symmetric band matrix form. Upper or lower part is to be stored in accordance with Uplo. [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 Uplo had an illegal value. (Uplo <> "U" nor "L") = -2: The argument Trans had an illegal value. (Trans <> "N", "T" nor "C") = -3: The argument Diag had an illegal value. (Diag <> "N" nor "U") = -4: The argument N had an illegal value. (N < 0) = -5: The argument Kd had an illegal value. (Kd < 0) = -6: The argument Ab() is invalid. = -7: The argument B() is invalid. = -9: The argument Nrhs had an illegal value. (Nrhs < 0) = i > 0: The i-th diagonal element of A is zero, indicating that the matrix is singular and the solutions X have not been computed. [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 Solve the system of linear equations Ax = B and estimate the reciprocal of the condition number (RCond) of A, where ( -0.15-0.23i 0 0 ) A = ( -0.57-0.30i -0.37-2.84i 0 ) ( 0 -0.04-0.01i -0.18-0.04i ) ( -0.0932+0.3296i ) B = ( 0.4796-1.3938i ) ( -0.1056-0.0724i ) Sub Ex_Ztbtrs() Const N = 3, Kd = 1 Dim Ab(Kd, N - 1) As Complex, B(N - 1) As Complex Dim RCond As Double, Info As Long Ab(0, 0) = Cmplx(-0.15, -0.23): Ab(0, 1) = Cmplx(-0.37, -2.84): Ab(0, 2) = Cmplx(-0.18, -0.04) Ab(1, 0) = Cmplx(-0.57, -0.3): Ab(1, 1) = Cmplx(-0.04, -0.01) B(0) = Cmplx(-0.0932, 0.3296): B(1) = Cmplx(0.4796, -1.3938): B(2) = Cmplx(-0.1056, -0.0724) Call Ztbtrs("L", "N", "N", N, Kd, Ab(), B(), Info) If Info = 0 Then Call Ztbcon("1", "L", "N", N, Kd, Ab(), RCond, Info) Debug.Print "X =", Debug.Print Creal(B(0)), Cimag(B(0)), Creal(B(1)), Cimag(B(1)), Creal(B(2)), Cimag(B(2)) Debug.Print "RCond =", RCond Debug.Print "Info =", Info End Sub Example Results X = -0.82 -0.94 0.74 0.2 0.48 0.21 RCond = 0.063468564549167 Info = 0