Zcgesv Zgbsv Zgbsvx Zgesv Zgesvx Zgtsv Zgtsvx Zspsv Zspsvx Zsysv Zsysvx

Zgtsv() Sub Zgtsv ( N As  Long, Dl() As  Complex, D() As  Complex, Du() As  Complex, B() As  Complex, Info As  Long, Optional Nrhs As  Long = 1  ) (Simple driver) Solution to system of linear equations AX = B for a complex tridiagonal matrix Purpose This routine solves the equation A * X = B where A is an N x N tridiagonal matrix, by Gaussian elimination with partial pivoting. Note that the equation A^T*X = B may be solved by interchanging the order of the arguments du and dl. Parameters [in] N Order of the matrix A. (N >= 0) (If N = 0, returns without computation) [in,out] Dl() Array Dl(LDl - 1) (LDl >= N - 1) [in] N-1 sub-diagonal elements of A. [out] N-2 elements of the second super-diagonal of the upper triangular matrix U from the LU factorization of A, in Dl(0), ..., Dl(N-3). [in,out] D() Array D(LD - 1) (LD >= N) [in] Diagonal elements of A. [out] Diagonal elements of U. [in,out] Du() Array Du(LDu - 1) (LDu >= N - 1) [in] N-1 super-diagonal elements of A. [out] N-1 elements of the first super-diagonal of U. [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 N had an illegal value. (N < 0) = -2: The argument Dl() is invalid. = -3: The argument D() is invalid. = -4: The argument Du() is invalid. = -5: The argument B() is invalid. = -7: The argument Nrhs had an illegal value. (Nrhs < 0, or, Nrhs <> 1 and B() is 1D array) = i > 0: The i-th diagonal element of the factor U is exactly zero, and the solution has not been computed. The factorization has not been completed unless i = n. [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 ( 0.81+0.37i -0.20-0.11i 0 ) A = ( 0.64+0.51i -0.80-0.92i -0.93-0.32i ) ( 0 0.71+0.59i -0.29+0.86i ) ( -0.0484+0.2644i ) B = ( -0.2644-1.0228i ) ( -0.5299+1.5025i ) Sub Ex_Zgtsv() Const N = 3 Dim Dl(N - 2) As Complex, D(N - 1) As Complex, Du(N - 2) As Complex Dim B(N - 1) As Complex, Info As Long Dl(0) = Cmplx(0.64, 0.51): Dl(1) = Cmplx(0.71, 0.59) D(0) = Cmplx(0.81, 0.37): D(1) = Cmplx(-0.8, -0.92): D(2) = Cmplx(-0.29, 0.86) Du(0) = Cmplx(0.2, -0.11): Du(1) = Cmplx(-0.93, -0.32) B(0) = Cmplx(-0.0484, 0.2644): B(1) = Cmplx(-0.2644, -1.0228): B(2) = Cmplx(-0.5299, 1.5025) Call Zgtsv(N, Dl(), D(), Du(), B(), 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 "Info =", Info End Sub Example Results X = -0.15 0.19 0.2 0.94 0.79 -0.13 Info = 0