Dgbsv Dgbsvx Dgesv Dgesvx Dgtsv Dgtsvx Dsgesv

Dgtsv() Sub Dgtsv ( N As  Long, Dl() As  Double, D() As  Double, Du() As  Double, B() As  Double, Info As  Long, Optional Nrhs As  Long = 1  ) (Simple driver) Solution to system of linear equations AX = B for a general 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, where ( -0.58 1.14 0 ) ( -0.5960 ) A = ( -1.56 2.21 0.16 ), B = ( -0.6798 ) ( 0 0.24 0.25 ) ( -0.0406 ) Sub Ex_Dgtsv() Const N = 3 Dim Dl(N - 2) As Double, D(N - 1) As Double, Du(N - 2) As Double Dim B(N - 1) As Double, Info As Long Dl(0) = -1.56: Dl(1) = 0.24 D(0) = -0.58: D(1) = 2.21: D(2) = 0.25 Du(0) = 1.14: Du(1) = 0.16 B(0) = -0.596: B(1) = -0.6798: B(2) = -0.0406 Call Dgtsv(N, Dl(), D(), Du(), B(), Info) Debug.Print "X =", B(0), B(1), B(2) Debug.Print "Info =", Info End Sub Example Results X = -0.82 -0.94 0.74 Info = 0