Dgbsv Dgbsvx Dgesv Dgesvx Dgtsv Dgtsvx Dsgesv

Dgesv() Sub Dgesv ( N As  Long, A() As  Double, IPiv() As  Long, B() As  Double, Info As  Long, Optional Nrhs As  Long = 1  ) (Simple driver) Solution to system of linear equations AX = B for a general matrix Purpose This routine computes the solution to a real system of linear equations A * X = B where A is an n x n matrix and X and B are n x nrhs matrices. The LU decomposition with partial pivoting and row interchanges is used to factor A as A = P * L * U where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B. Parameters [in] N Number of linear equations, i.e., order of the matrix A. (N >= 0) (If N = 0, returns without computation) [in,out] A() Array A(LA1 - 1, LA2 - 1) (LA1 >= N, LA2 >= N) [in] N x N coefficient matrix A. [out] Factors L and U from the factorization A = P*L*U; the unit diagonal elements of L are not stored. [out] IPiv() Array IPiv(LIPiv - 1) (LIPiv >= N) Pivot indices that define the permutation matrix P; 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 N had an illegal value. (N < 0) = -2: The argument A() is invalid. = -3: The argument IPiv() is invalid. = -4: The argument B() is invalid. = -6: The argument Nrhs had an illegal value. (Nrhs < 0) = i > 0: The i-th diagonal element of the factor U is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be 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 ( 0.2 -0.11 -0.93 ) ( -0.3727 ) A = ( -0.32 0.81 0.37 ), B = ( 0.4319 ) ( -0.8 -0.92 -0.29 ) ( -1.4247 ) Sub Ex_Dgesv() Const N = 3 Dim A(N - 1, N - 1) As Double, B(N - 1) As Double, IPiv(N - 1) As Long Dim ANorm As Double, RCond As Double, Info As Long A(0, 0) = 0.2: A(0, 1) = -0.11: A(0, 2) = -0.93 A(1, 0) = -0.32: A(1, 1) = 0.81: A(1, 2) = 0.37 A(2, 0) = -0.8: A(2, 1) = -0.92: A(2, 2) = -0.29 B(0) = -0.3727: B(1) = 0.4319: B(2) = -1.4247 ANorm = Dlange("1", N, N, A()) Call Dgesv(N, A(), IPiv(), B(), Info) If Info = 0 Then Call Dgecon("1", N, A(), ANorm, RCond, Info) Debug.Print "X =", B(0), B(1), B(2) Debug.Print "RCond =", RCond Debug.Print "Info =", Info End Sub Example Results X = 0.86 0.64 0.51 RCond = 0.232708473186076 Info = 0