Dgbcon Dgbtrf Dgbtrs Dgecon Dgetrf Dgetri Dgetrs Dgtcon Dgttrf Dgttrs

Dgetri() Sub Dgetri ( N As  Long, A() As  Double, IPiv() As  Long, Info As  Long  ) Inverse of a general matrix Purpose This routine computes the inverse of a matrix using the LU factorization computed by Dgetrf. This method inverts U and then computes inv(A) by solving the system inv(A)*L = inv(U) for inv(A). Parameters [in] N Order of the matrix A. (N >= 0) (If N = 0, returns without computation) [in] A() Array A(LA1 - 1, LA2 - 1) (LA1 >= N, LA2 >= N) [in] The factors L and U from the factorization A = P*L*U as computed by Dgetrf. [out] If info = 0, the inverse of the original matrix A. [in] IPiv() Array IPiv(LIPiv - 1) (LIPiv >= N) Pivot indices from Dgetrf; for 1 <= i <= n, row i of the matrix was interchanged with row IPiv(i-1). [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. = i > 0: The i-th diagonal element of U is exactly zero; the matrix is singular and its inverse could not be computed. Reference LAPACK Example Program Compute the inverse matrix of A, where ( 0.2 -0.11 -0.93 ) A = ( -0.32 0.81 0.37 ) ( -0.8 -0.92 -0.29 ) Sub Ex_Dgetri() Const N = 3 Dim A(N - 1, N - 1) As Double, IPiv(N - 1) As Long Dim 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 Call Dgetrf(N, N, A(), IPiv(), Info) If Info = 0 Then Call Dgetri(N, A(), IPiv(), Info) Debug.Print "Inv(A) =" Debug.Print A(0, 0), A(0, 1), A(0, 2) Debug.Print A(1, 0), A(1, 1), A(1, 2) Debug.Print A(2, 0), A(2, 1), A(2, 2) Debug.Print "Info =", Info End Sub Example Results Inv(A) = -0.129835926770076 -1.01370476663992 -0.876977075036551 0.478485386997209 0.986999177910909 -0.275178324415061 -1.1597855676599 -0.334742863331381 -0.156049246582423 Info = 0