Zgbcon Zgbtrf Zgbtrs Zgecon Zgetrf Zgetri Zgetrs Zgtcon Zgttrf Zgttrs Zspcon Zsptrf Zsptri Zsptrs Zsycon Zsytrf Zsytri Zsytrs

Zgetri() Sub Zgetri ( N As  Long, A() As  Complex, IPiv() As  Long, Info As  Long  ) Inverse of a complex matrix Purpose This routine computes the inverse of a matrix using the LU factorization computed by Zgetrf. 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 Zgetrf. [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 ( 0.2-0.11i -0.93-0.32i 0.81+0.37i ) A = ( -0.8-0.92i -0.29+0.86i 0.64+0.51i ) ( 0.71+0.59i -0.15+0.19i 0.2+0.94i ) Sub Ex_Zgetri() Const N = 3 Dim A(N - 1, N - 1) As Complex, IPiv(N - 1) As Long Dim Info As Long A(0, 0) = Cmplx(0.2, -0.11): A(0, 1) = Cmplx(-0.93, -0.32): A(0, 2) = Cmplx(0.81, 0.37) A(1, 0) = Cmplx(-0.8, -0.92): A(1, 1) = Cmplx(-0.29, 0.86): A(1, 2) = Cmplx(0.64, 0.51) A(2, 0) = Cmplx(0.71, 0.59): A(2, 1) = Cmplx(-0.15, 0.19): A(2, 2) = Cmplx(0.2, 0.94) Call Zgetrf(N, N, A(), IPiv(), Info) If Info = 0 Then Call Zgetri(N, A(), IPiv(), Info) Debug.Print "Inv(A) =" Debug.Print Creal(A(0, 0)), Cimag(A(0, 0)), Creal(A(0, 1)), Cimag(A(0, 1)) Debug.Print Creal(A(0, 2)), Cimag(A(0, 2)) Debug.Print Creal(A(1, 0)), Cimag(A(1, 0)), Creal(A(1, 1)), Cimag(A(1, 1)) Debug.Print Creal(A(1, 2)), Cimag(A(1, 2)) Debug.Print Creal(A(2, 0)), Cimag(A(2, 0)), Creal(A(2, 1)), Cimag(A(2, 1)) Debug.Print Creal(A(2, 2)), Cimag(A(2, 2)) Debug.Print "Info =", Info End Sub Example Results Inv(A) = -0.201994189100174 -0.220248055307507 -0.368148317320952 0.290272208608198 0.360511523756756 -0.418803146203832 -0.614836963994613 0.455294217428579 6.83276126510658E-02 -0.256899969150471 9.45427369503751E-02 -0.502999571841184 0.47052389723088 9.18669160683443E-02 4.42160986558556E-02 -0.409830677026182 8.10655554407012E-02 -0.424831215613866 Info = 0