Zpocon Zpotrf Zpotri Zpotrs Zppcon Zpptrf Zpptri Zpptrs

Zpotri() Sub Zpotri ( Uplo As  String, N As  Long, A() As  Complex, Info As  Long  ) Inverse of a Hermitian positive definite matrix Purpose This routine computes the inverse of a Hermitian positive definite matrix A using the Cholesky factorization A = U^H*U or A = L*L^H computed by Zpotrf. Parameters [in] Uplo = "U": Upper triangular factor U is stored in A(). = "L": Lower triangular factor L is stored in A(). [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 triangular factor U or L from the Cholesky factorization A = U^H*U or A = L*L^H, as computed by Zpotrf. [out] If Info = 0, the upper or lower triangle of the (Hermitian) inverse of A, overwriting the input factor U or L. [out] Info = 0: Successful exit. = -1: The argument Uplo had an illegal value. (Uplo <> "U" nor "L") = -2: The argument N had an illegal value. (N < 0) = -3: The argument A() is invalid. = i > 0: The i-th diagonal element of the factor U or L is zero, and the inverse could not be computed. Reference LAPACK Example Program Compute the inverse matrix of A, where ( 2.20 -0.11+0.93i 0.81-0.37i ) A = ( -0.11-0.93i 2.32 -0.80+0.92i ) ( 0.81+0.37i -0.80-0.92i 2.29 ) Sub Ex_Zpotri() Const N = 3 Dim A(N - 1, N - 1) As Complex, Info As Long A(0, 0) = Cmplx(2.2, 0) A(1, 0) = Cmplx(-0.11, -0.93): A(1, 1) = Cmplx(2.32, 0) A(2, 0) = Cmplx(0.81, 0.37): A(2, 1) = Cmplx(-0.8, -0.92): A(2, 2) = Cmplx(2.29, 0) Call Zpotrf("L", N, A(), Info) If Info = 0 Then Call Zpotri("L", N, A(), 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) = 0.96823675342099 0 0 0 0 0 -0.186364825657161 0.652567887151733 1.07415978942926 0 0 0 -0.669749382959094 -3.34014351483294E-03 0.335735031475792 0.692472480506973 1.06960504827267 0 Info = 0