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

Zgetrf() Sub Zgetrf ( M As  Long, N As  Long, A() As  Complex, IPiv() As  Long, Info As  Long  ) LU factorization of a complex matrix Purpose This routine computes an LU factorization of a complex m x n matrix A using partial pivoting with row interchanges. The factorization has the form A = P * L * U where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n). This is the right-looking Level 3 BLAS version of the algorithm. Parameters [in] M Number of rows of the matrix A. (M >= 0) (If M = 0, returns without computation) [in] N Number of columns of the matrix A. (N >= 0) (If N = 0, returns without computation) [in,out] A() Array A(LA1 - 1, LA2 - 1) (LA1 >= M, LA2 >= N) [in] M x N matrix to be factored. [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 >= min(M, N)) Pivot indices; for 1 <= i <= min(M, N), row i of the matrix was interchanged with row IPiv(i-1). [out] Info = 0: Successful exit. = -1: The argument M had an illegal value. (M < 0) = -2: The argument M had an illegal value. (N < 0) = -3: The argument A() is invalid. = -4: The argument IPiv() is invalid. = 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, and division by zero will occur if it is used to solve a system of equations. Reference LAPACK Example Program Solve the system of linear equations Ax = B and estimate the reciprocal of the condition number (RCond) of A, where ( 0.2-0.11i -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 ) ( -0.5853-0.9457i ) B = ( -2.1697-1.0006i ) ( 0.0116-0.5094i ) Sub Ex_Zgetrf() Const N = 3 Dim A(N - 1, N - 1) As Complex, B(N - 1) As Complex, IPiv(N - 1) As Long Dim ANorm As Double, RCond As Double, 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) B(0) = Cmplx(-0.5853, -0.9457): B(1) = Cmplx(-2.1697, -1.0006): B(2) = Cmplx(0.0116, -0.5094) ANorm = Zlange("1", N, N, A()) Call Zgetrf(N, N, A(), IPiv(), Info) If Info = 0 Then Call Zgetrs("N", N, A(), IPiv(), B(), Info) If Info = 0 Then Call Zgecon("1", N, A(), ANorm, RCond, Info) Debug.Print "X =", Creal(B(0)), Cimag(B(0)), Creal(B(1)), Cimag(B(1)), Creal(B(2)), Cimag(B(2)) Debug.Print "RCond =", RCond Debug.Print "Info =", Info End Sub Example Results X = 0.79 -0.13 0.13 0.75 -0.91 0.3 RCond = 0.250214147937285 Info = 0