Dgbcon Dgbtrf Dgbtrs Dgecon Dgetrf Dgetri Dgetrs Dgtcon Dgttrf Dgttrs

Dgetrf() Sub Dgetrf ( M As  Long, N As  Long, A() As  Double, IPiv() As  Long, Info As  Long  ) LU factorization of a general matrix Purpose This routine computes an LU factorization of a general 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 -0.11 -0.93 ) ( -0.3727 ) A = ( -0.32 0.81 0.37 ), B = ( 0.4319 ) ( -0.8 -0.92 -0.29 ) ( -1.4247 ) Sub Ex_Dgetrf() 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 Dgetrf(N, N, A(), IPiv(), Info) If Info = 0 Then Call Dgetrs("N", 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