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

Zgttrf() Sub Zgttrf ( N As  Long, Dl() As  Complex, D() As  Complex, Du() As  Complex, Du2() As  Complex, IPiv() As  Long, Info As  Long  ) LU factorization of a complex tridiagonal matrix Purpose This routine computes an LU factorization of a complex tridiagonal matrix A using elimination with partial pivoting and row interchanges. The factorization has the form A = L * U where L is a product of permutation and unit lower bidiagonal matrices and U is upper triangular with nonzeros in only the main diagonal and first two super-diagonals. Parameters [in] N Order of the matrix A. (N >= 0) (If N = 0, returns without computation) [in,out] Dl() Array Dl(LDl - 1) (LDl >= N - 1) [in] N-1 sub-diagonal elements of A. [out] N-1 multipliers that define the matrix L from the LU factorization of A. [in,out] D() Array D(LD - 1) (LD >= N) [in] Diagonal elements of A. [out] N diagonal elements of the upper triangular matrix U from the LU factorization of A. [in,out] Du() Array Du(LDu - 1) (LDu >= N - 1) [in] N-1 super-diagonal elements of A. [out] N-1 elements of the first super-diagonal of U. [out] Du2() Array Du2(LDu2 - 1) (LDu2 >= N - 2) N-2 elements of the second super-diagonal of U. [out] IPiv() Array IPiv(LIPiv - 1) (LIPiv >= N) Pivot indices; for 1 <= i <= N, row i of the matrix was interchanged with row IPiv(i-1). IPiv(i-1) will always be either i or i+1; IPiv(i-1) = i indicates a row interchange was not required. [out] Info = 0: Successful exit. = -1: The argument N had an illegal value. (N < 0) = -2: The argument Dl() is invalid. = -3: The argument D() is invalid. = -4: The argument Du() is invalid. = -5: The argument Du2() is invalid. = -6: 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 ( 0.81+0.37i -0.20-0.11i 0 ) A = ( 0.64+0.51i -0.80-0.92i -0.93-0.32i ) ( 0 0.71+0.59i -0.29+0.86i ) ( -0.0484+0.2644i ) B = ( -0.2644-1.0228i ) ( -0.5299+1.5025i ) Sub Ex_Zgttrf() Const N = 3 Dim Dl(N - 2) As Complex, D(N - 1) As Complex, Du(N - 2) As Complex Dim Du2(N - 3) As Complex, IPiv(N - 1) As Long Dim B(N - 1) As Complex, ANorm As Double, RCond As Double, Info As Long Dl(0) = Cmplx(0.64, 0.51): Dl(1) = Cmplx(0.71, 0.59) D(0) = Cmplx(0.81, 0.37): D(1) = Cmplx(-0.8, -0.92): D(2) = Cmplx(-0.29, 0.86) Du(0) = Cmplx(0.2, -0.11): Du(1) = Cmplx(-0.93, -0.32) B(0) = Cmplx(-0.0484, 0.2644): B(1) = Cmplx(-0.2644, -1.0228): B(2) = Cmplx(-0.5299, 1.5025) ANorm = Zlangt("1", N, Dl(), D(), Du()) Call Zgttrf(N, Dl(), D(), Du(), Du2(), IPiv(), Info) If Info = 0 Then Call Zgttrs("N", N, Dl(), D(), Du(), Du2(), IPiv(), B(), Info) If Info = 0 Then Call Zgtcon("1", N, Dl(), D(), Du(), Du2(), IPiv(), ANorm, RCond, Info) Debug.Print "X =", Debug.Print 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 = -0.15 0.19 0.2 0.94 0.79 -0.13 RCond = 0.187722560135325 Info = 0