Zpbcon Zpbtrf Zpbtrs Zptcon Zpttrf Zpttrs

Zpttrf() Sub Zpttrf ( N As  Long, D() As  Double, E() As  Complex, Info As  Long  ) LDLH factorization of a Hermitian positive definite tridiagonal matrix Purpose This routine computes the L*D*L^H factorization of a Hermitian positive definite tridiagonal matrix A. The factorization may also be regarded as having the form A = U^H*D*U. Parameters [in] N Order of the matrix A. (N >= 0) (If N = 0, returns without computation) [in,out] D() Array D(LD - 1) (LD >= N) [in] N diagonal elements of the Hermitian positive definite tridiagonal matrix A. [out] N diagonal elements of the diagonal matrix D from the factorization A = L*D*L^H. [in,out] E() Array E(LE - 1) (LE >= N - 1) [in] N-1 sub-diagonal elements of the Hermintian positive definite tridiagonal matrix A. [out] N-1 sub-diagonal elements of the unit bidiagonal factor L from the L*D*L^H factorization of A. E can also be regarded as the super-diagonal of the unit bidiagonal factor U from the U^H*D*U factorization of A. [out] Info = 0: Successful exit. = -1: The argument N had an illegal value. (N < 0) = -2: The argument D() is invalid. = -3: The argument E() is invalid. = i > 0: The leading minor of order i is not positive definite. If i < N, the factorization could not been completed, while if i = N, the factorization was completed, but D(N-1) <= 0. Reference LAPACK Example Program Solve the system of linear equations Ax = B and estimate the reciprocal of the condition number (RCond) of A, where ( 2.88 0.29-0.44i 0 ) A = ( 0.29+0.44i 0.62 -0.01-0.02i ) ( 0 -0.01+0.02i 0.46 ) ( 1.6236-0.7300i ) B = ( 0.1581+0.1537i ) ( 0.1132-0.2290i ) Sub Ex_Zpttrf() Const N As Long = 3 Dim D(N - 1) As Double, E(N - 2) As Complex, B(N - 1) As Complex Dim ANorm As Double, RCond As Double, Info As Long D(0) = 2.88: D(1) = 0.62: D(2) = 0.46 E(0) = Cmplx(0.29, 0.44): E(1) = Cmplx(-0.01, 0.02) B(0) = Cmplx(1.6236, -0.73): B(1) = Cmplx(0.1581, 0.1537): B(2) = Cmplx(0.1132, -0.229) ANorm = Zlanht("1", N, D(), E()) Call Zpttrf(N, D(), E(), Info) If Info = 0 Then Call Zpttrs("L", N, D(), E(), B(), Info) If Info = 0 Then Call Zptcon(N, D(), E(), 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 = 0.59 -0.28 -0.2 -0.04 0.24 -0.49 RCond = 0.124521368143895 Info = 0