Dsbgv Dsbgvd Dsbgvx Dspgv Dspgvd Dspgvx Dsygv Dsygvd Dsygvx

Dsygv() Sub Dsygv ( IType As  Long, Jobz As  String, Uplo As  String, N As  Long, A() As  Double, B() As  Double, W() As  Double, Info As  Long  ) (Simple driver) Generalized eigenvalue problem of symmetric matrices Purpose This routine computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form Ax = λBx, ABx = λx or BAx = λx. Here A and B are assumed to be symmetric and B is also positive definite. Parameters [in] IType Specifies the problem type to be solved. = 1: Ax = λBx = 2: ABx = λx = 3: BAx = λx [in] Jobz = "N": Compute eigenvalues only. = "V": Compute eigenvalues and eigenvectors. [in] Uplo = "U": Upper triangles of A and B are stored. = "L": Lower triangles of A and B are stored. [in] N Order of the matrices A and B. (N >= 0) (If N = 0, returns without computation) [in,out] A() Array A(LA1 - 1, LA2 - 1) (LA1 >= N, LA2 >= N) [in] N x N symmetric matrix A. The upper or lower triangular part is to be stored in accordance with Uplo. [out] jobz = "V": If Info = 0, A() contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows:   IType = 1 or 2: Z^T*B*Z = I   IType = 3: Z^T*inv(B)*Z = I Jobz = "N": The upper triangle (if Uplo = "U") or the lower triangle (if Uplo = "L") of A(), including the diagonal, is destroyed. [in,out] B() Array B(LB1 - 1, LB2 - 1) (LB1 >= N, LB2 >= N) [in] N x N symmetric positive definite matrix B. The upper or lower triangular part is to be stored in accordance with Uplo. [out] If Info <= N, the part of B() containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U^T*U or B = L*L^T. [out] W() Array W(LW - 1) (LW >= N) If Info = 0, the eigenvalues in ascending order. [out] Info = 0: Successful exit. = -1: The argument Itype had an illegal value. (Itype < 1 or Itype > 3) = -2: The argument Jobz had an illegal value. (Jobz <> "V" nor "N") = -3: The argument Uplo had an illegal value. (Uplo <> "U" nor "L") = -4: The argument N had an illegal value. (N < 0) = -5: The argument A() is invalid. = -6: The argument B() is invalid. = -7: The argument W() is invalid. = i (0 < i <= N): Dsyev failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero. = i (i > N): The leading minor of order i-N of B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed. Reference LAPACK Example Program Compute the eigenvalues and the eigenvectors of a generalized symmetric-definite eigenproblem of the form Ax = λBx, where A is a symmetric matrix and B is a symmetric positive definite matrix. ( 0.54 -0.90 -0.94 ) ( 1.18 0.54 -1.22 ) A = ( -0.90 0.70 1.04 ) B = ( 0.54 0.60 -0.71 ) ( -0.94 1.04 1.65 ) ( -1.22 -0.71 1.66 ) Sub Ex_Dsygv() Const N = 3 Dim A(N - 1, N - 1) As Double, B(N - 1, N - 1) As Double, W(N - 1) As Double Dim Info As Long A(0, 0) = 0.54 A(1, 0) = -0.9: A(1, 1) = 0.7 A(2, 0) = -0.94: A(2, 1) = 1.04: A(2, 2) = 1.65 B(0, 0) = 1.18 B(1, 0) = 0.54: B(1, 1) = 0.6 B(2, 0) = -1.22: B(2, 1) = -0.71: B(2, 2) = 1.66 Call Dsygv(1, "V", "L", N, A(), B(), W(), Info) Debug.Print "Eigenvalues =", W(0), W(1), W(2) Debug.Print "Eigenvectors =" Debug.Print A(0, 0), A(0, 1), A(0, 2) Debug.Print A(1, 0), A(1, 1), A(1, 2) Debug.Print A(2, 0), A(2, 1), A(2, 2) Debug.Print "Info =", Info End Sub Example Results Eigenvalues = -0.297963342573455 0.510423243055614 7.37370278804149 Eigenvectors = 1.17970064313729 1.46384155786189 9.13803098094183E-02 0.497345303675336 -0.442269445774234 -1.71612038711754 0.524910948248221 1.35130854246605 -0.947378600715302 Info = 0