Dsbev Dsbevd Dsbevx Dspev Dspevd Dspevx Dstev Dstevd Dstevr Dstevx Dsyev Dsyevd Dsyevr Dsyevx

Dsyevd() Sub Dsyevd ( Jobz As  String, Uplo As  String, N As  Long, A() As  Double, W() As  Double, Info As  Long  ) (Divide and conquer driver) Eigenvalues and eigenvectors of a symmetric matrix Purpose This routine computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix A. If only eigenvalues are desired, it uses a QL or QR method. If eigenvectors are also desired, it uses a divide and conquer algorithm. Parameters [in] Jobz = "N": Compute eigenvalues only. = "V": Compute eigenvalues and eigenvectors. [in] Uplo = "U": Upper triangle of A is stored. = "L": Lower triangle of A is stored. [in] N Order of the matrix A. (N >= 0) (If N = 0, returns without computation) [in,out] A() Array A(LA1 - 1, LA2 - 1) (LA1 >= N, LA2 >= N) [in] The symmetric matrix A. If Uplo = "U", the leading N x N upper triangular part of A() contains the upper triangular part of the matrix A. If Uplo = "L", the leading N x N lower triangular part of A() contains the lower triangular part of the matrix A. [out] Jobz = "V": If Info = 0, A() contains the orthonormal eigenvectors of the matrix A.   Jobz = "N": The lower triangle (if Uplo = "L") or the upper triangle (if Uplo = "U") of A(), including the diagonal, is destroyed. [out] W() Array W(LW - 1) (LW >= N) If Info = 0, the eigenvalues in ascending order. [out] Info = 0: Successful exit. = -1: The argument Jobz had an illegal value. (Jobz <> "V" nor "N") = -2: The argument Uplo had an illegal value. (Uplo <> "U" nor "L") = -3: The argument N had an illegal value. (N < 0) = -4: The argument A() is invalid. = -5: The argument W() is invalid. = i > 0: If Jobz = "N", the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero.   If Jobz = "V", the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns i/(N+1) through mod(i, N+1). Reference LAPACK Example Program Compute all eigenvalues and eigenvectors of the symmetric matrix A, where ( 2.20 -0.11 -0.32 ) A = ( -0.11 2.93 0.81 ) ( -0.32 0.81 2.37 ) Sub Ex_Dsyevd() Const N = 3 Dim A(N - 1, N - 1) As Double, W(N - 1) As Double, Info As Long A(0, 0) = 2.2 A(1, 0) = -0.11: A(1, 1) = 2.93 A(2, 0) = -0.32: A(2, 1) = 0.81: A(2, 2) = 2.37 Call Dsyevd("V", "L", N, A(), 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 = 1.70705954911046 2.22943643244226 3.56350401844728 Eigenvectors = 0.399322077213382 0.894521385341403 0.200931256445799 -0.481026444340548 0.390994588677271 -0.78468897753835 0.780484105216166 -0.216690384632057 -0.586421212707156 Info = 0