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

Dstevd() Sub Dstevd ( Jobz As  String, N As  Long, D() As  Double, E() As  Double, Z() As  Double, Info As  Long  ) (Divide and conquer driver) Eigenvalues and eigenvectors of a symmetric tridiagonal matrix Purpose This routine computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix. If eigenvectors are desired, it uses a divide and conquer algorithm. Parameters [in] Jobz = "N": Compute eigenvalues only. = "V": Compute eigenvalues and eigenvectors. [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 symmetric tridiagonal matrix A. [out] If Info = 0, the eigenvalues in ascending order. [in,out] E() Array E(LE - 1) (LE >= N - 1) [in] N - 1 subdiagonal elements of the symmetric tridiagonal matrix A stored in elements 0 to N - 2 of E(). [out] The contents of E() are destroyed. [in] ldz Leading dimension of the two dimensional array Z(). (ldz >= 1 (Jobz = "N"), ldz >= max(1, N) (Jobz = "V")) [out] Z() Array A(LZ1 - 1, LZ2 - 1) (LZ1 >= N, LZ2 >= N) Jobz = "V": If Info = 0, Z() contains the orthonormal eigenvectors of the matrix A, with the i-th row of Z() holding the eigenvector associated with D(i). Jobz = "N": Z() is not referenced. [out] Info = 0: Successful exit. = -1: The argument Jobz had an illegal value. (Jobz <> "V" nor "N") = -2: The argument N had an illegal value. (N < 0) = -3: The argument D() is invalid. = -4: The argument E() is invalid. = -5: The argument Z() is invalid. = i > 0: The algorithm failed to converge; i off-diagonal elements of E() did not converge to zero Reference LAPACK Example Program Compute all eigenvalues and eigenvectors of the symmetric tridiagonal matrix A, where ( 2.58 -0.99 0 ) A = ( -0.99 0.69 -0.03 ) ( 0 -0.03 0.18 ) Sub Ex_Dstevd() Const N = 3 Dim D(N - 1) As Double, E(N - 2) As Double, Z(N - 1, N - 1) As Double Dim Info As Long D(0) = 2.58: D(1) = 0.69: D(2) = 0.18 E(0) = -0.99: E(1) = -0.03 Call Dstevd("V", N, D(), E(), Z(), Info) Debug.Print "Eigenvalues =", D(0), D(1), D(2) Debug.Print "Eigenvectors =" Debug.Print Z(0, 0), Z(0, 1), Z(0, 2) Debug.Print Z(1, 0), Z(1, 1), Z(1, 2) Debug.Print Z(2, 0), Z(2, 1), Z(2, 2) Debug.Print "Info =", Info End Sub Example Results Eigenvalues = 0.171899161473039 0.274429936398504 3.00367090212846 Eigenvectors = 0.106563041190365 -0.378750155986403 -0.919343590608286 0.259206614996466 -0.882055576996614 0.393433463029321 0.959925126764757 0.280225406466732 -4.18002107893757E-03 Info = 0