Ddisna Dopgtr Dopmtr Dorgtr Dormtr Dpteqr Dsbtrd Dsptrd Dstebz Dstedc Dstein Dstemr Dsteqr Dsterf Dsytrd

Dsteqr() Sub Dsteqr ( Compz As  String, N As  Long, D() As  Double, E() As  Double, Z() As  Double, Info As  Long  ) Eigenvalues and eigenvectors of a symmetric tridiagonal matrix (QL or QR method) Purpose This routine computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method. The eigenvectors of a full or band symmetric matrix can also be found if Dsytrd, Dsptrd or Dsbtrd has been used to reduce this matrix to tridiagonal form. Parameters [in] Compz = "N": Compute eigenvalues only. = "V": Compute eigenvalues and eigenvectors of the original symmetric matrix. On entry, Z() must contain the orthogonal matrix used to reduce the original matrix to tridiagonal form. = "I": Compute eigenvalues and eigenvectors of the tridiagonal matrix. Z() is initialized to the identity matrix. [in] N Order of the matrix. (N >= 0) (If N = 0, returns without computation) [in,out] D() Array D(LD - 1) (LD >= N) [in] The diagonal elements of the tridiagonal matrix. [out] If Info = 0, the eigenvalues in ascending order. [in,out] E() Array E(LE - 1) (LE >= N - 1) [in] The (N - 1) subdiagonal elements of the tridiagonal matrix. [out] E() has been destroyed. [in,out] Z() Array Z(LZ1 - 1, LZ2 - 1) (LZ1 >= N, LZ2 >= N) [in] If Compz = "V", then Z() contains the orthogonal matrix used in the reduction to tridiagonal form. [out] If Info = 0, then if Compz = "V", Z() contains the orthonormal eigenvectors of the original symmetric matrix, and if Compz = "I", Z() contains the orthonormal eigenvectors of the symmetric tridiagonal matrix. If Compz = "N", then Z() is not referenced. [out] Info = 0: Successful exit. = -1: The argument Compz had an illegal value. (Compz <> "N", "V" nor "I") = -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 has failed to find all the eigenvalues in a total of 30*N iterations. i elements of E() have not converged to zero. On exit, D() and E() contain the elements of a symmetric tridiagonal matrix which is orthogonally similar to the original matrix. 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 ) Reduces to tridiagonal form by Dsytrd, then Dorgtr and Dsteqr are applied. Sub Ex_Dsytrd_Dsteqr() Const N = 3 Dim A(N - 1, N - 1) As Double, Info As Long Dim D(N - 1) As Double, E(N - 2) As Double, Tau(N - 2) As Double 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 Dsytrd("L", N, A(), D(), E(), Tau(), Info) If Info <> 0 Then Debug.Print "Error in Dsytrd: Info =", Info Exit Sub End If Call Dorgtr("L", N, A(), Tau(), Info) If Info <> 0 Then Debug.Print "Error in Dorgtr: Info =", Info Exit Sub End If Call Dsteqr("V", N, D(), E(), A(), Info) If Info <> 0 Then Debug.Print "Error in Dsterf: Info =", Info Exit Sub End If Debug.Print "Eigenvalues =", D(0), D(1), D(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) 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