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

Dspevd() Sub Dspevd ( Jobz As  String, Uplo As  String, N As  Long, Ap() As  Double, W() As  Double, Z() As  Double, Info As  Long  ) (Divide and conquer driver) Eigenvalues and eigenvectors of a symmetric matrix in packed form Purpose This routine computes all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix A in packed form. 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] Ap() Array Ap(LAp - 1) (LAp >= N(N + 1)/2) [in] The upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array Ap() as follows. Uplo = "U": Ap(i + j*(j + 1)/2) = Aij for 0 <= i <= j <= N - 1. Uplo = "L": Ap((i + j*(2*N - j - 1)/2) = Aij for 0 <= j < = i <= N - 1. [out] Ap() is overwritten by values generated during the reduction to tridiagonal form. If Uplo = "U", the diagonal and first superdiagonal of the tridiagonal matrix T overwrite the corresponding elements of A. If Uplo = "L", the diagonal and first subdiagonal of T overwrite the corresponding elements of A. [out] W() Array W(LW - 1) (LW >= N) If Info = 0, the eigenvalues in ascending order. [out] Z() Array Z(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 column of Z() holding the eigenvector associated with W(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 Uplo had an illegal value. (Uplo <> "U" nor "L") = -3: The argument N had an illegal value. (N < 0) = -4: The argument Ap() is invalid. = -5: The argument W() is invalid. = -6: The argument Z() is invalid. = i > 0: The algorithm failed to converge. i off-diagonal elements of an intermediate tridiagonal form did not converge to zero 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_Dspevd() Const N = 3 Dim Ap(N * (N + 1) / 2) As Double, W(N - 1) As Double, Z(N - 1, N - 1) As Double Dim Info As Long Ap(0) = 2.2 Ap(1) = -0.11: Ap(3) = 2.93 Ap(2) = -0.32: Ap(4) = 0.81: Ap(5) = 2.37 Call Dspevd("V", "L", N, Ap(), W(), Z(), Info) Debug.Print "Eigenvalues =", W(0), W(1), W(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 = 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