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

Dsbevd() Sub Dsbevd ( Jobz As  String, Uplo As  String, N As  Long, Kd As  Long, Ab() As  Double, W() As  Double, Z() As  Double, Info As  Long  ) (Divide and conquer driver) Eigenvalues and eigenvectors of a symmetric band matrix Purpose This routine computes all the eigenvalues and, optionally, eigenvectors of a real symmetric band 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] Kd Number of superdiagonals of the matrix A if Uplo = "U" or number of subdiagonals if Uplo = "L". (Kd >= 0) [in,out] Ab() Array Ab(LAb1 - 1, LAb2 - 1) (LAb1 >= Kd + 1, LAb2 >= N) [in] The upper or lower triangle of the symmetric band matrix A, stored in the first Kd + 1 columns of the array. The j-th column of A is stored in the j-th column of the array Ab() as follows. Uplo = "U": Ab(Kd + i - j, j) = Aij for max(0, j - Kd - 1) <= i <= j <= N - 1. Uplo = "L": Ab(i - j, j) = Aij for 0 <= j <= i <= min(N - 1, j + Kd - 1). [out] Ab() is overwritten by values generated during the reduction to tridiagonal form. If Uplo = "U", the first superdiagonal and the diagonal of the tridiagonal matrix T are returned in rows Kd and Kd + 1 of Ab(). If Uplo = "L", the diagonal and first subdiagonal of T are returned in the first two rows of Ab(). [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__N = -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 Kd had an illegal value. (Kd < 0) = -5: The argument Ab() is invalid. = -6: The argument W() is invalid. = -7: 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 band matrix A, where ( 0.61 0.79 0 ) A = ( 0.79 2.23 0.25 ) ( 0 0.25 2.87 ) Sub Ex_Dsbevd() Const N = 3, Kd = 1 Dim Ab(Kd, N - 1) As Double, W(N - 1) As Double, Z(N - 1, N - 1) As Double Dim Info As Long Ab(0, 0) = 0.61: Ab(0, 1) = 2.23: Ab(0, 2) = 2.87 Ab(1, 0) = 0.79: Ab(1, 1) = 0.25 Call Dsbevd("V", "L", N, Kd, Ab(), 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 = 0.285074336232239 2.43057331973532 2.99435234403244 Eigenvectors = 0.924204695519984 -0.35289670385953 0.145978070900713 -0.380123828036851 -0.813258637555945 0.440586272822087 3.67635163909111E-02 0.462681645244035 0.885761897474061 Info = 0