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

Dstein() Sub Dstein ( N As  Long, D() As  Double, E() As  Double, M As  Long, W() As  Double, Iblock() As  Long, Isplit() As  Long, Z() As  Double, Ifail() As  Long, Info As  Long  ) Eigenvectors of a symmetric tridiagonal matrix (Inverse iteration method) Purpose This routine computes the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration. The maximum number of iterations allowed for each eigenvector is specified by an internal parameter Maxits (currently set to 5). Parameters [in] N Order of the tridiagonal matrix. (N >= 0) (If N = 0, returns without computation) [in] D() Array D(LD - 1) (LD >= N) The N diagonal elements of the tridiagonal matrix T. [in] E() Array E(LE - 1) (LE >= N - 1) The (N - 1) off-diagonal elements of the tridiagonal matrix T. [in] M The number of eigenvectors to be found. (0 <= M <= N) [in] W() Array W(LW - 1) (LW >= N) The first M elements of W() contain the eigenvalues for which eigenvectors are to be computed. The eigenvalues should be grouped by split-off block and ordered from smallest to largest within the block. (The output array w[] from Dstebz with Order = "B" is expected here.) [in] Iblock() Array Iblock(LIblock - 1) (LIblock >= N) The submatrix indices associated with the corresponding eigenvalues in W(). Iblock(i) = 1 if eigenvalue w(i) belongs to the first submatrix from the top, = 2 if w(i) belongs to the second submatrix, etc. (The output array Iblock() from Dstebz is expected here.) [in] Isplit() Array Isplit(LIsplit - 1) (LIsplit >= N) The splitting points, at which T breaks up into submatrices. The first submatrix consists of rows/columns 1 to Isplit(0), the second of rows/columns Isplit(0) + 1 through Isplit(1), etc. (The output array Isplit() from Dstebz is expected here.) [out] Z() Array Z(LZ1 - 1, LZ2 - 1) (LZ1 >= N, LZ2 >= M) The computed eigenvectors. The eigenvector associated with the eigenvalue W(i) is stored in the i-th column of Z(). Any vector which fails to converge is set to its current iterate after Maxits iterations. [out] Ifail() Array Ifail(LIfail - 1) (LIfail >= M) On normal exit, all elements of Ifail() are zero. If one or more eigenvectors fail to converge after Maxits iterations, then their indices are stored in array Ifail(). [out] Info = 0: Successful exit. = -1: The argument N had an illegal value. (N < 0) = -2: The argument D() is invalid. = -3: The argument E() is invalid. = -4: The argument M had an illegal value. (M < 0 or M > N) = -5: The argument W() is invalid. = -6: The argument Iblock() is invalid. = -7: The argument Isplit() is invalid. = -8: The argument Z() is invalid. = -9: The argument Ifail() is invalid. = i > 0: Eigenvectors failed to converge in Maxits iterations. Their indices are stored in array ifail(). Reference LAPACK Example Program See example of Dstebz.