Fancy Matlab

 EIGS  Find a few eigenvalues and eigenvectors of a matrix using ARPACK.
    D = EIGS(A) returns a vector of A's 6 largest magnitude eigenvalues.
    A must be square and should be large and sparse.

    [V,D] = EIGS(A) returns a diagonal matrix D of A's 6 largest magnitude
    eigenvalues and a matrix V whose columns are the corresponding eigenvectors.

    [V,D,FLAG] = EIGS(A) also returns a convergence flag.  If FLAG is 0
    then all the eigenvalues converged; otherwise not all converged.

    EIGS(A,B) solves the generalized eigenvalue problem A*V == B*V*D.  B must
    be symmetric (or Hermitian) positive definite and the same size as A.
    EIGS(A,[],...) indicates the standard eigenvalue problem A*V == V*D.

    EIGS(A,K) and EIGS(A,B,K) return the K largest magnitude eigenvalues.

    EIGS(A,K,SIGMA) and EIGS(A,B,K,SIGMA) return K eigenvalues based on SIGMA:
       'LM' or 'SM' - Largest or Smallest Magnitude
    For real symmetric problems, SIGMA may also be:
       'LA' or 'SA' - Largest or Smallest Algebraic
       'BE' - Both Ends, one more from high end if K is odd
    For nonsymmetric and complex problems, SIGMA may also be:
       'LR' or 'SR' - Largest or Smallest Real part
       'LI' or 'SI' - Largest or Smallest Imaginary part
    If SIGMA is a real or complex scalar including 0, EIGS finds the eigenvalues
    closest to SIGMA.  For scalar SIGMA, and also when SIGMA = 'SM' which uses
    the same algorithm as SIGMA = 0, B need only be symmetric (or Hermitian)
    positive semi-definite since it is not Cholesky factored as in the other cases.

    EIGS(A,K,SIGMA,OPTS) and EIGS(A,B,K,SIGMA,OPTS) specify options:
    OPTS.issym: symmetry of A or A-SIGMA*B represented by AFUN [{0} | 1]
    OPTS.isreal: complexity of A or A-SIGMA*B represented by AFUN [0 | {1}]
    OPTS.tol: convergence: Ritz estimate residual <= tol*NORM(A) [scalar | {eps}]
    OPTS.maxit: maximum number of iterations [integer | {300}]
    OPTS.p: number of Lanczos vectors: K+1 &less; p ≤ N [integer | {2K}]
    OPTS.v0: starting vector [N-by-1 vector | {randomly generated by ARPACK}]
    OPTS.disp: diagnostic information display level [0 | {1} | 2]
    OPTS.cholB: B is actually its Cholesky factor CHOL(B) [{0} | 1]
    OPTS.permB: sparse B is actually CHOL(B(permB,permB)) [permB | {1:N}]

    EIGS(AFUN,N) accepts the function AFUN instead of the matrix A.
    Y = AFUN(X) should return
       A*X            if SIGMA is not specified, or is a string other than 'SM'
       A\X            if SIGMA is 0 or 'SM'
       (A-SIGMA*I)\X  if SIGMA is a nonzero scalar (standard eigenvalue problem)
       (A-SIGMA*B)\X  if SIGMA is a nonzero scalar (generalized eigenvalue problem)
    N is the size of A. The matrix A, A-SIGMA*I or A-SIGMA*B represented by AFUN is
    assumed to be real and nonsymmetric unless specified otherwise by OPTS.isreal
    and OPTS.issym. In all these EIGS syntaxes, EIGS(A,...) may be replaced by
    EIGS(AFUN,N,...).

    EIGS(AFUN,N,K,SIGMA,OPTS,P1,P2,...) and EIGS(AFUN,N,B,K,SIGMA,OPTS,P1,P2,...)
    provide for additional arguments which are passed to AFUN(X,P1,P2,...).

    Examples:
       A = delsq(numgrid('C',15));  d1 = eigs(A,5,'SM');
    Equivalently, if dnRk is the following one-line function:
       function y = dnRk(x,R,k)
       y = (delsq(numgrid(R,k))) \ x;
    then pass dnRk's additional arguments, 'C' and 15, to EIGS:
       n = size(A,1);  opts.issym = 1;  d2 = eigs(@dnRk,n,5,'SM',opts,'C',15);

    See also EIG, SVDS, ARPACKC.

# posted by samuel @ 5:32 AM