gistfile1.txt

octave-3.4.0:75> help eigs
`eigs' is a function from the file /Applications/Octave340/Octave.app/Contents/Resources/libexec/octave/3.4.0/oct/x86_64-apple-darwin10.7.3/eigs.oct

 -- Loadable Function: D = eigs (A)
 -- Loadable Function: D = eigs (A, K)
 -- Loadable Function: D = eigs (A, K, SIGMA)
 -- Loadable Function: D = eigs (A, K, SIGMA, OPTS)
 -- Loadable Function: D = eigs (A, B)
 -- Loadable Function: D = eigs (A, B, K)
 -- Loadable Function: D = eigs (A, B, K, SIGMA)
 -- Loadable Function: D = eigs (A, B, K, SIGMA, OPTS)
 -- Loadable Function: D = eigs (AF, N)
 -- Loadable Function: D = eigs (AF, N, B)
 -- Loadable Function: D = eigs (AF, N, K)
 -- Loadable Function: D = eigs (AF, N, B, K)
 -- Loadable Function: D = eigs (AF, N, K, SIGMA)
 -- Loadable Function: D = eigs (AF, N, B, K, SIGMA)
 -- Loadable Function: D = eigs (AF, N, K, SIGMA, OPTS)
 -- Loadable Function: D = eigs (AF, N, B, K, SIGMA, OPTS)
 -- Loadable Function: [V, D] = eigs (A, ...)
 -- Loadable Function: [V, D] = eigs (AF, N, ...)
 -- Loadable Function: [V, D, FLAG] = eigs (A, ...)
 -- Loadable Function: [V, D, FLAG] = eigs (AF, N, ...)
     Calculate a limited number of eigenvalues and eigenvectors of A,
     based on a selection criteria.  The number of eigenvalues and
     eigenvectors to calculate is given by K and defaults to 6.

     By default, `eigs' solve the equation `A * v = lambda * v', where
     `lambda' is a scalar representing one of the eigenvalues, and `v'
     is the corresponding eigenvector.  If given the positive definite
     matrix B then `eigs' solves the general eigenvalue equation `A * v
     = lambda * B * v'.

     The argument SIGMA determines which eigenvalues are returned.
     SIGMA can be either a scalar or a string.  When SIGMA is a scalar,
     the K eigenvalues closest to SIGMA are returned.  If SIGMA is a
     string, it must have one of the following values.

    'lm'
          Largest Magnitude (default).

    'sm'
          Smallest Magnitude.

    'la'
          Largest Algebraic (valid only for real symmetric problems).

    'sa'
          Smallest Algebraic (valid only for real symmetric problems).

    'be'
          Both Ends, with one more from the high-end if K is odd (valid
          only for real symmetric problems).

    'lr'
          Largest Real part (valid only for complex or unsymmetric
          problems).

    'sr'
          Smallest Real part (valid only for complex or unsymmetric
          problems).

    'li'
          Largest Imaginary part (valid only for complex or unsymmetric
          problems).

    'si'
          Smallest Imaginary part (valid only for complex or
          unsymmetric problems).

     If OPTS is given, it is a structure defining possible options that
     `eigs' should use.  The fields of the OPTS structure are:

    `issym'
          If AF is given, then flags whether the function AF defines a
          symmetric problem.  It is ignored if A is given.  The default
          is false.

    `isreal'
          If AF is given, then flags whether the function AF defines a
          real problem.  It is ignored if A is given.  The default is
          true.

    `tol'
          Defines the required convergence tolerance, calculated as
          `tol * norm (A)'.  The default is `eps'.

    `maxit'
          The maximum number of iterations.  The default is 300.

    `p'
          The number of Lanzcos basis vectors to use.  More vectors
          will result in faster convergence, but a greater use of
          memory.  The optimal value of `p' is problem dependent and
          should be in the range K to N.  The default value is `2 * K'.

    `v0'
          The starting vector for the algorithm.  An initial vector
          close to the final vector will speed up convergence.  The
          default is for ARPACK to randomly generate a starting vector.
          If specified, `v0' must be an N-by-1 vector where `N = rows
          (A)'

    `disp'
          The level of diagnostic printout (0|1|2).  If `disp' is 0 then
          diagnostics are disabled.  The default value is 0.

    `cholB'
          Flag if `chol (B)' is passed rather than B.  The default is
          false.

    `permB'
          The permutation vector of the Cholesky factorization of B if
          `cholB' is true.  That is `chol (B(permB, permB))'.  The
          default is `1:N'.

     It is also possible to represent A by a function denoted AF.  AF
     must be followed by a scalar argument N defining the length of the
     vector argument accepted by AF.  AF can be a function handle, an
     inline function, or a string.  When AF is a string it holds the
     name of the function to use.

     AF is a function of the form `y = af (x)' where the required
     return value of AF is determined by the value of SIGMA.  The four
     possible forms are

    `A * x'
          if SIGMA is not given or is a string other than 'sm'.

    `A \ x'
          if SIGMA is 0 or 'sm'.

    `(A - sigma * I) \ x'
          for the standard eigenvalue problem, where `I' is the
          identity matrix of the same size as A.

    `(A - sigma * B) \ x'
          for the general eigenvalue problem.

     The return arguments of `eigs' depend on the number of return
     arguments requested.  With a single return argument, a vector D of
     length K is returned containing the K eigenvalues that have been
     found.  With two return arguments, V is a N-by-K matrix whose
     columns are the K eigenvectors corresponding to the returned
     eigenvalues.  The eigenvalues themselves are returned in D in the
     form of a N-by-K matrix, where the elements on the diagonal are the
     eigenvalues.

     Given a third return argument FLAG, `eigs' returns the status of
     the convergence.  If FLAG is 0 then all eigenvalues have converged.
     Any other value indicates a failure to converge.

     This function is based on the ARPACK package, written by R.
     Lehoucq, K. Maschhoff, D. Sorensen, and C. Yang.  For more
     information see `http://www.caam.rice.edu/software/ARPACK/'.

     See also: eig, svds



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octave-3.4.0:76>