orthovald

Orthogonal (and its derivatives) evaluation.


Syntax
   f = orthovald(N, ord, x, domain, basis)

Description
   f = orthovald(N, ord, x, domain, basis) returns the value of 
   a polynomial evaluated (orthogonally) at x. The diference betwwen 
   orthovalv and orthovald is that the former returns f in the basis, 
   while the latter returns f along with its derivatives.
   Relation: sum(orthovald(N, 0, x, ...)) = orthovalv(ones(10, 1), x, ...), 
   if x is a scalar. This function is useful, for instance, to build the 
   C block for the initial/boundary conditions.

Inputs
   N      = matrix such that NPa = diff(P) (double matrix).
   ord    = derivative order (integer scalar).
   x      = input for evaluation (double scalar).
   domain = domain [a b] of orthogonality (double vector).
   basis  = orthogonal polynomial basis (integer scalar or char).
            1 or 'ChebyshevT' to Chebyshev of first kind, 
            2 or 'ChebyshevU' to Chebyshev of second kind, 
            3 or 'LegendreP' to Legendre, 
            4 or 'HermiteH' to Hermite,
            5 or 'LaguerreL' to Laguerre and
            6 or 'GegenbauerC' to Gegenbauer.

Output
   f      = [P0^(ord)(x), P1^(ord)(x), ...] (double vector).

See also
  orthovalv, orthovalvj, orthovalM and orthovalMj.