/*****************************************************************************
*                                                                            *
*   POLYVAL.SPL    Copyright (C) 1998-2003 DSP Development Corporation       *
*                               All Rights Reserved                          *
*                                                                            *
*   Author:      Matthew Tom                                                 *
*                                                                            *
*   Synopsis:    Calculates p(x) for a given polynomial p and value x.       *
*                                                                            *
*   Revisions:    3 May 1998  MAT  Creation                                  *
*                21 Aug 1998  MAT  Help Menu Entry                           *
*                 4 Sep 2003  RRR  refactored with polygraph                 *
*                                                                            *
*****************************************************************************/

#include 

#if @HELP_POLYVAL

    POLYVAL

    Purpose: Calculates P(x) for a given polynomial P and value x.

    Syntax:  POLYVAL(p, x, form)

                 p - A series, the coefficients of the polynomial.

                 x - A scalar or series. The values where the polynomial will
                     be evaluated.

              form - Optional. An integer, the form of the polynomial
                     coefficients, 0: ascending powers, 1: decreasing powers.
                     Defaults to 1 (highest degree to lowest).

    Returns: A scalar or series, the result of P(x).

    Example:
             polyval({1, 2, -1}, 2)

             returns 7 the value of P(x) = x^2 + 2x - 1 at x = 2.

    Example:
             polyval({1, 2, -1}, 0..3)

             returns the series {-1, 2, 7, 14}.

    Remarks:
             POLYVAL is similar to POLYGRAPH except the default form is
             in decreasing powers (highest degree to lowest). Unlike
             POLYGRAPH, POLYVAL returns a scalar for a scalar input.

    See Also:
             Polyfit
             Polygraph

#endif


/* evaluate polynomial P(x) */
polyval(p, x, form)
{
        local scalarval = FALSE;

        if (argc < 3)
        {
                if (argc < 2)
                {
                        error("polyval - polynomial coefficents and x range required");
                }
                
                form = 1;
        }

        /* check for scalar or series */
        if (isscalar(x))
        {
                scalarval = TRUE;
                x = castseries(x);
        }
        
        if (isscalar(p))
        {
                p = castseries(p);
        }

        /* degenerate cases */
        if (length(x) == 0)
        {
                return({});
        }

        if (length(p) == 0)
        {
                return(zeros(length(x), 1));
        }

        /* evaluate polynomial, return values only, (no x) */
        y = polygraph(p, x, 0, form);

        /* cast to scalar if necessary */
        if (scalarval)
        {
                y = y[1];
        }

        return(y);
}