section of routines in cheby.i

functions in cheby.i -

 
 
 
cheby_conv


             fit = cheby_conv(poly, interval)  
 
    convert polynomial coefficients POLY = [a0, a1, ..., aN] to a  
    Chebyshev fit suitable for input to cheby_eval.  The INTERVAL  
    = [xmin,xmax] is the most stable region for evaluation.  Omitting  
    INTERVAL gives the natural interval [-1,1] for Chebyshev polynomials.  
    You may also pass another Chebyshev fit (from cheby_fit) as the  
    INTERVAL to use the same interval as that fit.  
SEE ALSO: cheby_fit,   cheby_eval,   cheby_poly  
 
 
 
cheby_deriv


             cheby_deriv(fit)  
 
    returns Chebyshev fit to the derivative of the function of the  
    input Chebyshev FIT.  
    
SEE ALSO: cheby_fit,   cheby_integ  
 
 
 
cheby_eval


             cheby_eval(fit, x)  
 
    evaluates the Chebyshev fit (from cheby_fit) at points X.  
    the return values have the same dimensions as X.  
    
SEE ALSO: cheby_fit  
 
 
 
cheby_fit


             fit = cheby_fit(f, interval, n)  
         or fit = cheby_fit(f, x, n)  
 
    returns the Chebyshev fit (for use in cheby_eval) of degree N  
    to the function F on the INTERVAL (a 2 element array [a,b]).  
    In the second form, F and X are arrays; the function to be  
    fit is the piecewise linear function of xp interp(f,x,xp), and  
    the interval of the fit is [min(x),max(x)].  You can use the  
    nterp= keyword to set a different interpolator, which must have  
    the same calling sequence as interp (e.g.- nterp=spline).  
    
    The return value is the array [a,b, c0,c1,c2,...cN] where [a,b]  
    is the interval over which the fit applies, and the ci are the  
    Chebyshev coefficients.  It may be useful to use a relatively  
    large value of N in the call to cheby_fit, then to truncate the  
    resulting fit to fit(1:3+m) before calling cheby_eval.  
    
SEE ALSO: cheby_eval,   cheby_integ,   cheby_deriv,  
cheby_poly,   cheby_conv,   cheby_trunc,  
rcheby_fit  
 
 
 
cheby_integ


             cheby_integ(fit)  
         or cheby_integ(fit, x0)  
 
    returns Chebyshev fit to the integral of the function of the  
    input Chebyshev FIT.  If X0 is given, the returned integral will  
    be zero at X0 (which should be inside the fit interval fit(1:2)),  
    otherwise the integral will be zero at x=fit(1).  
    
SEE ALSO: cheby_fit,   cheby_deriv  
 
 
 
cheby_poly


             cheby_poly(fit)  
 
    returns coefficients An of x^n as [A0, A1, A2, ..., An] for  
    the given FIT returned by cheby_fit.  You should only consider  
    actually using these for very low degree polynomials; cheby_eval  
    is nearly always a superior way to evaluate the polynomial.  
    
SEE ALSO: cheby_fit,   cheby_conv  
 
 
 
cheby_trunc


             tfit = cheby_trunc(fit, err)  
         or tfit = cheby_trunc(fit, err, e)  
 
    truncate cheby_fit FIT to relative error ERR by dropping trailing  
    Chebyshev coefficients smaller than ERR.  If ERR is omitted, it  
    defaults to 1.e-9.  Optionally returns E, which is the list of  
    relative errors incurred by dropping each order [e0, e1, ... eN].  
    Often there will be a sudden improvement with some order, which  
    can assist you with selecting an appropriate truncation.  
SEE ALSO: cheby_fit