Yorick Standard Library

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Package cheby (in cheby.i) -

Index of documented functions or symbols:

C

cheby_conv

DOCUMENT 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

DOCUMENT cheby_deriv(fit)
  returns Chebyshev fit to the derivative of the function of the
  input Chebyshev FIT.

cheby_eval

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

cheby_fit

DOCUMENT 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.

cheby_integ

DOCUMENT 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).

cheby_poly

DOCUMENT 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.

cheby_trunc

DOCUMENT 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.