Chebyshev approximation in Nim

This module implements Chebyshev polynomial approximation to an
interval of a function.  The approximation works for a single
variable, and also for large scale sparse matrix operations as
well.

User has to define a set of operations, specifically, apply,
assign, and newOneOf, to be able to use the interface. When
concept in Nim matures, we will use concept to enforce those.

See the end of the source code of this module for examples of use
cases.

Types

    Chebyshev = object
      coef*: seq[float]            ## Coefficients.
      center*, halfwidth*: float   ## Center and half width of the approximation interval.
      degree*: int                 ## Degree of the approximation.

    Parameters for Chebyshev approximation.

Templates

    template newChebyshev(ab: Slice[float]; n: int; fx: untyped): Chebyshev

    Create a Chebyshev object with computed coefficients, given
    the interval as in [a, b], maximum degree n, and the
    function, fx given as an expression of type float, which uses
    x as the parameter of type float.

    template apply(chebyshev: Chebyshev; res: typed; op: typed; arg: typed)

    Apply the chebyshev approximation of an Operator, op, on an
    argument arg. The return type is the same as the arg. A proc
    apply must be defined for op, as op.apply(output,input).

    template chebyshevT(res: typed; n: int; op: typed; arg: typed)

    Apply the Chebyshev polynomial of the first kind with degree,
    n, of the operator op to the operand arg, and save the result
    in res.

License

    MIT license.  See the file, LICENSE, for detail.