Here is what is available in the daub directory.

Use it at your own risk...
When 10 digits are printed for phi(4,2.1), this does not mean that all digits
are correct (in fact, an argument like 2.1 is first converted to a dyadic
rational k/2^Ndyad). However both the values of Digits and Ndyad can be
increased to get more precision: in this sense the precision of the
results of the daub package is arbitrary, a feature not found elsewhere.

One perfect application for daub is in teaching numerical analysis,
where one can show on graphs the dilation equation, piece by piece:
    > p := 2; c:=array( 0..2*p-1, daubc(p) );
    > plot({ seq( sum(c[k]*phi(p,2*x-k),k=0..m), m=0..2*p-1) }, x=0..2*p-1);


First the main package.
======================

 daub.mpl - Coefficients, values, graphs, moments, and (anti)derivatives
            of Daubechies scaling functions/wavelets in Maple V.
 daub.hlp - Help text for the daub package, read by daub.mpl.  ( >?daub )
 daub.mac - macro definitions for all the global function names.
            (for library maintainance, read by daub.mpl via daubut.mpl)

Some utility routines.
=====================

 daubut.mpl - Accuracy estimation and refinement of approximations for
              the coefficients of Daubechies low pass filters.  ( >?daubut )
 daubut.hlp - Help text for the daubut package, read by daubut.mpl.


A demo prints 3 graphs and checks the
numerical accuracy of function values.
=====================================

 daubdemo.mpl - Demonstration of facilities in the daub.mpl package.
                (This uses all functions and is a good test of validity
                 of the daub package)

Optional functions for testing purposes.
=======================================

 daubcc.mpl - Correct coefficients of Daubechies low pass filters.
 daubcc.hlp - Help text for the daubcc package, read by daubcc.mpl.( >?daubcc )


 daubdd.mpl - Find the 2p coefficients of the Daubechies Minium Phase filter
              using the Deslauriers-Dubuc Lagrange interpolation method.
 daubdd.hlp - Help text for the daubdd package, read by daubdd.mpl.( >?daubdd )


 daublh.mpl - Find the 2p coefficients of the Daubechies Minium Phase filter
              using the original spectral method of Daubechies.
 daublh.hlp - Help text for the daublh package, read by daublh.mpl.( >?daubdd )


Minimal test
============

 test.mpl -  Hopefully, will print lots of "ok".



To verify installation on my system, i would type
=================================================

C:\maplev\daub> mplle

> read `test.mpl`;

> Digits:=40;

> read `daubdemo.mpl`;

> ?daub

This should print a series of "ok", with odd 10^(-19) or so here and there.
If it also prints graphs looking like Daubechies filter functions and the
numerical integration errors are (almost) all near the precision limit,
it works!


Jacques Gelinas, Ph.D., Maths, College Militaire Royal de Saint-Jean,
                 Richelain, P. Quebec, Canada J0J 1R0.

Until june 1995:   gelinas@cmr.ca
After june 1995:   College Militaire Royal de Saint-Jean, 1952-1995, is closed.
