To Compile:
------------
Copy all files in one directory.
Make sure you have the g++ compiler; It is available here for free: http://gcc.gnu.org/

Do the following:

>make
>./runDaubechies

The input and output files are defined in main.cpp. 
They all have the extension .dat
The program generates 2 pgm figures with extension .pgm
they can be converted to gif or jpeg using the command convert

References:
------------
The program is based on the book by Van Fleet, "Discrete Wavelet Transformations", 
with all algorithms debugged and tested on several square matrices.
(see comments in the program concerning the error in the algorithm; inverse
Daubechies transformation is incorrect as it is in the book)
I also used the books by Stephane Mallat, "A wavelet tour of signal processing"
and "Wavelets and Multiwavelets", by  Fritz Keinert concerning the theory
The Daubechies coefficients are taken from the program
http://www.musicdsp.org/files/daub.h
generated by Kazuo Hatano
I verified the coefficients for Daubechies order 1, 2, 8 and assumed that
the others were correct.
The quicksort algorithm comes from
http://linux.wku.edu/~lamonml/algor/sort/quick.html
However, this web page seems to be very unstable. 
His algorithm worked for integers and I extended it to reals
The quick sort algorithm is very standard now and described on
http://en.wikipedia.org/wiki/Quicksort

To Do:
------------
-Consider rectangular matrices as well as square as in the version here.
-Routine Entropy is set, however Entropy is not calculated and not implemented.
 Need to give a practical definition for reals, when 2 reals are close
 Not particularly useful at the moment.
-Compression of data routine is set, and implemented but not used

Author:
------------
Pierre Carrier, carri101@umn.edu
Department of Computer Science & Engineering,
University of Minnesota