This source contains the following files:

	Neuron.c    -	source for content addressible memory program
	NOut.ex1    -	an example output report generated by the program
	NOut.ex2    -	another example output report generated by the program
	Neuron.doc  -	this file.

    The program Neuron.c simulates a SIMPLE stable state neural network
reporting on both input and output states and energy levels after each
iteration (namely set up for 8, though usually the network stabilizes after
about 4). The program demonstrates a very straight-forward method of
programming a content-addressable memory and receiving output from that
memory. This program is based on a BASIC program developed in Ed Rietman's book
"Experiments in Artificial Neural Networks" published by TAB Books copyright
1988.
    The program allows you to create an input vector (vector u - either created
randomly or by entry), a connection strength matrix (matrix T - either created
randomly or by entry), enter a threshold value, a information value (see pg. 27
of "Exp. in ANN"), and a seed for generating the random vector and matrices (if
necessary - this also allows reproducible tests). It outputs a vector (vector
v) and feeds this vector back into the connection strength matrix until the
network stabilizes (the network can have multiple Lorenz strange attractors).

    The executable was created on an AMIGA 2000 computer with 1M using a Manx
C Compiler Ver 3.4a and can be run either from the CLI or Workbench (please
use the ICON supplied or incorporate the tool window line into your ICON as
this is what creates the window for the program to run in). This program should
execute on an AMIGA 500/1000/2000 with no difficulty. The source should be
equally compilable on most C compilers as I tried to stay as system independent
as possible.

    The program creates an output report to a file called "Neuron.Output". Two
example reports are included in the archive file (NOut.ex1 and NOut.ex2) for
comparison purposes.

    Feel free to repost this archive to other BBS's so long as you keep the
copyright and this doc file intact (at least I would appreciate it). Also,
feel free to modify or use this program in any way you like provided it is not
for commercial purposes (i.e. this was written in the spirit of learning and
promoting Neural Networks, Parrallel Distributed Processing and NOT for anyone
to make money!!!).

    For more detailed analysis of this program I suggest researching Ed
Rietman's book.

    Remember, this is just a simple program demonstrating the programming of
matrix mathematics and content addressible memories. Other programs will be
on the way demonstrating other aspects of PDP and NNets (such as Hebb's
learning rule, Grossberg's revision, interactive activation, etc.) just as
soon as I research them myself (I'm still in the learning curve.)

    If you have any questions regarding this program, PDP, NNet's, or anything
dealing with computers and their use (I've been an IBM Mainframe (4300 VM/VSE)
systems programmer for 5 years and an IBM applications programmer before that
for 5 years) send me some EMAIL (check the BBS you got this from - I might be
there - if not I've included my USENET address as that's where I check for mail
most often. If you can't find me check with somebody else on your BBS - I
usually can be tracked down.).

    Hope this program helps some newcomers to the field of PDP and NNets,

						  Shawn P. Legrand, CCP

USENET: spl@cup.portal.com    or    ...sun!cup.portal.com!spl

------------------------------ cut here for source -----------------------------
/*

   Original Author: Shawn P. Legrand      15-Sep-88

	This program simulates a simple neural network by  calculating the 
    inner product of a vector and a matrix where the matrix T is symmetric
    {T(i,j) = T(j,i)}, dilute (more 0's than 1's), and T(i,i)=0 (to prevent
    oscillations and chaotism). Reports are sent to a report file showing the
    input and output matrices and the energy level of the matrix after each
    iteration.	

	This program is based on information contained in a book by Ed Rietman,
    'Experiments in Artificial Neural Networks', published by TAB.

    Copyright 1988 	Shawn P. Legrand, CCP 		All Rights Reserved
	
*/

#include <stdio.h>

/*
 * Random number generator -
 * adapted from the FORTRAN version 
 * in "Software Manual for the Elementary Functions"
 * by W.J. Cody, Jr and William Waite.
*/

static long int iy = 100001;

sran(seed)
long seed;
{
        iy = seed;
}

double ran()
{
        iy *= 125;
        iy -= (iy/2796203) * 2796203;
        return (double) iy/ 2796203.0;
}

/*
 * Main program logic.
*/

main()
{
    int neurons, io, info, vector, matrix, i, j, iterate, sigma=0;
    long seed;
    float energy=0;
    double r;
    int t[100][100], u[100], v[100];
    FILE *fp;

/* Open new CLI device */

    if ((fp = fopen("Neuron.output","w")) == NULL) {
       printf("Error opening Neuron.output!!!\n");
       exit(10);
    }   

/* Retrive initial values */

    printf("Input the random seed: ");
    scanf("%ld",&seed);
    sran(seed);
     
    printf("Enter the number of neurons (100 maximum): ");
    scanf("%d",&neurons);						       	
    printf("Input the threshold value (0 to 2 are reasonable values): ");
    scanf("%d",&io);
    printf("Enter the value of the information (0 to 1 is a good value): ");
    scanf("%d",&info);
    printf("Do you want to enter the input vector yourself (1/Yes, 0/No)? ");
    scanf("%d",&vector);
    printf("Do you want to enter the T matrix (1/Yes, 0/No)? ");
    scanf("%d",&matrix);

/* Initialize the weight matrix (matrix T) */    

    if (!matrix) {
    	for (i=0; i<neurons; i++) {
	    for (j=0; j<neurons; j++) {
	        if (i==j) {
		    t[i][j] = 0;
		} else {
                    r=ran();
		    if (r<0.8) {
		        t[i][j] = 0;
		    } else {
		        t[i][j] = 1;
		    }
		}    
	    }
	}
    } else {
        for (i=0; i<neurons; i++) {
	    for (j=0; j<neurons; j++) {
	        printf("T(%d,%d): ",i,j);
		scanf("%d",&t[i][j]);
	    }
        }
    }

/* Output initial values */
    
    fprintf(fp,"Seed = %ld\n",seed); 
    fprintf(fp,"Threshold = %d\n",io);
    fprintf(fp,"Information = %d\n",info);
    fprintf(fp,"T matrix:\n");
    for (i=0; i<neurons; i++) {
        for (j=0; j<neurons; j++) {
	    fprintf(fp,"%d",t[i][j]);
	}
	fprintf(fp,"\n");
    }
    fprintf(fp,"\n\n");    
    
/* Retrieve input vector (vector u) */

    if (!vector) {
        for (i=0; i<neurons; i++) {
	    r=ran();
	    if (r<0.5) {
	        u[i]=0;
	    } else {
	        u[i]=1;
	    }
	}
    } else {
        for (i=0; i<neurons; i++) {
	    fprintf(fp,"Input u(%d): ",i);
	    fscanf(fp,"%d",&u[i]);
	}
    }

/* Perform calculations, Report input and output vector, Energy level, 
   Iterate using feedback from prior calculation */    

    for (iterate=0; iterate<8; iterate++) {
        for (i=0; i<neurons; i++) {
	    for (j=0; j<neurons; j++) {
	        sigma+=t[i][j]*u[j];
	    }
	    sigma+=info;
	    if (sigma>io) {
	        sigma=1;
	    } else {
	        sigma=0;
	    }
	    v[i]=sigma;
	    sigma=0;
	}
	fprintf(fp,"Iteration %d:\n",iterate);
	fprintf(fp,"Input vector U:\n");
	for (i=0; i<neurons; i++) {
	    fprintf(fp,"%d",u[i]);
	}
	fprintf(fp,"\nOutput vector V:\n");
	for (i=0; i<neurons; i++) {
	    fprintf(fp,"%d",v[i]);
	}
	fprintf(fp,"\n");
	fprintf(fp,"            Energy: ");
	for (i=0; i<neurons; i++) {
	    energy+=(float) (u[i]*v[i]);
	}
	energy*=-0.5;
	fprintf(fp,"%f\n\n",energy);
	for (i=0; i<neurons; i++) {
	    u[i]=v[i];
	}
	energy=0;
    }
    
}
------------------------------- cut here for example one -----------------------
Seed = 16000
Threshold = 1
Information = 1
T matrix:
0001010000100000
0000100010000000
0000000000000000
0110000000010000
0110010010000000
1000000011001000
0000000000000000
0010100001000001
0000000000000000
0000101000000001
1001000000000000
0010000000001010
0010000100000100
0010000101000010
0000000000000100
0000001000110000


Iteration 0:
Input vector U:
1101010011110001
Output vector V:
1101110101100101
            Energy: -3.500000

Iteration 1:
Input vector U:
1101110101100101
Output vector V:
1101110101101111
            Energy: -5.000000

Iteration 2:
Input vector U:
1101110101101111
Output vector V:
1101110101111111
            Energy: -6.000000

Iteration 3:
Input vector U:
1101110101111111
Output vector V:
1101110101111111
            Energy: -6.500000

Iteration 4:
Input vector U:
1101110101111111
Output vector V:
1101110101111111
            Energy: -6.500000

Iteration 5:
Input vector U:
1101110101111111
Output vector V:
1101110101111111
            Energy: -6.500000

Iteration 6:
Input vector U:
1101110101111111
Output vector V:
1101110101111111
            Energy: -6.500000

Iteration 7:
Input vector U:
1101110101111111
Output vector V:
1101110101111111
            Energy: -6.500000

---------------------------------- cut here for example 2 ----------------------
Seed = 10
Threshold = 1
Information = 1
T matrix:
0001001000110001
0010000010000000
0000100000000100
0000010010000010
0101000000000000
0000001000001001
0010000110000001
0000001000010000
1000101000000010
0001000100010000
1110001001000000
1001100000000000
0010011001000000
0000000000001010
1011010010100000
0000000010000000


Iteration 0:
Input vector U:
0000010101101000
Output vector V:
1001011001101110
            Energy: -2.000000

Iteration 1:
Input vector U:
1001011001101110
Output vector V:
1011110111111110
            Energy: -4.000000

Iteration 2:
Input vector U:
1011110111111110
Output vector V:
1111111111111111
            Energy: -6.500000

Iteration 3:
Input vector U:
1111111111111111
Output vector V:
1111111111111111
            Energy: -8.000000

Iteration 4:
Input vector U:
1111111111111111
Output vector V:
1111111111111111
            Energy: -8.000000

Iteration 5:
Input vector U:
1111111111111111
Output vector V:
1111111111111111
            Energy: -8.000000

Iteration 6:
Input vector U:
1111111111111111
Output vector V:
1111111111111111
            Energy: -8.000000

Iteration 7:
Input vector U:
1111111111111111
Output vector V:
1111111111111111
            Energy: -8.000000

---------------------------------- End of File ---------------------------------