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Neuron Digest Volume 07 Number 17
Neuron Digest Wednesday, 3 Apr 1991 Volume 7 : Issue 17
Today's Topics:
ART1&2 source code (WAS: Detailed description of ART-1 & 2 wanted)
Send submissions, questions, address maintenance and requests for old issues to
"neuron-request@hplabs.hp.com" or "{any backbone,uunet}!hplabs!neuron-request"
Use "ftp" to get old issues from hplpm.hpl.hp.com (15.255.176.205).
------------------------------------------------------------
Subject: ART1&2 source code (WAS: Detailed description of ART-1 & 2 wanted)
From: mcsun!hp4nl!fwi.uva.nl!smagt@uunet.uu.net (Patrick van der Smagt)
Organization: FWI, University of Amsterdam
Date: 27 Feb 91 15:39:04 +0000
[[ Editor's Note: I normally don't flood the network with source code,
but this is small enough not to be too burdonsome. Further, enough
people have asked for ART implementations that widespread distribution
seems like a good deal. Many thanks to Patrick. -PM ]]
root@blakex.RAIDERNET.COM (Blake McBride) writes:
>Am looking for a source for a detailed description of Adaptive Resonance
>Theory (ART) by Grossberg & Carpenter. Both 1 & 2. In addition, if
>anyone has any source it sure would be appreciated!
Well, I do have a description of ART-1, whereas one of my students
tried to disentangle ART itself. But one had better read Lippmann
and reconstruct ART-1 from that. Anyway, here is some source code
for ART-1 and ART-2; I wrote neither but looked at both. I also
have another ART-2 source code, but I will not clobber the net
by including that one, too.
Patrick van der Smagt
/\/\
\ /
Organisation: Faculty of Mathematics & Computer Science / \
University of Amsterdam, Kruislaan 403, _ \/\/ _
NL-1098 SJ Amsterdam, The Netherlands | | | |
Phone: +31 20 525 7524 | | /\/\ | |
Fax: +31 20 525 7490 | | \ / | |
| | / \ | |
email: smagt@fwi.uva.nl | | \/\/ | |
| \______/ |
\________/
/\/\
``The opinions expressed herein are the author's only and do \ /
not necessarily reflect those of the University of Amsterdam.'' / \
\/\/
=---------art1.c-------------cut here-----------------art1.c-----------------
/* Simiulation of ART-1 Neural network (Ref: Lippman 87)
Written by Jagath Samarabandu <bandu@cs.buffalo.edu>
To compile, type cc art1.c -o art1 */
#include <stdio.h>
#define N 25 /* No. of nodes in F1 */
#define M 20 /* No. of nodes in F2 */
initialize(top_down,bot_up,n,m) /* initialize the LTM traces */
double top_down[],bot_up[]; /* top down and bot. up LTM traces */
int n,m; /* No. of nodes in F1 and F2 */
{
int i;
double t;
t = 1.0/(1.0+n);
for (i=0;i<n*m;i++) {
top_down[i] = 1.0; bot_up[i] = t;
}
}
compute_matching_scores(mu,bot_up,input,n,m) /* calculate matching scores */
double mu[],bot_up[],input[]; /* mu - matching score */
int n,m; /* No. of F1 and F2 nodes */
{
int i,j;
for (j=0; j<m; j++)
for (i=0, mu[j]=0.0; i<n; i++)
mu[j] += bot_up[i*m+j]*input[i];
}
double vigilance(top_down,input,jmax,n,m) /* returns |T.X|/|X| */
double top_down[],input[];
int n,m,jmax;
{
int i;
double x,t;
for (i=0,x=0.0; i<n; i++)
x += input[i];
for (i=0,t=0.0; i<n; i++)
t += top_down[i*m+jmax]*input[i];
return(t/x);
}
int find_max(array,len) /* find the max of array and return the index */
double array[];
int len;
{
int j,jmax;
for (j=0,jmax=0; j<len; j++)
if (array[j]>array[jmax])
jmax = j;
return (jmax);
}
adapt_LTM(top_down,bot_up, input,jmax,n,m) /* change top down and bot.up LTM */
double top_down[],bot_up[],input[];
int n,m,jmax;
{
int i,ij;
double sum,t;
for (i=0,sum=0.5; i<n; i++)
sum += top_down[i*m+jmax]*input[i];
for (i=0,ij=jmax; i<n; i++,ij += m) {
t = top_down[ij]*input[i];
bot_up[ij] = t/sum;
top_down[ij] = t;
}
}
load_data(d,max,n,fname) /* load data from file */
int d[],max,n;
char *fname[];
{
FILE *fp;
int n_pat,n_var,i,j;
if (!(fp=fopen(fname,"r"))) exit(perror(fname));
fscanf(fp,"%d %d\n",&n_pat,&n_var);
if (n_pat>max) {
printf("Warning! only %2d patterns out of %d are read\n",max,n_pat);
n_pat = max;
}
if (n_var!=n)
exit(printf("wrong pattern size: should be %2d. was %2d\n",n,n_var));
for (i=0;j<n_pat;i++)
for (j=0;j<n_var;j++)
fscanf(fp,"%d",&d[i*n+j]);
fclose(fp);
}
display(in,top_down,x,y,m) /* display input and top down weights */
double in[],top_down[];
int x,y,m;
{
int i,ix,iy,j;
for (iy=0,i=0; iy<y; iy++){
for (ix=0,i=iy*y; ix<x; ix++,i++)
printf("%c",(in[i]>0.5)?'#':' ');
printf(" | ");
for (j=0; j<m; j++) {
for (ix=0,i=iy*y; ix<x; ix++,i++)
printf("%c",(top_down[i*m+j]>0.5)?'#':' ');
printf(" ");
}
printf("\n");
}
printf("\n");
}
/***************** main routine starts here *******************************/
int data[20][N]={
#include "art1.data"
};
main(argc,argv)
int argc;
char *argv[];
{
char ch;
double t[N][M],b[N][M],x[N],mu[M],rho;
int max_j,i,j,n_pat,ok,seq[M];
if (argc>1)
n_pat = load_data(data,20,N,argv[1]);
else n_pat=20;
initialize(t,b,N,M);
printf("Vigilance threshold: "); scanf("%lf",&rho);
printf("\nSimulation of ART1 network with vigilance Threshold = %3.3lf\n\n",rho);
do {
for (i=0; i<n_pat; i++) {
for (j=0; j<N; j++)
x[j] = (double)data[i][j];
compute_matching_scores(mu,b,x,N,M);
bzero((char *)seq,M*sizeof(int)); j=1;
do {
max_j = find_max(mu,M); seq[max_j] = j++;
if (vigilance(t,x,max_j,N,M)>rho) {
adapt_LTM(t,b,x,max_j,N,M);
seq[max_j] = -1;
break;
}
else
mu[max_j] = 0.0;
} while (1);
printf("IN:%2d ",i);
for (j=0;j<M; j++) {
if (seq[j]>0)
printf("%1d ",seq[j]);
else if (seq[j]==0)
printf(" ");
else {
printf("R\n"); break;
}
}
display(x,t,5,5,M);
}
printf("Another round? (1-yes): "); scanf("%d",&ok);
} while (ok);
ok =1;
do {
printf("\n[A-T] or ESC to quit :"); scanf("%s",&ch);
printf("\n");
if ((ch == 27) || ((ch < 'A') || (ch > 'T'))) ok =0;
else
{
for (j=0; j<N; j++)
x[j] = (double)data[ch -'A'][j];
compute_matching_scores(mu,b,x,N,M);
bzero((char *)seq,M*sizeof(int)); j=1;
do {
max_j = find_max(mu,M); seq[max_j] = j++;
if (vigilance(t,x,max_j,N,M)>rho) {
adapt_LTM(t,b,x,max_j,N,M);
seq[max_j] = -1;
break;
}
else
mu[max_j] = 0.0;
} while (1);
printf("IN:%2d ",i++);
for (j=0;j<M; j++) {
if (seq[j]>0)
printf("%1d ",seq[j]);
else if (seq[j]==0)
printf(" ");
else {
printf("R\n"); break;
}
}
display(x,t,5,5,M);
}
} while (ok);
}
=----------------------end-------------end------------------------------------
=------art1 data file--------cut here-------------art1 data file--------------
/* art1 data file - 20x25 */
{1,1,1,1,1,
1,0,0,0,1,
1,1,1,1,1,
1,0,0,0,1,
1,0,0,0,1,},
{1,1,1,1,0,
1,0,0,0,1,
1,1,1,1,0,
1,0,0,0,1,
1,1,1,1,0,},
{1,1,1,1,1,
1,0,0,0,0,
1,0,0,0,0,
1,0,0,0,0,
1,1,1,1,1,},
{1,1,1,1,0,
1,0,0,0,1,
1,0,0,0,1,
1,0,0,0,1,
1,1,1,1,0,},
{1,1,1,1,1,
1,0,0,0,0,
1,1,1,1,1,
1,0,0,0,0,
1,1,1,1,1,},
{1,1,1,1,1,
1,0,0,0,0,
1,1,1,1,1,
1,0,0,0,0,
1,0,0,0,0,},
{1,1,1,1,1,
1,0,0,0,0,
1,0,1,1,1,
1,0,0,0,1,
1,1,1,1,1,},
{1,0,0,0,1,
1,0,0,0,1,
1,1,1,1,1,
1,0,0,0,1,
1,0,0,0,1,},
{1,1,1,1,1,
0,0,1,0,0,
0,0,1,0,0,
0,0,1,0,0,
1,1,1,1,1,},
{1,1,1,1,1,
0,0,1,0,0,
0,0,1,0,0,
0,0,1,0,0,
1,1,1,0,0,},
{1,0,0,0,1,
1,0,0,1,0,
1,1,1,0,0,
1,0,0,1,0,
1,0,0,0,1,},
{1,0,0,0,0,
1,0,0,0,0,
1,0,0,0,0,
1,0,0,0,0,
1,1,1,1,1,},
{1,0,0,0,1,
1,1,0,1,1,
1,0,1,0,1,
1,0,0,0,1,
1,0,0,0,1,},
{1,0,0,0,1,
1,1,0,0,1,
1,0,1,0,1,
1,0,0,1,1,
1,0,0,0,1,},
{1,1,1,1,1,
1,0,0,0,1,
1,0,0,0,1,
1,0,0,0,1,
1,1,1,1,1,},
{1,1,1,1,1,
1,0,0,0,1,
1,1,1,1,1,
1,0,0,0,0,
1,0,0,0,0,},
{1,1,1,1,1,
1,0,0,0,1,
1,0,1,0,1,
1,0,0,1,1,
1,1,1,1,1,},
{1,1,1,1,1,
1,0,0,0,1,
1,1,1,1,1,
1,0,0,1,0,
1,0,0,0,1,},
{1,1,1,1,1,
1,0,0,0,0,
1,1,1,1,1,
0,0,0,0,1,
1,1,1,1,1,},
{1,1,1,1,1,
0,0,1,0,0,
0,0,1,0,0,
0,0,1,0,0,
0,0,1,0,0,},
=--------------------end------------------end---------------------------------
=------------art2.c-----------cut here-----------------art2.c-----------------
#include <stdio.h>
#include <math.h>
#include <strings.h> /* dans addition */
#define M 10
#define N 8
#define STREQ(s1,s2) (strcmp((s1),(s2)) == 0)
/*****************************************************************/
/** art2 algorithm **/
/** simulates the art2 algorithm for clustering vectors **/
/** Steve Lehar Sept 89 **/
/*****************************************************************/
/**** global variables & functions ****/
int reset;
float w[M],p[M],oldp[M],x[M],q[M],v[M],u[M],r[M],topdown[M];
float w1[M],p1[M],x1[M],q1[M],v1[M],u1[M];
float rho,normp,normu,normv,normw,normr;
float normq1,normp1,normu1,normv1,normw1,normr1;
float zup[M][N],zdn[N][M],oldzdn[M];
float I[M], F1[M], F2[N],F2val[N];
int F2winner,F2reset[N];
float pchange=1.0,zchange=1.0,diff();
float a=5.0, b=5.0, c=0.225, e=0.000001, theta = 0.3,del_t = 0.1;
char pattern[80];
FILE *fp;
int iter,learning,nreset=0;
float f(),floatval();
main(argc,argv)
int argc;
char *argv[];
{
int i,j,k;
char key;
/**** initialize ****/
init_weights();
get_commandline_args(argc,argv);
/**** learn training patterns ****/
for(i=0;i<10;i++){
fscanf(fp,"%s ",pattern);
learning = 1;
/****
if(STREQ(pattern,"E") || STREQ(pattern,"F")) learning = 0;
else learning = 1;
****/
read_input();
init_reset();
print_input();
restart:;
init_nodes();
/**** equilibrate f0 ****/
for(iter=0;iter<10;iter++){
update_f0();
}
/**** equilibrate f1 ****/
for(iter=0;iter<10;iter++){
update_f1();
}
/**** equilibrate f1 & f2 ****/
for(iter=0;iter<10;iter++){
update_f1();
update_f2();
update_r();
}
/**** check for reset ****/
if(reset){
printf("RESET\n");
reset = 0;
nreset++;
if(nreset==N)goto nextpattern;
if(learning) goto restart;
}
if(!learning) goto skip;
/**** learn resonant pattern ****/
for(k=0;k<1000;k++){
update_zup();
update_zdn();
update_f1();
}
skip:;
print_vals();
if(is_arg("-v",argc,argv)) print_f0();
print_f1();
print_f2();
print_z(F2winner);
}
printf("\n");
nextpattern:;
fclose(fp);
}
/****
zchange = diff(zdn[F2winner],oldzdn,N);
pchange = diff(p,oldp,M);
print_f2();
print_all();
****/
/*****************************************************************/
/** function f() **/
/** returns 0 if x<theta, else returns theta **/
/*****************************************************************/
float f(x)
float x;
{
if(x<theta) return(0.0); else return(x);
}
/*****************************************************************/
/** diff **/
/*****************************************************************/
float diff(v1,v2,n)
float v1[],v2[];
int n;
{
int i;
float d;
d = 0.0;
for(i=0;i<n;i++){
d += (v1[i] - v2[i])*(v1[i] - v2[i]);
v2[i] = v1[i];
}
return(d);
}
/*****************************************************************/
/** initialize weights **/
/*****************************************************************/
init_weights()
{
int i,j;
/**** initialize weights ****/
for(j=0;j<N;j++){
for(i=0;i<M;i++){
zup[i][j] = 1.0/(0.2*sqrt((float)M));
zdn[j][i] = 0.0;
}
}
}
/*****************************************************************/
/** init_reset **/
/*****************************************************************/
init_reset()
{
int j;
for(j=0;j<N;j++){
F2reset[j] = 0;
}
nreset = 0;
}
/*****************************************************************/
/** initialize nodes **/
/*****************************************************************/
init_nodes()
{
int i,j;
/**** initialize nodes ****/
for(i=0;i<M;i++){
F1[i] = 0.0;
w1[i] = 0.0;
x1[i] = 0.0;
v1[i] = 0.0;
u1[i] = 0.0;
p1[i] = 0.0;
q1[i] = 0.0;
w[i] = 0.0;
x[i] = 0.0;
v[i] = 0.0;
u[i] = 0.0;
p[i] = 0.0;
q[i] = 0.0;
}
for(j=0;j<M;j++){
F2[j] = 0.0;
}
}
/*****************************************************************/
/** get_commandline_args **/
/*****************************************************************/
get_commandline_args(argc,argv)
int argc;
char *argv[];
{
/**** open data file & get rho ****/
/* if (!is_arg("-i",argc,argv)){
printf("ERROR no input file given [-i file]\n");
exit(1);
}
if (!is_arg("-r",argc,argv)){
printf("ERROR no rho value given [-r rho]\n");
exit(1);
}
fp = fopen(strval("-i",argc,argv),"r"); */
fp = fopen("data","r");
/* rho = floatval("-r",argc,argv); */
rho = 0.7;
}
/*****************************************************************/
/** read_input **/
/*****************************************************************/
read_input()
{
int i,j;
/**** read input vector ****/
for(i=0;i<M;i++){
fscanf(fp,"%f",&I[i]);
}
}
/*****************************************************************/
/** update_f0 **/
/*****************************************************************/
update_f0()
{
int i,j;
/**** update w nodes ****/
normw1 = 0.0;
for(i=0;i<M;i++){
w1[i] = I[i] + a*u1[i];
normw1 += w1[i] * w1[i];
}
normw1 = sqrt(normw1);
/**** update p nodes ****/
normp1 = 0.0;
for(i=0;i<M;i++){
p1[i] = u1[i];
normp1 += p1[i] * p1[i];
}
normp1 = sqrt(normp1);
/**** update x nodes ****/
for(i=0;i<M;i++){
x1[i] = w1[i] / (e+normw1);
}
/**** update q nodes ****/
normq1 = 0.0;
for(i=0;i<M;i++){
q1[i] = p1[i] / (e+normp1);
normq1 += q1[i] * q1[i];
}
normq1 = sqrt(normq1);
/**** update v nodes ****/
normv1 = 0.0;
for(i=0;i<M;i++){
v1[i] = f(x1[i]) + b*f(q1[i]);
normv1 += v1[i] * v1[i];
}
normv1 = sqrt(normv1);
/**** update u nodes ****/
for(i=0;i<M;i++){
u1[i] = v1[i] / (e+normv1);
}
}
/*****************************************************************/
/** update_f1 **/
/*****************************************************************/
update_f1()
{
int i,j;
/**** update w nodes ****/
normw = 0.0;
for(i=0;i<M;i++){
w[i] = q1[i] + a*u[i];
normw += w[i] * w[i];
}
normw = sqrt(normw);
/**** update top-down value ****/
for(i=0;i<M;i++){
topdown[i] = 0.0;
for(j=0;j<N;j++){
topdown[i] += F2[j] * zdn[j][i];
}
}
/**** update p nodes ****/
normp = 0.0;
for(i=0;i<M;i++){
p[i] = u[i] + topdown[i];
normp += p[i] * p[i];
}
normp = sqrt(normp);
/**** update x nodes ****/
for(i=0;i<M;i++){
x[i] = w[i] / (e+normw);
}
/**** update q nodes ****/
for(i=0;i<M;i++){
q[i] = p[i] / (e+normp);
}
/**** update v nodes ****/
normv = 0.0;
for(i=0;i<M;i++){
v[i] = f(x[i]) + b*f(q[i]);
normv += v[i] * v[i];
}
normv = sqrt(normv);
/**** update u nodes ****/
normu = 0.0;
for(i=0;i<M;i++){
u[i] = v[i] / (e+normv);
normu += u[i] * u[i];
}
normu = sqrt(normu);
}
/*****************************************************************/
/** update_f2 **/
/*****************************************************************/
update_f2()
{
int i,j;
float max;
/**** compute F2 ****/
for(j=0;j<N;j++){
F2[j] = 0.0;
for(i=0;i<M;i++){
F2[j]+= p[i] * zup[i][j];
}
F2val[j] = F2[j];
}
/**** compute F2winner ****/
max = 0.0;
for(j=0;j<N;j++){
if(F2[j] > max && !F2reset[j]){
max = F2[j];
F2winner = j;
}
F2[j] = 0.0;
}
F2[F2winner] = 0.8;
}
/*****************************************************************/
/** update_r **/
/*****************************************************************/
update_r()
{
int i,j;
float cnormp;
/**** compute cnormp ****/
cnormp = 0.0;
for(i=0;i<M;i++){
cnormp += c * p[i] * p[i];
}
cnormp = sqrt(cnormp);
/**** compute reset ****/
normr = 0.0;
for(i=0;i<M;i++){
r[i] = (q1[i] + c*p[i]) / (e + normq1 + c*normp);
normr += r[i] * r[i];
}
normr = sqrt(normr);
if(rho/(e+normr) > 1.0) reset = 1; else reset = 0;
if(reset){
F2reset[F2winner] = 1.0;
}
}
/*****************************************************************/
/** update_zup **/
/*****************************************************************/
update_zup()
{
int i,j;
for(i=0;i<M;i++){
zup[i][F2winner] += del_t * (p[i] - zup[i][F2winner]);
}
}
/*****************************************************************/
/** update_zdn **/
/*****************************************************************/
update_zdn()
{
int i,j;
/**** set top-down weights ****/
for(i=0;i<M;i++){
zdn[F2winner][i] += del_t * (p[i] - zdn[F2winner][i]);
}
}
/*****************************************************************/
/** print_f0 **/
/*****************************************************************/
print_f0()
{
int i,j;
/**** print values ****/
printf("**** F 0 iteration %2d ****\n",iter);
for(i=0;i<M;i++){
printf("%s%2d: I=%5.2f w1=%5.2f x1=%5.2f v1=%5.2f ",
pattern, i, I[i], w1[i], x1[i], v1[i]);
printf("u1=%5.2f p1=%5.2f q1=%5.2f\n",
u1[i], p1[i], q1[i]);
}
}
/*****************************************************************/
/** print_f1 **/
/*****************************************************************/
print_f1()
{
int i,j;
/**** print F1 values ****/
printf("w: ");
for(i=0;i<M;i++){
printf("%5.2f ",w[i]);
}
printf("\n");
printf("x: ");
for(i=0;i<M;i++){
printf("%5.2f ",x[i]);
}
printf("\n");
printf("v: ");
for(i=0;i<M;i++){
printf("%5.2f ",v[i]);
}
printf("\n");
printf("u: ");
for(i=0;i<M;i++){
printf("%5.2f ",u[i]);
}
printf("\n");
printf("p: ");
for(i=0;i<M;i++){
printf("%5.2f ",p[i]);
}
printf("\n");
printf("q: ");
for(i=0;i<M;i++){
printf("%5.2f ",q[i]);
}
printf("\n");
}
/*****************************************************************/
/** print_f2 **/
/*****************************************************************/
print_f2()
{
int i,j;
/**** print f2 values ****/
printf("F2: ");
for(j=0;j<N;j++){
printf("%5.2f ",F2val[j]);
}
printf("\n");
/**** underline winner ****/
printf(" ");
for(j=0;j<N;j++){
if(j==F2winner) printf("^WINS^");
else printf(" ");
}
printf("\n");
}
/*****************************************************************/
/** print_z **/
/*****************************************************************/
print_z(node)
int node;
{
int i,j;
printf("zup%1d:",node);
for(i=0;i<M;i++){
printf("%5.2f ",zup[i][node]);
}
printf("\n");
printf("zdn%1d:",node);
for(i=0;i<M;i++){
printf("%5.2f ",zdn[node][i]);
}
printf("\n");
}
/*****************************************************************/
/** print_input **/
/*****************************************************************/
print_input()
{
int i,j;
/**** print input ****/
printf("\n %s: ",pattern);
for(i=0;i<M;i++){
printf("%5.2f ",I[i]);
}
printf("\n");
}
/*****************************************************************/
/** print_vals **/
/*****************************************************************/
print_vals()
{
printf("rho=%5.2f normr=%5.2f\twinner=%1d",rho,normr,F2winner);
if(reset)printf(" RESET");
if(learning) printf(" learning");
printf("\n");
}
/*****************************************************************/
/** print_all **/
/*****************************************************************/
print_all(iter)
int iter;
{
int i,j;
/**** print values ****/
printf("**** iteration %2d ****\n",iter);
for(i=0;i<3;i++){
printf("%s I=%5.2f v1=%5.2f q1=%5.2f v=%5.2f ",
pattern,I[i], v1[i], q1[i], v[i]);
printf("p=%5.2f r=%5.2f \n",
p[i], r[i]);
}
printf("normr=%5.2f ",normr);
if(reset) printf("RESET\n");
printf("\n");
}
/*----------------------------------------dans additions --------*/
int is_arg(str,arg_c,arg_v)
char str[],*arg_v[];
int arg_c;
{
int result;
result = 0;
while (arg_c > 0)
{
result = (strcmp(str,arg_v[--arg_c]) == 0) ? 1 : 0;
}
return(result);
}
float floatval(str,arg_c,arg_v)
char str[],*arg_v[];
int arg_c;
{
float result;
result = 0.0;
while (arg_c > 0)
{
if (strcmp(str,arg_v[--arg_c]) == 0) break;
}
if (arg_c > 0)
{
if (sscanf(arg_v[arg_c+1],"%lf",result) < 1)
printf("\n\7ERR: syntax error - expecting a float, got %s\n",
arg_v[arg_c+1]);
}
return(result);
}
char strval(str,arg_c,arg_v)
char str[],*arg_v[];
int arg_c;
{
char result[128];
int ll;
for (ll = 0; ll < 128; result[ll++] = 'A'); /* clear out result str */
result[127] = '\n'; /* null terminate */
while (arg_c > 0)
{
if (strcmp(str,arg_v[--arg_c]) == 0) break;
}
if (arg_c > 0)
{
if (sscanf(arg_v[arg_c+1],"%s",result) < 1)
printf("\n\7ERR: syntax error - expecting a string, got nothing \n");
}
return(result);
}
------------------------------
End of Neuron Digest [Volume 7 Issue 17]
****************************************
