Chapter 8: Simulation Runs: Function Approximation:
This simulation run uses a finite amount of discrete data
collected in an x-y grid to approximate the function
on the interval -3.0 £ x £ 3.0 and
-3.0 £ y £ 3.0 . Hence, there are two inputs
and one analog output.
The training set of 256 samples consists of the triples
(xi,yj,zij), where
| xi |
= |
-3.0 + .4(i-1), 1 £ i £ 16 |
| yj |
= |
-3.0 + .4(j-1), 1 £ j £ 16 |
| zij |
= |
f(xi,yj). |
The test set of 51 samples is constructed in a simpler fashion:
| xi |
= |
-3.0 + .12(i-1), 1 £ i £ 51 |
| yi |
= |
-3.0 + .12(j-1), 1 £ i £ 51 |
| zii |
= |
f(xi,yi). |
The actual graph of this function is
presented in Figure 8.1 using
the the graphic generation capabilities of
MATLAB with 3721 data points.
Figure 8.1:
8.1 The Application Code:
The application is generated using three files:
-
test_generator.c:
- This function generates
the training files used to build the CMAC model,
the testing file used to validate the CMAC model,
and a file containing the data points required to accurately
graph the true function surface.
- simul.c:
- This function builds the CMAC model.
- testmodel.c:
- This function generates data files
which are used to graph the surface generated by the CMAC model.
The graphing itself will be done via MATLAB using a procedure called
picture.m.
The procedure picture.m is listed below with explanatory comments
prefaced by %% to the right of each line.
fid = fopen('data','r'); %% open the file called data containing the
%% x y z triples needed to graph the surface
%% We assume there are N x data points,
%% that are linearly ordered from xmin to xmax;
%% N y data points linearly ordered from
%% ymin to ymax for a total of N*N
%% x y z triples. Beware: We think
%% of our data as being indexed from 0 to N-1
%% whilke MATLAB uses the standard Fortran
%% indexing scheme of 1 to N.
%% The triples are ordered as follows:
%% x(0),y(0), z(0,0)
%% x(0),y(1), z(0,1)
%% x(0),y(2), z(0,2)
%% .
%% .
%% .
%% x(0),y(N-1), z(0,N-1)
%% x(1),y(0), z(1,0)
%% x(1),y(1), z(1,1)
%% x(1),y(2), z(1,2)
%% .
%% .
%% .
%% x(1),y(N-1), z(1,N-1)
%% .
%% .
%% .
%% x(N-1),y(0), z(N-1,0)
%% x(N-1),y(1), z(N-1,1)
%% x(N-1),y(2), z(N-1,2)
%% .
%% .
%% .
%% x(N-1),y(N-1), z(N-1,N-1)
for i = 1:N %% You must supply the value of N here
for j = 1:N
X(i,j)= fscanf(fid,'%f',1); %% Reads from the file the
%% contents of data field 1
%% and stores the x values
%% into a N x N array; so row i of this
%% matrix is constant row having x(i-1)
%% repeated N times.
Y(i,j)= fscanf(fid,'%f',1); %% Reads from the file the
%% contents of data field 2 and stores the
%% y values
%% into a N x N array; row i of this
%% matrix has the form
%% y(0), y(1),...,y(N-1)
Z(i,j)= fscanf(fid,'%f',1); %% Read from the file the
%% contents of data field 3 and stores the
%% z values
%% into a N x N array; row i of this
%% matrix has the form
%% z(i-1,0), z(i-1,1),...,z(i-1,N-1)
end
end
surf(X,Y,Z); %% Parametric surface plot with
%% surface coordinates (X(i,j),Y(i,j),Z(i,j))
view(40,20); %% Observer views surface from this position
fclose('all'); %% Close the data file
In the MATLAB session below, the MATLAB script picture.m is
loaded and executed by simply typing its name at the MATLAB prompt.
The default extension .m is not required to be entered.
To use this script to generate surface plots, edit picture.m
to insert your chosen data file name and your data point size N and use it
as follows:
albert% MATLAB
>> picture %% edit file to add your N
%% and your file name
>> print -deps file_name.eps %% print plot to file_name.eps
8.1.1 The MakeFile: MakeApplication
There are three separate make files:
The Make File for test_generator.c
# -------------------------- #
# paths for this simulation #
# -------------------------- #
INCLUDE_PATH_UTILITY = /home/peterson/programs/utility
INCLUDE_PATH_CMAC = /home/peterson/programs/cmacclass
INCLUDE_PATH_CONSTANTS = /home/peterson/Xheaders
INCLUDES = -I$(INCLUDE_PATH_UTILITY) -I$(INCLUDE_PATH_CMAC) \
-I$(INCLUDE_PATH_CONSTANTS)
LIBRARY_PATH_UTILITY = /home/peterson/programs/utility
LIBRARY_PATH_CMAC = /home/peterson/programs/cmacclass
SIMLIBS = -lcmac -lutility
# ----------- #
# Definitions #
# ----------- #
CC = CC
LIBS = -ll -lm -lgen
COMPILE_FLAGS_LINK = -g $(INCLUDES)
COMPILE_FLAGS_SOURCES = -c -g $(INCLUDES)
LIBRARY_FLAGS_SOURCES = -L$(LIBRARY_PATH_UTILITY) \
-L$(LIBRARY_PATH_CMAC)
# ------------- #
# Define target #
# ------------- #
TARGET = test_generator
FILESOBJ = test_generator.o
SOURCES = $(FILESOBJ:.o=.c)
$(TARGET): $(SOURCES) $(FILESOBJ)
$(CC) $(COMPILE_FLAGS_LINK) -o $(TARGET) $(FILESOBJ) \
$(LIBRARY_FLAGS_SOURCES) $(SIMLIBS) $(LIBS)
# --------------------------------------------- #
# Dependencies of source files on header files #
# --------------------------------------------- #
$(FILESOBJ):
$(CC) $(COMPILE_FLAGS_SOURCES) $(LIBRARY_FLAGS_SOURCES) \
$(SIMLIBS) $(LIBS) $*.c
test_generator.c: simul.h
@touch $@
The Make File for simul.c
# -------------------------- #
# paths for this simulation #
# -------------------------- #
INCLUDE_PATH_UTILITY = /home/peterson/programs/utility
INCLUDE_PATH_CMAC = /home/peterson/programs/cmacclass
INCLUDE_PATH_CONSTANTS = /home/peterson/Xheaders
INCLUDES = -I$(INCLUDE_PATH_UTILITY) -I$(INCLUDE_PATH_CMAC) \
-I$(INCLUDE_PATH_CONSTANTS)
LIBRARY_PATH_UTILITY = /home/peterson/programs/utility
LIBRARY_PATH_CMAC = /home/peterson/programs/cmacclass
SIMLIBS = -lcmac -lutility
# ----------- #
# Definitions #
# ----------- #
CC = CC
LIBS = -ll -lm -lgen
COMPILE_FLAGS_LINK = -g $(INCLUDES)
COMPILE_FLAGS_SOURCES = -c -g $(INCLUDES)
LIBRARY_FLAGS_SOURCES = -L$(LIBRARY_PATH_UTILITY) \
-L$(LIBRARY_PATH_CMAC)
# ------------- #
# Define target #
# ------------- #
TARGET = usecmac
FILESOBJ = simul.o
SOURCES = $(FILESOBJ:.o=.c)
$(TARGET): $(SOURCES) $(FILESOBJ)
$(CC) $(COMPILE_FLAGS_LINK) -o $(TARGET) $(FILESOBJ) \
$(LIBRARY_FLAGS_SOURCES) $(SIMLIBS) $(LIBS)
# --------------------------------------------- #
# Dependencies of source files on header files #
# --------------------------------------------- #
$(FILESOBJ):
$(CC) $(COMPILE_FLAGS_SOURCES) $(LIBRARY_FLAGS_SOURCES) \
$(SIMLIBS) $(LIBS) $*.c
simul.c: simul.h
@touch $@
The Make File for testmodel.c
# -------------------------- #
# paths for this simulation #
# -------------------------- #
INCLUDE_PATH_UTILITY = /home/peterson/programs/utility
INCLUDE_PATH_CMAC = /home/peterson/programs/cmacclass
INCLUDE_PATH_CONSTANTS = /home/peterson/Xheaders
INCLUDES = -I$(INCLUDE_PATH_UTILITY) -I$(INCLUDE_PATH_CMAC) \
-I$(INCLUDE_PATH_CONSTANTS)
LIBRARY_PATH_UTILITY = /home/peterson/programs/utility
LIBRARY_PATH_CMAC = /home/peterson/programs/cmacclass
SIMLIBS = -lcmac -lutility
# ----------- #
# Definitions #
# ----------- #
CC = CC
LIBS = -ll -lm -lgen
COMPILE_FLAGS_LINK = -g $(INCLUDES)
COMPILE_FLAGS_SOURCES = -c -g $(INCLUDES)
LIBRARY_FLAGS_SOURCES = -L$(LIBRARY_PATH_UTILITY) \
-L$(LIBRARY_PATH_CMAC)
# ------------- #
# Define target #
# ------------- #
TARGET = testmodel
FILESOBJ = testmodel.o
SOURCES = $(FILESOBJ:.o=.c)
$(TARGET): $(SOURCES) $(FILESOBJ)
$(CC) $(COMPILE_FLAGS_LINK) -o $(TARGET) $(FILESOBJ) \
$(LIBRARY_FLAGS_SOURCES) $(SIMLIBS) $(LIBS)
# --------------------------------------------- #
# Dependencies of source files on header files #
# --------------------------------------------- #
$(FILESOBJ):
$(CC) $(COMPILE_FLAGS_SOURCES) $(LIBRARY_FLAGS_SOURCES) \
$(SIMLIBS) $(LIBS) $*.c
testmodel.c: simul.h
@touch $@
8.1.2 The Application Code:
test_generator.c
#include "simul.h"
int main(int argc,char *argv[])
{
int i,j;
unsigned int seed;
float xmin,xmax,ymin,ymax,xdiv,ydiv,x,y,z;
char *test_file_name,*train_file_name,*full_data;
FILE *fdtrain,*fdtest,*fdfull;
// echo command line arguments
printf("argc = %d\n",argc);
if( !(argc==4) ){
printf(" Incorrect Number of Command Line Arguments!\n");
exit(1);
}
else{
switch(argc){
case 4:
test_file_name = argv[1];
printf("test_file_name file = %s\n",test_file_name);
train_file_name = argv[2];
printf("train_file_name file = %s\n",train_file_name);
full_data = argv[3];
printf("full_data file = %s\n",full_data);
break;
default:
printf("We should never be in this case!\n");
exit(1);
}
}
if((fdtrain=fopen(train_file_name,"w")) == NULL){
printf("\nCan't open file %s\n",train_file_name);
exit(0);
}
if((fdtest=fopen(test_file_name,"w")) == NULL){
printf("\nCan't open file %s\n",test_file_name);
exit(0);
}
if((fdfull=fopen(full_data,"w")) == NULL){
printf("\nCan't open file %s\n",full_data);
exit(0);
}
xmin = -3.0;
xmax = 3.0;
ymin = -3.0;
ymax = 3.0;
xdiv = .1;
ydiv = .1;
/* generate the functional data */
seed = 50;
srand(seed);
/*===============================================================
original functions
z = 3*pow(1-x,2)*exp(-pow(x,2)-pow(y+1,2))
-10*(x/5-pow(x,3)-pow(y,5))*exp(-pow(x,2)-pow(y,2))
-1/3*exp(-pow(x+1,2)-pow(y,2));
z = (x/2-pow(x,2)-pow(y,2))*exp(-.5*pow(x,2)-.5*pow(y,2))*pow(cos(y),2);
z = exp(.1*pow(x,2)+.1*pow(y,2))*sin(2*x+y);
================================================================*/
for(i=1;i<=61;++i){
for(j=1;j<=61;++j){
x = xmin + xdiv*(i-1);
y = ymin + ydiv*(j-1);
z = exp(.1*pow(x,2)+.1*pow(y,2))*sin(2*x+y);
fprintf(fdfull,"%f %f %f\n",x,y,z);
}
}
/* generate the training data */
xdiv = .4;
ydiv = .4;
for(i=1;i<=16;++i){
for(j=1;j<=16;++j){
x = xmin + xdiv*(i-1);
y = ymin + ydiv*(j-1);
z = exp(.1*pow(x,2)+.1*pow(y,2))*sin(2*x+y);
fprintf(fdtrain,"%f %f %f\n",x,y,z);
}
}
/* generate the testing data */
xdiv = .12;
ydiv = .12;
for(i=1;i<=51;++i){
x = xmin + xdiv*(i-1);
y = ymin + ydiv*(i-1);
z = exp(.1*pow(x,2)+.1*pow(y,2))*sin(2*x+y);
fprintf(fdtest,"%f %f %f\n",x,y,z);
}
fclose(fdtrain);
fclose(fdtest);
fclose(fdfull);
return(0);
}
simul.c
#include "simul.h"
#define DESIRED_TOL (1.0e-6)
#define STOP_TOL (1.0e-5)
#define RUN_MAX (100)
#define FREQ (5)
int main(int argc,char *argv[])
{
int run,trainsize,testsize;
int echo_input,do_train;
float **intr,**inte,**outtr,**outte,rms,rmstest;
echo_input = 1;
do_train = 1;
// set up CMAC architecture
CMAC cmac(argv[1]);
cmac.read_training_data(&intr,&outtr);
cmac.read_testing_data(&inte,&outte);
cmac.initialize();
cmac.number();
if(echo_input)
cmac.echo();
cmac.gettrainsize(&trainsize).gettestsize(&testsize);
//compute rms on test set
rmstest = cmac.compute_rms(testsize,inte,outte);
//compute cmac rms on training
rms = cmac.compute_rms(trainsize,intr,outtr);
if(do_train){
for(run=0;run<RUN_MAX;++run){
//compute rms on test set
rmstest = cmac.compute_rms(testsize,inte,outte);
//compute cmac rms on training
rms = cmac.compute_rms(trainsize,intr,outtr);
if(rms>STOP_TOL){
cmac.train(1,DESIRED_TOL,trainsize,intr,outtr);
if(run%FREQ==0){
printf("rms[%3d] = %12.6e ",run,rms);
printf("rmstest[%3d] = %12.6e\n",run,rmstest);
}
}/* rms > STOP_TOL loop */
}//run loop
printf("rms[%3d] = %12.6e ",run,rms);
printf("rmstest[%3d] = %12.6e\n",run,rmstest);
cmac.write_wts();
}//
else{
//compute rms on test set
rmstest = cmac.compute_rms(testsize,inte,outte);
//compute cmac rms on training
rms = cmac.compute_rms(trainsize,intr,outtr);
printf("rms[%3d] = %12.6e ",run,rms);
printf("rmstest[%3d] = %12.6e\n",run,rmstest);
}
return(1);
}
testmodel.c
#include "simul.h"
int main(int argc,char *argv[])
{
int i,k,count,run,testsize,out_size;
float x,y,z,**inte,**outte,rms;
float *values;
char *source_file,*destination_file;
FILE *in_file_pointer,*out_file_pointer;
// echo command line arguments
printf("argc = %d\n",argc);
if( !(argc==4) ){
printf(" Incorrect Number of Command Line Arguments!\n");
exit(1);
}
else{
switch(argc){
case 4:
//argv[1] contains the name of the CMAC
//initialization file.
source_file = argv[2];
printf("source file = %s\n",source_file);
destination_file = argv[3];
printf("source file = %s\n",destination_file);
break;
default:
printf("We should never be in this case!\n");
exit(1);
}
}
/*=======================================================
open the file which contains ordered triples
x y z
where x, y and z are floating point numbers.
The pair (x,y) denotes a data point in the
domain of the function f(x,y). The scalar
value z denotes the true value of the function
f at the domain value (x,y).
=======================================================*/
if((in_file_pointer=fopen(source_file,"r")) == NULL){
printf("\nCan't open file %s\n",source_file);
exit(1);
}
/*=======================================================
open an output file to put the model results into
in the following format
x y w
where x, y and w are floating point numbers.
The pair (x,y) denotes a data point in the
domain of the function f(x,y). The scalar
value w denotes the value of the CMAC model
for the function f at the domain value (x,y).
It is important to realize that w and z need not be
the same.
=======================================================*/
if((out_file_pointer=fopen(destination_file,"w")) == NULL){
printf("\nCan't open file $s\n",destination_file);
exit(1);
}
// initialize counters
count = 0;
// count the number of samples in the source file
while( fscanf(in_file_pointer,"%f %f %f",&x,&y,&z) !=EOF)
++count;
fclose(in_file_pointer);
// reopen the source file with read only status
if((in_file_pointer=fopen(source_file,"r")) == NULL){
printf("\nCan't open file %s\n",source_file);
exit(1);
}
fclose(in_file_pointer);
// set up CMAC architecture and read in weights
CMAC cmac(argv[1]);
cmac.read_training_data(&inte,&outte).initialize().number();
cmac.echo();
/*=====================================================
Generate a file of test inputs and cmac outputs for
3d graphing purposes: we assume there are only 2 inputs
and 1 output
====================================================*/
printf("Howdy! We have finished with the cmac inits\n");
cmac.getoutputsize(&out_size);
printf("count = %d\n",count);
values = new float[out_size];
for(k=0;k<count;++k){
values = cmac.cmaceval(1,inte[k]);
outte[k][0] = values[0];
for(i=0;i<2;++i){
fprintf(out_file_pointer,"%8.3f ",inte[k][i]);
//printf("%8.3f ",inte[k][i]);
}
fprintf(out_file_pointer,"%8.3f\n",values[0]);
fprintf(out_file_pointer,"\n");
}
fclose(out_file_pointer);
//compute rms on model data
rms = cmac.compute_rms(count,inte,outte);
delete inte;
delete outte;
return(1);
}
8.1.3 Configuration Files:
The configuration files needed by the simulation program are
ASCII text files containing the information such as that given below:
-
func.cfg:
- basic configuration
-
funcinit.txt:
- file containing names of
configuration files for CMAC architectures;
one file name per output component
- func_train.txt:
- training file
- func_test.txt:
- testing file
- func.fin:
- CMAC weights can be initialized
using contents of this file
- func.fin:
- CMAC weights for a training run
are stored in this file
- 121:
- number of training samples
- 50:
- number of testing samples
- 2:
- number of input components
- 1:
- number of output components
- .95:
- the learning rate
- 0.0:
- the setting for setup.inflate_bottom
- 0.0:
- the setting for setup.inflate_top
- setfunc.cfg:
- specifies CMAC structure
-
3:
- the number of levels
- 26:
- the hash size
- .8:
- the receptive field width
- funcinit.txt:
- contains a file name for each output component;
here, there is only one output component, so there is just
one file name --- setfunc.cfg
-
setfunc.cfg:
- CMAC configuration file for output 1
The actual terminal output for the simulation run
corresponding to the configuration files above is presented below.
First, we generate training and testing data for this function
using test_generator().
albert% test_generator test1.txt train1.txt full1.txt
argc = 4
test_file_name file = test1.txt
train_file_name file = train1.txt
full_data file = full1.txt
Next, we train the given CMAC model on the data using
usecmac().
albert% usecmac func.cfg
startup_file = func.cfg
funcinit.txt
train1.txt
test1.txt
func.fin
func.fin
setup.training_set_size = 256 !!! setup.training_set_size
setup.testing_set_size = 51 !!! setup.testing_set_size
setup.in_dimensions = 2 !!! setup.in_dimensions
setup.out_dimensions = 1 !!! setup.out_dimensions
setup.learning_rate = 0.950000 !!! setup.learning_rate
setup.echo_input = 1 !!! setup.echo_input
setup.do_training = 1 !!! setup.do_training
setup.read_in_wts = 0 !!! setup.read_in_wts
setup.autosize = 1 !!! setup.autosize
setup.inflate_bottom = 0 !!! setup.inflate_bottom
setup.inflate_top = 0 !!! setup.inflate_top
setfunc.cfg
Input[0]::min/max of input widths= -3.000000/ 3.000000
Input[1]::min/max of input widths= -3.000000/ 3.000000
Input[0]::min/max of input widths= -3.000000/ 3.000000
Input[1]::min/max of input widths= -3.000000/ 3.000000
setup.startup_file = func.cfg
setup.cmac_file = funcinit.txt
setup.training_file = train1.txt
setup.testing_file = test1.txt
setup.initfile = func.fin
setup.wtfile = func.fin
setup.training_set_size = 256
setup.testing_set_size = 51
setup.learning_rate = 0.950000
setup.in_dimensions = 2
setup.out_dimensions = 1
input interval[ 0] = [ -3.000000, 3.000000]
input interval[ 1] = [ -3.000000, 3.000000]
setup.file[ 0] = setfunc.cfg
*************************
CMAC[ 0] parameters
*************************
number levels = 3
hash = 26
offset = 0.333333
width = 0.800000
LEVEL INPUT OFFSET FIELD WIDTH HASH_SIZE
0 0 0.000000 0.800000 26
0 1 0.000000 0.800000 26
1 0 0.266667 0.800000 26
1 1 0.266667 0.800000 26
2 0 0.533333 0.800000 26
2 1 0.533333 0.800000 26
sensors[output = 0][level = 0][input = 0] = 216368
sensors[output = 0][level = 0][input = 1] = 909127728
sensors[output = 0][level = 1][input = 0] = 216384
sensors[output = 0][level = 1][input = 1] = 807411744
sensors[output = 0][level = 2][input = 0] = 216400
sensors[output = 0][level = 2][input = 1] = 775303216
flattened sensors[output = 0, levels = 3][0 input] = 23
flattened sensors[output = 0, levels = 3][1 input] = 23
flattened sensors[output = 0, levels = 3, input = 2] = 529
Total flattened sensors for 1 outputs = 529
rms[ 0] = 1.677679e+00 rmstest[ 0] = 1.891320e+00
rms[ 1] = 1.399867e+00 rmstest[ 1] = 1.795955e+00
rms[ 2] = 1.382564e+00 rmstest[ 2] = 1.944340e+00
rms[ 3] = 1.357107e+00 rmstest[ 3] = 1.805224e+00
rms[ 4] = 1.346904e+00 rmstest[ 4] = 1.796974e+00
rms[ 5] = 1.352754e+00 rmstest[ 5] = 1.822708e+00
rms[ 6] = 1.354311e+00 rmstest[ 6] = 1.830258e+00
rms[ 7] = 1.353011e+00 rmstest[ 7] = 1.825351e+00
rms[ 8] = 1.352653e+00 rmstest[ 8] = 1.824166e+00
rms[ 9] = 1.353043e+00 rmstest[ 9] = 1.825368e+00
rms[ 10] = 1.353172e+00 rmstest[ 10] = 1.825570e+00
rms[ 11] = 1.353148e+00 rmstest[ 11] = 1.825254e+00
rms[ 12] = 1.353192e+00 rmstest[ 12] = 1.825204e+00
rms[ 13] = 1.353262e+00 rmstest[ 13] = 1.825271e+00
rms[ 14] = 1.353309e+00 rmstest[ 14] = 1.825279e+00
rms[ 15] = 1.353344e+00 rmstest[ 15] = 1.825267e+00
rms[ 16] = 1.353376e+00 rmstest[ 16] = 1.825270e+00
rms[ 17] = 1.353405e+00 rmstest[ 17] = 1.825277e+00
rms[ 18] = 1.353428e+00 rmstest[ 18] = 1.825279e+00
rms[ 19] = 1.353447e+00 rmstest[ 19] = 1.825280e+00
rms[ 20] = 1.353464e+00 rmstest[ 20] = 1.825281e+00
rms[ 21] = 1.353477e+00 rmstest[ 21] = 1.825283e+00
rms[ 22] = 1.353488e+00 rmstest[ 22] = 1.825283e+00
rms[ 23] = 1.353498e+00 rmstest[ 23] = 1.825283e+00
rms[ 24] = 1.353505e+00 rmstest[ 24] = 1.825284e+00
rms[ 25] = 1.353505e+00 rmstest[ 25] = 1.825284e+00
Finally, we generate the data needed to plot the surface
corresponding to the CMAC model using testmodel().
This function call requires that we slighly modify the original
func.cfg configuration file as follows:
funcinit.txt
full1.txt <==== New training file is full1.txt
test1.txt
func.fin
func.fin
3721!!! setup.training_set_size <==== New training size
51!!! setup.testing_set_size
2!!! setup.in_dimensions
1!!! setup.out_dimensions
.95!!! setup.learning_rate
0!!! setup.echo_input
0!!! setup.do_training
1!!! setup.read_in_wts <===== Read in the trained CMAC weights
0!!! setup.autosize <==== Use a fixed domain size
-3.1!!! setup.inflate_bottom <==== Set common_start
3.1!!! setup.inflate_top <==== Set common_end
albert% testmodel func2.cfg full1.txt MATLAB1.txt
The CMAC model built to approximate this function using
three levels, a hash size of 26 and a receptive field width of 0.8
is shown in Figure 8.2.
This model is the result of the sample session
shown above.
Figure 8.2:
8.2 64 Level Approximation:
The function data
generated above was used to calculate the
CMAC response for the data points (xi,yj) for
a CMAC simulation run using the
basic configuration below:
-
setfunc.cfg:
- specifies CMAC structure
-
64: the number of levels
- 373: hash size
- 0.3 field width
The resulting surface model is shown in Figure 8.3.
Figure 8.3:
8.3 20 Level Approximation:
What happens if the number of levels and the receptive width are decreased?
An entire series of CMAC simulation runs can be completed using
20 levels and the
basic configuration:
-
setfunc.cfg:
- specifies CMAC structure
-
20: the number of levels
- 373: hash size
- 0.2 width
As is seen in
Figure 8.4,
the approximation is now much worse, with clearly defined
spikes in the surface plot.
There are significant hashing collisions in this model and
a very fine field width. There are about 900 sensors per
level with a hash size of 373. This model is not very good.
Figure 8.4:
We will recalculate this model using a larger receptive field width:
-
setfunc.cfg:
- specifies CMAC structure
-
20: the number of levels
- 373: hash size
- 0.4 width
As is seen in
Figure 8.5,
the approximation is now much worse, with clearly defined
spikes in the surface plot.
Figure 8.5:
8.4 Eight or Fewer Level Approximation:
If the number of levels is further decreased, there is a concommittant
further decrease in performance.
An entire series of CMAC simulation runs can also be completed using
just eight levels and the
basic configuration
-
setfunc.cfg:
- specifies CMAC structure
-
8: the number of levels
- 373: hash size
- 1.2 width
Figure 8.6:
