>

restart:with(LinearAlgebra):with(Statistics):with(RandomTools):
Dim:=506:
ourdata:=readdata("C:\\Temp\\housing.txt",Dim):
ourMatrix:=Matrix(ourdata):
# Scale all data to zero mean and unit variance.
M:=Transpose(ourMatrix):
T:=M[14]:
meant:=(max(T)+min(T))/2:tstd:=(max(T)-min(T))/2:
ones:=[seq(1,i=1..Dim)]:TT:=(convert(M[14],listlist)-ones.meant)/tstd:
M6:=(convert(M[6],listlist)-ones.Mean(M[6]))/StandardDeviation(M[6]):
M9:=(convert(M[9],listlist)-ones.Mean(M[9]))/StandardDeviation(M[9]):
M13:=(convert(M[13],listlist)-ones.Mean(M[13]))/StandardDeviation(M[13]):
X:=Transpose(Matrix([[seq(1,i=1..Dim)],M6,M9,M13])):
ww[1]:=0.1*Matrix(4,1,Generate(rational(denominator=10),makeproc=true)):
epochs:=10:eta:=0.001:k:=1:
for n from 1 to epochs do
for j from 1 to Dim do
yk:=evalf(map(x->tanh(x),X[j].ww[k]));
err:=evalm(yk-[TT[j]])[1];
g:=Transpose(X[j]).(1-yk.yk)*err;
ww[k+1]:=ww[k]-eta*Matrix(4,1,g);
k:=k+1;
end do;end do;

>

with(plots):NumPoints:=epochs*Dim:
points1:=[[a,ww[a][1][1]]$a=1..NumPoints]:
points2:=[[a,ww[a][2][1]]$a=1..NumPoints]:
points3:=[[a,ww[a][3][1]]$a=1..NumPoints]:
points4:=[[a,ww[a][4][1]]$a=1..NumPoints]:
plot({points1,points2,points3,points4},x=0..NumPoints,style=point,symbol=point,labels=["Number of Iterations","Weights"]);

>

restart:with(LinearAlgebra):
X:=Matrix([[1,1,1,1,1],[1,-1,-1,1,-1],[-1,1,-1,1,1]]);
W:=Transpose(X).X/5-3*IdentityMatrix(5)/5;
with(combinat,randperm):
n:=randperm(5);
# The input vector.
xinput:=Matrix([-1,-1,-1,1,-1]);xtest:=xinput:
hsgn:=(v,x)->piecewise(v>0,1,v=0,x,v<0,-1):
for j from 1 to 5 do
m:=n[j]:
v:=W[m].Transpose(xtest):
xtest([m]):=hsgn(v(1),xtest(m)):end do:
xoutput=xtest;
if convert(xtest,list)=convert(X[1],list)
then print("Net has converged to X1"):
elif convert(xtest,list)=convert(X[2],list)
then print("Net has converged to X2"):
elif convert(xtest,list)=convert(X[3],list)
then print("Net has converged to X3"):
else print("Iterate again: May have converged to a spurious steady-state"):
end if:

>

restart:x:=array(0..100000):y:=array(0..100000):
b1:=-2:b2:=3:w11:=-20:w21:=-6:w12:=6:imax:=10000:
x[0]:=1:y[0]:=0.2:
for i from 0 to imax do
x[i+1]:=evalf(b1+w11/(1+exp(-x[i]))+w12/(1+exp(-y[i]))):
y[i+1]:=evalf(b2+w21/(1+exp(-x[i]))):end do:
with(plots):
points:=[[x[n],y[n]]$n=50..imax]:
pointplot(points,style=point,symbol=point,color=blue,axes=BOXED,font=[TIMES,ROMAN,15]);

>

restart:start:=7:Max:=7:b2:=3:b1:=2:w12:=-4:w21:=5:
halfN:=9999:N1:=1+halfN:itermax:=2*halfN+1:
x[0]:=-3:y[0]:=-2:
# Ramp w11 up.
for n from 0 to halfN do
w11:=start-n*Max/halfN:
x[n+1]:=evalf(b1+w11*tanh(x[n])+w12*tanh(0.3*y[n])):
y[n+1]:=evalf(b2+w21*tanh(x[n])):
end do:
with(plots):
points:=[[start-j*Max/N1,x[j]]$j=0..halfN]:
P1:=pointplot(points,style=point,symbol=point,color=blue,axes=BOXED,font=[TIMES,ROMAN,15]):
# Ramp w11 udown.
for n from N1 to itermax do
w11:=(n-N1)*Max/halfN:
x[n+1]:=evalf(b1+w11*tanh(x[n])+w12*tanh(0.3*y[n])):
y[n+1]:=evalf(b2+w21*tanh(x[n])):
end do:
with(plots):
points:=[[start+(j-N1)*Max/N1,x[N1+j]]$j=0..halfN]:
P2:=pointplot(points,style=point,symbol=point,color=blue,axes=BOXED,font=[TIMES,ROMAN,15]):
display({P1,P2},labels=['w11','x[n]']);