static Func<double,double> G=(x)=>-Cos(x); //anti-derivative of g
static void Main(){
int n=5; //number of sets of parameters
var ann=new network(n,f,df,F); //creating a new "network" using n and our activation function f
double a=-PI,b=2*PI; //a: "start" value, b: "end" value
int nx=30; //length of xs and ys
var xs=new double[nx];
var ys=new double[nx];
for(int i=0;i<nx;i++){
xs[i]=a+(b-a)*i/(nx-1); //interval of x inbetween a and b
ys[i]=g(xs[i]); //function values of function to fit
Write($"{xs[i]} {ys[i]} {dg(xs[i])} {G(xs[i])}\n");
}
Write("\n\n");
for(int i=0;i<ann.n;i++){
ann.p[3*i+0]=a+(b-a)*i/(ann.n-1); //a
ann.p[3*i+1]=1; //b
ann.p[3*i+2]=1; //w
}
ann.p.fprint(Console.Error,"p=");
ann.train(xs,ys); //calling "train" which minimizes the deviation given our x's and y's
double offset = G(xs[0])-ann.feedF(xs[0]);
ann.p.fprint(Console.Error,"p=");
for(double z=a;z<=b;z+=1.0/64)
Write($"{z} {ann.feed(z)} {ann.feeddf(z)} {ann.feedF(z)+offset}\n"); //calling "feed" which returns the output signal
}//Main
static void Main()
{
WriteLine("______ Assignment A ______\n");
WriteLine("Testing the neural network for fitting to a function:\n");
Func <double, double> F_fit = delegate(double x){
return(Cos(5 * x - 1) * Exp(-x * x));
};
int n = 5;
var ann = new network(n);
double a = -1, b = 1;
int nx = 20;
vector xs = new vector(nx);
vector ys = new vector(nx);
for (int i = 0; i < nx; i++)
{
xs[i] = a + (b - a) * i / (nx - 1);
ys[i] = F_fit(xs[i]);
Error.Write($"{xs[i]} {ys[i]}\n");
}
Error.Write("\n\n");
for (int i = 0; i < ann.n; i++)
{
ann.p[3 * i + 0] = a + (b - a) * i / (ann.n - 1);
ann.p[3 * i + 1] = 1;
ann.p[3 * i + 2] = 1;
}
ann.p.print("Before training: p =");
(int nsteps, int ncalls) = ann.train(xs, ys);
ann.p.print("After training: p =");
WriteLine($"Minimization steps: {nsteps}");
WriteLine($"Function calls: {ncalls}");
for (double z = a; z <= b; z += 1.0 / 64)
{
Error.Write($"{z} {ann.feed(z)}\n");
}
Error.Write("\n\n");
WriteLine("The fitted function can be seen in the figure Fit.svg.");
Write("\n\n\n");
WriteLine("______ Assignment B ______\n");
WriteLine("We now use different feeders to get the derivative and antiderivative.\nThese can be seen in the figures Derivative.svg and Antiderivative.svg");
for (double z = a; z <= b; z += 1.0 / 64)
{
Error.Write($"{z} {ann.feedDeriv(z)}\n");
}
Error.Write("\n\n");
for (double z = a; z <= b; z += 1.0 / 64)
{
Error.Write($"{z} {ann.feedInt(z)}\n");
}
Error.Write("\n\n");
}
public static int Main()
{
Func <double, double> activate = delegate(double x){
return(Exp(-x * x));
};
Func <double, double> df = delegate(double x){
return(-2 * Exp(-x * x) * x);
};
Func <double, double> adf = delegate(double x){
return(Sqrt(PI) * math.erf(x) / 2);
};
Func <double, double> fitfun = delegate(double x){
return(x * Exp(-x * x)); // I'm not terribly imaginative with my functions
};
Write("Part A:\n");
int n = 8; // Wikibooks said this was a typical amount
var ann = new network(n, activate, df, adf);
double a = -2;
double b = 2;
int nx = 50;
double[] xs = new double[nx];
double[] ys = new double[nx];
for (int i = 0; i < nx; i++)
{
xs[i] = a + (b - a) * i / (nx - 1);
ys[i] = fitfun(xs[i]);
Error.Write("{0}\t{1}\n", xs[i], ys[i]);
}
Error.Write("\n\n");
for (int i = 0; i < n; i++)
{
ann.p[3 * i] = a + (b - a) * i / (n - 1);
ann.p[3 * i + 1] = 1.0;
ann.p[3 * i + 2] = 1.0;
}
ann.p.print("Initial p=");
vector time = ann.train(xs, ys); // time=[minimizeriterations, functioncalls]
ann.p.print("Post-training p=");
Write($"The minimiztion took {time[0]} iterations, and the deviation function was called {time[1]} times\n");
double z = a;
for (int i = 1; i <= 100; i++)
{
Error.Write($"{z}\t{ann.feed(z)}\n");
z += (b - a) / 100;
}
Write("\n The calculated function can be seen in A.svg\n\n");
Write("Part B:\n");
// Create derivative and anti-derivative functions
Func <double, double> dfun = delegate(double x){
return(Exp(-x * x) * (1 - 2 * x * x));
};
Func <double, double> adfun = delegate(double x){
return(-Exp(-x * x) / 2.0);
};
Error.Write("\n\n");
z = a;
for (int i = 1; i <= 100; i++) // For the derivative
{
Error.Write($"{z}\t{ann.dfeed(df, z)}\t{dfun(z)}\n");
z += (b - a) / 100;
}
Error.Write("\n\n");
z = a;
for (int i = 1; i <= 1000; i++) // For the antiderivative
{
Error.Write($"{z}\t{ann.adfeed(adf, z)}\t{adfun(z)}\n");
z += (b - a) / 1000;
}
Write("The resulting derivates and antiderivatives can be seen in B.svg\n");
return(0);
}
