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import java.util.ArrayList;
public class CalculusExamples {
// (y^(0.5)*x^(1.5) + y^(2.2)*x^(-0.7))^(-2.6)
public static FunctionExpression equationExample1(){
FunctionExpression Q1=FunctionExpression.exp(new Function("y","y",0),0.5);
FunctionExpression Q2=FunctionExpression.exp(new Function("x","x",0),1.5);
Q1=FunctionExpression.product(Q1, Q2);
FunctionExpression a1=FunctionExpression.exp(new Function("y","y",0),2.2);
FunctionExpression a2=FunctionExpression.exp(new Function("x","x",0),-0.7);
a1=FunctionExpression.product(a1, a2);
a1=FunctionExpression.sum(Q1, a1);
return FunctionExpression.exp(a1, -2.6);
}
// (ln(y)^(0.5)*ln(x)^(1.5) + ln(y)^(2.2)*ln(x)^(-0.7))^(-2.6)
public static FunctionExpression equationExample2(){
FunctionExpression Q1=FunctionExpression.exp(new Function("ln","y",0),0.5);
FunctionExpression Q2=FunctionExpression.exp(new Function("ln","x",0),1.5);
Q1=FunctionExpression.product(Q1, Q2);
FunctionExpression a1=FunctionExpression.exp(new Function("ln","y",0),2.2);
FunctionExpression a2=FunctionExpression.exp(new Function("ln","x",0),-0.7);
a1=FunctionExpression.product(a1, a2);
a1=FunctionExpression.sum(Q1, a1);
return FunctionExpression.exp(a1, -2.6);
}
// ((ln(y)^(0.5)*ln(x)^(1.5) + ln(y)^(2.2)*ln(x)^(-0.7))^(-2.6) + (y^(0.5)*x^(1.5) + y^(2.2)*x^(-0.7))^(-2.6) )^(4.2)
public static FunctionExpression equationExample3(){
FunctionExpression a= FunctionExpression.sum(equationExample1(),equationExample2());
return FunctionExpression.exp(a,4.2);
}
//sin(cos( (y^(0.5)*x^(1.5) + y^(2.2)*x^(-0.7))^(-2.6) )^(-2.5))
public static FunctionExpression equationExample4(){
Function s=new Function("cos", "~", 0);
FunctionExpression Q1=FunctionExpression.exp(new Function("y","y",0),0.5);
FunctionExpression Q2=FunctionExpression.exp(new Function("x","x",0),1.5);
Q1=FunctionExpression.product(Q1, Q2);
s.compose=equationExample1();
FunctionExpression a=FunctionExpression.exp(s, -2.5);
Function d=new Function("sin", "~", 0);
d.compose=a;
return new FunctionExpression(d);
}
// (y^(2.3)+x^(4.1))(y^(1.9)+x^(-4.7))
public static FunctionExpression equationExample5(){
FunctionExpression Q1=FunctionExpression.exp(new Function("y","y",0),2.3);
FunctionExpression Q2=FunctionExpression.exp(new Function("x","x",0),4.1);
Q1=FunctionExpression.sum(Q1, Q2);
FunctionExpression a1=FunctionExpression.exp(new Function("y","y",0),1.9);
FunctionExpression a2=FunctionExpression.exp(new Function("x","x",0),-4.7);
a1=FunctionExpression.sum(a1, a2);
a1=FunctionExpression.product(Q1, a1);
return a1;
}
// sin( sin(cos( (y^(0.5)*x^(1.5) + y^(2.2)*x^(-0.7))^(-2.6) )^(-2.5) ) + cos((y^(2.3)+x^(4.1))(y^(1.9)+x^(-4.7))) )
public static FunctionExpression equationExample6(){
Function d=new Function("cos", "~", 0);
d.compose=equationExample5();
FunctionExpression t=FunctionExpression.sum(equationExample4(), d);
Function e=new Function("sin", "~", 0);
e.compose=t;
return new FunctionExpression(e);
}
public static void derivativeExample(FunctionExpression functionExpression){
//define variables that will be used
ArrayList<String> variables=new ArrayList<String>();
ArrayList<Double> values=new ArrayList<Double>();
values.add(92.3);
variables.add("x");
values.add(111.4);
variables.add("y");
//machine that handles computations
Calculus.setVariables(variables);
Calculus.setValues(values);
FunctionExpression f=functionExpression;
//simplyfing the expression
f=FunctionExpression.simplifyExpression(f);
//printing the expression tree, by level
//f.printByLevel();
//f evaluated at specified point
System.out.println("Function evaluated:\n"+Calculus.compute(f)+"\n");
//computing the first derivative od f, with respect to x
FunctionExpression firstDerivativeX=Calculus.computeDerivative("x", f);
if(firstDerivativeX!=null){
firstDerivativeX=FunctionExpression.simplifyExpression(firstDerivativeX);
//f.printByLevel();
System.out.println("First derivative d/dx\n"+Calculus.compute(firstDerivativeX)+"\n");
}
//computing the first derivative od f, with respect to x
FunctionExpression firstDerivativeY=Calculus.computeDerivative("y", f);
if(firstDerivativeY!=null){
firstDerivativeY=FunctionExpression.simplifyExpression(firstDerivativeY);
//f.printByLevel();
System.out.println("First derivative d/dy\n"+Calculus.compute(firstDerivativeY)+"\n");
}
FunctionExpression secondDerivativeXX=null;
if(firstDerivativeX!=null) secondDerivativeXX=Calculus.computeDerivative("x", firstDerivativeX);
if(secondDerivativeXX!=null){
secondDerivativeXX=FunctionExpression.simplifyExpression(secondDerivativeXX);
//f.printByLevel();
System.out.println("Second derivative d(d/dx)/dx\n"+Calculus.compute(secondDerivativeXX)+"\n");
}
FunctionExpression secondDerivativeYY=null;
if(firstDerivativeY!=null) secondDerivativeYY=Calculus.computeDerivative("y", firstDerivativeY);
if(secondDerivativeYY!=null){
secondDerivativeYY=FunctionExpression.simplifyExpression(secondDerivativeYY);
//secondDerivativeYY.printByLevel();
System.out.println("Second derivative d(d/dy)/dy\n"+Calculus.compute(secondDerivativeYY)+"\n");
}
FunctionExpression secondDerivativeXY=null;
if(firstDerivativeX!=null) secondDerivativeXY=Calculus.computeDerivative("y", firstDerivativeX);
if(secondDerivativeXY!=null){
secondDerivativeXY=FunctionExpression.simplifyExpression(secondDerivativeXY);
//f.printByLevel();
System.out.println("Mixed second derivative d(d/dx)/dy\n"+Calculus.compute(secondDerivativeXY));
}
FunctionExpression thirdDerivativeXXX=null;
if(secondDerivativeXX!=null) thirdDerivativeXXX=Calculus.computeDerivative("x", secondDerivativeXX);
if(thirdDerivativeXXX!=null){
thirdDerivativeXXX=FunctionExpression.simplifyExpression(thirdDerivativeXXX);
//f.printByLevel();
System.out.println("\nThird derivative d(d(d/dx)/dx)/dx\n"+Calculus.compute(thirdDerivativeXXX));
}
FunctionExpression thirdDerivativeYYY=null;
if(secondDerivativeYY!=null) thirdDerivativeYYY=Calculus.computeDerivative("y", secondDerivativeYY);
if(thirdDerivativeYYY!=null){
thirdDerivativeYYY=FunctionExpression.simplifyExpression(thirdDerivativeYYY);
//f.printByLevel();
System.out.println("\nThird derivative d(d(d/dy)/dy)/dy\n"+Calculus.compute(thirdDerivativeYYY));
}
}
public static FunctionExpression equationExample7(){
ArrayList<Double> startPoint=new ArrayList<Double>();
ArrayList<String> variables=new ArrayList<String>();
startPoint.add(18.0);
variables.add("x");
startPoint.add(25.0);
variables.add("y");
Calculus.setVariables(variables);
FunctionExpression f=FunctionExpression.exp(new Function("y","y",0),3.0);
//f=FunctionExpression.product(f, new Function("x", "x", 0));
FunctionExpression f2=FunctionExpression.exp(new Function("x","x",0),3.0);
//f2=FunctionExpression.product(f2, new Function("y", "y", 0));
FunctionExpression f3=FunctionExpression.product(new Function("y","y",0), new Function("x","x",0));
f=FunctionExpression.sum(f, f2);
f=FunctionExpression.sum(f, f3);
//f.printByLevel();
return f;
}
public static FunctionExpression equationExample8(){
FunctionExpression temp =FunctionExpression.div(equationExample7(), FunctionExpression.exp(new Function("x","x",0),3.0));
return FunctionExpression.div(temp,equationExample1());
}
public static void derivativesExample(){
ArrayList<Double> startPoint=new ArrayList<Double>();
ArrayList<String> variables=new ArrayList<String>();
startPoint.add(-350.0);
variables.add("x");
startPoint.add(-250.0);
variables.add("y");
Calculus.setVariables(variables);
Calculus.setValues(startPoint);
//trasforms the function, ensuring a convex space for optimization
FunctionExpression functionExpression=Calculus.lengthOfGradient(equationExample7());
ArrayList<FunctionExpression> derivatives=Calculus.getDerivatives(functionExpression);
ArrayList<FunctionExpression> secondDerivativesByX=Calculus.getDerivatives(derivatives.get(0));
ArrayList<FunctionExpression> secondDerivativesByY=Calculus.getDerivatives(derivatives.get(1));
System.out.println("d/dx :"+Calculus.compute(derivatives.get(0)));
System.out.println("d/dy :"+Calculus.compute(derivatives.get(1)));
System.out.println("\nd(d/dx)/dx :"+Calculus.compute(secondDerivativesByX.get(0)));
System.out.println("d(d/dy)/dy :"+Calculus.compute(secondDerivativesByY.get(1)));
System.out.println("\nd(d/dx)/dy :"+Calculus.compute(secondDerivativesByX.get(1)));
System.out.println("d(d/dy)/dx :"+Calculus.compute(secondDerivativesByY.get(0)));
ArrayList<Double> d=GradientDescent.descent(startPoint, functionExpression);
for(int i=0;i<d.size();i++){
System.out.println(d.get(i));
}
}
public static void main(String[] args){
derivativeExample(equationExample6());
//derivativesExample();
}
}