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Commit d35fc52

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yueminglyuemingl
committed
add Black-Scholez example
1 parent 2af37e1 commit d35fc52
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‎src/symjava/bytecode/TestByteCode.java‎

Copy file name to clipboardExpand all lines: src/symjava/bytecode/TestByteCode.java
+1-1Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -1,7 +1,7 @@
11
package symjava.bytecode;
22

33
public class TestByteCode {
4-
public double fun(double[] args) {
4+
public static double fun(double[] args) {
55
// return args[0] + args[1];
66
double s = Math.pow(2, 3);
77
return s;
Collapse file

‎src/symjava/domains/Interval.java‎

Copy file name to clipboardExpand all lines: src/symjava/domains/Interval.java
+1-1Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -16,7 +16,7 @@ public Interval(Expr start, Expr end) {
1616
}
1717

1818
public Interval(Expr start, Expr end, Expr coordVar) {
19-
super("["+start+","+end+"]", x);
19+
super("["+start+","+end+"]", coordVar);
2020
this.start = start;
2121
this.end = end;
2222
}
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‎src/symjava/examples/BlackScholez.java‎

Copy file name to clipboardExpand all lines: src/symjava/examples/BlackScholez.java
+19-18Lines changed: 19 additions & 18 deletions
Original file line numberDiff line numberDiff line change
@@ -12,12 +12,12 @@
1212
public class BlackScholez {
1313

1414
public static void main(String[] args) {
15-
// TODO Auto-generated method stub
16-
Symbol spot = new Symbol("spot");
17-
Symbol strike = new Symbol("strike");
15+
//Construct the Balck-Scholez equation
16+
Symbol spot = new Symbol("spot"); //spot price
17+
Symbol strike = new Symbol("strike"); //strike price
1818
Symbol rd = new Symbol("rd");
1919
Symbol rf = new Symbol("rf");
20-
Symbol vol = new Symbol("\\sigma");
20+
Symbol vol = new Symbol("\\sigma"); //volatility
2121
Symbol tau = new Symbol("\\tau");
2222
Symbol phi = new Symbol("\\phi");
2323

@@ -28,34 +28,35 @@ public static void main(String[] args) {
2828

2929
Expr dp = (log(fwd/strike)+0.5*pow(stdDev,2))/stdDev;
3030
Expr dm = (log(fwd/strike)-0.5*pow(stdDev,2))/stdDev;
31-
System.out.println(dp);
32-
System.out.println(dm);
3331

34-
Domain I1 = Interval.apply(-oo, phi*dp, z);
32+
//Domain I1 = Interval.apply(-oo, phi*dp, z);
33+
Domain I1 = Interval.apply(-10, phi*dp, z); //Good enough for -10, it will take a long time to use -oo
3534
Expr cdf1 = Integrate.apply(exp(-0.5*pow(z,2)), I1)/sqrt(PI2);
36-
Domain I2 = Interval.apply(-oo, phi*dm, z);
35+
36+
//Domain I2 = Interval.apply(-oo, phi*dm, z);
37+
Domain I2 = Interval.apply(-10, phi*dm, z);
3738
Expr cdf2 = Integrate.apply(exp(-0.5*pow(z,2)), I2)/sqrt(PI2);
3839

3940
Expr res = phi*domDf*(fwd*cdf1-strike*cdf2);
40-
System.out.println(res);
41-
42-
System.out.println(res.diff(vol));
41+
System.out.println("Balck-Scholez equation:");
42+
System.out.println(res+"\n");
43+
System.out.println("The first derivative of Balck-Scholez equation with respect to volatility \\sigma:");
44+
System.out.println(res.diff(vol)+"\n"); //Let computer do it for us.
4345

44-
45-
// Calculate Black-Scholes price for a given vol
46+
// Calculate Black-Scholes price for a given volatility: \sigma=0.1423
4647
BytecodeFunc blackScholesPrice = JIT.compile(new Expr[]{spot, strike, rd, rf, vol, tau, phi}, res);
4748
double price = blackScholesPrice.apply(100.0, 110.0, 0.002, 0.01, 0.1423, 0.5, 1);
4849

49-
System.out.println("Newtom method:");
50+
System.out.println("Use Newtom method to recover the volatility by given the market data:");
5051
Expr[] freeVars = {vol};
51-
Expr[] params = {spot, strike, rd, rf, tau, phi};
52+
Expr[] params = {spot, strike, rd, rf, tau, phi}; //Specify the params in the given order
5253
Eq[] eq = new Eq[] {
53-
new Eq(res-price, C0, freeVars, params)
54+
new Eq(res-price, C0, freeVars, params)
5455
};
5556

5657
double[] guess = new double[]{ 0.10 };
57-
58-
Newton.solve(eq, guess, 1000, 1e-5);
58+
double[] constParams = new double[] {100.0, 110.0, 0.002, 0.01, 0.5, 1};
59+
Newton.solve(eq, guess, constParams, 1000, 1e-5);
5960
}
6061

6162
}
Collapse file

‎src/symjava/examples/Example3.java‎

Copy file name to clipboardExpand all lines: src/symjava/examples/Example3.java
+1-1Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -14,7 +14,7 @@ public static void example1() {
1414
Expr[] freeVars = {x};
1515
double num = 612;
1616
Eq[] eq = new Eq[] {
17-
new Eq(x*x-num, C0, freeVars, null)
17+
new Eq(x*x-num, C0, freeVars)
1818
};
1919

2020
double[] guess = new double[]{ 10 };
Collapse file

‎src/symjava/examples/Newton.java‎

Copy file name to clipboardExpand all lines: src/symjava/examples/Newton.java
+33-6Lines changed: 33 additions & 6 deletions
Original file line numberDiff line numberDiff line change
@@ -15,13 +15,21 @@
1515
*/
1616
public class Newton {
1717
public static void solve(Eq[] eqs, double[] init, int maxIter, double eps) {
18+
solve(eqs, init, new double[0], maxIter, eps);
19+
}
20+
21+
public static void solve(Eq[] eqs, double[] init, double[] params, int maxIter, double eps) {
1822
for(Eq eq : eqs) {
1923
if(!Symbol.C0.symEquals(eq.rhs)) {
2024
System.out.println("The right hand side of the equation must be 0.");
2125
return;
2226
}
2327
}
2428
Expr[] unknowns = eqs[0].getUnknowns();
29+
Expr[] funParams = eqs[0].getParams();
30+
if(funParams.length != params.length) {
31+
throw new RuntimeException("funParams.length != params.length");
32+
}
2533
int m = eqs.length;
2634
int n = unknowns.length;
2735

@@ -40,24 +48,43 @@ public static void solve(Eq[] eqs, double[] init, int maxIter, double eps) {
4048
System.out.println(hess);
4149

4250
//Convert symbolic staff to Bytecode staff to speedup evaluation
43-
NumMatrix NH = new NumMatrix(hess, unknowns);
44-
NumVector NG = new NumVector(lhss, unknowns);
51+
Expr[] args = new Expr[unknowns.length + funParams.length];
52+
int ii=0;
53+
for(int j=0; j<unknowns.length; j++)
54+
args[ii++] = unknowns[j];
55+
for(int j=0; j<funParams.length; j++)
56+
args[ii++] = funParams[j];
57+
NumMatrix NH = new NumMatrix(hess, args);
58+
NumVector NG = new NumVector(lhss, args);
4559

4660
System.out.println("Iterativly sovle ... ");
61+
double[] funArgs = new double[args.length];
62+
for(int j=0; j<init.length;j++)
63+
funArgs[j] = init[j];
64+
for(int j=init.length; j<funArgs.length; j++)
65+
funArgs[j] = params[j-init.length];
66+
4767
for(int i=0; i<maxIter; i++) {
4868
//Use JAMA to solve the system
49-
Matrix A = new Matrix(NH.eval(init));
50-
Matrix b = new Matrix(NG.eval(init), NG.dim());
69+
Matrix A = new Matrix(NH.eval(funArgs));
70+
// System.out.println("Matrix:");
71+
// for(int j=0;j<A.getRowDimension();j++) {
72+
// for(int k=0; k<A.getColumnDimension(); k++) {
73+
// System.out.println(A.get(j,k)+" ");
74+
// }
75+
// System.out.println();
76+
// }
77+
Matrix b = new Matrix(NG.eval(funArgs), NG.dim());
5178
Matrix x = A.solve(b); //Lease Square solution
5279
for(int j=0; j<init.length; j++) {
53-
System.out.print(String.format("%s=%.5f",unknowns[j], init[j])+" ");
80+
System.out.print(String.format("%s=%.5f",unknowns[j], funArgs[j])+" ");
5481
}
5582
System.out.println();
5683
if(x.norm2() < eps)
5784
break;
5885
//Update initial guess
5986
for(int j=0; j<init.length; j++) {
60-
init[j] = init[j] - x.get(j, 0);
87+
funArgs[j] = funArgs[j] - x.get(j, 0);
6188
}
6289
}
6390
}
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‎src/symjava/relational/Eq.java‎

Copy file name to clipboardExpand all lines: src/symjava/relational/Eq.java
+4Lines changed: 4 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -15,11 +15,15 @@ public class Eq extends Relation {
1515
public Eq(Expr lhs, Expr rhs) {
1616
this.lhs = lhs;
1717
this.rhs = rhs;
18+
this.freeVars = new Expr[0];;
19+
this.params = new Expr[0];
1820
}
1921

2022
public Eq(Expr lhs, Expr rhs, Expr[] freeVars) {
2123
this.lhs = lhs;
2224
this.rhs = rhs;
25+
this.freeVars = freeVars;
26+
this.params = new Expr[0];
2327
//Find dependent variables
2428
List<Expr> list = Utils.extractSymbols(lhs, rhs);
2529
List<Expr> depList = new ArrayList<Expr>();
Collapse file

‎src/symjava/symbolic/Func.java‎

Copy file name to clipboardExpand all lines: src/symjava/symbolic/Func.java
+5-1Lines changed: 5 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -55,6 +55,10 @@ public boolean isAbstract() {
5555
}
5656

5757
public BytecodeFunc toBytecodeFunc() {
58+
return toBytecodeFunc(false, false);
59+
}
60+
61+
public BytecodeFunc toBytecodeFunc(boolean isWriteFile, boolean staticMethod) {
5862
try {
5963
if(this.expr instanceof SymReal<?>) {
6064
SymReal<?> r = (SymReal<?>)this.expr;
@@ -64,7 +68,7 @@ public BytecodeFunc toBytecodeFunc() {
6468
* Return an instance of BytecodeFunc generated by this Func without writing a class file to disk.
6569
*/
6670
FuncClassLoader fcl = new FuncClassLoader();
67-
return fcl.newInstance(BytecodeUtils.genClass(this, false));
71+
return fcl.newInstance(BytecodeUtils.genClass(this, isWriteFile, staticMethod));
6872
//return (BytecodeFunc)Class.forName("symjava.bytecode."+this.label).newInstance();
6973
} catch (Exception e) {
7074
e.printStackTrace();
Collapse file

‎src/symjava/symbolic/Integrate.java‎

Copy file name to clipboardExpand all lines: src/symjava/symbolic/Integrate.java
+1-1Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -75,7 +75,7 @@ public Expr diff(Expr expr) {
7575
if(domain instanceof Interval) {
7676
Interval I = (Interval)domain;
7777
Expr end = I.getEnd();
78-
Expr intSubs = integrand.subs(domain.getCoordVars()[0], expr);
78+
Expr intSubs = integrand.subs(domain.getCoordVars()[0], end);
7979
return intSubs.multiply(end.diff(expr));
8080
}
8181
return null;
Collapse file

‎src/symjava/symbolic/utils/BytecodeSupport.java‎

Copy file name to clipboardExpand all lines: src/symjava/symbolic/utils/BytecodeSupport.java
+39Lines changed: 39 additions & 0 deletions
Original file line numberDiff line numberDiff line change
@@ -1,5 +1,7 @@
11
package symjava.symbolic.utils;
22

3+
import java.lang.reflect.Method;
4+
35
public class BytecodeSupport {
46
public static double powi(double base, int exp) {
57
if(exp == 0) return 1.0;
@@ -30,9 +32,46 @@ public static double log(double base, double expr) {
3032
return Math.log(expr)/Math.log(base);
3133
}
3234

35+
public static double numIntegrate1D(double begin, double end, double step, String className) {
36+
37+
Method method;
38+
try {
39+
method = BytecodeSupport.class.getClassLoader().
40+
loadClass("symjava.bytecode."+className).
41+
getMethod("apply", new Class[] {double[].class});
42+
double[] args = { 0 };
43+
double sum = 0.0;
44+
for(double i=begin; i<=end; i+=step) {
45+
args[0] = i;
46+
Double val = (Double)method.invoke(null, args);
47+
//Double val = test_pdf(args);
48+
sum += val*step;
49+
}
50+
return sum;
51+
} catch (Exception e) {
52+
e.printStackTrace();
53+
}
54+
// for (Method m : methods) {
55+
// if (methodName.equals(m.getName())) {
56+
// // for static methods we can use null as instance of class
57+
// m.invoke(null, new Object[] {args});
58+
// break;
59+
// }
60+
// }
61+
return 0.0;
62+
}
63+
64+
public static double test_pdf(double[] args) {
65+
double x = args[0];
66+
return Math.exp(-0.5*x*x);
67+
//return Math.exp(-0.5*x*x)/Math.sqrt(2*Math.PI);
68+
}
69+
3370
public static void main(String[] args) {
3471
System.out.println(powi(2,-3));
3572
System.out.println(powi(2,0));
3673
System.out.println(powi(2,3));
74+
75+
System.out.println(numIntegrate1D(-10,10,0.1,"integrand_ae3c65a143de42739270977b140b4fdf")/Math.sqrt(2*Math.PI));
3776
}
3877
}
Collapse file

‎src/symjava/symbolic/utils/BytecodeUtils.java‎

Copy file name to clipboardExpand all lines: src/symjava/symbolic/utils/BytecodeUtils.java
+20-10Lines changed: 20 additions & 10 deletions
Original file line numberDiff line numberDiff line change
@@ -1,7 +1,6 @@
11
package symjava.symbolic.utils;
22

3-
import static com.sun.org.apache.bcel.internal.Constants.ACC_PUBLIC;
4-
import static com.sun.org.apache.bcel.internal.Constants.ACC_SUPER;
3+
import static com.sun.org.apache.bcel.internal.Constants.*;
54

65
import java.util.ArrayList;
76
import java.util.Arrays;
@@ -127,7 +126,7 @@ public int compare(Expr o1, Expr o2) {
127126
return rlt;
128127
}
129128

130-
public static ClassGen genClass(Func fun, boolean writeClassFile) {
129+
public static ClassGen genClass(Func fun, boolean writeClassFile, boolean staticMethod) {
131130
String packageName = "symjava.bytecode";
132131
String clsName = fun.getName();
133132
String fullClsName = packageName+"."+clsName;
@@ -137,7 +136,10 @@ public static ClassGen genClass(Func fun, boolean writeClassFile) {
137136
InstructionList il = new InstructionList();
138137
InstructionFactory factory = new InstructionFactory(cg);
139138

140-
MethodGen mg = new MethodGen(ACC_PUBLIC, // access flags
139+
short acc_flags = ACC_PUBLIC;
140+
if(staticMethod)
141+
acc_flags |= ACC_STATIC;
142+
MethodGen mg = new MethodGen(acc_flags, // access flags
141143
Type.DOUBLE, // return type
142144
new Type[] { // argument types
143145
new ArrayType(Type.DOUBLE, 1)
@@ -163,6 +165,8 @@ public static ClassGen genClass(Func fun, boolean writeClassFile) {
163165
System.out.println(
164166
String.format(">>>Using args: %s", Utils.joinLabels(fExprArgs, ","))
165167
);
168+
} else {
169+
fExprArgs = fun.args;
166170
}
167171
HashMap<Expr, Integer> argsMap = new HashMap<Expr, Integer>();
168172
for(int i=0; i<fExprArgs.length; i++) {
@@ -182,7 +186,10 @@ public static ClassGen genClass(Func fun, boolean writeClassFile) {
182186
if(argIdx == null) {
183187
throw new IllegalArgumentException(ins+" is not in the argument list of "+fun.getLabel());
184188
}
185-
il.append(new ALOAD(1));
189+
if(staticMethod)
190+
il.append(new ALOAD(0)); //for static method
191+
else
192+
il.append(new ALOAD(1));
186193
il.append(new PUSH(cp, argIdx));
187194
il.append(new DALOAD());
188195
} else if(ins instanceof SymReal<?>) {
@@ -255,12 +262,15 @@ public static ClassGen genClass(Func fun, boolean writeClassFile) {
255262
} else if(ins instanceof Infinity) {
256263
il.append(new PUSH(cp, Double.NaN));
257264
} else if(ins instanceof Integrate) {
258-
Func f = new Func("integrand"+java.util.UUID.randomUUID().toString().replaceAll("-", ""),((Integrate) ins).integrand);
259-
BytecodeFunc ff = f.toBytecodeFunc();
265+
Integrate INT = (Integrate)ins;
266+
Func f = new Func("integrand_"+java.util.UUID.randomUUID().toString().replaceAll("-", ""),INT.integrand);
267+
//System.out.println(f);
268+
f.toBytecodeFunc(true, true); //Load class, could be better method to load a class
260269
//http://stackoverflow.com/questions/19119702/injecting-code-in-an-existing-method-using-bcel/19219759#19219759
261-
il.append(new PUSH());
262-
il.append(factory.createInvoke("symjava.symbolic.utils.BytecodeSupport", "numIntegrate",
263-
Type.DOUBLE, new Type[] { Type.DOUBLE, Type.DOUBLE, Type.OBJECT }, Constants.INVOKESTATIC));
270+
il.append(new PUSH(cp, 0.001)); //step, could be provide by INT
271+
il.append(new PUSH(cp, f.getName()));
272+
il.append(factory.createInvoke("symjava.symbolic.utils.BytecodeSupport", "numIntegrate1D",
273+
Type.DOUBLE, new Type[] { Type.DOUBLE, Type.DOUBLE, Type.DOUBLE, Type.STRING }, Constants.INVOKESTATIC));
264274
} else {
265275
throw new RuntimeException(ins.getClass() + " is not allowed when generating bytecode function!");
266276
}

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