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package bisection;
/**
* Represents an expression using dual numbers.
*
* Useful for automatically differentiating expressions.
*/
public class DualExpr {
/**
* Represents the various types of dual expressions.
*/
public static enum ExprType {
/**
* A fixed number.
*/
CONSTANT,
/**
* An addition operation.
*/
ADDITION,
/**
* A subtraction operation.
*/
SUBTRACTION,
/**
* A multiplication operation.
*/
MULTIPLICATION,
/**
* A division operation.
*/
DIVISION,
/**
* A sine operation.
*/
SIN,
/**
* A cosine operation.
*/
COS,
/**
* An exponential function.
*/
EXPONENTIAL,
/**
* A logarithm function.
*/
LOGARITHM,
/**
* A power operation.
*/
POWER,
/**
* An absolute value.
*/
ABSOLUTE
}
/**
* The type of the expression.
*/
public final DualExpr.ExprType type;
/**
* The dual number value, for constants.
*/
public Dual number;
/**
* The left (or first) part of the expression.
*/
public DualExpr left;
/**
* The right (or second) part of the expression.
*/
public DualExpr right;
/**
* The power to use, for power operations.
*/
public int power;
/**
* Create a new constant dual number.
*
* @param num
* The value of the dual number.
*/
public DualExpr(Dual num) {
this.type = ExprType.CONSTANT;
number = num;
}
/**
* Create a new unary dual number.
*
* @param type
* The type of operation to perform.
* @param val
* The parameter to the value.
*/
public DualExpr(DualExpr.ExprType type, DualExpr val) {
this.type = type;
left = val;
}
/**
* Create a new math expression.
*
* The type of operation to perform.
* @param left
* The left operand
* @param right
* The right operand
*/
public DualExpr(DualExpr.ExprType type, DualExpr left, DualExpr right) {
this.type = type;
this.left = left;
this.right = right;
}
/**
* Create a new power expression.
*
* @param left
* The expression to raise.
* @param power
* The power to raise it by.
*/
public DualExpr(DualExpr left, int power) {
this.type = ExprType.POWER;
this.left = left;
this.power = power;
}
/**
* Evaluate an expression to a number.
*
* Uses the rules provided in
* https://en.wikipedia.org/wiki/Automatic_differentiation
*
* @return The evaluated expression.
*/
public Dual evaluate() {
/* The evaluated dual numbers. */
Dual lval, rval;
/* Perform the right operation for each type. */
switch (type) {
case CONSTANT:
return number;
case ADDITION:
lval = left.evaluate();
rval = right.evaluate();
return new Dual(lval.real + rval.real, lval.dual + rval.dual);
case SUBTRACTION:
lval = left.evaluate();
rval = right.evaluate();
return new Dual(lval.real - rval.real, lval.dual - rval.dual);
case MULTIPLICATION:
lval = left.evaluate();
rval = right.evaluate();
{
double lft = lval.dual * rval.real;
double rght = lval.real * rval.dual;
return new Dual(lval.real * rval.real, lft + rght);
}
case DIVISION:
lval = left.evaluate();
rval = right.evaluate();
{
if (rval.real == 0) {
throw new IllegalArgumentException("ERROR: Attempted to divide by zero.");
}
double lft = lval.dual * rval.real;
double rght = lval.real * rval.dual;
double val = (lft - rght) / (rval.real * rval.real);
return new Dual(lval.real / rval.real, val);
}
case SIN:
lval = left.evaluate();
return new Dual(Math.sin(lval.real), lval.dual * Math.cos(lval.real));
case COS:
lval = left.evaluate();
return new Dual(Math.cos(lval.real), -lval.dual * Math.sin(lval.real));
case EXPONENTIAL:
lval = left.evaluate();
{
double val = Math.exp(lval.real);
return new Dual(val, lval.dual * val);
}
case LOGARITHM:
lval = left.evaluate();
if (lval.real <= 0) {
throw new IllegalArgumentException("ERROR: Attempted to take non-positive log.");
}
return new Dual(Math.log(lval.real), lval.dual / lval.real);
case POWER:
lval = left.evaluate();
if (lval.real == 0) {
throw new IllegalArgumentException("ERROR: Raising zero to a power.");
}
{
double rl = Math.pow(lval.real, power);
double lft = Math.pow(lval.real, power - 1);
return new Dual(rl, power * lft * lval.dual);
}
case ABSOLUTE:
lval = left.evaluate();
return new Dual(Math.abs(lval.real), lval.dual * Math.signum(lval.real));
default:
String msg = "ERROR: Unknown expression type %s";
throw new IllegalArgumentException(String.format(msg, type));
}
}
@Override
public String toString() {
switch (type) {
case ABSOLUTE:
return String.format("abs(%s)", left.toString());
case ADDITION:
return String.format("(%s + %s)", left.toString(), right.toString());
case CONSTANT:
return String.format("%s", number.toString());
case COS:
return String.format("cos(%s)", left.toString());
case DIVISION:
return String.format("(%s / %s)", left.toString(), right.toString());
case EXPONENTIAL:
return String.format("exp(%s)", left.toString());
case LOGARITHM:
return String.format("log(%s)", left.toString());
case MULTIPLICATION:
return String.format("(%s * %s)", left.toString(), right.toString());
case POWER:
return String.format("(%s ^ %d)", left.toString(), power);
case SIN:
return String.format("sin(%s)", left.toString());
case SUBTRACTION:
return String.format("(%s - %s)", left.toString(), right.toString());
default:
return String.format("UNKNOWN_EXPR");
}
}
}
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