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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,33 @@ | ||
| package function; | ||
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| /** | ||
| * Represents the identity function f(x)=x | ||
| */ | ||
| public class Identity extends Function { | ||
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| @Override | ||
| public double evaluate(double x) throws ArithmeticException { | ||
| return x; | ||
| } | ||
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| @Override | ||
| public Function derive() { | ||
| return Constant.of(1); | ||
| } | ||
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| @Override | ||
| public String substitute(String x) { | ||
| return x; | ||
| } | ||
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| @Override | ||
| public boolean equals(Object obj) { | ||
| return obj instanceof Identity; | ||
| } | ||
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| @Override | ||
| public Function compose(Function inner) { | ||
| return inner; | ||
| } | ||
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| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,100 @@ | ||
| package function.arithmetics; | ||
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| import function.Constant; | ||
| import function.Function; | ||
| import function.elementary.LogarithmicFunction; | ||
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| /** | ||
| * Represents the function left^right | ||
| */ | ||
| public class Power extends FunctionArithmetic { | ||
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| public static Function inverse(Function other) { | ||
| return other.pow(Constant.of(-1)); | ||
| } | ||
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| public Power(Function left, Function right) { | ||
| super(left, right); | ||
| } | ||
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| @Override | ||
| public double evaluate(double x) throws ArithmeticException { | ||
| double leftVal = left.evaluate(x); | ||
| double rightVal = right.evaluate(x); | ||
| if (leftVal == 0 && rightVal < 0) | ||
| throw new ArithmeticException("Can't divide by 0"); | ||
| return Math.pow(leftVal, rightVal); | ||
| } | ||
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| @Override | ||
| public Function derive() { | ||
| // f^g is equivalent to e^(ln(f)*g) | ||
| // deriving ln(f)*g gives us (f'g/f + ln(f)*g') | ||
| // Therefore, the derivative would be (f'g/f + ln(f)*g') * e^(ln(f) * g), which | ||
| // is equivalent to (f'g/f + ln(f)*g') * (f^g) | ||
| Function innerDerivative = left.derive().times(right).div(left) | ||
| .plus(right.derive().times(new LogarithmicFunction().compose(left))); | ||
| return innerDerivative.times(this); | ||
| } | ||
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| @Override | ||
| public String substitute(String x) { | ||
| return left.substitute(x, true) + "^" + right.substitute(x, true); | ||
| } | ||
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| @Override | ||
| public Function times(Function other) { | ||
| if (other instanceof Power) { | ||
| Power pow = (Power) other; | ||
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| // apply rule #1: a^n * a^m = a^(n+m) | ||
| if (left.equals(pow.left)) | ||
| return left.pow(right.plus(pow.right)); | ||
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| // don't apply rule #2: a^n * b^n = (ab)^n, unless simpler: | ||
| if (right.equals(pow.right) && !(left.times(pow.left) instanceof Product)) | ||
| return left.times(pow.left).pow(right); | ||
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| } | ||
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| // apply rule #1 again: | ||
| if (left.equals(other)) | ||
| return times(new Power(other, Constant.of(1))); | ||
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| return super.times(other); | ||
| } | ||
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| @Override | ||
| public Function div(Function other) { | ||
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| if (other instanceof Power) { | ||
| Power pow = (Power) other; | ||
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| // apply rule #1: a^n / a^m = a^(n-m) | ||
| if (left.equals(pow.left)) | ||
| return left.pow(right.minus(pow.right)); | ||
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| // don't apply rule #2: a^n / b^n = (a/b)^n, unless simpler: | ||
| if (right.equals(pow.right) && !(left.div(pow.left) instanceof Quotient)) | ||
| return left.div(pow.left).pow(right); | ||
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| } | ||
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| // apply rule #1 again: | ||
| if (left.equals(other)) | ||
| return div(new Power(other, Constant.of(1))); | ||
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| return super.div(other); | ||
| } | ||
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| @Override | ||
| public Function compose(Function inner) { | ||
| return left.compose(inner).pow(right.compose(inner)); | ||
| } | ||
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| @Override | ||
| public Function pow(Function exponent) { | ||
| return left.pow(right.times(exponent)); // apply rule (a^b)^c = a^(bc) | ||
| } | ||
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| } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,47 +1,21 @@ | ||
| package function.elementary; | ||
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| import function.Function; | ||
| import function.FunctionVector; | ||
| import function.Constant; | ||
| import function.Identity; | ||
| import function.arithmetics.Power; | ||
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| public class ExponentialFunction extends Function { | ||
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| private double base; | ||
| /** | ||
| * Represents the function e to the power of f(x) | ||
| */ | ||
| public class ExponentialFunction extends Power { | ||
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| public ExponentialFunction() { | ||
| this(Math.E); | ||
| } | ||
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| public ExponentialFunction(double base) { | ||
| if (base < 0) | ||
| throw new IllegalArgumentException("Can only pick a positive base"); | ||
| if (base == 1 || base == 0) | ||
| throw new IllegalArgumentException("Pick a constant of " + base + " instead"); | ||
| this.base = base; | ||
| } | ||
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| @Override | ||
| public double evaluate(double x) throws ArithmeticException { | ||
| return Math.pow(base, x); | ||
| } | ||
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| @Override | ||
| public Function derive() { | ||
| return FunctionVector.scale(new ExponentialFunction(base), Math.log(base)); | ||
| super(Constant.of(Math.E), new Identity()); | ||
| } | ||
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| @Override | ||
| public String substitute(String x) { | ||
| String baseStr = String.valueOf(base); | ||
| if (base == Math.E) | ||
| baseStr = "e"; | ||
| return baseStr + "^" + x; | ||
| } | ||
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| @Override | ||
| public boolean equals(Object obj) { | ||
| if (!(obj instanceof ExponentialFunction)) | ||
| return false; | ||
| return base == ((ExponentialFunction) obj).base; | ||
| return "e^" + x; | ||
| } | ||
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| } |
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