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Provides support for fairly simple symbolic math analysis
(to solve algebraic equations, integrate, differentiate, calculate
expressions, and so on).
{@link org.jscience.mathematics.function.Function Functions} defined in this package
can be {@link org.jscience.mathematics.function.Variable multivariate}
and operate on various kind of objects such as physical measurements,
vectors, matrices, all types of numbers or even the functions
themselves (functions of functions)!
Here is an example using {@link org.jscience.mathematics.number.Complex complex}
{@link org.jscience.mathematics.function.Polynomial polynomial} functions:[code]
// Defines two local variables (x, y).
Variable varX = new Variable.Local("x");
Variable varY = new Variable.Local("y");
// f(x) = ix² + 2x + 1
Polynomial x = Polynomial.valueOf(Complex.ONE, varX);
Polynomial fx = x.pow(2).times(Complex.I).plus(
x.times(Complex.valueOf(2, 0)).plus(Complex.ONE));
System.out.println(fx);
System.out.println(fx.pow(2));
System.out.println(fx.differentiate(varX));
System.out.println(fx.integrate(varY));
System.out.println(fx.compose(fx));
// Calculates expression.
varX.set(Complex.valueOf(2, 3));
System.out.println(fx.evaluate());
> [0.0 + 1.0i]x^2 + [2.0 + 0.0i]x + [1.0 + 0.0i]
> [-1.0 + 0.0i]x^4 + [0.0 + 4.0i]x^3 + [4.0 + 2.0i]x^2 + [4.0 + 0.0i]x + [1.0 + 0.0i]
> [0.0 + 2.0i]x + [2.0 + 0.0i]
> [0.0 + 1.0i]x^2y + [2.0 + 0.0i]xy + [1.0 + 0.0i]y
> [0.0 - 1.0i]x^4 + [-4.0 + 0.0i]x^3 + [-2.0 + 6.0i]x^2 + [4.0 + 4.0i]x + [3.0 + 1.0i]
> -7.0 + 1.0i
[/code]
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| Function.java | Class | This abstract class represents a mapping between two sets such that
there is a unique element in the second set assigned to each element
in the first set.
Functions can be discrete or continuous and multivariate functions
(functions with multiple variables) are also supported as illustrated
below:[code]
// Defines local variables.
Variable.Local varX = new Variable.Local("x");
Variable.Local varY = new Variable.Local("y");
// f(x, y) = x² + x·y + 1;
Polynomial x = Polynomial.valueOf(Rational.ONE, varX);
Polynomial y = Polynomial.valueOf(Rational.ONE, varY);
Polynomial fx_y = x.pow(2).plus(x.times(y)).plus(Rational.ONE);
System.out.println("f(x,y) = " + fx_y);
// Evaluates f(1,0)
System.out.println("f(1,0) = " + fx_y.evaluate(Rational.ONE, Rational.ZERO));
// Calculates df(x,y)/dx
System.out.println("df(x,y)/dx = " + fx_y.differentiate(varX));
> f(x,y) = [1/1]x^2 + [1/1]xy + [1/1]
> f(1,0) = 2/1
> df(x,y)/dx = [2/1]x + [1/1]y
[/code]
Functions are often given by formula (e.g. |