216 lines
3.5 KiB
Text
216 lines
3.5 KiB
Text
CLASS:: Complex
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summary:: complex number
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categories:: Math
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related::Classes/Polar, Classes/SimpleNumber, Classes/Float, Classes/Integer
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DESCRIPTION::
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A class representing complex numbers.
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Note that this is a simplified representation of a complex number, which does not implement the full mathematical notion of a complex number.
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CLASSMETHODS::
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method:: new
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Create a new complex number with the given real and imaginary parts.
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argument:: real
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the real part
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argument:: imag
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the imaginary part
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returns:: a new instance of Complex.
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discussion::
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code::
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a = Complex(2, 5);
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a.real;
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a.imag;
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::
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INSTANCEMETHODS::
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subsection:: math support
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method:: real
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The real part of the number.
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method:: imag
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The imaginary part of the number.
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method:: conjugate
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the complex conjugate.
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discussion::
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code::
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Complex(2, 9).conjugate
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::
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method:: +
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Complex addition.
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discussion::
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code::
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Complex(2, 9) + Complex(-6, 2)
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::
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method:: -
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Complex subtraction
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discussion::
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code::
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Complex(2, 9) - Complex(-6, 2)
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::
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method:: *
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Complex multiplication
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discussion::
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code::
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Complex(2, 9) * Complex(-6, 2)
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::
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method:: /
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Complex division.
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discussion::
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code::
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Complex(2, 9) / Complex(-6, 2)
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::
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method:: exp
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Complex exponentiation with base e.
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discussion::
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code::
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exp(Complex(2, 9))
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::
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code::
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exp(Complex(0, pi)) == -1 // Euler's formula: true
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::
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method:: squared
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Complex self multiplication.
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discussion::
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code::
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squared(Complex(2, 1))
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::
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method:: cubed
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complex triple self multiplication.
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discussion::
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code::
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cubed(Complex(2, 1))
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::
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method:: **, pow
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Complex exponentiation
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discussion::
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not implemented for all combinations - some are mathematically ambiguous.
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code::
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Complex(0, 2) ** 6
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::
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code::
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2.3 ** Complex(0, 2)
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::
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code::
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Complex(2, 9) ** 1.2 // not defined
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::
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method:: <
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the comparison of just the real parts.
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discussion::
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code::
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Complex(2, 9) < Complex(5, 1);
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::
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method:: ==
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the comparison assuming that the reals (floats) are fully embedded in the complex numbers
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discussion::
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code::
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Complex(1, 0) == 1;
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Complex(1, 5) == Complex(1, 5);
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::
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method:: neg
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negation of both parts
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discussion::
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code::
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Complex(2, 9).neg
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::
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method:: abs
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the absolute value of a complex number is its magnitude.
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discussion::
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code::
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Complex(3, 4).abs
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::
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method:: magnitude
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distance to the origin.
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method:: magnitudeApx
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method:: rho
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the distance to the origin.
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method:: angle, phase, theta
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the angle in radians.
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subsection:: conversion
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method:: asPoint
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Convert to a link::Classes/Point::.
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method:: asPolar
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Convert to a Polar
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method:: asInteger
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real part as link::Classes/Integer::.
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method:: asFloat
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real part as link::Classes/Float::.
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method:: asComplex
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returns this
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subsection:: misc
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method:: coerce
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method:: hash
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a hash value
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method:: printOn
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print this on given stream
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method:: performBinaryOpOnSignal
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method:: performBinaryOpOnComplex
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method:: performBinaryOpOnSimpleNumber
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method:: performBinaryOpOnUGen
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EXAMPLES::
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Basic example:
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code::
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a = Complex(0, 1);
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a * a; // returns Complex(-1, 0);
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::
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Julia set approximation:
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code::
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f = { |z| z * z + Complex(0.70176, 0.3842) };
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(
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var n = 80, xs = 400, ys = 400, dx = xs / n, dy = ys / n, zoom = 3, offset = -0.5;
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var field = { |x| { |y| Complex(x / n + offset * zoom, y / n + offset * zoom) } ! n } ! n;
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w = Window("Julia set", bounds:Rect(200, 200, xs, ys)).front;
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w.view.background_(Color.black);
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w.drawFunc = {
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n.do { |x|
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n.do { |y|
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var z = field[x][y];
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z = f.(z);
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field[x][y] = z;
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Pen.color = Color.gray(z.rho.linlin(-100, 100, 1, 0));
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Pen.addRect(
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Rect(x * dx, y * dy, dx, dy)
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);
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Pen.fill
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}
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}
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};
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fork({ 6.do { w.refresh; 2.wait } }, AppClock)
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)
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::
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