829 lines
15 KiB
Racket
829 lines
15 KiB
Racket
#lang scribble/manual
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@(require (for-label racket))
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@title{AbstractFunction}
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An object which responds to a set of messages that represent mathematical functions@section{categories}
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Core>Kernel
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@section{related}
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Classes/UGen,Classes/Pattern,Classes/Function,Overviews/Operators
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@section{description}
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An AbstractFunction is an object which responds to a set of messages that represent
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mathematical functions. Subclasses override a smaller set of messages to respond
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to the mathematical functions.
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The intent is to provide a mechanism for functions that do not calculate values directly but instead compose structures for calculating (lazy evaluation).
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Function, Pattern, Stream and UGen are subclasses of AbstractFunction.
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For example, if you multiply two UGens together the receiver responds by returning a new
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instance of class BinaryOpUGen which has the two operands as inputs.
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@racketblock[
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{ var a, b; a = LFSaw.ar(220); b = LFPulse.ar(1442); [a, b, a * b] }.plot;
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::
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For an overview of common operators, see link::Overviews/Operators::, for specific examples, see also e.g. link::Classes/Function::, link::Classes/UGen::, link::Classes/Pattern::.
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To see which classes implement a specific method, see that method in the generated link::Overviews/Methods:: overview.
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]
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@section{instanceMethods}
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@section{subsection}
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Unary Messages
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The following messages return an object which represents a delayed unary operation, i.e. an operation on one object. For example, the reciprocal of a function will result in a new function that, when called, returns the reciprocal of the evaluation of the operand.
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All of the following messages send the message composeUnaryOp to the receiver with the
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unary message selector as an argument.
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See link::Classes/UnaryOpFunction::.
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@section{method}
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neg
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@racketblock[
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a = { 10.rand.postln }; b = a.neg; b.value;
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// Patterns, Streams, UGens, and Proxies are AbstractFunctions, too:
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a = Pgeom(1, 2, 5).neg; a.asStream.nextN(8);
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{ a = LFNoise1.ar(1500); [a, a.neg] }.plot;
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::
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]
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@section{method}
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reciprocal
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@racketblock[
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a = { 10.rand.postln }; b = a.reciprocal; b.value;
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a = Pgeom(1, 2, 5).reciprocal; a.asStream.nextN(8);
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{ a = LFNoise1.ar(1500) + 2; [a, a.reciprocal] }.plot;
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::
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]
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@section{method}
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bitNot
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Bitwise integer negation.
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@section{method}
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abs
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Absolute value
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@racketblock[
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a = { 10.rand - 10.rand }; b = a.abs; b.value;
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a = Pseries(3, -1.8, inf).abs; a.asStream.nextN(8);
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{ a = LFNoise1.ar(1500); [a, a.abs] }.plot;
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::
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]
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@section{method}
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asFloat
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@racketblock[
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a = { "123.471".scramble }; b = a.asFloat; b.value;
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::
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]
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@section{method}
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asInt
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@racketblock[
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a = { "123471".scramble }; b = a.asInt; b.value;
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::
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]
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@section{method}
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ceil, floor, frac
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@racketblock[
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a = { 10.0.rand2.postln }; b = a.ceil; b.value;
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a = { 10.0.rand2.postln }; b = a.floor; b.value;
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a = Pgeom(1, 1.2, inf).ceil; a.asStream.nextN(8);
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a = Pgeom(1, 1.2, inf).floor; a.asStream.nextN(8);
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{ a = SinOsc.ar(150) * 1.5; [a, a.ceil, a.floor, a.frac] }.plot.superpose_(true);
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::
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]
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@section{method}
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sign
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Returns a function that returns -1 if receiver returns a negative number, 1 if positive, and 0 if zero.
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@racketblock[
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a = { 10.0.rand2.postln }; b = a.sign; b.value;
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{ a = LFNoise1.ar(1500) * 1.5; [a, a.sign] }.plot;
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::
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]
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@section{method}
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squared
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@racketblock[
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a = { |x| x + 1 }; b = a.squared; [a.value(1), b.value(1)];
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a = Pseries(0, 1, inf).squared; a.asStream.nextN(8);
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{ a = LFNoise1.ar(1500); [a, a.squared] }.plot;
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::
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]
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@section{method}
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cubed
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@racketblock[
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a = { |x| x + 1 }; b = a.cubed; [a.value(1), b.value(1)];
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a = Pseries(0, 1, inf).cubed; a.asStream.nextN(8);
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{ a = LFNoise1.ar(1500); [a, a.cubed] }.plot;
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::
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]
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@section{method}
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sqrt
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@racketblock[
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a = { |x| x + 1 }; b = a.sqrt; [a.value(1), b.value(1)];
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a = Pseries(0, 1, inf).sqrt; a.asStream.nextN(8);
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{ a = LFNoise1.ar(1500); [a, a.sqrt] }.plot;
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::
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]
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@section{method}
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exp
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Returns e to the power of this.
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@racketblock[
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a = { |x| x + 1 }; b = a.exp; [a.value(1), b.value(1)];
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a = Pseries(0, 0.25, inf).exp; a.asStream.nextN(8);
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{ a = LFNoise1.ar(1500); [a, a.exp] }.plot;
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::
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]
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@section{method}
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midicps
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Converts midinote into cycles per seconds (Hz).
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@racketblock[
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a = { |x, root = 60| x + root }; b = a.midicps; [a.value(9), b.value(9)];
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a = Pseries(60, 1, inf).midicps; a.asStream.nextN(12);
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{ a = LFNoise1.ar(1) * 5 + 60; Pulse.ar(a.round.midicps) * 0.1 }.play;
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::
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]
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@section{method}
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cpsmidi
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Converts cycles per seconds (Hz) into midinote.
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@racketblock[
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a = { |x| #[440, 720, 801, 1020.2].at(x) }; b = a.cpsmidi; [a.value(3), b.value(3)];
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a = Pseries(220, 220, inf).cpsmidi; a.asStream.nextN(12); // overtone series as midinotes
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// follow but round to next midinote
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{ a = Pitch.kr(SoundIn.ar).at(1); Pulse.ar(a.cpsmidi.round.midicps) * 0.1 }.play;
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::
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]
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@section{method}
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midiratio
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@section{method}
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ratiomidi
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@section{method}
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ampdb
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@section{method}
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dbamp
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@section{method}
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octcps
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@section{method}
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cpsoct
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@section{method}
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log
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@section{method}
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log2
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@section{method}
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log10
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@section{method}
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sin
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@section{method}
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cos
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@section{method}
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tan
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@section{method}
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asin
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@section{method}
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acos
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@section{method}
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atan
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@section{method}
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sinh
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@section{method}
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cosh
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@section{method}
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tanh
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@section{method}
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rand
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@section{method}
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rand2
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@section{method}
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linrand
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@section{method}
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bilinrand
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@section{method}
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sum3rand
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@section{method}
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distort
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@section{method}
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softclip
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@section{method}
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coin
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@section{method}
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even
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@section{method}
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odd
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@section{method}
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isPositive
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@section{method}
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isNegative
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@section{method}
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isStrictlyPositive
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@section{method}
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rho
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@section{method}
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theta
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@section{subsection}
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Binary Messages
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The following messages return an object which represents a delayed binary operation, i.e. an operation between two objects. For example, adding two functions will result in a new function that, when called, adds the results of the evaluation of the two operands.
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All of the following messages send the message composeBinaryOp to the receiver with the
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binary message selector and the second operand as arguments.
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See: link::Classes/BinaryOpFunction::.
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Examples:
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@racketblock[
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(
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// Add two functions:
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var x = { |x| x + 1000 } + { |x| x * 100 };
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// Evaluate the result, passing in one argument:
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x.value(2); // posts 1202
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)
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// either operand can be another object:
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(
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// Add two functions:
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var x = 1871 + { |x| x * 12 };
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x.value(12);
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)
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::
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]
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@racketblock[
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(
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// Add two UGens
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{
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SinOsc.ar(440, 0, 0.2) + PinkNoise.ar(0.1);
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}.play
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)
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::
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// Add two Patterns
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]
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@racketblock[
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(Pseq([1, 2, 3, 4]) + Prand([0, 0.1, -0.1], inf)).asStream.nextN(5);
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::
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// Add two NodeProxies
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]
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@racketblock[
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Ndef(\x, { SinOsc.ar(440, 0, 0.2) });
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Ndef(\y, { PinkNoise.ar(0.1) });
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Ndef(\z, Ndef(\x) + Ndef(\y)).play;
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::
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]
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@section{method}
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+
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@racketblock[
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({ |x| x.squared } + 3).value(2);
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::
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]
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@section{method}
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-
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@racketblock[
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({ |x| x.squared } - 3).value(2);
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::
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]
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@section{method}
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*
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@racketblock[
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({ |x| x.squared } * { |x| x.squared }).value(2);
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::
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]
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@section{method}
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/
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@racketblock[
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({ |x| x.squared } / 4).value(2);
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::
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]
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@section{method}
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div
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@racketblock[
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({ |x| x.squared } div: 3).value(2);
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::
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]
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@section{method}
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%
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@racketblock[
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({ |x| x.squared } % 3).value(2);
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::
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]
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@section{method}
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**
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@racketblock[
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({ |x| x.squared } ** 3).value(2);
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::
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]
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@section{method}
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min
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@racketblock[
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({ |x| x.squared } min: 0).value(2);
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::
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]
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@section{method}
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max
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@racketblock[
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({ |x| x.squared } max: 0).value(2);
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::
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]
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@section{method}
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<
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@racketblock[
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({ |x| x.squared } < 3).value(2);
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::
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]
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@section{method}
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<=
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@racketblock[
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({ |x| x.squared } <= 3).value(2);
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::
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]
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@section{method}
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>
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@racketblock[
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({ |x| x.squared } > 3).value(2);
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::
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]
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@section{method}
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>=
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@racketblock[
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({ |x| x.squared } >= 3).value(2);
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::
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]
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@section{method}
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&
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@racketblock[
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a = { |min, max| ({ rrand(min, max) } ! 4).postln };
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(a & a).value(0, 8);
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::
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]
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@section{method}
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@racketblock[
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a = { |min, max| ({ rrand(min, max) } ! 4).postln };
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(a | a).value(0, 8);
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::
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]
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@section{method}
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lcm
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@racketblock[
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a = { |min, max| rrand(min, max).postln };
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(a lcm: a).value(0, 8);
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::
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]
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@section{method}
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gcd
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@racketblock[
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a = { |min, max| rrand(min, max).postln };
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(a gcd: a).value(0, 8);
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::
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]
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@section{method}
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round
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@racketblock[
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a = { |max| max.rand.postln };
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(a round: 0.5).value(1.0);
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::
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]
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@section{method}
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trunc
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@racketblock[
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a = { |max| max.rand.postln };
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(a trunc: 2).value(10);
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::
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]
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@section{method}
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atan2
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@racketblock[
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a = { 1.0.rand2 };
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a.atan2.dup(10);
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::
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]
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@section{method}
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hypot
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@racketblock[
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a = { 1.0.rand2 };
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a.hypot.dup(10);
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::
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]
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@section{method}
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hypotApx
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@racketblock[
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a = { 1.0.rand2 };
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a.hypotApx.dup(10);
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::
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]
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@section{method}
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>>
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@racketblock[
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a = { [2r10010, 2r101011, 2r11100].choose.postln };
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b = a >> 2;
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b.value.asBinaryDigits.join;
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::
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]
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@section{method}
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+>>
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@racketblock[
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a = { [2r10010, 2r101011, 2r11100].choose.postln };
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b = a +>> 2;
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b.value.asBinaryDigits.join;
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::
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]
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@section{method}
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ring1
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(a * b) + a
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@racketblock[
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({ [5, 6, 2].choose.postln } ring1: { [2, -1, 3].choose.postln }).value
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// UGens are also abstract functions
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(
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{ a = SinOsc.ar(335); b = SinOsc.ar(MouseX.kr(1, 1000, 1));
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ring1(a, b) * 0.1 }.play;
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)
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|
::
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]
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|
@section{method}
|
|
ring2
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((a*b) + a + b)
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|
|
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|
@racketblock[
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({ [5, 6, 2].choose.postln } ring2: { [2, -1, 3].choose.postln }).value
|
|
|
|
(
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|
{ a = SinOsc.ar(335); b = SinOsc.ar(MouseX.kr(1, 1000, 1));
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ring2(a, b) * 0.1 }.play;
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)
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|
::
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|
]
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|
@section{method}
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|
ring3
|
|
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(a * a * b)
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|
|
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|
@racketblock[
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|
({ [5, 6, 2].choose.postln } ring3: { [2, -1, 3].choose.postln }).value
|
|
|
|
(
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|
{ a = SinOsc.ar(335); b = SinOsc.ar(MouseX.kr(1, 1000, 1));
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|
ring3(a, b) * 0.1 }.play;
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|
)
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|
::
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|
]
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|
@section{method}
|
|
ring4
|
|
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|
((a*a *b) - (a*b*b))
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|
|
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|
@racketblock[
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|
({ [5, 6, 2].choose.postln } ring4: { [2, -1, 3].choose.postln }).value
|
|
|
|
(
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|
{ a = SinOsc.ar(335); b = SinOsc.ar(MouseX.kr(1, 1000, 1));
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|
ring4(a, b) * 0.1 }.play;
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|
)
|
|
::
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|
]
|
|
@section{method}
|
|
difsqr
|
|
|
|
(a*a) - (b*b)
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|
|
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|
@racketblock[
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|
({ [5, 6, 2].choose.postln } difsqr: { [2, -1, 3].choose.postln }).value
|
|
|
|
(
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|
{ a = SinOsc.ar(335); b = SinOsc.ar(MouseX.kr(1, 1000, 1));
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|
difsqr(a, b) * 0.1 }.play;
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|
)
|
|
::
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|
]
|
|
@section{method}
|
|
sumsqr
|
|
|
|
(a*a) + (b*b)
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|
|
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|
@racketblock[
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|
({ [5, 6, 2].choose.postln } sumsqr: { [2, -1, 3].choose.postln }).value
|
|
|
|
(
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|
{ a = SinOsc.ar(335); b = SinOsc.ar(MouseX.kr(1, 1000, 1));
|
|
sumsqr(a, b) * 0.1 }.play;
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|
)
|
|
::
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|
]
|
|
@section{method}
|
|
sqrdif
|
|
|
|
(a - b) ** 2
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|
|
|
|
|
@racketblock[
|
|
({ [5, 6, 2].choose.postln } sqrdif: { [2, -1, 3].choose.postln }).value
|
|
|
|
(
|
|
{ a = SinOsc.ar(335); b = SinOsc.ar(MouseX.kr(1, 1000, 1));
|
|
ring4(a, b) * 0.1 }.play;
|
|
)
|
|
::
|
|
]
|
|
@section{method}
|
|
sqrsum
|
|
|
|
(a + b) ** 2
|
|
|
|
|
|
@racketblock[
|
|
({ [5, 6, 2].choose.postln } sqrsum: { [2, -1, 3].choose.postln }).value
|
|
|
|
(
|
|
{ a = SinOsc.ar(335); b = SinOsc.ar(MouseX.kr(1, 1000, 1));
|
|
sqrsum(a, b) * 0.1 }.play;
|
|
)
|
|
::
|
|
]
|
|
@section{method}
|
|
absdif
|
|
|
|
(a - b).abs
|
|
|
|
|
|
@racketblock[
|
|
({ [5, 6, 2].choose.postln } absdif: { [2, -1, 3].choose.postln }).value
|
|
|
|
(
|
|
{ a = SinOsc.ar(335); b = SinOsc.ar(MouseX.kr(1, 1000, 1));
|
|
absdif(a, b) * 0.1 }.play;
|
|
)
|
|
::
|
|
|
|
]
|
|
@section{method}
|
|
moddif
|
|
absolute difference in modulo arithmetics.
|
|
|
|
@section{method}
|
|
amclip
|
|
0 when b <= 0, a*b when b > 0
|
|
|
|
@section{method}
|
|
scaleneg
|
|
a * b when a < 0, otherwise a.
|
|
|
|
@section{method}
|
|
clip2
|
|
clips receiver to +/- aNumber
|
|
|
|
@section{method}
|
|
excess
|
|
Returns the difference of the receiver and its clipped form.
|
|
@section{method}
|
|
<!
|
|
@section{method}
|
|
rrand
|
|
|
|
@racketblock[
|
|
a = { |x| sin(x) } rrand: { |x| sin(x) * -1 };
|
|
(0..1000).normalize(0, 5pi).collect(a).plot;
|
|
|
|
(
|
|
{ a = SinOsc.ar(335); b = SinOsc.ar(MouseX.kr(1, 1000, 1));
|
|
rrand(a, b) * 0.1 }.play;
|
|
)
|
|
::
|
|
]
|
|
@section{method}
|
|
exprand
|
|
@section{method}
|
|
rotate
|
|
@section{method}
|
|
dist
|
|
@section{method}
|
|
bitAnd
|
|
@section{method}
|
|
bitOr
|
|
@section{method}
|
|
bitXor
|
|
@section{method}
|
|
bitHammingDistance
|
|
@section{method}
|
|
@
|
|
|
|
@section{subsection}
|
|
Messages with more arguments (n-ary Operators)
|
|
|
|
The following messages return an object which represents a delayed n-ary operation, i.e. an operation between several objects (often three). For example, rescaling a function with linlin will result in a new function that, when called, scales the results of the evaluation of all operands.
|
|
|
|
All of the following messages send the message
|
|
@racketblock[composeNAryOp:: to the receiver with the
|
|
binary message selector and the other operands as arguments.
|
|
See link::Classes/NAryOpFunction::.
|
|
|
|
]
|
|
@section{method}
|
|
clip
|
|
@section{method}
|
|
wrap
|
|
@section{method}
|
|
fold
|
|
@section{method}
|
|
blend
|
|
@section{method}
|
|
linlin
|
|
@section{method}
|
|
linexp
|
|
@section{method}
|
|
explin
|
|
@section{method}
|
|
expexp
|
|
|
|
@section{subsection}
|
|
other
|
|
|
|
@section{method}
|
|
applyTo
|
|
|
|
Interface that allows us to combine selectors (Symbols) and Functions. Sends valueArray(args) to this.
|
|
@section{discussion}
|
|
|
|
|
|
@racketblock[
|
|
// example:
|
|
|
|
f = [{ |a, b| a * b * 100.rand }, { |a, b| sin(a) * sin(b) }, '*', '/'];
|
|
f.choose.postcs.applyTo(3, 4);
|
|
|
|
// this is used in SequenceableCollection reduce:
|
|
(1..10).reduce('+');
|
|
(1..10).reduce({ |a, b| a * b * 1.0.rand });
|
|
::
|
|
|
|
]
|
|
@section{method}
|
|
asUGenInput
|
|
|
|
@section{returns}
|
|
the result of sending the value(for) message to this.
|
|
@section{discussion}
|
|
|
|
|
|
@racketblock[
|
|
// example:
|
|
(
|
|
var f, g, product;
|
|
f = { SinOsc.ar(400) };
|
|
g = { LFPulse.kr(8) };
|
|
product = f * g * 0.1;
|
|
{ Pan2.ar(product, SinOsc.kr(0.3)) }.play;
|
|
)
|
|
::
|
|
|
|
]
|
|
@section{method}
|
|
sampled
|
|
Sample a function.
|
|
@section{discussion}
|
|
|
|
|
|
@racketblock[
|
|
//sample a function
|
|
f = { |x| sin(3*x)*cos(8*x) }
|
|
f.plotGraph(from:0,to:2);
|
|
f.sampled(10,0,2).plotGraph(from:0,to:2);
|
|
f.sampled(80,0,2).plotGraph(from:0,to:2);
|
|
|
|
//on complicated functions a sampled function is less cpy heavy.
|
|
f = { |x| 60.collect{ 2**((x-rrand(0.0,1.0))) }.sum/60 };
|
|
f.plotGraph(from:0,to:1);
|
|
g = f.sampled(200);
|
|
g.plotGraph(from:0,to:1);
|
|
{ 200.collect{ f.(rand(0.0,1.0)) } }.bench;
|
|
{ 200.collect{ g.(rand(0.0,1.0)) } }.bench;
|
|
::
|
|
|
|
]
|
|
@section{subsection}
|
|
Function Composition
|
|
|
|
When unary, binary or n-ary operators are applied to an abstract function, it returns an object that represents
|
|
this operation, without evaluating the function: link::Classes/UnaryOpFunction::, link::Classes/BinaryOpFunction::, link::Classes/NAryOpFunction::.
|
|
Note that different subclasses like link::Classes/Pattern:: or link::Classes/UGen:: have their own composition scheme analogous to the one of AbstractFunction itself. For more about functions, see link::Classes/Function::.
|
|
|
|
|
|
@racketblock[
|
|
// compose a function that will return an array of random length
|
|
a = { |n| { 16.rand } ! n } <> { |x, y| rrand(4, 8) };
|
|
a.value;
|
|
// compose a function from a that selects only odd values
|
|
b = { |x| x.select(_.odd) } <> a;
|
|
b.value;
|
|
::
|
|
|
|
|
|
]
|
|
@section{examples}
|
|
|
|
|
|
|
|
@racketblock[
|
|
// examples
|
|
|
|
a = { 1.0.rand } + 8;
|
|
a.value;
|
|
|
|
|
|
y = { 8 } + { 1.0.rand };
|
|
y.value;
|
|
::
|
|
|
|
]
|
|
|
|
@racketblock[
|
|
// arguments are passed into both functions
|
|
|
|
y = { |x=0| x } + { 1.0.rand };
|
|
y.value(10);
|
|
|
|
|
|
y = { |x=0| x * 3 } + { |x=0| x + 1.0.rand };
|
|
y.value(10);
|
|
|
|
y.postcs;
|
|
|
|
y = { |x=0| x * 3 } + { |x=0| x + 1.0.rand } * { |x=0| [50, 100].choose + x } + 1.0;
|
|
y.value(10);
|
|
::
|
|
|
|
]
|
|
|
|
@racketblock[
|
|
// environments can be used as a lookup with valueEnvir:
|
|
|
|
(
|
|
Environment.use {
|
|
~y = 10;
|
|
~x = 2;
|
|
~z = { |x=8| x } + { |y=0| y + 1.0.rand };
|
|
~z.valueEnvir;
|
|
}
|
|
)
|
|
::
|
|
|
|
]
|
|
|
|
@racketblock[
|
|
// n-ary operators:
|
|
|
|
a = blend({ 3.0.rand }, { 1000.rand }, { |frac| frac });
|
|
a.value(0.5);
|
|
|
|
a.value((0, 0.06..1)); // creates a range of values..
|
|
::
|
|
|
|
]
|
|
|
|
|