Tendency creates dynamic random number distributions

Inherits from: Object

Tendency stores data for creating random values where the parameters for the random number generation occur over time.

Some Important Issues Regarding Tendency

Though the parameters 'parX' and 'parY' (see *new method below) are gnerally used to describe bounds over time, in certain distributions, these actual parameters may control other aspects of a random distribution. See the descriptions of the \cauchy, \gauss and \poisson distributions for more details.

Creation / Class Methods

*new (parX, parY, parA, parB, defDist)

Creates a new Tendency object. Any of the values below may be a SimpleNumber, Env or Function. If a Function is used, the current time will be passed into the Function.

parX - For the most common usage, describes the upper bounds of the distribution. Default value is 1.0.

parY - For the most common usage, describes the upper bounds of the distribution.. Default value is 0.0.

parA - For some distributions, the control of a specific parameter. Default value is 0.1

parB - For some distributions, the control of a specific parameter. Default value is 0.1.

defDist - A default distribution to use. Defaults to \uniform.

g = Tendency.new(1.0, 0.0);

Using Tendency

The basic usage of Tendency will be through the 'at' method. A random value wll be calculated according to the state of 'parX' and 'parY' at 'time' for a specific 'dist'.

at (time, dist)

Short prose description of method.

time - The time to calculate a random number for. Default value is 0.0.

dist - The distribution to use. The kind of distribution may change the meaning of some of the initial args (e.g., 'parX' may be treated as a 'mean'). If supplied, the defDist is overridden.

(

// basic Example.

g = Tendency.new(

Env([1.0, 0.5, 1.0], [0.5, 0.5]),

Env([0.9, 0.0, 0.9], [0.8, 0.2], [-10, 5]));

n = 500; // get 500 samples

o = n.collect({arg i; i = i / n; g.at(i)});

o.plot(discrete: true);

)

below is a listing of how inputs will map to parameters. n/a means a parameter is not used in a

distribution

dist parX parY parA parB

\uniform low high n/a n/a

\lpRand low high n/a n/a

\hpRand low high n/a n/a

\meanRand low high n/a n/a

\betaRand low high lowProb highProb

\cauchy mean spread posOnly n/a

\gauss dev mean n/a n/a

\poisson mean n/a n/a n/a

\expRand low high n/a n/a

\exponential density n/a n/a n/a

\gamma mode n/a n/a n/a

\laplace dispersion n/a n/a n/a

\alaplace dispersion n/a n/a n/a

\hcos dispersion n/a n/a n/a

\logistic dispersion n/a n/a n/a

\arcsin dispersion n/a n/a n/a

/*

Statistical Dsitributions using Tendency

*/

// create a tendency object giving fixed upper and lower bounds

a = Tendency.new(1.0, 0.0);

// Linear Distributions:

// uniform

z = 500.collect({arg i; a.at(i)})

z.plot(discrete: true)

// lowpass

z = 500.collect({arg i; a.at(i, \lpRand)})

z.plot(discrete: true)

// highpass

z = 500.collect({arg i; a.at(i, \hpRand)})

z.plot(discrete: true)

// mean (bandpass)

z = 500.collect({arg i; a.at(i, \meanRand)})

z.plot(discrete: true)

// Non-linear distributions

// exponential

// we need to redefine the range to avoid 0.0

a = Tendency.new(0.0001, 1.0);

z = 500.collect({arg i; a.at(i, \expRand)})

z.plot(discrete: true)

// exponential with 'parX' parameter control on density

a = Tendency.new(0.5);

z = 500.collect({arg i; a.at(i, \exponential)})

z.plot(discrete: true, minval: 0, maxval: 5)

a = Tendency.new(1);

z = 500.collect({arg i; a.at(i, \exponential)})

z.plot(discrete: true, minval: 0, maxval: 5)

a = Tendency.new(2);

z = 500.collect({arg i; a.at(i, \exponential)})

z.plot(discrete: true, minval: 0, maxval: 5)

// gamma

// 'parX' value controls mode or peak

a = Tendency.new(2.0);

z = 500.collect({arg i; a.at(i, \gamma)})

z.plot(discrete: true, minval: 0, maxval: 12)

a = Tendency.new(4.0);

z = 500.collect({arg i; a.at(i, \gamma)})

z.plot(discrete: true, minval: 0, maxval: 12)

a = Tendency.new(8.0);

z = 500.collect({arg i; a.at(i, \gamma)})

z.plot(discrete: true, minval: 0, maxval: 12)

// laplace

// 'parX' value controls dispersion

a = Tendency.new(0.01);

z = 500.collect({arg i; a.at(i, \laplace)})

z.plot(discrete: true, minval: -3, maxval: 3)

a = Tendency.new(0.1, 0);

z = 500.collect({arg i; a.at(i, \laplace)})

z.plot(discrete: true, minval: -3, maxval: 3)

a = Tendency.new(1.0, 0);

z = 500.collect({arg i; a.at(i, \laplace)})

z.plot(discrete: true, minval: -3, maxval: 3)

// alaplace (anti-laplace)

// special case of laplace, creates a gap in the center

// 'parX' value controls dispersion

a = Tendency.new(0.01);

z = 500.collect({arg i; a.at(i, \alaplace)})

z.plot(discrete: true, minval: -3, maxval: 3)

a = Tendency.new(0.1);

z = 500.collect({arg i; a.at(i, \alaplace)})

z.plot(discrete: true, minval: -3, maxval: 3)

a = Tendency.new(1.0, 0);

z = 500.collect({arg i; a.at(i, \alaplace)})

z.plot(discrete: true, minval: -3, maxval: 3)

// hcos

// hyperbolic cosine distribution

// 'parX' value controls dispersion

a = Tendency.new(0.01);

z = 500.collect({arg i; a.at(i, \hcos)})

z.plot(discrete: true, minval: -3, maxval: 3)

a = Tendency.new(0.1);

z = 500.collect({arg i; a.at(i, \hcos)})

z.plot(discrete: true, minval: -3, maxval: 3)

a = Tendency.new(1.0);

z = 500.collect({arg i; a.at(i, \hcos)})

z.plot(discrete: true, minval: -3, maxval: 3)

// logistic distribution

// 'parX' value controls dispersion

a = Tendency.new(0.01);

z = 500.collect({arg i; a.at(i, \logistic)})

z.plot(discrete: true, minval: -3, maxval: 3)

a = Tendency.new(0.1);

z = 500.collect({arg i; a.at(i, \logistic)})

z.plot(discrete: true, minval: -3, maxval: 3)

a = Tendency.new(1.0);

z = 500.collect({arg i; a.at(i, \logistic)})

z.plot(discrete: true, minval: -3, maxval: 3)

// poisson

// 'parX' value is the mean of the distribution

// this distribution has a discrete histogram (not continuous)

// it returns always integer values

a = Tendency.new(4)

z = 500.collect({arg i; a.at(i, \poisson)})

z.plot(discrete: true)

z.histo.plot(discrete: true)

a = Tendency.new(6)

z = 500.collect({arg i; a.at(i, \poisson)})

z.plot(discrete: true)

z.histo.plot(discrete: true)

// arcsin

// arcsin distribution

// 'parX' value controls dispersion (spread)

// output range is between 0 and this value

// histogram shape is similar to beta with parA=parB=0.5

a = Tendency.new(0.01);

z = 500.collect({arg i; a.at(i, \arcsin)})

z.maxItem;

z.plot(discrete: true, minval: 0, maxval: 10)

z.histo.plot(discrete: true)

a = Tendency.new(0.1);

z = 500.collect({arg i; a.at(i, \arcsin)})

z.maxItem;

z.plot(discrete: true, minval: 0, maxval: 1)

a = Tendency.new(1.0);

z = 500.collect({arg i; a.at(i, \arcsin)})

z.maxItem;

z.plot(discrete: true, minval: 0, maxval: 1)

// Symmetrical non-linear distributions

// beta

// this distribution takes two extra parameters parA and parB

// to describe where the likelihood that a random value will occur

// near parX (parA) or parY (parB)

// parA = parB = 0.5

// histogram has symmetrical shape

a = Tendency.new(1.0, 0.0, 0.5, 0.5);

z = 500.collect({arg i; a.at(i, \betaRand)})

z.plot(discrete: true)

z.histo.plot(discrete: true)

// parA = 0.5, parB = 0.25

// histogram lopsided towards parX end

a = Tendency.new(1.0, 0.0, 0.5, 0.25);

z = 500.collect({arg i; a.at(i, \betaRand)})

z.plot(discrete: true)

z.histo.plot(discrete: true)

// parA = 0.25, parB = 0.5

// histogram lopsided towards low end

a = Tendency.new(1.0, 0.0, 0.25, 0.5);

z = 500.collect({arg i; a.at(i, \betaRand)})

z.plot(discrete: true)

z.histo.plot(discrete: true)

// cauchy

// this distribution has a symmetrical histogram around 0

// for this implementation 'parX' controls its dispersion

// if parA = 1, only positive values are returned

// small dispersion around 0.0

a = Tendency.new(0.01)

z = 500.collect({arg i; a.at(i, \cauchy)})

z.plot(discrete: true, minval: -3, maxval: 3)

// larger dispersion around 0.0

a = Tendency.new(0.1)

z = 500.collect({arg i; a.at(i, \cauchy)})

z.plot(discrete: true, minval: -3, maxval: 3)

// even larger dispersion around 0.0, return only positive half

a = Tendency.new(1.0, parA: 1)

z = 500.collect({arg i; a.at(i, \cauchy)})

z.plot(discrete: true, minval: -3, maxval: 3)

// gaussian

// this distribution has a bell-shaped symmetrical histogram

// 'parX' is the deviation or width of the bell

// small deviation

a = Tendency.new(0.01)

z = 500.collect({arg i; a.at(i, \gauss)})

z.plot(discrete: true, minval: -3, maxval: 3)

// larger deviation

a = Tendency.new(0.1)

z = 500.collect({arg i; a.at(i, \gauss)})

z.plot(discrete: true, minval: -3, maxval: 3)

// even larger deviation

a = Tendency.new(1.0)

z = 500.collect({arg i; a.at(i, \gauss)})

z.plot(discrete: true, minval: -3, maxval: 3)

// Using them with envelopes and time:

a = Tendency.new(Env([0.01, 1.0], [1]), 1.0);

// Tendency at takes a time for the Envs

z = 500.collect({arg i; a.at(i / 500, \gauss)})

z.plot(discrete: true, minval: -3, maxval: 3)

a = Tendency.new(Env([0.01, 1.0], [1]));

z = 500.collect({arg i; a.at(i / 500, \arcsin)})

z.plot(discrete: true, minval: 0, maxval: 1)

asStream (dist)

SynthDef(\tendency, {arg freq;

Out.ar(0, SinOsc.ar(freq, 0, XLine.kr(0.1, 0.0001, 1, doneAction: 2)));

}).send(s);

(

Routine.run({

g = Tendency.new(1760.0, 440.0, Env([0.01, 2.0], [10], \sin), Env([0.01, 2.0], [10], \sin)).asStream(\betaRand);

t = Main.elapsedTime;

while({

Synth(\tendency, [\freq, g.next]);

0.02.wait;

(Main.elapsedTime - t) < 10;

})

})

)