gauss
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## gauss

gauss — Gaussian distribution random number generator.

## Description

Gaussian distribution random number generator. This is an x-class noise generator.

## Syntax

    ares gauss krange

    ires gauss krange

    kres gauss krange

## Performance

krange -- the range of the random numbers (-krange to +krange). Outputs both positive and negative numbers.

gauss returns random numbers following a normal distribution centered around 0.0 (mu = 0.0) with a variance (sigma) of krange / 3.83. Thus more than 99.99% of the random values generated are in the range -krange to +krange. If a mean value different of 0.0 is desired, this mean value has to be added to the generated numbers (see example below).

For more detailed explanation of these distributions, see:

1. C. Dodge - T.A. Jerse 1985. Computer music. Schirmer books. pp.265 - 286

2. D. Lorrain. A panoply of stochastic cannons. In C. Roads, ed. 1989. Music machine . Cambridge, Massachusetts: MIT press, pp. 351 - 379.

## Examples

Here is an example of the gauss opcode. It uses the file gauss.csd.

Example 311. Example of the gauss opcode.

See the sections Real-time Audio and Command Line Flags for more information on using command line flags.

    <CsoundSynthesizer>
    <CsOptions>
      -d -o dac
    </CsOptions>
    <CsInstruments>
    instr 1
    irange   = p4
    imu      = p5
    isamples = p6
    indx     = 0
    icount   = 1
    ix       = 0.0
    ix2      = 0.0

    loop:
    i1       gauss   irange
    i1       =       i1 + imu
    ix       =       ix + i1
    ix2      =       ix2 + i1*i1
    if i1 >= -(irange+imu) && i1 <= (irange+imu) then
      icount = icount+1
    endif
             loop_lt indx, 1, isamples, loop

    imean    =       ix / isamples                         ;mean value
    istd     =       sqrt(ix2/isamples - imean*imean)      ;standard deviation
             prints "mean = %3.3f, std = %3.3f, ", imean, istd
             prints "samples inside the given range: %3.3f\%\n", icount*100.0/isamples
    endin
    </CsInstruments>
    <CsScore>
    i 1 0   0.1 1.0   0   100000  ; range = 1, mu = 0.0, sigma = 1/3.83 = 0.261
    i 1 0.1 0.1 3.83  0   100000  ; range = 3.83, mu = 0.0, sigma = 1
    i 1 0.2 0.1 5.745 2.7 100000  ; range = 5.745, mu = 2.7, sigma = 5.745/3.83 = 1.5
    </CsScore>
    </CsoundSynthesizer>

Its output should include lines like this:

    mean = 0.000, std = 0.260, samples inside the given range: 99.993%
    mean = 0.005, std = 0.999, samples inside the given range: 99.998%
    mean = 2.700, std = 1.497, samples inside the given range: 100.000%

## See Also

seed, betarand, bexprnd, cauchy, exprand, linrand, pcauchy, poisson, trirand, unirand, weibull

## Credits

Author: Paris Smaragdis
MIT, Cambridge
1995

Precisions about mu and sigma added by François Pinot after a discussion with Joachim Heintz on the Csound List, December 2010.

Example written by François Pinot, adapted from a csd file by Joachim Heintz, December 2010.

Existed in 3.30

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