gauss — Gaussian distribution random number generator.
ares gauss krange
ires gauss irange
kres gauss krange
ares gauss kmean, ksdev
ires gauss imean, isdev
kres gauss kmean, ksdev
krange -- the range of the random numbers (-krange to +krange). Outputs both positive and negative numbers.
kmean -- normal distribution mean.
ksdev -- normal distribution standard deviation.
The first version of 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).
The second version takes mean and standard deviation as parameters. They use the more mathematically sound Box-Muller algorithm to compute the normal distribution.
For more detailed explanation of these distributions, see:
C. Dodge - T.A. Jerse 1985. Computer music. Schirmer books. pp.265 - 286
D. Lorrain. A panoply of stochastic cannons. In C. Roads, ed. 1989. Music machine . Cambridge, Massachusetts: MIT press, pp. 351 - 379.
Here is an example of the gauss opcode. It uses the file gauss.csd.
Example 413. 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%
Author (first version): Paris Smaragdis |
MIT, Cambridge |
1995 |
Author (second version): Victor Lazzarini |
Maynooth University, Ireland |
2020 |
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