Quaternion Function Reference

randvmf

von Mises-Fisher distribution of unit quaternions

Syntax

Y = randvmf(μ, κ, varargin)

Description

randvmf returns unit quaternions distributed on the 4-sphere according to the von Mises-Fisher distribution. See also randf for the 3-sphere case.

The first parameter μ must be a full quaternion (the mean direction in 4-space). The second parameter κ is the concentration parameter which controls the spread of the distribution on the 4-sphere. It must be non-negative. A value of zero results in a uniform distribution on the sphere. Larger values result in greater concentration of the distribution in the mean direction μ.

The remaining parameters are as for the MATLAB® function rand (q.v.). The result may be scalar, vector, matrix or array depending on the parameters supplied. Each pure quaternion returned is the result of at least two calls on rand, and two calls on randn, and hence randf modifies the state of the generator used by both rand and randn. To initialise the generator or control the choice of generator, use rand and/or randn.

See Also

QTFM functions: randf, randq, randv

References

  1. R. A. Fisher, 'Dispersion on a sphere', Proceedings of the Royal Society of London, Series A., 217, pp295-305, (1953).
  2. K. V. Mardia and P. E. Jupp, Directional Statistics (2nd edition), John Wiley (2000). [§9.3.]

© 2008-2013 Stephen J. Sangwine and Nicolas Le Bihan

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