4.6.14. pde.tools.spectral module

Functions making use of spectral decompositions

make_colored_noise

Return a function creating an array of random values that obey
make_colored_noise(shape, dx=1.0, exponent=0, scale=1, rng=None)[source]

Return a function creating an array of random values that obey

\[\langle c(\boldsymbol k) c(\boldsymbol k’) \rangle = \Gamma^2 |\boldsymbol k|^\nu \delta(\boldsymbol k-\boldsymbol k’)\]

in spectral space on a Cartesian grid. The special case \(\nu = 0\) corresponds to white noise.

Parameters

  • shape (tuple of ints) – Number of supports points in each spatial dimension. The number of the list defines the spatial dimension.

  • dx (float or list of floats) – Discretization along each dimension. A uniform discretization in each direction can be indicated by a single number.

  • exponent (float) – Exponent \(\nu\) of the power spectrum

  • scale (float) – Scaling factor \(\Gamma\) determining noise strength

  • rng (Generator) – Random number generator (default: default_rng())

Returns

a function returning a random realization

Return type

callable