nifty7.library.dynamic_operator module

dynamic_lightcone_operator(*, target, harmonic_padding, sm_s0, sm_x0, key, lightcone_key, sigc, quant, causal=True, minimum_phase=False)[source]

Extends the functionality of dynamic_operator() to a Green’s function which is constrained to be within a light cone.

The resulting Green’s function is constrained to be within a light cone. This is achieved via convolution of the function with a light cone in space-time. Thereby the first axis of the space is set to be the teporal axis.

Parameters
  • target (RGSpace) – The harmonic space in which the Green’s function shall be constructed. It needs to have at least two dimensions.

  • harmonic_padding (None, int, list of int) – Amount of central padding in harmonic space in pixels. If None the field is not padded at all.

  • sm_s0 (float) – Cutoff for dynamic smoothness prior.

  • sm_x0 (float, list of float) – Scaling of dynamic smoothness along each axis.

  • key (String) – Key for dynamics encoding parameter.

  • lightcone_key (String) – Key for lightspeed paramteter.

  • sigc (float, list of float) – Variance of lightspeed parameter.

  • quant (float) – Quantization of the light cone in pixels.

  • causal (boolean) – Whether or not the Green’s function shall be causal in time. Default is True.

  • minimum_phase (boolean) – Whether or not the Green’s function shall be a minimum phase filter. Default is False.

Returns

  • Operator – The Operator encoding the dynamic Green’s function in harmonic space.

  • Dictionary of Operator – A collection of sub-chains of Operator which can be used for plotting and evaluation.

Notes

The first axis of the domain is interpreted the time axis.

dynamic_operator(*, target, harmonic_padding, sm_s0, sm_x0, key, causal=True, minimum_phase=False)[source]

Constructs an operator encoding the Green’s function of a linear homogeneous dynamic system.

When evaluated, this operator returns the Green’s function representation in harmonic space. This result can be used as a convolution kernel to construct solutions of the homogeneous stochastic differential equation encoded in this operator. Note that if causal is True, the Green’s function is convolved with a step function in time, where the temporal axis is the first axis of the space. In this case the resulting function only extends up to half the length of the first axis of the space to avoid boundary effects during convolution. If minimum_phase is true then the spectrum of the Green’s function is used to construct a corresponding minimum phase filter.

Parameters
  • target (RGSpace) – The harmonic space in which the Green’s function shall be constructed.

  • harmonic_padding (None, int, list of int) – Amount of central padding in harmonic space in pixels. If None the field is not padded at all.

  • sm_s0 (float) – Cutoff for dynamic smoothness prior.

  • sm_x0 (float, list of float) – Scaling of dynamic smoothness along each axis.

  • key (String) – key for dynamics encoding parameter.

  • causal (boolean) – Whether or not the Green’s function shall be causal in time. Default is True.

  • minimum_phase (boolean) – Whether or not the Green’s function shall be a minimum phase filter. Default is False.

Returns

  • Operator – The Operator encoding the dynamic Green’s function in target space.

  • Dictionary of Operator – A collection of sub-chains of Operator which can be used for plotting and evaluation.

Notes

The first axis of the domain is interpreted the time axis.