pynkowski.theory.base_th

  1"""This submodule contains the base abstract class for theoretical fields, `TheoryField`."""
  2import numpy as np
  3
  4def _prepare_lkc(dim=None, lkc_ambient=None):
  5    """Define the Lipschitz–Killing Curvatures of the ambient manifold as the default ones (unit volume and the rest are 0), or verify their consistency. 
  6    If no argument is given, it defaults to a 2D space.
  7
  8    Parameters
  9    ----------
 10    dim : int, optional
 11        The dimension of the ambient manifold.
 12        
 13    lkc_ambient : list, optional
 14        A list of the Lipschitz–Killing Curvatures of the ambient manifold. Its lenght must be `dim+1` if both arguments are given.
 15        
 16    Returns
 17    ----------
 18    dim : int 
 19        The dimension of the ambient manifold.
 20        
 21    lkc_ambient : np.array or None, optional
 22        An array of the Lipschitz–Killing Curvatures of the ambient manifold.
 23    """
 24    if lkc_ambient is None: 
 25        if dim is None:
 26            dim = 2
 27        lkc_ambient = np.zeros(dim+1)
 28        lkc_ambient[-1] = 1.
 29    else:
 30        if dim is None:
 31            dim = len(lkc_ambient) -1
 32        else:
 33            assert len(lkc_ambient) == dim +1, 'If both dim and lkc_ambient are given, len(lkc_ambient) == dim +1'
 34    return dim, lkc_ambient
 35
 36class TheoryField():
 37    """General class for Theoretical fields, to be used as base for all fields.
 38
 39    Parameters
 40    ----------
 41    dim : int
 42        Dimension of the space where the field is defined.
 43    
 44    name : str, optional
 45        Name of the field.
 46        Defaul : `'TheoryField'`
 47    
 48    sigma : float, optional
 49        The standard deviation of the field.
 50        Default : 1.
 51        
 52    mu : float, optional
 53        The derivative of the covariance function at the origin, times $-2$.
 54        Default : 1.
 55        
 56    nu : float, optional
 57        The second derivative of the covariance function at the origin.
 58        Default : 1.
 59        
 60    lkc_ambient : np.array or None, optional
 61        The values for the Lipschitz–Killing Curvatures of the ambient space. If `None`, it is assumed that the volume is 1 and the rest is 0. This (times the volume) is exact for many spaces like Euclidean spaces or the sphere, and exact to leading order in μ for the rest.
 62        Default : None
 63        
 64    Attributes
 65    ----------
 66    dim : int
 67        Dimension of the space where the field is defined.
 68    
 69    name : str
 70        Name of the field.
 71    
 72    sigma : float
 73        The standard deviation of the field.
 74        
 75    mu : float
 76        The derivative of the covariance function at the origin, times $-2$. Equal to the variance of the first derivatives of the field.
 77
 78    nu : float
 79        The second derivative of the covariance function at the origin.
 80        
 81    lkc_ambient : np.array or None
 82        The values for the Lipschitz–Killing Curvatures of the ambient space.
 83        
 84    """   
 85    def __init__(self, dim, name='TheoryField', sigma=1., mu=1., nu=1., lkc_ambient=None):
 86        self.name = name
 87        self.sigma = sigma
 88        self.mu = mu
 89        self.nu = nu
 90        self.dim, self.lkc_ambient = _prepare_lkc(dim, lkc_ambient)
 91        
 92    def __repr__(self):
 93        return(f'"{self.name}" TheoryField, {self.dim}D, σ = {self.sigma:.1f}, μ = {self.mu:.1f}')
 94        
 95      
 96__all__ = ["TheoryField"]
 97
 98__docformat__ = "numpy"
 99
100