'''

deft.py (v1.1)

Written by by Justin B. Kinney, Cold Spring Harbor Laboratory

Last updated on 6 August 2014

Description:

Density Estimation using Field Theory (DEFT) in 1D and 2D

Reference:

Kinney JB (2014) Estimation of probability densities using scale-free field theories.

Phys Rev E 90:011301(R). arXiv:1312.6661 [physics.data-an].

Functions:

deft_1d: Performs density estimation in one dimension

deft_2d: Performs density estimation in two dimensions

Dependencies:

scipy

numpy

copy

time

'''

# Import stuff

import scipy as sp

from scipy.integrate import ode

from scipy.fftpack import fft, ifft, fft2, ifft2

from scipy.linalg import eig, det

from scipy.interpolate import interp1d, RectBivariateSpline

from scipy.sparse import csr_matrix, diags

from scipy.sparse.linalg import spsolve

from numpy.random import choice, randn

from copy import deepcopy

import time

import warnings

# Empty container class for storing results

class Results: pass;

# Used to compute the log determinant of Lambda

def get_log_det_Lambda(Lambda, coeff):

return log_det, coeff

################################################################################

# 1D DEFT

################################################################################

def deft_1d(xis_raw, bbox, G=100, alpha=2, num_samples=0, ti_shift=-5,

return Q_star_func

################################################################################

# 2D DEFT

################################################################################

def deft_2d(xis_raw, yis_raw, bbox, G=20, alpha=2, num_samples=0, tol=1E-3, ti_shift=-1, tf_shift=0, verbose=False, details=False):