Project: s41467-024-51026-0 | Function: Local_Phasing (python)

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**DESCRIPTION:** Local phasing algorithm implementing Expectation-Maximization to aggregate allelic information from individual SNPs to gene bins, maximizing likelihood while preserving single-cell resolution for detecting allele-specific copy number alterations

**KEY TERMS:** {
  "AD": "Alternative allele depth matrix (ALT counts)",
  "BD": "Reference allele depth matrix (REF counts = DP - AD)",
  "Z": "N×2 probability matrix for phase assignment",
  "thetas": "M×2 allelic ratio parameters for each cell",
  "logLik_mat": "Log-likelihood matrix for EM optimization",
  "epsilon_conv": "Convergence threshold for EM iterations"
}

**CONTEXT CODE:** # This file contains methods for phasing alleles on SNPs or genomic regions by 
# spatial correlations on allelic ratio
# Author: Yuanhua Huang
# Date: 12/11/2020

import numpy as np
from scipy.stats import entropy
from scipy.optimize import linear_sum_assignment
from scipy.special import logsumexp, digamma, betaln, binom

from .base_utils import normalize, loglik_amplify


def Local_Phasing(AD, DP, min_iter=10, max_iter=1000, epsilon_conv=1e-2,
                  init_mode='warm', verbose=False):
    """
    Phase the small blocks into a medium sized bin by assuming the allelic
    ratio is the same for all blocks. This is equavilent to a binary clustering,
    whose likelihood can be maximised by an EM alogrithm

    # Note that AD DP should be in in Compressed Sparse Column format.
    # or other sparse format.

    Parameters
    ----------
    AD : sparse matrix of integers
        Read counts for ALT allele in N blocks and M cells
    DP : sparse matrix of integers
        Read counts for REF allele in N blocks and M cells

    Returns
    -------
    ad_sum, dp_sum, Z, thetas, logLik
    """
    # MASKED: Local phasing algorithm implementing Expectation-Maximization to aggregate allelic information from individual SNPs to gene bins, maximizing likelihood while preserving single-cell resolution for detecting allele-specific copy number alterations
    raise NotImplementedError("Function has been masked for testing purposes")
        
    
'''
def Global_Phasing(thetas, step_size=1, n_prefix=1):
    """
    Phase the medium-sized bins into large scale regions, e.g., whole 
    chromosome. The assumption here is that the allelic ratio is similar within
    a neibougdhood. A dynamic programming for recercive optimization is used for
    this.
    """
    
    def _Dyna_Programming(thetas):
        """recursive optimization
        """
        is_flips = np.zeros(thetas.shape[0], bool)
        distances = np.zeros(thetas.shape[0])
        thetas_new = thetas + 0
        
        if thetas.shape[0] == 1:
            # print("Bottom:", thetas.shape[0])
            return is_flips, distances, thetas_new
        else:
            is_filps_pre, distances_pre, thetas_pre = _Dyna_Programming(thetas[:-1, :])
            
            theta_tmp0 = 0 + thetas[-1, :]
            theta_tmp1 = 1 - thetas[-1, :]
            
            _dist_tmp0 = (theta_tmp0 - thetas_pre[-1, :])**2
            _dist_tmp1 = (theta_tmp1 - thetas_pre[-1, :])**2
            _dist_tmp0 = np.sum(_dist_tmp0[_dist_tmp0 >=0 ])
            _dist_tmp1 = np.sum(_dist_tmp1[_dist_tmp1 >=0 ])

            # print(thetas.shape[0], _dist_tmp0, _dist_tmp1)
            
            is_flips[:-1]  = is_filps_pre
            distances[:-1] = distances_pre
            if _dist_tmp0 < _dist_tmp1:
                is_flips[-1] = False
                distances[-1]  = _dist_tmp0 + 0
                thetas_new[-1, :] = theta_tmp0 + 0
            else:
                is_flips[-1] = True
                distances[-1]  = _dist_tmp1 + 0
                thetas_new[-1, :] = theta_tmp1 + 0
            
            return is_flips, distances, thetas_new
    
    ## Return Dynamical programming results
    return _Dyna_Programming(thetas)

'''


def Global_Phasing(thetas, step_size=1, n_prefix=1, n_neighbors=5):
    """
    Phase the medium-sized bins into large scale regions, e.g., whole 
    chromosome. The assumption here is that the allelic ratio is similar within
    a neighborhood. A dynamic programming for recursive optimization is used for
    this.

    Parameters
    ----------
    thetas : np.ndarray
        Array of shape (n_bins, n_states)
    n_neighbors : int
        Number of previous bins to average for distance calculation
    """
    def _Dyna_Programming(thetas):
        """recursive optimization with neighborhood averaging"""
        is_flips = np.zeros(thetas.shape[0], bool)
        distances = np.zeros(thetas.shape[0])
        thetas_new = thetas + 0
        
        if thetas.shape[0] == 1:
            return is_flips, distances, thetas_new
        else:
            is_flips_pre, distances_pre, thetas_pre = _Dyna_Programming(thetas[:-1, :])


Complete the function implementation replacing "raise NotImplementedError".