# -*- coding: utf-8 -*-
"""
Created on Mon Dec 20 16:53:39 2021
modified: https://gist.github.com/fabianp/9396204419c7b638d38f
@author: pan
"""

import numpy as np
from numpy.linalg import inv
from osgeo import gdal, gdal_array
import os, time,glob
from sklearn import linear_model
from sklearn import preprocessing
from matplotlib import pyplot as plt

def partial_corr(C):
    """
    Returns the sample linear partial correlation coefficients between pairs of variables in C, controlling 
    for the remaining variables in C.
    Parameters
    ----------
    C : array-like, shape (n, p)
        Array with the different variables. Each column of C is taken as a variable
    Returns
    -------
    P_corr : array-like, shape (p, p)
        P_corr[i, j] contains the partial correlation of C[:, i] and C[:, j] controlling
        for the remaining variables in C.
    """
    
    C = np.asarray(C)
    p = C.shape[1]
    P_corr = np.zeros((p, p)) # sample linear partial correlation coefficients
    
    corr = np.corrcoef(C,rowvar=False) # Pearson product-moment correlation coefficients.
    corr_inv = inv(corr) # the (multiplicative) inverse of a matrix.
    
    for i in range(p):
        P_corr[i, i] = 1
        for j in range(i+1, p):
            pcorr_ij = -corr_inv[i,j]/(np.sqrt(corr_inv[i,i]*corr_inv[j,j]))
            P_corr[i,j]=pcorr_ij
            P_corr[j,i]=pcorr_ij
        
    return P_corr