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from numba import jit 
import numpy as np 

@jit(nopython=True)
def resid_lstsq(x,y):
	ret = np.linalg.lstsq(x,y)
	coef = ret[0]
	yHat = np.dot(x,coef)
	residuls = y - yHat

	return residuls

#np.dot((np.dot(np.linalg.inv(np.dot(x.T,x)),x.T)),y)

@jit(nopython=True)
def resid_matrixReverse(x,y):
	
	coef = np.dot(np.dot(np.linalg.inv(np.dot(x.T,x)),x.T),y)
	yHat = np.dot(x,coef)
	residuls = y - yHat

	return residuls


@jit(nopython=True)
def resid_matrixSolve(x,y):
	
	coef = np.linalg.solve(np.dot(x.T, x), np.dot(x.T, y))
	yHat = np.dot(x,coef)
	residuls = y - yHat

	return residuls

def residCalculatorVector(x,y,method='matrixReverse'):
	'''
	get the residuls of regression for one period
	x: the independent variables
	y: the dependent variables
	'''
	if method == 'lstsq':
		return resid_lstsq(x,y)

	elif method == 'matrixReverse':
		return resid_matrixReverse(x,y)

	elif method == 'matrixSolve':
		return resid_matrixSolve(x,y)

	elif method == 'sklearn':
		pass 



def residCalculatorTensor(newFactorTesor,oldFactorTensor,method='matrixReverse'):
	'''
	calculate the residuals between one new factor with several old factors for each date and each stocks
	newFactorTesor: (i,j,k)(i:stock ID, j: trade date, k:factors+target)
	oldFactorTensor (i,j,k)(i:stock ID, j: trade date, k:factors)
	return: the residual tensor for each factors and each trade date and each factors 
	'''


	stockNum = newFactorTesor.shape[0]		#stock number in the period  
	trDateNum = newFactorTesor.shape[1]		#trade date number 
	newFacNum = newFactorTesor.shape[2]		#new factor number + 1 (plus target) 

	ResidTensor = np.full(fill_value=np.nan,shape=(stockNum,trDateNum,newFacNum))	#the last column is the residul of target 
	
	for factor_i in range(newFacNum):
		
		for trDate_j in range(trDateNum):
			y_i_j = newFactorTesor[:,trDate_j,factor_i]		#factor_i in date_j for all stocks 
			x_j = oldFactorTensor[:,trDate_j,:]		#old factors in date_j for all stocks
			idx = np.where(~np.isnan(y_i_j))[0]	#the index which is NAs
			y_i_j_ = y_i_j[idx]		#rows without NA
			x_j_ = x_j[idx]			#rows without NA
			factorResid_i_j = residCalculatorVector(x_j_,y_i_j_,method=method)
			ResidTensor[idx,trDate_j,factor_i] = factorResid_i_j

	return ResidTensor

newF_01 = np.random.randn(3000,500,50)
oldFTen_01 = np.random.randn(3000,500,100)

%time ans = residCalculatorTensor(newFactorTesor=newF_01,oldFactorTensor=oldFTen_01,method='matrixSolve')

CPU times: user 21min 18s, sys: 51.2 s, total: 22min 9s
Wall time: 1min 23s