import?numpy?as?np
import?math

def?epsilon（time_delta）:
	alpha0=5.0??#
	alpha1=1.25?#
	E=math.exp（-time_delta/alpha0）-math.exp（-time_delta/alpha1）
	H=1?if?time_delta?>=?0.0?else?0
	return?E*H

def?window（time_delta）:
	alpha=2.0
	return?math.exp（-time_delta/alpha）?if?time_delta>=0.0?else?0.0
	
def?training（weights?input_spikes?output_spikes）:
	#input_spikes=[abc...]
	#output_spikes=[[ab][abc]...]
	input_node_num=len（weights[0]）
	output_node_num=len（weights）
	
	max_epoch=100
	fire_voltage=10
	min_voltage=0.001
	threshold=0.001
	
	#for?each?output?spike?node?do?training
	for?outnd?in?range（output_node_num）:
		outspks=output_spikes[outnd]
		wts=weights[outnd]
		for?epoch?in?range（max_epoch）:
			#for?each?output?spike?of?this?output?spike?node
			#training
			for?outspk?in?outspks:
				#?compute?voltage
				voltage=0.0
				for?i?in?range（input_node_num）:
					voltage+=wts[i]*epsilon（outspk-input_spikes[i]）
				if?abs（voltage-fire_voltage）>threshold:
					#?filtering
					f=[]
					for?i?in?range（input_node_num）:
						if?epsilon（outspk-input_spikes[i]）>=min_voltage:
							f.append（i）
					#?adjust?weight
					denom=0.0