Weighted Estimation of a Constant

WEstOfConstant.py

# -*- coding: utf-8 -*-
"""
Created on Thu Jun 23 21:45:31 2022

@author: personF
"""
import numpy as np
import matplotlib.pyplot as plt

class Resistor:
    def __init__(self,ohm):
        self.ohm = ohm

class Sensor:
    def __init__(self,mean,std):
        self.inputVal = []
        self.outputVal = []
        self.err_std = std
        self.mean = mean        
    
    def measure(self,realVal):
        self.inputVal.append(realVal)
        self.outputVal.append(realVal+np.random.normal(self.mean,self.err_std))
        
    def meanOfResult(self):
        return np.sum(self.outputVal)/len(self.outputVal)
    
# Create a resistor and sensors
resistor = Resistor(355)

sensorCheap = Sensor(0,11)
sensorExpensive = Sensor(0,3)

numberOfMeasurement = 3

# Measurement:
for i in range(0,numberOfMeasurement):
    sensorCheap.measure(resistor.ohm)
    sensorExpensive.measure(resistor.ohm)

# The histograph of the measurements
fig, axs = plt.subplots(2)
axs[0].hist(sensorCheap.outputVal)
axs[0].set_title("Cheap Multimeter")
axs[1].hist(sensorExpensive.outputVal)
axs[1].set_title("Expensive Multimeter")

x_lim = (min(sensorCheap.outputVal + sensorExpensive.outputVal)-1,max(sensorCheap.outputVal + sensorExpensive.outputVal)+1)
plt.setp(axs, xlim=x_lim)
plt.show()

# To verify
sensorCheapStd = np.std(sensorCheap.outputVal)
sensorExpensiveStd = np.std(sensorExpensive.outputVal)

# The mean of the measurements
cheapRes = sensorCheap.meanOfResult()
expensiveRes = sensorExpensive.meanOfResult()

###############################################
######### WEIGHTED
allMeasurements = np.concatenate((sensorCheap.outputVal,sensorExpensive.outputVal))

#For print the math equation
str_coeff_measurementWithWeights=[]
str_coeff_sensorsWithWeights=[]

#For math
coeff_measurementWeights=[]
coeff_sensorWeights=[]
coeff_measurementWithWeights=[]

measurementWithWeights = 0
sensorsWithWeights = 0

for i in range(0,len(allMeasurements)):
    if i<=(len(allMeasurements)/2)-1:
        sensor = sensorCheap
    else:
        sensor = sensorExpensive        
    
    # Keep each step values in a list
    coeff_measurementWeights.append(1/(sensor.err_std)**2)
    coeff_sensorWeights.append(1/(sensor.err_std**2))
    coeff_measurementWithWeights.append(allMeasurements[i]/((sensor.err_std)**2))
    
    tmp = "%.1f/%.1f" % (allMeasurements[i],(sensor.err_std)**2)
    str_coeff_measurementWithWeights.append(tmp)    
    tmp = "1/%d" % (sensor.err_std**2)
    str_coeff_sensorsWithWeights.append(tmp)    

        
weightedResult = (sum(coeff_sensorWeights)**(-1))*sum(coeff_measurementWithWeights)
print("The generic equation\t:\t(%s) (%s)" % ("+".join(str_coeff_sensorsWithWeights),"+".join(str_coeff_measurementWithWeights)))

# Calculate and print total coefficients of each measurement
totalCoeff =[x*(sum(coeff_sensorWeights)**-1) for x in coeff_measurementWeights]
str_totalCoeffMeasurement = []
for i in range(0,len(allMeasurements)):
    tmp = "%.3f*%.3f" % (totalCoeff[i],allMeasurements[i])
    str_totalCoeffMeasurement.append(tmp)
print("Weighted measurements\t:\t%s" % " + ".join(str_totalCoeffMeasurement))


# The bar of the estimations and real value
x = np.array(["Real", "Cheap", "Exp", "Weighted"])
y = np.array([resistor.ohm, cheapRes, expensiveRes, weightedResult])
plt.figure()
plt.axhline(y = resistor.ohm, color = 'k', linestyle = '--') #real
plt.axhline(y = weightedResult, color = 'b', linestyle = 'dashed') #weighted
plt.axhline(y = cheapRes, color = 'r', linestyle = 'dashed') #cheap
plt.axhline(y = expensiveRes, color = 'g', linestyle = 'dashed') #expensive
plt.legend(['real','weighted','cheap','expensive'])
plt.show()