Cumulative

[Edoardo-Pedicillo]

This PR implements and benchmarks a new function to evaluate the cumulative distribution.
To compare the old method (method1) with the new one (method2), you can use the following code

import time

import numpy as np
import matplotlib.pyplot as plt

REPETITIONS = 100

def cum_method1(real_values_combined, real_values_state0):
    return  [
            sum(map(lambda x: x.real >= real_value, real_values_state0))
            for real_value in real_values_combined
        ]

def cum_method2(input_data, points):
    # data and points sorted
    input_data = np.sort(input_data)
    points = np.sort(points)
 
    prob = []
    app = 0
    for val in input_data:
        app += np.max(np.searchsorted(points[app::], val), 0)
        prob.append(app)

    return np.array(prob)

def time_compare(method, input1, input2):
    start = time.time()
    for _ in range(REPETITIONS):
       cum =  method(input1, input2)
    end = time.time()
    return (end-start)/REPETITIONS, cum

state0_center = [0.0, 0.0]
state1_center = [2.0, 2.0]
cov = 0.1 * np.eye(2)
size = 100  # print(points, input_data)

data_0 = np.random.multivariate_normal(state0_center, cov, size=size)
data_1 = np.random.multivariate_normal(state1_center, cov, size=size)

all_data = np.concatenate((data_0, data_1), axis = 0)

#method1
time1, cum1 = time_compare(cum_method1,all_data[:,0],data_0[:,0])
print("Method 1: ", time1)

#method2
time2, cum2 = time_compare(cum_method2,all_data[:,0],data_0[:,0])
print("Method 2: ", time2)

#Plots
plt.figure(figsize=(14, 7), dpi=80)
plt.subplot(1,2,1)
plt.scatter(data_0[:, 0], data_0[:, 1], label = "0")
plt.scatter(data_1[:, 0], data_1[:, 1], label = "1")

plt.subplot(1,2,2)
plt.scatter(all_data[:,0],cum1, label = f"method1 ({round(time1, 4)})")
plt.scatter(np.sort(all_data[:, 0]), cum2, label = f"method2 ({round(time2,4)})")
plt.legend()
plt.show()

From the outputs we can see:

1. the new method is four time faster
2. the old method has a bug ( we have to change the condition x.real >= real_value in x.real <= real_value)

Method 1:  0.0026085638999938966
Method 2:  0.0008060479164123535

With the change proposed in point 2 this is the result

Checklist:

• Reviewers confirm new code works as expected.
• Tests are passing.
• Coverage does not decrease.
• Documentation is updated.

[codecov]

Codecov Report

Merging #313 (c9a4e3a) into main (159c5ed) will increase coverage by 0.19%.
The diff coverage is 81.81%.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #313      +/-   ##
==========================================
+ Coverage   37.85%   38.05%   +0.19%     
==========================================
  Files          42       42              
  Lines        2800     2809       +9     
==========================================
+ Hits         1060     1069       +9     
  Misses       1740     1740              

Flag	Coverage Δ
unittests	38.05% <81.81%> (+0.19%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

Impacted Files	Coverage Δ
src/qibocal/fitting/methods.py	71.92% <0.00%> (ø)
src/qibocal/fitting/utils.py	100.00% <100.00%> (ø)

[andrea-pasquale]

@Edoardo-Pedicillo could we add a quick test for the cumulative?

[Edoardo-Pedicillo]

Done