This is a Python implementation of the p-square algorithm

# Introduction

This is a python implementation of this paper, which proposes a heuristic algorithm for dynamic calculation of the median and other percentiles. It has the advantage of running in O(1) at each iteration and is hence particularly useful when dealing with continuously (and fastly) incoming data.

# Install

1. From sources

```git clone git@gitlab.octo.com:bdalab/psquare.git
cd psquare
python setup.py install
```
2. Using pip

```pip install psquare
```

# Example of use

In the following example, we will estimate the value of the 95th percentile of a N(0,1) distribution using p square algorithm. We will compare our estimates as we continuously draw from the distribution, by comparing with the truth value given by the `numpy.percentile` function. At the end, we will plot the residuals, and the execution time using psquare and `numpy.percentile`.

```import numpy as np
import matplotlib
import matplotlib.pyplot as plt
import time

from psquare.psquare import PSquare

NB_ITERATIONS = 30000

def random_generator():
return np.random.normal(0, 1, 1)

def exact_value_for_quantile(values, quantile):
return np.percentile(values, quantile)

def main():
values = [random_generator() for _ in range(5)]
quantile_to_estimate = 95

psquare = PSquare(quantile_to_estimate)
exact_quantiles = []
estimated_quantiles = []
psquare_exec_time = []
numpy_exec_time = []

for val in values:  # p square algorithm necessitates 5 values to start
psquare.update(val)

for _ in range(NB_ITERATIONS):
new_val = random_generator()
values.append(new_val)

psquare_start = time.time()
psquare.update(new_val)
estimated_quantiles.append(psquare.p_estimate())
psquare_end = time.time()

numpy_start = time.time()
exact_quantiles.append(exact_value_for_quantile(values, quantile_to_estimate))
numpy_end = time.time()

psquare_exec_time.append(psquare_end - psquare_start)
numpy_exec_time.append(numpy_end - numpy_start)

matplotlib.rc('figure', figsize=(10, 5))
errors = np.abs(np.array(estimated_quantiles) - np.array(exact_quantiles))
plt.plot(errors)
plt.title('Absolute error between p-square predicted value and exact percentile value')
plt.ylabel('Difference between exact percentile value and p-square estimation')
plt.xlabel('Size of the dataset')
plt.rcParams["figure.figsize"] = (10, 5)
plt.show()

plt.plot(psquare_exec_time[1:], label='p-square')
plt.plot(numpy_exec_time[1:], label='numpy percentile')
plt.title('Execution time to compute percentile on a growing dataset')
plt.ylabel('Execution time (in seconds)')
plt.xlabel('Size of the dataset')
plt.legend()
plt.rcParams["figure.figsize"] = (10, 5)
plt.show()

if __name__ == '__main__':
main()
```

## Error between estimated and exact value

Using previous example we obtain the following figures:

• Errors between exact and predicted percentile value

• Execution time between p-square estimations and numpy percentile function: