# Least squared deviation (CostL2)#

## Description#

This cost function detects mean-shifts in a signal. Formally, for a signal $$\{y_t\}_t$$ on an interval $$I$$,

$c(y_{I}) = \sum_{t\in I} \|y_t - \bar{y}\|_2^2$

where $$\bar{y}$$ is the mean of $$\{y_t\}_{t\in I}$$.

## Usage#

import numpy as np
import matplotlib.pylab as plt
import ruptures as rpt

# creation of data
n, dim = 500, 3  # number of samples, dimension
n_bkps, sigma = 3, 5  # number of change points, noise standart deviation
signal, bkps = rpt.pw_constant(n, dim, n_bkps, noise_std=sigma)

Then create a CostL2 instance and print the cost of the sub-signal signal[50:150].

c = rpt.costs.CostL2().fit(signal)
print(c.error(50, 150))

You can also compute the sum of costs for a given list of change points.

print(c.sum_of_costs(bkps))
print(c.sum_of_costs([10, 100, 200, 250, n]))

In order to use this cost class in a change point detection algorithm (inheriting from BaseEstimator), either pass a CostL2 instance (through the argument custom_cost) or set model="l2".

c = rpt.costs.CostL2()
algo = rpt.Dynp(custom_cost=c)
# is equivalent to
algo = rpt.Dynp(model="l2")