# Peak Integration in Python

Learn how to integrate the area between peaks and bassline in Python.

#### New to Plotly?¶

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```
import plotly.plotly as py
import plotly.graph_objs as go
from plotly.tools import FigureFactory as FF
import numpy as np
import pandas as pd
import scipy
import peakutils
```

#### Tips¶

Our method for finding the area under any peak is to find the area from the `data values`

to the x-axis, the area from the `baseline`

to the x-axis, and then take the difference between them. In particular, we want to find the areas of these functions defined on the x-axis interval $I$ under the peak.

Let $T(x)$ be the function of the data, $B(x)$ the function of the baseline, and $Area$ the peak integration area between the baseline and the first peak. Since $T(x) \geq B(x)$ for all $x$, then we know that

$$ \begin{align} A = \int_{I} T(x)dx - \int_{I} B(x)dx \end{align} $$#### Import Data¶

For our example below we will import some data on milk production by month:

```
milk_data = pd.read_csv('https://raw.githubusercontent.com/plotly/datasets/master/monthly-milk-production-pounds.csv')
time_series = milk_data['Monthly milk production (pounds per cow)']
time_series = np.asarray(time_series)
df = milk_data[0:15]
table = FF.create_table(df)
py.iplot(table, filename='milk-production-dataframe')
```

#### Area Under One Peak¶

```
baseline_values = peakutils.baseline(time_series)
x = [j for j in range(len(time_series))]
time_series = time_series.tolist()
baseline_values = baseline_values.tolist()
rev_baseline_values = baseline_values[:11]
rev_baseline_values.reverse()
area_x = [0,1,2,3,4,5,6,7,8,9,10,11,10,9,8,7,6,5,4,3,2,1]
area_y = time_series[:11] + rev_baseline_values
trace = go.Scatter(
x=x,
y=time_series,
mode='lines',
marker=dict(
color='#B292EA',
),
name='Original Plot'
)
trace2 = go.Scatter(
x=x,
y=baseline_values,
mode='markers',
marker=dict(
size=3,
color='#EB55BF',
symbol='open-circle'
),
name='Bassline'
)
trace3 = go.Scatter(
x=area_x,
y=area_y,
mode='lines+markers',
marker=dict(
size=4,
color='rgb(255,0,0)',
),
name='1st Peak Outline'
)
first_peak_x = [j for j in range(11)]
area_under_first_peak = np.trapz(time_series[:11], first_peak_x) - np.trapz(baseline_values[:11], first_peak_x)
area_under_first_peak
annotation = go.Annotation(
x=80,
y=1000,
text='The peak integration for the first peak is approximately %s' % (area_under_first_peak),
showarrow=False
)
layout = go.Layout(
annotations=[annotation]
)
trace_data = [trace, trace2, trace3]
fig = go.Figure(data=trace_data, layout=layout)
py.iplot(fig, filename='milk-production-peak-integration')
```