Notebook

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Imports¶

The tutorial below imports NumPy, Pandas, SciPy and PeakUtils.

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import plotly.plotly as py
import plotly.graph_objs as go
import plotly.figure_factory 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:

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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')

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Area Under One Peak¶

In [5]:

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',
    ),
    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')

/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/plotly/graph_objs/_deprecations.py:144: DeprecationWarning:

plotly.graph_objs.Annotation is deprecated.
Please replace it with one of the following more specific types
  - plotly.graph_objs.layout.Annotation
  - plotly.graph_objs.layout.scene.Annotation

Out[5]:

In [6]:

from IPython.display import display, HTML

display(HTML('<link href="//fonts.googleapis.com/css?family=Open+Sans:600,400,300,200|Inconsolata|Ubuntu+Mono:400,700" rel="stylesheet" type="text/css" />'))
display(HTML('<link rel="stylesheet" type="text/css" href="http://help.plot.ly/documentation/all_static/css/ipython-notebook-custom.css">'))

! pip install git+https://github.com/plotly/publisher.git --upgrade
import publisher
publisher.publish(
    'python-Peak-Integration.ipynb', 'python/peak-integration/', 'Peak Integration | plotly',
    'Learn how to integrate the area between peaks and bassline in Python.',
    title='Peak Integration in Python | plotly',
    name='Peak Integration',
    language='python',
    page_type='example_index', has_thumbnail='false', display_as='peak-analysis', order=4,
    ipynb= '~notebook_demo/121')

Collecting git+https://github.com/plotly/publisher.git
  Cloning https://github.com/plotly/publisher.git to /private/var/folders/tc/bs9g6vrd36q74m5t8h9cgphh0000gn/T/pip-req-build-iKhEAt
Building wheels for collected packages: publisher
  Running setup.py bdist_wheel for publisher ... done
  Stored in directory: /private/var/folders/tc/bs9g6vrd36q74m5t8h9cgphh0000gn/T/pip-ephem-wheel-cache-1Y3Gor/wheels/99/3e/a0/fbd22ba24cca72bdbaba53dbc23c1768755fb17b3af0f33966
Successfully built publisher
Installing collected packages: publisher
  Found existing installation: publisher 0.11
    Uninstalling publisher-0.11:
      Successfully uninstalled publisher-0.11
Successfully installed publisher-0.11

/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/IPython/nbconvert.py:13: ShimWarning:

The `IPython.nbconvert` package has been deprecated since IPython 4.0. You should import from nbconvert instead.

/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/publisher/publisher.py:53: UserWarning:

Did you "Save" this notebook before running this command? Remember to save, always save.

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