peak-integration.md

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jupytext kernelspec plotly notebook_metadata_filter text_representation all extension format_name format_version jupytext_version .md markdown 1.1 1.1.1 display_name language name Python 2 python python2 description display_as has_thumbnail language layout name order page_type permalink thumbnail Learn how to integrate the area between peaks and baseline in Python. peak-analysis false python base Peak Integration 4 example_index python/peak-integration/ /images/static-image

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Imports

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

importplotly.plotlyaspyimportplotly.graph_objsasgoimportplotly.figure_factoryasffimportnumpyasnpimportpandasaspdimportscipyimportpeakutils

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= [jforjinrange(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_valuestrace=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= [jforjinrange(11)] area_under_first_peak=np.trapz(time_series[:11], first_peak_x) -np.trapz(baseline_values[:11], first_peak_x) area_under_first_peakannotation=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')

fromIPython.displayimportdisplay, HTMLdisplay(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">')) ! pipinstallgit+https://github.com/plotly/publisher.git--upgradeimportpublisherpublisher.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')