#!/usr/bin/env python
# coding: utf-8

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# #### Imports
# The tutorial below imports [NumPy](http://www.numpy.org/), [Pandas](https://plot.ly/pandas/intro-to-pandas-tutorial/), [SciPy](https://www.scipy.org/) and [PeakUtils](http://pythonhosted.org/PeakUtils/).

# In[3]:


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:

# In[4]:


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

# 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')


# 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">'))

get_ipython().system(' 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')


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