notebook.community

Edit and run



In [1]:

    
import pandas as pd



In [2]:

    
ts = pd.Series.from_csv('data/coherence_timeseries.csv')



In [3]:

    
ts.head()









    Out[3]:





0.0   -0.902547
0.4   -0.356314
0.8    1.000000
1.2    0.866656
1.6   -0.351326
dtype: float64

Alternatively, we can read the CSV file into a data frame.



In [4]:

    
df = pd.read_csv('data/coherence_timeseries.csv', header=None)



In [5]:

    
df.columns = ['time', 'signal']



In [6]:

    
df.head()



In [7]:

    
import matplotlib
%matplotlib inline
matplotlib.style.use('ggplot')
import matplotlib.pyplot as plt



In [8]:

    
plt.plot(df['time'], df['signal'])
plt.xlabel('time (fs)')
plt.ylabel('signal (a.u.)')
plt.title('Decoherence')









    Out[8]:





<matplotlib.text.Text at 0x7fa36a953748>

At first glance, we can identify two different parts in this time series: before and after roughly $t = 20$ fs. The signal looks pseudo-periodic before $20$ fs, and noisy after $20$ fs.



In [9]:

    
ts.loc[:20.0].plot()









    Out[9]:





<matplotlib.axes._subplots.AxesSubplot at 0x7fa36a944048>

There are about 10 pseudo-periods so one pseudo-period is $T \sim 2$ fs. Note that angles are easier on the eye when no sharper than $70$ degrees.



In [10]:

    
ts.loc[:8].plot()









    Out[10]:





<matplotlib.axes._subplots.AxesSubplot at 0x7fa36a8dd470>

What about a scatter plot?



In [11]:

    
df[:20].plot(kind='scatter', x='time', y='signal')









    Out[11]:





<matplotlib.axes._subplots.AxesSubplot at 0x7fa36a843cc0>

Maybe add a 'fitting' sine (line) as a guide to the eye?

We may want to use an inset in order to visualize both time scales (pseudo-period $T$ in the main plot and decoherence duration $t$ in the inset).



In [12]:

    
# Main axes
plt.plot(df['time'][:20], df['signal'][:20])
plt.xlabel('time (fs)')
plt.ylabel('signal (a.u.)')
plt.title('Decoherence')

# This is an inset axes over the main axes
inset = plt.axes([.67, .65, .2, .2], axisbg='w')
inset.plot(df['time'][:120], df['signal'][:120])
plt.setp(inset, yticks=[])









    Out[12]:





[]

plotly offers a more intuitive syntax.



In [13]:

    
import plotly
plotly.__version__









    Out[13]:





'1.8.3'



In [14]:

    
import plotly.plotly as py
import plotly.graph_objs as pgo



In [15]:

    
periods_trace = pgo.Scatter(x=df['time'][:20], y=df['signal'][:20])
decoherence_trace = pgo.Scatter(x=df['time'][:120], y=df['signal'][:120], xaxis='x2', yaxis='y2')

data = pgo.Data([periods_trace, decoherence_trace])

layout = pgo.Layout(xaxis2=pgo.XAxis(domain=[0.6, 0.95], anchor='y2', zeroline=False),
                    yaxis2=pgo.YAxis(domain=[0.6, 0.95], anchor='x2', zeroline=False),
                    showlegend=False,
                    xaxis=pgo.XAxis(zeroline=False),
                    yaxis=pgo.YAxis(zeroline=False))

fig = pgo.Figure(data=data, layout=layout)



In [16]:

    
py.iplot(fig, filename = 'inset-two-timescales')









    Out[16]:

Comparisons
Small variations vs orders of magnitude
Multivariate Analysis

	time	signal
0	0.0	-0.902547
1	0.4	-0.356314
2	0.8	1.000000
3	1.2	0.866656
4	1.6	-0.351326