## Fit your data like the FB Data Science team¶

Plotly is a web-based platform for making graphs and analyzing data. Among other features, you can make fits using Python, MATLAB, R, and with Plotly's native fitting tools. We'll use all of those options in this IPython Notebook.

To get started, let's re-make a graph from the FB Data Science Team. We can go to WebPlotDigitizer, access the data, and make a plot from Plotly's GUI.

In [1]:
from IPython.display import HTML # use IPython tools for embedding

In [2]:
HTML('<center><iframe width="650" height="650" frameborder="0" seamless="seamless" scrolling="no" src="https://plot.ly/~cimar/38/.embed?width=650&height=650"></iframe></center>')

Out[2]:

Not bad. Note the flexibility of fitting options: linear, polynomial, exponential, peak, inverse, and inverse squared. You also get calculated attributes and values; storage of data, code, and graphs together; and exportable figures accessible via the GUI, API, or URLs. Plotly also translates the figure between languages.
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The point being: it's interoperable. Read on to learn more, then head over to our docs to get started on some of these:

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## I. Fitting with Python¶

You can copy and paste the code below and use the key from our Python sandbox account. You'll want to install our API. You can also sign-up. Accounts are free, you own your data, and you control privacy and sharing.

Let's start out by making a plot with matplotlib and translating it into Plotly.

In [3]:
import plotly
plotly.__version__

Out[3]:
'1.0.34'
In [4]:
import matplotlib.pyplot as plt # side-stepping mpl's backend
import plotly.plotly as py
import plotly.tools as tls
from plotly.graph_objs import *
%matplotlib inline
py.sign_in("IPython.Demo", "1fw3zw2o13")

In [5]:
fig1 = plt.figure()

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(-2.0, 2.0, 10000) # The x-values
sigma = np.linspace(0.4, 1.0, 4) # Some different values of sigma

# Evaluate a Gaussian for each sigma
gaussians = [(2*np.pi*s**2)**-0.5 * np.exp(-0.5*x**2/s**2) for s in sigma]

ax = plt.axes()

for s,y in zip(sigma, gaussians):
ax.plot(x, y, lw=1.25, label=r"$\sigma = %3.2f$"%s)

formula = r"$y(x)=\frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{x^2}{2\sigma^2}}$"

ax.text(0.05, 0.80, formula, transform=ax.transAxes, fontsize=20)
ax.set_xlabel(r"$x$", fontsize=18)
ax.set_ylabel(r"$y(x)$", fontsize=18)
ax.legend()
plt.show()

In [16]:
py.iplot_mpl(fig1) # Translate figure to Plotly


Though the translation is not perfect, we can easily clean it up with Python or our GUI.

More generally, Plotly will:

• Save the data and plot at a URL (https://plot.ly/~IPython.Demo/4182)
• Save the data for analysis or re-plotting
• Save revisions online

You control the privacy and sharing (like a Google Doc). It's free and you own your data. These features are true for every graph.

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We've now edited it in the GUI and styled it. Let's embed and investigate the figure.

In [7]:
from plotly.graph_objs import Data, Layout, Figure

In [8]:
tls.embed('MattSundquist', '1896')

In [9]:
# Convert MPL figure to Plotly
my_fig = tls.mpl_to_plotly(fig1)

In [10]:
print my_fig.to_string() # check out your graph.

Figure(
data=Data([
Scatter(
x=[-2.0, -1.9995999599959997, -1.9991999199919992, -1.998799879...],
y=[3.7167987868357507e-06, 3.7354293180981496e-06, 3.7541494803...],
name='$\\sigma = 0.40$',
mode='lines',
line=Line(
dash='solid',
color='#0000FF',
width=1.25,
opacity=1
),
xaxis='x1',
yaxis='y1'
),
Scatter(
x=[-2.0, -1.9995999599959997, -1.9991999199919992, -1.998799879...],
y=[0.0025704649938185107, 0.0025761834897230665, 0.002581913559...],
name='$\\sigma = 0.60$',
mode='lines',
line=Line(
dash='solid',
color='#007F00',
width=1.25,
opacity=1
),
xaxis='x1',
yaxis='y1'
),
Scatter(
x=[-2.0, -1.9995999599959997, -1.9991999199919992, -1.998799879...],
y=[0.02191037561696068, 0.021937780710823064, 0.021965214590068...],
name='$\\sigma = 0.80$',
mode='lines',
line=Line(
dash='solid',
color='#FF0000',
width=1.25,
opacity=1
),
xaxis='x1',
yaxis='y1'
),
Scatter(
x=[-2.0, -1.9995999599959997, -1.9991999199919992, -1.998799879...],
y=[0.053990966513188063, 0.054034176567683667, 0.05407741254993...],
name='$\\sigma = 1.00$',
mode='lines',
line=Line(
dash='solid',
color='#00BFBF',
width=1.25,
opacity=1
),
xaxis='x1',
yaxis='y1'
)
]),
layout=Layout(
width=480,
height=320,
autosize=False,
margin=Margin(
l=60,
r=47,
b=40,
t=31,
),
hovermode='closest',
showlegend=False,
annotations=Annotations([
Annotation(
x=0.049865951742627333,
y=0.79678714859437749,
text='$y(x)=\\frac{1}{\\sqrt{2\\pi\\sigma^2}}e^{-\\frac{x^2...', xref='paper', yref='paper', showarrow=False, font=Font( size=20.0, color='#000000' ), opacity=1, xanchor='left', yanchor='bottom' ), Annotation( x=0.84248977989278806, y=0.91129032258064524, text='$\\sigma = 0.40$', xref='paper', yref='paper', showarrow=False, font=Font( size=12.0, color='#000000' ), opacity=1, xanchor='left', yanchor='bottom' ), Annotation( x=0.84248977989278806, y=0.83198924731182788, text='$\\sigma = 0.60$', xref='paper', yref='paper', showarrow=False, font=Font( size=12.0, color='#000000' ), opacity=1, xanchor='left', yanchor='bottom' ), Annotation( x=0.84248977989278806, y=0.75268817204301075, text='$\\sigma = 0.80$', xref='paper', yref='paper', showarrow=False, font=Font( size=12.0, color='#000000' ), opacity=1, xanchor='left', yanchor='bottom' ), Annotation( x=0.84248977989278806, y=0.67338709677419362, text='$\\sigma = 1.00$', xref='paper', yref='paper', showarrow=False, font=Font( size=12.0, color='#000000' ), opacity=1, xanchor='left', yanchor='bottom' ) ]), xaxis1=XAxis( title='$x$', domain=[0.0, 1.0], range=[-2.0, 2.0], type='linear', showline=True, ticks='inside', nticks=9, showgrid=False, zeroline=False, titlefont=Font( size=18.0, color='#000000' ), tickfont=Font( size=10.0 ), anchor='y1', side='bottom', mirror='ticks' ), yaxis1=YAxis( title='$y(x)$', domain=[0.0, 1.0], range=[0.0, 1.0], type='linear', showline=True, ticks='inside', nticks=6, showgrid=False, zeroline=False, titlefont=Font( size=18.0, color='#000000' ), tickfont=Font( size=10.0 ), anchor='x1', side='left', mirror='ticks' ) ) )  In [11]: help(Data) # check out data  Help on class Data in module plotly.graph_objs.graph_objs: class Data(PlotlyList) | A list of traces to be shown on a plot/graph. | | Any operation that can be done with a standard list may be used with Data. | Instantiation requires an iterable (just like list does), for example: | | Data([Scatter(), Heatmap(), Box()]) | | Valid entry types: (dict or any subclass of Trace, i.e., Scatter, Box, etc.) | | | Quick method reference: | | Data.update(changes) | Data.strip_style() | Data.get_data() | Data.to_graph_objs() | Data.validate() | Data.to_string() | Data.force_clean() | | Method resolution order: | Data | PlotlyList | __builtin__.list | __builtin__.object | | Methods defined here: | | to_graph_objs(self, caller=True) | Change any nested collections to subclasses of PlotlyDict/List. | | Procedure: | 1. Attempt to convert all entries to a subclass of PlotlyTrace. | 2. Call to_graph_objects on each of these entries. | | ---------------------------------------------------------------------- | Methods inherited from PlotlyList: | | __init__(self, *args) | | force_clean(self, caller=True) | Attempts to convert to graph_objs and calls force_clean() on entries. | | Calling force_clean() on a PlotlyList will ensure that the object is | valid and may be sent to plotly. This process will remove any entries | that end up with a length == 0. It will also remove itself from | enclosing trivial structures if it is enclosed by a collection with | length 1, meaning the data is the ONLY object in the collection. | | Careful! This will delete any invalid entries *silently*. | | get_data(self) | Returns the JSON for the plot with non-data elements stripped. | | get_ordered(self, caller=True) | | strip_style(self) | Strip style from the current representation. | | All PlotlyDicts and PlotlyLists are guaranteed to survive the | stripping process, though they made be left empty. This is allowable. | | Keys that will be stripped in this process are tagged with | 'type': 'style' in the INFO dictionary listed in graph_objs_meta.py. | | This process first attempts to convert nested collections from dicts | or lists to subclasses of PlotlyList/PlotlyDict. This process forces | a validation, which may throw exceptions. | | Then, each of these objects call strip_style on themselves and so | on, recursively until the entire structure has been validated and | stripped. | | to_string(self, level=0, indent=4, eol='\n', pretty=True, max_chars=80) | Returns a formatted string showing graph_obj constructors. | | Example: | | print obj.to_string() | | Keyword arguments: | level (default = 0) -- set number of indentations to start with | indent (default = 4) -- set indentation amount | eol (default = ' | ') -- set end of line character(s) | pretty (default = True) -- curtail long list output with a '...' | max_chars (default = 80) -- set max characters per line | | update(self, changes) | Update current list with changed_list, which must be iterable. | The 'changes' should be a list of dictionaries, however, | it is permitted to be a single dict object. | | validate(self, caller=True) | Recursively check the validity of the entries in a PlotlyList. | | PlotlyList may only contain suclasses of PlotlyDict, or dictionary-like | objects that can be re-instantiated as subclasses of PlotlyDict. | | The validation process first requires that all nested collections be | converted to the appropriate subclass of PlotlyDict/PlotlyList. Then, | each of these objects call validate and so on, recursively, | until the entire list has been validated. | | ---------------------------------------------------------------------- | Data descriptors inherited from PlotlyList: | | __dict__ | dictionary for instance variables (if defined) | | __weakref__ | list of weak references to the object (if defined) | | ---------------------------------------------------------------------- | Data and other attributes inherited from PlotlyList: | | __metaclass__ = <class 'plotly.graph_objs.graph_objs.ListMeta'> | A meta class for PlotlyList class creation. | | The sole purpose of this meta class is to properly create the __doc__ | attribute so that running help(Obj), where Obj is a subclass of PlotlyList, | will return useful information for that object. | | ---------------------------------------------------------------------- | Methods inherited from __builtin__.list: | | __add__(...) | x.__add__(y) <==> x+y | | __contains__(...) | x.__contains__(y) <==> y in x | | __delitem__(...) | x.__delitem__(y) <==> del x[y] | | __delslice__(...) | x.__delslice__(i, j) <==> del x[i:j] | | Use of negative indices is not supported. | | __eq__(...) | x.__eq__(y) <==> x==y | | __ge__(...) | x.__ge__(y) <==> x>=y | | __getattribute__(...) | x.__getattribute__('name') <==> x.name | | __getitem__(...) | x.__getitem__(y) <==> x[y] | | __getslice__(...) | x.__getslice__(i, j) <==> x[i:j] | | Use of negative indices is not supported. | | __gt__(...) | x.__gt__(y) <==> x>y | | __iadd__(...) | x.__iadd__(y) <==> x+=y | | __imul__(...) | x.__imul__(y) <==> x*=y | | __iter__(...) | x.__iter__() <==> iter(x) | | __le__(...) | x.__le__(y) <==> x<=y | | __len__(...) | x.__len__() <==> len(x) | | __lt__(...) | x.__lt__(y) <==> x<y | | __mul__(...) | x.__mul__(n) <==> x*n | | __ne__(...) | x.__ne__(y) <==> x!=y | | __repr__(...) | x.__repr__() <==> repr(x) | | __reversed__(...) | L.__reversed__() -- return a reverse iterator over the list | | __rmul__(...) | x.__rmul__(n) <==> n*x | | __setitem__(...) | x.__setitem__(i, y) <==> x[i]=y | | __setslice__(...) | x.__setslice__(i, j, y) <==> x[i:j]=y | | Use of negative indices is not supported. | | __sizeof__(...) | L.__sizeof__() -- size of L in memory, in bytes | | append(...) | L.append(object) -- append object to end | | count(...) | L.count(value) -> integer -- return number of occurrences of value | | extend(...) | L.extend(iterable) -- extend list by appending elements from the iterable | | index(...) | L.index(value, [start, [stop]]) -> integer -- return first index of value. | Raises ValueError if the value is not present. | | insert(...) | L.insert(index, object) -- insert object before index | | pop(...) | L.pop([index]) -> item -- remove and return item at index (default last). | Raises IndexError if list is empty or index is out of range. | | remove(...) | L.remove(value) -- remove first occurrence of value. | Raises ValueError if the value is not present. | | reverse(...) | L.reverse() -- reverse *IN PLACE* | | sort(...) | L.sort(cmp=None, key=None, reverse=False) -- stable sort *IN PLACE*; | cmp(x, y) -> -1, 0, 1 | | ---------------------------------------------------------------------- | Data and other attributes inherited from __builtin__.list: | | __hash__ = None | | __new__ = <built-in method __new__ of type object> | T.__new__(S, ...) -> a new object with type S, a subtype of T  In [12]: # Strip out the data from the Figure my_data = my_fig.get_data() my_data  Out[12]: {'data': [{'name': '$\\sigma = 0.40$', 'x': [-2.0, -1.9995999599959997, -1.9991999199919992, -1.9987998799879989, -1.9983998399839984, -1.9979997999799981, -1.9975997599759976, -1.9971997199719973, -1.9967996799679968, -1.9963996399639965, -1.995999599959996, -1.9955995599559957, -1.9951995199519952, -1.9947994799479949, -1.9943994399439944, -1.9939993999399941, -1.9935993599359936, -1.9931993199319933, -1.9927992799279928, -1.9923992399239925, -1.991999199919992, 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Or learn more about our matplotlib support. We also have a tutorial on fitting from our grid or you can see some of our favorite graphs with fits. ## II. Fits with MATLAB¶ We can also also make interactive plots with Plotly's MATLAB API by adding fig2plotly(); to MATLAB scripts. Normally we might have to email around code, plots, and data to collaborate (see below), hoping that others on our team know MATLAB and have a license. Not so with Plotly; it works with the GUI, MATLAB, and all our other APIs. Here is our MATLAB code, which yields the graph below and a Plotly graph: https://plot.ly/~MattSundquist/1891. rng('default'); % for reproducibility r = normrnd(10,1,100,1); h = histfit(r,10,'normal'); fig2plotly();  In [13]: tls.embed('MattSundquist', 1891) # our MATLAB figure with a bit of styling  ## III. Fitting with R and ggplot2¶ The code from the ggplot2 cheatsheet produces a plot to which we'll add a fit. Head over to our R API and ggplot2 docs for more plots. Just like with matplotlib or MATLAB, we add one line of code to make it a Plotly graph. In this case: py$ggplotly().

library(ggplot2)
library(gridExtra)
set.seed(10005)

xvar <- c(rnorm(1500, mean = -1), rnorm(1500, mean = 1.5))
yvar <- c(rnorm(1500, mean = 1), rnorm(1500, mean = 1.5))
zvar <- as.factor(c(rep(1, 1500), rep(2, 1500)))
xy <- data.frame(xvar, yvar, zvar)
plot<-ggplot(xy, aes(xvar)) + geom_histogram()
py\$ggplotly()
</div>

</a>

In [14]:
tls.embed('MattSundquist', 1899)


We're @plotlygraphs and available at feedback at plot dot ly.

In [15]:
from IPython.display import display, HTML
import urllib2