From Polar Forms to Parametric Ones

Examples of Highmaps

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<script src='https://code.highcharts.com/modules/exporting.js'></script>
<script src='https://code.highcharts.com/modules/offline-exporting.js'></script>
<script src='https://code.highcharts.com/mapdata/custom/europe.js'></script>
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Plotting Symbols

Interactive Integral Plotting

Tachyon 3D Ray Tracers

Text Classification

20newsgroups.ipynb

import pylab; from sklearn.datasets import fetch_20newsgroups
from sklearn.feature_extraction.text import TfidfVectorizer
from sklearn.neural_network import MLPClassifier
import warnings; warnings.filterwarnings('ignore')
train=fetch_20newsgroups(
    subset='train',shuffle=True,remove=('headers','footers','quotes'))
test=fetch_20newsgroups(
    subset='test',shuffle=True,remove=('headers','footers','quotes'))
y_train,y_test=train.target,test.target
vectorizer=TfidfVectorizer(
    sublinear_tf=True,max_df=.5,stop_words='english')
x_train=vectorizer.fit_transform(train.data)
x_test=vectorizer.transform(test.data)
del train,test 
print(x_train.shape,x_test.shape,y_train.shape,y_test.shape)
clf=MLPClassifier(
    hidden_layer_sizes=(128,),max_iter=3,solver='adam',
    verbose=2,random_state=1,learning_rate_init=.01)
clf.fit(x_train,y_train); print(clf.score(x_test,y_test))
y_test_predictions=clf.predict(x_test)
pylab.figure(figsize=(6,4))
pylab.scatter(range(100),y_test[:100],s=100)
pylab.scatter(range(100),y_test_predictions[:100],s=25)
pylab.tight_lauoyt(); pylab.show()

Fun Plotly

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Additional Python Modules 5

Additional Python Modules 4

Additional Python Modules 3

Additional Python Modules 2

russian-notes-pythondataanalysis-2-40.ipynb

You can install additional packages

!python3 -m pip install --upgrade pip \
--user --quiet --no-warn-script-location
!python3 -m pip install pygal \
--user --quiet --no-warn-script-location

And apply them

import pygal,pandas as pd
from IPython.display import SVG, display
from pygal.style import BlueStyle
columns=['Fresh','Milk','Grocery','Frozen',
         'Detergents_Paper','Delicatessen']
colors=['#1b2c45','#5a8bbd','#008b8b','#ff5a8b']
index= ['C1','C2','C3']
data=[[26373,36423,22019,5154,4337,16523],
      [16165,4230,7595,201,4003,57],
      [14276,803,3045,485,100,518]]
samples=pd.DataFrame(data,columns=columns,index=index) 
line=pygal.Line(
    fill=False,height=int(400),width=int(900),
    style=BlueStyle(
        opacity='.3',colors=colors,background='transparent'))
line.title='Samples of the Wholesale Customers Dataset'
line.x_labels=columns
line.add('C1',data[0]); line.add('C2',data[1])
line.add('C3',data[2]); line.add('MEAN',samples.mean())
line.render_to_file('samples.svg')
display(SVG(open('samples.svg','rb').read()))

Drawing by Parametric Functions 2

Additional Python Modules

russian-notes-pythondataanalysis-2-40.ipynb

import pandas,geopandas,pylab,warnings,fiona
fiona._env.set_gdal_config('OGR_GEOMETRY_ACCEPT_UNCLOSED_RING','YES')
fiona._env.logging.disable(level='WARNING')
warnings.filterwarnings('ignore',category=FutureWarning)
pylab.style.use('fivethirtyeight')
fpath='https://raw.githubusercontent.com/OlgaBelitskaya/'+\
      'OlgaBelitskaya.github.io/master/map.geojson'
df=geopandas.GeoDataFrame.from_file(fpath)
ax=df.boundary.plot(
    figsize=(12,7),markersize=0,linewidth=.1,edgecolor='gray')
footways=df['geometry'][df['highway']=='footway'].loc[2176:]
geopandas.plotting.plot_linestring_collection(
    ax,footways,linewidth=.8,
    color='steelblue',label='footways')
df[df['highway']=='street_lamp'].plot(
    ax=ax,edgecolor='g',markersize=10,label='lamps')
df[df['highway']=='traffic_signals'].plot(
    ax=ax,edgecolor='r',markersize=20,label='traffic signals') 
pylab.xlim(37.613,37.636); pylab.ylim(55.752,55.762)
pylab.legend(); pylab.tight_layout(); pylab.show()

Functions with Summation

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Drawing by Parametric Functions

Functions with Summation

Surface drawing by parametric plots 2

Surface drawing by parametric plots

3D Function Drawing in Polar Coordinates

Artificial Clusters

makeCluster[class_,\[Mu]_,\[Rho]_]:=
RandomVariate[MultinormalDistribution[\[Mu],{{1,4\[Rho]},

{4 \[Rho],4}}],500]->class;
clusters=makeCluster@@@{{1,{1.5,1.8},-.2},{2,{-1.5,1.1},.3},

{3,{-1.6,-2.3},-.4},{4,{1.8,-2.2},.1}};
lp1=ListPlot[Keys[clusters],PlotStyle ->"BrightBands"];
clf=Classify[Flatten[Thread/@clusters],Method->"NearestNeighbors"]
sample={{2.5,2.8},{-1.7,1.5},{-0.9,-2.1},{1.6,-1.8}};
lp2=ListPlot[List/@sample,

PlotMarkers->clf[sample],PlotStyle->Black];
Show[lp1,lp2,ImageSize->Large,PlotRange->{{-5,5},{-5,5}}]

HTML Objects

EmbeddedHTML["<ul style='list-style-type:circle;'>
<li style='color:#3636ff;'>Coffee</li>
<li style='color:#36ff36;'>Tea</li>
<li style='color:#ff3636;'>Milk</li></ul>"]
EmbeddedHTML["<svg width='150' height='150'>
<circle style='fill:steelblue; stroke:silver;'
stroke-width='5' cx='75' cy='75' r='50'/></svg>"]

Logical Functions

bc=Tuples[{False,True},10]; Length[bc]
LF=Function[{x1,x2,x3,x4,x5,x6,x7,x8,x9,x10},
f1=((x1||(! x2))&&(x3||(!x4))); f2=((x3||(!x4))&&(x5||(!x6)));
f3=((x5||(!x6))&&(x7||(!x8))); f4=((x7||(! x8))&&(x9||(! x10)));
f1&&f2&&f3&&f4];
LFvalues=Table[Apply[LF,bc[[i]]],{i,Range[1,Length[bc],1]}];
Count[LFvalues,True]

1024
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Integration & Plotting

G[x_]=Integrate[Cos[x^2]*Exp[x],x,GeneratedParameters -> C];
Plot[Evaluate[{G[x]/.Table[{C[1]->i},{i,Range[0,10,5]}]}],
{x,3,5},PlotTheme->"Detailed",ImageSize->Large]

Limits & Plotting

F[x_,y_]=(1-Sqrt[1-x^2+x*y^3-y^4])/Sin[x^2+y^4];
FL[x_,y_]=Limit[F[x,y],{x,y}->{0,0}];
Plot3D[{F[x,y],FL[x,y]},{x,-1/4,1/4},{y,-1/4,1/4},PlotRange->All,
               PlotStyle->{Opacity[0.9],Opacity[0.4]},PlotTheme->"Web",Mesh->False,
      PlotLabel->"Limits for Functions with Two Variables",
      Boxed->False,Axes->False,ImageSize->Large]

Interactive Plotting with Parameters

Manipulate[Show[Table[Plot[Sin[t-2*l]-t^2,{t,-1,1},
PlotStyle->Hue[Sin[l/L]]],{l,Range[-1.25,1.25,0.05]}],
PlotRange->All,Axes->False,ImageSize->Large],{L,Range[1,10,1]}]

Sets of Mesh Surfaces

k=7; f1[x_,y_,z_]=x^2/9+y^2/16-z^2/25;
f2[x_,y_,z_]=x^2/4+y^2/9-z^2/16;
cp1=ContourPlot3D[f1[x,y,z]==1,{x,-k,k},{y,-k,k},{z,-k,k},
Mesh->20,MeshStyle->Blue,ContourStyle->{Blue,Opacity[0.1]}];
cp2=ContourPlot3D[f2[x,y,z]==0,{x,-k,k},{y,-k,k},{z,-k,k},
Mesh->30,MeshStyle->Red,ContourStyle->{Red,Opacity[0.2]}];
Show[cp1,cp2,Boxed->False,Axes->False,ImageSize->Large]

Colorized Curves

Show[Table[Plot[Sin[x],{x,i*Pi/24,(i+1)*Pi/24},
PlotStyle->{Hue[i/48],Thickness[0.02]}],{i,Range[0,47,1]}],
         ImageSize->Large,GridLines->Automatic,PlotRange->All]

Texts & Strings

corpus ={"Have you already set your goals for the New Year?",
"Do you want to lose ten kilos, run a marathon or speak fluent English?",
"Some experts believe that you need systems, not goals.",
"A system is something you do on a regular basis.",
"This means focusing on what you can control (your actions) rather than what you can not.",
"For example, do not focus on losing ten kilos.",
"Focus on shopping for healthy food and cooking something light every day.",
"Do not focus on the marathon.","Focus on the training schedule.",
"Invent a system to improve your English, one step at a time.","Good luck!"};
wcorpus=StringReplace[StringJoin[corpus], PunctuationCharacter :> " "];
wc=KeySort[WordCounts[ToLowerCase[wcorpus]]]; fc=[]
WordCloud[wcorpus,fc,WordOrientation->"Random",PlotTheme->"Web"]
BarChart[wc,ChartLabels->Placed[Normal[Keys[wc]],Axis,Rotate[#,Pi/2] &],
ChartStyle->"Pastel",ChartElementFunction->"GlassRectangle",ImageSize->600]