Visualization Notes: 12/23/19

Monday, December 23, 2019

Data Visualizations

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import pandas,pylab
fp='https://raw.githubusercontent.com/'+\
   'OlgaBelitskaya/data/main/external_json/'
se=pandas.read_json(fp+'h7rb-945c.json')
fl=['graduation_rate','city','council_district']
se=se[fl].dropna()
se['graduation_rate_range']=se.shape[0]*['0']
se['graduation_rate']=se['graduation_rate']\
.astype('str').str.replace('N/A','0').astype('float')
se['council_district']=se['council_district']\
.astype('int').astype('str')
se.loc[se['graduation_rate']<=.5,
       'graduation_rate_range']='gr <= 0.5'
se.loc[(se['graduation_rate']>.5)&(se['graduation_rate']<=.75),
       'graduation_rate_range']='0.5 < gr <= 0.75'
se.loc[(se['graduation_rate']>.75)&(se['graduation_rate']<=.9),
       'graduation_rate_range'] = '0.75 < gr <= 0.9'
se.loc[se['graduation_rate']>.9,
       'graduation_rate_range']='gr > 0.9'
gr_list=['gr <= 0.5','0.5 < gr <= 0.75',
         '0.75 < gr <= 0.9','gr > 0.9']
fig,ax=pylab.subplots(nrows=2,ncols=1,figsize=(6.5,6.5))
s='Student Graduation Rate by Council Districts and Cities'
pandas.crosstab(se['council_district'],se['graduation_rate_range'])[gr_list]\
.plot.bar(ax=ax[0],cmap=pylab.cm.bwr)
ax[0].tick_params('x',rotation=90)
city_list=['New York','Bronx','Brooklyn','Staten Island',
           'Jamaica','Flushing','Long Island City','Manhattan']
data=se.loc[se['city'].isin(city_list)]
pandas.crosstab(data['city'],se['graduation_rate_range'])[gr_list]\
.plot.barh(ax=ax[1],cmap=pylab.cm.bwr)
ax[1].tick_params('y',labelsize=7,rotation=60)
pylab.suptitle(s); pylab.show()

Implicit Plots

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f=[lambda x,y:(abs(cos((x+I*y)^2))-1),
   lambda x,y:(abs(sin((x+I*y)^4))-1)]
d=1.8; seg=(-d,d)
p=sum([implicit_plot(f[i],seg,seg,plot_points=400) 
       for i in [0,1]])
p.show(figsize=7,aspect_ratio=1)

Evolutes of Curves

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def sefs(string):
    t=var('t')
    return sage.calculus.calculus\
          .symbolic_expression_from_string(
        string,syms={'t':t},accept_sequence=True)
@interact
def _(function=['[2t,t^2]','[7sin(t),4cos(t)+6]',
                '[cos(t)^2*2t,cos(t)^2*t^2]']):
    n=10; var('t'); c=['#3636ff','#ff3636']
    print(function)
    f=(sefs(function)); print(f)
    df=(f[0].diff(),f[1].diff())
    d2f=(df[0].diff(),df[1].diff())
    def norm(g): return sqrt(sum(el^2 for el in g))
    fnormal=(df[1]/norm(df),-df[0]/norm(df)) 
    r=norm(df)^3/(df[1]*d2f[0]-df[0]*d2f[1])
    centers=(f[0]+r*fnormal[0],f[1]+r*fnormal[1])
    print('f: x(t)=%s; y(t)=%s'%(f[0],f[1]))
    p=parametric_plot(f,(t,-n,n),color=c[0],thickness=2)
    p+=parametric_plot(centers,(t,-n,n),color=c[1],
                       thickness=3,linestyle='--')
    p+=sum(line2d([(f[0](t=i),f[1](t=i)),
                   (centers[0](t=i),centers[1](t=i))], 
           thickness=1,rgbcolor=Color('silver').rgb()) 
           for i in sxrange(-n,n,.1))
    p.show(xmin=-8,xmax=8,ymin=-2,ymax=14,figsize=5)

Function Animations

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var('t,k'); f=exp(-(-t+k)^2)*sin(2*pi*(t+k))
cm=sample(['hsv','bwr','cool','jet'],1)[0]
c=[colormaps[cm](25*i)[:3] for i in range(10)]
fragments=[plot(f(t=t,k=k),(t,-3,3),fill='axis',
                fillcolor=c[k]) for k in range(7)]
animate(fragments,title=cm,gridlines=True,
        xmin=-3,xmax=3,ymin=-1,ymax=1)

Set Operations

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@interact
def _(A='a,3,2,c,1,ф,!,D,p',
      B='ф,7,a,!,2,1,B,θ,S',
      C='8,N,a,θ,4,P,!,r,p'):
    S=[sorted(list(el.split(','))) 
       for el in [A,B,C]]
    st=r'<left style=%s>'%'color:%s'
    s1=r'$\large{A \cap B = %s}$'
    s2=r'$\large{A \cap C = %s}$'
    s3=r'$\large{B \cap C = %s}$'
    s4=r'$\large{A \cap B \cap C = %s}$'
    AB=list(set(S[0])&set(S[1]))
    AC=list(set(S[0])&set(S[2]))
    BC=list(set(S[1])&set(S[2])) 
    ABC=list(set(AB)&set(S[2]))
    pretty_print(html(st%'#ff3636'+\
                      s1%('{'+','.join(AB)+'}')))
    pretty_print(html(st%'#36ff36'+\
                      s2%('{'+','.join(AC)+'}')))
    pretty_print(html(st%'#3636ff'+\
                      s3%('{'+','.join(BC)+'}')))
    pretty_print(html(st%'#ff36ff'+\
                      s4%('{'+','.join(ABC)+'}')))