NN Training Process

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print(r.eval("""

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library(datasets); library(nnet); data(longley)

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features<-longley[,1:6]; targets<-longley[,7]

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model<-nnet(Employed~.,longley,size=18,

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            maxit=400,linout=T,decay=.01)

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predictions<-predict(model,features,type='raw')

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mean((targets-predictions)^2)

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"""))

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Messages

Differentiation Examples

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import sympy; sympy.init_printing(use_unicode=True)

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x,y,z,t,u,v,w=sympy.symbols('x,y,z,t,u,v,w')

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A=sympy.Array(

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    [[[x*sympy.cos(u)*z^2-y,x^3*u*v^6-sympy.sin(w*t)],

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      [t*sympy.tan(u*w),sympy.exp(y)*z*u-w]],

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     [[y^3*v^5-t,x*sympy.log(w)*z^4],

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      [x-sympy.exp(z)*w^7,y*t^8*u*v]]])

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for el in [x,y,z,t,u,v,w]:

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    display(A.diff(el),70*'-')

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Messages

Graph Representation

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import warnings; warnings.filterwarnings('ignore')

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g=graphs.SzekeresSnarkGraph()

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[g.set_edge_label(u,v,u) for u,v,l in g.edges()]

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gp=g.graphplot(vertex_shape='H',vertex_color='lightgrey',

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               vertex_size=400,color_by_label=True)

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gp.show(figsize=(5,5))

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Messages

Interactive Parameters

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@interact

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def _(n=[24,22,..,2],h=[21,19,..,3],

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      k=[60,120,..,360]):

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    def L(i): return [n*cos(2*pi*i/k)+h*cos((n/2)*2*pi*i/k),

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                      n*sin(2*pi*i/k)-h*sin((n/2)*2*pi*i/k)]

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    l=sum([line([L(j),L(j+1)],color=hue(j/k)) for j in range(k)])

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    l.show(figsize=(5,5))

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Messages

Interactive Polygon Plotting

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@interact

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def _(n=[2,3,4,5]):

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    L1=[[0,0]]+[[.5+.004*i,.9+.3*sin(n*.01*i)] 

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                for i in range(200)]+[[2,0]]

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    L2=[[0,0]]+[[.5,1.5]]+[[1.5,1.5]]+[[2,0]]

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    p=polygon2d(L1,color='#3636ff',edgecolor='darkgrey',

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                thickness=3,axes=False)

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    p+=polygon2d(L2,color='silver',edgecolor='darkgrey',

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                 alpha=.3,thickness=3)

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    p.show(figsize=(6,4))

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Messages

HTML Exercises

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%%html

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<style>

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@import 'https://fonts.googleapis.com/css?family=Ewert&effect=3d';

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</style>

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<button style='background-color:#3636ff; color:#fff; 

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               font-family:Ewert; font-size:160%;' 

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type='button' 

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onclick='document.getElementById("demo").innerHTML=Date()'>

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Click to Display Date and Time</button>

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<p id='demo' class='font-effect-3d' style='color:#3636ff;'></p>

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Messages

Installed Packages

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print(r.eval("""

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today<-Sys.Date()

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print(format(today,format='%d %B %Y'))

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ip<-as.data.frame(installed.packages()[,c(1,3)])

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rownames(ip)<-NULL; ip"""))

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Messages

Matrix Operations

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import sympy; sympy.init_printing(use_unicode=True)

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A=sympy.Matrix([[-3,-3,-6],[-4,-7,8]])

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B=sympy.Matrix([[2,8,7],[-5,-6,-2],[-8,4,-8],[7,4,-6]])

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C=sympy.Matrix([[-2,-4],[3,-5]])

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D=sympy.Matrix([[-2,-3,-1,3],[-2,-9,8,9]])

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alpha,beta=int(2),int(-5)

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alpha*A*B.transpose()+beta*C.transpose()*D

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Messages

Interactive Contour Plots

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@interact

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def _(cmap=['cool','prism','jet','flag',

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            'gnuplot','tab10','tab20']):

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    var('x,y'); f(x,y)=(x^2-y)*sin(x*y); t=3

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    ld={-t:'f=-%d'%t,0:'f=0',t:'f=%d'%t}

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    cp=contour_plot(f,(x,-t,t),(y,-t,t),

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                    contours=[-t,0,t],fill=False,

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                    cmap=cmap,labels=True,label_inline=True,

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                    label_fmt=ld,label_colors='black')

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    cp.show(figsize=(5,5))

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Messages

Interactive Graph Exploration 2

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import warnings; warnings.filterwarnings('ignore')

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pretty_print('Probability of Edges in Percentage')

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@interact

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def _(p=(100,0,-10)):

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    g=graphs.RandomGNP(16,p/100) 

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    ec={(1,1,1):list(g.edges())}

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    vc={Color('#3636ff'):list(g)}

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    g.show3d(edge_colors=ec,vertex_colors=vc)

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---

Messages

Interactive Graph Exploration

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import warnings; warnings.filterwarnings('ignore')

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@interact

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def _(Graph=['Petersen','Moebius Kantor','Dodecahedral',

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             'Icosahedral','Kittell','Flower Snark']):

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    graph_dict={'Moebius Kantor':graphs.MoebiusKantorGraph(),

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                'Flower Snark':graphs.FlowerSnark(),

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                'Dodecahedral':graphs.DodecahedralGraph(),

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                'Icosahedral':graphs.IcosahedralGraph(),

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                'Kittell':graphs.KittellGraph(),

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                'Petersen':graphs.PetersenGraph()}

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    g=graph_dict[Graph]

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    [g.set_edge_label(u,v,u) for u,v,l in g.edges()]

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    gp=g.graphplot(vertex_labels=False,vertex_size=0,

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                   color_by_label=True)

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    gp.show(figsize=(5,5))

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---

Messages

Complex Functions

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i=CDF.gen(); N=500 

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z=[zeta(0.1*(5+n*i)) for n in range(N)]

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sum([line([(z[n].real(),z[n].imag()),

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           (z[n+1].real(),z[n+1].imag())],

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          gridlines=True,

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          color=colormaps.hsv(abs(255-n))[:3]) 

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     for n in range(N-1)]).show(figsize=(5,5))

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---

Messages

HTML Exercises

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%%html

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<style>

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@import 'https://fonts.googleapis.com/css?family=Ewert';

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.animated {background-color:#3636ff; font-family:'Ewert'; 

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           color:#fff; text-align:center; font-size:25px; 

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           border-radius:15px; padding:10px; width:350px; 

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           transition:all .7s; cursor:pointer; margin:2px;}

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.animated span {cursor:pointer; display:inline-block; 

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                position: relative; transition:.7s;}

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.animated span:after {content:'\22d9'; position:absolute; opacity:0; 

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                      top:0; right:-10px; transition:.7s;}

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.animated:hover span {padding-right:18px;}

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.animated:hover span:after {opacity:1; mright:0;}

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</style>

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<button class='animated'><span>Animated Button</span></button>

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Messages

TSV Files & Data Frames

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print(r.eval("""

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fn<-'https://olgabelitskaya.github.io/huge_cities.tsv'

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huge_cities<-data.frame(read.csv(fn,header=T,sep='\t'))

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summary(huge_cities)"""))

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Messages

Graph Construction

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import networkx as nx,pylab as pl

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g=nx.MultiDiGraph(); pl.figure(figsize=(6,5))

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edge_list=[('1','2'),('1','3'),('1','4'),('1','5'),

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           ('2','5'),('3','5'),('3','7'),('3','8'),

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           ('4','3'),('4','7'),('5','8'),('7','8'),

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           ('8','9'),('8','10'),('9','10'),('9','11')]

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edge_list=[(n1,n2) for (n1,n2) in edge_list]

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g.add_edges_from(edge_list); pos=nx.shell_layout(g)

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nx.draw_networkx_edges(

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    g,pos,width=3,alpha=.5,edge_color='silver',

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    arrowsize=35,arrowstyle='-|>')

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nx.draw_networkx_nodes(

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    g,pos,node_size=1500,alpha=.8,

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    node_color='steelblue',node_shape='h')

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nx.draw_networkx_labels(

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    g,pos,font_size=24,font_weight='bold')

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pl.axis('off'); pl.tight_layout(); pl.show()

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Messages

Linear Systems of Equations

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var('x1,x2,x3,x4')

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x=vector(SR,[x1,x2,x3,x4])

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A=matrix(SR,[[8,-5,-2,-2],[-2,4,-4,1],

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             [-2,1,4,4],[4,1,3,10]])

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b=vector(SR,[35,-8,-11,10])

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Ab=A.augment(b,subdivide=True)

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sAb=solve(list(A*x-b),x1,x2,x3,x4)

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ppl=[['Decision Methods:'],

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     [Ab.rref()],[sAb],

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     [A.solve_right(b)],[A.inverse()*b],

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     ['For the Linear System of Equations: '],[Ab]]

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table(ppl)

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Messages

Colormap Shadows

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@interact

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def _(colormap=['winter','spring','summer','autumn'],

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      n=[24,36,48,60]):

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    p=sum([arrow2d((0,0),(cos(i*pi/n),sin(i*pi/n)),

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           color=colormaps[colormap](int(250*i/n/2))[:3]) 

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           for i in [0..2*n]])

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    p.show(figsize=(5,5))

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Messages

Interactive Region Plots 2

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@interact

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def _(n=[2..5],m=[2..5]):

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    var('x,y'); ineq=sin(x^n)*sin(y^n)*sin(x*y)>=.1^m

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    rp=region_plot(ineq,(x,-4,4),(y,-4,4),incol='#3636ff',

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                   bordercol='black',borderstyle='dotted')

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    rp.show(figsize=(5,5))

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---

Messages

HTML Exercises

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%%html

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<style>

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.pressed {display:inline-block; padding:15px 15px; 

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          outline:none; font-size:20px; 

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          cursor:pointer; text-align:center; 

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          color:#fff; background-color:#3636ff; 

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          border:none; border-radius:10px; 

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          box-shadow:0 5px slategray;}

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.pressed:hover {background-color:#ff3636}

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.pressed:active {background-color:#36ff36; 

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                 box-shadow:0 5px #aaa; 

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                 transform:translateY(5px);}

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</style>                        

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<button class='pressed'>$\mathbb{Pressed \; Effect}$

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</button>

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Messages

Basic Clustering Examples

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print(r.eval("""

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kmeans_clust<-kmeans(mtcars$wt,5)

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kmeans_clust"""))

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---

Messages