If you want to experiment with PyTorch

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#!python3 -m pip install torch==1.8.0 \

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#--user --quiet --no-warn-script-location

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#!python3 -m pip install torchvision==0.9.0 \

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#--user --quiet --no-warn-script-location

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#spath='/home/sc_work/.sage/local/lib/python3.9/site-packages'

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#import sys; sys.path.append(spath)

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import numpy as np,pandas as pd,pylab as pl,torch

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from sklearn.datasets import make_classification

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dev=torch.device('cuda:0' \

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if torch.cuda.is_available() else 'cpu')

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class Perceptron():

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    def __init__(self,num_features):

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        self.num_features=num_features

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        self.weights=torch.zeros(num_features,int(1), 

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                                 dtype=torch.float32,device=dev)

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        self.bias=torch.zeros(1,dtype=torch.float32,device=dev)

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    def forward(self,x):

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        values=torch.add(torch.mm(x,self.weights),self.bias)

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        a=torch.ones(values.size()[0],int(1))

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        b=torch.zeros(values.size()[0],int(1))

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        predictions=torch.where(values>float(0.),a,b).float()

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        return predictions        

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    def backward(self,x,y):  

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        predictions=self.forward(x)

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        errors=y-predictions

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        return errors        

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    def train(self,x,y,epochs):

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        for e in range(epochs):            

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            for i in range(y.size()[0]):

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                errors=self.backward(

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                    x[i].view(int(1),self.num_features),

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                    y[i]).view(-int(1))

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                self.weights+=(errors*x[i]).view(

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                    self.num_features,int(1))

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                self.bias+=errors                

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    def acc(self,x,y):

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        predictions=self.forward(x).view(-int(1))

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        accuracy=torch.sum(predictions==y).float()/y.size()[0]

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        return accuracy

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Messages

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N=500; n=int(.2*N)

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X,y=make_classification(

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    n_samples=N,n_features=2,n_redundant=0,n_informative=2)

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mu,std=np.mean(X,axis=0),np.std(X,axis=0)

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X=(X-mu)/std

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X,y=X.astype('float32'),y.astype('int32')

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shuffle_ids=np.arange(N)

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np.random.RandomState(23).shuffle(shuffle_ids)

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X,y=X[shuffle_ids],y[shuffle_ids]

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X_test,X_train=X[:n],X[n:]

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y_test,y_train=y[:n],y[n:]

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model=Perceptron(num_features=2)

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tX_train=torch.tensor(

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    X_train,dtype=torch.float32,device=dev)

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ty_train=torch.tensor(

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    y_train,dtype=torch.float32,device=dev)

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model.train(tX_train,ty_train,epochs=int(5))

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tX_test=torch.tensor(

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    X_test,dtype=torch.float32,device=dev)

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ty_test=torch.tensor(

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    y_test,dtype=torch.float32,device=dev)

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acc_test=model.acc(tX_test,ty_test).numpy()

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print('Test accuracy: %.2f%%'%(acc_test*int(100)))

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W,b=model.weights.numpy(),model.bias.numpy()

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x_min=-int(2); x_max=int(2)

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y_min=((-(W[int(0)]*x_min)-b[int(0)])/W[int(1)])

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y_max=((-(W[int(0)]*x_max)-b[int(0)])/W[int(1)])

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fig,ax=pl.subplots(2,1,sharex=True,figsize=(6.5,6))

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ax[0].plot([x_min,x_max],[y_min,y_max],c='red')

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ax[1].plot([x_min,x_max],[y_min,y_max],c='red')

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ax[0].scatter(X_train[:,0],X_train[:,1],

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              c=y_train,s=10,cmap=pl.cm.cool)

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ax[1].scatter(X_test[:,0], X_test[:,1],

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              c=y_test,s=10,cmap=pl.cm.cool)

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ax[0].grid(); ax[1].grid()

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pl.tight_layout(); pl.show()

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Messages

If you want to experiment with one neuron

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import numpy as np,pylab as pl

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# functions for neuron construction

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def sigmoid(x): return 1.0/(1+np.exp(-x))

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def sigmoid_derivation(x): return x*(1.0-x)

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# artificial data for the experiment

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X=np.array([[.11,.05,.95],[.09,.03,.08],[.01,.09,.91],

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            [.04,.92,.07],[.05,.02,.04],[.07,.97,.05],

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            [.06,.02,.98],[.02,.06,.03],[.01,.09,.03],

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            [.02,.94,.01],[.06,.03,.95],[.04,.91,.09]])

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Y=np.array([[1,0,1,2,0,2,1,0,1,2,1,2]]).T

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fig,ax=pl.subplots(nrows=2,ncols=1,figsize=(6.5,4))

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ax[0].imshow(X.T,cmap=pl.cm.cool)

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ax[0].set_xticks([])

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ax[0].text(-.3,1,str(Y.T)[2:-2],color='white',fontsize=32)

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ax[0].set_title('Real Labels with One Error')

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# the start point for iterations

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synapse0=np.random.randn(3,1); layer0=X

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# the steps of iterations

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for iter in range(100):

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    layer1=sigmoid(np.dot(layer0,synapse0))

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    # finding errors and directions for correction

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    layer1_error=layer1-Y

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    layer1_delta=layer1_error*sigmoid_derivation(layer1)

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    # correction values & coefficients

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    synapse0_derivative=np.dot(layer0.T,layer1_delta)

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    synapse0-=synapse0_derivative

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# comparing predictions and real data

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# the error in the start labeling (the 9th image) had been corrected

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def labeling(x):

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    if (x<.7): return 0

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    if (x>.7) and (x<.99): return 1

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    else: return 2

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predict_Y=np.array([[labeling(layer1[i,0]) for i in range(12)]]).T

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ax[1].imshow(X.T,cmap=pl.cm.cool)

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ax[1].set_xticks([])

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ax[1].text(-.3,1,str(predict_Y.T)[2:-2],color='white',fontsize=32)

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ax[1].set_title('Predicted Labels'); pl.show()

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print(np.hstack((np.hstack((X,Y)),(layer1.round(3)),(predict_Y))))

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---

Messages

Highcharts.js for 3D Plotting

<script src='https://code.highcharts.com/highcharts.js'></script>
<script src='https://code.highcharts.com/highcharts-3d.js'></script>
<script src='https://code.highcharts.com/modules/accessibility.js'></script>
was added in the page head.

HTML & JavaScript & SageMathCell

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%%html

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<figure class='highcharts-figure'>

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<div id='hich' style='width:500px; height:500px;'>

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the javascript cell is launching here...</div></figure>

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Messages

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%%javascript

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function randi(min,max) {

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    return Math.floor(Math.random()*(max-min+1))+min;};

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var d=.005,l=5,n=3,a=randi(11,19),b=randi(24,64);

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function ar(k,a,b) {return Array(1280).fill(k).map((k,t)=>

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    [k*(Math.cos(d*t)+Math.sin(a*d*t)/2-Math.cos(b*d*t)/6),

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     k*(Math.sin(d*t)+Math.cos(a*d*t)/2-Math.sin(b*d*t)/6),k]);};

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Highcharts.setOptions({

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    colors:Highcharts.getOptions().colors.map(function(color) {

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    return {

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radialGradient:{cx:.4,cy:.3,r:.2},

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stops:[[0,color],

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       [1,Highcharts.color(color).brighten(-0.2).get('rgb')]]};})});

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var series=[];

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for (var i=1; i<n+1; i++){

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    series.push({name:i,colorByPoint:true,

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                 accessibility:{exposeAsGroupOnly:true},

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                 marker:{radius:1},data:ar(i,a,b)})};

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var chart=new Highcharts.Chart({

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    chart:{renderTo:'hich',margin:100,type:'scatter3d',

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    animation:false,

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    options3d:{enabled:true,alpha:20,beta:20,depth:250,

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               viewDistance:5,fitToPlot:false,

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               frame:{bottom:{size:1,color:'rgba(0,0,0,0.05)'},

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                      back:{size:1,color:'rgba(0,0,0,0.1)'},

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                      side:{ size:1,color:'rgba(0,0,0,0.15)'}}} },

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  title:{text:'Scatter 3D with rotation in space'},

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  plotOptions:{scatter:{width:l,height:l,depth:l}},

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  yAxis:{min:-l,max:l,title:null},

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  xAxis:{min:-l,max:l,gridLineWidth:1},

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  zAxis:{min:0,max:l,showFirstLabel:false},

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  legend:{enabled:false},series:series});

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(function(H){function dragStart(eStart){

34

    eStart=chart.pointer.normalize(eStart);

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    var posX=eStart.chartX,posY=eStart.chartY,

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        alpha=chart.options.chart.options3d.alpha,

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        beta=chart.options.chart.options3d.beta,

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        sensitivity=3,handlers=[];

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    function drag(e){

40

      e=chart.pointer.normalize(e);

41

      chart.update({chart:{

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          options3d:{alpha:alpha+(e.chartY-posY)/sensitivity,

43

                     beta:beta+(posX-e.chartX)/sensitivity}}},

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                    undefined,undefined,false);}

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    function unbindAll(){handlers.forEach(function(unbind){

46

        if (unbind){unbind();}});

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        handlers.length=0;}

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    handlers.push(H.addEvent(document,'mousemove', drag));

49

    handlers.push(H.addEvent(document,'touchmove', drag));

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    handlers.push(H.addEvent(document,'mouseup',unbindAll));

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    handlers.push(H.addEvent(document,'touchend',unbindAll));}

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  H.addEvent(chart.container,'mousedown',dragStart);

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  H.addEvent(chart.container,'touchstart',dragStart);

54

}(Highcharts));

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---

Messages

D3.js for Plotting with Random Coefficients

<script src='https://d3js.org/d3.v4.min.js'></script> was added in the page head.

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%%html

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<svg id='d303' style='background-color:silver;'/>

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<script>

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var n=6400,m=6,d=.001,margin={top:m,right:m,bottom:m,left:m},

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    width=600-margin.left-margin.right,

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    height=600-margin.top-margin.bottom,

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    tr='translate('+margin.left+','+margin.top+')'; 

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function fx(t,a,b,k){

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    return Math.cos(d*t+k*Math.PI/6)+

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           Math.cos(a*d*t)/2+Math.sin((a+b)*d*t)/3};

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function fy(t,a,b,k){

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    return Math.sin(d*t+k*Math.PI/6)+

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           Math.sin(a*d*t)/2+Math.cos((a+b)*d*t)/3};

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function randi(xmin,xmax){

15

    return Math.floor(Math.random()*(xmax-xmin+1))+xmin;};

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function rcolor(i){

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    var r=randi(i,255),g=randi(i,50),b=randi(i,255);

18

    return '#'+r.toString(16)+g.toString(16)+b.toString(16);}

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var a=randi(7,15),b=randi(10,48);

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function make_data(k){return d3.range(1,n).map(function(t){

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    return {'x':fx(t,a,b,k),

22

            'y':fy(t,a,b,k)}});};    

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var xScale=d3.scaleLinear()

24

             .domain([-2,2]).range([0,width+10]),

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    yScale=d3.scaleLinear()

26

             .domain([-2,2]).range([height+10,0]); 

27

var svg=d3.select('#d303')

28

          .attr('width',width+margin.left+margin.right)

29

          .attr('height',height+margin.top+margin.bottom)

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          .attr('transform',tr);

31

var line=d3.line().curve(d3.curveMonotoneX)

32

           .x(function(d){return xScale(d.x);})

33

           .y(function(d){return yScale(d.y);});

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for (var i=1; i<m; i++) {var data=make_data(i),col=rcolor(i);

35

     svg.append('path').datum(data)

36

        .attr('class','line').attr('d',line)

37

        .attr('stroke',col).attr('fill','none');};

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Messages

Exercises in R and Python in the Same Cell

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import rpy2.robjects as ro,pandas as pd,pylab as pl

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import warnings as wr; wr.filterwarnings('ignore')

3

from rpy2.robjects.packages import importr

4

from rpy2.robjects.conversion import localconverter

5

from rpy2.robjects import r,pandas2ri

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pandas2ri.activate()

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pd_dict={'real_values':[random() for i in range(10)],

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         'str_values':['😀','😁','😂','😃','😄',

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                       '😉','😊','😋','😌','😍']} 

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pd_df=pd.DataFrame(pd_dict)

11

base=importr('base')

12

with localconverter(ro.default_converter+pandas2ri.converter):

13

    df_summary=base.summary(pd_df)

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ppd_df=pd_df.plot(kind='line',x='str_values',y='real_values',

15

                  marker='*',lw=1,figsize=(6.5,4))

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ppd_df.set_xticks(list(range(10)))

17

ppd_df.set_xticklabels(pd_df.str_values)

18

print(df_summary); pl.show()

19

r_df=ro.r('df<-data.frame(x=c(1:10),'+\

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          'y=.1*sample(c(1:10),10),'+\

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          'stringsAsFactors=F)')

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ro.r('svg(filename="Rplots.svg",width=6.5,height=5,'+\

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     'onefile=T,family="sans",bg="white",pointsize=10,'+\

24

     'antialias=c("default","none","gray","subpixel")); '+\

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     'plot(df,type="o",ylim=c(0,1),pch=8,col="steelblue"); '+\

26

     'dev.off()')

27

with localconverter(ro.default_converter+pandas2ri.converter):

28

    print(base.summary(ro.r('df')))

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---

Messages

Plotting Exercises in R and Python

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r.eval("""

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X3<-Z3<-X4<-Z4<-Y5<-Z5<-seq(from=-5,to=5,by=.1)

3

cylinder1<-function(p,q,X,Z){

4

    for (x in X){for (z in Z){

5

        y<-q*(1-x^2/p^2)^0.5; v<-c(x,y,z,x,-y,z)

6

        if (sum(is.na(v))==0){

7

            write.table(matrix(v,nrow=2,ncol=3,byrow=TRUE),

8

                        file ='cylinder1.csv',

9

                        append=TRUE,quote=FALSE,

10

                        col.names=FALSE,row.names=FALSE)}}}}

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cylinder2<-function(p,q,X,Z){

12

    for (x in X){for (z in Z){

13

        y<-q*(x^2/p^2-1)^0.5; v<-c(x,y,z,x,-y,z)

14

        if (sum(is.na(v))==0){

15

            write.table(matrix(v,nrow=2,ncol=3,byrow=TRUE),

16

                        file='cylinder2.csv',

17

                        append=TRUE,quote=FALSE,

18

                        col.names=FALSE,row.names=FALSE)}}}}

19

cylinder3<-function(p,Y,Z){

20

    for (y in Y){for (z in Z){

21

        x<-y^2/2/p; v<-c(x,y,z)

22

        write.table(matrix(v,nrow=1,ncol=3,byrow=TRUE),

23

                    file ='cylinder3.csv',

24

                    append=TRUE,quote=FALSE,

25

                    col.names=FALSE,row.names=FALSE)}}}

26

cylinder1(3,4,X3,Z3); cylinder2(2,3,X4,Z4); cylinder3(2,Y5,Z5)

27

""")

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---

Messages

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import pylab,numpy

2

from mpl_toolkits.mplot3d import Axes3D

3

from matplotlib.lines import Line2D

4

files=['cylinder1.csv','cylinder2.csv',

5

       'cylinder3.csv']

6

colors=['#36ff36','#36ffff','#ff36ff']

7

labels=['$x^2/3^2+y^2/4^2=1$',

8

        '$x^2/2^2-y^2/3^2=1$',

9

        '$y^2=2*2*x$']

10

XYZ=[numpy.array(numpy.loadtxt(files[i],\

11

     delimiter=' ',unpack=True)) for i in range(3)]

12

fig=pylab.figure(figsize=(6.5,6.5))

13

ax=fig.add_subplot(111,projection='3d')

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[ax.scatter(XYZ[i][0],XYZ[i][1],XYZ[i][2],s=1,\

15

 c=colors[i],marker='1') for i in range(3)]

16

fake2Dlines=[Line2D([0],[0],linestyle='none',\

17

             c=c,marker='1') for c in colors]

18

ax.legend(fake2Dlines,labels,loc=9) 

19

pylab.tight_layout(); pylab.show()

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---

Messages

Magic Functions for Querying

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import sqlite3; import pandas as pd

2

from IPython.display import display

3

from IPython.core.magic import register_line_magic

4

@register_line_magic

5

def get_query(q):

6

    connection=sqlite3.connect('db.db')

7

    cursor=connection.cursor()

8

    url='https://raw.githubusercontent.com/noahgift/'+\

9

        'mma/master/data/ufc_fights_all.csv'

10

    mma=pd.read_csv(url).dropna()

11

    mma.to_sql('mma',con=connection,

12

           if_exists='replace')

13

    pretty_print(html('<p>SQL Queries => UFC Fights</p>'))

14

    q=pd.read_sql_query(q,con=connection)

15

    thp=[('font-size','15px'),('text-align','center'),

16

         ('font-weight','bold'),('padding','5px 5px'),

17

         ('color','white'),('background-color','slategray')]

18

    tdp=[('font-size','14px'),('padding','5px 5px'),

19

         ('text-align','center'),('color','darkblue'),

20

         ('background-color','silver')]

21

    style_dict=[dict(selector='th',props=thp),

22

                dict(selector='td',props=tdp)]

23

    display(q.style.set_table_styles(style_dict))

24

    if connection is not None:

25

        connection.close()

26

    if os.path.exists('db.db'):

27

        os.remove('db.db')

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---

Messages

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1

%get_query \

2

SELECT method, \

3

       COUNT(*) AS number, \

4

       AVG(round) AS avg_round \

5

FROM mma \

6

GROUP BY method;

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---

Messages