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Example of Computations

Your Experiments

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t=Tachyon(camera_center=(2,6,2.5),look_at=(2,0,0),raydepth=10)
t.texture('mirror',ambient=.01,diffuse=.01,
          specular=.9,opacity=.9,color=(.3,.3,.3))
t.texture('t1',texfunc=1)
t.texture('t2',color=(0,.1,.6),texfunc=2)
t.plane((0,0,0),(0,0,1),'t1'); t.plane((0,0,3),(0,0,4),'t2')
t.sphere((4,-1,1),1,'mirror'); t.sphere((0,-1,1),1,'mirror')
t.sphere((2,-1,1),.5,'mirror'); t.sphere((2,2,1),.5,'mirror')
t.light((7,7,1),1,(2,2,1)); show(t)

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@interact
def _(proj=['perspective','fisheye','perspective_dof'],
      cm=['hsv','jet','cool','hot','prism']):
    k=1; e=[[[k,-k,k],[0,0,0]],[[0,0,0],[k,k,k]],
            [[k,k,k],[-k,k,k]],[[-k,k,k],[-k,-k,k]],
            [[-k,-k,k],[k,-k,k]],[[k,-k,k],[k,k,k]],
            [[k,k,k],[k,k,-k]],[[k,k,-k],[-k,k,-k]],
            [[-k,k,-k],[-k,-k,-k]],[[-k,-k,-k],[k,-k,-k]],
            [[k,-k,-k],[k,k,-k]],[[k,k,-k],[0,0,0]],
            [[0,0,0],[k,-k,-k]],[[k,-k,-k],[k,-k,k]]]
    if proj=='perspective_dof':
        t=Tachyon(xres=500,yres=500,projection=proj,
                  camera_center=(-3.5,0.,0.),
                  antialiasing=3,raydepth=5,
                  focallength='2.',aperture='.003')
    else: t=Tachyon(xres=500,yres=500,projection=proj,
                    camera_center=(-3.5,0.,0.))
    for i in [0..13]:
        t.texture('t%s'%str(i),opacity=.3,
                  color=colormaps[cm](.077*i)[:3])
        t.fcylinder(e[i][0],e[i][1],.06,'t%s'%str(i)) 
    t.light((-5,-5,5),.1,(1,1,1)); t.show()

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Messages

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y(k,x)=x^2*k^2-12*x^2+k^2*x-3*sqrt(3)*k*x+6*x+k^2-sqrt(3)*k-6
pretty_print(html('<p>$y=%s$</p>'%latex(y(k,x))))
n=31; k=[.12*i for i in [0..n]]
c=[colormaps.hsv(.03*i)[:3] for i in [0..n]]
p=sum([plot(y(k[i],x),(x,-2,2),color=c[i],
            legend_label='%.2f'%k[i]) for i in [0..n]])
p.set_legend_options(loc=(1.1,-.1))
p.show(ymin=-8,ymax=2,figsize=(7,5),gridlines=True)

Python Modules

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import numpy,pylab,time
from sklearn import manifold,datasets
X,y=datasets.load_digits(return_X_y=True)
tsne=manifold.TSNE(n_components=2,learning_rate=700.)
t0=time.time(); X_emb=tsne.fit_transform(X)
t=time.time()-t0
x_min,x_max=numpy.min(X_emb,0),numpy.max(X_emb,0)
X_emb=(X_emb-x_min)/(x_max-x_min)
f,ax=pylab.subplots(1,figsize=(7,7))
for i in range(X_emb.shape[0]):
    pylab.text(X_emb[i,0],X_emb[i,1],str(y[i]),
               color=pylab.cm.hsv(.1*y[i]))
pylab.title('t-SNE embedding %f s'%t)
pylab.axis('off'); pylab.show()

Other Languages (R, HTML, ...)

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%%r
library('MASS'); library('nnet'); data(Boston); n<-dim(Boston)[1];
svg(filename='Rplots.svg',width=7,height=4,pointsize=12,
    onefile=T,family='courier',bg='white',
    antialias=c('default','none','gray','subpixel'))
model<-nnet(as.matrix(Boston[1:430,-14]),as.matrix(Boston[1:430,14]),
            size=42,trace=F,maxit=1.5*10^3,linout=T,decay=5*.1^4)
predictions<-predict(model,as.matrix(Boston[431:n,-14]),type='raw')
plot(as.matrix(Boston[431:n,14]),col='#3636ff',type='o',
     xlab='',ylab='',yaxt='n'); par(new=T)
plot(predictions,col='#ff3636',type='o',
     cex=1.3,ylab='Targets & Predictions'); dev.off()

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%%html
<style>#svg1 {background-color:silver;} 
text {fill:#fff; font-size:135%;} 
.line {fill:none; stroke:#3636ff; stroke-width:2;}             
.grid line,.grid path {stroke:#fff; stroke-opacity:.9; 
                       shape-rendering:crispEdges;}       
</style><svg id='svg1'/><script>
var n=630,m=35,margin={top:m,right:m,bottom:m,left:m},
    width=500-margin.left-margin.right,
    height=500-margin.top-margin.bottom; 
var xScale=d3.scaleLinear().domain([-2,2]).range([0,width]),
    yScale=d3.scaleLinear().domain([-2,2]).range([height,0]);
function make_x_gridlines() {return d3.axisBottom(xScale).ticks(11)};
function make_y_gridlines() {return d3.axisLeft(yScale).ticks(11)};            
var data=d3.range(0,n).map(function(i){return {
    'x':Math.cos(.01*i)+Math.cos(.11*i)/2+Math.sin(.3*i)/3,
    'y':Math.sin(.01*i)+Math.sin(.11*i)/2+Math.cos(.3*i)/3}});
var tt1='translate('+margin.left+','+margin.top+')',
    tt2='translate(0,'+height+')';
var lineColor=d3.scaleSequential().domain([0,n])
                .interpolator(d3.interpolateCool);                       
var svg=d3.select('#svg1')
          .attr('width',width+margin.left+margin.right)
          .attr('height',height+margin.top+margin.bottom)
          .append('g').attr('transform',tt1);
svg.append('g').attr('class','x axis')
   .call(d3.axisBottom(xScale).tickSize(.5)).attr(tt2); 
svg.append('g').attr('class','y axis')
   .call(d3.axisLeft(yScale).tickSize(.5));    
svg.append('g').attr('class','grid').attr('transform',tt2)
               .call(make_x_gridlines()
               .tickSize(-height).tickFormat(''));
svg.append('g').attr('class','grid').call(make_y_gridlines()
               .tickSize(-width).tickFormat(''));
var line=d3.line().curve(d3.curveMonotoneX)
                  .x(function(d) {return xScale(d.x);})
                  .y(function(d) {return yScale(d.y);});
svg.append('path').datum(data).attr('class','line').attr('d',line);

📑 SageMath Online Mini Campus. Code Set 24

Example of Computations

Your Experiments

Python Modules

Other Languages (R, HTML, ...)