Random Lines

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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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#d3ch2 {background:ivory;}

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#d3ch2 text {fill:#ff3636; font-size:130%; font-family:Ewert} 

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.grid2 line,.grid2 path {

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    stroke:#ff3636; stroke-opacity:.5; stroke-width:.3; 

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    stroke-opacity:.5; shape-rendering:crispEdges;}

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</style>

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<svg id='d3ch2'/><script>

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var m=30,x1=-7,x2=7,y1=-7,y2=7,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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function randi(min,max) {

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

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function randcolR(i) {

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    var r=randi(100+i,255),gb=randi(10+i,100);

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

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function make_x_gridlines(){

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    return d3.axisBottom(xScale).ticks(11).tickFormat('')};

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function make_y_gridlines(){

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    return d3.axisLeft(yScale).ticks(10).tickFormat('')}; 

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var xScale=d3.scaleLinear().domain([x1,x2]).range([0,width]),

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    yScale=d3.scaleLinear().domain([y1,y2]).range([height,0]);

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var ttr1='translate('+margin.left+','+margin.top+')',

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    ttr2='translate(0,'+height+')';

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var svg=d3.select('#d3ch2')

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

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

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          .append('g').attr('transform',ttr1);

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svg.append('g').attr('class','x axis')

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   .call(d3.axisBottom(xScale).tickSize(.5)).attr('transform',ttr2); 

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svg.append('g').attr('class','y axis')

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   .call(d3.axisLeft(yScale).tickSize(.5));    

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svg.append('g').attr('class','grid2').attr('transform',ttr2)

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   .call(make_x_gridlines().tickSize(-height));

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svg.append('g').attr('class','grid2')

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   .call(make_y_gridlines().tickSize(-width));

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function fx(a,b,c,d,e,q,n,t,k) {

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    var x1=Math.cos(Math.PI*t/n+k*Math.PI/q)+

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           Math.cos(a*Math.PI*t/n+k*Math.PI/q),

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        x2=Math.cos(b*Math.PI*t/n+k*Math.PI/q)+

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           Math.cos(c*Math.PI*t/n+k*Math.PI/q),

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        x3=Math.cos(d*Math.PI*t/n+k*Math.PI/q)+

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           Math.cos(e*Math.PI*t/n+k*Math.PI/q);

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    return x1+x2+x3}

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function fy(a,b,c,d,e,q,n,t,k) {

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    var y1=Math.sin(Math.PI*t/n+k*Math.PI/q)+

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           Math.sin(a*Math.PI*t/n+k*Math.PI/q),

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        y2=Math.sin(b*Math.PI*t/n+k*Math.PI/q)+

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           Math.sin(c*Math.PI*t/n+k*Math.PI/q),

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        y3=Math.sin(d*Math.PI*t/n+k*Math.PI/q)+

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           Math.sin(e*Math.PI*t/n+k*Math.PI/q);

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    return y1+y2+y3}

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function make_data(a,b,c,d,e,q,n,k) {

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    return d3.range(0,2*n+1).map(function(t) {

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      return {'x':fx(a,b,c,d,e,q,n,t,k),

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              'y':fy(a,b,c,d,e,q,n,t,k)}; }) }

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var a=randi(5,9),b=randi(10,14),c=randi(15,19),

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    d=randi(20,36),e=randi(37,81),q=randi(3,12),n=randi(3,15);

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

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

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

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for (var i=1; i<2*(q+n+1); i++) {

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    var data=make_data(a,b,c,d,e,q,n,i),col=randcolR(i);

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    svg.append('path').datum(data).attr('class','line').attr('d',line)

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       .attr('stroke',col).attr('stroke-width',.3)

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

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Messages

Functions with Summation

<script src='https://d3js.org/d3.v6.min.js'></script> was added in the page head.

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%%html

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<style>

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@import 'https://fonts.googleapis.com/css?family=Orbitron|Akronim';

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#d3ch1 {background:whitesmoke;}

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#d3ch1 text {fill:#3636ff; font-size:110%; font-family:Orbitron} 

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.grid line,.grid path {stroke:#3636ff; stroke-opacity:.5; 

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                       shape-rendering:crispEdges;}

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</style>

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<svg id='d3ch1'/><script>

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var m=30,x1=0,x2=4,y1=-100,y2=100;

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var 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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function make_x_gridlines(){

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    return d3.axisBottom(xScale).ticks(11).tickFormat('')};

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function make_y_gridlines(){

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    return d3.axisLeft(yScale).ticks(10).tickFormat('')}; 

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var xScale=d3.scaleLinear().domain([x1,x2]).range([0,width]),

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    yScale=d3.scaleLinear().domain([y1,y2]).range([height,0]);

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var ttr1='translate('+margin.left+','+margin.top+')',

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    ttr2='translate(0,'+height+')';

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var svg=d3.select('#d3ch1')

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

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

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          .append('g').attr('transform',ttr1);

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svg.append('g').attr('class','x axis')

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               .call(d3.axisBottom(xScale).tickSize(.5))

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               .attr('transform',ttr2); 

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svg.append('g').attr('class','y axis')

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               .call(d3.axisLeft(yScale).tickSize(.5));    

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svg.append('g').attr('class','grid').attr('transform',ttr2)

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               .call(make_x_gridlines().tickSize(-height));

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svg.append('g').attr('class','grid')

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               .call(make_y_gridlines().tickSize(-width));

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function sumfunction(n,x) {

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  var funsum=0;

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

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      funsum+=Math.sqrt(Math.pow(Math.E,-i*x)+

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           Math.pow(x,i-1))/(Math.cos(i*x)+Math.sin(i*x));};

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  return funsum*Math.log(n*x-1)};

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var xy=Array(400).fill(50).map((r,x)=>

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       ({'x':.0075*(x+r),'y':sumfunction(3,.0075*(x+r))}));

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svg.selectAll('circle').data(xy).enter()

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    .append('circle').attr('r',3)

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    .attr('cx',d=>xScale(d.x)).attr('cy',d=>yScale(d.y))

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    .attr('fill','#3636ff').attr('stroke','#fff');

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Messages

Building Clusters as Hierarchical Trees

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# suppress ClusterWarning

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import warnings; warnings.simplefilter('ignore')

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import sklearn.cluster as scl

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

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from IPython.core.magic import register_line_magic

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from scipy.spatial.distance import pdist,squareform

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from scipy.cluster.hierarchy import linkage,dendrogram

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variables=['a','b','c']

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labels=['id'+str(i) for i in range(1,10)]

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X=np.random.random_sample([9,3])*10

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df=pd.DataFrame(X,columns=variables,index=labels)

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ac=scl.AgglomerativeClustering(

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    n_clusters=3,affinity='euclidean',linkage='complete')

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ac_labels=ac.fit_predict(X)

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print('Cluster labels: %s'%ac_labels)

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@register_line_magic

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def dist_clusters(method):

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    row_dist=pdist(df,metric='euclidean')

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    if method=='False':

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        row_dist=squareform(row_dist)

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    row_clusters=linkage(

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        row_dist,method='complete',metric='euclidean')

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    c=row_clusters.shape[0]

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    rc=pd.DataFrame(

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        row_clusters,

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        columns=['row label 1','row label 2','distance','n_items'],

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        index=['cl%d'%(i+1) for i in range(c)])

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    display(rc)

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    fig=pl.figure(figsize=(6.5,5))

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    axd=fig.add_axes([.1,.1,.31,.6])

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    d=dendrogram(row_clusters,orientation='left',labels=labels)

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    df_cl=df.iloc[d['leaves'][::-1]]

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    axd.set_xticks([]); axd.set_yticks([])

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    for i in axd.spines.values(): i.set_visible(False)

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    axm=fig.add_axes([.2,.1,.6,.6])

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    cax=axm.matshow(df_cl,interpolation='nearest',cmap='cool')

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    fig.colorbar(cax)

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    ac=[str(ac_labels[int(el[2])-1])+'-'+el 

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        for el in list(df_cl.index)]

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    axm.set_xticks(axm.get_xticks().tolist())

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    axm.set_yticks(axm.get_yticks().tolist())

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    axm.set_xticklabels(['']+list(df_cl.columns)+[''])

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    axm.set_yticklabels(['']+ac+[''])

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    if method=='False': pl.title('incorrect')

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    else: pl.title('correct')

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    pl.show()

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%dist_clusters False

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%dist_clusters True

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Messages

If you want to build datasets 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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from torch.utils.data import Dataset as tds

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from torch.utils.data import DataLoader as tdl

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import numpy as np,pylab as pl,torch,zipfile,h5py,urllib

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from IPython.core.magic import register_line_magic

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class TData(tds):

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    def __init__(self,x,y):   

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        self.x=torch.tensor(x,dtype=torch.float32)

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        self.y=torch.tensor(y,dtype=torch.int32)

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    def __getitem__(self,index):

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        img,lbl=self.x[index],self.y[index]

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        return img,lbl

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    def __len__(self):

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        return self.y.shape[0]

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@register_line_magic

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def display_examples(data):

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    for images,labels in dataloaders[data]:  

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        print('Image dimensions: %s'%str(images.shape))

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        print('Label dimensions: %s'%str(labels.shape))

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        n=np.random.randint(1,3)

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        fig=pl.figure(figsize=(6,2))

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        for i in range(n,n+5):

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            ax=fig.add_subplot(1,5,i-n+1,xticks=[],yticks=[])

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            ax.set_title(names[labels[i].item()],fontsize=10)

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            ax.imshow(np.transpose(images[i],(1,2,0)))

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        pl.tight_layout(); pl.show(); break

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Messages

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path='https://olgabelitskaya.github.io/'

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zf='TomatoCultivarImages.h5.zip'

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input_file=urllib.request.urlopen(path+zf)

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output_file=open(zf,'wb'); 

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output_file.write(input_file.read())

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output_file.close(); input_file.close()

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zipf=zipfile.ZipFile(zf,'r')

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zipf.extractall(''); zipf.close()

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f=h5py.File(zf[:-4],'r'); keys=list(f.keys())

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x_test=np.array(f[keys[0]])

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y_test=np.array(f[keys[1]])

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names=['Kumato','Beefsteak','Tigerella',

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       'Roma','Japanese Black Trifele',

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       'Yellow Pear','Sun Gold','Green Zebra',

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       'Cherokee Purple','Oxheart','Blue Berries',

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       'San Marzano','Banana Legs',

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       'German Orange Strawberry','Supersweet 100']

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num_classes=len(names); batch_size=int(16)

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x_test=np.transpose(x_test,(0,3,1,2))

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print(x_test.mean(),x_test.std())

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test=TData(x_test,y_test)

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dataloaders={'test':tdl(

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    dataset=test,shuffle=True,batch_size=batch_size)}

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%display_examples test

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Messages