Monday, December 16, 2019

Matrix, Table & Grid Forms


MatrixForm[Array[Subscript[A,##] &,{5,5}]]
TableForm[{{2,3,4},{5,6,7}},
TableHeadings -> {{"row a", "row b"},
{"column x", "column y","column z"}}]

Style[Grid[{{1, 2, 3},{4, 5, 6},{7, 8, 9}},
Background ->{{LightRed,None,Pink},{None,LightBlue, None}},
                        Dividers->All],FontSize->32]


Neural Network Classifiers


DeleteObject[images];
images=ResourceObject["CIFAR-10"]
train=RandomSample[ResourceData[images],5000];

RandomSample[train,5]
classes=Union@Values[train]


NN= NetChain[{ConvolutionLayer[32,5],Ramp, PoolingLayer[2,2],
ConvolutionLayer[96,5],Ramp, PoolingLayer[2,2],
FlattenLayer[],512,Ramp,10,SoftmaxLayer[]},
"Output" -> NetDecoder[{"Class",classes}],
"Input" -> NetEncoder[{"Image",{32,32}}]]

NNTrained = NetTrain[NN,train,MaxTrainingRounds -> 5]


Plotting Derivatives


f[x_]=Cos[x]; g[x_]=Sqrt[x]*Sin[x]; h[x_]=Cos[Sqrt[x]*Sin[x]];
Plot[{f[x],f'[x],g[x],g'[x],h[x],h'[x]},{x,0,15},
         PlotStyle->{RGBColor["#3636FF"],Darker[Blue],RGBColor["#FF3636"],
         Darker[Red],RGBColor["#FF36FF"],Darker[Magenta]},
         Filling->Axis,FillingStyle->Opacity[0.2],ImageSize->Large,
         GridLines->Automatic,PlotLegends->"Expressions"]



Elliptic Curves


EF[x_,y_,i_]:=y^2+(i-5)*x*y+(i-1)*y -(x^3+(i+5)*x^2+(i+1)*x+(i+3));
Show[Table[ContourPlot[EF[x,y,i]==0,{x,-15,15},{y,-35,35},
ContourStyle->Hue[i/9]],{i,Range[0,8,1]}],
  ImageSize->Large,GridLines->Automatic,

PlotLabel->"Elliptic Curves"]



Interactive Color Exploration


Manipulate[Plot3D[3Sin[x^2-6 Pi*y(1 -y)],{x,-Pi ,Pi},{y,0,1}, PlotPoints->30,
                                MaxRecursion->1,Mesh->Full,MeshStyle->Gray,
                Boxed->False,Axes->False,ImageSize->Large,
                                PlotStyle->Opacity[0.8],

ColorFunction->(ColorData[scheme][#3] &)],
          {scheme,{"Pastel","NeonColors","BrightBands","MintColors"}}]