function [Zexact, Ztop5, Ztop10, Ztop20, Z99per, Z98per, Z97per, Z95per, Z90per, Z85per, Z80per, DistComp, RuntimeNystrom, RuntimeFD]=RepLearnFINAL(X, Dictionary, gamma)

% Input

% X: original data (nxm)

% Dictionary: kShape's centroids (cxm) or randomly chosen time series

% Dim: Dimensions to keep in the end over the learned representation

% gamma: kernel's parameter

% Output

% Ktilde: Approximated kernel matrix (nxn)

% Z: New learned representation (nxDim)

tic;

DistComp = 0;

[nrowsX, ncolumnsX] = size(X);

[nrowsDic, ncolumnsDic] = size(Dictionary);

W = zeros(nrowsDic,nrowsDic);

for i=1:nrowsDic

for j=1:nrowsDic

W(i,j) = SINK(Dictionary(i,:),Dictionary(j,:),gamma);

DistComp = DistComp 1;

end

end

E = zeros(nrowsX,nrowsDic);

for i=1:nrowsX

disp(i);

for j=1:nrowsDic

E(i,j) = SINK(X(i,:),Dictionary(j,:),gamma);

DistComp = DistComp 1;

end

end

[Ve, Va] = eig(W);

va = diag(Va);

inVa = diag(va.^(-0.5));

Zexact = E * Ve * inVa;

RuntimeNystrom = toc;

Zexact = CheckNaNInfComplex(Zexact);

tic;

[BSketch, ~] = FrequentDirections(Zexact, ceil(0.5*size(Zexact,2)));

[V2, L2] = eig(BSketch'*BSketch);

%[V2, L2] = eig(Zexact'*Zexact);

eigvalue = diag(L2);

[dump, index] = sort(-eigvalue);

eigvalue = eigvalue(index);

V2 = V2(:, index);

RuntimeFD = toc;

VarExplainedCumSum = cumsum(eigvalue)/sum(eigvalue);

DimFor99 = find(VarExplainedCumSum>=0.99,1);

DimFor98 = find(VarExplainedCumSum>=0.98,1);

DimFor97 = find(VarExplainedCumSum>=0.97,1);

DimFor95 = find(VarExplainedCumSum>=0.95,1);

DimFor90 = find(VarExplainedCumSum>=0.90,1);

DimFor85 = find(VarExplainedCumSum>=0.85,1);

DimFor80 = find(VarExplainedCumSum>=0.80,1);

Ztop5 = CheckNaNInfComplex( Zexact*V2(:,1:5) );

Ztop10 = CheckNaNInfComplex( Zexact*V2(:,1:10) );

Ztop20 = CheckNaNInfComplex( Zexact*V2(:,1:20) );

Z99per = CheckNaNInfComplex( Zexact*V2(:,1:DimFor99) );

Z98per = CheckNaNInfComplex( Zexact*V2(:,1:DimFor98) );

Z97per = CheckNaNInfComplex( Zexact*V2(:,1:DimFor97) );

Z95per = CheckNaNInfComplex( Zexact*V2(:,1:DimFor95) );

Z90per = CheckNaNInfComplex( Zexact*V2(:,1:DimFor90) );

Z85per = CheckNaNInfComplex( Zexact*V2(:,1:DimFor85) );

Z80per = CheckNaNInfComplex( Zexact*V2(:,1:DimFor80) );

end

function Z = CheckNaNInfComplex(Z)

for i=1:size(Z,1)

for j=1:size(Z,2)

if (isnan(Z(i,j)) || isinf(Z(i,j)) || ~isreal(Z(i,j)))

Z(i,j)=0;

end

end

end

end