C9: approximate sum and difference marginalizations

We take each row in turn

% row 1

% left

a=-22; b=64; x=-5:5;

p=1/10*ones(11,1); p=p*p';

[X1 X2]=meshgrid(x,x);

figure(1); clf; hold on

mesh(X1,X2,p)

x1=-4.5:4.5; x2=-4.5:4.5;

p1=1/10*ones(10,1); p2=1/10*ones(10,1); p=p1*p2';

[X1 X2]=meshgrid(x2,x1); X1=X1(:); X2=X2(:); p=p(:);

for n=1:length(X1), plot3(X1(n)*[1 1],X2(n)*[1 1],[0 p(n)],'k-'); end

p=p1*p2'; [X1 X2]=meshgrid(x2,x1);

plot3(X1,X2,1.01*p,'k.')

plot3(6*[1 1],[-5 5],.01*[1 1],'k-','LineWidth',2)

plot3([-5 5],6*[1 1],.01*[1 1],'k-','LineWidth',2)

plot3(6*[1 1],-5*[1 1],[0 .01],'k--')

plot3(6*[1 1],5*[1 1],[0 .01],'k--')

plot3(-5*[1 1],6*[1 1],[0 .01],'k--')

plot3(5*[1 1],6*[1 1],[0 .01],'k--')

view(a,b);

% right

a=-26.5; b=28;

Fnum=2;

v=[-4.5:4.5]';

vp=[v ones(length(v),1)/length(v)];

SumDiffFig(vp,vp,Fnum,3,8)

view(a,b);

%%%%%%%%%

% row 2 %

% left

V=2.65;

a=-26.5; b=28; x=-11:11;

p=npdf(x,0,V)'; p=p*p';

[X1 X2]=meshgrid(x,x);

figure(1); clf; hold on

mesh(X1,X2,p)

x=-10.5:10.5;

p=npdf(x,0,V)'; p=p*p';

[X1 X2]=meshgrid(x,x);

X1=X1(:); X2=X2(:); p=p(:);

plot3(X1,X2,p,'k.')

plot3((max(x)+1.5)*ones(101,1),linspace(min(x)-.5,max(x)+.5,101),max(p)*npdf(linspace(min(x)-.5,max(x)+.5,101),0,V)/npdf(0,0,V),'k-','LineWidth',2)

plot3(linspace(min(x)-.5,max(x)+.5,101),(max(x)+1.5)*ones(101,1),max(p)*npdf(linspace(min(x)-.5,max(x)+.5,101),0,V)/npdf(0,0,V),'k-','LineWidth',2)

view(a,b); axis([min(x)-.5 max(x)+1.5 min(x)-.5 max(x)+1.5 0 1.05*max(p)])

% right

a=-26.5; b=28; Fnum=2;

v=x'; vp=[v npdf(v,0,V)];

SumDiffFig(vp,vp,Fnum,1,8)

view(a,b);

%%%%%%%%%

% row 3 %

% left

V=2.65; a=-26.5; b=28; x=-11:11;

p=npdf(x,0,V)'; p=p*p';

[X1 X2]=meshgrid(x,x);

figure(1); clf; hold on

mesh(X1,X2,p); colormap bone

x=-10.5:10.5;

p=npdf(x,0,V)'; p=p*p';

[X1 X2]=meshgrid(x,x);

X1=X1(:); X2=X2(:); p=p(:);

plot3(X1,X2,p,'k.')

plot3((max(x)+1.5)*ones(101,1),linspace(min(x)-.5,max(x)+.5,101),max(p)*npdf(linspace(min(x)-.5,max(x)+.5,101),0,V)/npdf(0,0,V),'k-','LineWidth',2)

plot3(linspace(min(x)-.5,max(x)+.5,101),(max(x)+1.5)*ones(101,1),max(p)*npdf(linspace(min(x)-.5,max(x)+.5,101),0,V)/npdf(0,0,V),'k-','LineWidth',2)

view(a,b); axis([min(x)-.5 max(x)+1.5 min(x)-.5 max(x)+1.5 0 1.05*max(p)])

% right

a=-26.5; b=28; Fnum=2;

v=x'; vp=[v npdf(v,0,V)];

SumDiffFig(vp,vp,Fnum,1,8)

view(a,b);