Solve in comments ( MATLAB )

% Q1: What is done to calculate x on line 6 and y on line 12 below?

I = 41;

Dx = 1;

xmin = 0;

xmax = 40;

x = xmin + (xmax-xmin)*[0:I-1]'/(I-1);

J = 41;

Dy = 1;

ymin = 0;

ymax = 40;

y = ymin + (ymax-ymin)*[0:J-1]'/(J-1);

% Q2: What is happening in the below sequence of operations

N0 = floor(I*J/10);

rowindex0=unidrnd(I,N0,1);

colindex0=unidrnd(J,N0,1);

% Q3: What's happening from lines 20-36?

A = zeros(I,J);

rowindex=zeros(N0,1);

colindex=zeros(N0,1);

N=0;

for i = [1:N0]

if ( A(rowindex0(i),colindex0(i)) == 0 )

N=N+1;

rowindex(N)=rowindex0(i);

colindex(N)=colindex0(i);

end

A(rowindex0(i),colindex0(i)) = 1;

end

rowindex=rowindex(1:N);

colindex=colindex(1:N);

xobs = x(rowindex);

yobs = y(colindex);

N=length(xobs);

% Q4: What's happening from lines 39-42?

kappa = 0.1;

dtrue = 10*sin(kappa*xobs).*exp(-kappa*yobs);

sigmad = 0.1;

dobs = dtrue + random('Normal',0.0,sigmad,N,1);

% Q5: Why do we need the below four lines?

A = zeros(I,J);

for i = [1:N]

A(rowindex(i),colindex(i)) = dobs(i);

end

figure(1);

clf;

set(gca,'LineWidth',2);

hold on;

axis ij;

axis equal;

axis([0, I, 0, J]);

bw=0.9*(256-linspace(0,255,256)')/256;

colormap([bw,bw,bw]);

range=max(max(A))-min(min(A));

if( range==0 )

range=1;

end

imagesc( [0, I], [0, J], (A-min(min(A)))/range);

hold on;

xlabel('y');

ylabel('x');

title('data');

figure(2);

clf;

set(gca,'LineWidth',2);

hold on;

axis ij;

axis equal;

axis([0, I, 0, J]);

bw=0.9*(256-linspace(0,255,256)')/256;

colormap([bw,bw,bw]);

range=max(max(A))-min(min(A));

if( range==0 )

range=1;

end

imagesc( [0, I], [0, J], (A-min(min(A)))/range);

hold on;

xlabel('y');

ylabel('x');

title('data + triangulation');

% Q6: What's happening on line 90?

mytri = DelaunayTri(xobs,yobs);

XY=mytri.X;

[NXY, i] = size(XY);

TRI=mytri.Triangulation;

[NTRI, i] = size(TRI);

for i = [1:NTRI]

v1=TRI(i,1); v2=TRI(i,2); v3=TRI(i,3);

plot( [XY(v1,2), XY(v2,2)], [XY(v1,1), XY(v2,1)], 'k-', 'LineWidth', 2);

plot( [XY(v2,2), XY(v3,2)], [XY(v2,1), XY(v3,1)], 'k-', 'LineWidth', 2);

plot( [XY(v3,2), XY(v1,2)], [XY(v3,1), XY(v1,1)], 'k-', 'LineWidth', 2);

end

% Q7: What's happening from lines 105-113?

x0=[20,30];

tri0 = pointLocation(mytri, x0);

plot( x0(2), x0(1), 'ko', 'LineWidth', 2);

if( ~isnan(tri0) )

v1=TRI(tri0,1); v2=TRI(tri0,2); v3=TRI(tri0,3);

plot( [XY(v1,2), XY(v2,2)], [XY(v1,1), XY(v2,1)], 'k-', 'LineWidth', 3);

plot( [XY(v2,2), XY(v3,2)], [XY(v2,1), XY(v3,1)], 'k-', 'LineWidth', 3);

plot( [XY(v3,2), XY(v1,2)], [XY(v3,1), XY(v1,1)], 'k-', 'LineWidth', 3);

end

%Q 8: What's happening from lines 116-125?

xp = zeros(I*J,1);

yp = zeros(I*J,1);

dp = zeros(I*J,1);

for i = [1:I]

for j = [1:J]

k = j + J*(i-1);

xp(k) = x(i);

yp(k) = y(j);

end

end

% Q9: What's happening on line 128?

dp=griddata(xobs,yobs,dobs,xp,yp,'linear');

% Q10: What's happening from lines 131-137?

B = zeros(I,J);

for i = [1:I]

for j = [1:J]

k = j + J*(i-1);

B(i,j) = dp(k);

end

end

figure(3);

clf;

set(gca,'LineWidth',2);

hold on;

axis ij;

axis equal;

axis([0, I, 0, J]);

bw=0.9*(256-linspace(0,255,256)')/256;

colormap([bw,bw,bw]);

range=max(max(B))-min(min(B));

if( range==0 )

range=1;

end

imagesc( [0, I], [0, J], (B-min(min(B)))/range);

hold on;

xlabel('y');

ylabel('x');

title('linear interpolation');

dpp=griddata(xobs,yobs,dobs,xp,yp,'cubic');

C = zeros(I,J);

for i = [1:I]

for j = [1:J]

k = j + J*(i-1);

C(i,j) = dpp(k);

end

end

figure(4);

clf;

set(gca,'LineWidth',2);

hold on;

axis ij;

axis equal;

axis([0, I, 0, J]);

bw=0.9*(256-linspace(0,255,256)')/256;

colormap([bw,bw,bw]);

range=max(max(C))-min(min(C));

if( range==0 )

range=1;

end

imagesc( [0, I], [0, J], (C-min(min(C)))/range);

hold on;

xlabel('y');

ylabel('x');

title('cubic interpolation');