Smoothing 3D Matrix

I have a 3D surfrace plotted but it is quite rough and I need to smooth it out. I have tried using interpt2 and I keep recieving error codes.

below is the code I have been trying

x=0:21;

y=0:17;

[x,y]=meshgrid(x,y);

z=[-5 -5 0 0 0 0 0 0 0 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5;0 0 5 0 1 0 2 0 0 1 0 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5; 0 2 0 1 0 0 0 1 0 0 2 0 3 0 0 1 -5 -5 -5 -5 -5;0 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 -5 -5 -5 -5;-5 -5 0 2 0 0 0 0 13 0 0 0 0 0 0 0 0 0 -5 -5 -5;-5 -5 0 0 0 0 0 0 0 0 0 0 24 0 0 0 0 0 0 -5 -5;-5 -5 -5 0 0 0 0 0 0 1 0 0 24 24 0 0 0 0 0 0 -5;-5 -5 -5 -5 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0;-5 -5 -5 -5 -5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -5 -5;-5 -5 -5 -5 -5 0 0 0 2 0 0 0 0 0 0 0 0 0 -5 -5 -5;-5 -5 -5 -5 -5 -5 0 0 0 0 0 0 0 0 0 0 1 0 -5 -5 -5;-5 -5 -5 -5 -5 -5 -5 0 3 0 0 0 0 0 23 0 0 -5 -5 -5 -5;-5 -5 -5 -5 -5 -5 -5 -5 0 0 0 0 0 27 27 0 -5 -5 -5 -5 -5;-5 -5 -5 -5 -5 -5 -5 -5 0 0 0 0 0 0 0 -5 -5 -5 -5 -5 -5;-5 -5 -5 -5 -5 -5 -5 -5 -5 0 0 0 0 -5 -5 -5 -5 -5 -5 -5 -5;-5 -5 -5 -5 -5 -5 -5 -5 -5 0 0 0 -5 -5 -5 -5 -5 -5 -5 -5 -5;-5 -5 -5 -5 -5 -5 -5 -5 -5 -5 0 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5];

surf(z)

xlabel('Width')

ylabel('Length')

zlabel('Number of Earthquakes')

xi=0:.1:10;

yi=0:.1:10;

[xi,yi]=meshgrid(xi,yi);

zc=interp2(x,y,z,xi,yi,'cubic');

surf(xi,yi,zc)

These are the errors that keep popping up

Error using griddedInterpolant

GridVectors must define a grid whose size is

compatible with the Values array.

Error in interp2>makegriddedinterp (line 226)

F = griddedInterpolant(varargin{:});

Error in interp2 (line 134)

F = makegriddedinterp(X, Y, V, method,extrap);

Error in MultiVaribleProject (line 12)

zc=interp2(x,y,z,xi,yi,'cubic');

Answer 1

[Voss]

x=0:21;
y=0:17;
[x,y]=meshgrid(x,y);
z=[-5 -5 0 0 0 0 0 0 0 -5 -5 -5	-5 -5 -5 -5 -5 -5 -5 -5	-5;0 0 5 0 1 0 2 0 0 1 0 -5 -5 -5 -5 -5	-5 -5 -5 -5 -5; 0 2 0 1 0 0 0 1 0 0 2 0 3 0 0 1 -5 -5 -5 -5 -5;0 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 -5	-5 -5 -5;-5 -5 0 2 0 0 0 0 13 0 0 0	0 0 0 0	0 0 -5 -5 -5;-5 -5 0 0 0 0 0 0 0 0 0 0 24 0 0 0 0 0 0 -5 -5;-5 -5 -5 0 0 0 0 0 0 1 0 0 24 24 0 0 0 0 0 0 -5;-5 -5 -5 -5 0 0 0 0 0 0 4 0	0 0 0 0	0 0 0 0	0;-5 -5 -5 -5 -5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -5 -5;-5 -5 -5 -5 -5 0 0 0 2 0 0 0 0 0	0 0 0 0 -5 -5 -5;-5 -5 -5 -5 -5 -5 0 0 0 0 0 0 0 0 0 0 1 0 -5 -5 -5;-5 -5 -5 -5 -5 -5 -5 0 3 0 0 0 0 0 23 0 0 -5 -5 -5 -5;-5 -5 -5 -5 -5 -5 -5 -5 0 0 0 0 0 27 27 0 -5 -5 -5 -5 -5;-5 -5 -5 -5 -5 -5 -5 -5 0 0 0 0 0 0 0 -5 -5 -5 -5 -5 -5;-5 -5 -5 -5 -5 -5 -5 -5 -5 0 0 0 0 -5 -5 -5 -5 -5 -5 -5 -5;-5 -5 -5 -5 -5 -5 -5 -5 -5 0 0 0 -5 -5 -5 -5 -5 -5 -5 -5 -5;-5 -5 -5 -5 -5 -5 -5 -5 -5 -5 0 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5];
whos x y z

  Name       Size            Bytes  Class     Attributes

  x         18x22             3168  double              
  y         18x22             3168  double              
  z         17x21             2856  double              

As you can see there, z has one fewer row and column than x and y. That's what the error message from interp2 is complaining about.

Defining x and y to start with 1 allows interp2 to work (I have no idea if this is an appropriate fix in this situation):

x=1:21;
y=1:17;
[x,y]=meshgrid(x,y);
z=[-5 -5 0 0 0 0 0 0 0 -5 -5 -5	-5 -5 -5 -5 -5 -5 -5 -5	-5;0 0 5 0 1 0 2 0 0 1 0 -5 -5 -5 -5 -5	-5 -5 -5 -5 -5; 0 2 0 1 0 0 0 1 0 0 2 0 3 0 0 1 -5 -5 -5 -5 -5;0 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 -5	-5 -5 -5;-5 -5 0 2 0 0 0 0 13 0 0 0	0 0 0 0	0 0 -5 -5 -5;-5 -5 0 0 0 0 0 0 0 0 0 0 24 0 0 0 0 0 0 -5 -5;-5 -5 -5 0 0 0 0 0 0 1 0 0 24 24 0 0 0 0 0 0 -5;-5 -5 -5 -5 0 0 0 0 0 0 4 0	0 0 0 0	0 0 0 0	0;-5 -5 -5 -5 -5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -5 -5;-5 -5 -5 -5 -5 0 0 0 2 0 0 0 0 0	0 0 0 0 -5 -5 -5;-5 -5 -5 -5 -5 -5 0 0 0 0 0 0 0 0 0 0 1 0 -5 -5 -5;-5 -5 -5 -5 -5 -5 -5 0 3 0 0 0 0 0 23 0 0 -5 -5 -5 -5;-5 -5 -5 -5 -5 -5 -5 -5 0 0 0 0 0 27 27 0 -5 -5 -5 -5 -5;-5 -5 -5 -5 -5 -5 -5 -5 0 0 0 0 0 0 0 -5 -5 -5 -5 -5 -5;-5 -5 -5 -5 -5 -5 -5 -5 -5 0 0 0 0 -5 -5 -5 -5 -5 -5 -5 -5;-5 -5 -5 -5 -5 -5 -5 -5 -5 0 0 0 -5 -5 -5 -5 -5 -5 -5 -5 -5;-5 -5 -5 -5 -5 -5 -5 -5 -5 -5 0 -5 -5 -5 -5 -5 -5 -5 -5 -5 -5];
whos x y z % all the same size now

  Name       Size            Bytes  Class     Attributes

  x         17x21             2856  double              
  y         17x21             2856  double              
  z         17x21             2856  double              

surf(z)
xlabel('Width')
ylabel('Length')
zlabel('Number of Earthquakes')

xi=0:.1:10;
yi=0:.1:10;
[xi,yi]=meshgrid(xi,yi);
zc=interp2(x,y,z,xi,yi,'cubic');
surf(xi,yi,zc)

However, notice that the resulting higher-resolution surface doesn't really have the same shape as the orginal. This is because the query points xi and yi only go up to 10 rather than 21 or 17 like the original x and y, respectively, so this surface only covers roughly a quarter of the original region. To fix that, define xi and yi to span the original region defined by x and y. For instance:

xi = linspace(x(1),x(end),50);
yi = linspace(y(1),y(end),50);
[xi,yi]=meshgrid(xi,yi);
zc=interp2(x,y,z,xi,yi,'cubic');
surf(xi,yi,zc)
xlabel('Width')
ylabel('Length')
zlabel('Number of Earthquakes')

Now it covers the same region as the original surface, and has ~2.5x the resolution. Adjust the 50 used in defining xi and yi to adjust the resolution.