Compute values in the nodes of a 3d matrix

Hi,

Let S2 a surface below the surface S1, I would to compute values in the nodes below S2, starting from the values computed at the boundary between S1 and S2, using coefficients C2.

      % Create the surfaces:
      x = rand(100,1)*4 - 2;
      y = rand(100,1)*4 - 2;
      S1 = x.*exp(-x.^2-y.^2) * 1000;
      S2 = S1 - 100;
      % Create positive coefficients
      C1 = 0.02 + (0.08 - 0.02).*rand(100,1);
      C2 = 0.03 + (0.05 - 0.03).*rand(100,1);
      % Construct the interpolant:
      F1 = TriScatteredInterp(x,y,S1);
      F2 = TriScatteredInterp(x,y,S2);
      G1 = TriScatteredInterp(x,y,C1);
      G2 = TriScatteredInterp(x,y,C2);
      % Evaluate the interpolant at the locations [XI,YI].
      XI = -2:0.25:2;
      YI = -2:0.1:2;
      [XImat,YImat] = ndgrid(XI,YI);
      ZI_1 = F1(XImat,YImat);
      ZI_2 = F2(XImat,YImat);
      C_1 = G1(XImat,YImat);
      C_2 = G2(XImat,YImat);
      % Define a set of ZI locations
      ZI = -500:100:500;
      % Find the nodes below the surface S1 and S2
      BW1 = bsxfun(@le, ZI_1, reshape(ZI,1,1,[]));
      BW2 = bsxfun(@le, ZI_2, reshape(ZI,1,1,[]));
      % Create a 3d grid where to compute the value in each node
      [Z,Z,Z] = ndgrid(XI,YI,ZI);
      % Compute value below S1 with coefficients C1
      T = 18 + bsxfun(@times, C_1, Z .* BW1);

Whith the help of a file-exchange find_ndim, I've found the index where the surface S2 starts.

index = find_ndim(BW2,3,'first')
T = ???? + bsxfun(@time, C2, Z .* BW2);

Thanks for any suggestion, Gianluca

[José-Luis]

I don't understand the question. What does ???? mean?

[gianluca]

T = T(index) + bsxfun(@time, C2, Z .* BW2);

but it don't works

[Sven]

Gianluca, can you explain more clearly the following:

"% Compute value below S1 with coefficients C1"

Also, what do you expect the size(T) of your final value T should be? We're just having a bit of trouble understanding what your final answer will look like... once we understand that, we can show you the syntax to get that answer.

[gianluca]

hi, the values of T (dependent variable) change as function of Z (independent variable) from a initial value (T = 18) at the surface S1 following a linear trend defined by the coefficient C1 (gradient). When we pass below the surface S2 the linear trend changes from C1 to C2.

   T = 18 + bsxfun(@times, C_1, Z .* BW1);

computes in all the nodes of the 3d matrix the variable T (also below S2). I would in a second step compute T only in the nodes below S2 rewriting the old values. In this second step the variable T starts from the values computed previously at surface S2.

index = find_ndim(BW2,3,'first')

Finds the first indexes of S2 in the third dimension, that is the indexes from which the surface S2 begins.

T2 = T(index)

don't works, an error message occurs. I expect that T2 is double and the final T double.

thanks

[gianluca]

I expect that T2 is 17x41 double and the final T 17x41x11 double.

Answer 1

[Andrei Bobrov]

d = cumsum(BW2(:,:,end:-1:1),3);
index = bsxfun(@eq,sum(BW2,3) - 1,d(:,:,end:-1:1) - cumsum(BW2,3));
T2 = T.*index + bsxfun(@times, C_2, Z .* BW2);

[gianluca]

Hi, you given me an useful tool with which try again. I would store the results in the same variable T.