3D interpolation on a table

Hello All,

I'm pretty new to matlab and I want to perform a 3D interpolation on a 70 x 7 matrix table. I've read the documentation for 3D but I don't seem to be able to apply it. Here is an example. For instance, if A = 0.33; B = 2.5, what will be the value of C at 75%? Thanks.

 A    B              C
            1%  25% 50% 75% 100%
0.30  2     1.1 1.5 1.0 0.3 0.8
0.30  3     1.6 1.8 1.0 0.5 0.8
0.30  4     1.3 1.1 1.0 0.8 0.8
0.30  5     1.2 1.1 1.0 0.6 0.7
0.30  6     1.3 1.1 1.0 0.8 0.7
0.30  7     1.3 1.2 1.0 0.8 0.7
0.30  8     1.3 1.1 1.0 0.8 0.7
0.30  9     1.3 1.1 1.0 0.8 0.7
0.30  10    1.3 1.1 1.0 0.8 0.7
0.30  11    1.8 1.3 1.0 0.8 0.7
0.35  2     1.3 1.8 1.0 0.9 0.1
0.35  3     1.6 1.9 1.0 0.9 0.8
0.35  4     1.4 1.2 1.0 0.9 0.8
0.35  5     1.2 1.1 1.0 0.8 0.8
0.35  6     1.4 1.2 1.0 0.8 0.7
0.35  7     1.3 1.1 1.0 0.8 0.7
0.35  8     1.2 1.1 1.0 0.8 0.7
0.35  9     1.3 1.5 1.0 0.8 0.7
0.35  10    1.9 1.4 1.0 0.8 0.7
0.35  11    1.3 1.1 1.0 0.8 0.8

Answer 1

[Andrei Bobrov]

>> f = fopen('yourdata.txt');
cc = textscan(f,'%f %f %f %f %f %f %f ','HeaderLines',2,'CollectOutput',1 );
fclose(f);
g = cc{:};

[A,B,C] = ndgrid(unique(g(:,1)),unique(g(:,2)),[1 25 50 75 100]);
n = size(A);
V = permute(reshape(g(:,3:end),n([2,1,3])),[2,1,3]);
F = griddedInterpolant(A,B,C,V);

>> out = F(.35,4,1)
out =
    1.4000

[Ruby pca]

Thanks so much Andrei, it works but I noticed that some interpolations don't give the correct answer. For instance:

out = F(0.35,4,1) returns out as 1.3 instead of 1.4 out = F(0.35,9,25) returns out as 1.1 instead of 1.5

[Andrei Bobrov]

corrected

[Ruby pca]

Thanks! It works perfectly now.

Answer 2

[Andrés Medina]

First of all I want to thank Andrei for his invaluable contribution to the forum. Thanks for the example. Now my question goes. How can I do to be able to repeatedly interpolate with your code?. If I enter a value it works correctly. but not when I try to do it for many values, g in my case is a 5041x7 matrix.

Thanks a lot!!

theta_l=atan(abs(tan (deltal).*cos (gamma1))); %longitudinal angle, in rad 
theta_t=atan(tan (deltal).*abs(sin (gamma1))) %transversal angle, in rad
%disp(['Angulo longitudinal = ', num2str(theta_l), '   Angulo transversal = ', num2str(theta_t)])


Z1 = theta_l;
Z11 = reshape(Z1,[1,8760]);


Z2= theta_t;
Z22 = reshape(Z2,[1,8760]);


f = fopen('concentracion_txt.txt');
cc = textscan(f,'%f %f %f %f %f %f %f ','HeaderLines',2,'CollectOutput',1 );
fclose(f);
g = cc{:};

[A,B,C] = ndgrid(unique(g(:,1)),unique(g(:,2)),[1 25 50 75 100]);
n = size(A);
V = permute(reshape(g(:,3:end),n([2,1,3])),[2,1,3]);
F = griddedInterpolant(A,B,C,V);

concentracion = F(Z11,Z22,1)