interpolation of scatter data

Hi, I am new in Matlab and I have difficulty in solving this problem. I have a matrix as bellow where Fd is a function of Id and Iq and also Fq is a function of Id and Iq. I want to extend my results for a 128*128 matrix of Id and Iq. The code that I used is as:

Id_vector = linspace(-200,0,128);   
Iq_vector = linspace(-200,0,128);
[ Id , Iq ] = meshgrid(Id_vector,Iq_vector);

but I can not create a function for Fd and Fq using two variables. I tried the interp1 and ppval without any success. would you please help me?

Id  Iq  Fd  Fq
0  0  0.001  -0.172
-50.0  0  0.001  -0.186
-100  0  0.001  -0.196
-150  0  0.001  -0.204
-200  0  0.001  -0.210
0  -50  -0.020  -0.172
-50  -50  -0.019  -0.186
-100  -50  -0.017  -0.196
-150  -50  -0.016  -0.204
-200  -50  -0.015  -0.210
0.0  -100.0  -0.042  -0.171
-50.0  -100.0  -0.039  -0.185
-100.0  -100.0  -0.036  -0.195
-150.0  -100.0  -0.034  -0.203
-200.0  -100.0  -0.032  -0.209
0.0  -150.0  -0.064  -0.168
-50.0  -150.0  -0.060  -0.182
-100.0  -150.0  -0.056  -0.192
-150.0  -150.0  -0.052  -0.200
-200.0  -150.0  -0.049  -0.206
0.0  -200.0  -0.085  -0.164
-50.0  -200.0  -0.079  -0.178
-100.0  -200.0  -0.074  -0.188
-150.0  -200.0  -0.069  -0.196
-200.0  -200.0  -0.065  -0.203

Answer 1

[Star Strider]

Your data are gridded, so you simply need to reshape the vectors to create matrices:

%     Id  Iq  Fd  Fq
M = [  0  0  0.001  -0.172
    -50.0  0  0.001  -0.186
    -100  0  0.001  -0.196
    -150  0  0.001  -0.204
    -200  0  0.001  -0.210
    0  -50  -0.020  -0.172
    -50  -50  -0.019  -0.186
    -100  -50  -0.017  -0.196
    -150  -50  -0.016  -0.204
    -200  -50  -0.015  -0.210
    0.0  -100.0  -0.042  -0.171
    -50.0  -100.0  -0.039  -0.185
    -100.0  -100.0  -0.036  -0.195
    -150.0  -100.0  -0.034  -0.203
    -200.0  -100.0  -0.032  -0.209
    0.0  -150.0  -0.064  -0.168
    -50.0  -150.0  -0.060  -0.182
    -100.0  -150.0  -0.056  -0.192
    -150.0  -150.0  -0.052  -0.200
    -200.0  -150.0  -0.049  -0.206
    0.0  -200.0  -0.085  -0.164
    -50.0  -200.0  -0.079  -0.178
    -100.0  -200.0  -0.074  -0.188
    -150.0  -200.0  -0.069  -0.196
    -200.0  -200.0  -0.065  -0.203];

IdMtx = reshape(M(:,1), 5, []);
IqMtx = reshape(M(:,2), 5, []);
FdMtx = reshape(M(:,3), 5, []);
FqMtx = reshape(M(:,4), 5, []);

figure(1)
surf(IdMtx, IqMtx, FdMtx)
grid on
xlabel('Id')
ylabel('Iq')
zlabel('Fd')

figure(2)
surf(IdMtx, IqMtx, FqMtx)
grid on
xlabel('Id')
ylabel('Iq')
zlabel('Fq')

Use the griddata (link) function to interpolate to a finer mesh. I would not extrapolate beyond the limits of your data, because you have no idea what your data are outside those limits.

IdIq = linspace(min(IdMtx(:)), max(IdMtx(:)), 250);             % Create Interpolation Vector (250 elements)
[Idi,Iqi] = meshgrid(IdIq);                                     % Create Interpolation Matrices

Fdi = griddata(IdMtx, IqMtx, FdMtx, Idi, Iqi);                  % Interpolate ‘Fd’
Fqi = griddata(IdMtx, IqMtx, FqMtx, Idi, Iqi);                  % Interpolate ‘Fq’

figure(3)
mesh(Idi, Iqi, Fdi)
grid on
xlabel('Id')
ylabel('Iq')
zlabel('Fd')

figure(4)
mesh(Idi, Iqi, Fqi)
grid on
xlabel('Id')
ylabel('Iq')
zlabel('Fq')

I use the default 'linear' interpolation method here, because it seems appropriate to these surfaces.

Experiment to get the result you want.

[Solmaz Kahourzade]

Dear Star Strider,

Thank you so much. It is exactly what I needed.

[Star Strider]

My pleasure.

If my Answer helped you solve your problem, please Accept it!

Answer 2

[KSSV]

A = [0  0  0.001  -0.172
-50.0  0  0.001  -0.186
-100  0  0.001  -0.196
-150  0  0.001  -0.204
-200  0  0.001  -0.210
0  -50  -0.020  -0.172
-50  -50  -0.019  -0.186
-100  -50  -0.017  -0.196
-150  -50  -0.016  -0.204
-200  -50  -0.015  -0.210
0.0  -100.0  -0.042  -0.171
-50.0  -100.0  -0.039  -0.185
-100.0  -100.0  -0.036  -0.195
-150.0  -100.0  -0.034  -0.203
-200.0  -100.0  -0.032  -0.209
0.0  -150.0  -0.064  -0.168
-50.0  -150.0  -0.060  -0.182
-100.0  -150.0  -0.056  -0.192
-150.0  -150.0  -0.052  -0.200
-200.0  -150.0  -0.049  -0.206
0.0  -200.0  -0.085  -0.164
-50.0  -200.0  -0.079  -0.178
-100.0  -200.0  -0.074  -0.188
-150.0  -200.0  -0.069  -0.196
-200.0  -200.0  -0.065  -0.203] ;

Id = A(:,1) ; Iq = A(:,2) ; Fd = A(:,3) ;Fq = A(:,4) ;
% Do interpolation 
Id_vector = linspace(-200,0,128);   
Iq_vector = linspace(-200,0,128);
[ Idi , Iqi ] = meshgrid(Id_vector,Iq_vector);

F1 = scatteredInterpolant(Id,Iq,Fd) ;
Fdi = F1(Idi,Iqi) ;      

F2 = scatteredInterpolant(Id,Iq,Fq) ;
Fqi = F2(Idi,Iqi) ;