I want to draw pathline for two particle for a 2d problem

I have the results for the space and velocity variables xn, yn, un, vn all in 50*300*2085 dimensions. My space points xn,yn are changing with time along with un, vn. I tried to write the following

M = size(xn,1); N = size(xn,2); Nt = size(xn,3);
dt = 5*0.005;   % need to be same as the data stored
% target point index
X0 = [0 0 ]; Y0 = [1.5 -1.5];
plot(X0,Y0,'r*','LineWidth',1); hold on;
for i = 1 : length(X0)
    X(i) = X0(i); Y(i) = Y0(i);
    for n = 1 : Nt
        x = xn(:,:,n); y = yn(:,:,n);
        u = un(:,:,n); v = vn(:,:,n);
        F = griddedInterpolant(x,y,u,"spline","spline");
        U = F(X(i),Y(i));
        F1 = griddedInterpolant(x,y,v,'spline','spline');
        V = F1(X(i),Y(i));
        
        X(i) = X(i) + dt*U; Y(i) = Y(i) + dt*V;    
        XX(i,n) = X(i); YY(i,n) = Y(i);
    end
end
plot(XX(i,:),YY(i,:),'b','LineWidth',1.2); hold on;

But end up with the error

'Error using griddedInterpolant

Grid arrays must have NDGRID structure.'

Can you please help me with this?

Answer 1

[Walter Roberson]

When you use griddedInterpolant, then your x must have all of its columns the same, and the row values must be sorted. Your y must have all of its rows the same and the column values must be sorted.

[X,Y] = ndgrid(1:3, 4:7)

X = 3×4

1 1 1 1 2 2 2 2 3 3 3 3

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Y = 3×4

4 5 6 7 4 5 6 7 4 5 6 7

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Here, X and Y are valid for griddedInterpolant(X,Y,V)

X(2,2) = 2.01; X(2,3) = 2.02; X(2,4) = 2.03

X = 3×4

1.0000 1.0000 1.0000 1.0000 2.0000 2.0100 2.0200 2.0300 3.0000 3.0000 3.0000 3.0000

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This X is not valid for griddedInterpolant because the columns are not all the same as each other.

There is a different major sorting order,

[X2, Y2] = meshgrid(1:3, 4:7)

X2 = 4×3

1 2 3 1 2 3 1 2 3 1 2 3

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Y2 = 4×3

4 4 4 5 5 5 6 6 6 7 7 7

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For this arrangement, all of the rows of X2 are the same as each other and the columns are sorted.

These two orders are connected by

[Y3,X3] = meshgrid(4:7, 1:3);
X3, Y3

X3 = 3×4

1 1 1 1 2 2 2 2 3 3 3 3

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Y3 = 3×4

4 5 6 7 4 5 6 7 4 5 6 7

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Anyhow, this "meshgrid" arrangement of data is not valid for griddedInterpolant.

Generally speaking, if you have meshgrid data, then you can

F = griddedInterpolant(x.',y.',u.',"spline","spline");

[Subhankar]

Thank you sir for your valuable comment. I understand the things now. Since my points are not in order like meshgrid or ndgrid, I am getting this error. So, to get ndgrid form, may be, I can convert the datas like the following:

for j = 1: N
    for i = 1 : M
        t = i+(j-1)*M ;
        xy(t,1) = xn(i,j,n); xy(t,2) = yn(i,j,n);
        u(t,1) = un(i,j,n);   v(t,1) = vn(i,j,n);
    end
end

Then, I think the following will work

F = griddedInterpolant(xy(:,1),xy(:,2),u,"spline","spline");

[Walter Roberson]

F = scatteredInterpolant(xy, u, "linear", "linear");

would be more natural. On the other hand scatteredInterpolant does not handle spline.

[Subhankar]

working now with scatterdataInterpolant. Thank you