The function scatteredInterpolant in MATLAB is used to perform interpolation on a scattered dataset that cannot be gridded without introducing significant errors. From the error message you received, it seems there is an issue with the dimensions of the input arrays.
When you call scatteredInterpolant, the inputs must satisfy the following conditions:
- The nodes input must be an M-by-N matrix, where M is the number of points and N is the number of dimensions (in your case, N=2 for x and y coordinates).
- The v input must be an M-by-P matrix where M is the number of points (which should match the number of nodes) and P is the number of values you want to interpolate at each point (in your case, P=2 for ic_sol_1 and ic_sol_2).
Your v should be a two-column matrix where each column corresponds to one of the functions you want to interpolate (ic_sol_1 and ic_sol_2). The columns represent different value sets, and each value set should be a column vector. It seems you've structured v correctly based on the code you provided.
The error suggests that MATLAB is not interpreting v as an M-by-2 matrix. This could be due to a few reasons:
- The dimensions of nodes and v might not match correctly.
- The v array might not be properly formatted as a column vector for each variable you are interpolating.
If you are sure that ic_sol_1 and ic_sol_2 are column vectors of the same length as nodes, your code should work. Let's double-check your variables' dimensions to ensure they are in the correct format:
If all dimensions are correct, the following code should work:
v = [ic_sol_1, ic_sol_2];
F_ic = scatteredInterpolant(nodes, v);
Regarding interp2, this function is not suitable for scattered data directly as it requires data to be on a regular grid. If you have scattered data and you want to use interp2, you would first need to create a grid (using `grid
data` for example) and then interpolate your scattered data onto this grid. The problem with this approach is that it can introduce significant errors if your data is not well-suited to a grid due to irregular spacing.
If you want to use interp2 and you need to create a grid from scattered data, you could use griddata to interpolate onto a regular grid:
[xq, yq] = meshgrid(linspace(min(nodes(:,1)), max(nodes(:,1)), numPoints), ...
linspace(min(nodes(:,2)), max(nodes(:,2)), numPoints));
vq1 = griddata(nodes(:,1), nodes(:,2), ic_sol_1, xq, yq, 'linear');
vq2 = griddata(nodes(:,1), nodes(:,2), ic_sol_2, xq, yq, 'linear');
This gives you vq1 and vq2, which are the interpolated values on the grid, and you can now use interp2 with these gridded data. However, if your original data is not too scattered or has some structure to it, you may be able to form a grid without much error and then use interp2.
But if you can resolve the dimensionality issue with scatteredInterpolant, it would be a better choice since it's designed for scattered data and you won't need to generate an intermediate grid.
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