UsegriddedInterpolantto interpolate a 1-D data set.

Create a vector of scattered sample pointsv。The points are sampled at random 1-D locations between 0 and 20.

x = sort(20*rand(100,1)); v = besselj(0,x);

Create a gridded interpolant object for the data. By default,griddedInterpolant用途the'linear'interpolation method.

F = griddedInterpolant(x,v)

F = griddedInterpolant with properties: GridVectors: {[100x1 double]} Values: [100x1 double] Method: 'linear' ExtrapolationMethod: 'linear'

Query the interpolantFat 500 uniformly spaced points between 0 and 20. Plot the interpolated results(xq,vq)on top of the original data(x,v)。

xq = linspace(0,20,500); vq = F(xq); plot(x,v,'ro') holdonplot(xq,vq,'.') legend('Sample Points',的强度rpolated Values')

Interpolate 3-D data using two methods to specify the query points.

Create and plot a 3-D data set representing the functionevaluated at a set of gridded sample points in the range [-5,5].

[x,y] = ndgrid(-5:0.8:5); z = sin(x.^2 + y.^2) ./ (x.^2 + y.^2); surf(x,y,z)

Create a gridded interpolant object for the data.

F = griddedInterpolant(x,y,z);

Use a finer mesh to query the interpolant and improve the resolution.

[xq,yq] = ndgrid(-5:0.1:5); vq = F(xq,yq); surf(xq,yq,vq)

In cases where there are a lot of sample points or query points, and where memory usage becomes a concern, you can usegrid vectorsto improve memory usage.

Alternatively, execute the previous commands using grid vectors.

x = -5:0.8:5; y = x'; z = sin(x.^2 + y.^2) ./ (x.^2 + y.^2); F = griddedInterpolant({x,y},z); xq = -5:0.1:5; yq = xq'; vq = F({xq,yq}); surf(xq,yq,vq)

Use the default grid to perform a quick interpolation on a set of sample points. The default grid uses unit-spaced points, so this interpolation is useful when the exactxyspacing between the sample points is not important.

Create a matrix of sample function values and plot them against the default grid.

x = (1:0.3:5)'; y = x'; V = cos(x) .* sin(y); n = length(x); surf(1:n,1:n,V)

Interpolate the data using the default grid.

F = griddedInterpolant(V)

F = griddedInterpolant with properties: GridVectors: {[1 2 3 4 5 6 7 8 9 10 11 12 13 14] [1x14 double]} Values: [14x14 double] Method: 'linear' ExtrapolationMethod: 'linear'

Query the interpolant and plot the results.

[xq,yq] = ndgrid(1:0.2:n); Vq = F(xq,yq); surf(xq',yq',Vq)

Interpolate coarsely sampled data using a full grid with spacing of0.5。

Define the sample points as a full grid with range [1, 10] in both dimensions.

[X,Y] = ndgrid(1:10,1:10);

Sampleat the grid points.

V = X.^2 + Y.^2;

Create the interpolant, specifying cubic interpolation.

F = griddedInterpolant(X,Y,V,'cubic');

Define a full grid of query points with0.5spacing and evaluate the interpolant at those points. Then plot the result.

[Xq,Yq] = ndgrid(1:0.5:10,1:0.5:10); Vq = F(Xq,Yq); mesh(Xq,Yq,Vq);

Compare results of querying the interpolant outside the domain ofFusing the'pchip'and'nearest'extrapolation methods.

Create the interpolant, specifying'pchip'as the interpolation method and'nearest'as the extrapolation method.

x = [1 2 3 4 5]; v = [12 16 31 10 6]; F = griddedInterpolant(x,v,'pchip','nearest')

F = griddedInterpolant with properties: GridVectors: {[1 2 3 4 5]} Values: [12 16 31 10 6] Method: 'pchip' ExtrapolationMethod: 'nearest'

Query the interpolant, and include points outside the domain ofF。

xq = 0:0.1:6; vq = F(xq); figure plot(x,v,'o',xq,vq,'-b'); legend ('v','vq')

Query the interpolant at the same points again, this time using the pchip extrapolation method.

F.ExtrapolationMethod ='pchip'; figure vq = F(xq); plot(x,v,'o',xq,vq,'-b'); legend ('v','vq')