I have a vector field with discrete values and I want to interpolate these values to create a differentiable vector field.

I have matrices which give the vector values of the velocity - $vx, vy, vz$. They have dimensions of $(5,5,5)$. I put these together to get a vector field which looks like $(vx,vy,vz)$ with dimensions $(5,5,5,3)$ i.e. each coordinate has a vector at it.

But the interpolation function on this matrix doesn't seem to work.

interpolation = ListInterpolation[together] 

No errors here, but when I plot it I get a blank graph, whereas from the "raw" data I get what I would expect.

All Code:

vx = {{{1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}}, {{1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}}, {{1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}}, {{1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}}, {{1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}}}; vy = {{{3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}}, {{3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}}, {{3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}}, {{3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}}, {{3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}, {3, 3, 3, 3, 3}}}; vz = {{{2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}}, {{2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}}, {{2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}}, {{2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}}, {{2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}, {2, 2, 2, 2, 2}}}; together = ArrayReshape[Transpose[Flatten /@ {vx, vy, vz}], {5, 5, 5, 3}] interpolation = ListInterpolation[together] ListVectorPlot3D[together] VectorPlot3D[interpolation[x, y, z], {x, 1, 5}, {y, 1, 5}, {z, 1, 5}] 

From ListVectorPlot:

From VectorPlot3D (interpolation):