![]() ![]() W_temp2 = Array ( Float64, Nalal, Naa ) Xx = xx + ( xmax - xx )/(( Nxx - i + 1 )^ spacing )į_util ( c ) = c. Consider the following minimal working example preserving the irregular grid of the original problem which highlights the point I think (the only action is in the loop, the other stuff is just generating the irregular grid): The interpolation itself was much faster now than MATLAB's interp1 but somewhere on the way that advantage was lost. #Gridded interpolation matlab code#The Julia code was still 3 times slower which left me puzzled again. Equipped with that, I went back to my original problem and reran it. He translated the interpolation method into C and made it such that it uses multiple threads (I am working with 12 threads). So I asked a friend of mine who knows a little bit of C and he was so kind to help me out. Nobody knows what exactly the interp1 is doing. The bottom line was that the Dierckx package apparently calls some Fortran code which seems to pretty old (and slow, and doesn't use multiple cores. The post is messy and you don't need to read through it I think. It gave exactly the same result but it was about 50 times slower which puzzled me. I was translating my MATLAB code into Julia and used the Dierckx package in Julia to do the interpolation (there weren't some many alternatives that did spline on an irregular grid as far as I recall). Gridding is the process of converting irregularly spaced data to a regular grid (gridded data).My original problem is a dynammic programming problem in which I need to interpolate the value function on an irregular grid using a cubic spline method. Radial basis function ( Polyharmonic splines are a special case of radial basis functions with low degree polynomial terms).Polyharmonic spline (the thin-plate-spline is a special case of a polyharmonic spline).tetrahedron) interpolation (see barycentric coordinate system) Triangulated irregular network-based linear interpolation (a type of piecewise linear function).Triangulated irregular network-based natural neighbor.They should all work on a regular grid, typically reducing to another known method. Schemes defined for scattered data on an irregular grid are more general. The cubic Hermite spline article will remind you that C I N T x ( f − 1, f 0, f 1, f 2 ) = b ( x ) ⋅ ( f − 1 f 0 f 1 f 2 ) -dimensional summation. Tensor product splines for N dimensions Ĭatmull-Rom splines can be easily generalized to any number of dimensions. See also Padua points, for polynomial interpolation in two variables. The colours represent the interpolated values. Three of the methods applied on the same dataset, from 25 values located at the black dots. n-cubic interpolation (see bi- and tricubic interpolation)īitmap resampling is the application of 2D multivariate interpolation in image processing.n-linear interpolation (see bi- and trilinear interpolation and multilinear polynomial).Their heights above the ground correspond to their values.įor function values known on a regular grid (having predetermined, not necessarily uniform, spacing), the following methods are available. Comparison of some 1- and 2-dimensional interpolations.īlack and red/ yellow/ green/ blue dots correspond to the interpolated point and neighbouring samples, respectively. ![]()
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