On Monday, March 23, 2015 at 10:34:37 PM UTC+1, Tim Holy wrote: > > On Monday, March 23, 2015 02:22:25 PM Patrick Kofod Mogensen wrote: > > I will look into that, thanks. I don't *really* care if I have three or > two > > methods (or just include the one I need and have one), >
Excellent. FYI Matlab has also moved to doing interpolation in two stages, > see > their griddedInterpolant class. I think it's a much cleaner separation > between > "here are the inputs" and "here is where I'd like to evaluate it." > > Nice to know. I do agree, and I really like how yi[xi] works in Interpolations.jl, but for my use, a given pair (x,y) is only used to produce yi once, so I thought the two-step approach was over-kill to implement, but if I had known Interpolations.jl had a version I could use, I would have probably gone with that. I use chebyshev polynomials for interpolation quite a lot, and I have a multi-step approach there, but in that application I define a grid once, and do interpolation based on that repeatedly. > > but I would much > > prefer to use a library (Interpolations.jl). I just wasn't able to dig > out > > the non-uniform-method, and, frankly, the abstraction level of that > library > > is scary to a junior technical programmer as myself :) > > Understood. 1d is nice because you don't need all the metaprogramming > mumbo > jumbo; however, even there it can be convenient for supporting many > different > orders of interpolation, boundary conditions, etc. > > --Tim > > I agree; totally. The problem here is totally on my side, as I simply havn't spent the time it takes to understand it. > > > > Best, > > Patrick > > > > On Monday, March 23, 2015 at 12:31:11 PM UTC+1, Tim Holy wrote: > > > - Interpolations.jl currently only handles uniform grids, which is why > it > > > gets > > > a Range input. Grid.jl has an undocumented non-uniform interpolation > in > > > 1d. > > > > > > - You'd probably be interested in `searchsorted`. > > > > > > - Yes, you can simplify your interface down to 2 methods. Look at more > > > generic > > > functions like `similar,` `ind2sub`, etc. > > > > > > --Tim > > > > > > On Monday, March 23, 2015 02:46:37 AM Patrick Kofod Mogensen wrote: > > > > As a part of teaching a course in economics, I had to supply Matlab > code > > > > for solving a particular kind of problem. Many times, we have to > > > > > > evaluate a > > > > > > > function outside of the grid where we know the value, and we use > linear > > > > interpolation to approximate these values. > > > > > > > > I wanted to use Interpolations.jl, but it seems that everything has > to > > > > > > be > > > > > > > done based on x (grid where we know the function values) being a > range. > > > > > > It > > > > > > > may seem weird, but I do not know from the beginning what the x's > are > > > > > > going > > > > > > > to be, as the are calculated and changed throughout the algorithm. > > > > > > > > At some point in the algorithm, I have a matrix filled with x_i's > > > > > > (points > > > > > > > where I want to interpolate), and (x,y) which is the tuple of grids > > > > > > where I > > > > > > > know the function values and the function values themselves. My > question > > > > is, is there any way of simplifying the handling of the differences > > > > > > between > > > > > > > scalars, vector, and matrices? *(<- this is where my question is > hidden > > > > > > in > > > > > > > the wall of text)* Maybe it would be easier if there was a function > such > > > > > > as > > > > > > > histc to calculate loc (location aka what bin are we in). > > > > > > > > I probably also have to add, that it is on purpose that I treat < > first > > > > grid point and between the first and second grid point (and likewise > in > > > > > > the > > > > > > > upper end) the same. If we are outside of the grid, I want to use > the > > > > nearest gradient to extrapolate. > > > > > > > > > > > > function interp1 (x::Vector, y::Vector, xi::Float64) > > > > > > > > N = length(x) > > > > loc = zeros(m,n) > > > > place = 1 > > > > for i = 2:(N-1) > > > > > > > > place+= xi[j,k] >= x[i] > > > > > > > > end > > > > loc=place > > > > return y[loc]+(xi-x[loc]).*(y[loc+1]-y[loc])./(x[loc+1]-x[loc]) > > > > > > > > end > > > > > > > > function interp1 (x::Vector, y::Vector, xi::Matrix) > > > > > > > > m,n = size(xi) > > > > N = length(x) > > > > loc = zeros(m,n) > > > > for k = 1:n > > > > > > > > for j = 1:m > > > > > > > > place = 1 > > > > for i = 2:(N-1) > > > > > > > > place+= xi[j,k] >= x[i] > > > > > > > > end > > > > loc[j,k]=place > > > > > > > > end > > > > > > > > end > > > > return y[loc]+(xi-x[loc]).*(y[loc+1]-y[loc])./(x[loc+1]-x[loc]) > > > > > > > > end > > > > > > > > function interp1 (x::Vector, y::Vector, xi::Vector) > > > > > > > > n = length(xi) > > > > N = length(x) > > > > loc = zeros(n) > > > > for k = 1:n > > > > > > > > place = 1 > > > > for i = 2:(N-1) > > > > > > > > place+= xi[k] >= x[i] > > > > > > > > end > > > > loc[k]=place > > > > > > > > end > > > > return y[loc]+(xi-x[loc]).*(y[loc+1]-y[loc])./(x[loc+1]-x[loc]) > > > > > > > > end > >
