Hello Tim, good morning In this case, where we have discrete points (P_NOM = [1.5, 2.2, 3.7, 5.6, 7.5, 11.2, 14.9] and ETA = [93, 94, 94, 95, 95, 95.5, 95.5 ]), as would be "A" for P_NOM(2.8) value ? Since function f (x) is more intuitive.
Em quarta-feira, 9 de março de 2016 23:22:54 UTC-3, Tim Holy escreveu: > > A is the array of values you want to interpolate. x are the positions. > Effectively, `A = [f(xx) for xx in x]` assuming you want to interpolate > the > function `f`. > > --Tim > > On Wednesday, March 09, 2016 02:25:24 PM jmarcell...@ufpi.edu.br > <javascript:> wrote: > > I did not understand how to use the "A". "A" is a vector tuple ...? > > > > Em domingo, 28 de fevereiro de 2016 18:32:23 UTC-3, Tomas Lycken > escreveu: > > > Gridded here is the *interpolation scheme*, as opposed to (implicitly > > > uniform) BSpline interpolation; it’s simply the way Interpolations.jl > > > lets you specify which algorithm you want to use. Compare the > following > > > incantations: > > > > > > itp = interpolate(A, BSpline(Linear()), OnGrid()) # linear b-spline > > > interpolation; x is implicitly 1:length(A) itp = interpolate((x,), A, > > > Gridded(Linear())) # linear, "gridded" interpolation; x can be > irregular > > > itp = interpolate(A, BSpline(Cubic(Flat())), OnCell()) # cubic > b-spline > > > with free boundary condition > > > > > > That is; you give the data to be interpolated (A and, where > applicable, x) > > > as well as one or more arguments specifying the algortihm you want to > use > > > (for details on OnGrid/OnCell, see the readme). Gridded is what just > > > we’ve called the family of algorithms that support irregular grids. > > > > > > This is all documented in the readme, but documentation is not just > about > > > putting the information in writing - it’s also about putting it in the > > > correct place, where it seems obvious to look for it. If you have > > > suggestions on how this information can be made easier to find and > digest, > > > please file an issue or PR. All feedback is most welcome! :) > > > > > > // T > > > > > > On Sunday, February 28, 2016 at 7:37:42 PM UTC+1, Uwe Fechner wrote: > > > > > > Hello, > > > > > >> thanks for your explanations. > > >> > > >> Nevertheless I like the syntax of the package Dierckx much more. > > >> The expression Gridded(Linear()) is very confusing for me. What is > > >> gridded, > > >> in this example? > > >> > > >> Furthermore the Readme file of Interpolations is missing the > information, > > >> how > > >> to use it for the given problem. > > >> > > >> Best regards: > > >> > > >> Uwe > > >> > > >> On Saturday, February 27, 2016 at 4:57:07 PM UTC+1, Matt Bauman > wrote: > > >>> Interpolations is very similar, but it currently only supports > linear > > >>> and nearest-neighbor schemes for gridded interpolations: > > >>> > > >>> using Interpolations > > >>> > > >>> itp = interpolate((P_NOM,), ETA, Gridded(Linear())) # You pass the > > >>> x-values as a tuple, since this generalizes to multi-dimensional > > >>> coordinates println(itp[3.5]) > > >>> > > >>> x = linspace(1.5, 14.9, 1024) > > >>> y = itp[x] > > >>> > > >>> plot(x,y) > > >>> > > >>> On Saturday, February 27, 2016 at 10:10:28 AM UTC-5, Uwe Fechner > wrote: > > >>>> Thanks. The following code works: > > >>>> > > >>>> using Dierckx > > >>>> > > >>>> P_NOM = [1.5, 2.2, 3.7, 5.6, 7.5, 11.2, 14.9] > > >>>> ETA = [93., 94., 94., 95., 95., 95.5, 95.5] > > >>>> calc_eta = Spline1D(P_NOM, ETA, k=1) > > >>>> > > >>>> println(calc_eta(3.5)) > > >>>> > > >>>> Nevertheless I would be interested how to do that with > > >>>> Interpolations.jl. Sometimes you don't have Fortran available. > > >>>> > > >>>> Best regards: > > >>>> > > >>>> Uwe > > >>>> > > >>>> On Saturday, February 27, 2016 at 3:58:11 PM UTC+1, Yichao Yu > wrote: > > >>>>> On Sat, Feb 27, 2016 at 9:40 AM, Uwe Fechner <uwe.fec...@gmail.com> > > > >>>>> > > >>>>> wrote: > > >>>>>> Hello, > > >>>>>> > > >>>>>> I don't think, that this works on a non-uniform grid. The array > xg is > > >>>>>> evenly spaced, and it > > >>>>>> is NOT passed to the function InterpGrid. > > >>>>> > > >>>>> I've recently tried Dierckx which support non-uniform > interpolation. I > > >>>>> only need very basic functions so I don't know if it has all the > > >>>>> flexibility you need but it's probably worth a look if you > haven't. > > >>>>> > > >>>>>> Uwe > > >>>>>> > > >>>>>> > > >>>>>> On Saturday, February 27, 2016 at 3:33:06 PM UTC+1, Cedric > St-Jean > > >>>>>> > > >>>>>> wrote: > > >>>>>>> Hi Uwe, > > >>>>>>> > > >>>>>>> Have you tried Grid.jl? I haven't tried it, but this example > looks > > >>>>>>> like it might work with a non-uniform grid. > > >>>>>>> > > >>>>>>> # Let's define a quadratic function in one dimension, and > evaluate > > >>>>>>> it on an evenly-spaced grid of 5 points: c = 2.3 # center > > >>>>>>> a = 8.1 # quadratic coefficient > > >>>>>>> o = 1.6 # vertical offset > > >>>>>>> qfunc = x -> a*(x-c).^2 + o > > >>>>>>> xg = Float64[1:5] > > >>>>>>> y = qfunc(xg) > > >>>>>>> yi = InterpGrid(y, BCnil, InterpQuadratic) > > >>>>>>> > > >>>>>>> > > >>>>>>> > > >>>>>>> > > >>>>>>> On Saturday, February 27, 2016 at 9:21:53 AM UTC-5, Uwe Fechner > > >>>>>>> > > >>>>>>> wrote: > > >>>>>>>> Hello, > > >>>>>>>> > > >>>>>>>> I am trying to port the following function from python to > julia: > > >>>>>>>> > > >>>>>>>> # -*- coding: utf-8 -*- > > >>>>>>>> from scipy.interpolate import InterpolatedUnivariateSpline > > >>>>>>>> import numpy as np > > >>>>>>>> from pylab import plot > > >>>>>>>> > > >>>>>>>> P_NOM = [1.5, 2.2, 3.7, 5.6, 7.5, 11.2, 14.9] > > >>>>>>>> ETA = [93., 94., 94., 95., 95., 95.5, 95.5] > > >>>>>>>> > > >>>>>>>> calc_eta = InterpolatedUnivariateSpline(P_NOM, ETA, k=1) > > >>>>>>>> > > >>>>>>>> # plotting code, only for testing > > >>>>>>>> > > >>>>>>>> if __name__ == "__main__": > > >>>>>>>> X = np.linspace(1.5, 14.9, 1024, endpoint=True) > > >>>>>>>> ETA = [] > > >>>>>>>> > > >>>>>>>> for alpha in X: > > >>>>>>>> eta = calc_eta(alpha) > > >>>>>>>> ETA.append(eta) > > >>>>>>>> > > >>>>>>>> plot(X, ETA) > > >>>>>>>> > > >>>>>>>> The resulting plot is shown at the end of this posting. > > >>>>>>>> > > >>>>>>>> How can I port this to Julia? > > >>>>>>>> > > >>>>>>>> I am trying to use the package "Interpolations.jl", but I do > not > > >>>>>>>> see any > > >>>>>>>> example, that shows the interpolation on a non-uniform grid. > > >>>>>>>> > > >>>>>>>> For now I need only linear interpolation, but I want to use > > >>>>>>>> B-Splines > > >>>>>>>> later. > > >>>>>>>> > > >>>>>>>> Any hint appreciated! > > >>>>>>>> > > >>>>>>>> Uwe Fechner > > >>>>>>>> > > >>>>>>>> > > >>>>>>>> > > >>>>>>>> < > https://lh3.googleusercontent.com/-8OofwCQWohg/VtGwKR-1BOI/AAAAAAA > > >>>>>>>> AAQI/UTLksCCMIPo/s1600/LinearInterpolation.png>>>>>> > > >>>>> > >
