Questions on the interpolation functions in Mathematica (Interpolation[], ListInterpolation[], FunctionInterpolation[], InterpolatingPolynomial[], etc.)

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11
votes
2answers
185 views

Arbitrary precision spline interpolation

Current implementation of Interpolation does not allow arbitrary precision spline interpolation. Yu-Sung Chang say here that "it is not hard to implement it ...
1
vote
1answer
131 views

Is linear interpolation applicable here

From my understanding about Linear Interpolation especially of that of Newton's Divided Difference Polynomial, we could get the value of F(x) from the given set of ...
2
votes
0answers
96 views

Slow integration of interpolating function

I have a large file with irregularly spaced data in the format: ...
5
votes
1answer
81 views
1
vote
1answer
146 views

Interpolate a curve in 3D

I have a sequence $\{(x_k, y_k, z_k)\}_{k=1}^n \subset \mathbb{R}^3$, all points along a path represented by the function $\gamma \colon \mathbb{R} \to \mathbb{R}^3$, which maps the distance along the ...
4
votes
2answers
369 views

Finding a 3d curve from torsion and curvature with NDSolve

I'm trying to use the Frenet–Serret formulas to find the curve that matches the torsion and curvature I specify numerically with an InterpolatingFunction. The ...
1
vote
1answer
173 views

Interpolation of a table with 4 parameters

I have a huge data file which I need to do some analysis on it. The file is built in this way that for each 4 variables, there is a value of the function: ...
1
vote
1answer
135 views

Finding Minimum of a list after interpolation

I have a set of lists called Er[l], where l is from 1 to 13. I want to find the minimum point in the plot in these lists after interpolation by spline method. I need the values and the points on the ...
8
votes
2answers
346 views

How to make use of an interpolating function outside of Mathematica? [duplicate]

I'm currently working on a project where I have to solve some partial differential equations. Initially, I made some approximations so that an analytic solution could be obtained, and my ...
2
votes
2answers
120 views

Interpolating a list with exclusion [closed]

I have a list, data, where the elements data[[i]] range over i from ...
1
vote
1answer
119 views

Partitioning a numerical integral: need to integrate spectra

I am trying to integrate a spectrum I obtained from a fourier transform infrared spectroscopy experiment, in order to determine the global warming potential of green house gases. In order to do this, ...
0
votes
1answer
131 views

Interpolation problem on the list

I have a List of Latitude, Longitude and Measurement. a = {{{93, 104}, 290}, {{94, 103}, 292}, {{95, 105}, 291}, {{97, 109}, 294}, {{97, 102}, 295}}; And, I ...
2
votes
1answer
288 views

Find fit for complex function for smooth derivatives

I need to fit my data dropbox of the form {x,y} because I need the fit function for further derivative calculation. My derivative curve should be smooth. I tried ...
2
votes
1answer
319 views

How to make a 3D-Plot from 2D-interpolated data

I have data of the form {x,y} for different concentrations. Therefore I added the concentration as z, resulting now in ...
4
votes
1answer
229 views

ListPlot3D of a set of points in a non-convex region

I would like to plot a set of points in the same style as ListPlot3D does, but only in a non-convex region that I can specify (e.g. using a ...
1
vote
1answer
246 views

Cubic Splines Functions

I have this set of three data points and want the natural cubic spline functions for them: dat = {{-.0247500, .5}, {.3349375, -.25}, {1.101000, 0}}; I tried: ...
3
votes
2answers
214 views

Interpolating data with a step

Suppose I have some data with a step in it: data = {{1, 1}, {2, 2}, {3, 3}, {3, 4}, {4, 5}, {5, 6}}; Interpolation will complain about this and not give you an ...
4
votes
3answers
186 views

Variable partitioning of the data in the form of “list of lists”

I am looking for a way for variable partitioning of the data in the form of a "list of lists" for interpolating the imported data from excel. The data looks like: ...
2
votes
1answer
146 views

NDSolve much slower when using InterpolatingFunctions inside

I am solving an ODE system with Mathematica. Let's say the system is of the form (to simplify). ...
2
votes
0answers
421 views

Interpolate throughout a 3d data list without extrapolation

I have a 3D list of data for which I'd like to plot an interpolated surface. There are several ways to achieve this, but none I cannot find a method which ONLY plots the ENTIRE interpolated surface ...
5
votes
3answers
244 views

Interpolation steeply drops to 0 beyond data

I use Interpolation on unstructured 3-D-Data to visualize different regions via RegionPlot. A problem I run into is that the interpolating function steeply drops to zero beyond my set of data. This is ...
4
votes
1answer
226 views

Create ParametricFunction object without ParametricNDSolve

Documentation of v9 states that ParametricFunction is generated by ParametricNDSolve and ...
1
vote
1answer
337 views

Interpolation Problem

I have the following list: ...
0
votes
1answer
327 views

Can graph interpolating function, but not use it. Any thoughts?

When solving a system of differential equations numerically, I get two interpolating functions. I can graph both of these, but when I try to evaluate either of the functions at a point, it just spits ...
0
votes
2answers
172 views

Interpolating a ParametricFunction

Original domain of my independent variable t is 0 to 10 nanometers, but in Mathematica (as in most numerical software), it's good idea to solve differential ...
1
vote
1answer
130 views

Linear interpolation between defined anchorpoints in an array (where anchorpoints are set each time we see a new element)

This question is an update and a correction my earlier question: Linear interpolation of a list between periodic anchorpoints (which was nicely answered). Imagine I have a list of the form: ...
3
votes
2answers
91 views

Linear interpolation of a list between periodic anchorpoints

I have a list of the form: list = {1,1,1,2,2,2,3,3,3,4,4,4,7,7,7,19,19,19}; Where we can see that there are an ordered set of integer values that repeat ...
25
votes
4answers
305 views

How can the behavior of InterpolationOrder->0 be controlled?

In ListPlot and Interpolation, the option InterpolationOrder->0 uses two different ...
0
votes
1answer
178 views

Transforming Sin into Abs[Sin] dynamically

Is it possible to interpolate a polynomial that approximates Sin, and then be able to manipulate the polynomial or a sample of its points to make sections of the ...
2
votes
0answers
31 views

Plotting list-valued interpolating function [duplicate]

I have an interpolation function which returns a list, e.g.: f=Interpolation[{{1,{1,2,3}},{2,{4,5,6}}}]; When I try to plot it, I get single-colored curves. ...
-2
votes
1answer
296 views

Interpolating Function inside of NDSolve

I have a problem and it seems to be connected to an Interpolating function inside of an NDSolve command. The resistivity[x] ...
2
votes
1answer
193 views

Forcing Interpolation to be smooth at its boundaries

I'm looking at a piecewise function of two lines, which has a kink, such as: ...
1
vote
2answers
158 views

How to know form of plotted Bezier function

Simple scenario is to see the Bezier function, but how to know which polynomial approximate it? ...
16
votes
4answers
766 views

Generating an “average curve” from a dense set of “semicontinuous curves” which clear trends

This question is related to a previous one of mine: Partitioning a superset of coordinates into subsets that generate continuous curves, where the challenge was to partition a data set into two ...
9
votes
2answers
213 views

Partitioning a superset of coordinates into subsets that generate continuous curves

Consider the data set corresponding to recorded trajectories for a particle: ...
3
votes
2answers
169 views

Interpolating a sparse list of two-dimensional coordinates

I've run into a problem where I have an ordered array of sets of coordinates, for example: ...
1
vote
1answer
66 views

List-manipulation Interpolation

For example, I have the following list: AA={{0, 20000.}, {26.6, 19950.}, {53.2, 19950.}, {79.8, 19950.}, {97.1198, 18644.1}, {102.681, 16452.3}} Another ...
2
votes
2answers
133 views

Graph two interpolations together

I have created two functions, inter1=Interpolation[points1] and inter2=Interpolation[points2]. This creates two functions, I ...
24
votes
1answer
430 views

What's inside InterpolatingFunction[{{1., 4.}}, <>]?

I'm curious what's inside the InterpolationFunction object? For example: ...
7
votes
1answer
258 views

StreamPlot with interpolating functions

While working my way through the Wolfram Blog post on simulating fluid flow I started playing with StreamPlot because I preferred quick and ugly visualizations over ...
0
votes
1answer
364 views

How does ListPlot3D interpolate data?

I have data of the form {{x1, y1, f(x1, y1}, {x2, y2, f(x2, y2)}, ...}. I need to interpolate the data to get an interpolated ...
1
vote
0answers
231 views

Change of coordinates for an InterpolatingFunction

This is a toy example of the question I have but I think it illustrates the point. I have a function y[x] which is an interpolating function. Let's define it ...
2
votes
1answer
149 views

Coarse-graining and/or sorting of a list of arbitrary triades {x,y,z} in the (x,y) plane [duplicate]

In general my question is related to an approach to make an interpolation of a data which is not on a regular mesh. Another aspect of this question has already been discussed after my question ...
4
votes
1answer
228 views

ListDensityPlot performance when scaling axes

I need to visualize 3D data having 200*200 data points. ListDensityPlot is a good candidate, but it seems to have strange performance issues. I created a small ...
1
vote
2answers
396 views

Interpolating and plotting a surface for a sparse set of 3d data points

I have a set of $(x,y,z)$ coordinates which sparsely cover a surface, e.g.: data = {{51, 15, 0.1}, {300, 11, 0.99}, {140, 22, 0.123}, {54, 12, 0.66}, ...}; What ...
4
votes
1answer
287 views

InverseFunction on an Interpolating Function is misbehaving

I am getting strange behavior when I try to calculate the inverse of an interpolating function for two similar data sets. My data sets are: ...
3
votes
1answer
392 views

White spots in ListDensityPlot

I have a problem with ListDensityPlot. I have some data on an irregular grid. I try to plot them with ...
4
votes
2answers
290 views

How to make BSplineFunction pass each data point and naturally smooth?

(Old package, works good) ...
6
votes
2answers
1k views

Finding y given x from an interpolating function

I would like to put a dot on the point of a curve that has a specific y value but I don't know the x value. A simple example of my code is ...
1
vote
1answer
114 views

Find limit of Interpolated function

I have an interpolated function f = Interpolation[data] I would like to calculate limits such as ...