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

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28
votes
3answers
650 views

No warning when extrapolating with Plot

One of the most annoying "features" of Mathematica is that the Plot family does extrapolation on InterpolatingFunctions without ...
24
votes
2answers
3k views

How does Interpolation really work?

I'm looking for some explanation or advice, not help in solving something. Recently I finished my program and my supervisor said "Ok, now it's time for your first paper: write a scientific text about ...
22
votes
4answers
260 views

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

In ListPlot and Interpolation, the option InterpolationOrder->0 uses two different ...
21
votes
1answer
343 views

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

I'm curious what's inside the InterpolationFunction object? For example: ...
18
votes
2answers
1k views

Joining and interpolating data points

I wonder what is the best practice for interpolating curves? Usually I'm using BSplineCurve and adjusting SplineWeights so it ...
17
votes
4answers
930 views

How to integrate functions of linearly interpolated data?

At first, consider integration of pure InterpolatingFunction. Importing some data (works in v.9, for earlier versions one can use this link to download zipped ...
16
votes
5answers
555 views

Finding the intersection of a curve with an interpolation function

There are no issues trying to find the intersection points of two defined curves. ...
16
votes
4answers
662 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 ...
16
votes
1answer
367 views

How to fix broken InterpolatingFunction?

I have an InterpolatingFunction based on irregularly-gridded data, like this: ...
15
votes
2answers
850 views

Higher order periodic interpolation (curve fitting)

I have a list of points in 3D, and I want to get a smooth interpolation or curve fit (it is more for illustration) of these points such that the first and second derivatives at the start and end ...
15
votes
2answers
1k views

Fast Spherical Linear Interpolation of list of quaternions

An accurate way to interpolate between two quaternions is to use Spherical Linear Interpolation (Slerp) because it preserves the unit length, whereas straightforward linear interpolation does not, as ...
15
votes
2answers
727 views

Improved interpolation of mostly-structured 3d data

This question arose in response to a comment by Leonid to my answer for this question. He noted that for unstructured grids, Interpolation can only use ...
14
votes
4answers
2k views

Getting the interpolation function from a list plot

I have conducted a chemistry experiment and obtained a list of concentrations of a reactant against time. I plot a graph of this using Mathematica's ListPlot ...
14
votes
3answers
730 views

Monotone, periodic 1d-interpolation with continuous 1st order derivative

Lately, we had this thread about interpolation where J. M. linked two interpolation methods. The background for my question is that I estimated a parameter in polar coordinates with dependence on the ...
14
votes
1answer
303 views

Why does LogLinearPlot sample its argument outside the specified domain?

I experience a weird bug in the function LogLinearPlot. If the input is an interpolation function, such as the one created like this, ...
13
votes
3answers
571 views

How to splice together several instances of InterpolatingFunction?

I have a set of InterpolatingFunction returned by NDSolve which are valid over different (but overall continuous) domains. How ...
12
votes
3answers
2k views

Data interpolation and ListContourPlot

I am fairly new to Mathematica and I have two quick questions on using it for a Hydrology and Hydrogeology class. One is about data interpolation and interpolating without any data defined in an area. ...
11
votes
4answers
485 views

How to reduce the InterpolatingFunction building overhead?

I want a linear interpolation from the following example list: ...
11
votes
1answer
1k views

Fitting a spline to data with FindFit?

I am trying to find a function that fits my almost linear data. A high order polynomial model has too much residual. So I was hoping to use Mathematica to fit splines to the curve. This is what I ...
10
votes
2answers
3k views

interpolation of 3D data

I have a 3D surface given in data-points of the form ${x,y,z}$. What is the easiest way to get the interpolated value $z=f(X,Y)$ for given coordinates ${X,Y}$ (which are of course not in the data ...
10
votes
2answers
550 views

How to add an interpolating point to InterpolatingFunction?

Suppose I have an InterpolatingFunction object defined on $[\epsilon,1]$; let's call it f. What is the best way to construct a ...
10
votes
3answers
715 views

Derivatives (divergence, gradient, curl) of interpolated 3D data

How can I calculate a vector derivative (i.e. divergence, gradient, curl) of interpolated data? For sample data, you can use: ...
10
votes
1answer
435 views

How to get zeroth-order (piecewise constant) interpolation of scattered data?

Given a collection of scattered data points in 2D and associated function values, data = RandomReal[1, {100, 3}]; we can get a piecewise linear interpolating ...
9
votes
2answers
184 views

Partitioning a superset of coordinates into subsets that generate continuous curves

Consider the data set corresponding to recorded trajectories for a particle: ...
9
votes
2answers
538 views

Interpolation of mostly-structured 3D data

this question relates to interpolation of 3D data and Improved interpolation of mostly-structured 3d data I have an irregular 3d data set that is quite large (around 70,000 triplets---let's call it ...
9
votes
1answer
299 views

Test if argument is inside domain of InterpolatingFunction

The documentation says In standard output format, only the domain element of an InterpolatingFunction object is printed explicitly. The remaining elements are indicated by <> But this is not the ...
8
votes
3answers
726 views

Ηow to create an interpolated CDF from its samples?

I want to use a distribution I have only aggregate statistics on, namely its CDF sampled at certain points. I would like to keep it "nonparametric" (remain noncommittal on the parametric form), but I ...
8
votes
3answers
604 views

Approximately Fit Data Without FindFit

I have some noisy data, and I'd like to analyze the derivative of the function the data approximately matches. Interpolation is normally great, but doesn't work ...
8
votes
4answers
600 views

Numerical integration of a numeric data available as a nested list

I have some numerical data in the form of a list with the following structure: {...{x,y,z},...} defining a surface z=z(x,y) in a 3D space (x,y,z). The data came from a simulation, and I am ...
8
votes
1answer
116 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 ...
8
votes
2answers
265 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 ...
8
votes
1answer
120 views

Prevent Plus from threading InterpolatingFunction

For an InterpolatingFunction $y:\ \mathbb{R}\to\mathbb{R}^2$, Plus is unaware of this, so when I do any modifications to it in ...
7
votes
1answer
218 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 ...
7
votes
1answer
184 views

The only usage for the option InterpolationOrder in NDSolve is to be set to All?

We know that changing the option InterpolationOrder in ListLinePlotListPlot3D、...
7
votes
2answers
419 views

Function Interpolation with Automatic / Algorithmic Values Mesh

I have an underlying function f(x,y,z) that is computationally intensive, but is smooth and continuous. I'm needing to find the function values along a line in xyz. Currently, I'm calculating f at ...
7
votes
0answers
359 views

Creating and using an explicit piecewise function in a convenient way

I have a set of data points that define a function in the form curvePts = {data1,data2,...} where ...
6
votes
1answer
375 views

How to use Interpolation to fill in missing data

I have a bit of data that looks like this: ...
6
votes
2answers
861 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 ...
6
votes
1answer
311 views

BSplineCurve Interpolation

Can I get interpolated values from this B-spline, (shown in red)? ...
6
votes
1answer
522 views

Getting an InterpolatingFunction from a ContourPlot

I have a function, say minimizeme[Ω_][β_][ϵ_] = ϵ^2 Ω - Log[2 (Cosh[2 β] + Cosh[2 β ϵ])]/(2 β); I want to find its critical points in $\epsilon$ for a given ...
6
votes
1answer
479 views

Smoothing/Averaging 2D Vector Fields

I have a list of 2D vectors defined by {{x,y},{u,v}} and would like to smooth or average the vectors. For example here are 2 vector fields, the second has noise ...
5
votes
3answers
204 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 ...
5
votes
2answers
276 views

How can I force points in a list to have distinct x values?

I have a list of points that may be used for linear interpolation using Interpolation and need to ensure that no two points have the same $x$ value, since, if they ...
5
votes
2answers
146 views

How to get the boolean value of an inequality involving an InterpolatingFunction?

Here's the code: yan = FunctionInterpolation[x^2, {x, -1, 1}]; FullSimplify[yan[x] > -1, -1 < x < 1] Needless to say, what I expect to see in the output ...
5
votes
2answers
395 views

ListContourPlot interpolation screws up on concave set of data

I want to create ListContourPlots for sets of Data (from a physics simulation) given as Triplets {x, y, f(x, y)}. Certain parameter regions in the x-y-plane are ...
5
votes
2answers
289 views

How to find Matano plane

I have discrete collection of data points (10 to 10^4). I want to describe them by a continuous function and find a x value z, ...
5
votes
3answers
304 views

Interpolation with boundary conditions

I'm working on a sales projection, trying to create some flexibility in handle the forecast using locators. The toy code is something like this: ...
5
votes
3answers
2k views

Get polynomial interpolation formula

I'm attempting to get a polynomial interpolation formula out of Mathematica but I am absolutely lost. I stared out using ...
5
votes
1answer
2k views

How do I prevent NIntegrate::inumr errors within other functions?

I believe this question is best illustrated with a simple example. If I run FunctionInterpolation[NIntegrate[a + b, {a, 0, 1}], {b, 0, 1}] I get errors of the ...
5
votes
1answer
84 views

Finding minimum fly-by radius between Mars and spacecraft from interpolating function

I've written an interplanetary trajectory solver/plotter that plots the path taken by a spacecraft on an Earth-Mars mission, but have run into a little trouble when the spacecraft actually reaches ...