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

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9
votes
4answers
914 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
239 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: ...
3
votes
1answer
297 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). ...
7
votes
2answers
315 views

How can I speed up my compiled RBF interpolating function?

Overview I have a function that acts like the Interpolation on sparse $n$-dimensional data using a simple implementation of RBF interpolation method. I want my ...
5
votes
0answers
732 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 ...
6
votes
3answers
386 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
289 views

Create ParametricFunction object without ParametricNDSolve

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

Interpolation Problem

I have the following list: ...
0
votes
1answer
1k 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
240 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
150 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
114 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 ...
32
votes
4answers
707 views

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

In ListPlot and Interpolation, the option InterpolationOrder->0 uses two different ...
2
votes
0answers
39 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
797 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
413 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: ...
9
votes
2answers
276 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
224 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
74 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
152 views

Graph two interpolations together

I have created two functions, inter1=Interpolation[points1] and inter2=Interpolation[points2]. This creates two functions, I ...
43
votes
1answer
1k views

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

I'm curious what's inside the InterpolationFunction object? For example: ...
7
votes
1answer
487 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 ...
1
vote
2answers
778 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
457 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
225 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
426 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
779 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 ...
1
vote
0answers
480 views

Interpolating function as a model in Mathematica's procedures for fitting

Is it possible to use interpolating function with parameters as a model for NonLinearModelFit (and other integrated methods for fitting)? Similar question was ...
4
votes
1answer
636 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: ...
4
votes
1answer
1k 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 ...
8
votes
2answers
577 views
7
votes
2answers
3k 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
280 views

Find limit of Interpolated function

I have an interpolated function f = Interpolation[data] I would like to calculate limits such as ...
0
votes
1answer
479 views

Interpolation of data on non-rectangular grid [duplicate]

I have a smooth data distribution on a 2D regular grid that is not a rectangular (it is a cross-section of a channel) and I need to find an Interpolating function ...
2
votes
1answer
91 views

Why do I have to perform a second ReplaceAll in this InterpolatingFunction?

I have an InterpolatingFunction that I'd like to plot, and I wonder why I have to perform a ReplaceAll on the following function: ...
0
votes
1answer
175 views

Interpolation and points of non-differentiability

I have some data, which if expressed by some elementary functions, would contain a non-differentiable point. I would like to be able to use something like interpolate to convert the data into a ...
0
votes
2answers
1k views

Correct use of ListInterpolation

I have a small problem with ListInterpolation. I want to use ListInterpolation to postprocess result of a numerical simulation. ...
0
votes
1answer
182 views

Notation for numerical solutions to differential equations

Can somebody explain this notation to me? Using Mathematica's first example in the NDSolve documentation: ...
7
votes
0answers
585 views

Creating and using an explicit piecewise function in a convenient way [closed]

I have a set of data points that define a function in the form curvePts = {data1,data2,...} where ...
7
votes
1answer
1k 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 ...
1
vote
2answers
3k views

Using FindRoot with an interpolating function

This question bears resemblance to a few other questions on mathematica.SE about finding points of intersection of crossing curves. I know that the guidebook of numerics has an entry about the whole ...
-5
votes
1answer
277 views

Problem with interpolation

I have a problem with the function interpolation. when I use it my points are all very shifted. Do you have an idea of the solution? ...
1
vote
2answers
113 views

Interpolation of an upper-triangular list

I have 2d list which is upper triangular. I would like to interpolate it, but I cannot unless I set the interpolation order to 1. I tried making the list rectangular by filling the bottom half with ...
2
votes
1answer
122 views

InterpolatingFunction with growing Domain

I want to find roots of a function that is very slow to calculate (the function itself involves a bunch of FindMaxima) so I interpolate the function in a region where I think it likely the the root ...
4
votes
1answer
2k views

Join a piecewise plot

I wrote some code to get a piecewise plot which is displayed correctly. Now I'd like to join the various parts of the plot, using some kind of interpolation, to get a continuous chart even though it's ...
3
votes
0answers
481 views

How to make 3D object smooth?

This thread considers mathematical methods here to make the 3D object smooth but this question consider how to achieve the goal of smoothing a 3D object in Mathematica. I want to get smoother ...
4
votes
0answers
463 views

Cubic polynomial interpolation with velocities listed rather than some points

I am trying to use the function BSplineFunction[] to create a natural cubic spline. Normally what is done is that you specify "SplineDegree -> 3" and include a list of points and it will carry out ...
2
votes
1answer
435 views

Interpolation on large 2D list results in erratic function

Previously, I've had problems with Mathematica interpolating and plotting 3D lists, but I finally managed to do so by rescaling the x and y-axes with the help of the methods proposed here. Now my ...
2
votes
2answers
399 views
-4
votes
4answers
3k views

Piecewise linear Interpolation between data points [closed]

Is there some sort of functionality built into Mathematica that will let me linearly interpolate between (x, y) pairs of data in an array? Example: I have the two points (1, 10) and (2, 20), how can ...