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

learn more… | top users | synonyms

1
vote
1answer
116 views

How to convolve a Unit function (like “UnitTriangle”) with a InterpolatedFunction

Recently discovered what InterpolatingFunction's are in Mathematica...really amazing/useful. As I understand it, it's basically a curve fitter....sorta. So how ...
5
votes
1answer
109 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 ...
1
vote
2answers
113 views

How to work with lists of functions

I have some lists of interpolated functions and I want to know if there is an easy way to operate with them. A simplified example: ...
2
votes
1answer
557 views

Interpolation: Unstructured grid error

If I try to make a table SimpleTable and to interpolate a function of two variables, I encounter a problem. For example: ...
0
votes
1answer
47 views

ContourListPlot not evaluating all of interpolated area

I am trying to plot a contour for a matrix, but it seems not to be evaluating all the points. Here is the interpolated figure, followed by the MatrixPlot version itself. I used this colormap because ...
1
vote
1answer
147 views

Integrate with FunctionInterpolation differs from NIntegrate

In working with interpolating functions and integration, I noticed a lot of differences between NIntegrate and Integrate in the ...
1
vote
1answer
191 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
2answers
244 views

How to resolve the duplicate error during interpolation

I have few hundred data points corresponding to an irregular shape closed curve. As the result I have data points that have the same value of y but different values of x. I want to create an ...
0
votes
0answers
31 views

FindRoot gives strange results when used on an interpolating function with vector output [duplicate]

I am currently experiencing a problem when I try to use FindRoot with an interpolating function that outputs a vector. I have constructed a minimal example that ...
0
votes
0answers
212 views

Interpolation of multidimensional data organized logarithmically

The following threads call our attention to the fact that "accuracy of Interpolation will be worse with an unstructured grid", in the context of interpolation of 3d data: interpolation of 3D data ...
1
vote
0answers
95 views

NMaximize and Accuracy

I have a problem with NMaximize which is best depicted by the following figure. The result indicates, that the solution mathematica finds seems to be smooth except a few outliers. How can I get rid of ...
1
vote
1answer
175 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
140 views

Slow integration of interpolating function

I have a large file with irregularly spaced data in the format: ...
19
votes
4answers
1k 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 ...
5
votes
2answers
529 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
157 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
423 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
1answer
366 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 ...
1
vote
1answer
133 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
169 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
361 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 ...
5
votes
1answer
324 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
465 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
361 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
205 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
191 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
518 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
293 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 ...
1
vote
1answer
517 views

Interpolation Problem

I have the following list: ...
0
votes
2answers
207 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 ...
0
votes
1answer
536 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 ...
27
votes
2answers
4k 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 ...
17
votes
4answers
862 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 ...
0
votes
1answer
146 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
453 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 ...
1
vote
1answer
137 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
102 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 ...
26
votes
4answers
370 views

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

In ListPlot and Interpolation, the option InterpolationOrder->0 uses two different ...
0
votes
1answer
197 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
1answer
443 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
0answers
34 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
248 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
231 views
3
votes
2answers
179 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
69 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
136 views

Graph two interpolations together

I have created two functions, inter1=Interpolation[points1] and inter2=Interpolation[points2]. This creates two functions, I ...
27
votes
1answer
570 views

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

I'm curious what's inside the InterpolationFunction object? For example: ...
7
votes
1answer
340 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 ...
4
votes
1answer
281 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 ...
0
votes
1answer
461 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 ...