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

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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 ...
16
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5answers
844 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. ...
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0answers
150 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 ...
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0answers
99 views
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0answers
86 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 ...
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1answer
130 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 ...
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0answers
89 views

Slow integration of interpolating function

I have a large file with irregularly spaced data in the format: ...
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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 ...
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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 ...
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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 ...
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2answers
338 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
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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 ...
2
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2answers
120 views

Interpolating a list with exclusion [closed]

I have a list, data, where the elements data[[i]] range over i from ...
1
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1answer
117 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, ...
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1answer
130 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 ...
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1answer
281 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 ...
4
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1answer
226 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 ...
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1answer
243 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: ...
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2answers
210 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
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3answers
185 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
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1answer
144 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
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0answers
415 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 ...
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3answers
243 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 ...
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1answer
330 views

Interpolation Problem

I have the following list: ...
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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 ...
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1answer
321 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 ...
24
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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 ...
16
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4answers
762 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 ...
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1answer
128 views

Notation for numerical solutions to differential equations

Can somebody explain this notation to me? Using Mathematica's first example in the NDSolve documentation: ...
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0answers
399 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 ...
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1answer
129 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: ...
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2answers
89 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
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4answers
302 views

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

In ListPlot and Interpolation, the option InterpolationOrder->0 uses two different ...
0
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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 ...
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1answer
291 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
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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
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1answer
186 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: ...
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2answers
156 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? ...
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2answers
212 views

Partitioning a superset of coordinates into subsets that generate continuous curves

Consider the data set corresponding to recorded trajectories for a particle: ...
3
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2answers
168 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: ...
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1answer
65 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
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2answers
132 views

Graph two interpolations together

I have created two functions, inter1=Interpolation[points1] and inter2=Interpolation[points2]. This creates two functions, I ...
23
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1answer
423 views

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

I'm curious what's inside the InterpolationFunction object? For example: ...
7
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1answer
257 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
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1answer
225 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 ...
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1answer
356 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 ...
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0answers
228 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
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1answer
147 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 ...
1
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2answers
391 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 ...
3
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1answer
386 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 ...