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

learn more… | top users | synonyms

0
votes
0answers
278 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
100 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
194 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
170 views

Slow integration of interpolating function

I have a large file with irregularly spaced data in the format: ...
19
votes
4answers
2k 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 ...
6
votes
2answers
605 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
197 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
518 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
414 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
150 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
199 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
520 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
363 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
655 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
461 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
214 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
226 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). ...
3
votes
0answers
587 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
329 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
673 views

Interpolation Problem

I have the following list: ...
0
votes
1answer
743 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 ...
30
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
927 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
155 views

Notation for numerical solutions to differential equations

Can somebody explain this notation to me? Using Mathematica's first example in the NDSolve documentation: ...
8
votes
0answers
505 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
142 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
108 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 ...
28
votes
4answers
480 views

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

In ListPlot and Interpolation, the option InterpolationOrder->0 uses two different ...
-2
votes
1answer
566 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
38 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
299 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
243 views
3
votes
2answers
194 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
70 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
138 views

Graph two interpolations together

I have created two functions, inter1=Interpolation[points1] and inter2=Interpolation[points2]. This creates two functions, I ...
7
votes
1answer
400 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
336 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
536 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
351 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
183 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
vote
2answers
569 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
825 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 ...
7
votes
2answers
2k 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
200 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
376 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
83 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: ...
15
votes
2answers
2k 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 ...
0
votes
2answers
869 views

Correct use of ListInterpolation

I have a small problem with ListInterpolation. I want to use ListInterpolation to postprocess result of a numerical simulation. ...
6
votes
1answer
455 views

BSplineCurve Interpolation

Can I get interpolated values from this B-spline, (shown in red)? ...
4
votes
2answers
324 views

Convert BSplineFunction into two Interpolating Functions

Is there a way to decompose a BSplineFunction output into two functions x[t], y[t] ...