Questions tagged [interpolation]

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

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6
votes
1answer
598 views

How can I get the interpolation line from Listplot?

My discrete data is: data={{1., 5827.}, {3., 6242.}, {15., 6066.}, {60., 5972.}} I want to get the interpolation line from ListPlot: ...
6
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2answers
313 views

Extract one dimension from an n-dimensional InterpolatingFunction

How can I extract a single dimension from an InterpolatingFunction? As an example: ...
6
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1answer
2k 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 ...
6
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1answer
131 views

Efficiently fill sparse matrix involving BSpline

Context In order to implement regularised fitting in 2 or 3 dimensions (as is done say here) using BSplineBasis one needs to evaluate a basis over a set of data. ...
6
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1answer
753 views

How to plot InterpolatingFunction across its domain

I'm using NDSolve to solve a system of coupled ODEs for a range of different parameters. For most points in the parameter space, the integration breaks down ...
6
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1answer
826 views

Multiply interpolating function with variable

I am always running into trouble when trying to use interpolating functions. I am trying to do: ...
6
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1answer
535 views

How to evaluate differential entropy from raw data?

I want to evaluate the differential entropy according to here $$h(X) = - \int f(x) \log{f(x)} dx$$ where $f$ is the probability density function. Lets create some test data (normal distribution): <...
6
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3answers
435 views

Interpolation impossible for ListPlot with Missing?

I have a list of data to plot. I would like to plot them with lines but delete some data before plotting and leave the lines disconnected where data is deleted. For example, ...
6
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1answer
148 views

Recycling solutions of multidimensional NDSolve

Dear wolfram community, I hope my problem is clear and easy to solve. I have already solved the following heat equation over a domain: ...
6
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1answer
352 views

What is wrong with this code? (Usage of FunctionInterpolation and how to make code efficient)

I am trying to create an interpolation out of a function that comes from an improper integral. The end goal is to make a 3d plot over a specific region. Specifically, I have the following code: ...
6
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1answer
159 views

2D interpolation of function with dependent interpolation border

My problem is to compute $$\int\limits_{x_{min}}^{x_{max}}\int\limits_{y_{min}}^{\sqrt{x^{2}-a^{2}}}W(x,y)g(x)\ dx\ dy$$ Because $W$ have highly oscillatory 2d complex numeric integral inside, dumb ...
6
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1answer
293 views

FunctionInterpolation error when specifying AccuracyGoal

Bug introduced in 8 or earlier and persisting through 11.0.1 or later In the help page ref/message/FunctionInterpolation/ncvb, it is mentioned that one should ...
6
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1answer
292 views

Evaluating InterpolatingFunction returned by NDSolve is very slow starting from some arguments

I use this code to solve a PDE: ...
6
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1answer
299 views

Multidimensional arbitrary precision spline interpolation on the grid

This question is a generalization of the previous one for multiple dimensions. In the answer to that question an implementation for the clamped spline interpolation for 1D case and arbitrary degree of ...
6
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1answer
1k 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: ...
6
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2answers
345 views

How to derive/interpolate a polynomial f(x,y) from several discrete polynomials f(x)?

I have 7 discrete degree 3 polynomials $f_i(x)$. Each of them represents a snapshot of data from an experiment and fits this data quite well. This graph depicts the 5 largest of the 7 polynomials: ...
6
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1answer
373 views

How to use BSplineFunction for calculating derivative

I have a set of data like the following data = {{x1,y1},{x2,y2},{x3,y3},......} Now I use ...
6
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1answer
188 views

Multi-variable FunctionInterpolation with the range of one variable as a function of another

How can I modify my FunctionInterpolation code so that the boundary of one of the variables is a function of another variable? ...
6
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1answer
223 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 ...
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0answers
152 views

Accuracy of Chebyshev Interpolation

I have been looking at how to interpolate a function using Chebyshev polynomials. There are several good posts such as this one by Michael E2 and this one by J. M. There is also an example in the help ...
6
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0answers
1k 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
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4answers
1k views

Finding intersections of two parametric curves

I am dealing with the root finding of two parametric data curves (data below). I have already checked Parametric Interpolation of 2D data, which I found useful for plotting, though it is not adequate ...
5
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4answers
459 views

How to easily find the coefficients of a cubic polynomial and its plot for the given 4 points

Given 4 points as points = {{0, 4}, {1, 0}, {2, -1}, {3, 0}};. I want to find the coefficients of ...
5
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4answers
170 views

Constructing a list

I need to use the interpolation function on some data so I can integrate it. I have an array with 1400 subsets and there are 1400 elements in each subset: ...
5
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3answers
303 views

Obtaining points with equal spacing from interpolated data

Beginning with five ordered pairs I made an interpolation, obtaining an a polynomial expression. I got several other points with equal spacing from the polynomial expression. Are there any commands ...
5
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3answers
2k views

How to (correctly) interpolate an array of points?

I'm trying to obtain an interpolation function for points of an x^(-5) function (which goes to infinity at x = 0). ...
5
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4answers
1k views

Interpolation of unevenly spaced data, is it possible?

I need to interpolate data, that consists of many points in the beginning and a few in the end of the interval, like in the following example: ...
5
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3answers
6k views

Smooth 4D (3D + color) plot from discrete points

I have a file containing isosurface $\{x,y,z,F\}$ data (around 9000 points). My goal is to generate a smooth (NOT a discrete set of points!) colored surface using ...
5
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3answers
1k views

How could I get the value of y[t] at each specific interpolation point?

sol = NDSolve[{Derivative[2][y][t] + Sin[y[t]] == 0, Derivative[1][y][0] == 0, y[0] == 1}, y, {t, 0, 2}] the above-mentioned differential equations can be solved ...
5
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2answers
280 views

Trying to build a function to compute divided difference for arbitrary list of points

As the title says Im trying to build a function to compute divided difference for arbitrary list of points. The divided difference of a set of points $\{(x_1,y_1),\ldots, (x_n,y_n)\}$ where $x_j<...
5
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2answers
451 views

Derivative of an interpolated function

I am trying to take the derivative of an interpolated function. I am given the function values and the derivatives at some irregular points. Here is my minimal working example to reproduce the error: ...
5
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2answers
255 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 ...
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2answers
167 views

Basic 3D Interpolation Failing

I've seen a few other posts asking about the "unstructured grid" error in Interpolation. Here's a minimal (non)working example of the issue: ...
5
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3answers
6k views

Retrieve values of InterpolatingFunction

While analyzing a large system of ODE's, I defined a particular ratio p, which contains some variables that are represented by ...
5
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2answers
144 views

Reshape interpolated data

I want to reshape/smooth the following data: ...
5
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3answers
295 views

Smooth initial data

I need something that produce pseudorandom smooth initial data for modelling phase separation equations (Cahn-Hilliard and simular). Generator code for now: ...
5
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3answers
349 views

How to complete function which is not defined for all interval

I have a function testF22 like this ...
5
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1answer
385 views

interpolating a smooth closed surface to a non-uniform data set (ListSurfacePlot3D)

I want to generate a smooth coloured surface from a discrete set of points of the form {x,y,z,F} using the ListSurfacePlot3D. My data set is quite non uniform; the ...
5
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2answers
396 views

Plot 1D slice of 2D InterpolatingFunction

I'm numerically solving a PDE (time+1D space) with NDSolve and want to plot some spatial profiles. Plot works, but is very slow ...
5
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2answers
749 views

Integrating an interpolating function

I have been using the following NDEigensystem command to generate the eigenfunctions of the laplacian with a square domain: ...
5
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1answer
2k views

Interpolating 2D data with missing values

I have a list (21 x 21) containing values. I want to eliminate slots containing zeros by interpolating the nearest values and overwriting the zeros. How do I use the Mathematica's ...
5
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1answer
68 views

Weirdness with Interpolation of data and InverseFunction

Bug introduced in 8 or earlier and persisting through 12.0 Something strange is happening with this list of data: ...
5
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2answers
564 views

How can I fit a function onto a histogram?

SampleData = RandomVariate[RayleighDistribution[3], 5000]; Histogram[SampleData] This creates a histogram that (in my case) looks something like this: I want to ...
5
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1answer
421 views

Strange extrapolation in ListContourPlot?

I have some Table of {x,y,z} values (energy as a function of radial and azimuthal frequencies in a galaxy if you care to know): ...
5
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1answer
872 views

Smooth 3D plot with colour of scattered data

I have a set of scattered 3D points with coordinate (x,y,z) and an intensity associated with it. I would like to do a smooth surface with the intensity being represented by the colour. My points ...
5
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2answers
439 views

NMinimize Constraints on Interpolating Functions

I have the following piece of code and am trying to use NMinimize (the last line in the following chunk of code) to minimize ...
5
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1answer
808 views

Intersection of a ListPlot3D surface with a plane

I'm trying to use Mathematica to analyze some physics data from an experiment, more precisely, I have to fit a 2D data series with a one dimension function. At the moment I'm able to load and plot ...
5
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1answer
2k views

Integrating a functional of an InterpolatingFunction

It is straightforward to Integrate an InterpolatingFunction. However, even for a simple functional of an ...
5
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1answer
586 views

How does ListInterpolation work?

ListInterpolation takes an array of data and interpolates between the entries. Let us interpolate between the elements of the identity matrix. For reference, this ...
5
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1answer
138 views

FunctionInterpolation produces many error messages when given high-precision input [duplicate]

Both FunctionInterpolation[1, {x, 0,1.00000000000000004}] and FunctionInterpolation[1.00000000000000004, {x, 0, 1}]; ...

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