# Questions tagged [interpolation]

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

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### Interpolation on an unstructured (mostly-structured) grid in 4D+

I frequently need to perform interpolations on an unstructured grid. Mostly, with the purpose of filling grid holes and then later continue with regular grid interpolations. Mathematica V9 and V10 ...
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### InterpolationOrder has no effect on ListContourPlot when the data is of the form {x,y,f[x,y]}

This is related to the issue brought up here, if you want to mark it as duplicate feel free to do so, but it is slightly separate. Take two sets of data, identical except for the form, ...
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### 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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### Evaluation of Mod of InterpolatingFunction prevents discontinuity processing by Plot

While trying out @MichaelSeifert's answer to Eliminating Discontinuities When Using Mod with NDSolve and Plot for Oscillators, I came across this odd behavior. Depending on how an ...
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### Why do some uses of PropertyList crash the kernel?

Bug introduced in 10.1.0 or earlier and fixed in 12.1.0 While looking at the question How to evaluate the "Domain" of an InterpolationObject? I noted that using ...
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### Interpolation on an unstructured grid with large aspect ratio

If you wish to interpolate on an unstructured grid then the solution is to use ElementMeshInterpolation from the Finite Element Method. I examined this here but now ...
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### DumpSave and precision of interpolation data

Consider the following prec = 32; x = N[Range[0, 1, 1/10], prec]; f = Interpolation[Transpose@{x, x}]; Then ...
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### Plotting InterpolationFunction over Quantities

What's the proper syntax to plot Interpolation functions defined over Quantities? points = {{0, 0}, {1, 1}, {2, 3}, {3, 4}, {4, 3}, {5, 0}}; Change domain to ...
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### 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 ...
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### Numerically solve a non-differential equation with InterpolatingFunction as output

I have some a function that I need to solve numerically over an entire domain (Ideally I would like an InterpolatingFunction object as output), which does not include any derivatives. I have found a ...
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### How do I truncate an interpolating function?

I have a very large interpolating function and want access the function at one point in time. I am running out of RAM running ...
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### Parallel evaluation of RandomVariate for an InterpolatingFunction

I need to generate a lot of point according to a given distribution. I don't have an analytic form of this distribution so I am using an InterpolatingFunction of ~100 points computed numerically. I ...
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### Reducing a FEM 3D Interpolation Function to a 2D Interpolation Function

I'm trying to solve the heat equation in 3D using FEM and back out a slice in the xz plane. My problem is when I define a function that is a slice in the xz plane it uses the full 3D interpolation ...
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### Export to PDF: DensityPlot & AllowRasterization->False

How to get production-quality vector graphic exported from Mathematica that looks like what is plotted in Mathematica. Example code: ...
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### Interpolate a 3D surface in 3D

We have taken measurements on a cylindrical flexible item. At each of the measurement locations we have an oscillating motion which is described in terms of three orthogonal directions. The ...
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### Data Interpolation of deaths by date

I am working with an ebola dataset from Guinea, 2014:(http://currents.plos.org/outbreaks/article/estimating-the-reproduction-number-of-zaire-ebolavirus-ebov-during-the-2014-outbreak-in-west-africa/). ...
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### Diagonalisation of equations for NDSolve

I have a linear matrix differential equation and I wish to speed up evaluation by diagonalising using eigenvectors. There is an example in Help for finite elements under "swinging beam" that is ...
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### Interpolation of Singular Functions

I am trying to interpolate discontinuous functions for R in interval $[0,100]$ and r in interval $[0,100]$: ...
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### Slow integration of interpolating function

I have a large file with irregularly spaced data in the format: ...
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### 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 ...
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I am trying to use a custom trilinear interpolation written in C in Mathematica (Windows). This is the code I start with: ...
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### Elegant way to handle a series of interpolation functions

In this post, I wrote a piece of code that can bypass singularities in numerical solutions of the first type of Painlevé ODE. The code is as follows ...
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### Numerical Galerkin method with parametrized interpolation function

modified Here I try to realize a numerical fit (Galerkin method) using parametrized Interpolation function to fit examplary Exp[x] in a given grid. So far I tried <...
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### Fractional derivatives (FractionalD) of an InterpolatingFunction to retun another InterpolatingFunction

Question I want to calculate the FractionalD of an InterpolatingFunction object, however, evaluating ...
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### Make NDSolve return solution over only part of domain

Consider the following pair of PDEs, for which I will solve in the mesh built below. The mesh needs to be much larger than the region of interest to mimic boundary conditions "at infinity". ...
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### Export Mathematica interpolating function to other programming language (C++)

I have an interpolating function in Mathematica from solving a complicated differential equation. I want to then use the interpolating function directly in my other program, which is written in C++. ...
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### Multi-dimensional interpolation of unstructured array returns unevaluated

Interpolation should work fine on an unstructured array of machine numbers with interpolation order 1. However, when both the arguments and output are multidimensional, it doesn't evaluate. The first ...
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### Analyzing anomalies of Bluetooth audio generation with Mathematica

I' m working on an audio generator for physics lab, using an Android device and Bluetooth . However, the response of the Bluetooth speaker is wrong. When programmed to deliver, say 3150 Hz, it may ...
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### Is it possible to modify options inside an InterpolationFunction object?

When dealing with a slow function (e.g., a numerical integration) it is sometimes useful to tabulate it and create an interpolation function to work with instead. I found that one can deal with a ...
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### Multivariate polynomial data fitting formula

A short description： consider $f(x,y,z)=x^2+y^2-z^2$ we can know that $f(1,0,1)=0,f(0,1,1)=0$ ,etc. so we can get the roots of this polynomial. Now if given the roots of polynomial, how to solve ...
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### Extra interpolation in ListPointPlot3D

I'm trying to plot a 3D surface using ListPointPlot3D and it looks almost right, but for some reason it's trying to connect points that should not connect. I think it's confused because the surface is ...
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### Derivative of an interpolation function is noisy

I have a set of numerical data of 1501 points, in the form of $\{x_i,a_i\}$ which I uploaded to here and here. I need to compute the numerical derivative of this data. In particular, I need the ...
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### A problem when interpolating the data

I have some data in a form data = {{x,y,f[x,y]},...}, where f[x,y] takes only positive values. When I try to interpolate it, <...
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### Contour lines in ListContourPlot with InterpolationOrder 0

I have a dataset and would not want Mathematica to interpolate at all while plotting the contours. This is because the data contains essential binning information and the "steps" in the ...
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### How to get ImageTransformation to not compute the function at *every* pixel

I am using ImageTransformation with a slow function. Is there a way to get ImageTransformation to compute the function at only a ...