# Questions tagged [interpolation]

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

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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 ...
203 views

### FEM 1D 3D region coupling - speed up coupling using boundary integration

I am working on a simulation of the heat equation involving a 3D solid simulation coupled to a 1D fluid simulation (convective term of heat equation). I am using the method of false transient as ...
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### Can I get an x-value for a given y-value using an interpolation function? [duplicate]

I'm brand new to Mathematica and struggling figure this all out. I made an interpolating function with the following (year, population) data. I'm trying to figure out what year the population reached ...
119 views

### How to find the best function which interpolates a set of data? [closed]

I have a set of data as follows: ...
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### FEM 1D 3D region coupling - integration too slow for coupling with energy conservation

EDIT: I reposted this question, removing everything that is not necessary for my coupling approach. Find the new post here. I am working on a 3D simulation of the heat equation which is coupled to a ...
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### Matrix as the discretization of a function $u$ over a rectangle in 3D, how to integrate fast along the axes

I have a function $u$ from 3D to 1D approximated in a list uu and I want to calculate e.g. $$\int_0^1 x\cdot u(x,y,z)dx$$ or \int_0^1\int_0^1\int_0^1 u(x,y,z)...
508 views

### Adding Regularisation to Built-in Interpolation function

tl;tr; How to improve performance of regularised Interpolation? Context Since Version 12, Mathematica now incorporates a range of (underrated IMHO) regularisation ...
101 views

### Taking a diagonal cut through a matrix

Lets say I have a gaussian data matrix, e.g. x=GaussianMatrix I would like to take a cut through this matrix at a 45 degree angle to get its intensity profile, ...
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### How to do Interpolation to this function after given b this values

χ[b_] := (Z/k)*NIntegrate[Subscript[f, pp1][q]*Subscript[F, pp1][q]*BesselJ[0, q*b]*q, {q, 0, b}]; bList = Table[b, {b, 0, 5.1 , 0.05}] where: ...
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### multi-dimensional interpolating function evaluation and extract dimension

I have an interpolating function which output dimension is greater than 1, so it's a vector. I get it as the result of a NDSolveValue. The problem is that I'm not able to Evaluate it. I would obtain ...
491 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 ...
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### Derivative of predictor function

Given some data dat, we would like to generate a predictor function. Therefore we use ...
41 views

### Integrating and seeing an interpolating function

I have the following piece of a Mathematica notebook: As I understand, the interpolating function M1hatInterp is piecewise polynomial and hence can be integrated ...
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### Does mathematica cache the interpolating function from ParametricNDSolve?

I want to evaluate the solution of a system of non-linear ODEs using ParametricNDSolve. The output of ParametricNDSolve is a ParametricFunction object. Let's call it $f_\theta(t)$, where $\theta$ is a ...
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### How to use NDSolve with limited RAM?

How can I use NDSolve when running out of RAM? The code I am implementing: ...
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### How to fit an interference pattern with Interpolation and FindFit？

I have two sets of experimental data. LightSourceSpectrum2.txt InterferencePattern2.txt The first one is the light source spectrum data, which can become a function of f[ν] using Interpolation. (Note ...
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### Creating a numerical table of values and using an interpolation of them to transform pixels in an image by the ImageTransformation command

I am trying to carry out point "Implementing Map" on this paper Interstellar wormholes however I am using my own equations not those given (only the same method). I have generated a list of ...
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### Reverse engineer visualizations to compactly extract underlying data

TL;DR How to implement in mathematica a tool such as WebPlotDigitizer by Ankit Rohatgi which would allow us to trace automatically curves from either (randomly ordered) data or imported images. ...
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### How to ParametricPlot an InterpolatingFunction

Hi I can Plot the result of an NDSolve (toy example), but I cannot ParametricPlot it. ...
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### Connecting simple lines from (large) unsorted list of points

Context We are trying to predict the formation of discs of intermediate mass black hole orbiting super massive black holes in galactic centres. This involves finding calorific curves in energy and ...
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### How can I fit a function onto a histogram?

SampleData = RandomVariate[RayleighDistribution, 5000]; Histogram[SampleData] This creates a histogram that (in my case) looks something like this: I want to ...
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### NIntegrate not evaluating. "Interpolating Function" [closed]

I am trying to numerically evaluate an integral. I have a function to be integrated, ftbI[s,a] with undetermined variable(s) a. ...
130 views

### Defining mesh size for NDSolve

I want to see the effect of mesh size on the solution curves while simulating convection-diffusion - point sink via NDSolve FEM. In the following code (ref also related to this post): I'd like to know ...
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### plot multiple curves : solution obtained from NDSolve

I want to plot the solution obtained from NDSolve as a multicurve plot like shown in the following sample image (image ref). Here, x1, x2 , x3, x4 .. are the solution computed at ...
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### Nintegrate of a list of numbers

I have an issue. I have a function in two variables obteined from the table of a numerical integral (done with Nintegrate). Now I have to compute another integral (Nintegral) over it so I will have a ...
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### Obtaining interpolating functions from NDSolve with two functions

In Mathematica's documentation on interpolating functions, they give an example of how to obtain an interpolating function as a solution of NDSolve, ...
1k views

### FindRoot of interpolating function from NDSolve

I am having issues finding the root of an interpolating function obtained from NDSolve. For example: ...
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### How to interpolate on log-log scales? I.e., How do I create an interpolation function which interpolates Log[x] vs Log[y]?

I would like to build and interpolation function that takes in x & y data points and interpolates between them logarithmically in both x and y. I see that this a reply on this post (Interpolate on ...
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### Find order of polynomial approximation and LeastSquares for given datapoints

I have a set of data, where I'd like to find the order of the polynomial that approximates the data, and also know what the Least squares is. My data: ...
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### Possible Bug in InverseFunction

MMA 12.1 For quite some time I have been chasing a bug that I could trace down to the following code. As it is not impossible to fool oneself, I would be glad if somebody could verify this before I ...
158 views

### Interpolating and plotting 3D data

I am having trouble interpolating and plotting a set of 3D data. As it appears I have an unstructured grid, tried Interpolation[data, InterpolationOrder->1] but ...
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### Getting the interpolation function from a list plot

I have conducted a chemistry experiment and obtained a list of concentrations of a reactant against time. I plot a graph of this using Mathematica's ListPlot ...
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### My plotting comes out to be gray not coloured using AbsArgPlot function in Mathematica. What is the reason for not getting a coloured graph??h

My graph comes out to be gray, not coloured using AbsArgPlot function in Mathematica. What is the reason for not getting a coloured graph or what I can deduce from ...
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### How to find the integrand by fitting data - spectrum reconstruction

Problem statement I have some experimental data of measurement values vs. temperature. Now, I want to find the spectrum which causes the measured temperature dependence. The measurement values are the ...
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### How can I get this type of interpolation [closed]

As shown in the figure, it should be a specific value
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### 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 ...
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### Integrate only one variable of a 2D interpolating function

Lets say I have generated a 2D interpolating function using the code: ...
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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 ...
118 views

### ListContourPlot Interpolation Order

I am trying the use ListContourPlot with interpolation of the measured data to get smooth contour lines. I tried the methods in Data interpolation and ListContourPlot but they work only for some data. ...
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### NDSolve of a 3-D function from interpolated data

I have a 3-D data set (linked in the comment below) obtained via numerical integration. I would like to generate an interpolating function, and then use this function to numerically solve an ODE. For ...
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### Using NSolve with an interporlated function

I have defined the interpolation function below ...
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### What does it mean by order -1 of InterpolatingFunction?

Bug introduced in 12.1 or earlier, fixed in 12.2. In the above code, the InterpolatingFunction object has order -1. In the documentation https://reference.wolfram.com/language/ref/InterpolationOrder....
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### 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 ...
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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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### Manipulating lists based on conditionals and 3D plotting the smooth surface that bounds a list of points

First of all I want to create a list of evenly spaceed points in a cubic region in $\mathbb{R}^3$. Then I want to keep the points in this list which satisfy a certain condition, i.e. a function that ...
55 views

### ParallelTable of NIntegrate of an Interpolating Function

I construct a 2D interpolating function using the following data (MWE): ...
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### Why ListInterpolation does not allow InterpolationOrder greater than 2 in the "y" direction?

The order is always reduced to 2 in the "y" direction; I would want a better approximation to my data. Independent of the method (spline or hermite), I can choose any order for the "x&...
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### Plotting an InterpolatingFunction outside its domain doesn't raise error messages

Let's make an InterpolatingFunction: if = Interpolation[Transpose[{#, Sin@#} &@Range[0, 4, 0.1]]]; As expected, evaluating ...
I'm trying to solve for the Lagrangian form of the interpolation polynomial. Right now, I'm just trying to solve for the $l_i(x)$ values which are equal to \$l_i(x)=\prod_{j\neq i, j=1}^{n}{\frac{x-x_j}...