# Questions tagged [interpolation]

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

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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 ...
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### 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, ...
38 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 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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### 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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### 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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### 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. ...
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### 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 ...
115 views

### 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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### 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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### 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, ...
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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 ...
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### 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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### 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 ...
61 views

### How can I get this type of interpolation [closed]

As shown in the figure, it should be a specific value
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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 ...
101 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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### 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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### 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 ...
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### 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 ...
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### 3D interpolation providing derivatives

I am trying to interpolate 3D data by also providing the 1st order derivaives in all directions, i.e., besides (x,y,z,f), I also have df/dx, df/dy and df/dz. According to the documentation I should do ...
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### Finding the arc length of a region defined implicitly with an interpolated function

I begin by defining an interpolation of some data I have stored at this link for brevity. The interpolating function is a function of two variables, x and ...
63 views

### What is the meaning/significance/importance of 'order of interpolation' used in Mathematica? [closed]

You can find details here - https://reference.wolfram.com/language/ref/InterpolationOrder.html.
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### PeriodicInterpolation does not work in ElementMeshInterpolation

I want to use ElementMeshInterpolation to generate interpolation function with periodic boundary condition. I use below data as an example ...
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Points ...
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### Convert list of InterpolatingFunctions to data [closed]

If I have g which is a list of Interpolation functions such (I cannot copy the interpolation functions for some reason): g= How ...
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### An issue with ParallelTable

Consider a function function[x_,y_,method_,distr_]:=NIntegrate[distr[x,y,z,t],{z,zmin[x,y],zmax[x,y]},{t,tmin[z,x,y],tmax[z,x,y]},Method->method] Here, ...
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### How can I interpolate time-series data?

I fetch financial data like this: data = FinancialData["SBUX", "Close", {{2013, 1, 1}, {2013, 8, 1}, "Week"}, "Value"]; ...
114 views

### Efficient sinc interpolation of a list

I'm looking for an efficient way to construct a sinc interpolation i.e. an interpolating function of a list of numbers in the form of a Fourier series with a chosen maximum frequency. The input list ...
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### InterpolatingPolynomial: magnitude of coeffictions

I have a list of the type {{x,y},f} and want to get an InterpolatingPolynomial for that list. The x values all run between 1.3 and 2, the y values between 0 and 1. ...
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### ListLinePlot's Interpolation method

I Interpolated some oscillating data points using ListLinePlot[] , and set the InterpolatingOrder->10 . This gives a nice ...
133 views

### How to integrate the interpolated data over the region in which it is non-zero?

Consider some toy-function which I then interpolate: ...
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### Derivative of a 3D Interpolated function

I cannot get the partial derivative of a set of data. I managed to get the accurate interpolation, but I cannot evaluate its derivatives. Here are my details: ...
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### InverseFunction and Plot them

I'm trying plot an inverse function ...
201 views

### Detrending or removing linear trend from 2D data

I have some data that when plotted I get an inclined graph, as described: ...
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### Interpolation for different Parameters

I am rather new to Mathematica and I tried to find a solution for my Problem on my own, also looking through this site and the suggested Similar Questions, but I at least could not make out that my ...
115 views

### Solve an interpolating function [duplicate]

I have been working with interpolating functions recently and have two functions as a result of an interpolation of two co-ordinate lists. The code I used: ...
403 views

### Nested optimization problem - Function approximation

I need to maximize the following function (the input to NMaximize below) ...
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### Lagrange polynomials

I need to plot the 9 Lagrange polynomials associated to the points {−4, −3, −2, −1, 0, 1, 2, 3, 4} all on the same axis. So my attempt: ` ...