# Questions tagged [interpolation]

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

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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 ...
57 views

### How to ParametricPlot an InterpolatingFunction

Hi I can Plot the result of an NDSolve (toy example), but I cannot ParametricPlot it. ...
28 views

### 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 ...
77 views

### 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)...
24 views

### 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: ...
35 views

### 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 ...
81 views

### 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: ...
87 views

### 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: ...
68 views

### 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 ...
125 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 ...
10k views

### 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 ...
68 views

### 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 ...
76 views

### 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
3k 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 ...
501 views

### Integrate only one variable of a 2D interpolating function

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

### 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 ...
46 views

### Derivative of predictor function

Given some data dat, we would like to generate a predictor function. Therefore we use ...
76 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. ...
68 views

### 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 ...
32 views

### Using NSolve with an interporlated function

I have defined the interpolation function below ...
199 views

### 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 ...
159 views

### 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....
7k 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 ...
29 views

### 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 ...
52 views

### 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 ...
48 views

### ParallelTable of NIntegrate of an Interpolating Function

I construct a 2D interpolating function using the following data (MWE): ...
30 views

### 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&...
67 views

### 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 ...
255 views

### How to put conditions on indices of product

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}...
418 views

### calculate missing values, Interpolation

I've following data: ...
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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 ...
76 views

### 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 ...
59 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.
137 views

### 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 ...
332 views

### Interpolation of non-rectangular data failed

I want to interpolate a type of data which is on a triangular lattice in order to make DensityPlot faster(ListDensityPlot is so slow). However, the interoplation failed with error, no matter setting <...
77 views

Points ...
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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, ...
200 views

### Extending matrix (x,y-axis + data) via Interpolation. Looking for elegant & efficient way to write

Please, feel free to edit the title, if necessary. Hi, this is my code working, but actually, the size of my real dataset is 100x100. So, this is very inefficient way. What would be the most ...
73 views

### Calculation using interpolating function

Say I have two replacement rules in terms of interpolating functions. ...
194 views

### 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"]; ...
68 views

### 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 ...
104 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 ...
81 views

### Finding the inverse of possibly non-invertible interpolation function

Consider the following sample code pts = Table[{i, i^2}, {i, -10, 10}]; foo = Interpolation[pts]; Plot[InverseFunction[foo][y], {y, 0, 10}] From the plot, we see ...
144 views

### Numerical Integration over experimental numbers

I have a large array {x,y,z} sigma = {{x1,y1,z1},{x2,y2,z2}, ......} where z is a function of x,y: z = f(x,y); the function is known only through its numerical ...
33 views

### 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. ...
50 views

### ListLinePlot's Interpolation method

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