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Questions tagged [interpolation]

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

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0answers
35 views

how to use interpolating functions to smoothly paint a polygon? [duplicate]

consider 4 different colors on the nodes (with different parameter values) how to interpolate when the color values are given on the nodes using the constructed interpolation functions to paint the ...
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2answers
159 views

Unstable NIntegrate result vs plot

Here I have a $\Psi$ function with a few arguments: ...
5
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1answer
69 views

Eigenvalues and numerical eigenfunctions for similar differential operators

I am looking to numerically approximate the eigenvalues and eigenfunctions for a differential operator I am working with, assuming $\pi$ periodic boundary conditions. Namely, I define the function $...
41
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5answers
1k views

How can the behavior of InterpolationOrder->0 be controlled?

In ListPlot and Interpolation, the option InterpolationOrder->0 uses two different ...
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1answer
33 views

Find Unknown coefficient using Contour plot

I have I really complicated equation, but for simplicity lets assume my function is F(x,y,z)= ax+by+c*z, where a, b and c are some unknown constants. From experiments we know that at: x=3, y=2, z=1 ...
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2answers
488 views

Morphing between two functions

Assume we have 2 peaked positive functions f[x_] := Exp[-(x + 3)^2] g[x_] := 1/2 Exp[-(x - 3)^2/4] that look like Would it be possible to numerically find a ...
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0answers
32 views

Get R^2 value between interpolating functions and a list of points

I am looking to compare the degree of accuracy of a theoretical model by comparing my theoretical curve to my experimental data points. My theoretical curve is an interpolating function generated ...
0
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0answers
34 views

How to fit a spline (not interpolate) through points in 3D?

I have coordinates of points in 3D and want to fit a spline through these points. I found a least square approach for 2D case: https://demonstrations.wolfram.com/...
1
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1answer
81 views

How to fit spline through points in $ \mathbb{R^3}$?

I have coordinates of points that represent a curve (for example, helix or centerline of moebius strip) in $ \mathbb{R^3}$. I want to fit a Bspline through these points. How to do this in Mathematica? ...
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3answers
138 views
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1answer
26 views

I am having trouble with the Show[] section of this code

Question: I am unsure how to graph the interpolated graph with the regular graph on the interval [1,4]. Not even the Show line works about im pretty sure its written correctly. Clear["Global`*"] f[...
0
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2answers
108 views

Non-linear differential equation with tricky variable dependence

My problem regards solving a differential equation and can be reduced to the problem of finding $f(x)$ such that $\frac{df}{dx}=\frac{dh}{df}$, with $h(f)$ a known function. I have this list of data,...
2
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1answer
38 views

Interpolating and subtracting two sets of data

I have a data set "data9k" with x varying from 0 to 365, and another data "data0" set with x varying from 0 to 365. But the x values for both data sets are not same but similar. I want to subtract the ...
0
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1answer
132 views

Is it possible to fit such a large range plot in mathematica?

I am trying to solve the coupled differential equation numerically with Mathematica. But the range of values are large so mathematica cannot give correct plot. Here is the code: ...
24
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4answers
6k views

Data interpolation and ListContourPlot

I am fairly new to Mathematica and I have two quick questions on using it for a Hydrology and Hydrogeology class. One is about data interpolation and interpolating without any data defined in an area. ...
6
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1answer
140 views

How can I accelerate repeated interpolation of a very large dataset?

I am solving a 4D time-dependent PDE using a discretization method. My query is not about solving this; because I am doing it in the following code. The code is OK and it works fine. My main problem ...
3
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0answers
49 views

Extracting part of an Interpolating Function [closed]

I get an InterpolatingFunction, call if F1, as a solution to NDSolveValue. I then need to do further operations on this function. However, I only need to work with a small part of the domain of the ...
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2answers
48 views

How can I convert a matrix of 3d experimental data into a 3d list which can be interpolated in a f(x,y) function

I have a 3d experimental *.txt data with the form: y1 y2 y3 x1 f(x1,y1) f(x1,y2) f(x1,y3) x2 f(x2,y1) f(x2,y2) f(x2,y3) x3 f(x3,y1) f(x3,y2) f(x3,y3) I need to ...
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1answer
185 views

Meaning of InterpolationOrder -> All for multidimensional interpolation

What specific method does Interpolation use for unstructured multi-dimensional data when we set InterpolationOrder -> All? ...
4
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3answers
127 views

questions about InterpolationOrder

I have a function $C_0(x)=e^{-(x-2.5)^2/2.0}$ which is differentiable to infinite order. I want to approximate the function with Interpolation such that it is smooth until 10th derivative. Here is ...
0
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2answers
55 views

Better fit for points with exaggerated deviations

I used the InterpolatingPolynomial function to get a polynomial that meets my points. But I noticed that there is a deviation in the final intervals. ...
2
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2answers
150 views

How to use NDSolve with limited RAM?

How can I use NDSolve when running out of RAM? The code I am implementing: ...
1
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1answer
32 views

NSolve with Interpolation function

I am trying to apply NSolve to an Interpolation function which I have evaluated before. For a function of 1 argument everything works out but as soon as I try to apply the procedure for a function of ...
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2answers
78 views
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1answer
58 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: ...
2
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1answer
41 views

Narrowing the range of an interpolating function while keeping integral the same?

Consider an interpolating function derived from some data, e.g. ...
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1answer
53 views

Factor to measure polynomial fit

I am trying to use InterpolatingPolynomial to fit a polynomial to a given set of points representing a relationship between two variables. I would like to find a ...
3
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2answers
175 views

How do I restrict an interpolated function to only take values > 0?

I have a list of points which looks like this when plotted with Joined -> True: I'm interested in the area under the curve with x-axis > 0 as a ratio to the ...
4
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2answers
106 views

Plotting perpendicular lines to a contour plot (electric field from equipotential curves)

I'm currently working on a experiment about Electric Fields and Equipotential Curves. The problem is that I want to plot (estimate) the curves of electric field using the fact that every one of these ...
6
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2answers
788 views

Integration of Interpolated function take an unacceptable amount of time

I have a simple integration which, when using an interpolation function, is taking too long to calculate: ...
3
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0answers
89 views

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 ...
0
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0answers
51 views

How to apply the utility Packages for Numerical Differential Equation Solving

I have solved two coupled equations with {Solf, Solg} = NDSolveValue[eqns, {f, g}, {x, 0, L}, {t, 0, tmax}] and want to extract the computational grid ...
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1answer
85 views

Interpolating 3D noisy data

I have some noisy 3D data that looks like this: ...
7
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1answer
198 views

How do you interpolate outside the range of data?

I've got a simple interpolation function using data from an external program. For values above 3,000, the function reaches a limit. ...
1
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1answer
64 views

Regression to fit data with an integral equation

I have a set data and I know that this data are best fitted by the following equation, assuming that f($\tau$) is a log normal distribution and $M_{eq}$ = 1.5: $M(t,\tau)= M_{eq} \int (1-e^{-t/\tau}) ...
1
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1answer
55 views

Interpolating data from Excel

Sorry for the probably mainstream question, but I have not found the answer I was looking for yet. I have this Excel file: https://drive.google.com/file/d/1UhkYdoaqXQIsf6opOx-EBgG7xPxxHga3/view and I ...
4
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1answer
167 views

Saved InterpolatingFunction behaving badly

Bug introduced in 10 and persists through 12.0 or later I created this InterpolatingFunction, and NIntegrate gives an absurd ...
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0answers
47 views

Interpolation of multidimensional data: some domains are lost

I am trying to make a reasonable interpolation of a dataset having the form dataset = {{x1,x2,x3,f[x1,x2,x3]},...}. I to the interpolation in the following way: <...
0
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1answer
125 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 values ...
1
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1answer
70 views

How to make that interpolation?

I have the following dataset: SetDirectory[NotebookDirectory[]]; TableSpectrum = Import["spectrum.dat", "Table"]; I want to make the interpolation. However, when ...
4
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2answers
133 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<...
0
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1answer
34 views

TargetUnits aren't working as expected on an InterpolatingFunction

Short version: My understanding of the use of TargetUnits in a Plot statement is that if the function being plotted has units, MMA will attempt to convert the output of that function to the unit form ...
3
votes
0answers
82 views

How to use an interpolating function as an intial condition for a PDE? [closed]

I want to be able to approximate a PDE, but my eigenfunction is an Interpolating function. Is there a way I can use an interpolating function as an initial condition in the PDE. For Example: ...
21
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1answer
628 views

Mismatch between Mathematica and COMSOL in 3D FEM problem

I would like to solve an advection-diffusion problem on a torus domain. There are three Dirichlet conditions: One at the inlet (concentration $c=0$), one at the outlet ($c=0.5$) and one at the wall ($...
2
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2answers
129 views

Fitting two-dimensional data

For this question, I cannot use random sample data. So the actual data can be found here. The data file contains three columns, where the first two are the coordinates $(x,y)$, while the third is the ...
3
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1answer
55 views

Problem with interpolating function returned by NDEigensystem

I'm trying to evaluate interpolating function returned by NDEigensystem at a point but Mathematica won't evaluate it. ...
1
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1answer
64 views

Transpose Error

I have this code: ...
7
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1answer
103 views

Weird behaviour for a vector InterpolatingFunction inside an NDSolve

I have run into some weird behaviour on the part of NDSolve which I find pretty bizarre and which I would like to understand better. Suppose, for the sake of ...
1
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2answers
72 views

Interpolating missing data

I have a data set that contains data of the form (x0, y0, f1, f2, i1, i2, i3). The (x0, y0) are the coordinates, while the values f1 and f2 are real numbers (i1, i2, i3 correspond to some integers ...