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

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1answer
26 views

Reduce array to specific amount of averages

The main issue which needs to be solved is: Let's say I have an array with 8 numbers, e.g. [2,4,8,3,5,4,9,2] and I use them as values for my x axis in an coordinate system to draw a line. But I can ...
4
votes
1answer
98 views

Defining a region from combination of data and geometric region

I would like to define a region in (x,y) by combining the region RegionPlot[ ImplicitRegion[ Sqrt[x^2 + y^2] <= 0.99, {{x, 0.01, 0.99}, {y, 0.01, 0.99}}]] ...
5
votes
2answers
122 views

How to speed up Integration of interpolation function?

I have a list of data and interpolate it to a function. Then I need to done something integration with the interpolation function. But I found the speed is unacceptable slow. My data is here (a ...
0
votes
0answers
26 views

Eigenvalues of a symbolic matrix using interpolating function

I have a 6x6 matrix with entries that depend on dependent and independent variables of an interpolating function. I would like to be able to evaluate the eigenvalues of this matrix using the ...
3
votes
2answers
228 views

Mathematica Interpolation or approximation

I have lists of points X and Y. {1212,1216,1217,1219...}, {1,2,3,4,5,6...} I combine ...
1
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2answers
61 views

Plotting the InterpolatingFunction from NDSolve [on hold]

I want to plot the solution of a differential equation which i solve it numerically with NDSolve. Here's the code: ...
0
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2answers
63 views

Interpolation of a vector [on hold]

How can we use a sample data for interpolation of a function within a domain. But I need all interpolated values at once in a vector format. For instance, below I create a range of values for ...
1
vote
1answer
76 views

How to make a 3D surface plot from DataSet

I am trying to plot some Aerodynamic data. I import my data like this: data = SemanticImport["roll-damp-due-to-roll-rate-semantic.csv"] The CSV file can be found here: data I want to make a 3D ...
0
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0answers
39 views

Extract Hermite Polynomial from Interpolation of Data

I have a set of data points which I interpolate like s = Import["data.dat"] sinterp = Interpolation[s] LogLogPlot[sinterp[x], {x, 100, 10000}] which gives me ...
0
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0answers
36 views

NIntegration and NDSOLVE and Interpolation [closed]

I am working on the Duffing equation to calculate the residual error from the x'[t] solution after integrating the Duffing once but the accuracy is not good I ...
1
vote
1answer
44 views

How to apply hermite InterpolatingPolynomial?

I found that to do hermite InterpolatingPolynomial I need to write: InterpolatingPolynomial[{{{1}, 2, 3}, {{2}, 6, 7, 8}}, x] however,i need to apply it on a ...
5
votes
1answer
121 views

How can I get the interpolation line from Listplot?

My discrete data is: data={{1., 5827.}, {3., 6242.}, {15., 6066.}, {60., 5972.}} I want to get the interpolation line from ListPlot: ...
14
votes
2answers
1k views

Getting an InterpolatingFunction from a ContourPlot

I have a function, say minimizeme[Ω_][β_][ϵ_] = ϵ^2 Ω - Log[2 (Cosh[2 β] + Cosh[2 β ϵ])]/(2 β); I want to find its critical points in $\epsilon$ for a given ...
1
vote
0answers
82 views

DeleteDuplicates [closed]

After having applied "DeleteDuplicates" to a list of data (15000 rows per 3 columns), when I try to interpolate that list of data it gives me back again: "There are duplicated abscissa points in.." ...
6
votes
2answers
137 views

Using ListInterpolation to get a vector-valued function

I wanted to construct a ColorFunction from an image, so I tried ...
0
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0answers
43 views

Check if interpolated function passes through a specified region

Is there an efficient way to check if a curve that was obtained as an Interpolating Function (from solving differential equations numerically) passes through a given region? I am solving for two ...
0
votes
2answers
67 views

Using an interpolating solution of NDSolve into an algebraic expression

I would like to use the interpolating solution of NDSolve into an algebraic expression without creating a system of a differential equation and algebraic equation. The example is the following, the ...
9
votes
4answers
914 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 ...
1
vote
1answer
55 views

FunctionInterpolation on a 2D function does not match original function when plotted together

I met with a problem when trying to find the interpolation function of a 2 variable function. The function is like below (already simplified for brevity): ...
14
votes
2answers
314 views

Finite Element Method and ElementMeshInterpolation issue in v10.3

Bug introduced in 10.3 I recently installed Mathematica v10.3 and checked a project I was working on few months ago under Mathematica v10.1. In this project I solve a PDE with ...
1
vote
1answer
89 views

Solve the interpolating function

I would have asked how to obtain the x given the y in an interpolating function, and I found the answer from here. But another question raised. I was dealing with measurement of the spectral ...
1
vote
1answer
29 views

Interpolate a data set for a defined time-step

I have a set of data which looks like: ...
4
votes
1answer
89 views

Overriding default ExtrapolationHandler

When modeling systems with WhenEvent and NDSolve I found that the default extrapolation settings used in the returned ...
4
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0answers
43 views

Multi-variable FunctionInterpolation with the range of one variable as a function of another

How can I modify my FunctionInterpolation code so that the boundary of one of the variables is a function of another variable? ...
1
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0answers
60 views

Obtaining values from interpolating functions

A similar question has been asked in the post HERE but the current question is more complicated: I have the following differential system ...
0
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0answers
38 views

NSolve with a term that is an interpolating function

I need to solve this system of equations Log[np[x]] + psi[x] + f[np[x], nm[x]] == 0 Log[nm[x]] - psi[x] + f[np[x], nm[x]] == 0 For ...
8
votes
1answer
193 views

Produce a spline from a set of {{x, y}, z} points and get its parameters/expression

I have produced a set of points in a variable of the type {{x1, y1}, z1},{{x2, y2}, z2}, ,... }, where {x, y} should be the ...
3
votes
1answer
55 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 ...
1
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0answers
56 views

Smoothing ListContourPlot contours for unstructured grids. Part 2

My question is motivated by the following discussion. Smoothing ListContourPlot contours I need to generate high-quality contour plots for some property generated on a non-rectangular grid. This is ...
1
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0answers
54 views

How to use interpolating functions in NSolve with a piecewise function?

I have a system of two non-linear differential equations that are piecewise, the solutions of which I would like to use to obtain the values of a third variable that is also piecewise. I have trouble ...
4
votes
1answer
120 views

interpolating a smooth closed surface to a non-uniform data set (ListSurfacePlot3D)

I want to generate a smooth coloured surface from a discrete set of points of the form {x,y,z,F} using the ListSurfacePlot3D. My data set is quite non uniform; the ...
4
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2answers
83 views

Extract one dimension from an n-dimensional InterpolatingFunction

How can I extract a single dimension from an InterpolatingFunction? As an example: ...
2
votes
4answers
115 views

2D interpolation

Consider following series of functions Do[f[k][w_] = Exp[-(w-Sin[k])^2], {k, 10}] depicted as Let us tabulate and interpolate them ...
3
votes
1answer
70 views

NDSolve with an interpolating function in Piecewise

Again I have question I hope someone can answer. I made a very simple example illustrating my more difficult problem. I want to solve a differential equation numerically with a conditional in the ...
15
votes
2answers
2k views

Find maximum value of interpolation function - obviously wrong result

Minimizing and maximizing interpolation function has already been asked and answered, see here for example. Yet, I observe a strange behaviour. Well, I can understand that the wrong guess of ...
1
vote
1answer
54 views

Merging of multiple 3D plots with Show using unified ColorBar

This question follows my initial question that can be found here. I created the following 4D plot (3 spacial coordinate + color) by interpolating points separately. The full data (1.4Mb) can be ...
2
votes
1answer
92 views

Results of ArgMax as a function of a parameter with InterpolatingFunctions

I would like to obtain a function and its derivatives, where the function is defined as the solution to a maximization problem. The obvious approach ...
5
votes
1answer
200 views

Smooth 3D plot with colour of scattered data

I have a set of scattered 3D points with coordinate (x,y,z) and an intensity associated with it. I would like to do a smooth surface with the intensity being represented by the colour. My points ...
3
votes
1answer
116 views

Strange extrapolation in ListContourPlot?

I have some Table of {x,y,z} values (energy as a function of radial and azimuthal frequencies in a galaxy if you care to know): ...
1
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2answers
778 views

How does ListPlot3D interpolate data?

I have data of the form {{x1, y1, f(x1, y1}, {x2, y2, f(x2, y2)}, ...}. I need to interpolate the data to get an interpolated ...
4
votes
2answers
107 views

Integrating an interpolating function

I have been using the following NDEigensystem command to generate the eigenfunctions of the laplacian with a square domain: ...
2
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1answer
76 views

Help with Time-Seried dataset

I can't seem to figure out the best way for directly inputting interpolated values into a dataset. I turn to your expertise for guidance. So, I have a multi-year time-series dataset. Column 1 is time ...
8
votes
1answer
182 views

Bug? Problem with derivative of interpolating function from FEM

Bug introduced in 10 or earlier and fixed in version 10.4 I am really not sure if this is a bug or I am missing something very trivial. QUESTION: What I am missing in order to obtain the partial ...
3
votes
2answers
56 views

Numbering indices / array element positions while creating an array (using 3 argument form)

I am new to Mathematica and trying to create a list that I can use within the InterpolatingPolynomial function. e.g. ...
5
votes
1answer
135 views

FunctionInterpolation error when specifying AccuracyGoal

Bug introduced in 8 or earlier and persisting through 10.4 or later In the help page ref/message/FunctionInterpolation/ncvb, it is mentioned that one should ...
0
votes
2answers
92 views

Plotting the solution of a differential equation with its derivative [closed]

The question requires checking of numerical solutions to a differential equation by substituting in those solutions. The original equation is as follows; ...
1
vote
1answer
77 views

Interpolation of a border between regions in ListDensityPlot

Let's say there is a scalar field dependent on two coordinates {x,y}, so a set {x, y, f}, and I use a ListDensityPlot to plot it: ...
1
vote
2answers
58 views

Export NDSolve data

I have calculated a solution of a system of differential equations using NDSolve and generated a plot. How could I extract the data of the solutions? The input is ...