Questions tagged [interpolation]

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

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163 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 ...
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2answers
41 views

Testing Positivity of Interpolating Function

I have an interpolating function and I want to test whether it is positive definite over an interval. Will any of Mathematica's numerical optimisation functions work for this or is there a simpler ...
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855 views

smooth spline through airfoil coordinates

I am trying to produce a smooth spline curve through a set of airfoil coordinates. An example for the data I am trying to use is here, and I am reading the file like so to get rid of some extraneous ...
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2answers
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How to make a natural cubic spline of {{x,y}, …} data

Consider data = {{0, 0}, {1, 0}, {2, 0}, {3, 1}, {4, 0}, {5, 0}, {6, 0}}; f = Interpolation[data, InterpolationOrder -> 3, Method -> "Spline"]; Then the ...
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1answer
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Find the two largest maximums of an interpolating function of a specific shape (fast)

I have an oscillating interpolating function f[x] and I would like to find the x values of the two largest maximums (or even ...
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Why do some uses of PropertyList crash the kernel?

Bug introduced in 10.1.0 or earlier and fixed in 12.1.0 While looking at the question How to evaluate the "Domain" of an InterpolationObject? I noted that using ...
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1answer
162 views

Different results using spline interpolation in Wolfram and MATLAB

I use the same data for interpolation in Mathematica and MATLAB, but the result is different. ...
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4answers
189 views

Can I Constrain ListInterpolation by Curvature?

Using image analysis, I have found the positions of a circular ring and imported them as xx and yy coordinates. I am using ...
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1answer
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Hermite interpolation

The well known Hermite interpolation uses piecewise cubic polynomials and fits the knot values and derivatives. In contrast the Mathematica piecewise Interpolation ...
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1answer
648 views

Hermite method in Mathematica

When I solve the example below, in the results it is mentioned that Mathematica 10 has used the Hermite method. I cannot find anything about this in the Mathematica documentation. Is there nothing ...
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NIntegrate 3D Interpolation function in a region extracted from ListContourPlot3D

I have a list of 3D volumetric data points, e.g. for every position in 3D space there is a value. What I want to do is to firstly use "Interpolation" to get a function form of the data f[x,y,z] and do ...
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2answers
60 views

How can I make ListDensityPlot show up only in a specified region?

Disclaimer: I am new to Mathematica and this is my first post here! I am trying to plot EEG data of different intensities of brain waves from an FFT to areas of the brain where they were collected. I ...
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Interpolating a density plot

I am solving a complicated series of equations (involving FindRoot and PolyLog), and finally I get this plot Code here: ...
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3answers
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Is it possible to compute with the trapezoidal rule by numerical integration?

Is it possible to compute trapezoidal rule numerical integration? I know that Mathematica has Interpolation, and that a list of points can be interpolated and then ...
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1answer
38 views

How to convert Piecewise function to Interpolation function?

In the following piece of code I am trying to convert a Piecewise function to a simple interpolation function f[t_] ...
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1answer
139 views

How to interpolate {{xi,yi},… ,{xn,yn}} with minimum bending energy?

Thin Plate Splines are explained here, and a Mathematica implementation of that for real samples { { x1, y2, z1 }, { x2, y2, z2 }, ... , { xn, yn, zn } } is ...
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1answer
51 views

How can I force an interpolated function to go through a certain point?

Let's take this interpolated function: f = ListInterpolation[{1, 2, 3, 5, 8, 5}] I want to make 1/f'[x] go through a certain ...
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2answers
73 views

Integral of a Wavelet function

I ran into problems integrating a function which contains both an If condition and a Wavelet which is an ...
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7answers
7k views

Extracting the function from InterpolatingFunction object

I've used Interpolation[] to generate an InterpolatingFunction object from a list of integers. ...
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46 views

How to extract the domain of the definition of the interpolating function? [duplicate]

When calling the interpolated function without specifying the value of the argument, Mathematica displays its domain of the interpolation. How to extract it?
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2answers
102 views

Extracting data from InterpolatingFunction 2D surface plot

I would like to directly extract the surface plot data from the solution to a differential equation (using NDSolve). While there are many examples of this I haven't been able to find an example in 2D. ...
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1answer
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Interpolation undefined on domain

I have made an interpolation of two variables of a fairly large set of numbers imported from a file (4 million lines in an .m file written out with C++). The ranges of the two parameters is 0 to 2.5 ...
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1answer
155 views

How to combine NDSolve interpolating functions?

In the following working example ...
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1answer
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How to interpolate a set of points with given local extrema?

I have a set of points on the 0xy plane: say (-3,0), (-2,4), (-1,0), (1,2), (3,0), (5,1), (6,0), (8,-2), (10,0) I would like to use software, like Mathematica, ...
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2answers
82 views

Interpolating a list

Here is a sample list data = {{1, 2.1, 55.2}, {2, 2.7, 60}, {3, 3.1, 65}, {4, 3.5, 67}, {5, 4.5, 72}, {6, 4.2, 77}, {7, 5.9, 80}} which contains three rows. Now,...
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0answers
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DumpSave and precision of interpolation data

Consider the following prec = 32; x = N[Range[0, 1, 1/10], prec]; f = Interpolation[Transpose@{x, x}]; Then ...
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1answer
40 views

finding the correct interpolation accuracy [closed]

Ciao, I need to interpolate this data: ...
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1answer
57 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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3answers
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Creating a 3D List Line Plot From Discrete Points

Given the following Runge-Kutta ODE solver and the graphical output below, how do I get a 3D line plot instead of a 3D point plot? I see that there is no ListLinePlot3D function, so I thought it might ...
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2answers
74 views

Change Equation E(T,u) and N(T,u) in T(E,N) and u(E,N)

I am pretty new on mathematica and I have three functions, each defined by an analytic expression: ...
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1answer
41 views

Interpolation of a “bit by bit” Function

I am facing a problem with integrating a function. I have to integrate the function "bit by bit". This is the smallest working example that shows the problem: ...
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1answer
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Integrating a function “bit by bit”

I am trying to integrate a function. But for this task I need to do it "bit by bit". I created a working example that shows the problem. ...
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1answer
52 views

InterpolatingPolynomial defining x

So InterpolatingPolynomial use integer x values? How do i manipulate them? InterpolatingPolynomial[FUNCTION of x, x] Guess i quite don't get the function definition cause my code is not working ...
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Plot function for interpolation not working? Messed something up [help]

$\left(\begin{array}{ccccc}{1} & {x_{0}} & {x_{0}^{2}} & {\dots} & {x_{0}^{n}} \\ {1} & {x_{1}} & {x_{1}^{2}} & {\dots} & {x_{1}^{n}} \\ {\vdots} & {\vdots} & {\...
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2answers
138 views

Bug in VectorFieldPlot[] with InterpolatingFunction[]?

Bug introduced in 11.3 or earlier and persisting through 12.0.0 or later While looking at https://mathematica.stackexchange.com/questions/192081/how-do-i-plot-a-divergence, I thought to suggest the ...
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0answers
43 views

Predicting value outside data set

I have a list with values at some points: ...
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2answers
50 views

Interpolation to generate elements?

I have a list with values at some points: ...
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1answer
178 views

Solving partial integro-differential equation

I want to solve a partial integro-differential equation of this form: using NDSolve, something like ...
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0answers
37 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
210 views

Unstable NIntegrate result vs plot

Here I have a $\Psi$ function with a few arguments: ...
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1answer
120 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 $...
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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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2answers
530 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
74 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 ...
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3answers
272 views
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2answers
113 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,...
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1answer
49 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 ...
27
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4answers
7k 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
156 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 ...

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