# Questions tagged [interpolation]

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

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### Interpolation,graph

I need to make a program in which for a function f(x) = e× ×(2x-7) / ( 3x2-4x+11) and values { 0,1,2,3,4,5,6} finds cubic spline interpolaric function for the corresponding values amd draw a graph for ...
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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 second derivative is ...
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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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### 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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### 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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### 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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### 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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### Is it possible to obtain the algebraic expression of an InterpolatingFunction? [duplicate]

Up until now, I have been trying to obtain an expression for an InterpolatingFunction obtained from NDSolve, by using the ...
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### WhenEvent action won't be applied (+ strange problem?)

I'm building a project about the dynamics of a 9-conf robotic industrial arm. I've come to the point where I have to integrate the solution of differential equations for a couple of movements, but can'...
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### 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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### How to combine NDSolve interpolating functions?

In the following working example ...
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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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### 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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### 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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### finding the correct interpolation accuracy [closed]

Ciao, I need to interpolate this data: ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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/...
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### 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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### Interpolation[] gives negative values when all the initial data is positive

I have this data: ...
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### 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 even if I'm pretty sure ...
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### 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 ...
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### 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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### 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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### 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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### 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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### 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. ...
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### 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: ...
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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 ...
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### 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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### How to use NDSolve with limited RAM?

How can I use NDSolve when running out of RAM? The code I am implementing: ...
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### 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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### 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 ...
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### 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: ...
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### 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 ...
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### 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: ...
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### 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 ...