# Questions tagged [interpolation]

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

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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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### Successive Numerical integration with interpolation [closed]

How to perform successive integrations with interpolation in mathematica with sinusoidal arguments (F, C1(w) and C2(w)). Note: F' has to be done by NIntegrate F'' has to be done by Interpolation. \...
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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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### 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 Failing on Data of a Certain Size [closed]

I'm trying to interpolate the following unstructured data set so I can compute and plot the gradient. ...
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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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### 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 ...
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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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### How can the behavior of InterpolationOrder->0 be controlled?

In ListPlot and Interpolation, the option InterpolationOrder->0 uses two different ...
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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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### 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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### 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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### 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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### 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. ...
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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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### Meaning of InterpolationOrder -> All for multidimensional interpolation

What specific method does Interpolation use for unstructured multi-dimensional data when we set InterpolationOrder -> All? ...
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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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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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### 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 ...
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### 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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### Interpolating 3D noisy data

I have some noisy 3D data that looks like this: ...
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### 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. ...
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### 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}) ...