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

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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 ...
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4answers
898 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 ...
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Evaluating interpolating functions embedded in equation [closed]

I have created an interpolating function v(x,y) that contains an interpolation. When called, it returns an equation that contains embedded interpolating functions. ...
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0answers
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how to find interpolating bicubic surface given a 4 x 4 grid P of 3 D points and parameter values? [closed]

The bicubic surface is N B M = P where N is the u parameter Vandermonde matrix and M is the v parameter matrix, B is the matrix of unknown control points, P is the matrix of given 3D points. The ...
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1answer
48 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): ...
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2answers
292 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 ...
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1answer
83 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 ...
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1answer
29 views

Interpolate a data set for a defined time-step

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

Overriding default ExtrapolationHandler

When modeling systems with WhenEvent and NDSolve I found that the default extrapolation settings used in the returned ...
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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? ...
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0answers
56 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 ...
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0answers
36 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 ...
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2answers
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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 ...
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1answer
51 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 ...
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0answers
52 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 ...
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0answers
49 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 ...
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1answer
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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 ...
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2answers
80 views

Extract one dimension from an n-dimensional InterpolatingFunction

How can I extract a single dimension from an InterpolatingFunction? As an example: ...
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4answers
107 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 ...
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1answer
69 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 ...
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2answers
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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 ...
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1answer
52 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
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1answer
90 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
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1answer
181 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 ...
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1answer
114 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): ...
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2answers
757 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 ...
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2answers
102 views

Integrating an interpolating function

I have been using the following NDEigensystem command to generate the eigenfunctions of the laplacian with a square domain: ...
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1answer
71 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 ...
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1answer
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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 ...
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2answers
55 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. ...
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1answer
131 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 ...
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2answers
86 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; ...
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1answer
71 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: ...
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2answers
54 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 ...
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1answer
45 views

How to exchange interpolating function results of NDSolve between different platforms?

For example, I have a interpolating function solution by NDSolve in a windows x64 platform and want to share the result to users in other windows x86. I tried the DumpSave and ".mx" binary format, ...
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2answers
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Using ListInterpolation to get a vector-valued function

I wanted to construct a ColorFunction from an image, so I tried ...
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1answer
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Why does `ListInterpolation` convert integers to reals in the internal representation?

This problem is mentioned in my self-answer here. Here is an illustration of the problem: ...
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1answer
75 views

How to fix the error InterpolatingPolynomial::ipdup: The abscissas are not distinct [closed]

I'm trying to plot the function Abs[InterpolatingPolynomial[..] - f[x]] where f is a function. I receive the error: InterpolatingPolynomial::ipdup: The ...
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2answers
3k views

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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2answers
796 views

Finding a 3d curve from torsion and curvature with NDSolve

I'm trying to use the Frenet–Serret formulas to find the curve that matches the torsion and curvature I specify numerically with an InterpolatingFunction. The ...
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1answer
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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 ...
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2answers
137 views

Unexpected view of the Comsol result when I postprocess it in Mma

I simulated some nonlinear PDE using Comsol. Here one can find the results u=u(x,y) in the form of an Excel table with the terms ...
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2answers
131 views

Getting an explicit representation of the function returned from Interpolation [duplicate]

I am using Interpolation to get an InterpolatingFunction that fits a set of points. For example, ...
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1answer
67 views

Interpolate the discrete list into continuous function

I have a data whose list plot shows up following graph I would like to interpolate the missing data and make the function continuous but for particular x-coordinate there is multiple values of $y$ ...
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1answer
95 views

FindRoot of interpolating function from NDSolve

I am having issues finding the root of an interpolating function obtained from NDSolve. For example: ...
9
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1answer
136 views

Non-rectilinear integration of InterpolatingFunction

Bug introduced in 7 or earlier and persisting through 10.3.1 [CASE:3487737] I have a 2-d array that I would like to resample into a different coordinate system and integrate along one of the new ...