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

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0answers
41 views

Error message when using Method -> “Spline” in Interpolation

I'm using LTNOspline = Interpolation[DiscreateLT, Method -> "Hermite"] where ...
2
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3answers
201 views

Approximation of definite integral by parabolas

This question is related to Trapezoid approximation to definite integral. As promised, I am now asking about how to draw an approximation of integrals by parabolas. I tried to modify MarcoB's code, ...
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1answer
89 views

Importing Data to interpolation

I have an external file in extension XLS with looks as follows: This file can be obtained by the link below: Velocidade Angular With certainty this file is generating a list inappropriate for the ...
5
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3answers
228 views

How to get the coordinates of the intersection of two lines from a ListLinePlot?

Suppose I have two curves intersect at some point, how can I read the coordinates from the graph, not read by eye, but find it with more precision by computer. For example, here are two lists created ...
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1answer
104 views

Approximating Integral under 2D Interpolation function

First, I have already been working on this problem, and have asked a similar question previously here. I am trying to find the integrals of 2D interpolation functions that are output from ...
4
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5answers
606 views

Interpolation gone awry?

Here's a simple example of an interpolation function that seems to me to have gone awry. Maybe someone would be so kind as to tell my what's going on with this? ...
3
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2answers
68 views

How to get value from InterpolatingFunction

I have numerically solved a system of ODEs using NDSolve. I can plot them using ParametricPlot but I am having trouble evaluating them at specific points and ...
2
votes
1answer
67 views

Offset parametric curve

I have a function ($a(x)=0.00005x^4-0.01x^3+0.68x^2-23.087x+322$) which defines a profile desired. I need to get a new function that is shifted relative to the first function using a list (...
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0answers
42 views

What is the Chebyshev method for `InterpolationFunction`?

With InterpolationOrder -> All, some methods of NDSolve returns interpolations with ...
13
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2answers
610 views

Data extraction from a picture of a graph

How can I extract data from this picture of a graph? i = Import["http://i.stack.imgur.com/Ac8m0.png"]; The caption of the picture reads: " Two-dimensional ...
3
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3answers
267 views

Error when compiling function containing InterpolationFunction [duplicate]

I'm trying to solve a coupled ODE system using NDSolve. The coupling can turn on and off in some regions, and when the coupling is off, the solution can be written ...
2
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1answer
147 views

How to generate specific function using BSpline command?

I want to generate an approximation function that fits a curve to points. My goal is to obtain an actual formula. Is this possible with BSplineFunction? Using the ...
7
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2answers
132 views

Inflection point and curvature

Through a coordinates list and then interpolating them I got a $f[x]$. ...
1
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0answers
59 views

Getting FindRoot::nlnum when trying to find root of an Interpolating function [closed]

I want to solve a system of differential equations and find a point where the solutions cross. So four steps: 1. Solve the system of differential equations: ...
1
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3answers
70 views

Derivative of a 2D Interpolating function

I cannot find a way to obtain the partial derivatives of a 2D Interpolating Function obtained with ListInterpolation. I didn't find anything useful on the web. Any ...
0
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0answers
33 views

Interpolation function inside a numerical integral [on hold]

Hello all and thanks in advance for your comments, I will be brief to explain my doubt. If you need any more information, please ask me. I have an interpolation function which comes from the ...
1
vote
1answer
47 views

Integration of a function of interpolating functions

I need to calculate the integral of a function of interpolating functions. Being more specific, the function I want to integrate is the following ...
1
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1answer
50 views

Partial Differentiation with interpolation function

I'm trying to take the partial differential of each component of an interpolation summed together. It works fine when I do it with an algebraic expression, but I can't understand why it doesn't work ...
3
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2answers
67 views

Picking a dimension from an interpolating function

I have an interpolation function. Lets think of it as f={fx,fy,fz}. I would like to operate on the fx part of interpolation and say, multiply it by five and plot ...
4
votes
1answer
118 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}}]] ...
0
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1answer
39 views

Interpolating data while imposing the behavior of a cumulative distribution function

I would like to interpolate a data set which represents a curve of an empirical cumulative distribution function (CDF). Hence, the y entries are between 0 and 1, continuous and non-decreasing, and at ...
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2answers
82 views

Interpolating initial conditions of orbits

I have a data file containing the $(x,y,p_x,p_y)$ initial conditions of two-dimensional orbits. Let's plot them on the $(x,y)$ plane. ...
1
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1answer
71 views

Predicting the initial conditions of orbits inside a closed curve

I have a data file containing the four orbital element $(x,y,p_x,p_y)$ of a two-dimensional closed loop orbit. Note that the exact implicit equation of the orbit is not known. The plot of the 2D ...
0
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1answer
30 views

Defining a function using an InterpolatedFunction from a data set

suppose I have two data sets A and B, which are tables/lists/arrays/whatever Mathematica calls it, from an imported CSV. there'd be lines that look like this: ...
2
votes
3answers
113 views

How to integrate numerically the product of result of NDsolve? [closed]

I am going to integrate the product of the results of NDsolve, in fact If x and y are the results as interpolating function, How I can integrate x*y numerically? <...
2
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3answers
130 views

NDSolve and differentiation of Abs

I have found several questions about the derivative of Abs and how it is not defined in the complex plane. What I have not found yet is a precise and simple ...
5
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1answer
92 views

How does ListInterpolation work?

ListInterpolation takes an array of data and interpolates between the entries. Let us interpolate between the elements of the identity matrix. For reference, this ...
8
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1answer
54 views

Is there a way to change the interpolation scheme used in ListDensityPlot?

Recently I was trying to answer this question on how to make a smooth ListDensityPlot when I found that the output depends on the order of the data if you are using ...
6
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1answer
152 views

Smoothing out data points in a ListDensityPlot

I stumbled upon this problem when I was trying to make some nice smooth ListDensityPlots of my numerical data. In short, my problem is that I let Mathematica plot two copies of basically the exact ...
0
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0answers
63 views

How to plot an interpolating function from data showing the median values and the scatter around the medians

I have a list of data points $x_{i}$, $y_{i,16}$, $y_{i,50}$, and $y_{i,84}$ where $y_{i}$ respectively correspond to $16th$, $50th$ and $84th$ percentiles value of the function at positions $x_{i}$. ...
5
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3answers
242 views

How to (correctly) interpolate an array of points?

I'm trying to obtain an interpolation function for points of an x^(-5) function (which goes to infinity at x = 0). ...
13
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4answers
566 views

Quirk in VertexColors interpolation when displaying Polygon

When using VertexColors, the docs state: The interior of the polygon is colored by interpolating between the colors specified by ...
12
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2answers
665 views

Joining points into 3D surface

This seems like a simple problem, but I can't find any questions like it here so I'm making a new one. Apologies if I missed one. I have a list of points contained in a file which can be visualized ...
5
votes
4answers
220 views

Interpolation of unevenly spaced data, is it possible?

I need to interpolate data, that consists of many points in the beginning and a few in the end of the interval, like in the following example: ...
28
votes
2answers
4k views

Joining and interpolating data points

I wonder what is the best practice for interpolating curves? Usually, I'm using BSplineCurve and adjusting SplineWeights so it ...
0
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0answers
28 views

Putting constraints on interpolation [duplicate]

I am attempting to construct a function by interpolation, but I'd like it to be strictly increasing and convex. Is there an easy way to add constraints to Interpolation or should I change it further ...
5
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1answer
73 views

FunctionInterpolation produces many error messages when given high-precision input [duplicate]

Both FunctionInterpolation[1, {x, 0,1.00000000000000004}] and FunctionInterpolation[1.00000000000000004, {x, 0, 1}]; ...
5
votes
2answers
184 views

How to speed up Integration of interpolation function?

I have a list of data, and I interpolate it to a function. Then I need to do an integration with the interpolating function. But I found that the speed is unacceptably slow. My data is here (a little ...
4
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0answers
64 views

N[Integrate] failing to return an accurate result from an interpolated integrand

I need to N[Integrate] a function Cos[alpha*x]*f(x) between x=0 and 30 at increasing alpha-values. Here f(x) is an interpolated function derived from a set of 120 ...
0
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1answer
51 views

Reduce array to specific amount of averages [closed]

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 ...
3
votes
2answers
263 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 ...
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vote
2answers
75 views

Plotting the InterpolatingFunction from NDSolve [closed]

I want to plot the solution of a differential equation which i solve it numerically with NDSolve. Here's the code: ...
2
votes
1answer
105 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 ...
1
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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
128 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: ...
15
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
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0answers
84 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
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2answers
149 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
46 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 ...