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

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Interpolation function inside a numerical integral

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 ...
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1answer
9 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 ...
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1answer
38 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 ...
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1answer
41 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
62 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 ...
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1answer
61 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 ...
4
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1answer
116 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}}]] ...
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1answer
34 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
80 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. ...
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1answer
68 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 ...
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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
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3answers
110 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
128 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
87 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 ...
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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
133 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
60 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
226 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
558 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
658 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
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4answers
210 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: ...
27
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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 ...
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0answers
32 views

Finding roots to Interpolation function [duplicate]

I am attempting to find the roots (intersection is constant Y-value) of an Interpolation function. I can do this by observing the plot and then entering search start values based on the visual ...
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
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2answers
170 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
55 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
49 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 ...
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0answers
32 views

Eigenvalues of a symbolic matrix using interpolating function

I have a 6x6 matrix with entries that depend on dependent and independent variables of an interpolating function. I would like to be able to evaluate the eigenvalues of this matrix using the ...
3
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2answers
255 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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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
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1answer
101 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
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1answer
126 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: ...
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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 ...
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0answers
83 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
147 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 ...
0
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2answers
72 views

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 ...
10
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4answers
947 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 ...
1
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1answer
56 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): ...
14
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2answers
324 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
93 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 ...
1
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1answer
32 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
102 views

Overriding default ExtrapolationHandler

When modeling systems with WhenEvent and NDSolve I found that the default extrapolation settings used in the returned ...
4
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0answers
43 views

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? ...
1
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0answers
63 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
40 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 ...
8
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1answer
194 views

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 ...