# Tagged Questions

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

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### Derivation of an interpolation function with multiple arguments

I have the following interpolation function: f[x_,a_,b_]:=70 s[a,b][[1,1,2]][x] where s[a,b] is the solution of a ...
56 views

### Make integration/ plot run faster? (takes hours)

I am using Mathematica 10.0.2.0. Here is the code I am working with: ...
61 views

### Interpolating functions and NDSolve

I've been working on trying to get Mathematica to solve this system for a while now, and I have a couple of questions relating to various parts of the system: Interpolating functions: As a number of ...
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### Interpolating functions and Look-up tables

This is just a general question about how InterpolatingFunctions work: If I have a complicated function that I don't want to have to evaluate many times over, does turning it into an ...
29 views

### 3DPlot, Logarithmic x and y axes, Interpolating function

I've used NDSolve to get an InterpolatingFunction that solves a certain difeq. I want to see the behavior of this function on a couple different scales, so I want to use some sort of Log Plot. For a ...
67 views

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

I'm using the code: ...
202 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, ...
90 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 ...
230 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 ...
105 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 ...
609 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? ...
69 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 ...
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### 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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### What is the Chebyshev method for InterpolationFunction?

With InterpolationOrder -> All, some methods of NDSolve returns interpolations with ...
615 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 ...
268 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 ...
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 ...
134 views

### Inflection point and curvature

Through a coordinates list and then interpolating them I got a $f[x]$. ...
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### 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: ...
72 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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### 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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### 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 ...
68 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 ...
119 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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### 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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### 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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### 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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### 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: ...
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? <...
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### 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 ...
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### 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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### 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 ...
158 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 ...
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### 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 $x_{i}$. ...
245 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). ...
568 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 ...
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 ...
223 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: ...
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 ...
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 ...
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### 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}]; ...
187 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 ...
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### 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 ...
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### 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 ...
265 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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### 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: ...
107 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 ...