# Tagged Questions

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

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### 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 ...
59 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 ...
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}}]] ...
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 ...
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. ...
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 ...
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: ...
109 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? <...
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 ...
86 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 ...
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 ...
131 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 ...
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 $x_{i}$. ...
223 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). ...
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 ...
656 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 ...
208 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 ...
31 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 ...
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 ...
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}]; ...
168 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 ...
54 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 ...
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 ...
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 ...
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 ...
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: ...
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 ...
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 ...
51 views

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### 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: ...
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 ...
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.." ...
147 views

### Using ListInterpolation to get a vector-valued function

I wanted to construct a ColorFunction from an image, so I tried ...
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 ...
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 ...
946 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 ...
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): ...
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 ...
91 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 ...
32 views

### Interpolate a data set for a defined time-step

I have a set of data which looks like: ...
101 views

### Overriding default ExtrapolationHandler

When modeling systems with WhenEvent and NDSolve I found that the default extrapolation settings used in the returned ...
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? ...
62 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 ...
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 ...
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 ...
59 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 ...
60 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 ...