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

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2D Interpolation of data file

I hae a datafile with 5 columns of the structure: x_i f(x_i,y_1) f(x_i,y_2) f(x_i,y_3) f(x_i,y_3) f(x_i,y_4) with i = 1 to about 100. Thus there are about ...
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0answers
42 views
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1answer
23 views

Many NSolves to interpolating function

I have an expression of the form: expr = TerribleNumericalFunction[U[p]] == SimpleFunction[p] The Simple function is a ...
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0answers
35 views
4
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1answer
32 views

Changing the `ExtrapolationHandler` Function in Any Interpolation

This is a related question to What's inside InterpolatingFunction[{{1., 4.}}, <>]? and Suppress extrapolation of interpolating function in a ContourPlot. When interpolating a set of ...
32
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1answer
657 views

What's inside InterpolatingFunction[{{1., 4.}}, <>]?

I'm curious what's inside the InterpolationFunction object? For example: ...
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1answer
73 views

Using InterpolatingFunction in equations

I tried to use InterpolatingFunction in another ODE, but it doesn't work, because it seems for Mathematica that 2 functions are unknown instead of one. ...
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0answers
50 views

Improving RationalInterpolation Result

The following code produces a {4,4} rational interpolation approximation accurate to 10^-6 or better over the range ...
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1answer
34 views

Calculate the partial vapor pressures of a variable at xB = 0.75 based on the interpolation functions of the data

I'm having troubles in solving an exercise for an assignment in my Chemistry course. Talking about interpolations, I've already have a graph but I need to:(c) Calculate the partial vapor pressures of ...
6
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1answer
172 views

Interpolation on a regular square grid spanning a triangular domain

Context I am trying to identify contours of a function which is sampled on a cartesian grid within an irregular (triangular) region. Here is the data ...
18
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3answers
1k views

Monotone, periodic 1d-interpolation with continuous 1st order derivative

Lately, we had this thread about interpolation where J. M. linked two interpolation methods. The background for my question is that I estimated a parameter in polar coordinates with dependence on the ...
2
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1answer
49 views

Interpolate a discrete vector field

I have a discrete vector field, from which I want to derive the continuous one. For example, the planar vector field is defined by: ...
17
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4answers
1k views

How to splice together several instances of InterpolatingFunction?

I have a set of InterpolatingFunction returned by NDSolve which are valid over different (but overall continuous) domains. How ...
0
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1answer
60 views

Interpolating a non-continuous set of points

I'm trying to create a pure function that I can feed into OutputResponse[ ] as the input u[t]. In order to do this, I've written code to create a square wave pulse train in the form of a collection of ...
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1answer
55 views

how to reduce noise in time series data?how to do interpolation for missing value data?

i have done this coding to plot the data. the problem is some value is missing for certain date and the graph is not smooth and noisy. one way to smooth the data is by interpolation but i dont know ...
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2answers
89 views

Numerical root-finding: Find leftmost root in a domain

This is surely a duplicate, but I cannot seem to find a similar question. I use NDSolve to find an InterpolatingFunction y[t] ...
1
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1answer
146 views

Line integrals over a path defined by a set of points (rather than an analytic formula)

I'm getting inaccurate results when computing (plotting) the value of a function against the length of a line integral, where the path comes from a set of numerically calculated points. (In contrast, ...
2
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3answers
206 views

Function to calculate average of multiple lists

I have several lists of experimental data f[x] with different intervals Δx including some noise. ...
0
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1answer
52 views

Numerical integration of a three dimensional array

I need to integrate a scalar valued function $f\left(\boldsymbol{x}\right)$ where $\boldsymbol{x}$ is a three dimensional position vector; in other words: $\int_{\Omega} f\left(\boldsymbol{x}\right) ...
2
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1answer
99 views

Find tangency of InterpolatingFunction and circle

I am trying to use a system of equations to solve for the common tangent of a (polar) InterpolatingFunction and a circle. Unfortunately, both NSolve and FindRoot don't yield results, even when I ...
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0answers
134 views

Interpolation on an unstructured (mostly-structured) grid in 4D+

I frequently need to perform interpolations on an unstructured grid. Mostly, with the purpose of filling grid holes and then later continue with regular grid interpolations. Mathematica V9 and V10 ...
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0answers
58 views

Interpolation of a NURBS curve

Known that NQ=P where N is the Bspline basis function, Q is the control point that we wish to locate, P is the data points given ( the curve must pass through it) is there any way to modify the "N" ...
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1answer
57 views

Making a movie from an interpolating function

Say I use some Mathematica procedures to find an interpolating function of two variables: $u(x,t)$. Is it possible to make a movie of this interpolating function, i.e. plot it on a certain line $x \in ...
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0answers
48 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): ...
3
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2answers
67 views

FunctionInterpolation with vector output and scalar input

Apparently it is possible to build and InterpolatingFunction that accepts a vector input and returns a vector output: ...
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2answers
90 views
15
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4answers
4k views

Getting the interpolation function from a list plot

I have conducted a chemistry experiment and obtained a list of concentrations of a reactant against time. I plot a graph of this using Mathematica's ListPlot ...
2
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0answers
88 views

Position from 3 dimensional acceleration data? [closed]

Per a previous post on Mathematica StackExchange here I'm trying to utilize 3-axis accelerometer data to determine approximate 3D position. I wanted to start with a simple case. To this end I've ...
2
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2answers
105 views

Derivative of Vectoral NDSolve Interpolated Function / Rule Solutions,/., and Vector NDSolve [duplicate]

I need to find the instantaneous phase and instantaneous frequency for a rotating system. I am having difficulty making the math work with interpolating functions. First, here is a problem without ...
6
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2answers
283 views

ListContourPlot interpolation fails if x and y axes have different scales

To summarize what is below: ListContourPlot doesn't work when the domain has different x and y scales (fails when x/y~10^4, which seems surprisingly small). Is it possible to call ListContourPlot ...
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1answer
52 views

How to fit this data to be used in NIntegrate later?

I have a list of data points that resemble a chi-squared distribution (long tailed gaussian) that I am having trouble fitting or finding an equation with. The goal is to use the fitted equation in an ...
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0answers
172 views

NDSolve: Equation with interpolating function [closed]

I have a question regarding DSolve and NDSolve functions in Mathematica 10. For instance, I'd like to solve an ODE: ...
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2answers
137 views

Aitken interpolation of a polynomial?

How I can approximate a polynomial using Aitken's scheme using two nodes for the interpolation? ...
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3answers
164 views

Transform an InterpolatingFunction

I'd like to transform an InterpolatingFunction from NDSolve but can't figure out how. Here's an example. The equation I want to solve is ...
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1answer
65 views

Interpolating a polynomial for with first and second derivative of points

I am trying to fit a polynomial for switch cutoff which is used in Molecular dynamics. I want a fifth order polynomial with six coefficient $c_0, ...,c_6$ between $r_1<r<r_2$ with these ...
20
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6answers
3k views

Finding the intersection of a curve with an interpolation function

There are no issues trying to find the intersection points of two defined curves. ...
2
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1answer
133 views

Smooth animation of ListLinePlot

I have a sequence of 2D-points from uniformly sampling a time dependent process and plot this sequence with ListLinePlot. For example: ...
2
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1answer
107 views

How do I find out what a Mathematica function is doing (which numerical method it uses and how)?

Long story short, I am working on a project which entails fixing a bug I have found in Mathematica (8 and 10). In general, I would like to know what a specific Mathematica function is actually doing ...
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1answer
85 views

Reduced interpolation order [closed]

I have a problem with Interpolation - the order is reduced to 1 no matter what, but I need a quadratic interpolation order. The ...
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2answers
722 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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1answer
72 views

how to make interpolated data as a function?

For example, data1 = 0 1 1 2 3 3 5 2 6 2 9 4 11 5 13 6 14 7 16 8 data2 = 0 2 1 3 2 2 3 1 4 2 6 3 8 4 9 6 11 4 16 7 each data have different x-axis interval. so ...
3
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1answer
104 views

List interpolation

Hi mathematica people! So i am looking for the best way to interpolate a function given a list of its values. I have an iterative algorithm which needs high precision otherwise the numerical noise is ...
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0answers
28 views

Why numerical functions can't digest InterpolatingFunction with units?

Answering this question gave me the idea that I must be missing something.. In brief, numerical functions generally 'understand' units: ...
1
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3answers
195 views

Developing a function of two variables from given data

Cross listed from MSE: http://math.stackexchange.com/questions/1029399/developing-a-function-of-two-variables-from-given-data (I believe Mathematica SE is an appropriate place to ask this, as well.) ...
1
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1answer
92 views

What extrapolation method does Interpolation use by default? [closed]

As far as I can tell, Interpolation uses cubic spline interpolation by default - please correct me if I'm wrong. What does it use for extrapolation outside of the ...
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0answers
47 views

How does Mathematica interpolates? [duplicate]

In manual for Interpolate function it is said, that possible method of interpolation is Hermite. Unfortunately, I can't see ...
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0answers
76 views

plotting the stable and unstable manifolds of a difference equation

I have a 2D non-linear system of difference equations for variables x and y defined as follows: ...
3
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1answer
128 views

Interpolation function rejected by ParametricPlot3D

I was playing around with the bouncing ball example, and decided to make a 3d version. I decided to use ParametricPlot3D for a simple independent 3D ...
3
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1answer
101 views

How to evaluate differential entropy from raw data?

I want to evaluate the differential entropy according to here $$h(X) = - \int f(x) \log{f(x)} dx$$ where $f$ is the probability density function. Lets create some test data (normal distribution): ...