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

learn more… | top users | synonyms

1
vote
0answers
425 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: ...
-3
votes
2answers
181 views

Aitken interpolation of a polynomial?

How I can approximate a polynomial using Aitken's scheme using two nodes for the interpolation? ...
4
votes
3answers
257 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 ...
1
vote
1answer
88 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 ...
2
votes
1answer
222 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
votes
1answer
151 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 ...
-1
votes
1answer
94 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 ...
11
votes
2answers
962 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
vote
1answer
97 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
votes
1answer
178 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 ...
1
vote
3answers
470 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
vote
1answer
225 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 ...
0
votes
0answers
48 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 ...
0
votes
0answers
183 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
votes
1answer
150 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 ...
4
votes
1answer
170 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): ...
1
vote
1answer
126 views

Series expansion of InterpolatingFunction obtained from NDSolve

I am trying to obtain a series expansion of the numerical solution of a differential equation. I encounter difficulties going beyond first-order expansions which I believe might be due to my inability ...
9
votes
3answers
5k views

Get polynomial interpolation formula

I'm attempting to get a polynomial interpolation formula out of Mathematica but I am absolutely lost. I stared out using ...
1
vote
1answer
92 views

NDSolve with a constant

I have a simple differential equation like this s = NDSolve[{y'[x] == A y[x] Cos[x + y[x]], y[0] == 1}, y, {x, 0, 30}] where $A$ is a constant. Mathematica gives ...
6
votes
2answers
361 views

2D smoothing spline interpolation

Does Mathematica have 2D smoothing spline interpolation built in? I requires an interpolation method with smooth first derivatives and cubic bivariate splines fulfill this nicely. In python I would ...
13
votes
1answer
846 views

Curve fit based on minimal data

Inspired by the fantastic answers here and here, I would like to ask a questions along similar lines. I have 6 curve types that follow these rules: Type A: If point 1 is positive and point 2 is ...
12
votes
2answers
278 views

Temporal database reconstruction in mathematica

<EDIT> after some internet research I found the database domain that deals with this kind of thing: Temporal Databases. I think my question therefore becomes how to reconstruct a temporal ...
3
votes
1answer
131 views

Fast list interpolation over common x,y for multiple variables

I have a (long, >50K elements) unstructured list with a header similar to; AList[[1]] = {x,y,z,var1,var2,var3,var4,...,varN} I want to interpolate z, var1, var2, ...
0
votes
2answers
141 views

Select pairs of columns from an array of data [closed]

I try to interpolate the first two columns of a seven-column file formatted as follows: ...
10
votes
5answers
737 views

Multidimensional interpolation with duplicate abscissa values [duplicate]

I am trying to do a first order interpolation on a multidimensional data set containing duplicate abscissa values (which Mathematica does not like), like this one: ...
2
votes
1answer
444 views

Can I use the values of interpolating points from NDSolve's output? And How?‎

The output of NDSolve is a (list of)InterpolatingFunction(s). In standard output format the ‎elements of interpolation are not ...
11
votes
1answer
218 views

Incompatible InterpolatingFunction between V9 (and earlier) and V10

Bug introduced in 10.0.0 and fixed in 10.0.1 I am encountering compatibility issues when loading DumpSave(d) definitions in V10 that have been created with ...
1
vote
0answers
64 views

Show actual Interpolation function [duplicate]

Is there a command to show the actual function when using the Interpolation command? For example, f = Interpolation[{1, 2, 3, 5, 8, 5}] returns ...
14
votes
2answers
818 views

Extracting the function from InterpolatingFunction object

I've used Interpolation[] to generate an InterpolatingFunction object from a list of integers. ...
0
votes
2answers
122 views

Replace $z$ with interpolated function and plotting

I start off with this equation $z(x,y) = sin(xy)$. I create an interpolation from $0 < x < 5$ and $0 < y < 5$. I then use this interpolation on a simple function $w(x,y) = x + y + z(x,y)$ ...
1
vote
2answers
252 views

Integrating Squared of Interpolating Function with respect to one variable

I am interested in evaluating a two dimensional interpolating function produced by solving the wave equation. Here is the code that includes the resulting interpolating function. ...
2
votes
2answers
299 views

How do I feed data points into an equation to solve NUMERICALLY?

I start with this equation and solve it numerically for $z(x,y)$ in the range $1 < x < 5$ and $1 < y < 5$: $$ \frac{3}{xyz} - 2x - 3y - 5z = 0 $$ Then using the data points of $z$ above, ...
8
votes
2answers
343 views

interpolating function over dates

I've got a bunch of readings at various dates and times. I'd like to be able to interpolate and then integrate over, say days. I can do this by converting my date/time to ...
20
votes
2answers
584 views

Object separation from a 2.5D surface

I'm trying to identify the shape and the boundaries of objects. The data was generated with a laser scanner and represent the surface of an area in which many boulders lay on the ground and making up ...
0
votes
1answer
321 views

Interpolation of 4D data

To create a table and an interpolation function of 3D data T=f(X,Y) I have the answer here: interpolation of 3D data How to create a table/interpolation function of 4D data T=f(X,Y,R)? If I do ...
3
votes
1answer
272 views

Issue in ParallelTable after evaluating another function using NDSolve and FindRoot. What is wrong with this inverse?

I am trying to find the inverse of a function which is defined through NDSolve and NIntegrate. The question is pretty similar ...
8
votes
2answers
378 views

Problem when defining function through NIntegrate and NDSolve and Interpolation - Bug?

More than a single question, I have some doubts about the output of certain functions when defined through the result of other calculations. I am an active user of Mathematica, but maybe I haven't ...
1
vote
3answers
121 views

Removing some data and replacing them with new ones

I have a data list where the elements have the form (time, velocity ). I need to remove some malformed elements in places where the data does not change smoothly and then replace those points by ...
1
vote
1answer
68 views

Interpolation function evaluation and timing

Lets define two identical functions $f$ and $g$ in a slightly different way ...
0
votes
1answer
237 views

Better code for two variable fractal interpolation functions

I am trying to write code for 2-variable fractal interpolation functions using two iterated function systems and two starting functions (both $y(x)=x$) which creates a sequence of piecewise defined ...
6
votes
3answers
801 views

Piecewise Polynomial Interpolation

Given some data pairs $(x_i,y_i)$, with $i=0,...,m$, and a degree $r$, I wish to build a piecewise polynomial function to interpolate these data. That interpolation should be continuous, and, on every ...
3
votes
3answers
217 views

Zero-order interpolation not going fully around

Connected to this question, I want to do a zero-order interpolation of a bunch of datapoints which is periodic. The code I use is as follows: ...
1
vote
1answer
332 views

Interpolate a curve in 3D

I have a sequence $\{(x_k, y_k, z_k)\}_{k=1}^n \subset \mathbb{R}^3$, all points along a path represented by the function $\gamma \colon \mathbb{R} \to \mathbb{R}^3$, which maps the distance along the ...
4
votes
3answers
2k views

Smooth 4D (3D + color) plot from discrete points

I have a file containing isosurface $\{x,y,z,F\}$ data (around 9000 points). My goal is to generate a smooth (NOT a discrete set of points!) colored surface using ...
0
votes
1answer
89 views

Strange behaviour of “Make Table” with exponential function

I am trying to create a simple interpolation of 1-Exp[-x^2] function, over the logarithmic grid, but I am stuck due to some unexpected behaviour: ...
1
vote
1answer
426 views

Find polynomial equation for set of 3D data

data was given in columns in the order {y, x, z}, with y dependent on x, z ...
5
votes
3answers
2k views

Creating a 3D List Line Plot From Discrete Points

Given the following Runge-Kutta ODE solver and the graphical output below, how do I get a 3D line plot instead of a 3D point plot? I see that there is no ListLinePlot3D function, so I thought it might ...
5
votes
2answers
227 views

Function that is a good fit to the plot made with SmoothHistogram

How can I find a function that fits the plot from the SmoothHistogram function? For instance if I have data like this and plot a Smooth Histogram, how can I get a function that fits the plot? ...