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

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15
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2answers
1k views

Fast Spherical Linear Interpolation of list of quaternions

An accurate way to interpolate between two quaternions is to use Spherical Linear Interpolation (Slerp) because it preserves the unit length, whereas straightforward linear interpolation does not, as ...
0
votes
2answers
503 views

Correct use of ListInterpolation

I have a small problem with ListInterpolation. I want to use ListInterpolation to postprocess result of a numerical simulation. ...
6
votes
1answer
355 views

BSplineCurve Interpolation

Can I get interpolated values from this B-spline, (shown in red)? ...
3
votes
2answers
251 views

Convert BSplineFunction into two Interpolating Functions

Is there a way to decompose a BSplineFunction output into two functions x[t], y[t] ...
1
vote
1answer
123 views

How to work with Interpolated Functions? [closed]

I am just a beginner and struggeling with experimental data and further processing in Mathematica: I first constructed a table from two columns (t20 and J20) in Excel: ...
6
votes
1answer
617 views

Smoothing/Averaging 2D Vector Fields

I have a list of 2D vectors defined by {{x,y},{u,v}} and would like to smooth or average the vectors. For example here are 2 vector fields, the second has noise ...
2
votes
1answer
222 views

Interpolation on large 2D list results in erratic function

Previously, I've had problems with Mathematica interpolating and plotting 3D lists, but I finally managed to do so by rescaling the x and y-axes with the help of the methods proposed here. Now my ...
5
votes
3answers
333 views

Interpolation with boundary conditions

I'm working on a sales projection, trying to create some flexibility in handle the forecast using locators. The toy code is something like this: ...
7
votes
2answers
458 views

Function Interpolation with Automatic / Algorithmic Values Mesh

I have an underlying function f(x,y,z) that is computationally intensive, but is smooth and continuous. I'm needing to find the function values along a line in xyz. Currently, I'm calculating f at ...
1
vote
1answer
365 views

How to add derivatives to Hermite Interpolation?

I try to use InterpolatingPolynomial[{f[1]=2,f'[1]=3,f[2]=6, f'[2]=7, f''[2]=8}, Method->"Hermite"] in WolframAlpha, but it's wrong.
4
votes
0answers
287 views

Cubic polynomial interpolation with velocities listed rather than some points

I am trying to use the function BSplineFunction[] to create a natural cubic spline. Normally what is done is that you specify "SplineDegree -> 3" and include a list of points and it will carry out ...
1
vote
2answers
1k views

Using FindRoot with an interpolating function

This question bears resemblance to a few other questions on mathematica.SE about finding points of intersection of crossing curves. I know that the guidebook of numerics has an entry about the whole ...
-4
votes
1answer
177 views

Problem with interpolation

I have a problem with the function interpolation. when I use it my points are all very shifted. Do you have an idea of the solution? ...
14
votes
3answers
811 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 ...
11
votes
4answers
532 views

How to reduce the InterpolatingFunction building overhead?

I want a linear interpolation from the following example list: ...
12
votes
3answers
2k views

Data interpolation and ListContourPlot

I am fairly new to Mathematica and I have two quick questions on using it for a Hydrology and Hydrogeology class. One is about data interpolation and interpolating without any data defined in an area. ...
28
votes
3answers
780 views

No warning when extrapolating with Plot

One of the most annoying "features" of Mathematica is that the Plot family does extrapolation on InterpolatingFunctions without ...
15
votes
1answer
325 views

Why does LogLinearPlot sample its argument outside the specified domain?

I experience a weird bug in the function LogLinearPlot. If the input is an interpolation function, such as the one created like this, ...
1
vote
2answers
91 views

Interpolation of an upper-triangular list

I have 2d list which is upper triangular. I would like to interpolate it, but I cannot unless I set the interpolation order to 1. I tried making the list rectangular by filling the bottom half with ...
2
votes
1answer
105 views

InterpolatingFunction with growing Domain

I want to find roots of a function that is very slow to calculate (the function itself involves a bunch of FindMaxima) so I interpolate the function in a region where I think it likely the the root ...
-4
votes
4answers
1k views

Piecewise linear Interpolation between data points

Is there some sort of functionality built into Mathematica that will let me linearly interpolate between (x, y) pairs of data in an array? Example: I have the two points (1, 10) and (2, 20), how can ...
3
votes
1answer
543 views

Join a piecewise plot

I wrote some code to get a piecewise plot which is displayed correctly. Now I'd like to join the various parts of the plot, using some kind of interpolation, to get a continuous chart even though it's ...
3
votes
0answers
320 views

How to make 3D object smooth?

This thread considers mathematical methods here to make the 3D object smooth but this question consider how to achieve the goal of smoothing a 3D object in Mathematica. I want to get smoother ...
13
votes
3answers
667 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 ...
8
votes
4answers
710 views

Numerical integration of a numeric data available as a nested list

I have some numerical data in the form of a list with the following structure: {...{x,y,z},...} defining a surface z=z(x,y) in a 3D space (x,y,z). The data came from a simulation, and I am ...
5
votes
2answers
480 views

ListContourPlot interpolation screws up on concave set of data

I want to create ListContourPlots for sets of Data (from a physics simulation) given as Triplets {x, y, f(x, y)}. Certain parameter regions in the x-y-plane are ...
8
votes
3answers
668 views

Approximately Fit Data Without FindFit

I have some noisy data, and I'd like to analyze the derivative of the function the data approximately matches. Interpolation is normally great, but doesn't work ...
3
votes
2answers
480 views

Ways to plot interpolating functions more economically?

I am interpolating a lot of data over geographic coordinates obtained via GPS, and frequently I need to plot these interpolated functions together. For example, I may have an interpolated elevation ...
3
votes
2answers
610 views
3
votes
1answer
644 views

Interpolating 2D data with missing values

I have a list (21 x 21) containing values. I want to eliminate slots containing zeros by interpolating the nearest values and overwriting the zeros. How do I use the Mathematica's ...
0
votes
1answer
788 views

Interpolating 2D data [duplicate]

Possible Duplicate: Interpolating 2D data with missing values I am trying to interpolate a 21x21 array of values. The 21x21 array sometimes has zero values and with the help of ...
1
vote
1answer
416 views

Optimizing the fitting of Ordinary Differential Equation(NDsolve) involving interpolation functions

I am a newbie to this forum. I am trying to use NDsolve to solve some ODEs involving the interpolation function. Then, I will compare the fitted curve and data to determine the ODE coefficients. ...
10
votes
1answer
484 views

How to get zeroth-order (piecewise constant) interpolation of scattered data?

Given a collection of scattered data points in 2D and associated function values, data = RandomReal[1, {100, 3}]; we can get a piecewise linear interpolating ...
0
votes
1answer
129 views

Solve 1-D function that has 2-D interpolating functions

I need some helps on NDSolve. Here are my equations: ...
9
votes
1answer
370 views

Test if argument is inside domain of InterpolatingFunction

The documentation says In standard output format, only the domain element of an InterpolatingFunction object is printed explicitly. The remaining elements are indicated by <> But this is not the ...
2
votes
2answers
210 views

How to create InterpolatingFunction from data?

If I have a function at a number of non-uniformly spaced data points: youtReal[7.8]=2.0332;, youtReal[8.54]=6.24352354;.................. ......... and the ...
1
vote
2answers
177 views

Doing an Interpolation through a list of lists into a single function

Suppose I have a list of lists, i.e. list = Table[{x, x^ k}, {k, 1, 10}, {x, 0, 1, 0.05}]; and I want to interpolate each of the lists by a function using ...
19
votes
2answers
1k 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 ...
8
votes
3answers
822 views

Ηow to create an interpolated CDF from its samples?

I want to use a distribution I have only aggregate statistics on, namely its CDF sampled at certain points. I would like to keep it "nonparametric" (remain noncommittal on the parametric form), but I ...
8
votes
1answer
123 views

Prevent Plus from threading InterpolatingFunction

For an InterpolatingFunction $y:\ \mathbb{R}\to\mathbb{R}^2$, Plus is unaware of this, so when I do any modifications to it in ...
5
votes
2answers
322 views

How can I force points in a list to have distinct x values?

I have a list of points that may be used for linear interpolation using Interpolation and need to ensure that no two points have the same $x$ value, since, if they ...
1
vote
2answers
728 views

Interpolating a function of two variables

I am trying to create the interpolating function for a function of two variables, over a finite area. Just for consistency we can think of a function: ...
9
votes
1answer
206 views

The only usage for the option InterpolationOrder in NDSolve is to be set to All?

We know that changing the option InterpolationOrder in ListLinePlotListPlot3D、...
3
votes
1answer
295 views

using interpolation functions in ParallelMap

Edit I am editing the question to give a simple workable example. It is at the bottom under the heading Example. The original question is now headed withe Background. Background I am trying to ...
5
votes
3answers
3k 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 ...
0
votes
1answer
418 views

Can an Interpolation function be 'saved'? [duplicate]

Possible Duplicate: Save interpolated function I am importing tables with sizes of 100k - 500k rows and 4 columns. The larger the table, the slower my Mathematica runs for all computations ...
2
votes
2answers
637 views

Area or NIntegrate curves defined by points?

Is there a convenient method to compute the AUC (Area Under the Curve) metric that quantifies a Receiver Operating Characteristic (ROC) like shown here? The data used to build the ROC are just ...
2
votes
1answer
227 views

How to generate a formula of a graph with three key points

I have three key points on a graph. How do I find out what the formula for this graph would be? The points are: (3,0) (5,2) (7,6). It is known that the graph will be a quadratic. Thanks