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

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2
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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 ...
3
votes
1answer
535 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
317 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 ...
4
votes
0answers
286 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 ...
2
votes
1answer
219 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 ...
2
votes
2answers
223 views
-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 ...
8
votes
4answers
700 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 ...
1
vote
1answer
220 views
5
votes
2answers
475 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
666 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
607 views

Parametric differentiable interpolation of a 2D data set

I have a set of data ...
3
votes
2answers
249 views

Convert BSplineFunction into two Interpolating Functions

Is there a way to decompose a BSplineFunction output into two functions x[t], y[t] ...
13
votes
3answers
661 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 ...
18
votes
4answers
1k views

How to integrate functions of linearly interpolated data?

At first, consider integration of pure InterpolatingFunction. Importing some data (works in v.9, for earlier versions one can use this link to download zipped ...
0
votes
1answer
775 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 ...
3
votes
2answers
478 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 ...
5
votes
3answers
330 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: ...
3
votes
1answer
639 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 ...
1
vote
1answer
415 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. ...
1
vote
1answer
360 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.
10
votes
1answer
480 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
368 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 ...
6
votes
1answer
353 views

BSplineCurve Interpolation

Can I get interpolated values from this B-spline, (shown in red)? ...
2
votes
2answers
209 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 ...
14
votes
3answers
806 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 ...
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
319 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
719 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: ...
28
votes
3answers
774 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 ...
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 ...
9
votes
1answer
205 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 ...
0
votes
1answer
412 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
636 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
4
votes
2answers
225 views

2D grid as a 2D polygonal or smooth domain

I have a series of points, as a list of pairs of real numbers, each multiple of a base value. So they represent a subset of a grid. Given that this list, when represented with ...
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 ...
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. ...
14
votes
4answers
3k 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 ...
4
votes
3answers
280 views

How could I get the value of y[t] at each specific interpolation point?

sol = NDSolve[{Derivative[2][y][t] + Sin[y[t]] == 0, Derivative[1][y][0] == 0, y[0] == 1}, y, {t, 0, 2}] the above-mentioned differential equations can be solved ...
11
votes
1answer
1k views

Fitting a spline to data with FindFit?

I am trying to find a function that fits my almost linear data. A high order polynomial model has too much residual. So I was hoping to use Mathematica to fit splines to the curve. This is what I ...
15
votes
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 ...
10
votes
3answers
797 views

Derivatives (divergence, gradient, curl) of interpolated 3D data

How can I calculate a vector derivative (i.e. divergence, gradient, curl) of interpolated data? For sample data, you can use: ...
16
votes
2answers
941 views

Higher order periodic interpolation (curve fitting)

I have a list of points in 3D, and I want to get a smooth interpolation or curve fit (it is more for illustration) of these points such that the first and second derivatives at the start and end ...
5
votes
2answers
151 views

How to get the boolean value of an inequality involving an InterpolatingFunction?

Here's the code: yan = FunctionInterpolation[x^2, {x, -1, 1}]; FullSimplify[yan[x] > -1, -1 < x < 1] Needless to say, what I expect to see in the output ...
1
vote
1answer
164 views

Trying to generate a function from InterpolatingFunction with FunctionInterpolation

Here is the code (I'm sorry to give you such a complex code sample but I failed to reproduce the error with a simpler InterpolatingFunction): ...
0
votes
1answer
627 views

Fourier series of interpolating function result of NDSolve

I am having a tough time formulating the right question but here goes. I know that solving the pde as in here gives me an interpolating function. I understand that the interpolating function object ...