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

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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.
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0answers
329 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 ...
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2answers
2k 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 ...
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1answer
190 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? ...
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3answers
884 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 ...
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4answers
560 views

How to reduce the InterpolatingFunction building overhead?

I want a linear interpolation from the following example list: ...
15
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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. ...
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3answers
942 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 ...
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1answer
355 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, ...
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2answers
96 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 ...
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1answer
108 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 ...
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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 ...
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1answer
717 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 ...
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0answers
348 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 ...
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4answers
832 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 ...
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2answers
561 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
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3answers
757 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 ...
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2answers
533 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 ...
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2answers
683 views
3
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1answer
790 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 ...
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1answer
969 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 ...
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1answer
447 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. ...
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1answer
537 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 ...
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1answer
131 views

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

I need some helps on NDSolve. Here are my equations: ...
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1answer
475 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 ...
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2answers
232 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 ...
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2answers
194 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 ...
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2answers
2k 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 ...
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3answers
908 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 ...
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1answer
130 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 ...
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2answers
371 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 ...
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2answers
824 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: ...
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1answer
225 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、...
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1answer
325 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 ...
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1answer
539 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 ...
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2answers
757 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
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1answer
288 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
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2answers
235 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 ...
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3answers
329 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
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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 ...
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3answers
907 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: ...
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2answers
1k 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 ...
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2answers
155 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 ...
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1answer
184 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): ...
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1answer
716 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 ...
5
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1answer
2k views

How do I prevent NIntegrate::inumr errors within other functions?

I believe this question is best illustrated with a simple example. If I run FunctionInterpolation[NIntegrate[a + b, {a, 0, 1}], {b, 0, 1}] I get errors of the ...
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2answers
660 views

Interpolation of mostly-structured 3D data

this question relates to interpolation of 3D data and Improved interpolation of mostly-structured 3d data I have an irregular 3d data set that is quite large (around 70,000 triplets---let's call it ...
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1answer
611 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 ...