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

learn more… | top users | synonyms

1
vote
2answers
744 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
208 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
307 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
447 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
662 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
236 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
227 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 ...
4
votes
3answers
288 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 ...
10
votes
3answers
831 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
988 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
169 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
647 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
votes
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 ...
9
votes
2answers
622 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 ...
6
votes
1answer
573 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
407 views

Interpolate specific columns of data

I have a txt file with 3 columns of data: x y1 y2 How do I import the file then create 2 functions, one interpolated with {x,y1} values and the other interpolated with {x,y2} values? This ...
2
votes
3answers
2k views

Retrieve values of InterpolatingFunction

While analyzing a large system of ODE's, I defined a particular ratio p, which contains some variables that are represented by ...
1
vote
1answer
262 views

Mapping and Interpolation

Does Mathematica have a mapping function like scipy or any of the multidimensional ones? By this I mean something like mapping $[1,100]$ onto $[7,20]$ for example. Looking at Interpolate I only ...
5
votes
2answers
1k views

Is it possible to compute trapezoidal rule numerical integration?

Is it possible to compute trapezoidal rule numerical integration? I know that Mathematica has Interpolation, and that a list of points can be interpolated and then ...
6
votes
1answer
408 views

How to use Interpolation to fill in missing data

I have a bit of data that looks like this: ...
5
votes
2answers
310 views

How to find Matano plane

I have discrete collection of data points (10 to 10^4). I want to describe them by a continuous function and find a x value z, ...
11
votes
2answers
4k views

interpolation of 3D data

I have a 3D surface given in data-points of the form ${x,y,z}$. What is the easiest way to get the interpolated value $z=f(X,Y)$ for given coordinates ${X,Y}$ (which are of course not in the data ...
15
votes
2answers
878 views

Improved interpolation of mostly-structured 3d data

This question arose in response to a comment by Leonid to my answer for this question. He noted that for unstructured grids, Interpolation can only use ...
3
votes
1answer
248 views

FunctionInterpolation Errors / Question re Evaluation Order and Options

I have using Mathematica functions that takes a Cartesian coordinate relative to the Earth (xyz) and converts it to a latitude, longitude, and altitude (lla). And here it is: ...
4
votes
2answers
1k views

Implicit Interpolating function in Mathematica and its explicit form in small sections

I have a set of points $\{x_i,y_i\}$ that represents a closed curve. I want to find a function $F(x,y)$ such that $F(x,y) = 0$ gives the needed curve and $F(x,y) \ne 0$ outside the curve. For ...
16
votes
1answer
388 views

How to fix broken InterpolatingFunction?

I have an InterpolatingFunction based on irregularly-gridded data, like this: ...
10
votes
2answers
599 views

How to add an interpolating point to InterpolatingFunction?

Suppose I have an InterpolatingFunction object defined on $[\epsilon,1]$; let's call it f. What is the best way to construct a ...