Questions on the interpolation functions in Mathematica (Interpolation[], ListInterpolation[], FunctionInterpolation[], InterpolatingPolynomial[], etc.)
27
votes
3answers
386 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 ...
18
votes
1answer
2k views
How does Interpolation really work?
I'm looking for some explanation or advice, not help in solving something. Recently I finished my program and my supervisor said "Ok, now it's time for your first paper: write a scientific text about ...
17
votes
2answers
504 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 ...
16
votes
1answer
308 views
How to fix broken InterpolatingFunction?
I have an InterpolatingFunction based on irregularly-gridded data, like this:
...
16
votes
2answers
426 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 ...
14
votes
3answers
371 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 ...
14
votes
2answers
498 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 ...
14
votes
1answer
214 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,
...
12
votes
4answers
1k 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 ...
12
votes
2answers
427 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 ...
12
votes
4answers
351 views
How to reduce the InterpolatingFunction building overhead?
I want a linear interpolation from the following example list:
...
12
votes
3answers
233 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 ...
11
votes
3answers
759 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. ...
10
votes
2answers
450 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 ...
10
votes
3answers
430 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:
...
10
votes
1answer
220 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 ...
10
votes
2answers
388 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 ...
10
votes
1answer
735 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 ...
9
votes
2answers
2k 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 ...
8
votes
3answers
443 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
3answers
354 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 ...
8
votes
4answers
225 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 ...
8
votes
1answer
149 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 ...
8
votes
1answer
97 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 ...
7
votes
3answers
322 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 ...
7
votes
1answer
142 views
The only usage for the option InterpolationOrder in NDSolve is to be set to All?
We know that changing the option InterpolationOrder in ListLinePlot、ListPlot3D、...
7
votes
2answers
325 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 ...
7
votes
0answers
144 views
Creating and using an explicit piecewise function in a convenient way
I have a set of data points that define a function in the form
curvePts = {data1,data2,...}
where
...
6
votes
1answer
296 views
6
votes
1answer
116 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 ...
5
votes
2answers
165 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 ...
5
votes
2answers
129 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 ...
5
votes
3answers
178 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:
...
5
votes
2answers
232 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, ...
5
votes
1answer
173 views
5
votes
1answer
380 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 ...
4
votes
2answers
642 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 ...
4
votes
3answers
133 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 ...
4
votes
2answers
183 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
2answers
732 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 ...
4
votes
0answers
141 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 ...
4
votes
0answers
129 views
Artifacts in Line Plot from InterpolatingFunction
I have a periodic solution from an NDSolve that is producing an InterpolatingFunction. With the default plot settings, there is not enough PlotPoints/MaxRecursion to resolve the peaks in the function:
...
3
votes
3answers
617 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 ...
3
votes
2answers
173 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 ...
3
votes
2answers
207 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
3answers
997 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 ...
3
votes
2answers
114 views
Convert BSplineFunction into two Interpolating Functions
Is there a way to decompose a BSplineFunction output into two functions x[t], y[t] ...
3
votes
1answer
166 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:
...
2
votes
1answer
104 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 ...
2
votes
2answers
208 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 ...
