Questions on the interpolation functions in Mathematica (Interpolation[], ListInterpolation[], FunctionInterpolation[], InterpolatingPolynomial[], etc.)
1
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2answers
285 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:
...
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、...
2
votes
1answer
198 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 ...
3
votes
3answers
1k 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
134 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 ...
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 ...
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 ...
2
votes
1answer
148 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
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
3answers
134 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 ...
10
votes
1answer
736 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
431 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:
...
12
votes
2answers
430 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
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 ...
1
vote
1answer
112 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
319 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 ...
2
votes
1answer
607 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 ...
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 ...
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 ...
1
vote
1answer
196 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 ...
3
votes
3answers
618 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
222 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 ...
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 ...
6
votes
1answer
296 views
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, ...
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 ...
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 ...
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:
...
4
votes
2answers
733 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
308 views
How to fix broken InterpolatingFunction?
I have an InterpolatingFunction based on irregularly-gridded data, like this:
...
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 ...
