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

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17
votes
2answers
194 views

Object separation from a 2.5D surface

I'm trying to identify the shape and the boundaries of objects. The data was generated with a laser scanner and represent the surface of an area in which many boulders lay on the ground and making up ...
0
votes
1answer
52 views

Interpolation of 4D data

To create a table and an interpolation function of 3D data T=f(X,Y) I have the answer here: interpolation of 3D data How to create a table/interpolation function of 4D data T=f(X,Y,R)? If I do ...
3
votes
1answer
142 views

Issue in ParallelTable after evaluating another function using NDSolve and FindRoot. What is wrong with this inverse?

I am trying to find the inverse of a function which is defined through NDSolve and NIntegrate. The question is pretty similar ...
11
votes
1answer
128 views

Incompatible InterpolatingFunction between V9 (and earlier) and V10

I am encountering compatibility issues when loading DumpSave(d) definitions in V10 that have been created with earlier versions. V10 appears to be unable to digest ...
16
votes
4answers
735 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 ...
6
votes
2answers
137 views

Problem when defining function through NIntegrate and NDSolve and Interpolation - Bug?

More than a single question, I have some doubts about the output of certain functions when defined through the result of other calculations. I am an active user of Mathematica, but maybe I haven't ...
1
vote
3answers
109 views

Removing some data and replacing them with new ones

I have a data list where the elements have the form (time, velocity ). I need to remove some malformed elements in places where the data does not change smoothly and then replace those points by ...
1
vote
1answer
26 views

Interpolation function evaluation and timing

Lets define two identical functions $f$ and $g$ in a slightly different way ...
0
votes
1answer
93 views

Better code for two variable fractal interpolation functions

I am trying to write code for 2-variable fractal interpolation functions using two iterated function systems and two starting functions (both $y(x)=x$) which creates a sequence of piecewise defined ...
4
votes
2answers
91 views

Piecewise Polynomial Interpolation

Given some data pairs $(x_i,y_i)$, with $i=0,...,m$, and a degree $r$, I wish to build a piecewise polynomial function to interpolate these data. That interpolation should be continuous, and, on every ...
3
votes
3answers
154 views

Zero-order interpolation not going fully around

Connected to this question, I want to do a zero-order interpolation of a bunch of datapoints which is periodic. The code I use is as follows: ...
3
votes
1answer
95 views

Interpolation function rejected by ParametricPlot3D

I was playing around with the bouncing ball example, and decided to make a 3d version. I decided to use ParametricPlot3D for a simple independent 3D ...
0
votes
0answers
34 views

Replace parameter of NDSolve by a Function

I dont know how to replace the paremeter inside of an interpolation function result from NDSolve by a function of another parameter. This is it: I have a ...
0
votes
2answers
62 views

Update: Interpolation error message? [closed]

I have the following data that needs to be analyzed : data = ToExpression@Import["http://pastebin.com/raw.php?i=8XKGYvSy", "Data"]; I have 6 sets of coordinates ...
2
votes
1answer
42 views

FunctionInterpolation error when specifying AccuracyGoal

In the help page ref/message/FunctionInterpolation/ncvb, it is mentioned that one should specify AccuracyGoal for some (even ...
1
vote
1answer
143 views

Interpolate a curve in 3D

I have a sequence $\{(x_k, y_k, z_k)\}_{k=1}^n \subset \mathbb{R}^3$, all points along a path represented by the function $\gamma \colon \mathbb{R} \to \mathbb{R}^3$, which maps the distance along the ...
2
votes
3answers
308 views

Smooth 4D (3D + color) plot from discrete points

I have a file containing isosurface $\{x,y,z,F\}$ data (around 9000 points). My goal is to generate a smooth (NOT a discrete set of points!) colored surface using ...
0
votes
1answer
68 views

Strange behaviour of “Make Table” with exponential function

I am trying to create a simple interpolation of 1-Exp[-x^2] function, over the logarithmic grid, but I am stuck due to some unexpected behaviour: ...
0
votes
2answers
85 views

Extract X value from corresponding Y value from a List or Transpose [closed]

I have a list of X values and Y values separately, and also together with: data=Transpose[{X,Y}] This data is from a chromatogram, and I want to extract the ...
0
votes
1answer
83 views

Find polynomial equation for set of 3D data

data was given in columns in the order {y, x, z}, with y dependent on x, z ...
4
votes
3answers
357 views

Creating a 3D List Line Plot From Discrete Points

Given the following Runge-Kutta ODE solver and the graphical output below, how do I get a 3D line plot instead of a 3D point plot? I see that there is no ListLinePlot3D function, so I thought it might ...
5
votes
2answers
150 views

Function that is a good fit to the plot made with SmoothHistogram

How can I find a function that fits the plot from the SmoothHistogram function? For instance if I have data like this and plot a Smooth Histogram, how can I get a function that fits the plot? ...
3
votes
4answers
232 views

Interpolating a plot with missing values

With data = {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {5, 5}, {6, 6}, {7, 5}, {8, 4}, {10, 3}, {10, 2}, {11, 1}} and ...
1
vote
1answer
79 views

Requiring NumericQ in Pure Function

Potential duplicate, but doesn't seem to solve my problem: Using patterns in pure functions I have a function that returns an InterpolatingFunction, and it works ...
0
votes
1answer
136 views

Zooming into Parametric Animation Plot that Uses InterpolatingFunctions

I have an interplanetary trajectory solver that calculates a spacecraft route from Earth to Mars, and I am trying to zoom into the spacecraft when it reaches its Mars intercept orbit but am having ...
3
votes
1answer
100 views

Integrating a functional of an InterpolatingFunction

It is straightforward to Integrate an InterpolatingFunction. However, even for a simple functional of an ...
2
votes
1answer
61 views

ReplaceAll in an expression including large InterpolatingFunction

I have a large InterpolatingFunction that I'm transforming to another basis with a few simple multiplications and additions by (symbolic) constants. The ...
4
votes
1answer
226 views

Create ParametricFunction object without ParametricNDSolve

Documentation of v9 states that ParametricFunction is generated by ParametricNDSolve and ...
11
votes
2answers
184 views

Arbitrary precision spline interpolation

Current implementation of Interpolation does not allow arbitrary precision spline interpolation. Yu-Sung Chang say here that "it is not hard to implement it ...
0
votes
0answers
42 views

How to approximate a computationally expensive 5-dimensional manifold?

I have a 4-parameter family of functions, which I'll refer to as y[a, b, c, d][x]. In this notation, a, b, c, d are the 4 ...
12
votes
3answers
619 views

Parametric Interpolation of 2D data

I want to create an interpolation through the following 2dim data points: ...
4
votes
1answer
286 views

InverseFunction on an Interpolating Function is misbehaving

I am getting strange behavior when I try to calculate the inverse of an interpolating function for two similar data sets. My data sets are: ...
2
votes
2answers
144 views

How can i integrate over a set of data

i need to integrate over my data, which is denoted as {q, I},here I is the Intensity i need to obtain the form of the following integration( its not a numeric integration, because it contain x, next ...
1
vote
0answers
43 views

Conjugate of InterpolatingFunction?

From NDSolve, I got this: {{a1 -> InterpolatingFunction[{{0., 40.}}, "<>"]}} What would be a sensible approach to ...
1
vote
0answers
60 views

Linear interpolation over 2 variables

I'm tuning a function to data over 4-5 variables using Differential Evolution. The objective function calls frequently interpolation function. I came to a point, where compiling the objective function ...
2
votes
1answer
40 views

Results of ArgMax as a function of a parameter with InterpolatingFunctions

I would like to obtain a function and its derivatives, where the function is defined as the solution to a maximization problem. The obvious approach ...
3
votes
2answers
100 views

Interpolation impossible for ListPlot with Missing?

I have a list of data to plot. I would like to plot them with lines but delete some data before plotting and leave the lines disconnected where data is deleted. For example, ...
2
votes
1answer
103 views

Calculating the volume under a surface with Riemann sum

I have a set of xyz data points. X and Y are coordinates of a regular grid of 10x10 units, Z is the independent variable. I am trying to calculate the volume under the set of points, using Riemann ...
0
votes
1answer
121 views

Interpolation and points of non-differentiability

I have some data, which if expressed by some elementary functions, would contain a non-differentiable point. I would like to be able to use something like interpolate to convert the data into a ...
0
votes
0answers
79 views

Numerical Differentiation of an interpolated list.

I have a synthetic spectrum with a wavelength range of .3 to .7 microns. I have interpolated this spectrum for re-sampling purposes. However, I am also attempting to calculate the first and second ...
0
votes
0answers
70 views

how to write my own interpolation method

I was comparing results of spline interpolation in Mathematica and C++/gsl-library Results of interpolation are different if I use: ...
1
vote
0answers
32 views

Integration of any interpolation generates invalid comparison errors [duplicate]

Integrating a simple interpolated function as follows generates invalid comparison errors. ...
1
vote
1answer
97 views

How to convolve a Unit function (like “UnitTriangle”) with a InterpolatedFunction

Recently discovered what InterpolatingFunction's are in Mathematica...really amazing/useful. As I understand it, it's basically a curve fitter....sorta. So how ...
5
votes
1answer
98 views

Finding minimum fly-by radius between Mars and spacecraft from interpolating function

I've written an interplanetary trajectory solver/plotter that plots the path taken by a spacecraft on an Earth-Mars mission, but have run into a little trouble when the spacecraft actually reaches ...
1
vote
2answers
108 views

How to work with lists of functions

I have some lists of interpolated functions and I want to know if there is an easy way to operate with them. A simplified example: ...
2
votes
1answer
332 views

Interpolation: Unstructured grid error

If I try to make a table SimpleTable and to interpolate a function of two variables, I encounter a problem. For example: ...
0
votes
1answer
43 views

ContourListPlot not evaluating all of interpolated area

I am trying to plot a contour for a matrix, but it seems not to be evaluating all the points. Here is the interpolated figure, followed by the MatrixPlot version itself. I used this colormap because ...
1
vote
1answer
95 views

Integrate with FunctionInterpolation differs from NIntegrate

In working with interpolating functions and integration, I noticed a lot of differences between NIntegrate and Integrate in the ...
1
vote
1answer
173 views

Interpolation of a table with 4 parameters

I have a huge data file which I need to do some analysis on it. The file is built in this way that for each 4 variables, there is a value of the function: ...