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

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4
votes
1answer
220 views

How to evaluate differential entropy from raw data?

I want to evaluate the differential entropy according to here $$h(X) = - \int f(x) \log{f(x)} dx$$ where $f$ is the probability density function. Lets create some test data (normal distribution): <...
3
votes
1answer
216 views

Hermite method in Mathematica

When I solve the example below, in the results it is mentioned that Mathematica 10 has used the Hermite method. I cannot find anything about this in the Mathematica documentation. Is there nothing ...
2
votes
2answers
180 views

BSpline or other curve through arbitrary ordered sequence of two-dimensional points

How does one create a BSplineCurve or other smooth curve passing through each point in an ordered list, where the curve may be non-simple, i.e., can double-back ...
3
votes
3answers
125 views

Combination of interpolations doesn't work?

I have tables of function values f[i_] and g[i_] and I need to plot various combinations of the function and its derivatives (...
2
votes
0answers
139 views

Interpolation of Singular Functions

I am trying to interpolate discontinuous functions for R in interval $[0,100]$ and r in interval $[0,100]$: ...
1
vote
1answer
144 views

Series expansion of InterpolatingFunction obtained from NDSolve

I am trying to obtain a series expansion of the numerical solution of a differential equation. I encounter difficulties going beyond first-order expansions which I believe might be due to my inability ...
1
vote
1answer
113 views

NDSolve with a constant

I have a simple differential equation like this s = NDSolve[{y'[x] == A y[x] Cos[x + y[x]], y[0] == 1}, y, {x, 0, 30}] where $A$ is a constant. Mathematica gives ...
6
votes
2answers
465 views

2D smoothing spline interpolation

Does Mathematica have 2D smoothing spline interpolation built in? I requires an interpolation method with smooth first derivatives and cubic bivariate splines fulfill this nicely. In python I would ...
8
votes
3answers
1k views

Suppress extrapolation of interpolating function in a ContourPlot

I have defined an interpolating function, myfcn[x], valid on the domain x = 0 to 1.5. I am then using ...
3
votes
1answer
163 views

Fast list interpolation over common x,y for multiple variables

I have a (long, >50K elements) unstructured list with a header similar to; AList[[1]] = {x,y,z,var1,var2,var3,var4,...,varN} I want to interpolate z, var1, var2, ...
12
votes
2answers
303 views

Temporal database reconstruction in mathematica

<EDIT> after some internet research I found the database domain that deals with this kind of thing: Temporal Databases. I think my question therefore becomes how to reconstruct a temporal ...
13
votes
1answer
916 views

Curve fit based on minimal data

Inspired by the fantastic answers here and here, I would like to ask a questions along similar lines. I have 6 curve types that follow these rules: Type A: If point 1 is positive and point 2 is ...
10
votes
5answers
945 views

Multidimensional interpolation with duplicate abscissa values [duplicate]

I am trying to do a first order interpolation on a multidimensional data set containing duplicate abscissa values (which Mathematica does not like), like this one: ...
1
vote
0answers
65 views

Show actual Interpolation function [duplicate]

Is there a command to show the actual function when using the Interpolation command? For example, f = Interpolation[{1, 2, 3, 5, 8, 5}] returns ...
3
votes
1answer
721 views

Can I use the values of interpolating points from NDSolve's output? And How?‎

The output of NDSolve is a (list of)InterpolatingFunction(s). In standard output format the ‎elements of interpolation are not ...
14
votes
2answers
1k views

Extracting the function from InterpolatingFunction object

I've used Interpolation[] to generate an InterpolatingFunction object from a list of integers. ...
8
votes
0answers
349 views

Interpolation on an unstructured (mostly-structured) grid in 4D+

I frequently need to perform interpolations on an unstructured grid. Mostly, with the purpose of filling grid holes and then later continue with regular grid interpolations. Mathematica V9 and V10 ...
10
votes
2answers
539 views

Interpolating an Antiderivative

I'd like to be able to make InterpolatingFunctions for antiderivatives of functions that can't be integrated symbolically. However, the following code returns ...
0
votes
2answers
133 views

Replace $z$ with interpolated function and plotting

I start off with this equation $z(x,y) = sin(xy)$. I create an interpolation from $0 < x < 5$ and $0 < y < 5$. I then use this interpolation on a simple function $w(x,y) = x + y + z(x,y)$ ...
1
vote
2answers
290 views

Integrating Squared of Interpolating Function with respect to one variable

I am interested in evaluating a two dimensional interpolating function produced by solving the wave equation. Here is the code that includes the resulting interpolating function. ...
2
votes
2answers
335 views

How do I feed data points into an equation to solve NUMERICALLY?

I start with this equation and solve it numerically for $z(x,y)$ in the range $1 < x < 5$ and $1 < y < 5$: $$ \frac{3}{xyz} - 2x - 3y - 5z = 0 $$ Then using the data points of $z$ above, ...
9
votes
2answers
398 views

interpolating function over dates

I've got a bunch of readings at various dates and times. I'd like to be able to interpolate and then integrate over, say days. I can do this by converting my date/time to ...
2
votes
1answer
116 views

Is there a reason why some specific arrangement of scattered grid points would yield bad RBF (Obtuse package) interpolation results?

I have an arrangement of grid points given by the figure below (the datagrid data is posted below at the end of the post): They correspond to electrode positions of an EEG signal. I am ...
20
votes
2answers
618 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 ...
16
votes
2answers
3k views

Find maximum value of interpolation function - obviously wrong result

Minimizing and maximizing interpolation function has already been asked and answered, see here for example. Yet, I observe a strange behaviour. Well, I can understand that the wrong guess of ...
0
votes
1answer
412 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 <...
11
votes
1answer
237 views

Incompatible InterpolatingFunction between V9 (and earlier) and V10

Bug introduced in 10.0.0 and fixed in 10.0.1 I am encountering compatibility issues when loading DumpSave(d) definitions in V10 that have been created with ...
3
votes
1answer
323 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 ...
1
vote
1answer
94 views

Interpolation function evaluation and timing

Lets define two identical functions $f$ and $g$ in a slightly different way ...
8
votes
2answers
457 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
122 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 ...
2
votes
1answer
147 views

How to generate specific function using BSpline command?

I want to generate an approximation function that fits a curve to points. My goal is to obtain an actual formula. Is this possible with BSplineFunction? Using the ...
6
votes
3answers
979 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
1answer
185 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 presentation....
3
votes
3answers
239 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: ...
5
votes
1answer
158 views

FunctionInterpolation error when specifying AccuracyGoal

Bug introduced in 8 or earlier and persisting through 10.4 or later In the help page ref/message/FunctionInterpolation/ncvb, it is mentioned that one should ...
5
votes
3answers
3k 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
2answers
693 views

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

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 ...
1
vote
1answer
599 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 ...
8
votes
3answers
3k 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
265 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? ...
0
votes
1answer
288 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 ...
3
votes
4answers
588 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 ...
4
votes
1answer
980 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
102 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 ...
2
votes
1answer
216 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
200 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 ...
0
votes
1answer
93 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: ...
16
votes
3answers
1k views

Parametric Interpolation of 2D data

I want to create an interpolation through the following 2dim data points: ...
2
votes
2answers
1k 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 ...