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

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1answer
215 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 ...
4
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3answers
1k 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
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1answer
80 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
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2answers
256 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 ...
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1answer
264 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
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3answers
1k 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
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2answers
193 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
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4answers
409 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
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1answer
117 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
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1answer
171 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
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1answer
384 views

Integrating a functional of an InterpolatingFunction

It is straightforward to Integrate an InterpolatingFunction. However, even for a simple functional of an ...
2
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1answer
84 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
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1answer
258 views

Create ParametricFunction object without ParametricNDSolve

Documentation of v9 states that ParametricFunction is generated by ParametricNDSolve and ...
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3answers
857 views

Parametric Interpolation of 2D data

I want to create an interpolation through the following 2dim data points: ...
4
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1answer
433 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
370 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
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0answers
53 views

Conjugate of InterpolatingFunction?

From NDSolve, I got this: {{a1 -> InterpolatingFunction[{{0., 40.}}, "<>"]}} What would be a sensible approach to ...
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0answers
78 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
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1answer
49 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
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2answers
122 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
259 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
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1answer
145 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 ...
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0answers
33 views

Integration of any interpolation generates invalid comparison errors [duplicate]

Integrating a simple interpolated function as follows generates invalid comparison errors. ...
1
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1answer
125 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 ...
1
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2answers
113 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
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1answer
682 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
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1answer
52 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 ...
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1answer
197 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 ...
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1answer
204 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: ...
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2answers
304 views

How to resolve the duplicate error during interpolation

I have few hundred data points corresponding to an irregular shape closed curve. As the result I have data points that have the same value of y but different values of x. I want to create an ...
0
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0answers
31 views

FindRoot gives strange results when used on an interpolating function with vector output [duplicate]

I am currently experiencing a problem when I try to use FindRoot with an interpolating function that outputs a vector. I have constructed a minimal example that ...
0
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0answers
245 views

Interpolation of multidimensional data organized logarithmically

The following threads call our attention to the fact that "accuracy of Interpolation will be worse with an unstructured grid", in the context of interpolation of 3d data: interpolation of 3D data ...
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0answers
97 views

NMaximize and Accuracy

I have a problem with NMaximize which is best depicted by the following figure. The result indicates, that the solution mathematica finds seems to be smooth except a few outliers. How can I get rid of ...
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1answer
190 views

Is linear interpolation applicable here

From my understanding about Linear Interpolation especially of that of Newton's Divided Difference Polynomial, we could get the value of F(x) from the given set of ...
2
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0answers
163 views

Slow integration of interpolating function

I have a large file with irregularly spaced data in the format: ...
19
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4answers
2k 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 ...
6
votes
2answers
588 views

Finding a 3d curve from torsion and curvature with NDSolve

I'm trying to use the Frenet–Serret formulas to find the curve that matches the torsion and curvature I specify numerically with an InterpolatingFunction. The ...
1
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1answer
189 views

Finding Minimum of a list after interpolation

I have a set of lists called Er[l], where l is from 1 to 13. I want to find the minimum point in the plot in these lists after interpolation by spline method. I need the values and the points on the ...
8
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2answers
479 views

How to make use of an interpolating function outside of Mathematica? [duplicate]

I'm currently working on a project where I have to solve some partial differential equations. Initially, I made some approximations so that an analytic solution could be obtained, and my ...
2
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1answer
397 views

How to make a 3D-Plot from 2D-interpolated data

I have data of the form {x,y} for different concentrations. Therefore I added the concentration as z, resulting now in ...
1
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1answer
145 views

Partitioning a numerical integral: need to integrate spectra

I am trying to integrate a spectrum I obtained from a fourier transform infrared spectroscopy experiment, in order to determine the global warming potential of green house gases. In order to do this, ...
0
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1answer
195 views

Interpolation problem on the list

I have a List of Latitude, Longitude and Measurement. a = {{{93, 104}, 290}, {{94, 103}, 292}, {{95, 105}, 291}, {{97, 109}, 294}, {{97, 102}, 295}}; And, I ...
2
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1answer
483 views

Find fit for complex function for smooth derivatives

I need to fit my data dropbox of the form {x,y} because I need the fit function for further derivative calculation. My derivative curve should be smooth. I tried ...
5
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1answer
352 views

ListPlot3D of a set of points in a non-convex region

I would like to plot a set of points in the same style as ListPlot3D does, but only in a non-convex region that I can specify (e.g. using a ...
1
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1answer
608 views

Cubic Splines Functions

I have this set of three data points and want the natural cubic spline functions for them: dat = {{-.0247500, .5}, {.3349375, -.25}, {1.101000, 0}}; I tried: ...
3
votes
2answers
427 views

Interpolating data with a step

Suppose I have some data with a step in it: data = {{1, 1}, {2, 2}, {3, 3}, {3, 4}, {4, 5}, {5, 6}}; Interpolation will complain about this and not give you an ...
4
votes
3answers
212 views

Variable partitioning of the data in the form of “list of lists”

I am looking for a way for variable partitioning of the data in the form of a "list of lists" for interpolating the imported data from excel. The data looks like: ...
3
votes
1answer
210 views

NDSolve much slower when using InterpolatingFunctions inside

I am solving an ODE system with Mathematica. Let's say the system is of the form (to simplify). ...
3
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0answers
564 views

Interpolate throughout a 3d data list without extrapolation

I have a 3D list of data for which I'd like to plot an interpolated surface. There are several ways to achieve this, but none I cannot find a method which ONLY plots the ENTIRE interpolated surface ...