# Tagged Questions

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

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### 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 ...
61 views

### Select pairs of columns from an array of data [on hold]

I try to interpolate the first two columns of a seven-column file formatted as follows: ...
50 views

### Interpolated lookups over time from an event log

"Interpolating" might be technically incorrect but it captures in my mind what I'm trying to do here. I am trying to reconstruct the history of a bug tracking system, and what I have access to is an ...
252 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: ...
172 views

### How to know form of plotted Bezier function

Simple scenario is to see the Bezier function, but how to know which polynomial approximate it? ...
82 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 ...
169 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 ...
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### 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 ...
161 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 several error messages: ...
185 views

### Extracting the function from InterpolatingFunction object

I've used Interpolation[] to generate an InterpolatingFunction object from a list of integers. ...
34 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 ...
74 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 $w(x,y) = x + y + z(x,y)$ ...
112 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. ...
190 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, ...
162 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 ...
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### 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 ...
351 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 ...
70 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 ...
157 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 ...
788 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 ...
153 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 ...
111 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 ...
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### Interpolation function evaluation and timing

Lets define two identical functions $f$ and $g$ in a slightly different way ...
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### 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 ...
110 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 ...
158 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: ...
99 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 ...
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### 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 ...
68 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 ...
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### FunctionInterpolation error when specifying AccuracyGoal

In the help page ref/message/FunctionInterpolation/ncvb, it is mentioned that one should specify AccuracyGoal for some (even ...
156 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 ...
384 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 ...
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### 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: ...
106 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 ...
92 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 ...
492 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 ...
155 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? ...
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### Evaluating InterpolatingFunction returned by NDSolve is very slow starting from some arguments

I use this code to solve a PDE: ...
250 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 ...
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### 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 ...
138 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 ...
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### Integrating a functional of an InterpolatingFunction

It is straightforward to Integrate an InterpolatingFunction. However, even for a simple functional of an ...
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### 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 ...
229 views

### Create ParametricFunction object without ParametricNDSolve

Documentation of v9 states that ParametricFunction is generated by ParametricNDSolve and ...
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### 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 ...
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 ...
650 views

### Parametric Interpolation of 2D data

I want to create an interpolation through the following 2dim data points: ...
304 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: ...