Questions tagged [interpolation]

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

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1 vote
1 answer
93 views

Problem solving a function using FindRoot and then plotting it

When I run the following code: ...
0 votes
1 answer
43 views

find the planar curve that passes two given points, whose tangent directions at these two points are also given

This is related to drawing the links and joints of a robot manipulator. I'd like to find a way to generate a link bwtween two given bars (joints), and the said link has to be normal to the two bars ...
9 votes
2 answers
329 views

Unexpected 'switch' of partial derivatives when differentiating InterpolatingFunction

Bug introduced in 11.3 or earlier and persisting through 12.1.0 or later - Fixed in Version: 12.1.1 In short, there is a simple initial boundary-value problem for which NDSolveValue produces an ...
1 vote
1 answer
223 views

Is it possible to fit such a large range plot in mathematica?

I am trying to solve the coupled differential equation numerically with Mathematica. But the range of values are large so mathematica cannot give correct plot. Here is the code: ...
1 vote
0 answers
59 views

Axial Symmetric 2D Cylindrical Field to Cartesian 3D Field

Previously, I've used 2-dimensioned [radius, zeta] output from NDSolve ({InterpolatingFunction, InterpolatingFunction}] and used the FieldTransform to convert the axial-symmetric cylindrical slice to ...
4 votes
2 answers
579 views

How can I resample a list of {x,y} data for evenly spaced points?

I have generated a list of {x,y} points using a position function of a particle moving in 2D space. If you run the following code you'll see a small bit of the particle's motion (I cut out most of it ...
4 votes
1 answer
177 views

How to represent flux in a shape

I used Tim Laska's solution here for raytracing, and modelled 10000 photons impinging onto a cone. ...
1 vote
1 answer
85 views

lookup table data with interpolation from reference list

I have data as: ...
1 vote
2 answers
1k views

Finding a third degree polynomial that passes through given points

If I have three points xi-1,xi, xi+1 where y(xi) =1 and y(xi-1)=0, y(xi+1)=0 (basis function) and I need to define a line that passes through these points I will use the line equation y-y1=(y2-y1) /(...
12 votes
2 answers
424 views

Rescaling data to make a "continuous" function

I have acquired many sets of data, which all represent a single function, but which are randomly rescaled by a constant (due to the measurement specifics). I'm looking to effectively stitch them ...
12 votes
3 answers
2k views

Approximately Fit Data Without FindFit

I have some noisy data, and I'd like to analyze the derivative of the function the data approximately matches. Interpolation is normally great, but doesn't work ...
2 votes
2 answers
56 views

Cannot understand meaning of "identical"

This came up in the context of plotting solutions to NDSolve, but I've reduced it to the following issue. This really has me scratching my head. ...
3 votes
3 answers
305 views

How to fit spline through points in $ \mathbb{R}^3$?

I have coordinates of points that represent a curve (for example, helix or centerline of moebius strip) in $ \mathbb{R^3}$. I want to fit a Bspline through these points. How to do this in Mathematica? ...
2 votes
1 answer
84 views

Extrapolation Handler and NIntegrate: Bug?

I have an list of data which I interpolate such that it returns the value 0 in case I give it values outside of its domain: ...
0 votes
0 answers
54 views

Evaluating Interpolating functions from NDSolve to solve for a specific time, and evaluating the functions at that time

For one of my homework assignments in a mathematical modeling class, we were supposed to take a 2d system of second order differential equations, and convert it to a 4d first order system of ...
2 votes
2 answers
117 views

How to make interpolation for data of closed shape?

I have a data that describes a closed shape, let here assume it is a circle ...
1 vote
2 answers
126 views

Adding an interpolated function to neural networks through ElementwiseLayer

1.Trying to add an interpolated function to neural networks. ...
0 votes
0 answers
71 views

Interpolated Hyperbolic tangent as a layer of a neural network

It is necessary to specify piecewise linear interpolation of the hyperbolic tangent. And substitute this function as a layer of a neural network. I tried a lot of things, please suggest your options.) ...
0 votes
1 answer
55 views

How do I combine `InterpolatingPolynomial` and `Integrate`?

I want to find a real-valued polynomial (or trig) function f[x] that yields 0 at x=-a, and ...
0 votes
1 answer
526 views

Lagrange Interpolation [duplicate]

I have the following table with 90 elements, and I want to write a loop that gives me the Lagrange operators. I want to construct an interpolation with Lagrange interpolation and show the loop to ...
2 votes
0 answers
58 views

Multivariate polynomial data fitting formula

A short description: consider $f(x,y,z)=x^2+y^2-z^2$ we can know that $f(1,0,1)=0,f(0,1,1)=0$ ,etc. so we can get the roots of this polynomial. Now if given the roots of polynomial, how to solve ...
5 votes
1 answer
231 views

Find a continuous map between two sets of 2D points

Given two sets of points in 2D points1 and points2 inside a rectangle, I would like to find a continuous map ...
1 vote
0 answers
59 views

Why doesn't Sort work in this case ? (Only numerical values)

Context I want to interpolate a complicated symmetric function f of 2 variables x and y defined by some numerical integral involving Bessel functions. Since computing the integral itself is a bit ...
0 votes
1 answer
96 views

How do I prevent the Interpolation function from giving negative values?

I've got an interpolation function: ...
0 votes
0 answers
84 views

Elegant solving and plotting of multivalued solutions for a system of 2 equations with parameters using NSolve?

This looks long and complicated, but it's really not. I just tried to pose the problem well. I have to solve a relatively complicated system of equations that has 2 variables and 3 parameters. I ...
0 votes
0 answers
76 views

Creating an interpolation matrix efficiently

I would like to know if there is a fast way to create the following matrix (note that the matrix is defined with arbitrary precision): ...
0 votes
2 answers
90 views

Numerical integration of an interpolating function with another analytic function [closed]

I have to numerically integrate over $x$ a complicated function that has this structure $f(x,y)g(x)$ with a parameter $y$. In my case the fastest way to deal with it is generate an interpolating ...
0 votes
1 answer
76 views

I am having trouble with the Show[] section of this code

Question: I am unsure how to graph the interpolated graph with the regular graph on the interval $[1,4]$. Not even the Show line works about even if I'm pretty sure ...
1 vote
2 answers
87 views

How to solve an algebraic equation with InterpolatingFunction?

How to solve the equation f[t]==0 for the function f[t] defined by differential equation,i.e. if ...
0 votes
0 answers
51 views

Is it possible to obtain the algebraic expression of an InterpolatingFunction? [duplicate]

Up until now, I have been trying to obtain an expression for an InterpolatingFunction obtained from NDSolve, by using the ...
0 votes
1 answer
47 views

Replacing sublists with criterion or Interpolation for a smooth curve

Supposing we have the following list (very small, can be copied into a notebook directly) ...
17 votes
3 answers
2k 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 ...
3 votes
2 answers
78 views

Testing Positivity of Interpolating Function

I have an interpolating function and I want to test whether it is positive definite over an interval. Will any of Mathematica's numerical optimisation functions work for this or is there a simpler ...
13 votes
2 answers
1k views

smooth spline through airfoil coordinates

I am trying to produce a smooth spline curve through a set of airfoil coordinates. An example for the data I am trying to use is here, and I am reading the file like so to get rid of some extraneous ...
3 votes
2 answers
446 views

How to make a natural cubic spline of {{x,y}, ...} data

Consider data = {{0, 0}, {1, 0}, {2, 0}, {3, 1}, {4, 0}, {5, 0}, {6, 0}}; f = Interpolation[data, InterpolationOrder -> 3, Method -> "Spline"]; Then the ...
0 votes
1 answer
94 views

Find the two largest maximums of an interpolating function of a specific shape (fast)

I have an oscillating interpolating function f[x] and I would like to find the x values of the two largest maximums (or even ...
5 votes
0 answers
122 views

Why do some uses of PropertyList crash the kernel?

Bug introduced in 10.1.0 or earlier and fixed in 12.1.0 While looking at the question How to evaluate the "Domain" of an InterpolationObject? I noted that using ...
6 votes
1 answer
337 views

Different results using spline interpolation in Wolfram and MATLAB

I use the same data for interpolation in Mathematica and MATLAB, but the result is different. ...
4 votes
4 answers
241 views

Can I Constrain ListInterpolation by Curvature?

Using image analysis, I have found the positions of a circular ring and imported them as xx and yy coordinates. I am using ...
3 votes
1 answer
96 views

Generating and analyzing an Interpolating function from many interpolating functions: speed up

Is there a clever way to speed up this code? ...
8 votes
1 answer
2k views

Hermite interpolation

The well known Hermite interpolation uses piecewise cubic polynomials and fits the knot values and derivatives. In contrast the Mathematica piecewise Interpolation ...
2 votes
1 answer
838 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 ...
1 vote
0 answers
90 views

NIntegrate 3D Interpolation function in a region extracted from ListContourPlot3D

I have a list of 3D volumetric data points, e.g. for every position in 3D space there is a value. What I want to do is to firstly use "Interpolation" to get a function form of the data f[x,y,z] and do ...
3 votes
2 answers
201 views

How can I make ListDensityPlot show up only in a specified region?

Disclaimer: I am new to Mathematica and this is my first post here! I am trying to plot EEG data of different intensities of brain waves from an FFT to areas of the brain where they were collected. I ...
1 vote
0 answers
70 views

Interpolating a density plot

I am solving a complicated series of equations (involving FindRoot and PolyLog), and finally I get this plot Code here: ...
9 votes
3 answers
5k views

Is it possible to compute with the trapezoidal rule by 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 ...
1 vote
1 answer
81 views

How to convert Piecewise function to Interpolation function?

In the following piece of code I am trying to convert a Piecewise function to a simple interpolation function f[t_] ...
2 votes
1 answer
213 views

How to interpolate {{xi,yi},... ,{xn,yn}} with minimum bending energy?

Thin Plate Splines are explained here, and a Mathematica implementation of that for real samples { { x1, y2, z1 }, { x2, y2, z2 }, ... , { xn, yn, zn } } is ...
3 votes
1 answer
79 views

How can I force an interpolated function to go through a certain point?

Let's take this interpolated function: f = ListInterpolation[{1, 2, 3, 5, 8, 5}] I want to make 1/f'[x] go through a certain ...
2 votes
2 answers
92 views

Integral of a Wavelet function

I ran into problems integrating a function which contains both an If condition and a Wavelet which is an ...

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