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

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How to retrieve values from an interpolated answer [duplicate]

I have a function called "system" and I am using NDSolve to retrieve the solution, which works perfectly. When I go to graph the solutions they graph fine, but when trying to retrieve the individual ...
3
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1answer
50 views

Second derivative of SmoothKernelDistribution PDF?

Does anyone know why I can't seem to get a second derivative of this interpolating function f? In this example, h[x] is zero ...
1
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3answers
85 views

2D Interpolation of data file

I hae a datafile with 5 columns of the structure: x_i f(x_i,y_1) f(x_i,y_2) f(x_i,y_3) f(x_i,y_3) f(x_i,y_4) with i = 1 to about 100. Thus there are about ...
2
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0answers
43 views

Construct single InterpolatingFunction from a mathematical combination of other IF's

Let's say I have an interpolated function f, like I might get as the solution to an NDSolve: ...
0
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1answer
24 views

Many NSolves to interpolating function

I have an expression of the form: expr = TerribleNumericalFunction[U[p]] == SimpleFunction[p] The Simple function is a ...
2
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0answers
35 views

Update NumericalFunction in NDSolve

I have NDSolve` StateData from an NDSolve` ...
7
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1answer
75 views

Changing the `ExtrapolationHandler` Function in Any Interpolation

This is a related question to What's inside InterpolatingFunction[{{1., 4.}}, <>]? and Suppress extrapolation of interpolating function in a ContourPlot. When interpolating a set of ...
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1answer
35 views

Calculate the partial vapor pressures of a variable at xB = 0.75 based on the interpolation functions of the data

I'm having troubles in solving an exercise for an assignment in my Chemistry course. Talking about interpolations, I've already have a graph but I need to:(c) Calculate the partial vapor pressures of ...
6
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1answer
177 views

Interpolation on a regular square grid spanning a triangular domain

Context I am trying to identify contours of a function which is sampled on a cartesian grid within an irregular (triangular) region. Here is the data ...
2
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1answer
49 views

Interpolate a discrete vector field

I have a discrete vector field, from which I want to derive the continuous one. For example, the planar vector field is defined by: ...
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1answer
73 views

Using InterpolatingFunction in equations

I tried to use InterpolatingFunction in another ODE, but it doesn't work, because it seems for Mathematica that 2 functions are unknown instead of one. ...
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1answer
61 views

Interpolating a non-continuous set of points

I'm trying to create a pure function that I can feed into OutputResponse[ ] as the input u[t]. In order to do this, I've written code to create a square wave pulse train in the form of a collection of ...
1
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1answer
58 views

how to reduce noise in time series data?how to do interpolation for missing value data?

i have done this coding to plot the data. the problem is some value is missing for certain date and the graph is not smooth and noisy. one way to smooth the data is by interpolation but i dont know ...
3
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2answers
89 views

Numerical root-finding: Find leftmost root in a domain

This is surely a duplicate, but I cannot seem to find a similar question. I use NDSolve to find an InterpolatingFunction y[t] ...
1
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1answer
147 views

Line integrals over a path defined by a set of points (rather than an analytic formula)

I'm getting inaccurate results when computing (plotting) the value of a function against the length of a line integral, where the path comes from a set of numerically calculated points. (In contrast, ...
2
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3answers
212 views

Function to calculate average of multiple lists

I have several lists of experimental data f[x] with different intervals Δx including some noise. ...
0
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1answer
55 views

Numerical integration of a three dimensional array

I need to integrate a scalar valued function $f\left(\boldsymbol{x}\right)$ where $\boldsymbol{x}$ is a three dimensional position vector; in other words: $\int_{\Omega} f\left(\boldsymbol{x}\right) ...
2
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1answer
99 views

Find tangency of InterpolatingFunction and circle

I am trying to use a system of equations to solve for the common tangent of a (polar) InterpolatingFunction and a circle. Unfortunately, both NSolve and FindRoot don't yield results, even when I ...
0
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0answers
59 views

Interpolation of a NURBS curve

Known that NQ=P where N is the Bspline basis function, Q is the control point that we wish to locate, P is the data points given ( the curve must pass through it) is there any way to modify the "N" ...
3
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0answers
49 views

Strange extrapolation in ListContourPlot?

I have some Table of {x,y,z} values (energy as a function of radial and azimuthal frequencies in a galaxy if you care to know): ...
1
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1answer
57 views

Making a movie from an interpolating function

Say I use some Mathematica procedures to find an interpolating function of two variables: $u(x,t)$. Is it possible to make a movie of this interpolating function, i.e. plot it on a certain line $x \in ...
3
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2answers
68 views

FunctionInterpolation with vector output and scalar input

Apparently it is possible to build and InterpolatingFunction that accepts a vector input and returns a vector output: ...
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2answers
91 views

calculate missing values, Interpolation

I've following data: ...
2
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0answers
89 views

Position from 3 dimensional acceleration data? [closed]

Per a previous post on Mathematica StackExchange here I'm trying to utilize 3-axis accelerometer data to determine approximate 3D position. I wanted to start with a simple case. To this end I've ...
2
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2answers
105 views

Derivative of Vectoral NDSolve Interpolated Function / Rule Solutions,/., and Vector NDSolve [duplicate]

I need to find the instantaneous phase and instantaneous frequency for a rotating system. I am having difficulty making the math work with interpolating functions. First, here is a problem without ...
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1answer
52 views

How to fit this data to be used in NIntegrate later?

I have a list of data points that resemble a chi-squared distribution (long tailed gaussian) that I am having trouble fitting or finding an equation with. The goal is to use the fitted equation in an ...
6
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2answers
285 views

ListContourPlot interpolation fails if x and y axes have different scales

To summarize what is below: ListContourPlot doesn't work when the domain has different x and y scales (fails when x/y~10^4, which seems surprisingly small). Is it possible to call ListContourPlot ...
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0answers
185 views

NDSolve: Equation with interpolating function [closed]

I have a question regarding DSolve and NDSolve functions in Mathematica 10. For instance, I'd like to solve an ODE: ...
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2answers
137 views

Aitken interpolation of a polynomial?

How I can approximate a polynomial using Aitken's scheme using two nodes for the interpolation? ...
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3answers
165 views

Transform an InterpolatingFunction

I'd like to transform an InterpolatingFunction from NDSolve but can't figure out how. Here's an example. The equation I want to solve is ...
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1answer
107 views

How do I find out what a Mathematica function is doing (which numerical method it uses and how)?

Long story short, I am working on a project which entails fixing a bug I have found in Mathematica (8 and 10). In general, I would like to know what a specific Mathematica function is actually doing ...
2
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1answer
134 views

Smooth animation of ListLinePlot

I have a sequence of 2D-points from uniformly sampling a time dependent process and plot this sequence with ListLinePlot. For example: ...
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1answer
85 views

Reduced interpolation order [closed]

I have a problem with Interpolation - the order is reduced to 1 no matter what, but I need a quadratic interpolation order. The ...
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0answers
50 views

Improving RationalInterpolation Result

The following code produces a {4,4} rational interpolation approximation accurate to 10^-6 or better over the range ...
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1answer
72 views

how to make interpolated data as a function?

For example, data1 = 0 1 1 2 3 3 5 2 6 2 9 4 11 5 13 6 14 7 16 8 data2 = 0 2 1 3 2 2 3 1 4 2 6 3 8 4 9 6 11 4 16 7 each data have different x-axis interval. so ...
3
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1answer
106 views

List interpolation

Hi mathematica people! So i am looking for the best way to interpolate a function given a list of its values. I have an iterative algorithm which needs high precision otherwise the numerical noise is ...
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0answers
28 views

Why numerical functions can't digest InterpolatingFunction with units?

Answering this question gave me the idea that I must be missing something.. In brief, numerical functions generally 'understand' units: ...
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1answer
67 views

Interpolating a polynomial for with first and second derivative of points

I am trying to fit a polynomial for switch cutoff which is used in Molecular dynamics. I want a fifth order polynomial with six coefficient $c_0, ...,c_6$ between $r_1<r<r_2$ with these ...
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1answer
94 views

What extrapolation method does Interpolation use by default? [closed]

As far as I can tell, Interpolation uses cubic spline interpolation by default - please correct me if I'm wrong. What does it use for extrapolation outside of the ...
1
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3answers
198 views

Developing a function of two variables from given data

Cross listed from MSE: http://math.stackexchange.com/questions/1029399/developing-a-function-of-two-variables-from-given-data (I believe Mathematica SE is an appropriate place to ask this, as well.) ...
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0answers
47 views

How does Mathematica interpolates? [duplicate]

In manual for Interpolate function it is said, that possible method of interpolation is Hermite. Unfortunately, I can't see ...
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0answers
78 views

plotting the stable and unstable manifolds of a difference equation

I have a 2D non-linear system of difference equations for variables x and y defined as follows: ...
3
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2answers
143 views

Interpolation function error: Interpolation::femimq and Interpolation::fememtlq

In Mathematica 10 the following command ...
3
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1answer
102 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): ...
2
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1answer
81 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 upon itself, loop, and so forth as for ...
0
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0answers
51 views

Combination of interpolations doesn't work?

I have a table valued functions f[i_] and g[i_] and I need to plot various combinations of the function and its derivatives (for example: f''f, f'/f). I tried interpolating f[i_] to ->f[x] and ...
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0answers
56 views

Interpolation of Singular Functions

I am trying to interpolate discontinuous (1/R-r)EllipticK[r/(R-r)^2] functions for R in interval $[0,100]$ and ...
1
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1answer
80 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
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1answer
71 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
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2answers
190 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 ...