# Tagged Questions

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

292 views

### Intersection of a ListPlot3D surface with a plane

I'm trying to use Mathematica to analyze some physics data from an experiment, more precisely, I have to fit a 2D data series with a one dimension function. At the moment I'm able to load and plot ...
56 views

### Using Quantity[] units causes errors in my calculation

I have an interpolation function in which I wish to use actual units. If I perform the calculation normally, it works fine and returns a proper FittedModel. To illustrate my problem, consider the ...
60 views

### How to generate commands which are very similar?

I have several data sets that I wish to interpolate and integrate like this: ...
201 views

### Approximation of definite integral by parabolas

This question is related to Trapezoid approximation to definite integral. As promised, I am now asking about how to draw an approximation of integrals by parabolas. I tried to modify MarcoB's code, ...
317 views

### Build an InterpolatingFunction with ElementMeshInterpolation

Suppose you have a function f[t_, x_, y_] := t (1 - x^2 - y^2) defined for {x,y} in ...
106 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 ...
236 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 ...
136 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: ...
133 views

### Many NSolves to interpolating function

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

### Update NumericalFunction in NDSolve

I have NDSolve StateData from an NDSolve ...
271 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 points,...
73 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 calculate the partial vapor pressures of ...
583 views

### Interpolation on a regular square grid spanning a triangular domain

Bug introduced in 10.0 and fixed in 10.1 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 <...
248 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: ...
134 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. ...
81 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 ...
262 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 ...
171 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] ...
210 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, ...
572 views

### Function to calculate average of multiple lists

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

181 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: ...
132 views

### calculate missing values, Interpolation

I've following data: ...
334 views

### Function for a series of joined slopes

I need a function for a series of joined slopes and my solution feels a bit kludgy. Is there a better way? A list of pairs of transition points and slopes: ...
143 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 ...
199 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 ...
75 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 ...
700 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 ...
226 views

### Aitken interpolation of a polynomial?

How I can approximate a polynomial using Aitken's scheme using two nodes for the interpolation? ...
350 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 ...
161 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 ...
251 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: ...
70 views

### Improving RationalInterpolation Result

The following code produces a {4,4} rational interpolation approximation accurate to 10^-6 or better over the range ...
118 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 ...
214 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 ...
95 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 ...
361 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 ...
610 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.) ...
51 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 ...
244 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: ...
402 views

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

In Mathematica 10 the following command ...
219 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): <...
215 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 ...
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 ...
I am trying to interpolate discontinuous functions for R in interval $[0,100]$ and r in interval $[0,100]$: ...