With Startup Code Editor opened, save and close the parent worksheet. Any unsaved changes in the Code Editor are lost.

A project that I have been working on is adding some functionality for Cluster Analysis to Maple (a small part of a much bigger project to increase Maple’s toolkit for exploratory data mining and data analysis). The launch of the MapleCloud package manager gave me a way to share my code for the project as it evolves, providing others with some useful new tools and hopefully gathering feedback (and collaborators) along the way.

At this point, there aren’t a lot of commands in the ClusterAnalysis package, but I have already hit upon several interesting applications. For example, while working on a command for plotting clusters of points, one problem I encountered was how to draw the minimal volume enclosing ellipsoid around a group (or cluster) of points. After doing some research, I stumbled upon Khachiyan’s Algorithm, which related to solving linear programming problems with rational data. The math behind this is definitely interesting, but I’m not going to spend any time on it here. For further reading, you can explore the following:

• Ellipsoid Method: https://en.wikipedia.org/wiki/Ellipsoid_method
• The Ellipsoid (Kachiyan) Method: https://web.stanford.edu/class/msande310/ellip.pdf
• A note on Approximate Minimum Volume Enclosing Ellipsoid of Ellipsoids: http://compgeom.com/~piyush/papers/emve.pdf

Khachiyan’s Algorithm had previously been applied in some other languages, but to the best of my knowledge, did not have any Maple implementations. As such, the following code is an implementation of Khachiyan’s Algorithm in 2-D, which could be extended to N-dimensional space rather easily.

This routine accepts an Nx2 dataset and outputs either a plot of the minimum volume enclosing ellipsoid (MVEE) or a list of results as described in the details for the ‘output’ option below.

MVEE( X :: DataSet, optional arguments, additional arguments passed to the plotting command );

The optional arguments are as follows:

• tolerance : realcons;  specifies the convergence criterion
• maxiterations : posint; specifies the maximum number of iterations
• output : {identical(data,plot),list(identical(data,plot))}; specifies the output. If output includes plot, then a plot of the enclosing ellipsoid is returned. If output includes data, then the return includes is a list containing the matrix A, which defines the ellipsoid, the center of the ellipse, and the eigenvalues and eigenvectors that can be used to find the semi-axis coordinates and the angle of rotation, alpha, for the ellipse.
• filled : truefalse; specifies if the returned plot should be filled or not

Code:

You can run this as follows:

As it stands, this is not an export from the “work in progress” ClusterAnalysis package – it’s actually just a local procedure used by the ClusterPlot command. However, it seemed like an interesting enough application that it deserved its own post (and potentially even some consideration for inclusion in some future more geometry-specific package). Here’s an example of how this routine is used from ClusterAnalysis:

The source code for this is stored on GitHub, here:

https://github.com/dskoog/Maple-ClusterAnalysis/blob/master/src/MVEE.mm

Comments and suggestions are welcomed.

If you don’t have a copy of the ClusterAnalysis package, you can install it from the MapleCloud window, or by running:

I tried to solve 4 simultaneous equations but the result is an empty matrix.

Is that because there is no solution or did I make something wrong?

You can download the file by using the link below.

SimEquations.mw

hi 

I have a matrix (for example a 6*6 matrix) and I want to add a row and a column between row and column of number 3 and 4. it means that finally, we have a 7*7 matrix.

tnx

The documentation says that Subgroup(c) returns the subgroup of the coset c.

Also, the display of Elements(lc) is garbled in Maple as well, not just in the image.

These worksheets provide the volume calculations  of a small causal diamond near the tip of the past light cone, using dimensional analysis and particular test metrics.

I recommend them for anyone working in causet theory on the problem of finding higher order corrections.

2D.mw

4D.mw

4Dflat.mw

I want to highlight the intersection between 2 graphs; pp(m,a) and the plane m=-0.2

PP := .8707945038*exp(-50.00000000*(m-0.842e-1)^2+(2.745342070*(m-0.842e-1))*(a-2.3722)-.1046792095*(a-2.3722)^2)

How can I do that?

Thank you

Hello every body

I have a plot that contains two curve. I need to chracterize the curves with `min(D_{T})` and `max(D_{E})`. Is it possible to write legend of plot such that when include it in latex file,  T and E be presented in indices?

With this app you will be able to interpret the curvatures generated by two position vectors, either in the plane or in space. Just enter the position vectors and drag the slider to calculate the curvature at different times and you will of course be able to observe its respective graph. At first I show you how it is developed using the natural syntax of Maple and then optimize our
 app with the use of buttons. App made in Maple for engineering students. In spanish.

Plot_of_Curvature.mw

Videotutorial:

https://www.youtube.com/watch?v=SbXFgr_5JDE

Lenin Araujo Castillo

Ambassador of Maple

i used this  commend to plot three equation and it actually work .my question her how to show any point cordinates just i pointed on it ? could i do it by maple or what ?
help please 
implicitplot3d({f[1], f[2], f[3]}, Q[h] = 0 .. 100, S[h] = 0 .. 100, R[h] = 0 .. 100);

when i evaluate this summation if Q[h],S[h],R[h] are big floating numbers it take along time how i decrease this time 
P := simplify(sum(sum((t+1)*Q[h]^2*(1-Q[h])^(t+T)/(t+1+(R[h]/S[h])^sigma*(T+1)), t = 0 .. infinity), T = 0 .. infinity))

The link below has my code for generating 2 matrices.  The 1st one does not generate flfoating point numerical data; whereas, the 2nd one does.  What is wrong with the 1st case?  I am attempting to single out one harmonic which works in the 2nd case.  Also, is there a way I can generate a spectrum of S2(k= 1 to 100, t= 0 to 1)?

?untitled6.mw

int(1/(s^2+1), s = 1-I*infinity .. 1+I*infinity); # as expected
                               0

evalf(Int(1/(s^2+1), s = 1-I*infinity .. 1+I*infinity)); # Pi?
                          3.141592654

So evalf(Int(...)) either doesn't know how to handle complex infinite endpoints or handles them in a way incompatible with how int() does it.

Hello every body

I have three vectors `X`, `Y` and `Z`. I need to plot `X` vs `Z` and `Y` vs `Z` in one plot. How can I do this?

Thanks in advance

Hi,

I have some matrix valued functions that that I can only define piecewise. Unfortunately I have some problems to manipulate those functions. Piecewise sees to do the job for  scalar valued functions. There I can easily differentiale and add results. For Matrix valued functions however, those features seem to not be availible.
 

I can work around these limitations by manually applying all operations to the operands of the piecewise function. Like I show here:

Download Scratch.mw

I think my workaround is very cumbersome and error prone. Is there a better way to tackle this probem? Or should I try to overload all needed operations, and is this even possible?

Thanks for all suggestions!

Honigmelone