— Cleve ]]>

— Cleve ]]>

I first encounter MATLAB in September 1993 (then it needed a mathematical co-processor – if I remember right…), at my graduate studies in Electrical Engineering (Electronics), on the third year. Before that, I heard something about it from a bit older students, how great it is, and they use it in DSP – among other things, etc… When I tried it, I was literally blown away! If someone ever tried to do something pretty simple (by hand) – as to find an inverse matrix, he or she have saw that it is a pretty tedious work, and there is always (!) a high possibility to make an small or big error in calculation. If someone done it for a square matrix, let’s say up to order 7-8, You still have a chance to do it correctly. BUT, if You try some “incredible” orders, like 20,30 or more, there is practically no way You can compute it effectively and correctly for a frequent projects/use. There come’s in MATLAB. What I was doing for hours, MATLAB solved in couple of milliseconds! It was unbelievable when I saw it. And, all that in a user friendly environment, with logical commands… Incredible. Not to mention solving (even more in later editions of MATLAB…) non-linear differential equation, or partial differential equations, d.e. unboundary solutions, etc… You need to spend hours, sometimes days – if You cannot figure out the solution – for some/whatever reason (or You make a not so obvious mistake – at least speaking in my name…), and MATLAB does it in a matter of few seconds! Please, for those who don’t know: then, at the time, 25 or more years ago, there wasn’t internet, You “dig” Your answers and knowledge from many books in library, looking for an appropriate solution – or method to solve a problem, keep trying and looking for solution, and for that – You need time, lots of time (often the whole night till the morning hours…), and the result is always questionable – is it correctly defined and calculated…etc…

I strongly believe, that MATLAB has accelerated the piece of science in the world (!) by a great, great amount, not to mention that it was a pivot – a example project, for other similar programs that came latter, but those other programs never (!) were so efficient, fast and user friendly as MATLAB is/was… And, I mentioned a tiny, tiny fraction of fractions what MATLAB is capable of doing…

For me personally and professionally, it is, and it will always be: MATLAB is the “eight” wonder of the world!

A, great and respectful – Thank You, in name of humanity and science.

]]>After reading your beautiful post on Pascal matrices, I would like to add a new interesting aspect of them, already commented by Professor Higham in Section 28.4 of his book: “A more subtle property of the Pascal matrix is that it is totally positive”.

In connection wit MATLAB, an “invisible hand” mysteriously invented the function ones(n,n). It happens that the matrix B = ones(n,n) is precisely the bidiagonal decomposition of the Pascal matrix of order n, and the work of Demmel and Koev has shown us the usefulness of that parameterization of totally nonnegative matrices. So, if we visit the software package of Plamen Koev “Accurate Computations with Totally Nonnegative Matrices” (http://www.math.sjsu.edu/~koev/software/TNTool.html)

we learn that the command P=TNExpand(B) computes the Pascal matrix of order n. More importantly, without computing the Pascal matrix the command TNEigenvalues(B) computes (with high relative accuracy) the corresponding eigenvalues, even for not small values of n. Several additional functions are included in the package.

Thank you, always, for your work.

José-Javier Martínez

]]>However, I’m a little surprised by the assertion that MATLAB’s nchoosek uses Pascal’s identity. I have R2014a. For that version, it appears to use factorials (though not explicitly computed). For example, when the data are of type int64, it calls binCoef: which is described as

% For integers, compute N!/((N-K)! K!) using prime factor cancellations

It also has the curious behaviour of not allowing the first argument to be zero, even though this is well-defined, mathematically.

Still: a fun post. Thanks for sharing.

Niall.

A\b, svd, why, ode45, eigshow, plot

Thanks for asking. ]]>

The list of functions and keywords today has expanded beyond the 1981 version of MATLAB, which 71 keywords and functions were mentioned.

This got me wondering, “What would Cleve put in his top 5 favorite MATLAB functions of all time?”.

I try to make an effort to learn some new functions each week, it is quite an ‘aha moment’ when I discover and use ones I’ve yet to learn.

]]>>> why % not ?

To fool the tall good and smart system manager.

and the fun never ends…

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