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From |
vwiggins@stata.com (Vince Wiggins, StataCorp) |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Mata question: -matrix languages evaluate matrix expressions-? |

Date |
Tue, 12 Apr 2005 16:17:15 -0500 |

Renzo Comolli <renzo.comolli@yale.edu> asks whether a comment at http://www.stata.com/stata9/mata.html concerns precision in Mata's computations. (Mata is the new matrix programming language in Stata 9.) The comment from the website is > "Everybody knows that matrix languages evaluate matrix expressions, > such as b=invsym(X'X)*X'y, and Mata is no exception. Because of > Mata's design, however, it is fast enough to work at the element > level". And Renzo asks > This looks like a disclaimer of some sort about some loss of > precision, but I got quite understand the implications of this. Can > anybody clarify? [...] Not a disclaimer at all. The comment concerns speed alone. The point is that vectorized computations, such as X'X, when done in internal C code are fast whether done in Stata or Mata. If, however, we write the triple loop required to multiply two matrices by hand, the loop will be about 2,000 times faster when programmed in Mata than when programmed in Stata ado-code. While we recommend that you try to avoid looping through a dataset in Stata ado-code, we make no such recommendation for Mata. Internal computations are still faster, but Mata is very fast at executing instructions and, therefore, at looping. Mata is what computer scientists call a p-coded (or byte-coded) language, meaning that what you type in Mata is first compiled into a series of byte codes (actually short integers). Then these codes are executed, and executed fast. For those familiar with Java, it is also a byte-coded language. For computing history buffs, Niklaus Wirth's Pascal compiled to p-code (pseudo-code). P-code and byte-code mean the same thing. Whether implemented internally or in Mata itself, good algorithms will produce good numeric results, at least to the precision computers afford. Because numerics can be important and problems differ, Mata provides four different linear solvers: Cholesky decomposition, LU decomposition, QR decomposition, and singular value decomposition. What's more, because the computation of cross products can be particularly sensitive to scale, Mata provides a quad-precision accumulator. You can see the online help for the latter using the help server on the Stata website by pointing your web browser at http://www.stata.com/help.cgi?mf_quadcross. At this point, I have to admit that the two best experts on Mata are in Europe. They attended the German User Group meeting and are now attending another conference in Spain. -- Vince vwiggins@stata.com * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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