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From |
"Katsuhide Isa" <katu@ier.hit-u.ac.jp> |

To |
Statalist <statalist@hsphsun2.harvard.edu> |

Subject |
st: manipulation of eigenvalues |

Date |
Fri, 15 Apr 2005 22:03:18 +0900 |

Dear Statalisters, I'm working with transition matrices (namely, the matrices whose rows all sum up to be unity) of 47 x 47 size for 20 years using Stata 8. And I have two questions as to this topic. (1) As is well known, their maximal eigenvalues are guaranteed to be unity. And one way to measure the speed of convergence to the long-run equilibrium state of the given transition matrix is to use the absolute value of the 2nd (largest) eigenvalue. So, it'd be convenient to sort eigenvalues in descending (or ascending) order for each matrix and (if possible) extract the 2nd eigenvalues alone to combine/graph them and check their time-series patten. # Currently I copy and paste each value from a log file. Is there any handy way to do so in Stata? (2) Regarding the above point, though the Programming Reference Manual says that the extracted eigenvalues are to be sorted in ascending order, it's not necessarily the case; when the codes below (the ones suggested in the Manual) are issued, forvalues i = 1/47 { di sqrt(re[1, `i']^2 + im[1,`i']^2) } following outputs are shown (sorry for lengthy texts): .40468505 .50863593 .57787482 .66516332 .70771485 .84072082 .87075128 .89745642 .90354965 .90619857 .91547048 .9183964 .92652875 .92758641 .93138665 .9430583 .94063044 .94064868 .95091566 .94943396 .95769209 .96646326 .97100423 .97126325 .99999999 .99876833 .97456569 .97597157 .97597157 .97759933 .97843964 .97892578 .98151891 .98151891 .99748731 .99651247 .9962227 .99432542 .99370197 .99310467 .98430497 .98498111 .98664358 .9900003 .98993781 .98887064 .98861453 You can check that these values are not necessarily monotonically increasing. Is this just a coincidence or an environment-specific phenomenon (or something else) ? Any suggestions welcome. Thanks in advance. K.I. * * 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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