# Pete Klosterman

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- Name: Pete Klosterman
- Login Name: pete
- Email: PSKlosterman at lbl.gov
- Phone:
- Department:
- Location: Berkeley
- Comment: went to work at Affymetrix, September 2005

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**Project**

- Enhance Ian's xrate evolutionary substitution rate matrices program (part of the DART package) to support asymmetric rate matrices. Thanks to Gerton Lunter for an implementation of general (real) matrix exponentiation.
- For more information on matrix exponentiation:
- Moler and Van Loan's classic "Nineteen Dubious Ways to Compute the Exponential of a Matrix": siam.org or EE221A notes
- 2003 revisiting of "Dubious Ways"
- Expokit

- For more information on matrix exponentiation:
- Gerton's matrix exponentiation code has been tested extensively. It is quite accurate, agreeing with an extensive Taylor expansion to less than 1.0e-14; we have identified cases in which Gerton's code appears to behave well and the Taylor expansion diverges. Gerton's code has also been exercised in the context of the DART Xrate Program. A small test facility, Matrix Exponentiation Test, compares matrix exponentiation, using eigenvalues and eigenvectors, invoking Gerton's code, with that using eigenvalues and eigenvectors calculated using Robert Davies' implementation of Jacobi's method.
- This code is now used by xgram.

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