Hello, Jason. You wrote 21 мая 2010 г., 3:48:03:
> A while ago someone talked about incorporating ALGLIB into Sage to > provide, among other things, multiprecision linear algebra. It was me :) I am working on this issue. I expect that interface between double precision ALGLIB and Python will be ready in 2-3 weeks, with multiple precision interface following several weeks later. > Does anyone have experience with mplapack? How does it compare to > ALGLIB in linear algebra (for algorithms that are implemented in both)? I haven't benchmarked mplapack, but I can say something about it and can compare it with ALGLIB: == ALGORITHMS ======================================================== MPLAPACK includes all LAPACK algorithms, especially wide set of generalized EVD/SVD solver. Nothing beyond LAPACK is included. ALGLIB includes subset of LAPACK: real/complex/SPD/HPD triangular factorizations, inverses, solvers; real/complex/Hermitian EVD, real SVD. However, it also includes algorithms beyond linear algebra: numerical integration, interpolation/fitting, optimization, many other algorithms (including those which won't benefit from multiple precision). == MULTIPLE PRECISION SUPPORT ======================================== MPLAPACK supports several multiple precision types: * mpf_t (GMP) * mpfr_t (MPFR) * double-double and quad-double (DD/QD package) * double (standard 64-bit floating point type) However, only mpfr_t (and double) support is important. Other multiple precision types are almost useless due to IEEE-nonconformance: * mpf_t is not recommended for numerical work (it leads to non-reproducible results and have very odd rounding rules; even GMP manual recommends to use MPFR) * DD/QD may look attractive (very high performance for 106 and 212 bits when compared with mpfr_t), but it is no good for numerical work too (except for BLAS internals; see page 31 of http://www.netlib.org/lapack/lawnspdf/lawn149.pdf ). ALGLIB supports mpfr_t and double. == PROGRAMMING LANGUAGE ============================================== MPLAPACK is written in C++ and uses C++ to handle multiple precision types like built-in floating point types (i.e. it uses "a=b+c/d" instead of directly calling MPFR functions). It leads to unnecessary allocation of temporaries and some performance penalty (about 25-30% for 128-bit precision). Multiple precision ALGLIB 2.5.0 is written in C++ and suffers from the same drawbacks. But what I develop for SAGE is a faster pure C library which caches all temporaries (it is really easy to develop - I just have to modify code generator which is used to generate ALGLIB source). == OPTIMIZATIONS ===================================================== Both packages rely on highly optimized MPFR for multiple precision computations. As for double precision, ALGLIB uses better optimized linear algebra code. == MULTITHREADING ==================================================== Both project don't support multithreading yet. Both want to :) == LICENSE =========================================================== MPLAPACK is LGPL 3+, ALGLIB is GPL 2+. -- With best regards, Sergey mailto:sergey.bochka...@alglib.net -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
