NAG

Robert Israel — Mon, 21 Nov 2011 06:44:26 Z

For a dense Matrix containing floats, if hardware precision is ok, it uses NAG routies F08KEF and F08MEF. F08KEF reduces the Matrix to bidiagonal form using orthogonal matrices. If only the singular values are required, F08MEF computes them using the differential qd algorithm. See
www.nag.com/numeric/Fl/manual/pdf/F08/f08kef.pdf and
www.nag.com/numeric/Fl/manual/pdf/F08/f08mef.pdf.

NAG & CLAPACK

acer — Mon, 21 Nov 2011 07:31:42 Z

See the documentation of the NAG Fortran Library function f08mef. This is like CLAPACK's dbdsqr function. It's documentation mentions the (QR based, or differential QD based) algorithms used.

You can see which NAG routine is used by LinearAlgebra, from userinfo messages.

> infolevel[LinearAlgebra]:=1:

> LinearAlgebra:-SingularValues(<>):
SingularValues: calling external function
SingularValues: NAG hw_f08kef
SingularValues: NAG hw_f08mef

Maple also ships with precompiled external libraries (shared objects clapack.dll or libclapack.so) containing the double-precision real and complex (dxxxx and zxxxx) routines from versions 3.0 of CLAPACK. If you want another routine from that library, you can call it yourself using the external-calling mechanism. (See here for an example of such user-defined wrapperless external-calling to CLAPACK from Maple.)

You can use these notes to help decide which CLAPACK function you'd like to use for singular value computation. Note that function dbdsdc for the divide and conquer algorithm is already avaliable in version 3.0. So you could call that directly from stock, shipped Maple, using define_external.

If you are interested in getting more state-of-the-art, then you could consider LAPACK 3.2.x or higher. See these release notes, and in particular section 2 for items 2.5 and 2.10 and the relevent references [5],[6]. Note that v.3.2.1 is avaliable aready as CLAPACK (which you can obtain as source or may be even precompiled). If you build such a more recent version of (C)LAPACK yourself (compiling, linking as shared dynamic library with appropriate exports, etc) then you would again be able to call its functions directly using the wrapperless forms of define_external.

acer

MaplePrimes - answers and comments on Question, Algorithm used for singular value decomposition in maple

NAG

NAG & CLAPACK