On Thu, 15 Aug 2024 at 16:51, Florent Bulkilol <bulki...@gmail.com> wrote: > > Hi, > > I need to perform a Smith decomposition on (a priori not square) matrices to > find a certain change of basis related to the Smith invariants. > > The Smith normal form is already implemented in SymPy in > `sympy.matrices.normalforms`, but it returns only the Smith normal form, not > its decomposition itself. > > In general, the Smith decomposition of a matrix A is defined in terms of > three matrices V, D, W so that > > A = V * D * W > > where V,W are both square, invertible, and integer-valued matrices. Is there > any way of obtaining those matrices without reimplementing the algorithm > myself? I assume that these matrices are computed at least implicitely, but I > could not find a way of returning them.
Just following up on this. The Smith normal form with the transform matrices is now available in SymPy's master branch (thanks to Isuru Fernando): https://github.com/sympy/sympy/pull/17451 To test it you can install sympy from master like: pip install git+https://github.com/sympy/sympy.git@master It returns the inverses of the matrices V and W that you were expecting: In [4]: from sympy.matrices.normalforms import smith_normal_decomp In [5]: A = randMatrix(3, 4) In [6]: D, v, w = smith_normal_decomp(A) In [7]: D == v*A*w Out[7]: True In [9]: V, W = v.inv(), w.inv() In [10]: A == V*D*W Out[10]: True -- Oscar -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAHVvXxRZ34TC5g%3DbtEPHG-axU1EvUeRY6zm0N-cvuSuWJzOASg%40mail.gmail.com.
