RDR^t

[Chris Kees]

Hi,

Does anybody have suggestions on sympy examples for symbolic eigenvector decompositions A=RDR^t where A is symmetric with real positive distinct eigenvalues? Or more specifically symbolic computations of A^{-1/2}.

Chris

[Aaron Meurer]

SymPy can do it, as long as it can compute the roots of the
characteristic polynomial. Is there any specific use-case you're
looking for? The syntax is Matrix.diagonalize (or sqrt(Matrix) if all
you want is the square root).

Aaron Meurer

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[Chris Kees]

Thanks. I don't know how I missed sqrt(Matrix).

Yes, the specific  context is solving hyperbolic  systems of PDE's so the matrices are small n-by-n were  n is usually 2,3,4, or 5, but I have to do it  at points on a large 2D or  3D mesh  so I'm looking for a nice way to generate C or Fortran code for symbolic  expressions of the form A^{-1}*B^{-1/2} where A is SPD and B is symmetric with non-negative eigenvalues.  There may be a point when I'm better off computing these with lapack  factorizations, but I'd like to have sympy-generated analytical expressions

Chris

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