constructor for complex triangular Schur from real quasitriangular Schur #40573
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dkarrasch
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Apr 23, 2021
Co-authored-by: Daniel Karrasch <daniel.karrasch@posteo.de>
shirodkara
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johanmon
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This adds a constructor
Schur{Complex}(S)that converts a real Schur factorizationSinto a complex one, based on code by @RalphAS from GenericSchur.jl. This is useful because the real Schur factorization is only "quasitriangular" — it can have 2×2 blocks along the diagonal corresponding to complex eigenvalue pairs — whereas many algorithms require the complex upper-triangular factorization.Previously, one obtained the complex Schur factorization by
schur(complex(A)), but this seems to be 2–3× slower thanSchur{Complex}(schur(A))for realA.In consequence, a number of the Schur-based algorithms, such as
asin(A)andA^3.2, are about 2× faster for realAafter this PR. There is also a smaller speedup forsqrtandlog.