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indentation
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@ -193,24 +193,24 @@ function check_property_T(name::String, S, Id, solver, upper_bound, tol, radius)
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if λ > 0
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isapprox(eigvals(P), abs(eigvals(P)), atol=tol) ||
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warn("The solution matrix doesn't seem to be positive definite!")
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warn("The solution matrix doesn't seem to be positive definite!")
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# @assert P == Symmetric(P)
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Q = real(sqrtm(Symmetric(P)))
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sgap = check_distance_to_positive_cone(Δ, λ, Q, 2*radius, tol=tol, rational=false)
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sgap = check_distance_to_positive_cone(Δ, λ, Q, 2*radius, tol=tol)
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if isa(sgap, Interval)
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sgap = sgap.lo
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sgap = sgap.lo
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end
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if sgap > 0
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info(logger, "λ ≥ $(Float64(trunc(sgap,12)))")
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Kazhdan_κ = Kazhdan_from_sgap(sgap, length(S))
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Kazhdan_κ = Float64(trunc(Kazhdan_κ, 12))
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info(logger, "κ($name, S) ≥ $Kazhdan_κ: Group HAS property (T)!")
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return true
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info(logger, "λ ≥ $(Float64(trunc(sgap,12)))")
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Kazhdan_κ = Kazhdan_from_sgap(sgap, length(S))
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Kazhdan_κ = Float64(trunc(Kazhdan_κ, 12))
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info(logger, "κ($name, S) ≥ $Kazhdan_κ: Group HAS property (T)!")
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return true
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else
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sgap = Float64(trunc(sgap, 12))
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info(logger, "λ($name, S) ≥ $sgap: Group may NOT HAVE property (T)!")
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return false
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sgap = Float64(trunc(sgap, 12))
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info(logger, "λ($name, S) ≥ $sgap: Group may NOT HAVE property (T)!")
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return false
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end
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end
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info(logger, "κ($name, S) ≥ $λ < 0: Tells us nothing about property (T)")
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