Revision of Fast direct relaxation of implicit functions

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1 file changed, 41 insertions

implicit_relaxation.jl(file created)

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1	+	using McCormick, BenchmarkTools
2	+
3	+	"""
4	+	Direct relaxation of implicit function
5	+	"""
6	+	function direct_relax(f, x, p)
7	+	delta = Inf
8	+	while delta > 1e-8
9	+	x_prev = x
10	+	x = f(x, p)
11	+	delta = abs(x_prev.cv - x.cv) + abs(x_prev.cc - x.cc)
12	+	end
13	+
14	+	return x
15	+	end
16	+
17	+	"""
18	+	Faster alternative
19	+	"""
20	+	function fast_direct_relax(f, x, p)
21	+	delta = Inf
22	+	while delta > 1e-8
23	+	x_prev = x
24	+	x_m = x.cv + .5 * (x.cc - x.cv)
25	+	x = f(x_m, p)
26	+	delta = abs(x_prev.cv - x.cv) + abs(x_prev.cc - x.cc)
27	+	end
28	+
29	+	return x
30	+	end
31	+
32	+	f(x, p) = (p - (p^3)/6 + (p^5)/120)*x^(-1/2) + 100
33	+
34	+	p = MC{1,NS}(1.0, 1.0, Interval(0.5, 5.0))
35	+	x = MC{1,NS}(1.0, 1.0)
36	+
37	+	res = @btime direct_relax(f, x, p)
38	+	println(res) # 342.860 μs (2414 allocations: 96.52 KiB) MC{1, NS}(99.8362536820914, 100.40188539116205, [97.9454, 103.135], [0.0], [0.0], true)
39	+
40	+	res = @btime fast_direct_relax(f, x, p)
41	+	println(res) # 2.972 μs (301 allocations: 4.75 KiB) MC{1, NS}(99.8675794497822, 100.37248484959062, [97.9679, 103.101], [0.0], [0.0], true)

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