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local template = require 'template'
local sin, cos, exp = math.sin, math.cos, math.exp
local pi = math.pi
local enso_N = 168
local enso_P = 9
local enso_x0 = gsl.vector { 10.0, 3.0, 0.5, 44.0, -1.5, 0.5, 26.0, 0.1, 1.5 }
local enso_x = gsl.vector {
1.0510749193E+01,
3.0762128085E+00,
5.3280138227E-01,
4.4311088700E+01,
-1.6231428586E+00,
5.2554493756E-01,
2.6887614440E+01,
2.1232288488E-01,
1.4966870418E+00 }
local enso_sumsq = 7.8853978668E+02
local enso_sigma = gsl.vector {
1.7488832467E-01,
2.4310052139E-01,
2.4354686618E-01,
9.4408025976E-01,
2.8078369611E-01,
4.8073701119E-01,
4.1612939130E-01,
5.1460022911E-01,
2.5434468893E-01 }
local enso_F = gsl.vector {
12.90000,
11.30000,
10.60000,
11.20000,
10.90000,
7.500000,
7.700000,
11.70000,
12.90000,
14.30000,
10.90000,
13.70000,
17.10000,
14.00000,
15.30000,
8.500000,
5.700000,
5.500000,
7.600000,
8.600000,
7.300000,
7.600000,
12.70000,
11.00000,
12.70000,
12.90000,
13.00000,
10.90000,
10.400000,
10.200000,
8.000000,
10.90000,
13.60000,
10.500000,
9.200000,
12.40000,
12.70000,
13.30000,
10.100000,
7.800000,
4.800000,
3.000000,
2.500000,
6.300000,
9.700000,
11.60000,
8.600000,
12.40000,
10.500000,
13.30000,
10.400000,
8.100000,
3.700000,
10.70000,
5.100000,
10.400000,
10.90000,
11.70000,
11.40000,
13.70000,
14.10000,
14.00000,
12.50000,
6.300000,
9.600000,
11.70000,
5.000000,
10.80000,
12.70000,
10.80000,
11.80000,
12.60000,
15.70000,
12.60000,
14.80000,
7.800000,
7.100000,
11.20000,
8.100000,
6.400000,
5.200000,
12.00000,
10.200000,
12.70000,
10.200000,
14.70000,
12.20000,
7.100000,
5.700000,
6.700000,
3.900000,
8.500000,
8.300000,
10.80000,
16.70000,
12.60000,
12.50000,
12.50000,
9.800000,
7.200000,
4.100000,
10.60000,
10.100000,
10.100000,
11.90000,
13.60000,
16.30000,
17.60000,
15.50000,
16.00000,
15.20000,
11.20000,
14.30000,
14.50000,
8.500000,
12.00000,
12.70000,
11.30000,
14.50000,
15.10000,
10.400000,
11.50000,
13.40000,
7.500000,
0.6000000,
0.3000000,
5.500000,
5.000000,
4.600000,
8.200000,
9.900000,
9.200000,
12.50000,
10.90000,
9.900000,
8.900000,
7.600000,
9.500000,
8.400000,
10.70000,
13.60000,
13.70000,
13.70000,
16.50000,
16.80000,
17.10000,
15.40000,
9.500000,
6.100000,
10.100000,
9.300000,
5.300000,
11.20000,
16.60000,
15.60000,
12.00000,
11.50000,
8.600000,
13.80000,
8.700000,
8.600000,
8.600000,
8.700000,
12.80000,
13.20000,
14.00000,
13.40000,
14.80000 }
local function enso_fdf (x, f, J)
local b0 = x[1]
local b1 = x[2]
local b2 = x[3]
local b3 = x[4]
local b4 = x[5]
local b5 = x[6]
local b6 = x[7]
local b7 = x[8]
local b8 = x[9]
if f then
for i = 1, enso_N do
local t = i
local y = b0
y = y + b1 * cos(2*pi*t/12)
y = y + b2 * sin(2*pi*t/12)
y = y + b4 * cos(2*pi*t/b3)
y = y + b5 * sin(2*pi*t/b3)
y = y + b7 * cos(2*pi*t/b6)
y = y + b8 * sin(2*pi*t/b6)
f[i] = enso_F[i] - y
end
end
if J then
for i = 1, enso_N do
local t = i
J:set(i, 1, -1)
J:set(i, 2, -cos(2*pi*t/12))
J:set(i, 3, -sin(2*pi*t/12))
J:set(i, 4, -b4*(2*pi*t/(b3*b3))*sin(2*pi*t/b3) +
b5*(2*pi*t/(b3*b3))*cos(2*pi*t/b3))
J:set(i, 5, -cos(2*pi*t/b3))
J:set(i, 6, -sin(2*pi*t/b3))
J:set(i, 7, -b7 * (2*pi*t/(b6*b6)) * sin(2*pi*t/b6) +
b8 * (2*pi*t/(b6*b6)) * cos(2*pi*t/b6))
J:set(i, 8, -cos(2*pi*t/b6))
J:set(i, 9, -sin(2*pi*t/b6))
end
end
end
local function enso_model_f(x, t)
local y = x[1]
y = y + x[2] * cos(2*pi*t/12)
y = y + x[3] * sin(2*pi*t/12)
y = y + x[5] * cos(2*pi*t/x[4])
y = y + x[6] * sin(2*pi*t/x[4])
y = y + x[8] * cos(2*pi*t/x[7])
y = y + x[9] * sin(2*pi*t/x[7])
return y
end
lm = template.load('num/lmfit.lua.in', {N= enso_N, P= enso_P})
lm.set(enso_fdf, enso_x0)
print(gsl.tr(lm.x))
for i=1, 80 do
lm.iterate()
print('ITER=', i, ': ', gsl.tr(lm.x))
if lm.test(0, 1e-7) then print('solution found'); break end
end
p = graph.plot()
pts = graph.ipath(gsl.sequence(function(i) return i, enso_F[i] end, enso_N))
fitln = graph.fxline(function(t) return enso_model_f(lm.x, t) end, 0, 168, 512)
p:addline(pts, 'blue', {{'marker', size=4}})
p:addline(fitln)
p.title = 'ENSO non-linear fit NIST test'
p:show()
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