use 'math'
local function demo1()
 local n = 40
 local sigrf = 0.1
 local yrf
 local fdf = function(x, f, J)
		 for i=1, n do
		 local A, lambda, b = x[1], x[2], x[3]
		 local t, y, sig = i-1, yrf[i], sigrf
		 local e = exp(- lambda * t)
		 if f then f[i] = (A*e+b - y)/sig end
		 if J then
			J:set(i, 1, e / sig)
			J:set(i, 2, - t * A * e / sig)
			J:set(i, 3, 1 / sig)
		 end
		 end
	 end
 local model = function(x, t)
		 local A, lambda, b = x[1], x[2], x[3]
		 return A * exp(- lambda * t) + b
		 end
 local xref = matrix.vec {5, 0.1, 1}
 local r = rng.new()
 r:set(0)
 yrf = matrix.new(n, 1, |i| model(xref, i-1) + rnd.gaussian(r, 0.1))
 local s = num.nlinfit {n= n, p= 3}
 s:set(fdf, matrix.vec {1, 0, 0})
 print(s.x, s.chisq)
 for i=1, 10 do
 s:iterate()
 print('ITER=', i, ': ', s.x, s.chisq)
 if s:test(0, 1e-8) then break end
 end
 local p = graph.plot('Non-linear fit example')
 local pts = graph.ipath(iter.sequence(function(i) return i-1, yrf[i] end, n))
 local fitln = graph.fxline(function(t) return model(s.x, t) end, 0, n-1)
 p:addline(pts, 'blue', {{'marker', size=5}})
 p:addline(fitln)
 p.clip = false
 p.pad = true
 p:show()
end
local function demo2()
 local n = 50
 local px = matrix.vec {1.55, -1.1, 12.5}
 local p0 = matrix.vec {2.5, -1.5, 5.3}
 local xs = |i| (i-1)/n
 local r = rng.new()
 local fmodel = function(p, t, J)
		 local e, s = exp(p[2] * t), sin(p[3] * t)
		 if J then
			J[1] = e * s
			J[2] = t * p[1] * e * s
			J[3] = t * p[1] * e * cos(p[3] * t)
		 end
		 return p[1] * e * s
		 end
 local y = matrix.new(n, 1, |i,j| fmodel(px, xs(i)) * (1 + rnd.gaussian(r, 0.1)))
 local x = matrix.new(n, 1, |i,j| xs(i))
 local function fdf(p, f, J)
 for k=1, n do
	 local ym = fmodel(p, xs(k), J and J[k])
	 if f then f[k] = ym - y[k] end
 end
 end
 local pl = graph.plot('Non-linear fit / A * exp(a t) sin(w t)') 
 pl:addline(graph.xyline(x, y), 'blue', {{'marker', size= 5, mark="triangle"}})
 pl:legend('data', 'blue', 'triangle', {{'stroke'}})
 local s = num.nlinfit {n= n, p= #p0}
 s:set(fdf, p0)
 print(s.x, s.chisq)
 pl:addline(graph.fxline(|x| fmodel(s.x, x), 0, xs(n)), 'red', {{'dash', 7, 3, 3, 3}})
 pl:legend('seed', 'red', 'line', {{'stroke'},{'dash',7,3}})
 for i=1, 10 do
 s:iterate()
 print('ITER=', i, ': ', s.x, s.chisq)
 if s:test(0, 1e-8) then break end
 end
 pl:addline(graph.fxline(|x| fmodel(s.x, x), 0, xs(n)), 'red')
 pl:legend('best fit', 'red', 'line')
 pl.pad = true
 pl:show()
 return pl
end
return {'Non-linear fit', {
 {
 name = 'nlfit1',
 f = demo1, 
 description = 'Simple non-linear fit'
 },
 {
 name = 'nlfit2',
 f = demo2, 
 description = 'Non-linear fit of oscillatory function'
 },
}}
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