| -rw-r--r-- | examples/linfit.lua | 132 |
diff --git a/examples/linfit.lua b/examples/linfit.lua index 47cce244..300963ed 100644 --- a/examples/linfit.lua +++ b/examples/linfit.lua @@ -1,64 +1,68 @@ -
-function demo1()
- local x0, x1, n = 0, 12.5, 32
- local a, b = 0.55, -2.4
- local xsmp = |i| (i-1)/(n-1) * x1
-
- local r = rng()
- local x = new(n, 1, xsmp)
- local y = new(n, 1, |i| a*xsmp(i) + b + rnd.gaussian(r, 0.4))
-
- fit, c = linfit(|x| {1, x}, x, y)
-
- print('Linear fit coefficients: ', tr(c))
-
- p = fxplot(fit, x0, x1)
- p:addline(xyline(x, y), 'blue', {{'marker', size=6}})
- p.title = 'Linear Fit'
-
- return p
-end
-
-function demo2()
- -- warning: this example may twist your brain and give headache :-)
- local order, x0, x1, n = 3, 0.0, 24.0, 64
- local bess = |x| besselJ(order, x)
- local xsmp = |i| (i-1)/(n-1) * x1
-
- local x = new(n, 1, xsmp)
- local y = new(n, 1, |i| besselJ(order, xsmp(i)))
-
- local xn = |x| (2*x - x0 - x1) / (x1-x0)
- local legmodel = |n| |x| ilist(|i| i == 0 and 1 or legendreP(i, xn(x)), 0, n)
-
- fitleg = linfit(legmodel(14), x, y)
- p = fxplot(fitleg, x0, x1)
- p:addline(xyline(x, y), 'darkgreen', {{'marker', size=6}})
- p.title = 'Legendre Polinomial fit of Bessel J3(x)'
-
- return p
-end
-
-function demo3()
- -- the same as before done slightly differently
- local order, x0, x1, n = 3, 0.0, 24.0, 64
- local bess = |x| besselJ(order, x)
- local xsmp = |i| (i-1)/(n-1) * x1
-
- local x = new(n, 1, xsmp)
- local y = new(n, 1, |i| besselJ(order, xsmp(i)))
-
- local xn = |x| (2*x - x0 - x1) / (x1-x0)
-
- local kfit = 14
- local legmodel = |j, x| j == 0 and 1 or legendreP(j, xn(x))
- local X = new(n, kfit+1, |i,j| legmodel(j-1, x[i]))
- local c = mlinear(X, y)
- local yfit = mul(X, c)
- p = plot('Legendre Polinomial fit of Bessel J3(x)')
- p:addline(xyline(x, yfit))
- p:addline(xyline(x, y), 'darkgreen', {{'marker', size=6}})
- p:show()
-
- return p
-end
+ +function demo1() + local x0, x1, n = 0, 12.5, 32 + local a, b = 0.55, -2.4 + local xsmp = |i| (i-1)/(n-1) * x1 + + local r = rng() + local x = new(n, 1, xsmp) + local y = new(n, 1, |i| a*xsmp(i) + b + rnd.gaussian(r, 0.4)) + + fit, c = linfit(|x| {1, x}, x, y) + + print('Linear fit coefficients: ', tr(c)) + + p = fxplot(fit, x0, x1) + p:add(xyline(x, y), 'blue', {{'stroke'}, {'marker', size=5}}) + p.title = 'Linear Fit' + + return p +end + +function demo2() + -- warning: this example may twist your brain and give headache :-) + local order, x0, x1, n = 3, 0.0, 24.0, 64 + local bess = |x| besselJ(order, x) + local xsmp = |i| (i-1)/(n-1) * x1 + + local x = new(n, 1, xsmp) + local y = new(n, 1, |i| besselJ(order, xsmp(i))) + + local xn = |x| (2*x - x0 - x1) / (x1-x0) + local legmodel = |n| |x| ilist(|i| i == 0 and 1 or legendreP(i, xn(x)), 0, n) + + fitleg = linfit(legmodel(14), x, y) + p = fxplot(fitleg, x0, x1) + p:addline(xyline(x, y), 'blue', {{'marker', size=5}}) + p.title = 'Legendre Polinomial fit of Bessel J3(x)' + + return p +end + +function demo3() + -- the same as before done slightly differently + local order, x0, x1, n = 3, 0.0, 24.0, 64 + local bess = |x| besselJ(order, x) + local xsmp = |i| (i-1)/(n-1) * x1 + + local x = new(n, 1, xsmp) + local y = new(n, 1, |i| besselJ(order, xsmp(i))) + + local xn = |x| (2*x - x0 - x1) / (x1-x0) + + local kfit = 14 + local legmodel = |j, x| j == 0 and 1 or legendreP(j, xn(x)) + local X = new(n, kfit+1, |i,j| legmodel(j-1, x[i])) + local c = mlinear(X, y) + local yfit = mul(X, c) + p = plot('Legendre Polinomial fit of Bessel J3(x)') + p:addline(xyline(x, yfit)) + p:addline(xyline(x, y), 'blue', {{'marker', size=5}}) + p:show() + + return p +end + +print 'demo1() - examples of linear regression of (x, y) data' +print 'demo2() - examples of linear regression based on legendre polynomials' +print 'demo3() - same of demo2 with slightly different procedure' |