gsl-shell.git - gsl-shell

diff --git a/examples/3d.lua b/examples/3d.lua
deleted file mode 100644
index 2ba4d878..00000000
--- a/examples/3d.lua
+++ /dev/null

@@ -1,26 +0,0 @@

-

-use 'math'

-

-require 'plot3d'

-

-function demo1()

- local x = |u,v| (1 + 1/2 * v *cos(u/2))*cos(u)

- local y = |u,v| (1 + 1/2 * v *cos(u/2))*sin(u)

- local z = |u,v| 1/2 * v * sin(u/2)

- return graph.surfplot({x, y, z}, 0, -1, 2*pi, 1, {gridu= 60, gridv= 4, stroke= true})

-end

-

-function demo2()

- local f = |x, y| exp(-(x^2+y^2))*sin(x)

- return graph.plot3d(f, -4, -4, 4, 4, {gridx= 31, gridy= 31})

-end

-

-function demo3()

- local f = |x, y| x^2 - y^2

- return graph.plot3d(f, -3, -3, 3, 3, {stroke= true})

-end

-

-echo([[

-demo1() - Plot the mobieus strip using a parametric rapresentation

-demo2() - Plot example of function f(x,y) = exp(-(x^2+y^2))*sin(x)

-demo3() - Plot example of function f(x,y) = x^2 - y^2]])

diff --git a/examples/bessel.lua b/examples/bessel.lua
deleted file mode 100644
index 497cf6df..00000000
--- a/examples/bessel.lua
+++ /dev/null

@@ -1,44 +0,0 @@

-

-function bessJ(x, n)

- local f = |t| cos(n*t - x*sin(t)) -- we define the function to integrate

- return 1/pi * integ {f= f, points={0, pi}}

-end

-

-function bessJext(x,alpha)

- local f1 = |t| cos(alpha*t - x*sin(t))

- local f2 = |t| exp(-x*sinh(t)-alpha*t)

- local t1 = 1/pi * integ {f= f1, points={0, pi}}

- local t2 = -sin(alpha*pi)/pi * integ {f= f2, points={0, '+inf'}}

- return t1 + t2

-end

-

-function fact(n)

- local p = n > 1 and n or 1

- for i=2,n-1 do p = p * i end

- return p

-end

-

-function bessJseriev1(x,alpha,nmax)

- local a, m = 0, nmax

- local t = (x/2)^2

- local sign = 1 - 2*(m % 2)

- local c = sign / (fact(m) * fact(m + alpha))

- for k=0,m do

- a = (a * t + c)

- c = - c * (m-k) * (m-k+alpha)

- end

- return a * (x/2)^alpha

-end

-

-function bessJserie(x, alpha, eps)

- local a, c, p = 0, 1/fact(alpha), 1

- local t = (x/2)^2

- for n = 0, 100 do

- a = a + c * p

- local r = (n + 1) * (n + alpha + 1)

- p = p * t

- c = - c / r

- if t / r < eps then break end

- end

- return a * (x/2)^alpha

-end

diff --git a/examples/cspline-example.lua b/examples/cspline-example.lua
deleted file mode 100644
index 466e3042..00000000
--- a/examples/cspline-example.lua
+++ /dev/null

@@ -1,42 +0,0 @@

-

-local function cubic(x, y, z, h)

- local N = #x - 1

- return function(xe)

- local i = N

- for j=2,N+1 do

- if x[j] >= xe then i = j-1; break end

- end

- return (z[i+1]*(xe - x[i])^3 + z[i]*(x[i+1] - xe)^3)/(6*h[i]) + (y[i+1]/h[i] - h[i]/6*z[i+1])*(xe-x[i]) + (y[i]/h[i] - h[i]/6*z[i])*(x[i+1]-xe)

- end

-end

-

-function cspline(x, y)

- local N = #x - 1

- local h = ilist(|i| x[i+1] - x[i], N)

-

- local function mterm(i,j)

- if i == 1 then

- return (j == 1 and 1 or 0)

- elseif i == N+1 then

- return (j == N+1 and 1 or 0)

- else

- return j == i-1 and h[i-1] or (j == i and 2*(h[i-1]+h[i]) or (j == i+1 and h[i] or 0))

- end

- end

-

- local M = new(N+1, N+1, mterm)

- local b = new(N+1, 1, |i| (i > 1 and i < N+1) and 6*((y[i+1] - y[i])/h[i] - (y[i] - y[i-1])/h[i-1]) or 0)

-

- local z = solve(M, b)

-

- return cubic(x, y, z, h)

-end

-

-x = {-1, -0.5, -0.3, 0, 0.3, 0.5, 1}

-y = ilist(|i| exp(-x[i]*x[i]), #x)

-

-f = cspline(x, y)

-

-p = fxplot(f, -1, 1)

-p.title = 'Cubic spline interpolation'

-p:addline(ipath(sequence(function(j) return x[j], y[j] end, #x)), 'blue', {{'marker', size= 6}})

diff --git a/examples/data/sige-sims-prof.csv b/examples/data/sige-sims-prof.csv
deleted file mode 100644
index 3fae93a6..00000000
--- a/examples/data/sige-sims-prof.csv
+++ /dev/null

@@ -1,316 +0,0 @@

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diff --git a/examples/eigensystems.lua b/examples/eigensystems.lua
deleted file mode 100644
index fc25b2e3..00000000
--- a/examples/eigensystems.lua
+++ /dev/null

@@ -1,39 +0,0 @@

-

-local function vandermonde(x)

- local n = #x

- return new(n, n, |i,j| x[i]^(n-j))

-end

-

-

-function demo1()

- local m = new(4, 4, |i,j| 1/(i+j-1))

- echo 'Matrix:'

- print(m)

- local e, v = eigsv(m)

- echo('Eigenvalues:')

- print(ilist(|i| e[i], 4))

-

- -- the following expression will give a diagonal matrix with the eigenvalues

- --- along the diagonal

- echo('Matrix diagonal form:')

- print(prod(v, m*v))

-end

-

-function demo2()

- local m = vandermonde {-1, -2, 3, 4}

- echo 'Matrix:'

- print(m)

-

- local e, v = eignsv(m)

- echo 'Eigenvalues:'

- print(ilist(|i| e[i], 4))

-

- -- the following expression will give a diagonal matrix with the eigenvalues

- --- along the diagonal

- echo('Matrix diagonal form:')

- print(inv(v) * m * v)

-end

-

-echo([[

-demo1() - example of eigensystem solving for a real symmetrix matrix

-demo2() - example of eigensystem solving for a real non-symmetrix matrix]])

diff --git a/examples/fractals.lua b/examples/fractals.lua
deleted file mode 100644
index 71fdb224..00000000
--- a/examples/fractals.lua
+++ /dev/null

@@ -1,234 +0,0 @@

-

-use 'stdlib'

-

-local function c_generator(n, n_angle, len_frac, g)

- local exp, real, imag = complex.exp, complex.real, complex.imag

- local w, r, k = ilist(|| 0, n+1), #g

-

- local s = len_frac^n

- local sz = cnew(n_angle, 1, |k| s * exp(2i*pi*(k-1)/n_angle))

-

- local sh = ilist(|k| g[k%r+1] - g[(k-1)%r+1], 0, r-1)

- local a = (g[1]*n) % n_angle

-

- local z = 0

- return function()

- if w[n+1] == 0 then

- local j

- z = z + sz[a+1]

- for j=1,n+1 do

- w[j] = (w[j] + 1) % r

- a = (a + sh[w[j]+1]) % n_angle

- if w[j] ~= 0 then

- break

- end

- end

- return real(z), imag(z)

- end

- end

-end

-

-local function levyc(n)

- local p = plot('Levy\'s C curve')

- local c = ipath(c_generator(n, 4, 1/2, {-1,0,0,1}))

- p:addline(c, 'red', {}, {{'rotate', angle= -pi/4}})

- p:addline(c, 'red', {}, {{'translate', x=1/sqrt(2), y=-1/sqrt(2)},{'rotate', angle= pi/4}})

- p.units = false

- p:show()

- return p

-end

-

-function demo1()

- local pl = plot()

-

- local t = path()

- t:move_to(0,0)

- t:line_to(1,0)

- t:line_to(0.5,-sqrt(3)/2)

- t:close()

-

- local v = ipath(c_generator(4, 6, 1/3, {0,1,-1,0}))

- local c = rgba(0,0,0.7,0.2)

- pl:add(v, c)

- pl:add(v, c, {}, {{'translate', x=1, y=0}, {'rotate', angle=-2*pi/3}})

- pl:add(v, c, {}, {{'translate', x=0.5, y=-sqrt(3)/2},

- {'rotate', angle=-2*2*pi/3}})

- pl:add(t, c)

-

- c = rgb(0,0,0.7)

-

- pl:addline(v, c)

- pl:addline(v, c, {}, {{'translate', x=1, y=0}, {'rotate', angle=-2*pi/3}})

- pl:addline(v, c, {}, {{'translate', x=0.5, y=-sqrt(3)/2},

- {'rotate', angle=-2*2*pi/3}})

-

- pl.units = false

- pl:show()

-end

-

-demo2 = function(n) return levyc(n and n or 6) end

-

-function demo3()

- local rdsd = sqrt(2)/2

- local ubox = rect(0, 0, 1, 1)

- local cf

-

- local function pitag_tree(pl, x, y, th, ll, depth)

- local col = cf(depth)

- pl:add(ubox, col, {}, {{'translate', x= x, y= y},

- {'rotate', angle= th},

- {'scale', ll}})

- if depth > 0 then

- x, y = x - ll*sin(th), y + ll*cos(th)

- pitag_tree(pl, x, y, th + pi/4, ll*rdsd, depth-1)

- x, y = x + ll*rdsd*cos(th+pi/4), y + ll*rdsd*sin(th+pi/4)

- pitag_tree(pl, x, y, th - pi/4, ll*rdsd, depth-1)

- end

- end

-

- local depth = 12

- local cfgen = color_function('darkgreen', 1)

- cf = |d| cfgen(1-d/depth)

- local pl = plot()

- pl.units = false

- pitag_tree(pl, 0, 0, 0, 1, depth)

- pl:show()

-end

-

-function demo3bis(n)

- n = n and n or 10

- local rdsd = sqrt(2)/2

- local m = new(2^(n+1)-1, 4)

-

- local function pitag_tree(x, y, th, ll, k, depth)

- m:set(k, 1, x)

- m:set(k, 2, y)

- m:set(k, 3, th)

- m:set(k, 4, depth)

- if depth > 0 then

- x, y = x - ll*sin(th), y + ll*cos(th)

- k = pitag_tree(x, y, th + pi/4, ll*rdsd, k+1, depth-1)

- x, y = x + ll*rdsd*cos(th+pi/4), y + ll*rdsd*sin(th+pi/4)

- k = pitag_tree(x, y, th - pi/4, ll*rdsd, k+1, depth-1)

- end

- return k

- end

-

- pitag_tree(0, 0, 0, 1, 1, n)

-

- local cfgen = color_function('darkgreen', 1)

-

- local pl = plot()

- pl:show()

-

- for d=n, 0, -1 do

- local dfact = rdsd^(n-d)

- local box = rect(0, 0, dfact, dfact)

- for k=1, 2^(n+1)-1 do

- if m:get(k,4) == d then

- local x, y, th = m:get(k,1), m:get(k,2), m:get(k,3)

- local tr = {{'translate', x=x, y=y}, {'rotate', angle=th}}

- pl:add(box, cfgen(1-d/n), {}, tr)

- pl:add(box, cfgen(1-(d-1)/n), {{'stroke', width= 2.5*dfact}}, tr)

- -- pl:addline(box, cfgen(1-(d-1)/n), {}, tr)

- end

- end

- end

-end

-

-function demo3ter(n)

- n = n and n or 10

- local cf

-

- local function pitag_tree(pl, x, y, th, ll, depth)

- local box = rect(0, 0, ll, ll)

- local col = cf(depth)

- pl:add(box, col, {}, {{'translate', x= x, y= y}, {'rotate', angle= th}})

- if depth > 0 then

- x, y = x - ll*sin(th), y + ll*cos(th)

- local a1 = th + atan2(12,16)

- pitag_tree(pl, x, y, a1, ll*4/5, depth-1)

- x, y = x + ll*4/5*cos(a1), y + ll*4/5*sin(a1)

- pitag_tree(pl, x, y, th + atan2(-12,9), ll*3/5, depth-1)

- end

- end

-

- local cfgen = color_function('darkgreen', 1)

- cf = |d| cfgen(1-d/n)

- local pl = plot()

- pl.units = false

- pl:show()

- pitag_tree(pl, 0, 0, 0, 1, n)

-end

-

-function demo4(n)

- local ubox = rect(0, 0, 1, 1)

- n = n and n or 10

- local col, coln

-

- local function pitag_tree(pl, x, y, th, ll, depth)

- if depth == 0 then

- local tr = {{'translate', x= x, y= y}, {'rotate', angle= th},

- {'scale', ll}}

- pl:add(ubox, col, {}, tr)

- pl:add(ubox, coln, {{'stroke', width= 2.5*ll}}, tr)

- end

- if depth > 0 then

- x, y = x - ll*sin(th), y + ll*cos(th)

- local a1 = th + atan2(12,16)

- pitag_tree(pl, x, y, a1, ll*4/5, depth-1)

- x, y = x + ll*4/5*cos(a1), y + ll*4/5*sin(a1)

- pitag_tree(pl, x, y, th + atan2(-12,9), ll*3/5, depth-1)

- end

- end

-

- local cfgen = color_function('darkgreen', 1)

-

- local pl = plot()

- pl.sync = false

- pl.clip = false

- pl:show()

-

- for k=0, n do

- col, coln = cfgen(k/n), cfgen((k+1)/n)

- pitag_tree(pl, 0, 0, 0, 1, k)

- pl:flush()

- end

-end

-

-function demo3q()

- local cf

- local llmt = 0.05

- local ta1, ta2 = atan2(12,16), atan2(-12,9)

-

- local function pitag_tree(pl, x, y, th, ll, k)

- if ll < llmt then return end

-

- local box = rect(0, 0, ll, ll)

- local tr = {{'translate', x= x, y= y}, {'rotate', angle= th}}

- pl:add(box, cf(k), {}, tr)

- pl:add(box, cf(k+1), {{'stroke', width= 2.5*ll}}, tr)

-

- x, y = x - ll*sin(th), y + ll*cos(th)

- local a1 = th + ta1

- pitag_tree(pl, x, y, a1, ll*4/5, k+1)

- x, y = x + ll*4/5*cos(a1), y + ll*4/5*sin(a1)

- pitag_tree(pl, x, y, th + ta2, ll*3/5, k+1)

- end

-

- local cfgen = color_function('darkgreen', 1)

-

- local pl = plot()

- pl.units = false

- pl:show()

-

- local n = ceil(log(llmt)/log(4/5))

-

- cf = |k| cfgen(k/n)

- pitag_tree(pl, 0, 0, 0, 1, 0)

-end

-

-echo 'demo1() - Von Koch\'s curve'

-echo 'demo2() - Levy\'s C curve'

-echo 'demo3() - Pythagorean Tree (symmetric)'

-echo 'demo4() - Pythagorean Tree (asymmetric)'

diff --git a/examples/interp.lua b/examples/interp.lua
deleted file mode 100644
index d0226e50..00000000
--- a/examples/interp.lua
+++ /dev/null

@@ -1,53 +0,0 @@

-use 'stdlib'

-

-function demo1()

-

- local w = window('v..')

- local N = 8

- local xsmp = |k| 2*pi*(k-1)/N

- local x, y = new(N+1, 1, xsmp), new(N+1, 1, |k| sin(xsmp(k)))

-

- local function interp_plot(tp)

- local p = plot(string.format('%s interpolation', tp))

- p:add(xyline(x, y), 'black', {{'marker', size=5}})

- local ap = interp(x, y, tp)

- p:addline(fxline(|x| ap:eval(x), 0, 2*pi), 'blue', {{'dash', 7, 3, 3, 3}})

- p:addline(fxline(|x| ap:deriv(x), 0, 2*pi))

- p:add(fxline(cos, 0, 2*pi), 'blue', {{'stroke', width=0.75}, {'dash', 7,3}})

- print(string.format('%s interp / integral between (%g, %g) = %g', tp,

- 0, 2*pi, ap:integ(0, 2*pi)))

- return p

- end

-

-

- local p = plot 'Akima Interpolation'

- w:attach(interp_plot('akima'), '1')

- w:attach(interp_plot('cspline'), '2')

-end

-

-function demo2()

- local N = 12

- local r = rng()

- local xlmt = 5

- local xp = 0

- local gp = function()

- local xn = xp

- xp = xp + xlmt*(1 + rnd.gaussian(r, 0.3))/N

- return xn

- end

- local x = new(N, 1, gp)

- local y = new(N, 1, |k| x[k]^2*exp(-x[k]))

- local p = plot 'Cubic Spline Interpolation'

- p:show()

- p:addline(xyline(x, y))

- p:add(xyline(x, y), 'black', {{'marker', size= 5}})

- local ap = interp(x, y, 'cspline')

- local a, b = 0, x[N]

- p:addline(fxline(|x| ap:eval(x), a, b), 'blue', {{'dash', 7, 3, 3, 3}})

- p:addline(fxline(|x| ap:deriv(x), a, b), 'green')

- print(string.format('Integral between (%g, %g) = %g', a, b, ap:integ(a, b)))

- return p, ap

-end

-

-echo 'demo1() - Akima interpolation of simple sine data'

-echo 'demo2() - Cubic Spline interpolation of a function with random sampling'

diff --git a/examples/minimize.lua b/examples/minimize.lua
deleted file mode 100644
index 2f33d1ac..00000000
--- a/examples/minimize.lua
+++ /dev/null

@@ -1,104 +0,0 @@

-

-use 'stdlib'

-

-require 'contour'

-

-f = function(x, g)

- local xc = vector {4.45, -1.2}

- local y = x - xc

- if g then set(g, 2*y) end

- return prod(y, y)[1]

- end

-

-

-fex = function(x, g)

- local x1, x2 = x[1], x[2]

- local z = 4*x1^2 + 2*x2^2 + 4*x1*x2 + 2*x2 + 1

- local e = exp(x1)

- if g then

- g:set(1,1, e * (z + 8*x1 + 4*x2))

- g:set(2,1, e * (4*x2 + 4*x1 + 2))

- end

- return e * z

- end

-

-frosenbrock = function(x, g)

- local x, y = x[1], x[2]

- local v = 100*(y-x^2)^2 + (1-x)^2

- if (g) then

- g:set(1,1, -4*100*(y-x^2)*x - 2*(1-x))

- g:set(2,1, 2*100*(y-x^2))

- end

- return v

- end

-

-local function cook(f)

- local p = new(2,1)

- return function(x,y)

- p:set(1,1, x)

- p:set(2,1, y)

- return f(p)

- end

-end

-

-function contour_minimize(f, m, x1, y1, x2, y2, contour_options)

- local p = contour(cook(f), x1, y1, x2, y2, contour_options)

- local c = path(m.x[1], m.x[2])

- local cx, cy = m.x[1], m.x[2]

- while m:step() == 'continue' do

- if cx ~= m.x[1] or cy ~= m.x[2] then

- c:line_to(m.x[1], m.x[2])

- cx, cy = m.x[1], m.x[2]

- end

- end

- c:line_to(m.x[1], m.x[2])

- print(m.x[1], m.x[2], m.value)

-

- p:addline(c, 'black', {{'marker', size=5}})

- p:addline(c, 'red')

- return p

-end

-

-function demo1()

- local w = window('v..')

-

- local x0 = vector {-1.2, 1.0}

- local m = fmultimin(frosenbrock, 2)

- m:set(x0, vector {0.5, 0.5}, 0.01^2/2)

-

- local copts = {levels= 12, show= false}

- local p1 = contour_minimize(frosenbrock, m, -1.5, -0.5, 1.5, 2, copts)

- p1.title = 'Rosenbrock function minimisation, algorithm w/o derivates'

- w:attach(p1, 1)

-

- local m = fdfmultimin(frosenbrock, 2, "bfgs")

- m:set(x0, 0.5)

-

- local p2 = contour_minimize(frosenbrock, m, -1.5, -0.5, 1.5, 2, copts)

- p2.title = 'Rosenbrock function minimisation, BFGS solver'

- w:attach(p2, 2)

-end

-

-function demo2()

- local x0 = vector {-1.2, 1.0}

- local m = fmultimin(f, 2)

- m:set(x0, vector {1, 1}, 0.01)

- local p = contour_minimize(f, m, -2, -3, 8, 2)

- p.title = 'Quadratic function minimisation'

- return p

-end

-

-

-function demo3()

- local x0 = vector {-0.5, 1.0}

- local m = fdfmultimin(fex, 2, "bfgs")

- m:set(x0, 0.5)

- local p = contour_minimize(fex, m, -2, -2.5, 1, 1.5,

- {gridx=30, gridy= 30, levels= 22})

- p.title = 'f(x,y) = exp(x) * (4 x^2 + 2 y^2 + 4 x y + 2 y + 1)'

- return p

-end

-

-echo "demo1() - minimization of Rosenbrock function with different algorithms"

-echo "demo2() - minimization of quadratic function without derivates"

-echo "demo3() - function minimization using BFGS solver"

diff --git a/examples/optical-disp.lua b/examples/optical-disp.lua
deleted file mode 100644
index 208145fa..00000000
--- a/examples/optical-disp.lua
+++ /dev/null

@@ -1,101 +0,0 @@

-

-require 'disp'

-

-datadir = 'packages/optical-disp'

-

-local function dispfit(ref, m, ps, p0)

- local nb = #ref

- local function fithook(x, f, J)

- for j = 1, #ps do m:apply(ps[j], x[j]) end

- for k = 1, nb do

- local lam, n = ref:sample(k)

- if f then

- local z = m:get_n(lam) - n

- f:set(k, 1, z)

- end

- if J then

- for j = 1, #ps do

- local z = m:get_n_deriv(ps[j], lam)

- J:set(k, j, z)

- end

- end

- end

- end

- return cnlfsolver {fdf= fithook, n= nb, p0= vector(p0)}

-end

-

-local function plotcfr(ref, m, title, get)

- get = get and get or real

- local lnr, lnm

- for lam, nref in ref:samples() do

- if not lnr then

- lnr, lnm = path(lam, get(nref)), path(lam, get(m:get_n(lam)))

- else

- lnr:line_to(lam, get(nref))

- lnm:line_to(lam, get(m:get_n(lam)))

- end

- end

- local pn = plot(title)

- pn:addline(lnr, 'blue', {{'marker', size=5}})

- pn:addline(lnm, 'red', {{'dash', a=7, b=3}})

- pn:show()

- return pn

-end

-

-function demo1()

- -- ho fit for silicon oxyde

- local oxho = disp.ho {{nosc= 145, en= 15.78}}

-

- local ps, p0 = {'nosc:0', 'en:0'}, {170, 15.78}

-

- local sio2 = disp.load_nk (datadir .. '/thermal-sio2.nk')

-

- local fit = dispfit(sio2, oxho, ps, p0)

-

- fit:run()

-

- print('Resulting parameters:', tr(fit.p))

- print('Chi square:', fit.f:norm() / #sio2)

-

- plotcfr(sio2, oxho, 'Fit result, n vs wavelngth')

-end

-

-function demo2()

- -- ho fit for crystalline silicon

-

- local siho = disp.ho {{nosc= 186.5385, en= 10.4963, eg= 1.1442, phi= 0.0532},

- {nosc= 0.1788, en= 3.3766, eg= 0.5510, phi= -8.1241},

- {nosc= 0.6134, en= 4.7829, eg= 0.6031, phi= -6.5940},

- {nosc= 1.0210, en= 4.9724, eg= 0.6961, phi= -1.9735},

- {nosc= 0.5096, en= 3.3572, eg= 2.2388, phi= 4.7374},

- {nosc= 0.05, en= 5.45, eg= 0.17, phi= 4.2}

- }

-

- local ps = {'nosc:0',

- 'nosc:1', 'en:1', 'eg:1', 'phi:1',

- 'nosc:2', 'en:2', 'eg:2', 'phi:2',

- 'nosc:3', 'en:3', 'eg:3', 'phi:3',

- 'nosc:4', 'en:4', 'eg:4', 'phi:4',

- 'nosc:5', 'en:5', 'eg:5', 'phi:5'}

- local p0 = {186,

- 0.18, 3.37, 0.5, -8.12,

- 0.6, 4.78, 0.55, -6.59,

- 1.0, 4.972, 0.69, -1.97,

- 0.5, 3.357, 2.23, 4.73,

- 0.05, 5.45, 0.07, 4.2}

-

- local si_w = disp.load_nk (datadir .. '/si-woollam-b.nk')

-

- local fit = dispfit(si_w, siho, ps, p0)

-

- print('Initial Chi square:', fit.f:norm() / #si_w)

-

- fit:run(200)

-

- print('Resulting parameters:', tr(fit.p))

- print('Final Chi square:', fit.f:norm() / #si_w)

-

- plotcfr(si_w, siho, 'Fit result, n vs wavelngth')

- plotcfr(si_w, siho, 'Fit result, k vs wavelngth', |z| -imag(z))

-end

-

diff --git a/examples/pre3d.lua b/examples/pre3d.lua
deleted file mode 100644
index 31d38eef..00000000
--- a/examples/pre3d.lua
+++ /dev/null

@@ -1,195 +0,0 @@

-

-use 'stdlib'

-

-local Pre3d = require 'pre3d/pre3d'

-local ShapeUtils = require 'pre3d/pre3d_shape_utils'

-

-local function setTransform(ct, rx, ry, dz)

- ct:reset()

- ct:rotateZ(0)

- ct:rotateY(ry)

- ct:rotateX(rx)

- ct:translate(0, 0, dz and -dz or -80)

-end

-

-local function draw(renderer, shape)

- renderer:bufferShape(shape)

- renderer:drawBuffer()

- renderer:emptyBuffer()

-end

-

-function star(r)

- local a, ae = 54*pi/180, 72*pi/180

- local li, hi = r*cos(a), r*sin(a)

- local he = li*tan(ae)

- local xv, yv = 0, - hi - he

- local xb, yb = - li, - hi

- local p = path(xv, yv)

- p:line_to(xb, yb)

- for k=1, 4 do

- local th = 2*pi*k/5

- p:line_to(xv*cos(th) + yv*sin(th), yv*cos(th) - xv*sin(th))

- p:line_to(xb*cos(th) + yb*sin(th), yb*cos(th) - xb*sin(th))

- end

- p:close()

- return p

-end

-

-function demo1()

- local win = window()

- win:layout('v(h..).')

-

- p1 = plot 'sin'

- p1:addline(fxline(sin, 0, 2*pi), 'blue')

- p2 = plot 'cos'

- p2:addline(fxline(cos, 0, 2*pi), 'green')

-

- win:attach(p1, '2')

- win:attach(p2, '1,1')

-

- local plt = canvas('Pre3D')

- local a = 0.6

- plt:limits(-a, -a, a, a)

- local r = rng.new()

- local darkgray = graph.rgb(0.9, 0.9, 0.9)

- local lightgray = graph.rgb(0.6, 0.6, 0.6)

- for k = 1, 50 do

- local x, y = (2*r:get()-1)*a*0.8, (2*r:get()-1)*a*0.8

- local d = rnd.gaussian(r, 0.015*a) + 0.03*a

- local s = star(d)

- plt:add(s, darkgray, {}, {{'translate', x=x, y=y}})

- plt:addline(s, lightgray, {}, {{'translate', x=x, y=y}})

- end

- plt.units = false

- plt.sync = false

- plt:pushlayer()

-

- win:attach(plt, '1,2')

-

- local renderer = Pre3d.Renderer(plt)

- -- shape = ShapeUtils.makeSphere(1, 12, 12)

- local shape = ShapeUtils.makeOctahedron()

-

- ShapeUtils.linearSubdivideTri(shape)

- ShapeUtils.forEachVertex(shape,

- function(v, i, s)

- -- TODO(deanm): inplace.

- s.vertices[i] = Pre3d.Math.unitVector3d(v)

- return false

- end

- )

- -- We need to rebuild the normals after extruding the vertices.

- ShapeUtils.rebuildMeta(shape)

-

- renderer.draw_overdraw = false

- renderer.draw_backfaces = false

- renderer.fill_rgba = rgb(0x4A/255, 0x92/255, 0xBF/255)

- renderer.fill_rgba_backside = rgb(0xBF/255, 0x92/255, 0x4A/255)

- renderer.set_light_intensity = true

- -- renderer.fill_rgba_alpha = 0.95

- renderer.stroke_rgba = rgb(0x66/255, 0x66/255, 0x66/255)

-

- renderer.camera.focal_length = 30;

-

- local N, tour = 256, 2*pi

- for j=0, N do

- local a = tour*j/N

- setTransform(renderer.camera.transform, a, 0.15 * a)

- draw(renderer, shape)

- end

-end

-

-

-function demo2()

- local win = window()

- local plt = canvas 'Rotating Sphere'

- plt:limits(-1, -1, 1, 1)

- plt.sync = false

- win:attach(plt, '')

-

- local renderer = Pre3d.Renderer(plt)

- local shape = ShapeUtils.makeSphere(1, 12, 12)

-

- renderer.draw_overdraw = true

- renderer.draw_backfaces = false

- renderer.fill_rgba = rgb(0x4A/255, 0x92/255, 0xBF/255)

- renderer.fill_rgba_backside = rgb(0xBF/255, 0x92/255, 0x4A/255)

- renderer.set_light_intensity = true

--- renderer.fill_rgba_alpha = 0.95

--- renderer.stroke_rgba = rgb(0x66/255, 0x66/255, 0x66/255)

-

- renderer.camera.focal_length = 40;

-

- local N, tour = 256, 2*pi

- for j=0, N do

- local a = tour*j/N

- setTransform(renderer.camera.transform, a, 0.15 * a)

- draw(renderer, shape)

- end

-end

-

-function demo3()

- local win = window()

- local plt = canvas 'Moebius strip'

- plt:limits(-1, -1, 1, 1)

- plt.sync = false

- win:attach(plt, '')

-

- local renderer = Pre3d.Renderer(plt)

- local x = |u,v| (1 + 1/2 * v *cos(u/2))*cos(u)

- local y = |u,v| (1 + 1/2 * v *cos(u/2))*sin(u)

- local z = |u,v| 1/2 * v * sin(u/2)

- local shape = ShapeUtils.makeUVSurface(y, z, x, 0, -1, 2*pi, 1, 60, 4)

-

- renderer.draw_overdraw = false

- renderer.draw_backfaces = true

- renderer.fill_rgba = rgb(0x4A/255, 0x92/255, 0xBF/255)

- renderer.fill_rgba_backside = rgb(0xBF/255, 0x92/255, 0x4A/255)

- renderer.set_light_intensity = true

- renderer.draw_overdraw = true

- renderer.stroke_rgba = rgb(0.2, 0.2, 0.2)

-

- renderer.camera.focal_length = 40;

-

- local N, tour = 256, 2*pi

- for j=0, N do

- local a = tour*j/N

- setTransform(renderer.camera.transform, -a, -0.15*a)

- draw(renderer, shape)

- end

-end

-

-function demo4()

- local win = window()

- local plt = canvas 'Pre3D'

- plt:limits(-0.1, -0.1, 0.5, 0.5)

- plt.sync = false

- win:attach(plt, '')

-

- local renderer = Pre3d.Renderer(plt)

- local shape = ShapeUtils.makeXYFunction(|x,y| 1.2*exp(-x^2-y^2), -2, -2, 2, 2, 20, 20)

-

- renderer.draw_overdraw = false

- renderer.draw_backfaces = true

- renderer.fill_rgba = rgb(0x4A/255, 0x92/255, 0xBF/255)

- renderer.fill_rgba_backside = rgb(0xBF/255, 0x92/255, 0x4A/255)

- renderer.set_light_intensity = true

- renderer.draw_overdraw = true

--- renderer.stroke_rgba = rgb(0x66/255, 0x66/255, 0x66/255)

-

- renderer.camera.focal_length = 30;

-

- local N, tour = 256, 2*pi

- for j=0, N do

- local a = tour*j/N

- setTransform(renderer.camera.transform, -a, -0.15*a)

- draw(renderer, shape)

- end

-end

-

-

-echo([[

-demo1() - multiple plots window with 3D animations on a fixed background

-demo2() - rotating sphere

-demo3() - rotating Moebius strip

-demo4() - rotating surface from (x,y) function / Warning: memory & CPU hungry]])

diff --git a/examples/qag-bessel.lua b/examples/qag-bessel.lua
deleted file mode 100644
index 4ed5261f..00000000
--- a/examples/qag-bessel.lua
+++ /dev/null

@@ -1,37 +0,0 @@

-use 'math'

-

-local template = require 'template'

-local qag = template.load('qag', {limit=64, order=21})

-local qng = template.load('qng', {})

-

-local epsabs, epsrel = 1e-6, 0.01

-

-function bessel_gen(n, q)

- local xs

- local fint = function(t) return cos(n*t - xs*sin(t)) end

- return function(x)

- xs = x

- return q(fint, 0, pi, epsabs, epsrel) / pi

- end

-end

-

-local J4 = bessel_gen(4, qag)

-local J4b = bessel_gen(4, qng)

-

-w = graph.window 'v..'

-

-p1 = graph.plot('J4 bessel function')

-p2 = graph.plot('J4 bessel function')

-p1:addline(graph.fxline(J4, 0, 30*pi), 'red')

-p2:addline(graph.fxline(J4b, 0, 8*pi), 'blue')

-w:attach(p1, 1)

-w:attach(p2, 2)

-

-local xold, xsmp = 0, 1

-for x=0, 12*pi, 0.001 do

- local y = J4(x)

- if x - xold > xsmp and y > -1 then

- print(y)

- xold = x

- end

-end

diff --git a/examples/qr-lssolve.lua b/examples/qr-lssolve.lua
deleted file mode 100644
index e707f627..00000000
--- a/examples/qr-lssolve.lua
+++ /dev/null

@@ -1,28 +0,0 @@

-

-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))

-

- X = new(n,2, |i,j| j == 1 and a or b * xsmp(i))

-

- qr = QR(X)

-

- xls, res = qr:lssolve(y)

-

- print('Linear fit coefficients: ', tr(xls))

-

- p = plot()

- p:addline(xyline(x, X * xls))

- p:add(xyline(x, y), 'blue', {{'stroke'}, {'marker', size=5}})

- p.title = 'Linear Fit'

- p:show()

-

- return p

-end

-

-echo 'demo1() - examples of linear regression using QR decomposition'

diff --git a/examples/randist.lua b/examples/randist.lua
deleted file mode 100644
index b89b998c..00000000
--- a/examples/randist.lua
+++ /dev/null

@@ -1,17 +0,0 @@

-

-demo1 =

- function()

- local a, sig, n = 2, 2.44, 40

- local idx = |k| a + (k-1)*5*sig/n -- sampling function

- local pdf = |x| pdf.gaussian_tail(x, a, sig)

- local cdf = |x| cdf.gaussian_tail(x, a, sig)

- local cdftest = |x| integ {f= pdf, points= {a, x}}

- local p = plot 'Gaussian tail pdf / cdf'

- p:addline(fxline(pdf, a, 5*sig))

- p:addline(fxline(cdf, a, 5*sig), 'blue')

- p:addline(fxline(cdftest, a, 5*sig), 'green', {{'dash', 5, 5}})

- p:show()

- return p

- end

-

-print 'demo1() - gaussian tail distribution pdf and cdf plot'

diff --git a/examples/sige.lua b/examples/sige.lua
deleted file mode 100644
index d50344cb..00000000
--- a/examples/sige.lua
+++ /dev/null

@@ -1,128 +0,0 @@

-

-function read_data(filename)

- local f = io.open(filename, "r")

- local t = {}

- for ln in f:lines() do

- local a, b = string.match(ln, "([0-9%.]+)%s*,%s*([0-9%.]+)")

- t[#t+1] = {tonumber(a), tonumber(b)}

- end

- return matrix(t)

-end

-

-function step_func(brs)

- return function(x)

- for p in brs:rows() do

- if p:get(1,1) > x then return p:get(1,2) end

- end

- error 'x out of range in step function'

- end

-end

-

-function step_func_gauss(brs, sg)

- return function(x)

- local xinf, xsup = x - 5*sg, x + 5*sg

- local xc = xinf

- local parz = 0

- for p in brs:rows() do

- local xi, yi = p:get(1,1), p:get(1,2)

- if xi > xc then

- local del = cdf.gaussian(xi-x, sg) - cdf.gaussian(xc-x, sg)

- parz = parz + yi * del

- end

- xc = xi

- if xc > xsup then break end

- end

- return parz

- end

-end

-

-dt = read_data('examples/data/sige-sims-prof.csv')

-brs, sg0 = matrix {{2, 0}, {4, 36}, {18,32}, {100, 0}}, 0.8

-

-mysf = step_func(brs)

-mycf = step_func_gauss(brs, sg0)

-

-p = canvas 'SiGe Ge% profile'

-p.units = true

-p:limits(0, 0, 30, 44)

-p:addline(xyline(dt:col(1), dt:col(2)))

-p:show()

-p.sync = false

-p:pushlayer()

-

-function apply_param(brs, xp)

- brs:set(1,1, xp[1])

- brs:set(2,1, xp[2])

- brs:set(2,2, xp[3])

- brs:set(3,1, xp[4])

- brs:set(3,2, xp[5])

-end

-

-function minf_gener(lbrs)

- local lbrs = copy(lbrs)

- local sigma

- local function compute(xp, g)

- if g then error 'cannot calc gradient' end

-

- if xp[1] > xp[2] or xp[2] > xp[4] then

- return 0/0

- end

-

- if xp[3] < 0 or xp[5] < 0 or xp[3] > 42 then

- return 0/0

- end

-

- apply_param(lbrs, xp)

- sigma = xp[6]

- local mycf = step_func_gauss(lbrs, xp[6])

-

- local resid = 0

- for r in dt:rows() do

- local xi, yi = r:get(1,1), r:get(1,2)

- resid = resid + (yi - mycf(xi))^2

- end

-

- return resid

- end

- local function coeffs()

- return lbrs, sigma

- end

- return compute, coeffs

-end

-

-function do_minimize()

- local f, coeffs = minf_gener(brs)

- local m = fmultimin(f, 6)

-

- local x0 = vector {2, 4, 36, 18, 32, 0.8}

- local dx = vector {0.8, 0.8, 6, 2, 6, 0.1}

-

- m:set(x0, dx, 0.3)

-

- while m:step() == 'continue' do

- print(tr(m.x), m.value)

-

- p:clear()

- local obrs, sg = coeffs()

- local sf = step_func(obrs)

- local cf = step_func_gauss(obrs, sg)

- p:addline(fxline(sf, 0, 27), "green")

- p:addline(fxline(cf, 0, 27), "blue")

- p:flush()

- end

-

- print('SUCCESS:', tr(m.x), m.value)

-

- return m.x

-end

-

-xopt = do_minimize()

--- xopt = vector {1.476, 2.66143, 42, 18.4212, 31.5867, 39.7966, 0.604194}

-

-apply_param(brs, xopt)

-

-p = plot'SiGe profile from SIMS data'

-p:addline(xyline(dt:col(1), dt:col(2)))

-p:addline(fxline(step_func(brs), 0, 27), "blue")

-p:addline(fxline(step_func_gauss(brs, xopt[6]), 0, 27), "green")

-p:show()

diff --git a/examples/vandermonde.lua b/examples/vandermonde.lua
deleted file mode 100644
index ff25d730..00000000
--- a/examples/vandermonde.lua
+++ /dev/null

@@ -1,56 +0,0 @@

-

-function demo1()

- local n = 7

- local r = num.rng()

- local x = matrix.new(n, 1, |i| i)

- local y = matrix.new(n, 1, |i| r:get())

- local m = matrix.new(n, n, |i,j| x[i]^(j-1))

- local us = matrix.solve(m, y)

-

- local poly_eval = |x| iter.isum(|i| us[i] * x^(i-1), #us)

-

- local p = graph.plot()

- p:addline(graph.xyline(x, y), 'blue', {{'marker', size=5}})

- p:addline(graph.fxline(poly_eval, x[1], x[#x]))

- p.title = 'Polynomial interpolation'

- p.clip = false

- p:show()

-

- return p

-end

-

-function demo2()

- local n = 7

- local r = num.rng()

- local x = matrix.new(n, 1, |i| i)

- local y = matrix.cnew(n, 1, |i| complex.new(r:get(), r:get()))

- local m = matrix.new(n, n, |i,j| x[i]^(j-1))

- local us = matrix.solve(m, y)

-

- local poly_eval = |x| iter.isum(|i| us[i] * x^(i-1), #us)

-

- local pr, pi = graph.plot(), graph.plot()

-

- local rit = iter.sequence(function(i) return x[i], complex.real(y[i]) end, n)

- local iit = iter.sequence(function(i) return x[i], complex.imag(y[i]) end, n)

- pr:addline(graph.ipath(rit), 'blue', {{'marker', size=5}})

- pi:addline(graph.ipath(iit), 'green', {{'marker', size=5}})

-

- pr:addline(graph.fxline(|x| complex.real(poly_eval(x)), x[1], x[#x]))

- pi:addline(graph.fxline(|x| complex.imag(poly_eval(x)), x[1], x[#x]), 'magenta')

-

- pr.title = 'Polynomial interpolation, real part'

- pr.clip = false

-

- pi.title = 'Imaginary part'

- pi.clip = false

-

- local w = graph.window 'v..'

- w:attach(pr, 2)

- w:attach(pi, 1)

-

- return pr, pi

-end

-

-echo 'demo1() - Polynomial interpolation using Vandermonde matrix'

-echo 'demo2() - Complex valued polynomial interpolation using Vandermonde matrix'

diff --git a/examples/zernike.lua b/examples/zernike.lua
deleted file mode 100644
index 0fb3e71a..00000000
--- a/examples/zernike.lua
+++ /dev/null

@@ -1,43 +0,0 @@

-

-local invf = |n| n >= 0 and 1/fact(n) or 0

-

-function zerR(n, m, p)

- local ip, im = (n+m)/2, (n-m)/2

- local z = 0

- for k=0, im do

- local f = fact(n-k) * (invf(k) * invf(ip-k) * invf(im-k))

- if f > 0 then z = z + (-1)^k * f * p^(n-2*k) end

- end

- return z

-end

-

--- function bfact(n, k)

--- return (k < 0 or k > n) and 0 or choose(n,k)

--- end

-

--- function zerR(n, m, p)

--- local im = (n-m)/2

--- local z = 0

--- for k=0, im do

--- z = z + (-1)^k * bfact(n-k, k) * bfact(n-2*k, im-k) * p^(n-2*k)

--- end

--- return z

--- end

-

-function zernicke(n, m, p, phi, even)

- local pf = even and cos(m*phi) or sin(-m*phi)

- return zerR(n, m, p) * pf

-end

-

-local Nlev = 15

-local levels = ilist(|k| (k - Nlev)/Nlev, 0, 2*Nlev)

-local N, M = 8, 2

-local Rcut = 0.9

-

-require 'contour'

-local p = polar_contour(|x,y| zernicke(N, M, sqrt(x^2+y^2), atan2(y,x)), Rcut, {gridx= 81, gridy= 81, levels= 10})

-p:addline(circle(0, 0, Rcut), 'gray')

-p.title = string.format('Zernike polynomial (N=%i, M=%i)', N, M)

-

-

--- contour(|x,y| zernicke(N, M, sqrt(x^2+y^2), atan2(y,x)), -1, -1, 1, 1, {gridx= 61, gridy= 61, levels= levels})