gsl-shell.git - gsl-shell

diff --git a/draw.lua b/draw.lua
index 23489d74..96513d9d 100644
--- a/draw.lua
+++ b/draw.lua

@@ -84,8 +84,8 @@ function segment(x1, y1, x2, y2)

return p

end

-local bcolors = {'red', 'green', 'blue', 'cyan', 'magenta', 'yellow'}

-local mcolors = {'dark', '', 'light'}

+local bcolors = {'red', 'blue', 'green', 'magenta', 'cyan', 'yellow'}

+local mcolors = {'', 'dark', 'light'}

function rainbow(n)

local p = #bcolors

diff --git a/examples/fft.lua b/examples/fft.lua
index d761aece..9705efed 100644
--- a/examples/fft.lua
+++ b/examples/fft.lua

@@ -63,8 +63,11 @@ function demo2()

for k=ncut, n/2 do bess:set(k,0) end

fft_inv(bess)

- p:addline(filine(|i| bess[i], n), 'red', {{'dash', a=7, b=3}})

+ p:addline(filine(|i| bess[i], n), 'red', {{'dash', 7, 3}})

p:show()

return p, fftplot

end

+

+print 'demo1() - GSL example with square function and frequency cutoff'

+print 'demo2() - frequency cutoff example on bessel function'

diff --git a/examples/hermite.lua b/examples/hermite.lua
index 99a6754a..b5cb25f1 100644
--- a/examples/hermite.lua
+++ b/examples/hermite.lua

@@ -1,31 +1,28 @@

-function hermiteLp(n,x)

- return 1/sqrt(fact(n) *2^n*sqrt(pi)) * exp(-x*x/2) * (-4)^(n/2) * fact(n/2) * laguerre(n/2, -1/2, x^2)

-end

-

-p = plot()

-p:addline(fxline(|x| hermiteLp(4, x), -12, 12), 'darkgreen')

-p:addline(fxline(|x| hermiteLp(2, x), -12, 12), 'blue')

-p:addline(fxline(|x| hermiteLp(50, x), -12, 12, 1024), 'magenta')

-p:show()

-

-function hermiteU(n,x)

- return 1/sqrt(fact(n) *2^n*sqrt(pi)) * exp(-x*x/2) * 2^n * hypergU((1-n)/2, 3/2, x^2)

-end

-

-function hermiteFp(n,x)

- return 1/sqrt(fact(n) *2^n*sqrt(pi)) * exp(-x*x/2) * (-1)^(n/2) * fact(n)/fact(n/2) * hyperg1F1(-n/2, 1/2, x^2)

-end

-

-

-p2 = plot()

-p2:addline(fxline(|x| hermiteFp(4, x), -12, 12), 'darkgreen')

-p2:addline(fxline(|x| hermiteFp(2, x), -12, 12), 'blue')

-p2:addline(fxline(|x| hermiteFp(50, x), -12, 12, 1024), 'magenta')

-p:show()

-

-

--- p3 = plot()

--- p3:add_line(fxline(|x| hermiteU(4, x), -12, 12), 'darkgreen')

--- p3:add_line(fxline(|x| hermiteU(2, x), -12, 12), 'blue')

--- p3:add_line(fxline(|x| hermiteU(50, x), -12, 12, 1024), 'magenta')

+

+local function hermiteLp(n,x)

+ return 1/sqrt(fact(n) *2^n*sqrt(pi)) * exp(-x*x/2) * (-4)^(n/2) * fact(n/2) * laguerre(n/2, -1/2, x^2)

+end

+

+local function hermiteU(n,x)

+ return 1/sqrt(fact(n) *2^n*sqrt(pi)) * exp(-x*x/2) * 2^n * hypergU((1-n)/2, 3/2, x^2)

+end

+

+local function hermiteFp(n,x)

+ return 1/sqrt(fact(n) *2^n*sqrt(pi)) * exp(-x*x/2) * (-1)^(n/2) * fact(n)/fact(n/2) * hyperg1F1(-n/2, 1/2, x^2)

+end

+

+local function demo_gen(hermiteFF)

+ local p = plot('Hermite functions')

+ p:addline(fxline(|x| hermiteFF(2, x), -10, 10), 'red')

+ p:addline(fxline(|x| hermiteFF(4, x), -10, 10), 'blue', {{'dash', 7, 3}})

+ p:addline(fxline(|x| hermiteFF(16, x), -10, 10, 512), 'green')

+ p:show()

+end

+

+demo1 = || demo_gen(hermiteLp)

+demo2 = || demo_gen(hermiteFp)

+demo3 = || demo_gen(hermiteU)

+

+print 'demo1() - hermite function using Laguerre polynomials'

+print 'demo2() - hermite function using Hypergeometric 1F1 function'

+print 'demo3() - hermite function using Hypergeometric U function (broken)'

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'

diff --git a/examples/ode.lua b/examples/ode.lua
index b77a24f2..7b7a5efd 100644
--- a/examples/ode.lua
+++ b/examples/ode.lua

@@ -40,7 +40,7 @@ function demo1()

return p

end

-function demo1bis()

+function demo2()

local odef = function(t, y, f)

f:set(1,1, -y[2]-y[1]^2)

f:set(2,1, 2*y[1] - y[2]^3)

@@ -87,7 +87,7 @@ function ode_lines(s, t0, y0, t1, tstep)

return p

end

-function demo2()

+function demo3()

local mu = 10

local odef = function(t, y, f)

@@ -104,7 +104,7 @@ function demo2()

return plot_lines(ln)

end

-function demo3()

+function demo4()

local mu = 10

local odef = function(t,y,f)

@@ -129,7 +129,7 @@ function demo3()

return plot_lines(ln)

end

-function demo4()

+function demo5()

local t0, t1, tstep = 0, 30, 0.05

local alpha = 1i - 0.08

local z0 = 1.0 + 0.0i

@@ -151,7 +151,7 @@ function demo4()

return p

end

-function demo4bis()

+function demo6()

local t0, t1, tstep = 0, 30, 0.05

local alpha = 1i - 0.08

local z0 = 1.0 + 0.0i

@@ -184,7 +184,7 @@ function demo4bis()

return p

end

-function demo5()

+function demo7()

local odef = function(t, y, f)

f:set(1,1, y[2])

f:set(2,1, -sin(y[1])*y[1])

@@ -198,3 +198,11 @@ function demo5()

local ln = ode_lines(s, t0, y0, t1, tstep)

return plot_lines(ln)

end

+

+print 'demo1() - ODE integration example'

+print 'demo2() - the same of demo1 but using GSL \'bsimp\' method'

+print 'demo3() - GSL example of Var der Pol oscillator integration'

+print 'demo4() - same as demo3 but using \'bsimp\' method'

+print 'demo5() - spriral obtained by ODE integration'

+print 'demo6() - spriral obtained by ODE integration using \'bsimp\' method'

+print 'demo7() - another ODE integration example'