Plot The Squeeze Theorem Correctly

General Usage
1

Hi all,

I am trying to plot something to follow the Squeeze Theorem. It turns out to become funny.

using Plots, LaTeXStrings
pyplot(fmt=:svg)

function pitick(start, stop, denom; mode=:text)
    a = Int(cld(start, π/denom))
    b = Int(fld(stop, π/denom))
    tick = range(a*π/denom, b*π/denom; step=π/denom)
    ticklabel = piticklabel.((a:b) .// denom, Val(mode))
    tick, ticklabel
end

function piticklabel(x::Rational, ::Val{:text})
    iszero(x) && return "0"
    S = x < 0 ? "-" : ""
    n, d = abs(numerator(x)), denominator(x)
    N = n == 1 ? "" : repr(n)
    d == 1 && return S * N * "π"
    S * N * "π/" * repr(d)
end

function piticklabel(x::Rational, ::Val{:latex})
    iszero(x) && return L"0"
    S = x < 0 ? "-" : ""
    n, d = abs(numerator(x)), denominator(x)
    N = n == 1 ? "" : repr(n)
    d == 1 && return L"%$S%$N\pi"
    L"%$S\frac{%$N\pi}{%$d}"
end

a, b = -2π, 2π
#plot(sin, a, b; xtick=pitick(a, b, 4), label="y = sin t", size=(720, 250))
#plot(cos, a, b; xtick=pitick(a, b, 4), label="y = cos t", size=(720, 250))

f(x) = 1 + sin(x+π)
g(x) = -1 + sin(x+π) 
h(x) = sin(4x+π)

plot(f, a, b; xtick=pitick(a, b, 4; mode=:latex), label="f", size=(720, 360), tickfontsize=10)
plot!(g, a, b; xtick=pitick(a, b, 4; mode=:latex), label="g", size=(720, 360), tickfontsize=10)
plot!(h, a, b; xtick=pitick(a, b, 4; mode=:latex), label="h", size=(720, 360), tickfontsize=10)

The result that I want is like this:

what-is-the-squeeze-theorem
what-is-the-squeeze-theorem1280×720 19.6 KB

what should I do to make it works?

The f and h functions are the sin that is translated toward y-axis, but how to draw the g that follow the movement of the outside functions?

Like putting Bollinger Bands indicator toward the securities chart.

2

The simplest is to define: g(x) = (f(x) + h(x))/2 or any other weighting, e.g., g(x) = 0.3*f(x) + 0.7*h(x)

3

It is great but I actually want it to look like this:

Capture d’écran_2022-09-01_17-06-56

I manage to create a simple one:

using Plots, LaTeXStrings
pyplot(fmt=:svg)

function pitick(start, stop, denom; mode=:text)
    a = Int(cld(start, π/denom))
    b = Int(fld(stop, π/denom))
    tick = range(a*π/denom, b*π/denom; step=π/denom)
    ticklabel = piticklabel.((a:b) .// denom, Val(mode))
    tick, ticklabel
end

function piticklabel(x::Rational, ::Val{:text})
    iszero(x) && return "0"
    S = x < 0 ? "-" : ""
    n, d = abs(numerator(x)), denominator(x)
    N = n == 1 ? "" : repr(n)
    d == 1 && return S * N * "π"
    S * N * "π/" * repr(d)
end

function piticklabel(x::Rational, ::Val{:latex})
    iszero(x) && return L"0"
    S = x < 0 ? "-" : ""
    n, d = abs(numerator(x)), denominator(x)
    N = n == 1 ? "" : repr(n)
    d == 1 && return L"%$S%$N\pi"
    L"%$S\frac{%$N\pi}{%$d}"
end

a, b = -2π, 2π

h(x) = x*cos(1/x)
i(x) = abs(x)
j(x) = -abs(x)

plot(i, a, b; xtick=pitick(a, b, 4; mode=:latex), label="f", size=(720, 360), tickfontsize=10)
plot!(j, a, b; xtick=pitick(a, b, 4; mode=:latex), label="g", size=(720, 360), tickfontsize=10)
plot!(h, a, b; xtick=pitick(a, b, 4; mode=:latex), label="h", size=(720, 360), tickfontsize=10)
4

Just for the mathematical fun, you could generalise refael’s answer as
g(x) = f(x) * k(x) + h(x) * (1-k(x)) and then pick any kind of function for k which is in [0,1]. For example k(x) = 0.5 + 0.5*cos(x) (which is exactly your example) or something crazy like k(x) = 0.5 + 0.5*cos(x + sin(4*x)) :smiley:

Maybe take f and h as interpolated functions, then you don’t have to find a crazy function by hand.

3 Likes
5

That’s what I love about Julia Discourse and Mathematics. Sharing thoughts and solving problems together.

2 Likes
6 
k(x) = 0.5 + 0.5*cos(x + sin(4*x))

this works great