//export MESA_LOADER_DRIVER_OVERRIDE=i965
clear

//ferme toutes les fenêtres actuellement ouvertes
for id=winsid() close(scf(id)) end

function [ismin, min] = my_min(a, b)
    ismin=a<b
    if ismin then min = a
    else min=b
    end
endfunction

function [sum, diff] = operations(a, b)
sum = a + b
diff = a - b
endfunction

function res=approx_exp_1(x)
    res=1+x
endfunction

function res=approx_exp_2(x)
    res=1+x+(x.^2)/2
endfunction

X=linspace(-1,1,100)
p1=scf()
subplot(2, 1, 1)
title("Exp and first 2 Taylor series ")
plot(X, exp(X), "-r")
plot(X, approx_exp_1(X), ":g")
plot(X, approx_exp_2(X), ":b")

subplot(2, 1, 2)
title("Error for 2 first Taylor series ")
plot(X, abs(approx_exp_1(X)-exp(X)), ":g")
plot(X, abs(approx_exp_2(X)-exp(X)), ":b")

function res=suite(n)
    V=1:1:n
    res=1./V^2
endfunction

function res=S_n(n)
    res=sum(suite(n))
endfunction

disp(S_n(20))
disp(S_n(50))
disp(%pi^2/6)

function res=S_n2(n)
    my_suite=suite(n)
    res=0;
    for i=1:n
        res=res+my_suite(i)
    end
endfunction

disp(S_n2(20))
disp(S_n2(50))

disp("--- timing suites ---")
timer();res=S_n(500);disp(timer())
timer();res=S_n2(500);disp(timer())

function [low, high] = split_median(tab)
    tab_size=size(tab,2)
    pivot=int(tab_size/2)
    sorted_tab=gsort(tab,"g","i")
    low=sorted_tab(1:pivot)
    high=sorted_tab(pivot+1:tab_size)
endfunction

a=[-5, 8, -3, 12, 8]
[low, high] = split_median(a)

function res=deriv(X,Y)
    for i=1:size(Y,2)-1
        res(1,i)=(Y(i+1)-Y(i))/(X(i+1)-X(i))
    end
endfunction

X=linspace(-10, 10, 4000)
Y=X.^4

p2=scf() //nouvelle figure
plot(X, Y, "black")

disp("--- timing dérivées (1ère méthode) ---")

//dérivée première
timer(); Y1=deriv(X,Y); disp(timer())
X=X(1:size(X,2)-1)
plot(X, Y1, "blue")

//dérivée seconde
timer(); Y2=deriv(X,Y1); disp(timer())
X=X(1:size(X,2)-1)
plot(X, Y2, "red")

//dérivée troisième
timer(); Y3=deriv(X,Y2); disp(timer())
X=X(1:size(X,2)-1)
plot(X, Y3, "green")

//dérivée quatrième
timer(); Y4=deriv(X,Y3); disp(timer())
X=X(1:size(X,2)-1)
plot(X, Y4, "blue")

function res=deriv2(dX, Y)
    res=(Y(2:size(Y,2))-Y(1:size(Y,2)-1))./dX
endfunction

p3=scf() //nouvelle figure

X=linspace(-1000, 1000, 10000)
Y=X^3+X^2
//plot(X,Y, "blue")

disp("--- timing dérivées (comparaison méthodes) ---")

X1=X(1:size(X,2)-1)
timer(); Y1=deriv(X,Y); disp(timer())
plot(X1, Y1, "red")
dX=X(2)-X(1)
timer(); Y1=deriv2(dX, Y); disp(timer())
plot(X1, Y1, "green")

function res=H(X)
    res(1,X>0)=1
    res(1,X<0)=0
endfunction

X=linspace(-10, 10, 100)
disp(H(X))

// Autre ecriture plus compacte de la fonction H
// H=0.*(X<=0)+1.*(X>0)
//

function res=f(X)
    f1=-1 <= X & X < 0
    res(1,f1)=exp(X(f1))-exp(-1)
    f2=0 <= X & X < 1
    res(1,f2)=exp(-X(f2))-exp(-1)
    res(1,~(f1|f2))=0
endfunction

// Autre ecriture plus compacte de la fonction f
// f=(exp(X)-exp(-1)).*(X<0).*(-1<=X)+(exp(-X)-exp(-1)).*(0<=X).*(X<1)
//


p4=scf()
X=linspace(-2, 2, 1000)
Fx=f(X)
plot(X(Fx~=0),Fx(Fx~=0))

p5=scf()
n=-20:20
Un=n.*cos(%pi*n)
plot(n,Un)
plot(n(pmodulo(n,2)==1),Un(pmodulo(n,2)==1))
plot(n(pmodulo(n,2)==0),Un(pmodulo(n,2)==0))