PMN KOLOS

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1.INTERPOLACJA LANGREGA
clc
clear
xdel

n=4
X=[-2;-1.5;3;5]
Y=[7;11;16;-1]
a = zeros(n)
for i = 1:n
il=1
for j = 1:n
if i <> j
il=il*(X(i)-X(j))
end
end
a(i) = Y(i)/il
end
disp('a')
disp(a)
function [w] = W(z)
fun = 0
for i = 1:n
il=1
for j = 1:n
if i <> j
il = (z - X(j)).* il
end
end
fun = fun + a(i)*il
end
w = fun
endfunction
disp('W(-0.5)')
disp(W(-0.5))
z = -3:0.1:6
plot(X,Y,'redx')
plot(z,W(z))
plot(-0.5,W(-0.5),'greeno')

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!112.INTERPOLACJA WIELOMIANOWA
clc
clear
xdel

n=5
x=[-3;-2;-0.5;1;3.5]
y=[4;4.8;-1.2;7;13]
X=zeros(5,5)
m = size(X,"r")
n = size(X,"c")
for i=1:n
    for j=1:n
        X(i,j)=x(i)^(j-1)
    end
    end
    disp(X)
a=inv(X)*y
disp('wektor a:')
for i=1:n
    disp(a(i))
end
function [w]=W(z)
    w=a(1)+a(2)*z+a(3)*z^2+a(4)*z^3+a(5)*z^4
endfunction
disp('wartosc dla 0.5:')
Res1=W(0.5)
disp(Res1)
s=-4:0.1:4
plot(s,W(s))
plot(x,y, 'redx')

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1111113.NEWTON I WZOR
clc
clear
xdel

disp('I wzor Newtona:')

n=6

x=[0.8;1;1.2;1.4;1.6;1.8]
y=[-3.52;-5;-6.72;-8.68;-10.88;-13.32]
for i=1:n

    z(i,1)=x(i,1)
    z(i,2)=y(i,1)
end
disp(z)

disp('tabela roznic:')
for j=3:n+1
    for i=1:n-j+2
        z(i,j)=z(i+1,j-1)-z(i,j-1)
end
end
disp(z)
h=0.2
s=1.3
//k=z(3,1)
k=3

q=((1.3-z(k,1))/h)

disp('q:')

disp(q)
function [w]=f(s)
q=(s-x(k))/h
w = z(k,2)+(z(k,3).*q)+(z(k,4).*(q.*(q-1))/2)+(z(k,5).*(q.*(q-1).*(q-2))/6)
endfunction
disp("W(s)=")
disp(f(s))
s=0.6:0.1:2
plot(x,y,'redx')
plot(s,f(s))

!!!!!!!!!!!!!!!!!!!!!!!!!!11!!!!!!!!!!!!!!!!!!!!!!!!4.NEWTON II WZOR
clc
clear
xdel

disp("2 wzor newtona:")
n=4

x=[50;100;150;200]
y=[-6.912;-7.605;-8.011;-8.298]
for i=1:n

    z(i,1)=x(i,1)
    z(i,2)=y(i,1)
end
disp(z)
disp('tabela roznic:')
for j=3:n+1
    for i=1:n-j+2
        z(i,j)=z(i+1,j-1)-z(i,j-1)
end
end
disp(z)
h=50
s=175
//k=z(3,1)
k=3

q=((1.3-z(k,1))/h)

disp('q:')

disp(q)
function [w]=f(s)
q=(s-x(k))/h
w = z(k,2)+(z(k-1,3).*q)+(z(k-2,4).*(q.*(q-1))/2)
endfunction
disp("W(s)=")
disp(f(s))
s=50:0.1:250
plot(x,y,'redx')
plot(s,f(s))

!!!!!!!!!!!!!!1!!!!!!!!!!!!!!!!!!!!!!!!!!!15.GAUSS
clc
clear
xdel

a=2
b=8
z=0
calka=0
n=4
ksi=[-0.86113;-0.339098;0.33998;0.86113]
w=[0.34785;0.65214;0.65214;0.34785]

function W1=f(z)
W1=3.5*z^(1/2)
endfunction

function W2 = F(ksi)
z =((b+a)/2)+((b-a)/2)*ksi
W2 =((b-a)/2)*f(z)
endfunction
for i =1:(n)

calka = calka + F(ksi(i))*w(i)
end
disp(calka)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!6.PROSTOKATY
clc
clear
xdel

a = 2;
b = 8;
n = 1000;
calka_pr = 0;
function W = f(z)
W = 3.5*z^(1/2)
endfunction

h = (b-a)/n

for i =1:(n)
x(i) = a + ((i-1) * h)

calka_pr = calka_pr + (h * f(x(i)))
end

disp(calka_pr);
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1!!!!!!!!!!!7.TRAPEZY
clc
clear
xdel

a = 2;
b = 8;
n = 1000;
calka_tr = 0;
wynik = 0;
x = zeros(n,1)
y = zeros(n,1)

function W = f(z)
W = 3.5*z^(1/2)
endfunction

h = (b-a)/n

for i =2:(n)
x(i+1) = a + ((i-1)*h)
y(i+1) = f(x(i+1))
if(i>0)
wynik = wynik + y(i+1)
end
end

calka_tr = h*(((y(1)+y(n))/2) + wynik)

disp(calka_tr)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!8.KUBATURA GAUSSA
clc
clear
xdel

n=3
i=0
calka=0
J=0
n=3
x=[1;3;1]
y=[1;3;3]
ksi=[0.5;0;0.5]
eta=[0.5;0.5;0]
wi=[1/3;1/3;1/3]
function wynik=f(x,y)
   wynik=3*log(x)*(y^2+7)
endfunction
J=((x(2)-x(1))*(y(3)-y(1)))-((x(3)-x(1))*(y(2)-y(1)))
disp(J)
function wynik1=F(ksi,eta)
    wynik1=abs(J)*f(x(1)+(x(2)-x(1))*ksi+(x(3)-x(1))*eta,y(1)+(y(2)-y(1))*ksi+(y(3)-y(1))*eta)
      endfunction
for i=1:n
    calka=calka+(F(ksi(i),eta(i))*wi(i))
end
disp(0.5*calka)