task3summerpractice

function [S_N,N] = int_left_rectangles(phi,c,d,eps)
N=1;
while 1
    h_N1=(d-c)/N;
    h_N2=(d-c)/(2*N);
    z1=c:h_N1:d;
    z2=c:h_N2:d;
    S_N=0;
    S_2N=0;
    for i=1:N
        S_N=S_N+phi(z1(i))*h_N1;
    end
    for i=1:2*N
        S_2N=S_2N+phi(z2(i))*h_N2;
    end
    if(abs(S_N-S_2N)<=eps)
        break;
    end
    N=N*2;
end
end

function [S_N,N] = int_center_rectangles(phi,c,d,eps)
N=1;
while 1
    h_N1=(d-c)/N;
    h_N2=(d-c)/(2*N);
    z1=c:h_N1:d;
    z2=c:h_N2:d;
    S_N=0;
    S_2N=0;
    for i=1:N
        S_N=S_N+phi((z1(i)+z1(i+1))/2)*h_N1;
    end
    for i=1:2*N
        S_2N=S_2N+phi((z2(i)+z2(i+1))/2)*h_N2;
    end
    if(abs(S_N-S_2N)<=eps)
        break;
    end
    N=N+1;
end
end

function [S_N,N] = int_trapez_(phi,c,d,eps)
N=1;
while 1
    h_N1=(d-c)/N;
    h_N2=(d-c)/(2*N);
    z1=c:h_N1:d;
    z2=c:h_N2:d;
    S_N=0;
    S_2N=0;
    for i=1:N
        S_N=S_N+h_N1/2*(phi(z1(i))+phi(z1(i+1)));
    end
    for i=1:2*N
        S_2N=S_2N+h_N2/2*(phi(z2(i))+phi(z2(i+1)));
    end
    if(abs(S_N-S_2N)<=eps)
        break;
    end
    N=N+1;
end
end


function [S_N,N] = int_simpson(phi,c,d,eps)
N=1;
while 1
    h_N1=(d-c)/N;
    h_N2=(d-c)/(2*N);
    z1=c:h_N1:d;
    z2=c:h_N2:d;
    S_N=0;
    S_2N=0;
    for i=1:N
        S_N=S_N+(h_N1/6)*(phi(z1(i))+4*phi((z1(i+1)+z1(i))/2)+phi(z1(i+1)));
    end
    for i=1:2*N
        S_2N=S_2N+(h_N2/6)*(phi(z2(i))+4*phi((z2(i+1)+z2(i))/2)+phi(z2(i+1)));
    end
    if(abs(S_N-S_2N)<=eps)
        break;
    end
    N=N+1;
end
end


function [S_N,N] = int_gauss(phi,c,d,eps)
N=1;
while 1
    h_N1=(d-c)/N;
    h_N2=(d-c)/(2*N);
    z1=c:h_N1:d;
    z2=c:h_N2:d;
    S_N=0;
    S_2N=0;
    for i=1:N
        S_N=S_N+(h_N1/2)*(phi(z1(i)+(h_N1/2)*(1-1/sqrt(3)))+phi(z1(i)+(h_N1/2)*(1+1/sqrt(3))));
    end
    for i=1:2*N
        S_2N=S_2N+(h_N2/2)*(phi(z2(i)+(h_N2/2)*(1-1/sqrt(3)))+phi(z2(i)+(h_N2/2)*(1+1/sqrt(3))));
    end
    if(abs(S_N-S_2N)<=eps)
        break;
    end
    N=N+1;
end
end

%main
% phi = @(t) sin((pi*t^2)/2);
% eps1=10^(-8);
% a=0; b=1.2;
% x=0:0.12:1.2;
% [S,k] = taylor_series_task1(x,eps1);
% S_N(1)=0;
% N(1)=0;
% for i=2:length(x)
%     [S_N(i),N(i)] = int_left_rectangles(phi,0,x(i),eps1);
% end
% error=abs(S-S_N);
% array2table([x;S;S_N;N;error]',...
%     'VariableNames',{'x','S(x)','S_N(x)','N','error'})
% format long

% phi = @(t) sin((pi*t^2)/2);
% eps1=10^(-8);
% a=0; b=1.2;
% x=0:0.12:1.2;
% [S,k] = taylor_series_task1(x,eps1);
% S_N(1)=0;
% N(1)=0;
% for i=2:length(x)
%     [S_N(i),N(i)] = int_center_rectangles(phi,0,x(i),eps1);
% end
% error=abs(S-S_N);
% array2table([x;S;S_N;N;error]',...
%     'VariableNames',{'x','S(x)','S_N(x)','N','error'})
% format long

% phi = @(t) sin((pi*t^2)/2);
% eps1=10^(-8);
% a=0; b=1.2;
% x=0:0.12:1.2;
% [S,k] = taylor_series_task1(x,eps1);
% S_N(1)=0;
% N(1)=0;
% for i=2:length(x)
%     [S_N(i),N(i)] = int_trapez_(phi,0,x(i),eps1);
% end
% error=abs(S-S_N);
% array2table([x;S;S_N;N;error]',...
%     'VariableNames',{'x','S(x)','S_N(x)','N','error'})
% format long

% phi = @(t) sin((pi*t^2)/2);
% eps1=10^(-8);
% a=0; b=1.2;
% x=0:0.12:1.2;
% [S,k] = taylor_series_task1(x,eps1);
% S_N(1)=0;
% N(1)=0;
% for i=2:length(x)
%     [S_N(i),N(i)] = int_simpson(phi,0,x(i),eps1);
% end
% error=abs(S-S_N);
% array2table([x;S;S_N;N;error]',...
%     'VariableNames',{'x','S(x)','S_N(x)','N','error'})
% format long

% phi = @(t) sin((pi*t^2)/2);
% eps1=10^(-6);
% a=0; b=1.2;
% x=0:0.12:1.2;
% [S,k] = taylor_series_task1(x,eps1);
% S_N(1)=0;
% N(1)=0;
% for i=2:length(x)
%     [S_N(i),N(i)] = int_gauss(phi,0,x(i),eps1);
% end
% error=abs(S-S_N);
% array2table([x;S;S_N;N;error]',...
%     'VariableNames',{'x','S(x)','S_N(x)','N','error'})
% format long

phi = @(t) sin((pi*t^2)/2);
eps1=10^(-8);
a=0; b=1.2;
x=0:0.12:1.2;
[S,k] = taylor_series_task1(x,eps1);
S_N_trapez(1)=0;
S_N_simpson(1)=0;
S_N_gauss(1)=0;
for i=2:length(x)
    S_N_trapez(i) = int_trapez_(phi,0,x(i),eps1);
    S_N_simpson(i)= int_simpson(phi,0,x(i),eps1);
    S_N_gauss(i)= int_gauss(phi,0,x(i),eps1);
end
error_trapez=abs(S-S_N_trapez);
error_simpson=abs(S-S_N_simpson);
error_gauss=abs(S-S_N_gauss);
array2table([x;error_trapez;error_simpson;error_gauss]',...
    'VariableNames',{'x','Трапеции','Симпсона','Гаусса'})
format long