%%2
%% 1. uzdevums

clear all, close all, clc
format longG
x=-4:0.0001:3;
f=@(x)3*sin(0.8*x)-x.^3+7*x-6;

plot(x,f(x),'r','LineWidth',3)
grid
%pirma_sakne=fzero(f,-3.0895)
%otra_sakne=fzero(f,0.67)
%tresa_sakne=fzero(f,2.38)

XN=[-3.0895 0.67 2.38]; % saknu tuvinajumi
iter=6;
syms x
n=length(XN);
fpr=diff(f(x),x);
for j=1:n
     xn=XN(j);
     for i=1:iter
         xn=xn-f(xn)/subs(fpr,x,xn);
         M(i,1)=double(xn);
         M(i,2)=double(f(xn));
     end
     saktuv=XN(j), M
end


%% 2. uzdevums

clear all, close all, clc
zim1 = ezplot('sin(x2+1)-x1-1.2',[-0.22, -0.2, 0.5, 0.55])
hold on
zim2 = ezplot('2*x2+cos(x1)-2',[-0.22, -0.2, 0.5, 0.55])
set(zim1,'Color','r','LineWidth',3)
set(zim2,'Color','b','LineWidth',3)
grid
%no grafika x1= -0.203   un  x2= 0.51

syms x1 x2
epsi=1; xtuv=[-0.203 0.51]; xpr=[x1 x2]; % saliek no grafika nolasitos p-tus
F=[sin(x2+1)-x1-1.2,2*x2+cos(x1)-2]; % ievada dotas funkcijas
Apr=[diff(F(1),xpr(1)) diff(F(1),xpr(2))
 diff(F(2),xpr(1)) diff(F(2),xpr(2))];
k=1;

while epsi > 10^(-3)
     for i=1:2
         B(i,1)=-subs(F(i),xpr,xtuv);
         for j=1:2
            A(i,j)=subs(Apr(i,j),xpr,xtuv);
         end
     end
     xdelta=double(A\B); xtuv=xtuv+xdelta';
     c=double(subs(F,xpr,xtuv)); epsi=norm(c);
     PR(k,1)=xtuv(1);
     PR(k,2)=xtuv(2);
     PR(k,3)=epsi;
     k=k+1;
end
format longG
%iegust atrisinajumu
PR   %x1    x2     epsi


%% 3. uzdevums

clear all, clc, close all

xint = [0,4]; % interv?ls
% s?kuma nosac?jumi
%x(0) = 3;
%y(0) = 2;
y0 = [3;2];

sol = ode45(@func_uzd3,xint,y0);
xx = [0:0.1:4]; % x v?rt?bu vektors

y = deval(sol,xx); % y v?rt?bu vektors
plot(xx,y(1,:),'r',xx,y(2,:),'g','LineWidth',3)
grid
legend('x(t)','y(t)')
xlabel('t')
ylabel('y')
%t=2.2;
%3.1 x(t) = -2.3
%3.2 y(t) = 0.2

%3.3  3?
%3.4  2.7?