Fund-Math-exercisesMATLAB/Exercises1.m at master · frankbastidas/Fund-Math-exercisesMATLAB · GitHub

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%% 1.2 Implementation Recurrence relation
clc;clear;
x = 5; % start point
Px=1.2;
p=1/Px;
iter=40;
xplt=1:(iter*2-1);
yplt=1:(iter*2-1);
for R = 1:2:(iter*2-1)
    if R > 1
        xplt(R-1)=x;
        yplt(R-1)=x;
    end
    xplt(R)=x;
    yplt(R)=1+(1-p)*(x); % equacao de recurenca 1+(1-p)*(x)
    x=yplt(R);
    disp(1+(1-p)*(x));   % print recurrence relation value
end

xRecurenca=-4:0.1:5;
yRecurenca=1+(1-p)*(xsen);
xfij=-3:0.4:5;
yfij=-3:0.4:5;
plot(xplt,yplt,'--rs',xRecurenca,yRecurencao,'-b',xfij,yfij,':g','LineWidth',2,...
                       'MarkerEdgeColor','k',...
                       'MarkerFaceColor','g',...
                       'MarkerSize',10)

%% 2. Gaussian elimination Ax=B
clc;clear;
mat=[0.667 1.333 0.667;-0.667 0.667 0.333;-1.667 0.667 1.333]'; %SELA(A)
B=[2 0 0]';
[m,n] = size(mat);
numdet=1;
fil=0;
respdet=0;
if m~=n
   disp("Isn't squard matrix");
else
    Nmat=[mat;mat(1:n-1,:)];
    for i = 1:m
        for j = 1:n
            Nmat(i+j-1,j);
            numdet=Nmat(j+i-1,j)*numdet;
        end
        respdet=respdet+numdet;
        numdet=1;
    end
    for i = 1:m
        for j = 1:n
            Nmat(i+j-1,n+1-j);
            numdet=Nmat(j+i-1,n+1-j)*numdet;
        end
        respdet=respdet-numdet;
        numdet=1;
    end
    if numdet==0
        disp("Matrix with determinant zero");
    else
        Nmat=[mat,B]
        disp("calculating Matrix..");
        for j=1:n-1
% With pivote
            infF=j;
            for i=j+1:n
               if (abs(Nmat(i,j))>abs(Nmat(infF,j)))
                   infF=i;
               end
            end
            if j~=infF
                Vtemp=Nmat(j,:);
                Nmat(j,:)=Nmat(infF,:);
                Nmat(infF,:)=Vtemp;
            end
% solving
            for i=j+1:n
                NV=Nmat(i,j)/Nmat(j,j);
                Nmat(i,:)=Nmat(i,:)-NV*Nmat(j,:);
            end
        end
        Nmat
        Xn=ones(1,m);
        disp("solving ...");
        A=0;
        for i=m:-1:1
            if i~=m
                for j=i+1:m
                   A=A-Nmat(i,j)*Xn(j);
                end
            end
            Xn(i)=(A+Nmat(i,m+1))/Nmat(i,i);
            A=0;
        end
    end
end
% Solution
Xn


% Compare
% det(mat);
% respdet;


%% 3. factorization LU
clc;clear;
mat=[1 2 2;-1 0 1;0 1 -2]; %SELA(A)
B=[2 0 0]';
[m,n] = size(mat);
numdet=1;
respdet=0;
Xn=ones(1,m);
if m~=n
   disp("Isn't squard matrix");
else
    %Solving determinant
    Nmat=[mat;mat(1:n-1,:)];
    for i = 1:m
        for j = 1:n
            Nmat(i+j-1,j);
            numdet=Nmat(j+i-1,j)*numdet;
        end
        respdet=respdet+numdet;
        numdet=1;
    end
    for i = 1:m
        for j = 1:n
            Nmat(i+j-1,n+1-j);
            numdet=Nmat(j+i-1,n+1-j)*numdet;
        end
        respdet=respdet-numdet;
        numdet=1;
    end
    % solving matrix if determinant != 0
    if numdet==0
        disp("Matrix with determinant zero");
    else
        Nmat=mat;
        disp("calculating Matrix U and L..");
        NV=eye(m);
        for j=1:n-1
            for i=j+1:n
                if Nmat(i,j)==0
                    continue;
                else
                    NV(i,j)=Nmat(i,j)/Nmat(j,j);
                    Nmat(i,:)=Nmat(i,:)-NV(i,j)*Nmat(j,:);
                end
            end
        end
        Nmat
        NV
        Yn=ones(1,m);
        disp("solving ...");
        A=0;
        for i=1:m
            if i~=1
                for j=1:i-1
                   A=A-NV(i,j)*Yn(j);
                end
            end
            Yn(i)=(A+B(i))/NV(i,i);
            A=0;
        end
        for i=m:-1:1
            if i~=m
                for j=i+1:m
                   A=A-Nmat(i,j)*Xn(j);
                end
            end
            Xn(i)=(A+Yn(i))/Nmat(i,i);
            A=0;
        end
    end
    % Solution
    Xn
end


%% 4.