linearAlgebra/la_assign.sce at master · deeksha-d/linearAlgebra · GitHub

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clc;clear;close;

function [U,L]=lud(A)
    U=A
    disp(A,'The given matrix is A=')
    m=det(U(1,1));
    n=det(U(2,1));
    a=n/m
    U(2,:)=U(2,:)-U(1,:)/(m/n)
    n=det(U(3,1));
    b=n/m
    U(3,:)=U(3,:)-U(1,:)/(m/n)
    m=det(U(2,2))
    n=det(U(3,2));
    c=n/m
    U(3,:)=U(3,:)-U(2,:)/(m/n)
    L=[1,0,0;a,1,0;b,c,1]
endfunction

function [B]=inverse(A)
    disp(A,'The given matrix is A=')
    n=length(A(1,:))
    aug=[A,eye(n,n)]

    for j=1:n-1
        for i=j+1:n
            aug(i,j:2*n)=aug(i,j:2*n)-aug(i,j)/aug(j,j)*aug(j,j:2*n)
        end
    end

    for j=n:-1:2
        aug(1:j-1,:)=aug(1:j-1,:)-aug(1:j-1,j)/aug(j,j)*aug(j,:)
    end

    for j=1:n
        aug(j,:)=aug(j,:)/aug(j,j)
    end
    B=aug(:,n+1:2*n)
endfunction

function[x,a]=gaussElim(a,b)
    disp(a,'The given matrix is A=')
    A_aug = [a b];
    a = A_aug;
    n=3;

    for i=2:n
        for j=2:n+1
            a(i,j)=a(i,j)-a(1,j)*a(i,1)/a(1,1)
    end
    a(i,1)=0;
    end

    for i=3:n
        for j=3:n+1
            a(i,j)=a(i,j)-a(i,2)*a(2,j)/a(2,2);
        end
        a(i,2)=0;
    end

    x(n)=a(n,n+1)/a(n,n);

    for i=n-1:-1:1
        sumk=0;
        for k=i+1:n
            sumk=sumk+a(i,k)*x(k);
        end
        x(i)=(a(i,n+1)-sumk)/a(i,i);
    end

    endfunction

function main()
    A=[0,0,0;0,0,0;0,0,0]
    A(1,1)=input("input a11: ")
    A(1,2)=input("input a12: ")
    A(1,3)=input("input a13: ")
    A(2,1)=input("input a21: ")
    A(2,2)=input("input a22: ")
    A(2,3)=input("input a23: ")
    A(3,1)=input("input a31: ")
    A(3,2)=input("input a32: ")
    A(3,3)=input("input a33: ")
    disp('1.Gaussian Elimination\n2.Gauss Jordan method\n3.LU Decomposition\n')
    choice=input("enter choice: ")
    if choice==1 then
        b=[0;0;0]
        b(1,1)=input("enter b1: ")
        b(2,1)=input("enter b2: ")
        b(3,1)=input("enter b3: ")
        [x,a]=gaussElim(A,b)
        disp(x(3),x(2),x(1),'The values of x,y,z are ');
        disp(a(1,1),a(2,2),a(3,3),'The pivots are');
    elseif choice==2 then
        [B]=inverse(A)
        disp(B,'The inverse of A is');
    elseif choice==3 then
        [U,L]=lud(A)
        disp(U,'The upper triangular matrix is U =')
        disp(L,'The lower triangular matrix is L =')
    end
endfunction
main();