solve larger than 3x3 matrix and error message

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amateurintraining
amateurintraining 2017-11-1
评论： amateurintraining 2017-11-1
I have a function:
function [A_new, b_new] = forward_elimination(A, b)
%FORWARD_ELIMINATION - Performs forward elimination to put A into unit
% upper triangular form.
% A - original matrix of Ax = b
% b - original vector of Ax = b
% A_new - unit upper triangular A formed using Gaussian Elimination
% b_new - the vector b associated with the transformed A
% Default output
A_new = A;
b_new = b;
[n,n]=size(A);
Ab=[A b];
Ab(1,:)=Ab(1,:)/Ab(1,1);
Ab(2,:)=Ab(2,:)/Ab(2,2);
Ab(3,:)=Ab(3,:)/Ab(3,3);
Ab(2,:)=Ab(1,:)*Ab(2,1)-Ab(2,:);
Ab(2,:)=Ab(2,:)/Ab(2,2);
Ab(3,:)=Ab(1,:)*Ab(3,1)-Ab(3,:);
Ab(3,:)=Ab(3,:)/Ab(3,2);
Ab(3,:)=Ab(2,:)*Ab(3,2)-Ab(3,:);
Ab(3,:)=Ab(3,:)/Ab(3,3);
A_new=Ab(:,1:end-1);
b_new=Ab(:,end);
if Ab(1,1)==0 || Ab(2,2)==0 || Ab(3,3)==0 || Ab(3,2)==0
error(zeros(n))
end
end
This produces the desired answer for a 3x3 matrix but how do I expand this for larger matrices. Also, how to i write the code such that if the system is unsolvable or is divided by 0, the algorithm responds an error message and returns a matrix of all zeros? I have attempted above.

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回答（1 个）

Nicolas Schmit
Nicolas Schmit 2017-11-1
how do I expand this for larger matrices.
use for loops
how to i write the code such that if the system is unsolvable or is divided by 0, the algorithm responds an error message and returns a matrix of all zeros?
You can first calculate the determinant of the matrix, and issue an error message if it is null.
  1 个评论
amateurintraining
amateurintraining 2017-11-1
I have attempted to fix the code:
function [A_new,b_new]=forward_elimination(A,b)
A_new=A;
b_new=b;
[n,n]=size(A)
if Ab(1,1)==0 || Ab(2,2)==0 || Ab(3,3)==0 || Ab(3,2)==0 || determinant_e7(A)==0
zeros(n)
error('function cannot compute')
end
for row=1:n-1
for i=row+1:n
factor=A(i,row)/A(row,row);
for j=row:n
A(i,j)=A(i,j)-factr*A(row,j);
end
b(i)=b(i)-factor*b(row);
end
A_new=A;
b_new=b;
end
end
But the code does not produce the UNIT matrices (with 1's in the diagonals and 0's under), and the error statement is incorrect. How should I go from here?

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