Help with function putting a matrix into upper triangluar form.

Question

Marc 2014-11-27

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评论： Geoff Hayes 2014-11-30

I have this function but it just is not doing what I want it to. When the function reaches to the end of the second for, it goes through that same for loop over again. How can I fix this? The Largest, swap and matCon are my own functions, they fins the row with the largest value, swap two rows and create a liner combination of the rows.

%%Converts a matrix to upper triangular form
function [upperMat]=upperTriangle(M)
rows=size(M,1);
cols=size(M,2);
for curRow=1:rows-1; 
    maxRow=Largest(M,curRow,curRow);
    if maxRow>curRow;
        M=swap(M,maxRow,curRow);
    end
    for workRow=curRow+1:rows 
        alpha=-M(workRow,curRow)/M(curRow,curRow);
        M=matCon(M,curRow,workRow,alpha);
    end
upperMat=M;
end
end

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Answer 1

Geoff Hayes 2014-11-29

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Marc - you probably need to post the code for your three functions as one of them may be causing a problem. If I take your code and use the following substations for your three

 function [maxRowIdx] = Largest(M,startRowIdx,colIdx)
    [~,maxRowIdx] = max(M(startRowIdx:end,colIdx));
 end
 function [M] = swap(M,row1Idx,row2Idx)
    temp         = M(row1Idx,:);
    M(row1Idx,:) = M(row2Idx,:);
    M(row2Idx,:) = temp;
 end
 function [M] = matCon(M,row1Idx,row2Idx,alpha)
    M(row2Idx,:) = alpha*M(row1Idx,:) + M(row2Idx,:);
 end

then the algorithm works. For example

 upperTriangle(magic(5))
 ans =
           23            5            7           14           16
            0       20.304      -4.1739      -2.3478       3.1739
            0            0       12.837       18.158       18.415
            0            0            0      -9.3786       -31.28
            0            0            0            0       90.173

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Marc 2014-11-29

编辑：Marc 2014-11-29

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Hi Geoff, the functions are as follows

Largest

function maxRow=Largest(M,r,c)
rows=size(M,1); % total number of rows
max=M(r,c);
maxRow=M(r,:);
for i=r:rows
    if abs(M(i,c))>max % Checks to see if the absolute value of a column is greater than max
        max=abs(M(i,c));
        maxRow=i; % updates maxRow
      end
end
end

swap

function newmat=swap(mat,row1,row2) % swaps two rows in a matrix
[r, c] = size(mat); % find number of rows and columns 
newmat=mat; % interchange values 
newmat(row2,:) = mat(row1,:);
newmat(row1,:) = mat(row2,:);
end

matCon

%%takes a matrix, two row numbers and a scalar as arguments and returns a matrix with a linear combination of the rows
function [newMat]=matCon(m,r1,r2,s)
newMat=[];
rows=size(m,1); % finds number of rows
cols=size(m,2); % finds number of columns
n=2; % will start from the second row
while n <= rows % runs the while statement to the last row of the matrix
    m(n,:)=s.*(m(n-1,:))+(m(n,:)); % Does the calculations
    n=n+1; % Makes the loop go to the second row
    newMat=m;
end
end

Marc 2014-11-30

I got the original function to work, thank you so much! It was the matCon function. I completely overlooked the fact that I had it running through the entire matrix.