47 lines
1.0 KiB
Matlab
47 lines
1.0 KiB
Matlab
function A = Alg6_RREF(A)
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% Algorithm 6: Reduced Row Echelon Form (RREF)
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% A = Alg6_RREF(A) returns RREF of matrix A.
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[M, N] = size(A);
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n = 0;
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for m = 1 : M
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n = n + 1;
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if n > N
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break
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end
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% We want the left-most coefficient to be 1 (pivot)
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row = A(m, :);
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if row(m) == 0
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n = n + 1;
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end
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row = row/row(n);
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A(m, :) = row;
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for i = 1 : M
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if i ~= m
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A(i, :) = A(i, :)-(A(i, n))*row;
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end
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end
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for i = m + 1 : M
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A(i:end, m+1:end); % Partial matrix (in which we are looking for non-zero pivots)
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A(i:end, m+1); % Left-most column
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if ~any(A(i:end, m+1)) % If the left-most column has only zeros check the next one
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m = m + 1;
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end
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A(i:end, m+1:end);
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if A(i, m+1) == 0
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non_zero_row = find(A(i:end,m+1), 1);
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if isempty(non_zero_row)
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continue
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end
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A([i, i+non_zero_row-1], :) = deal(A([i+non_zero_row-1, i], :));
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end
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end
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end
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end
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