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47 lines
1.5 KiB
47 lines
1.5 KiB
function [A, P] = lrPivot(A)
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% Gaussian Elimination for reforming the matrix into left-lower and right-upper triangular matrix
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% A: A R^(n \times n) matrix
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% P: Permutations-Matrix
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% actually not used here (but it was planned to be used): bsxfun, which makes this possible: bsxfun(@times, [1,2;3,4], [1;2]) = [1,2;6,8]. It multiplies the first row by 1, and the second one by 2.
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% newer (and actually (still not) used here): [1,2;3,4].*[1;2] = [1,2;6,8]
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% for convenience
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len = length(A)
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pvec = 1:len
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% Generate LR-Zerlegung
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for i = 1:len
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% pivot
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[maxVal, maxValPos] = max(abs(A(pvec(i:end), i)))
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% swap
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temp = pvec(i)
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pvec(i) = pvec(maxValPos + i - 1)
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pvec(maxValPos + i - 1) = temp
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prefactor = A(pvec(i),i)
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if prefactor == 0
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error("LR-Zerlegung failed. Please check that the matrix is regular!")
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end
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% elimination (find R)
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factors = zeros(len, 1)
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for j = (i+1):len
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factors(pvec(j)) = A(pvec(j), i) / prefactor
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end
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% A(:,i:len) describes the matrix A with only the last i cols (so, for example, a 3x3 matrix with (:,2,len) with len=3) is the last 2 cols of the matrix, and with that a 2x3 matrix
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% extra step for traceability, could also be compressed to a single line
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multmatrix = (-factors * A(pvec(i),i:len))
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A(:,i:len) = A(:,i:len) + multmatrix
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% save factors for L
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A(:,i) = A(:,i) + factors
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end
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P = eye(len)(:,pvec)
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end |