DO k = 1, n-1
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! Select the pivot
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ipivot = MAXLOC( ABS(a(k:n,k)) ) + k - 1
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! Swap the rows
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tmp(k:n) = a(ipivot,k:n)
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a(ipivot,k:n) = a(k,k:n)
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a(k,k:n) = tmp(k:n)
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! Update the submatrix
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FORALL ( i=k+1:n, j=k+1:n ) &
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& a(i,j) = a(i,j) - a(i,k)/tmp(k)*tmp(j)
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