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i := 1
j := 1
while (i <= m and j <= n) do
  Find pivot in column j, starting in row i:
  maxi := i
  for k := i+1 to m do
    if abs(A[k,j]) > abs(A[maxi,j]) then
      maxi := k
    end if
  end for
  if A[maxi,j] != 0 then
    swap rows i and maxi, but do not change the value of i
    Now A[i,j] will contain the old value of A[maxi,j].
    divide each entry in row i by A[i,j]
    Now A[i,j] will have the value 1.
    for u := i+1 to m do
      subtract A[u,j] * row i from row u
      Now A[u,j] will be 0, since A[u,j] - A[i,j] * A[u,j] = A[u,j] - 1 * A[u,j] = 0.
    end for
    i := i + 1
  end if
  j := j + 1
end while

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def gaus(matrix):
        (m, n) = (len(matrix), len(matrix[0]))  # Groesse der Matrix bestimmen
        i = 0
        j = 0
        # Index anpassen, denn 3+2 entspricht 0-2 und 0-1
        m -= 1
        n -= 1
        while i <= m and j <= n:
                maxi = i
                for k in range (i+1,m+1):
                        if matrix[k][j] > matrix[maxi][j]:
                                maxi = k
                if matrix[maxi][j] != 0:
                        # Reihen tauschen
                        line = matrix[i]
                        matrix[i] = matrix[maxi]
                        matrix[maxi] = line
                        # jede Spalte in Reihe i durch den Wer in [i][j] teilen
                        for spalte in range (0,n+1):
                                matrix[i][spalte] /= matrix[i][j]
                        # matrix[u][j]* Reihe i von Reihe u abziehen
                        for u in range (i,m+1):
                                for v in range (0,n+1):
                                        matrix[u][v] -= matrix[u][j]*matrix[i][v]
                        i = i+1
                j = j+1

matrix = [[2.0, 1.0, -1.0, 8.0],
        [-3.0, -1.0, 2.0, -11.0],
        [-2.0, 1.0, 2.0, -3.0]]

gaus(matrix)
print matrix

Code: Alles auswählen

divide each entry in row i by A[i,j] 
Now A[i,j] will have the value 1

Code: Alles auswählen

i := 1