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| | [[File:S__18382858.jpg]] | | [[File:S__18382858.jpg]] |
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| − | dikerjakan menggunakan hukum kontinuitas massa dimana masa yang masuk akan sama dengan yang dikeluarkan sehingga didapati rumus Q*''p''=Q*''p'' sehingga akan mendapatakan 4 persamaan dengan 4 variabel
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| − | 6C1 - 4C2 = 50
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| − | -2C1 - 1C3 + 4C4 = 50
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| − |
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| − | 7C2 - 3C3 - 4C4 = 0
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| − |
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| − | -4C1 + 4C3 = 0
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| − |
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| − |
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| − |
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| − | 6C1 - 4C2 + 0C3 + 0C4 = 50
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| − |
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| − | -2C1 + 0C2 - 1C3 + 4C4 = 50
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| − |
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| − | 0C1 + 7C2 - 3C3 - 4C4 = 0
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| − |
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| − | -4C1 + 0C2 + 4C3 + 0C4 = 0
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| − | yang kemudian dijadikan dalam modue python lalu didapatkan nilai C1 = 275/9 , C2 = 100/3 , C3 = 275/9, C4 = 425/12
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| − | <div border-style: inset;">
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| − | import numpy as np
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| − | class GEPP():
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| − | def __init__(self, A, b, doPricing=True):
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| − | #super(GEPP, self).__init__()
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| − | self.A = A # input: A is an n x n numpy matrix
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| − | self.b = b # b is an n x 1 numpy array
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| − | self.doPricing = doPricing
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| − | self.n = None # n is the length of A
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| − | self.x = None # x is the solution of Ax=b
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| − | self._validate_input() # method that validates input
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| − | self._elimination() # method that conducts elimination
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| − | self._backsub() # method that conducts back-substitution
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| − | def _validate_input(self):
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| − | self.n = len(self.A)
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| − | if self.b.size != self.n:
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| − | raise ValueError("Invalid argument: incompatible sizes between" +
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| − | "A & b.", self.b.size, self.n)
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| − | def _elimination(self):
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| − | """
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| − | k represents the current pivot row. Since GE traverses the matrix in the
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| − | upper right triangle, we also use k for indicating the k-th diagonal
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| − | column index.
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| − | :return
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| − | """
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| − | # Elimination
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| − | for k in range(self.n - 1):
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| − | if self.doPricing:
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| − | # Pivot
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| − | maxindex = abs(self.A[k:, k]).argmax() + k
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| − | if self.A[maxindex, k] == 0:
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| − | raise ValueError("Matrix is singular.")
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| − | # Swap
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| − | if maxindex != k:
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| − | self.A[[k, maxindex]] = self.A[[maxindex, k]]
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| − | self.b[[k, maxindex]] = self.b[[maxindex, k]]
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| − | else:
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| − | if self.A[k, k] == 0:
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| − | raise ValueError("Pivot element is zero. Try setting doPricing to True.")
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| − | # Eliminate
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| − | for row in range(k + 1, self.n):
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| − | multiplier = self.A[row, k] / self.A[k, k]
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| − | self.A[row, k:] = self.A[row, k:] - multiplier * self.A[k, k:]
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| − | self.b[row] = self.b[row] - multiplier * self.b[k]
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| − | def _backsub(self):
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| − | # Back Substitution
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| − | self.x = np.zeros(self.n)
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| − | for k in range(self.n - 1, -1, -1):
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| − | self.x[k] = (self.b[k] - np.dot(self.A[k, k + 1:], self.x[k + 1:])) / self.A[k, k]
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| − | def main():
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| − | A = np.array([[6., -4., 0., 0.],
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| − | [-4., 0., 4., 0.],
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| − | [-2., 0., -1., 4.],
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| − | [0., 7., -3., -4.]])
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| − | b = np.array([[50.],
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| − | [0.],
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| − | [50.],
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| − | [0.]])
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| − | print("ini matriks awal nya")
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| − | print(A)
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| − | print("ini hasil yang awal")
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| − | print(b)
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| − | GaussElimPiv = GEPP(np.copy(A), np.copy(b), doPricing=False)
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| − | print("ini hasil akhirnya")
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| − | print(GaussElimPiv.x)
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| − | print(GaussElimPiv.A)
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| − | print(GaussElimPiv.b)
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| − | GaussElimPiv = GEPP(A, b)
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| − | print(GaussElimPiv.x)
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| − | if __name__ == "__main__":
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| − | main()
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| − |
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| − | </div>
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| | | | |
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