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Gaussian Elimination with Partial Pivoting Modularized
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| import numpy as np | |
| class GEPP(): | |
| """ | |
| Gaussian elimination with partial pivoting. | |
| input: A is an n x n numpy matrix | |
| b is an n x 1 numpy array | |
| output: x is the solution of Ax=b | |
| with the entries permuted in | |
| accordance with the pivoting | |
| done by the algorithm | |
| post-condition: A and b have been modified. | |
| :return | |
| """ | |
| def __init__(self, A, b, doPricing=True): | |
| #super(GEPP, self).__init__() | |
| self.A = A # input: A is an n x n numpy matrix | |
| self.b = b # b is an n x 1 numpy array | |
| self.doPricing = doPricing | |
| self.n = None # n is the length of A | |
| self.x = None # x is the solution of Ax=b | |
| self._validate_input() # method that validates input | |
| self._elimination() # method that conducts elimination | |
| self._backsub() # method that conducts back-substitution | |
| def _validate_input(self): | |
| self.n = len(self.A) | |
| if self.b.size != self.n: | |
| raise ValueError("Invalid argument: incompatible sizes between" + | |
| "A & b.", self.b.size, self.n) | |
| def _elimination(self): | |
| """ | |
| k represents the current pivot row. Since GE traverses the matrix in the | |
| upper right triangle, we also use k for indicating the k-th diagonal | |
| column index. | |
| :return | |
| """ | |
| # Elimination | |
| for k in range(self.n - 1): | |
| if self.doPricing: | |
| # Pivot | |
| maxindex = abs(self.A[k:, k]).argmax() + k | |
| if self.A[maxindex, k] == 0: | |
| raise ValueError("Matrix is singular.") | |
| # Swap | |
| if maxindex != k: | |
| self.A[[k, maxindex]] = self.A[[maxindex, k]] | |
| self.b[[k, maxindex]] = self.b[[maxindex, k]] | |
| else: | |
| if self.A[k, k] == 0: | |
| raise ValueError("Pivot element is zero. Try setting doPricing to True.") | |
| # Eliminate | |
| for row in range(k + 1, self.n): | |
| multiplier = self.A[row, k] / self.A[k, k] | |
| self.A[row, k:] = self.A[row, k:] - multiplier * self.A[k, k:] | |
| self.b[row] = self.b[row] - multiplier * self.b[k] | |
| def _backsub(self): | |
| # Back Substitution | |
| self.x = np.zeros(self.n) | |
| for k in range(self.n - 1, -1, -1): | |
| self.x[k] = (self.b[k] - np.dot(self.A[k, k + 1:], self.x[k + 1:])) / self.A[k, k] | |
| def main(): | |
| A = np.array([[1., -1., 1., -1.], | |
| [1., 0., 0., 0.], | |
| [1., 1., 1., 1.], | |
| [1., 2., 4., 8.]]) | |
| b = np.array([[14.], | |
| [4.], | |
| [2.], | |
| [2.]]) | |
| GaussElimPiv = GEPP(np.copy(A), np.copy(b), doPricing=False) | |
| print(GaussElimPiv.x) | |
| print(GaussElimPiv.A) | |
| print(GaussElimPiv.b) | |
| GaussElimPiv = GEPP(A, b) | |
| print(GaussElimPiv.x) | |
| if __name__ == "__main__": | |
| main() |
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| import numpy as np | |
| class GEPP(): | |
| """ | |
| Gaussian elimination with partial pivoting. | |
| input: A is an n x n numpy matrix | |
| b is an n x 1 numpy array | |
| output: x is the solution of Ax=b | |
| with the entries permuted in | |
| accordance with the pivoting | |
| done by the algorithm | |
| post-condition: A and b have been modified. | |
| :return | |
| """ | |
| def __init__(self, A, b, doPricing=True): | |
| #super(GEPP, self).__init__() | |
| self.A = A # input: A is an n x n numpy matrix | |
| self.b = b # b is an n x 1 numpy array | |
| self.doPricing = doPricing | |
| self.n = None # n is the length of A | |
| self.x = None # x is the solution of Ax=b | |
| self._validate_input() # method that validates input | |
| self._elimination() # method that conducts elimination | |
| self._backsub() # method that conducts back-substitution | |
| def _validate_input(self): | |
| self.n = len(self.A) | |
| if self.b.size != self.n: | |
| raise ValueError("Invalid argument: incompatible sizes between" + | |
| "A & b.", self.b.size, self.n) | |
| def _elimination(self): | |
| """ | |
| k represents the current pivot row. Since GE traverses the matrix in the | |
| upper right triangle, we also use k for indicating the k-th diagonal | |
| column index. | |
| :return | |
| """ | |
| # Elimination | |
| for k in range(self.n - 1): | |
| if self.doPricing: | |
| # Pivot | |
| maxindex = abs(self.A[k:, k]).argmax() + k | |
| if self.A[maxindex, k] == 0: | |
| raise ValueError("Matrix is singular.") | |
| # Swap | |
| if maxindex != k: | |
| self.A[[k, maxindex]] = self.A[[maxindex, k]] | |
| self.b[[k, maxindex]] = self.b[[maxindex, k]] | |
| else: | |
| if self.A[k, k] == 0: | |
| raise ValueError("Pivot element is zero. Try setting doPricing to True.") | |
| # Eliminate | |
| for row in range(k + 1, self.n): | |
| multiplier = self.A[row, k] / self.A[k, k] | |
| self.A[row, k:] = self.A[row, k:] - multiplier * self.A[k, k:] | |
| self.b[row] = self.b[row] - multiplier * self.b[k] | |
| def _backsub(self): | |
| # Back Substitution | |
| self.x = np.zeros(self.n) | |
| for k in range(self.n - 1, -1, -1): | |
| self.x[k] = (self.b[k] - np.dot(self.A[k, k + 1:], self.x[k + 1:])) / self.A[k, k] | |
| def main(): | |
| A = np.array([[1., -1., 1., -1.], | |
| [1., 0., 0., 0.], | |
| [1., 1., 1., 1.], | |
| [1., 2., 4., 8.]]) | |
| b = np.array([[14.], | |
| [4.], | |
| [2.], | |
| [2.]]) | |
| GaussElimPiv = GEPP(np.copy(A), np.copy(b), doPricing=False) | |
| print(GaussElimPiv.x) | |
| print(GaussElimPiv.A) | |
| print(GaussElimPiv.b) | |
| GaussElimPiv = GEPP(A, b) | |
| print(GaussElimPiv.x) | |
| if __name__ == "__main__": | |
| main() |
Thanks @byteofsoren for example!
- Add conversion to
float - Change
self.A[k, k] == 0toabs(self.A[k, k]) <= sys.float_info.epsilon
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God script but it have a problem on row 71.
------ [The test code] ----
import numpy as np
from GEPP import *
print("Create matrix")
A = np.array([ [1,2,3],
[3,4,5],
[3,2,1]])
y = np.array([ [1],
[3],
[4]])
Gause = GEPP(np.copy(A), np.copy(y), doPricing=False)
print(Gause.x)
print(Gause.A)
print(Gause.b)
--- [end test code] --
Generates the output:
GEPP.py:71: RuntimeWarning: divide by zero encountered in true_divide
self.x[k] = (self.b[k] - np.dot(self.A[k, k + 1:], self.x[k + 1:])) / self.A[k, k]
[ nan -inf inf]
[[ 1 2 3]
[ 0 -2 -4]
[ 0 0 0]]
[[1]
[0]
[1]]