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import numpy as np
def GEPP(A, b, doPricing = True):
'''
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.
'''
n = len(A)
if b.size != n:
raise ValueError("Invalid argument: incompatible sizes between"+
"A & b.", b.size, n)
# 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.
# Elimination
for k in range(n-1):
if doPricing:
# Pivot
maxindex = abs(A[k:,k]).argmax() + k
if A[maxindex, k] == 0:
raise ValueError("Matrix is singular.")
# Swap
if maxindex != k:
A[[k,maxindex]] = A[[maxindex, k]]
b[[k,maxindex]] = b[[maxindex, k]]
else:
if A[k, k] == 0:
raise ValueError("Pivot element is zero. Try setting doPricing to True.")
#Eliminate
for row in range(k+1, n):
multiplier = A[row,k]/A[k,k]
A[row, k:] = A[row, k:] - multiplier*A[k, k:]
b[row] = b[row] - multiplier*b[k]
# Back Substitution
x = np.zeros(n)
for k in range(n-1, -1, -1):
x[k] = (b[k] - np.dot(A[k,k+1:],x[k+1:]))/A[k,k]
return x
if __name__ == "__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.]])
print GEPP(np.copy(A), np.copy(b), doPricing = False)
print GEPP(A,b)
@alipars10

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@alipars10 alipars10 commented Feb 19, 2016

Thanks for this, just a quick question. You mentioned that you fixed a bug. What exactly was the bug?

@jgcastro89

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@jgcastro89 jgcastro89 commented Oct 17, 2017

Awesome job! I have forked your code and modularized it. I needed to import it and apply it to an existing project. https://gist.github.com/jgcastro89/49090cc69a499a129413597433b9baab

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