\HUGE{Eliminacja Gaussa :}
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from numpy import *
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def RandomArray( sizeA,sizeB, startOfRange, endOfRange):
arr = random.rand(sizeA,sizeB)
arr[:,:] = arr[:,:]*(endOfRange - startOfRange) + startOfRange
return arr
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def GaussEquations( arrA, arrB):
A = copy(arrA)
B = copy(arrB)
(a_N,a_M) = A.shape
(b_N,b_M) = B.shape
if (a_N == b_N):
N = a_N
# ELIMINACJA
for k in range(0,N):
for i in range(k+1,N):
m_ik = A[i,k]/A[k,k]
B[i] = B[i] - m_ik * B[k]
A[i,:] = A[i,:] - m_ik *A[k,:]
## print A, B
# PODSTAWIANIE
X = zeros((1,N))
for i in range (N-1,-1,-1):
j = range(i+1,N)
s = sum(A[i,j]*X[0,j])
X[0,i] = (B[i] - s)/A[i,i]
## print X
return X
else :
print "Błąd wymiarow macierzy"
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def Validation(arrA, arrB, arrX, eps) :
VALID = dot(arrA,arrX.transpose())
s = sum((VALID[:]-arrB[:])**2)
if s < eps :
return True
else :
return False
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def main():
N = 5
## A = zeros((N,N))
A = RandomArray(N,N,-5,5)
## B = zeros((N,1))
B = RandomArray(N,1,-5,5)
## A = array([[1.,2.,3.],
## [1.,3.,4.],
## [1.,3.,5.]])
## B = array([[5.],
## [1.],
## [-2.]])
X = GaussEquations(A,B)
## print "A: \n",A
## print "B: \n",B
## print "X: ",X
eps = 1e-16;
stan = Validation(A,B,X,eps)
if stan :
print "Poprawnie rozwiazane!"
else :
print "Zle rozwiazane"
if __name__ == '__main__':
main()
Poprawnie rozwiazane! Poprawnie rozwiazane! |
C = array([[1.,2.,3.],
[1.,3.,4.],
[1.,3.,5.]])
D = array([[5.],
[1.],
[-2.]])
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print GaussEquations(C,D)
[[ 16. -1. -3.]] [[ 16. -1. -3.]] |
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