1717.sagews

\HUGE{Eliminacja Gaussa :}

from numpy import *

def RandomArray( sizeA,sizeB, startOfRange, endOfRange):
    arr = random.rand(sizeA,sizeB)
    arr[:,:] = arr[:,:]*(endOfRange - startOfRange) + startOfRange
    return arr

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"

def Validation(arrA, arrB, arrX, eps) :
    VALID = dot(arrA,arrX.transpose())
    s = sum((VALID[:]-arrB[:])**2)
    if s < eps :
        return True
    else :
        return False

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!

C = array([[1.,2.,3.],
          [1.,3.,4.],
          [1.,3.,5.]])
D = array([[5.],
          [1.],
          [-2.]])

print GaussEquations(C,D)

[[ 16. -1. -3.]]