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def Householder_step(A):
    #Dimensions of A
    m,n = np.shape(A)
    #Take out the first column in A. We want to mirror it to get ahat.
    a = A[:,0]
    #Calculate ahat=H*a
    ahat=array([norm(a)]+(m-1)*[0.])
    #Calculate v
    v = a - ahat
    v=v/norm(v)
    #Calculate H for this step
    H = eye(m)-2*outer(v,v)
    return H

def QRH(A):
    #Get dimensions of A
    m,n = np.shape(A)
    tempA = A
    #The Q matrix we will change after every step to the the final Q.
    Q = np.eye(m)
    for i in range(n):
        #Get the H matrix for every step
        Hi = Householder_step(tempA)
        #Get the matrix A which will be the input in the next step
        tempA = Hi@tempA
        #   remove first row and column
        tempA = np.delete(tempA,0,0)
        tempA = np.delete(tempA,0,1)
        #Calculate the accumulated Q
        Q = Q@np.block([[np.eye(i),  np.zeros((i,m-i))],[np.zeros((m-i,i)), Hi]])
    #Calculate R
    R = Q.T@A
    return Q,R