from cvxopt import matrix, spmatrix
from math import sqrt

def append_col(A,b):
    """
    Append the column ``b`` to the right side of the matrix ``A``.
    """
    return matrix([A.trans(),b.trans()]).trans()

def append_row(A,b):
    """
    Append the row ``b`` to the bottom of the matrix ``A``.
    """
    return matrix([A,b])

def identity(n):
    """
    Return the ``n``-by-``n`` identity matrix.
    """
    return spmatrix(1,range(n),range(n))

def norm(x):
    """
    Return the Euclidean norm of the given vector.
    """
    return sqrt(sum([z**2 for z in x]))