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def poinc_dist_np(points):
    u'''
    if expanded, the following is equal to:
    
    expd=np.expand_dims(points,2)
    tiled=np.tile(expd, points.shape[0])
    trans=np.transpose(points)
    num=np.sum(np.square(trans-tiled), axis=1)
    #num
    den1=1-np.sum(np.square(points),1)

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expd=tf.expand_dims(ptf,2) # from (n_emb x emb_dim) to (n_emb x emb_dim x 1)
tiled=tf.tile(expd, [1,1,tf.shape(ptf)[0]]) # copying the same matrix n times
trans=tf.transpose(ptf)
num=tf.reduce_sum(tf.squared_difference(trans,tiled), 1)
den1=1-tf.reduce_sum(tf.square(ptf),1)
den1=tf.expand_dims(den1, 1)
den=tf.matmul(den1, tf.transpose(den1))

tot=1+2*tf.div(num, den)

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for j range(3):
  res[j]=v_1[j]*v_2[j]

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res=v1 * v2

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def _dist_poinc(a, b):
    num=np.dot(a-b, a-b)
    den1=1-np.dot(a,a)
    den2=1-np.dot(b,b)
    return np.arccosh(1+ 2* (num) / (den1*den2))
def dist_poinc(a, A):
    res=np.empty(A.shape[0])
    for i, el in enumerate(A):
        res[i]=_dist_poinc(a, el)
    return res

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def meanshift(data, sigma, steps):
    d1 = np.copy(data)                        # Need to copy the data, don't want to modify the originals
    for it in range(steps):                   # at each step
        for i, p in enumerate(d1):            # for each point
            dists = dist_poinc( p, d1)        # we calculate the distance from that point to all the other ones
            weights = gaussian(dists, sigma)  # then we weight those distances by our gaussian kernel
            d1[i] = (np.expand_dims(weights,1)*d1).sum(0) / weight.sum()     # and substitute the point with the weighted sum
    return d1

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def _dist_poinc(a, b):
    num=np.dot(a-b, a-b)
    den1=1-np.dot(a,a)
    den2=1-np.dot(b,b)
    return np.arccosh(1+ 2* (num) / (den1*den2))
def dist_poinc(a, A):
    res=np.empty(A.shape[0])
    for i, el in enumerate(A):
        res[i]=_dist_poinc(a, el)
return res

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def num(points):
    expd=np.expand_dims(points,2) #need another dimension...
    tiled=np.tile(expd, points.shape[0]) #...to tile up the vectors
    trans=np.transpose(points) #Also need to transpose the points matrix to fit well with broadcasting
    diff=trans-tiled           #doing the difference, exploiting Numpy broadcasting capabilities
    num=np.sum(np.square(diff), axis=1) #an then obtain the squared norm of the difference
    return num

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def den(points):
    sq_norm=1-np.sum(np.square(points),1) #subtracting from 1 the squared norm of the vectors
    expd=np.expand_dims(sq_norm,1)   #this operation is needed to obtain a correctly transposed version of the vector
    den_all=expd * expd.T #multiply the object by his transpose
    return den_all

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def poinc_dist_vec(points):
    num=num(points)
    den=num(points)
    return np.arccosh(1+2*num/ den)