def compute_w_diff(x, y, w, b,  C=0.0):
    prod_xy = np.array(y).reshape((y.size, 1)) * x
    exp = np.exp(-prod_xy.dot(w) + b)
    big_sum = np.sum(prod_xy * (1 - 1/(1 + exp)), axis=0)
    return big_sum.reshape(w.shape)/y.size -  C * w

def compute_b_diff(x, y, w, b):
    prod_xy = np.array(y).reshape((y.size, 1)) * x
    return np.sum(np.array(y).reshape((y.size, 1)) * (1 - 1/(1 + np.exp(-prod_xy.dot(w) + b))))/y.size

class LinearClassifier(BaseEstimator, LinearClassifierMixin):
    def __init__(self, step, stop_function=lambda iters, dif : iters < 10000, rand_init=False, C=0.0):
        self.step = step
        self.stop_function = stop_function
        self.rand_init = rand_init
        self.C = C

    def fit(self, X, y):
        if self.rand_init:
            w = (np.random.rand(x.shape[1]).reshape((x.shape[1], 1)) - 0.5) / x.shape[0]
        else:
            w = np.zeros((x.shape[1], 1))
        b = 0
        current_iters = 0
        while True:
            w_dif = self.step * compute_w_diff(X, y, w, b, self.C)
            b_dif = self.step * compute_b_diff(X, y, w, b)
            w += w_dif
            b += b_dif
            if self.stop_function(current_iters, w_dif):
                self.coef_ = w
                self.intercept_ = b
                return self
            current_iters += 1

    def predict_proba(self, X):
        return super()._predict_proba_lr(X)