class LinearRegression_Multi:

    def stacked_lstsq(self, L, b, rcond=1e-10):
        """
        Solve L x = b, via SVD least squares cutting of small singular values
        L is an array of shape (..., M, N) and b of shape (..., M).
        Returns x of shape (..., N)
        """
u, s, v = np.linalg.svd(L, full_matrices=False)
s_max = s.max(axis=-1, keepdims=True)
s_min = rcond * s_max
inv_s = np.zeros_like(s)
inv_s[s >= s_min] = 1 / s[s >= s_min]
x = np.einsum('...ji,...j->...i', v, inv_s * np.einsum('...ji,...j->...i',
    u, b.conj()))
return np.conj(x, x)

def center_data(self, X, y):
    """ Centers data to have mean zero along axis 0. 
        """
X_mean = np.average(X, axis=1)
X_std = np.ones(X.shape[0::2])
X = X - X_mean[:, (None), :]
y_mean = np.average(y, axis=1)
y = y - y_mean[:, (None)]
return X, y, X_mean, y_mean, X_std

def set_intercept(self, X_mean, y_mean, X_std):
    """ Calculate the intercept_
        """
self.coef_ = self.coef_ / X_std
self.intercept_ = y_mean - np.einsum('ij,ij->i', X_mean, self.coef_)

def scores(self, y_pred, y_true):
    """ 
        The coefficient R^2 is defined as (1 - u/v), where u is the regression
        sum of squares ((y_true - y_pred) ** 2).sum() and v is the residual
        sum of squares ((y_true - y_true.mean()) ** 2).sum().        
        """
u = ((y_true - y_pred) ** 2).sum(axis=-1)
v = ((y_true - y_true.mean(axis=-1)[None].T) ** 2).sum(axis=-1)
r_2 = 1 - u / v
return r_2

def fit(self, X, y):
    """ Fit linear model.        
        """
X_, y, X_mean, y_mean, X_std = self.center_data(X, y)
self.coef_ = self.stacked_lstsq(X_, y)
self.set_intercept(X_mean, y_mean, X_std)

def predict(self, X):
    """Predict using the linear model
        """
return np.einsum('ijx,ix->ij', X, self.coef_) + self.intercept_[None].T
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