import numpy as np

def RSE(pred, true):

    return np.sqrt(np.sum((true - pred) ** 2)) / np.sqrt(np.sum((true - true.mean()) ** 2))

def CORR(pred, true):

    u = ((true - true.mean(0)) * (pred - pred.mean(0))).sum(0)

    d = np.sqrt(((true - true.mean(0)) ** 2 * (pred - pred.mean(0)) ** 2).sum(0))

    return (u / d).mean(-1)

def MAE(pred, true):

    return np.mean(np.abs(pred - true))

def MSE(pred, true):

    return np.mean((pred - true) ** 2)

def RMSE(pred, true):

    return np.sqrt(MSE(pred, true))

def MAPE(pred, true):

    return np.mean(np.abs((pred - true) / true))

def MSPE(pred, true):

    return np.mean(np.square((pred - true) / true))

def metric(pred, true):

    mae = MAE(pred, true)

    mse = MSE(pred, true)

    rmse = RMSE(pred, true)

    mape = MAPE(pred, true)

    mspe = MSPE(pred, true)

    return mae, mse, rmse, mape, mspe