residual and update target variable

error_residual

    # predictions by ith decisision tree
    
    predi = np.zeros(n)
    np.put(predi, left_idx, np.repeat(np.mean(yi[left_idx]), r))  # replace left side mean y
    np.put(predi, right_idx, np.repeat(np.mean(yi[right_idx]), n-r))  # right side mean y
    
    predi = predi[:,None]  # make long vector (nx1) in compatible with y
    predf = predf + predi  # final prediction will be previous prediction value + new prediction of residual
    
    ei = y - predf  # needed originl y here as residual always from original y    
    yi = ei # update yi as residual to reloop