Candidate Periods definition ---------------------------- | The choice of representative periods is preceded by the choice of candidate periods to become representative. We can note :math:`d\subset[0,T]` these periods and group them into a set :math:`\mathcal{D}`. .. math:: \mathcal{D} = \text{ Set of candidate periods} | To each period :math:`d` we can associate the load function normalized in absolute power: .. math:: \hat{f}_{|d}= \left\{\begin{array}{ccc} d & \longrightarrow & [0,1] \\ t & \mapsto & \frac{f(t)-f_{min}}{f_{max}-f_{min}} \end{array}\right. \text{ où } \left.\begin{array}{l} f_{min} = \underset{t\in[0,T]}{\text{min }} f(t) \\ f_{max} = \underset{t\in[0,T]}{\text{max }} f(t) \end{array}\right. .. note:: Potentially : :math:`\forall t \in d , \hat{f}_{|d}(t)>0 \text{ or } \forall t \in d , \hat{f}_{|d}(t)<1` | We associatethe duration function: .. math:: \tilde{C}(\hat{f}_{|d}) = \left\{\begin{array}{ccc} \mathbb{R}_+ & \longrightarrow & [0,1] \\ x & \mapsto & \frac{\lambda(\{t\in d|f(t)\geq x\})}{\lambda(d)} \end{array}\right. .. warning:: Currently in ``periods``, the set of candidate periods corresponds to a uniform split of the global period :math:`[0,T]`. It means that ``RP_length`` must divide ``TemporalData`` length. A periods of 336 hours would have 7 candidate periods of 48 hours partitioning the 336 hours. It could be possible to have overlapping candidate periods in future version.