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aƒ  
Author: Kishan Manani
License: BSD-3 Clause

An implementation of MSTL [1], an algorithm for time series decomposition when
there are multiple seasonal components.

This implementation has the following differences with the original algorithm:
- Missing data must be handled outside of this class.
- The algorithm proposed in the paper handles a case when there is no
seasonality. This implementation assumes that there is at least one seasonal
component.

[1] K. Bandura, R.J. Hyndman, and C. Bergmeir (2021)
MSTL: A Seasonal-Trend Decomposition Algorithm for Time Series with Multiple
Seasonal Patterns
https://arxiv.org/pdf/2107.13462.pdf
é    )ÚDictÚOptionalÚSequenceÚTupleÚUnionN)Úboxcox)ÚArrayLike1D)ÚSTL)Úfreq_to_periodc                   @   st  e Zd ZdZddddddœeeeeee f  eeeee f  eee	e
f  eeee
eeedf f  dœdd„Zdd	„ Zd
d„ Zeeee df eeee df eee ee f dœdd„Zeeee df ee dœdd„Zeeee df eee dœdd„Zedœdd„Zeeee ee f dœdd„ƒZeeedœdd„ƒZeeee dœdd„ƒZed d!„ ƒZdS )"ÚMSTLa
  
    MSTL(endog, periods=None, windows=None, lmbda=None, iterate=2,
         stl_kwargs=None)

    Season-Trend decomposition using LOESS for multiple seasonalities.

    .. versionadded:: 0.14.0

    Parameters
    ----------
    endog : array_like
        Data to be decomposed. Must be squeezable to 1-d.
    periods : {int, array_like, None}, optional
        Periodicity of the seasonal components. If None and endog is a pandas
        Series or DataFrame, attempts to determine from endog. If endog is a
        ndarray, periods must be provided.
    windows : {int, array_like, None}, optional
        Length of the seasonal smoothers for each corresponding period.
        Must be an odd integer, and should normally be >= 7 (default). If None
        then default values determined using 7 + 4 * np.arange(1, n + 1, 1)
        where n is number of seasonal components.
    lmbda : {float, str, None}, optional
        The lambda parameter for the Box-Cox transform to be applied to `endog`
        prior to decomposition. If None, no transform is applied. If "auto", a
        value will be estimated that maximizes the log-likelihood function.
    iterate : int, optional
        Number of iterations to use to refine the seasonal component.
    stl_kwargs: dict, optional
        Arguments to pass to STL.

    See Also
    --------
    statsmodels.tsa.seasonal.STL

    References
    ----------
    .. [1] K. Bandura, R.J. Hyndman, and C. Bergmeir (2021)
        MSTL: A Seasonal-Trend Decomposition Algorithm for Time Series with
        Multiple Seasonal Patterns. arXiv preprint arXiv:2107.13462.

    Examples
    --------
    Start by creating a toy dataset with hourly frequency and multiple seasonal
    components.

    >>> import numpy as np
    >>> import matplotlib.pyplot as plt
    >>> import pandas as pd
    >>> pd.plotting.register_matplotlib_converters()
    >>> np.random.seed(0)
    >>> t = np.arange(1, 1000)
    >>> trend = 0.0001 * t ** 2 + 100
    >>> daily_seasonality = 5 * np.sin(2 * np.pi * t / 24)
    >>> weekly_seasonality = 10 * np.sin(2 * np.pi * t / (24 * 7))
    >>> noise = np.random.randn(len(t))
    >>> y = trend + daily_seasonality + weekly_seasonality + noise
    >>> index = pd.date_range(start='2000-01-01', periods=len(t), freq='H')
    >>> data = pd.DataFrame(data=y, index=index)

    Use MSTL to decompose the time series into two seasonal components
    with periods 24 (daily seasonality) and 24*7 (weekly seasonality).

    >>> from statsmodels.tsa.seasonal import MSTL
    >>> res = MSTL(data, periods=(24, 24*7)).fit()
    >>> res.plot()
    >>> plt.tight_layout()
    >>> plt.show()

    .. plot:: plots/mstl_plot.py
    Né   )ÚperiodsÚwindowsÚlmbdaÚiterateÚ
stl_kwargs)Úendogr   r   r   r   r   c                C   sX   || _ |  |¡| _| jjd | _|| _|  ||¡\| _| _|| _	|  
|rL|ni ¡| _d S )Nr   )r   Ú_to_1d_arrayÚ_yÚshapeÚnobsr   Ú_process_periods_and_windowsr   r   r   Ú_remove_overloaded_stl_kwargsÚ_stl_kwargs)Úselfr   r   r   r   r   r   © r   úQ/home/sam/Atlas/atlas_env/lib/python3.8/site-packages/statsmodels/tsa/stl/mstl.pyÚ__init__g   s    
 ÿ
ÿzMSTL.__init__c                 C   sÔ  t | jƒ}|dkrdn| j}| jdkr@t| jdd�\}}|| _n| jrXt| j| jd�}n| j}| j dd¡}| j dd¡}t	j
|| jfd�}|}t|ƒD ]b}	t|ƒD ]T}
|||
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        Estimate a trend component, multiple seasonal components, and a
        residual component.

        Returns
        -------
        DecomposeResult
            Estimation results.
        é   ÚautoN)r   Ú
inner_iterÚ
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<listcomp>²   s     zMSTL.fit.<locals>.<listcomp>r#   )r$   Úcolumnsr   )ÚDecomposeResult)Úlenr   r   r   r   r   Z	est_lmbdar   ÚpopÚnpZzerosr   Úranger	   r   Úfitr#   ÚsqueezeÚTr&   ÚweightsÚ
isinstancer   ÚpdÚSeriesÚ	DataFramer$   ÚndimZstatsmodels.tsa.seasonalr,   )r   Únum_seasonsr   Úyr   Zstl_inner_iterZstl_outer_iterr#   ZdeseasÚ_ÚiÚresr&   Úrwr'   r$   Úcolsr,   r   r   r   r1   }   sV    


ýü û
zMSTL.fitc              	   C   s&   d| j › d| j› d| j› d| j› d�	S )NzMSTL(endog, periods=z
, windows=z, lmbda=z
, iterate=ú))r   r   r   r   ©r   r   r   r   Ú__str__½   s    $ÿzMSTL.__str__)r   r   Úreturnc                    s²   ˆ   |¡}|r2ˆ j|t|ƒd�}ˆ  ||¡\}}nˆ j|t|ƒd�}t|ƒ}t|ƒt|ƒkrdtdƒ‚t‡ fdd„|D ƒƒrªt d¡ t	‡ fdd„|D ƒƒ}|d t|ƒ… }||fS )N)r:   ú)Periods and windows must have same lengthc                 3   s   | ]}|ˆ j d  kV  qdS ©r   N©r   r(   rB   r   r   Ú	<genexpr>Ø   s     z4MSTL._process_periods_and_windows.<locals>.<genexpr>zTA period(s) is larger than half the length of time series. Removing these period(s).c                 3   s    | ]}|ˆ j d  k r|V  qdS rF   rG   r(   rB   r   r   rH   Ý   s     )
Ú_process_periodsÚ_process_windowsr-   Ú_sort_periods_and_windowsÚsortedÚ
ValueErrorÚanyÚwarningsÚwarnÚtuple)r   r   r   r   rB   r   r   Æ   s"    
ÿÿz!MSTL._process_periods_and_windows)r   rD   c                 C   s*   |d kr|   ¡ f}nt|tƒr&|f}n |S ©N)Ú_infer_periodr5   Úint)r   r   r   r   r   rI   ä   s
    
zMSTL._process_periods)r   r:   rD   c                 C   s*   |d kr|   |¡}nt|tƒr&|f}n |S rR   )Ú_default_seasonal_windowsr5   rT   )r   r   r:   r   r   r   rJ   ï   s
    
zMSTL._process_windows)rD   c                 C   sD   d }t | jtjtjfƒr(t| jjdd ƒ}|d kr8tdƒ‚t|ƒ}|S )NZinferred_freqz%Unable to determine period from endog)	r5   r   r6   r7   r8   Úgetattrr$   rM   r
   )r   Úfreqr"   r   r   r   rS   ü   s    zMSTL._infer_periodc                 C   s6   t | ƒt |ƒkrtdƒ‚ttt| |ƒƒŽ \} }| |fS )NrE   )r-   rM   ÚziprL   )r   r   r   r   r   rK     s    zMSTL._sort_periods_and_windows)r   rD   c                 C   s$   dddg}|D ]}|   |d ¡ q| S )Nr   r"   r#   )r.   )r   ÚargsÚargr   r   r   r     s    
z"MSTL._remove_overloaded_stl_kwargs)ÚnrD   c                 C   s   t dd„ td| d ƒD ƒƒS )Nc                 s   s   | ]}d d|  V  qdS )é   é   Nr   )r)   r=   r   r   r   rH     s     z1MSTL._default_seasonal_windows.<locals>.<genexpr>r   )rQ   r0   )r[   r   r   r   rU     s    zMSTL._default_seasonal_windowsc                 C   s2   t jt  t  | ¡¡t jd�}|jdkr.tdƒ‚|S )N)Zdtyper   zy must be a 1d array)r/   Zascontiguousarrayr2   ZasarrayÚdoubler9   rM   )Úxr;   r   r   r   r     s    
zMSTL._to_1d_array)Ú__name__Ú
__module__Ú__qualname__Ú__doc__r   r   r   rT   r   ÚfloatÚstrr   Úboolr   r1   rC   r   r   rI   rJ   rS   ÚstaticmethodrK   r   rU   r   r   r   r   r   r      sJ   Køø@üþü	þr   )rc   Útypingr   r   r   r   r   rO   Únumpyr/   Zpandasr6   Zscipy.statsr   Zstatsmodels.tools.typingr   Zstatsmodels.tsa.stl._stlr	   Zstatsmodels.tsa.tsatoolsr
   r   r   r   r   r   Ú<module>   s   