B ZU @sdZddlmZmZmZddlZddlmZddl Z ddl m Z ddl Z dadaejejejejdZiZiZiZiZiZiZiZiZiZiZiZiZ dLd d Z!e!dd ydd l"m#Z#Wn,e$k rd dddddZ%ddZ#YnXddZ&dMddZ'dNddZ(dOddZ)dPddZ*d d!Z+d"d#Z,dQd$d%Z-dRd&d'Z.dSd(d)Z/tr`dTd*d+Z0e/je0_ne/Z0dUd,d-Z1d.d/Z2dVd0d1Z3d2d3Z4dWd4d5Z5dXd6d7Z6d8d9Z7d:d;Z8dd?Z:dZd@dAZ;d[dBdCZd^dHdIZ?dJdKZ@dS)_z? Statespace Tools Author: Chad Fulton License: Simplified-BSD )divisionabsolute_importprint_functionN)solve_sylvester)_is_using_pandasFT)sdczc Cs|dkr6yddlm}d}Wntk r4d}YnX|snyddlm}Wn"tk rltdd}YnX|sddlm}ddlm}m}m}m }m }da t |j|j|j|jdt |j|j|j|jdt |j|j|j|jdt |j|j|j|j dt! |j"|j#|j$|j%dt& |j'|j(|j)|j*dt+ |j,|j-|j.|j/dt0 |j1|j2|j3|j4dt5 |j6|j7|j8|j9dt: |j;|j<|j=|j>dt? |j@|jA|jB|jCdtD |jE|jF|jG|jHdndd lmI}dd lJmK}da ydd lLmM} Wntk r:daNYnXt |j|j|j|jdt |j|j|j|jdt ||||dt dddddtNrt! |j"|j#|j$|j%dt& |j'|j(|j)|j*dt+ |j,|j-|j.|j/dt0 |j1|j2|j3|j4dt5 |j6|j7|j8|j9dt: |j;|j<|j=|j>dt? |j@|jA|jB|jCdtD |jE|jF|jG|jHddS) Nr) cython_blasFTz9Minimum dependencies not met. Compatibility mode enabled.)_representation_kalman_filter_kalman_smoother_simulation_smoother_tools)rrr r ) _statespace)_KalmanSmoother)dtrmm)O scipy.linalgr ImportErrorwarningswarnr rrrrcompatibility_modeprefix_statespace_mapupdateZ sStatespaceZ dStatespaceZ cStatespaceZ zStatespaceprefix_kalman_filter_mapZ sKalmanFilterZ dKalmanFilterZ cKalmanFilterZ zKalmanFilterprefix_kalman_smoother_mapZsKalmanSmootherZdKalmanSmootherZcKalmanSmootherZzKalmanSmootherprefix_simulation_smoother_mapZsSimulationSmootherZdSimulationSmootherZcSimulationSmootherZzSimulationSmootherprefix_pacf_mapZ-_scompute_coefficients_from_multivariate_pacfZ-_dcompute_coefficients_from_multivariate_pacfZ-_ccompute_coefficients_from_multivariate_pacfZ-_zcompute_coefficients_from_multivariate_pacf prefix_sv_mapZ_sconstrain_sv_less_than_oneZ_dconstrain_sv_less_than_oneZ_cconstrain_sv_less_than_oneZ_zconstrain_sv_less_than_one!prefix_reorder_missing_matrix_mapZsreorder_missing_matrixZdreorder_missing_matrixZcreorder_missing_matrixZzreorder_missing_matrix!prefix_reorder_missing_vector_mapZsreorder_missing_vectorZdreorder_missing_vectorZcreorder_missing_vectorZzreorder_missing_vectorprefix_copy_missing_matrix_mapZscopy_missing_matrixZdcopy_missing_matrixZccopy_missing_matrixZzcopy_missing_matrixprefix_copy_missing_vector_mapZscopy_missing_vectorZdcopy_missing_vectorZccopy_missing_vectorZzcopy_missing_vectorprefix_copy_index_matrix_mapZscopy_index_matrixZdcopy_index_matrixZccopy_index_matrixZzcopy_index_matrixprefix_copy_index_vector_mapZscopy_index_vectorZdcopy_index_vectorZccopy_index_vectorZzcopy_index_vectorrZ_pykalman_smootherrscipy.linalg.blasrhas_trmm) compatibilityr r rrrrrrrr+?lib/python3.7/site-packages/statsmodels/tsa/statespace/tools.pyset_mode$s                           r-)r*)find_best_blas_typerrr r )frFDGcCs2tddt|D\}}t|jd}||dfS)NcSsg|]\}}|j|fqSr+)dtype).0iZarr+r+r, sz'find_best_blas_type..r)max enumerate _type_convgetchar)Zarraysr3indexprefixr+r+r,r.sr.cCsd}t|tr|}d}d}nt|d}|dkr8tdt|tsLt|tryt|d}Wntk rtd}YnX|dkrt|}q|ddkrt ||d<d}nd}t|}tj ||||ft|j d}t |d|}|d|d|f}d||<|dk r|dkr|dkrJ|dd |d|dddf<n|rxt |D]2}||dj ||||d|d|f<qZWnXtj|d}xFt |D]:}t|||dj ||||d|d|f<qW|S)a Create a companion matrix Parameters ---------- polynomial : array_like or list If an iterable, interpreted as the coefficients of the polynomial from which to form the companion matrix. Polynomial coefficients are in order of increasing degree, and may be either scalars (as in an AR(p) model) or coefficient matrices (as in a VAR(p) model). If an integer, it is interpereted as the size of a companion matrix of a scalar polynomial, where the polynomial coefficients are initialized to zeros. If a matrix polynomial is passed, :math:`C_0` may be set to the scalar value 1 to indicate an identity matrix (doing so will improve the speed of the companion matrix creation). Returns ------- companion_matrix : array Notes ----- Given coefficients of a lag polynomial of the form: .. math:: c(L) = c_0 + c_1 L + \dots + c_p L^p returns a matrix of the form .. math:: \begin{bmatrix} \phi_1 & 1 & 0 & \cdots & 0 \\ \phi_2 & 0 & 1 & & 0 \\ \vdots & & & \ddots & 0 \\ & & & & 1 \\ \phi_n & 0 & 0 & \cdots & 0 \\ \end{bmatrix} where some or all of the :math:`\phi_i` may be non-zero (if `polynomial` is None, then all are equal to zero). If the coefficients provided are scalars :math:`(c_0, c_1, \dots, c_p)`, then the companion matrix is an :math:`n \times n` matrix formed with the elements in the first column defined as :math:`\phi_i = -\frac{c_i}{c_0}, i \in 1, \dots, p`. If the coefficients provided are matrices :math:`(C_0, C_1, \dots, C_p)`, each of shape :math:`(m, m)`, then the companion matrix is an :math:`nm \times nm` matrix formed with the elements in the first column defined as :math:`\phi_i = -C_0^{-1} C_i', i \in 1, \dots, p`. It is important to understand the expected signs of the coefficients. A typical AR(p) model is written as: .. math:: y_t = a_1 y_{t-1} + \dots + a_p y_{t-p} + \varepsilon_t This can be rewritten as: .. math:: (1 - a_1 L - \dots - a_p L^p )y_t = \varepsilon_t \\ (1 + c_1 L + \dots + c_p L^p )y_t = \varepsilon_t \\ c(L) y_t = \varepsilon_t The coefficients from this form are defined to be :math:`c_i = - a_i`, and it is the :math:`c_i` coefficients that this function expects to be provided. Fr Nz=Companion matrix polynomials must include at least two terms.rT)r3) isinstanceintlen ValueErrorlisttuple TypeErrornp asanyarrayeyezerosr3Z diag_indicesrangeTlinalginvdot) polynomialZidentity_matrixnmmatrixidxr5rLr+r+r,companion_matrixsDG      " $4:rSr cCst|d}|st|n|}|dk rlxF|dkrj|sN||d|d| }n|||d}|d8}q&W|stj||dd}n&x$|dkr|dd}|d8}qW|S)az Difference a series simply and/or seasonally along the zero-th axis. Given a series (denoted :math:`y_t`), performs the differencing operation .. math:: \Delta^d \Delta_s^D y_t where :math:`d =` `diff`, :math:`s =` `seasonal_periods`, :math:`D =` `seasonal\_diff`, and :math:`\Delta` is the difference operator. Parameters ---------- series : array_like The series to be differenced. diff : int, optional The number of simple differences to perform. Default is 1. seasonal_diff : int or None, optional The number of seasonal differences to perform. Default is no seasonal differencing. seasonal_periods : int, optional The seasonal lag. Default is 1. Unused if there is no seasonal differencing. Returns ------- differenced : array The differenced array. Nrr )axis)rrErFdiff)seriesZk_diffZk_seasonal_diffZseasonal_periodspandasZ differencedr+r+r,rUXs     rUcCsZtjdd|D}t|r.tj||d}n(t|s>|rNtj||d}ntd|S)a{ Concatenate a set of series. Parameters ---------- series : iterable An iterable of series to be concatenated axis : int, optional The axis along which to concatenate. Default is 1 (columns). allow_mix : bool Whether or not to allow a mix of pandas and non-pandas objects. Default is False. If true, the returned object is an ndarray, and additional pandas metadata (e.g. column names, indices, etc) is lost. Returns ------- concatenated : array or pd.DataFrame The concatenated array. Will be a DataFrame if series are pandas objects. cSsg|]}t|dqS)N)r)r4rr+r+r,r6szconcat..)rTzWAttempted to concatenate Pandas objects with non-Pandas objects with `allow_mix=False`.)rEZr_allpdconcat concatenaterA)rVrTZ allow_mixZ is_pandasZ concatenatedr+r+r,rZs rZA?cCs$tjt|}tt||kS)a Determine if a polynomial is invertible. Requires all roots of the polynomial lie inside the unit circle. Parameters ---------- polynomial : array_like or tuple, list Coefficients of a polynomial, in order of increasing degree. For example, `polynomial=[1, -0.5]` corresponds to the polynomial :math:`1 - 0.5x` which has root :math:`2`. If it is a matrix polynomial (in which case the coefficients are coefficient matrices), a tuple or list of matrices should be passed. threshold : number Allowed threshold for `is_invertible` to return True. Default is 1. Notes ----- If the coefficients provided are scalars :math:`(c_0, c_1, \dots, c_n)`, then the corresponding polynomial is :math:`c_0 + c_1 L + \dots + c_n L^n`. If the coefficients provided are matrices :math:`(C_0, C_1, \dots, C_n)`, then the corresponding polynomial is :math:`C_0 + C_1 L + \dots + C_n L^n`. There are three equivalent methods of determining if the polynomial represented by the coefficients is invertible: The first method factorizes the polynomial into: .. math:: C(L) & = c_0 + c_1 L + \dots + c_n L^n \\ & = constant (1 - \lambda_1 L) (1 - \lambda_2 L) \dots (1 - \lambda_n L) In order for :math:`C(L)` to be invertible, it must be that each factor :math:`(1 - \lambda_i L)` is invertible; the condition is then that :math:`|\lambda_i| < 1`, where :math:`\lambda_i` is a root of the polynomial. The second method factorizes the polynomial into: .. math:: C(L) & = c_0 + c_1 L + \dots + c_n L^n \\ & = constant (L - \zeta_1) (L - \zeta_2) \dots (L - \zeta_3) The condition is now :math:`|\zeta_i| > 1`, where :math:`\zeta_i` is a root of the polynomial with reversed coefficients and :math:`\lambda_i = \frac{1}{\zeta_i}`. Finally, a companion matrix can be formed using the coefficients of the polynomial. Then the eigenvalues of that matrix give the roots of the polynomial. This last method is the one actually used. See Also -------- companion_matrix )rErKeigvalsrSrXabs)rNZ thresholdr]r+r+r, is_invertiblesCr_c Cstj|jd|jd}|s|}tj||}t|||}dtttj||||}t ||| S|}tj||}t|||}dtttj||||}t ||| SdS)a Solves the discrete Lyapunov equation using a bilinear transformation. Notes ----- This is a modification of the version in Scipy (see https://github.com/scipy/scipy/blob/master/scipy/linalg/_solvers.py) which allows passing through the complex numbers in the matrix a (usually the transition matrix) in order to allow complex step differentiation. r)r3N) rErGshaper3ZconjZ transposerKrLrMr)aqZ complex_steprGZaHZaHI_invbr r+r+r,solve_discrete_lyapunovs  $$recCs|jd}tj||f|jd}|d|dd}xjt|D]^}xHt|D]<}||d|f||||d||df|||f<qJW|||||f<q.rr )rT) typerBrarIr@rxrrEr[Zreshape) rfr~rr=use_listrtsv_constrainedrlvarr+)rurfr,(constrain_stationary_multivariate_python<s G      rc st|tk}|rtj|dd}|j\}|}|dkr@tddkrPtd|dkrjt||g\}}}t|}tj||d}tj||d}t |||}t |||||\}tj |dtj ||d}|rfddt |D|fS)Nr )rTzMust have order at least 1z(Must have at least 1 endogenous variable)r3cs,g|]$}d||dfqS)Nr r+)r4r5)rlrur+r,r6sz5constrain_stationary_multivariate..) rrBrEr[rarAr.prefix_dtype_mapasfortranarrayr!r arrayrI) rfrrr=rrtr3_rr+)rlrur,!constrain_stationary_multivariates0    rc Csddlm}g}|dkr t|}|dkr6|djd}t|}xNt|D]B}||}|j|t||j dd\}} | |j ||| dqJW|S)a Transform matrices with singular values less than one to arbitrary matrices. Parameters ---------- constrained : list The partial autocorrelation matrices. Should be a list of length `order`, where each element is an array sized `k_endog` x `k_endog`. order : integer, optional The order of the autoregression. k_endog : integer, optional The dimension of the data vector. Returns ------- unconstrained : list Unconstrained matrices. A list of length `order`, where each element is an array sized `k_endog` x `k_endog`. Notes ----- Corresponds to the inverse of Lemma 2.2 in Ansley and Kohn (1986). See `unconstrain_stationary_multivariate` for more details. r)rKNT)ro) rprKr@rarErGrIrqrMrJrrrs) rlrtrurKrfrGr5PZB_invror+r+r,_unconstrain_sv_less_than_ones   rc Cst|}|jdkr&|ddtjf}|tj|dd8}|j\}}g}xrt|dD]b}|t||fx8t||D](}||t |||||7<qzW|||<qTW|S)a| Computer multivariate sample autocovariances Parameters ---------- endog : array_like Sample data on which to compute sample autocovariances. Shaped `nobs` x `k_endog`. Returns ------- sample_autocovariances : list A list of the first `maxlag` sample autocovariance matrices. Each matrix is shaped `k_endog` x `k_endog`. Notes ----- This function computes the forward sample autocovariances: .. math:: \hat \Gamma(s) = rac{1}{n} \sum_{t=1}^{n-s} (Z_t - ar Z) (Z_{t+s} - ar Z)' See page 353 of Wei (1990). This function is primarily implemented for checking the partial autocorrelation functions below, and so is quite slow. References ---------- .. [*] Wei, William. 1990. Time Series Analysis : Univariate and Multivariate Methods. Boston: Pearson. r Nr)rT) rErndimZnewaxisZmeanrarIrrrHZouter)endogmaxlagnobsrusample_autocovariancesrtr+r+r,"_compute_multivariate_sample_acovf s#   (rc sLddlm}ttkr0t}djdn*j\}|}fddt|D|dkrj|d}tdgfddt|Dj}t |j}||ddf<| ||fddtt ||dD}x@t||dD],} t ||d dfg7}qW|rHx$tt|D]} || j|| <q0W|S) a Compute multivariate autocovariances from vector autoregression coefficient matrices Parameters ---------- coefficients : array or list The coefficients matrices. If a list, should be a list of length `order`, where each element is an array sized `k_endog` x `k_endog`. If an array, should be the coefficient matrices horizontally concatenated and sized `k_endog` x `k_endog * order`. error_variance : array The variance / covariance matrix of the error term. Should be sized `k_endog` x `k_endog`. maxlag : integer, optional The maximum autocovariance to compute. Default is `order`-1. Can be zero, in which case it returns the variance. forward_autocovariances : boolean, optional Whether or not to compute forward autocovariances :math:`E(y_t y_{t+j}')`. Default is False, so that backward autocovariances :math:`E(y_t y_{t-j}')` are returned. Returns ------- autocovariances : list A list of the first `maxlag` autocovariance matrices. Each matrix is shaped `k_endog` x `k_endog`. Notes ----- Computes .. math:: \Gamma(j) = E(y_t y_{t-j}') for j = 1, ..., `maxlag`, unless `forward_autocovariances` is specified, in which case it computes: .. math:: E(y_t y_{t+j}') = \Gamma(j)' Coefficients are assumed to be provided from the VAR model: .. math:: y_t = A_1 y_{t-1} + \dots + A_p y_{t-p} + \varepsilon_t Autocovariances are calculated by solving the associated discrete Lyapunov equation of the state space representation of the VAR process. r)rKcs,g|]$}d||dfqS)Nr r+)r4r5) coefficientsrur+r,r6szA_compute_multivariate_acovf_from_coefficients..Nr csg|]}| qSr+r+)r4r5)rr+r,r6scs,g|]$}d||dfqS)Nr r+)r4r5)ru stacked_covr+r,r6s)rprKrrBr@rarIrSrJrErHreminrM) rr~rZforward_autocovariancesrKrtZ companionZselected_variancerr5r+)rrurr,-_compute_multivariate_acovf_from_coefficients?s27          rcCst||}t|S)a Computer multivariate sample partial autocorrelations Parameters ---------- endog : array_like Sample data on which to compute sample autocovariances. Shaped `nobs` x `k_endog`. maxlag : integer Maximum lag for which to calculate sample partial autocorrelations. Returns ------- sample_pacf : list A list of the first `maxlag` sample partial autocorrelation matrices. Each matrix is shaped `k_endog` x `k_endog`. )r/_compute_multivariate_pacf_from_autocovariances)rrrr+r+r,!_compute_multivariate_sample_pacfs rc Csddlm}|dkr t|d}|dkr6|djd}g}g}g}g}g}g} g} x6t|D](} t|} t|} g}g}|d}|dj}xJt| D]>}|t | |||d8}|t | |||dj8}qW| || || |j || dd| |j || dd| dkrt| | |ddf|dj| | | ddf|djjn~|| dj}x0t| D]$}|t | ||| |j8}qW| | | | df|jj| | || df|jxjt| D]^}| || |t |d| | |d| || |t |d| | |dqW| |j|| t || | | ddq^W| S)aa Compute multivariate partial autocorrelations from autocovariances. Parameters ---------- autocovariances : list Autocorrelations matrices. Should be a list of length `order` + 1, where each element is an array sized `k_endog` x `k_endog`. order : integer, optional The order of the autoregression. k_endog : integer, optional The dimension of the data vector. Returns ------- pacf : list List of first `order` multivariate partial autocorrelations. Notes ----- Note that this computes multivariate partial autocorrelations. Corresponds to the inverse of Lemma 2.1 in Ansley and Kohn (1986). See `unconstrain_stationary_multivariate` for more details. Notes ----- Computes sample partial autocorrelations if sample autocovariances are given. r)rKNr T)rork)rprKr@rarIrBr{rJrErMrrrzZ cho_solver|rs)rrtrurKrrrrrrr}rrrZforward_varianceZbackward_varianceriZtmp_sumr+r+r,rsf!          $ "rcCsZt|tkr$t|}|djd}n|j\}}||}t}dd||||dD}t|S)a Transform matrices corresponding to a stationary (or invertible) process to matrices with singular values less than one. Parameters ---------- constrained : array or list The coefficients matrices. If a list, should be a list of length `order`, where each element is an array sized `k_endog` x `k_endog`. If an array, should be the coefficient matrices horizontally concatenated and sized `k_endog` x `k_endog * order`. error_variance : array The variance / covariance matrix of the error term. Should be sized `k_endog` x `k_endog`. order : integer, optional The order of the autoregression. k_endog : integer, optional The dimension of the data vector. Returns ------- pacf : list List of first `order` multivariate partial autocorrelations. Notes ----- Note that this computes multivariate partial autocorrelations. Corresponds to the inverse of Lemma 2.1 in Ansley and Kohn (1986). See `unconstrain_stationary_multivariate` for more details. Notes ----- Coefficients are assumed to be provided from the VAR model: .. math:: y_t = A_1 y_{t-1} + \dots + A_p y_{t-p} + arepsilon_t rcSsg|] }|jqSr+)rJ)r4Zautocovariancer+r+r,r6sz@_compute_multivariate_pacf_from_coefficients..)r)rrBr@rarr)rlr~rtruZ_acovfrr+r+r,,_compute_multivariate_pacf_from_coefficientsds*  rcsttk}|s<j\}|}fddt|Dnt}djdt||}t||}|s~tj|dd}||fS)a Transform constrained parameters used in likelihood evaluation to unconstrained parameters used by the optimizer Parameters ---------- constrained : array or list Constrained parameters of, e.g., an autoregressive or moving average component, to be transformed to arbitrary parameters used by the optimizer. If a list, should be a list of length `order`, where each element is an array sized `k_endog` x `k_endog`. If an array, should be the coefficient matrices horizontally concatenated and sized `k_endog` x `k_endog * order`. error_variance : array The variance / covariance matrix of the error term. Should be sized `k_endog` x `k_endog`. This is used as input in the algorithm even if is not transformed by it (when `transform_variance` is False). Returns ------- unconstrained : array Unconstrained parameters used by the optimizer, to be transformed to stationary coefficients of, e.g., an autoregressive or moving average component. Will match the type of the passed `constrained` variable (so if a list was passed, a list will be returned). Notes ----- Uses the list representation internally, even if an array is passed. References ---------- .. [*] Ansley, Craig F., and Robert Kohn. 1986. "A Note on Reparameterizing a Vector Autoregressive Moving Average Model to Enforce Stationarity." Journal of Statistical Computation and Simulation 24 (2): 99-106. cs,g|]$}d||dfqS)Nr r+)r4r5)rlrur+r,r6sz7unconstrain_stationary_multivariate..rr )rT) rrBrarIr@rrrEr[)rlr~rrtr}rfr+)rlrur,#unconstrain_stationary_multivariates'     rcCst|}|dkr td||f|d|ksBtd|||df|d|ksdtd|||df|dkr|dks|d dkstd ||d kr|dk r|d d|gkrtd ||t|fdS) a Validate the shape of a possibly time-varying matrix, or raise an exception Parameters ---------- name : str The name of the matrix being validated (used in exception messages) shape : array_like The shape of the matrix to be validated. May be of size 2 or (if the matrix is time-varying) 3. nrows : int The expected number of rows. ncols : int The expected number of columns. nobs : int The number of observations (used to validate the last dimension of a time-varying matrix) Raises ------ ValueError If the matrix is not of the desired shape. )r`zTInvalid value for %s matrix. Requires a 2- or 3-dimensional array, got %d dimensionsrz:Invalid dimensions for %s matrix: requires %d rows, got %dr z=Invalid dimensions for %s matrix: requires %d columns, got %dNr`rkzInvalid dimensions for %s matrix: time-varying matrices cannot be given unless `nobs` is specified (implicitly when a dataset is bound or else set explicity)rzNInvalid dimensions for time-varying %s matrix. Requires shape (*,*,%d), got %s)r@rAstr)nameranrowsZncolsrrr+r+r,validate_matrix_shapes     rcCst|}|dkr td||f|d|ksBtd|||df|dkrj|dksj|ddksjtd||d kr|dd|gkrtd ||t|fdS) av Validate the shape of a possibly time-varying vector, or raise an exception Parameters ---------- name : str The name of the vector being validated (used in exception messages) shape : array_like The shape of the vector to be validated. May be of size 1 or (if the vector is time-varying) 2. nrows : int The expected number of rows (elements of the vector). nobs : int The number of observations (used to validate the last dimension of a time-varying vector) Raises ------ ValueError If the vector is not of the desired shape. )r r`zTInvalid value for %s vector. Requires a 1- or 2-dimensional array, got %d dimensionsrz:Invalid dimensions for %s vector: requires %d rows, got %dNr rkzInvalid dimensions for %s vector: time-varying vectors cannot be given unless `nobs` is specified (implicitly when a dataset is bound or else set explicity)r`zLInvalid dimensions for time-varying %s vector. Requires shape (*,%d), got %s)r@rAr)rrarrrr+r+r,validate_vector_shapes  rcCsJ|dkrt|fd}t|}|s0tj|dd}||t|||||S)a Reorder the rows or columns of a time-varying matrix where all non-missing values are in the upper left corner of the matrix. Parameters ---------- matrix : array_like The matrix to be reordered. Must have shape (n, m, nobs). missing : array_like of bool The vector of missing indices. Must have shape (k, nobs) where `k = n` if `reorder_rows is True` and `k = m` if `reorder_cols is True`. reorder_rows : bool, optional Whether or not the rows of the matrix should be re-ordered. Default is False. reorder_cols : bool, optional Whether or not the columns of the matrix should be re-ordered. Default is False. is_diagonal : bool, optional Whether or not the matrix is diagonal. If this is True, must also have `n = m`. Default is False. inplace : bool, optional Whether or not to reorder the matrix in-place. prefix : {'s', 'd', 'c', 'z'}, optional The Fortran prefix of the vector. Default is to automatically detect the dtype. This parameter should only be used with caution. Returns ------- reordered_matrix : array_like The reordered matrix. Nrr0)rt)r.r"rEr{r)rQmissingZ reorder_rowsZ reorder_cols is_diagonalinplacer=reorderr+r+r,reorder_missing_matrixJs#rcCsD|dkrt|fd}t|}|s0tj|dd}||t||S)a Reorder the elements of a time-varying vector where all non-missing values are in the first elements of the vector. Parameters ---------- vector : array_like The vector to be reordered. Must have shape (n, nobs). missing : array_like of bool The vector of missing indices. Must have shape (n, nobs). inplace : bool, optional Whether or not to reorder the matrix in-place. Default is False. prefix : {'s', 'd', 'c', 'z'}, optional The Fortran prefix of the vector. Default is to automatically detect the dtype. This parameter should only be used with caution. Returns ------- reordered_vector : array_like The reordered vector. Nrr0)rt)r.r#rEr{r)Zvectorrrr=rr+r+r,reorder_missing_vectorzsrc Csx|dkrt||fd}t|}|s2tj|dd}y|sBtWnt|}YnX|||t|||||S)aU Copy the rows or columns of a time-varying matrix where all non-missing values are in the upper left corner of the matrix. Parameters ---------- A : array_like The matrix from which to copy. Must have shape (n, m, nobs) or (n, m, 1). B : array_like The matrix to copy to. Must have shape (n, m, nobs). missing : array_like of bool The vector of missing indices. Must have shape (k, nobs) where `k = n` if `reorder_rows is True` and `k = m` if `reorder_cols is True`. missing_rows : bool, optional Whether or not the rows of the matrix are a missing dimension. Default is False. missing_cols : bool, optional Whether or not the columns of the matrix are a missing dimension. Default is False. is_diagonal : bool, optional Whether or not the matrix is diagonal. If this is True, must also have `n = m`. Default is False. inplace : bool, optional Whether or not to copy to B in-place. Default is False. prefix : {'s', 'd', 'c', 'z'}, optional The Fortran prefix of the vector. Default is to automatically detect the dtype. This parameter should only be used with caution. Returns ------- copied_matrix : array_like The matrix B with the non-missing submatrix of A copied onto it. Nrr0)rt)r.r$rEr{ is_f_contigrAr) rvrwrZ missing_rowsZ missing_colsrrr=r{r+r+r,copy_missing_matrixs% rcCsr|dkrt||fd}t|}|s2tj|dd}y|sBtWnt|}YnX|||t||S)aK Reorder the elements of a time-varying vector where all non-missing values are in the first elements of the vector. Parameters ---------- a : array_like The vector from which to copy. Must have shape (n, nobs) or (n, 1). b : array_like The vector to copy to. Must have shape (n, nobs). missing : array_like of bool The vector of missing indices. Must have shape (n, nobs). inplace : bool, optional Whether or not to copy to b in-place. Default is False. prefix : {'s', 'd', 'c', 'z'}, optional The Fortran prefix of the vector. Default is to automatically detect the dtype. This parameter should only be used with caution. Returns ------- copied_vector : array_like The vector b with the non-missing subvector of b copied onto it. Nrr0)rt)r.r%rEr{rrAr)rbrdrrr=r{r+r+r,copy_missing_vectors rc Csx|dkrt||fd}t|}|s2tj|dd}y|sBtWnt|}YnX|||t|||||S)aE Copy the rows or columns of a time-varying matrix where all non-index values are in the upper left corner of the matrix. Parameters ---------- A : array_like The matrix from which to copy. Must have shape (n, m, nobs) or (n, m, 1). B : array_like The matrix to copy to. Must have shape (n, m, nobs). index : array_like of bool The vector of index indices. Must have shape (k, nobs) where `k = n` if `reorder_rows is True` and `k = m` if `reorder_cols is True`. index_rows : bool, optional Whether or not the rows of the matrix are a index dimension. Default is False. index_cols : bool, optional Whether or not the columns of the matrix are a index dimension. Default is False. is_diagonal : bool, optional Whether or not the matrix is diagonal. If this is True, must also have `n = m`. Default is False. inplace : bool, optional Whether or not to copy to B in-place. Default is False. prefix : {'s', 'd', 'c', 'z'}, optional The Fortran prefix of the vector. Default is to automatically detect the dtype. This parameter should only be used with caution. Returns ------- copied_matrix : array_like The matrix B with the non-index submatrix of A copied onto it. Nrr0)rt)r.r&rEr{rrAr) rvrwr<Z index_rowsZ index_colsrrr=r{r+r+r,copy_index_matrixs% rcCsr|dkrt||fd}t|}|s2tj|dd}y|sBtWnt|}YnX|||t||S)aC Reorder the elements of a time-varying vector where all non-index values are in the first elements of the vector. Parameters ---------- a : array_like The vector from which to copy. Must have shape (n, nobs) or (n, 1). b : array_like The vector to copy to. Must have shape (n, nobs). index : array_like of bool The vector of index indices. Must have shape (n, nobs). inplace : bool, optional Whether or not to copy to b in-place. Default is False. prefix : {'s', 'd', 'c', 'z'}, optional The Fortran prefix of the vector. Default is to automatically detect the dtype. This parameter should only be used with caution. Returns ------- copied_vector : array_like The vector b with the non-index subvector of b copied onto it. Nrr0)rt)r.r'rEr{rrAr)rbrdr<rr=r{r+r+r,copy_index_vector>s rcCs`d}|dk rXt|d}|s$t|}|jdkrN|sD|dddf}n t|}|jd}||fS)Nrr )rrEZasarrayrrYZ DataFramera)ZexogZk_exogZexog_is_using_pandasr+r+r, prepare_exogks     r)N)r Nr )rF)r\)F)NN)FNN)FN)FN)NN)NF)NN)NN)FFFFN)FN)FFFFN)FN)FFFFN)FN)A__doc__Z __future__rrrZnumpyrErrrWrYZstatsmodels.tools.datarrrr)Zfloat32Zfloat64Z complex64Z complex128rrrrrr r!r"r#r$r%r&r'r-r(r.rr9rSrUrZr_rerjrnrxrrrrrrrrrrrrrrrrrrrr+r+r+r,s   , y 8 " G %% 1 - f -  .6 k  <E5/ . # 9 - 9 -