J/PhgdZddlZddlmZmZmZmZmZddl m Z erddl Z dZ dZ dZdZd Zd Zd Zd Zd ZdZdZd'dZd(dZd)dZ d*dZdZdZGddeZGddeZe eZ GddeZ!e e!Z"dZ#dZ$de$_%d Z&Gd!d"eZ'e e'Z(d#Z)d$Z*d%Z+d&Z,dS)+)crccteN) have_pandasatleast_2d_column_default no_picklingassert_no_picklingsafe_string_eq)stateful_transformc ddlm}n#t$rtdwxYw|dd|ddz }|dd|ddzdz }|dddz }tjtjd |f|tj|d fg}tj|jd z |jf}t|jd z D]I}d ||z |||f<d ||dzz |||d zf<|||f |||d zfz |||dzf<J| d ||}tj tj|j|tj|jgS) aReturns mapping of natural cubic spline values to 2nd derivatives. .. note:: See 'Generalized Additive Models', Simon N. Wood, 2006, pp 145-146 :param knots: The 1-d array knots used for cubic spline parametrization, must be sorted in ascending order. :return: A 2-d array mapping natural cubic spline values at knots to second derivatives. :raise ImportError: if scipy is not found, required for ``linalg.solve_banded()`` rlinalg*Cubic spline functionality requires scipy.N@@?)rr) scipyr ImportErrornparrayr_zerossizerange solve_bandedvstack) knotsrhdiagul_diagbanded_bdifms X/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/patsy/mgcv_cubic_splines.py_get_natural_fr*sH       HHHFGGGH abb E#2#JA crcFQqrrUNc !D"gmGxsG|,dBE'3,4GHIIH %*q.%*-..A 5:> " "--!*!Q$Aa!eHn!QU( Awh1a!e8,!QU(   VXq 1 1B 9bhuz**B0D0DE F FF #c||krtd|d|dtj|}||||k|z ||z zz|||k<|||||kz ||z zz |||k<|S)aHMaps values into the interval [lbound, ubound] in a cyclic fashion. :param x: The 1-d array values to be mapped. :param lbound: The lower bound of the interval. :param ubound: The upper bound of the interval. :return: A new 1-d array containing mapped x values. :raise ValueError: if lbound >= ubound. zInvalid argument: lbound (z) should be less than ubound ().) ValueErrorrcopy)xlboundubounds r) _map_cyclicr3=sj(. 8    AaF mf4&IIAa&jMfqV}4&IIAa&jM Hctjgd}tj|}tjgd}t|dd}tj||sJtj||sJdS)N)g?@g?g@gffffff%@)rr6g@g333333@g @g@ @)rrr/r3allclose)r0x_origexpected_mapped_xmapped_xs r)test__map_cyclicr<Ts +++,,A WQZZF!:!:!:;;1c3''H ;q& ! !!!! ;x!2 3 333333r4cddl}tjddd}|tt |dd|tt |dddS)Nrg?g@ g@r7)pytestrlinspaceraisesr.r3r?r0s r)test__map_cyclic_errorsrC]sXMMM Cb!!A MM*k1c3777 MM*k1c377777r4cB|dd|ddz }|jdz }tj||f}tj||f}||dz |dzdz |d<||dz dz |d|dz f<||dz dz ||dz df<d|dz d ||dz z z |d<d ||dz z |d|dz f<d ||dz z ||dz df<td|D]}||dz ||zdz |||f<||dz dz |||dz f<||dz dz ||dz |f<d||dz z d ||z z |||f<d ||dz z |||dz f<d ||dz z ||dz |f<tj||S) aoReturns mapping of cyclic cubic spline values to 2nd derivatives. .. note:: See 'Generalized Additive Models', Simon N. Wood, 2006, pp 146-147 :param knots: The 1-d array knots used for cubic spline parametrization, must be sorted in ascending order. :return: A 2-d array mapping cyclic cubic spline values at knots to second derivatives. rNrrr)rrrgr)rrrrrsolve)r!r"nbr&r's r) _get_cyclic_frHes abb E#2#JA QA !QA !QAQx!A$#%AdGAE(S.AaQhKAE(S.Aa!eQhKQqTkC!AE(N*AdG!a%.AaQhK!a%.Aa!eQhK 1a[[%%QU8ad?c)!Q$Ahn!QU( Ahn!a%( 1q5/C!A$J.!Q$Aa!eHn!QU( Aa!eHn!a%( 9??1a  r4ct|dkrtd|D]}|jdkrtd|djd}d}|D]2}|jd|krtd||jdz}3t j||f}|d|dd|djd df<|djd}|d ddD]{}| |jdz}t |jdD]=}|dd|f}t | dD]} |dd| f|z|dd|f<|dz }>||jdz}||S) a8Computes row-wise tensor product of given arguments. .. note:: Custom algorithm to precisely match what is done in 'mgcv', in particular look out for order of result columns! For reference implementation see 'mgcv' source code, file 'mat.c', mgcv_tensor_mm(), l.62 :param dms: A sequence of 2-d arrays (marginal design matrices). :return: The 2-d array row-wise tensor product of given arguments. :raise ValueError: if argument sequence is empty, does not contain only 2-d arrays or if the arrays number of rows does not match. rz3Tensor product arrays sequence should not be empty.rz.Tensor product arguments should be 2-d arrays.rz9Tensor product arguments should have same number of rows.rN)lenr.ndimshaperrr) dmsdmtp_nrowstp_ncolstpfilled_tp_ncolspjxjts r)_row_tensor_productrXs 3xx1}}NOOOOO 7a<<MNN N 1v|AHH   8A;( " "N  BHQK 8X& ' 'B!$RBqqq3r7=    "gmA&O"&b&k''  rx{ *rx{##  AAAAqDBO+Q//  aaad8b=111a4Q  28A;& Ir4c *ddl}|ttg|ttt jddg|ttt jddt jddg|ttt jdddt jdddgdS)Nrr ))r]r\)r?rAr.rXrarangereshaper?s r)test__row_tensor_product_errorsrasMMM MM*12666 MM*1BIaOO3DEEE MM*1BIaOORYqRS__3UVVV MM 1b   ! !& ) )29Q+;+;+C+CF+K+KLr4ctjddd}tjt |g|sJtjdd}t ||g}tj||sJt ||g}tj||sJd|z}t ||g}tj|d|zsJt ||g}tj|d|zsJtjddgddgg}tjddd}tjgd gd g} t ||g} tj| | sJtjgd gd g} t ||g} tj| | sJdS) Nrr]r]r])r]rr)rr\)rrr\rr])r]rZrfr> )rrrr]r\rf)r]rgrZr>rfrh)rr^r_ array_equalrXonesr) dm1rjtp1tp2twostp3tp4dm2dm3 expected_tp5tp5 expected_tp6tp6s r)test__row_tensor_productrws )Ar   " "6 * *C >-se44c : :::: 71::  f % %D tSk * *C >#s # #### sDk * *C >#s # #### t8D tSk * *C >#q3w ' '''' sDk * *C >#q3w ' '''' (QFQF# $ $C )Aq// ! !& ) )C8///1E1E1EFGGL sCj ) )C >#| , ,,,,8///1E1E1EFGGL sCj ) )C >#| , ,,,,,,r4cztj||dz }d||dk<|jdz |||jdz k<|S)aZFinds knots lower bounds for given values. Returns an array of indices ``I`` such that ``0 <= I[i] <= knots.size - 2`` for all ``i`` and ``knots[I[i]] < x[i] <= knots[I[i] + 1]`` if ``np.min(knots) < x[i] <= np.max(knots)``, ``I[i] = 0`` if ``x[i] <= np.min(knots)`` ``I[i] = knots.size - 2`` if ``np.max(knots) < x[i]`` :param x: The 1-d array values whose knots lower bounds are to be found. :param knots: The 1-d array knots used for cubic spline parametrization, must be sorted in ascending order. :return: An array of knots lower bounds indices. rrrr)r searchsortedr)r0r!lbs r)_find_knots_lower_boundsr{sK  " "Q &BBrRxL %zA~BrUZ!^ Ir4ct||}|dd|ddz }||}||dz|z }|||z }||z }||z }||z|zd|zz } d| |tj|k<||zdz } | | z } ||z|zd|zz } d| |tj|k<||zdz } | | z }||| ||fS)aComputes base functions used for building cubic splines basis. .. note:: See 'Generalized Additive Models', Simon N. Wood, 2006, p. 146 and for the special treatment of ``x`` values outside ``knots`` range see 'mgcv' source code, file 'mgcv.c', function 'crspl()', l.249 :param x: The 1-d array values for which base functions should be computed. :param knots: The 1-d array knots used for cubic spline parametrization, must be sorted in ascending order. :return: 4 arrays corresponding to the 4 base functions ajm, ajp, cjm, cjp + the 1-d array of knots lower bounds indices corresponding to the given ``x`` values. rNrrr)r{rmaxmin)r0r!rUr"hjxj1_xx_xjajmajpcjm_3cjm_1cjmcjp_3cjp_1cjps r)_compute_base_functionsrs !E**A abb E#2#JA 1B !a%L1 E uQxqQQQxzAQ QC 5Lr4cLt|||}|t||}|S)aBuilds a cubic regression spline design matrix. Returns design matrix with dimensions len(x) x n where: - ``n = len(knots) - nrows(constraints)`` for natural CRS - ``n = len(knots) - nrows(constraints) - 1`` for cyclic CRS for a cubic regression spline smoother :param x: The 1-d array values. :param knots: The 1-d array knots used for cubic spline parametrization, must be sorted in ascending order. :param constraints: The 2-d array defining model parameters (``betas``) constraints (``np.dot(constraints, betas) = 0``). :param cyclic: Indicates whether used cubic regression splines should be cyclic or not. Default is ``False``. :return: The (2-d array) design matrix. )rr)r0r!rrrOs r)_get_crs_dmatrixrbs/$ q% 0 0B [ 1 1 Ir4cHt|}|t||}|S)aNBuilds tensor product design matrix, given the marginal design matrices. :param design_matrices: A sequence of 2-d arrays (marginal design matrices). :param constraints: The 2-d array defining model parameters (``betas``) constraints (``np.dot(constraints, betas) = 0``). :return: The (2-d array) design matrix. )rXr)design_matricesrrOs r)_get_te_dmatrixr{s+ _ - -B [ 1 1 Ir4c ,||jdkrtd||jdkrtj|}||jdkrtd||jdkrtj|}||krtd|d|d|||dkrtd||||k||kz}tj|}|jdkr[tjdd |d zd d }tjtj|| }n|dkrtj g}ntd |d|d|d|tj|}|&||jkrtd|d|jd|j}tj ||kr td|||kd|dtj ||kr td|||kd|dntdtj ||g|f}tj|}|j|d zkr!td|d|jd|d|d |S)aGets all knots locations with lower and upper exterior knots included. If needed, inner knots are computed as equally spaced quantiles of the input data falling between given lower and upper bounds. :param x: The 1-d array data values. :param n_inner_knots: Number of inner knots to compute. :param inner_knots: Provided inner knots if any. :param lower_bound: The lower exterior knot location. If unspecified, the minimum of ``x`` values is used. :param upper_bound: The upper exterior knot location. If unspecified, the maximum of ``x`` values is used. :return: The array of ``n_inner_knots + 2`` distinct knots. :raise ValueError: for various invalid parameters sets or if unable to compute ``n_inner_knots + 2`` distinct knots. NrzXCannot set lower exterior knot location: empty input data and lower_bound not specified.zXCannot set upper exterior knot location: empty input data and upper_bound not specified.zlower_bound > upper_bound (z > )z)Invalid requested number of inner knots: drrrz$No data values between lower_bound(=z) and upper_bound(=z): cannot compute requested z inner knot(s).zNeeded number of inner knots=z/ does not match provided number of inner knots=.zSome knot values (z) fall below lower bound (r-z) fall above upper bound (z5Must specify either 'n_inner_knots' or 'inner_knots'.z!Unable to compute n_inner_knots(=z) + 2 distinct knots: z* data value(s) found between lower_bound(=) rr.rr~r}uniquer@asarray percentiletolistrany concatenate)r0 n_inner_knots inner_knots lower_bound upper_bound inner_knots_q all_knotss r)_get_all_sorted_knotsrs>(qv{{ 8     1fQii qv{{ 8     1fQii [  j5@[[+++ N   }8 1  *ANP  {aA$45 6 IaLL 6Q;;K3 0ABB1R4HM*R]1m6J6J6L6L%M%MNNKK a  (2,,KK*(3{{KKKP   i ,,  $+:J)J)J*8E {GWGWGWY $( 6+ + , , *&{['@AAA;;;P  6+ + , , *&{['@AAA;;;P   PQQQk :KHIII )$$I~***j}}afffkkk;;; @    r4czddl}|ttt jgd|ttt jgd|ttt jgdd|ttt jgdd|ttt jgdddt jtt jgdddddgsJ|ttt jgdddt jd d z}|tt|d t jt|ddd gsJt jt|ddd dd gsJt jt|d ddgdsJ|tt|d dd|tt|dddt jt|dddgdsJ|tt|dd d|tt|dd dg|tt|d dt jt|ddggdsJt jt|ddgd gdsJ|tt|ddgd|tt|ddgd dS)Nrrr)rrZ)rr\)rrrfrrJr>rg )rr]rfrg?gffffff?)rrr\)rre)rr\rer>)rr)rr\rer>r])rr)r?rAr.rrrrir^rBs r)test__get_all_sorted_knotsrsMMM MM*3RXb\\2FFF MM*3RXb\\1EEE MM*3RXb\\1RSMTTT MM*3RXb\\1RSMTTT MM)28B<<WX >bhrllA1!LLLqRSf   MM)28B<<WX ! qA MM*3Q;;; >/1552w ? ???? >aqAAAAq6   >aqAAA<<<   MM*3QqVWMXXX MM)1aSc >aqAAA999   MM*3QqVWMXXX MM*3Q1vMNNN MM*3QASTMUUU >/1vFFF V VVVV >aaVCCC]]]   MM)11a&a MM)11a&ar4cn|dd|jdfS)aComputes the centering constraint from the given design matrix. We want to ensure that if ``b`` is the array of parameters, our model is centered, ie ``np.mean(np.dot(design_matrix, b))`` is zero. We can rewrite this as ``np.dot(c, b)`` being zero with ``c`` a 1-row constraint matrix containing the mean of each column of ``design_matrix``. :param design_matrix: The 2-d array design matrix. :return: A 2-d array (1 x ncols(design_matrix)) defining the centering constraint. raxisr)meanr_rM)rs r)&_get_centering_constraint_from_dmatrixrs6   1  % % - -q-2Ea2H.I J JJr4cJeZdZdZdZdZ ddZdZ ddZe Z dS) CubicRegressionSplineaBase class for cubic regression spline stateful transforms This class contains all the functionality for the following stateful transforms: - ``cr(x, df=None, knots=None, lower_bound=None, upper_bound=None, constraints=None)`` for natural cubic regression spline - ``cc(x, df=None, knots=None, lower_bound=None, upper_bound=None, constraints=None)`` for cyclic cubic regression spline a  :arg df: The number of degrees of freedom to use for this spline. The return value will have this many columns. You must specify at least one of ``df`` and ``knots``. :arg knots: The interior knots to use for the spline. If unspecified, then equally spaced quantiles of the input data are used. You must specify at least one of ``df`` and ``knots``. :arg lower_bound: The lower exterior knot location. :arg upper_bound: The upper exterior knot location. :arg constraints: Either a 2-d array defining general linear constraints (that is ``np.dot(constraints, betas)`` is zero, where ``betas`` denotes the array of *initial* parameters, corresponding to the *initial* unconstrained design matrix), or the string ``'center'`` indicating that we should apply a centering constraint (this constraint will be computed from the input data, remembered and re-used for prediction from the fitted model). The constraints are absorbed in the resulting design matrix which means that the model is actually rewritten in terms of *unconstrained* parameters. For more details see :ref:`spline-regression`. This is a stateful transforms (for details see :ref:`stateful-transforms`). If ``knots``, ``lower_bound``, or ``upper_bound`` are not specified, they will be calculated from the data and then the chosen values will be remembered and re-used for prediction from the fitted model. Using this function requires scipy be installed. .. versionadded:: 0.3.0 cL||_||_i|_d|_d|_dSN)_name_cyclic_tmp _all_knots _constraints)selfnamers r)__init__zCubicRegressionSpline.__init__Us,    r4NcD|||||d}||jd<tj|}|jdkr|jddkr |dddf}|jdkrt d|jd|jdg|dS) N)dfr!rrrargsrrr Input to % must be 1-d, or a 2-d column vector.xs) rr atleast_1drLrMr.r setdefaultappend)rr0rr!rrrrs r)memorize_chunkz$CubicRegressionSpline.memorize_chunk\s&&&   ! & M!   6Q;;171:??!!!Q$A 6A::*IMU  T2&&--a00000r4c|jd}|jd}|`tj|}|d|dtd|d}d}|Nt |drd }n;tj|}|jd krtd |jd}d}|dSd }|js|dkrd }|d|krtd |dd |d|dd z |z}|jr|d z }t|||d|d|d|_ |t |dr)tt||j |j}|j j }|jr|d z}|jd |kr!td|d|jd d||_dSdS)Nrrrr!z$Must specify either 'df' or 'knots'.rrcenterrr,Constraints must be 2-d array or 1-d vector.z'df'=z" must be greater than or equal to rrr)rrrrrzConstraints array should have z columns but z found.)rrrr.r atleast_2drLrMrrrrrrr) rrrr0r n_constraintsrmin_dfdf_before_constraintss r)memorize_finishz%CubicRegressionSpline.memorize_finishxs9y  Yt_ I N2   : $w-"7CDD D=)   "k844 5!"  mK88 #q(($%VWWW + 1! 4  : !F< MQ$6$6DzF"" jDzzz666+!JN]:M| #" / 'W ]+]+      "k844 D)!T_T\RRR %)O$8 !| +%*% #'<<< j$9$9$9;;LQ;O;O;OQ!,D    # "r4c|}tj|}|jdkr|jddkr |dddf}|jdkrt d|jdt ||j|j|j }trFt|tj tjfr tj|}|j|_|S)Nrrrrrr)rrrLrMr.rrrrrr isinstancepandasSeries DataFrameindex) rr0rr!rrrr9rOs r) transformzCubicRegressionSpline.transforms M!   6Q;;171:??!!!Q$A 6A::*IMU  t 1$,     (&6=&2B"CDD (%b))!< r4)NNNNN) __name__ __module__ __qualname____doc__ common_docrrrrr __getstate__r4r)rr+sJ>!!! 11118:,:,:,~ 4LLLr4rc0eZdZdZer eejz ZdZdS)CRa(cr(x, df=None, knots=None, lower_bound=None, upper_bound=None, constraints=None) Generates a natural cubic spline basis for ``x`` (with the option of absorbing centering or more general parameters constraints), allowing non-linear fits. The usual usage is something like:: y ~ 1 + cr(x, df=5, constraints='center') to fit ``y`` as a smooth function of ``x``, with 5 degrees of freedom given to the smooth, and centering constraint absorbed in the resulting design matrix. Note that in this example, due to the centering constraint, 6 knots will get computed from the input data ``x`` to achieve 5 degrees of freedom. .. note:: This function reproduce the cubic regression splines 'cr' and 'cs' as implemented in the R package 'mgcv' (GAM modelling). c@t|dddS)NrFrrrrrs r)rz CR.__init__s#&&t$u&EEEEEr4Nrrrrrrrrr4r)rrsJ*4(33FFFFFr4rc0eZdZdZer eejz ZdZdS)CCa)cc(x, df=None, knots=None, lower_bound=None, upper_bound=None, constraints=None) Generates a cyclic cubic spline basis for ``x`` (with the option of absorbing centering or more general parameters constraints), allowing non-linear fits. The usual usage is something like:: y ~ 1 + cc(x, df=7, constraints='center') to fit ``y`` as a smooth function of ``x``, with 7 degrees of freedom given to the smooth, and centering constraint absorbed in the resulting design matrix. Note that in this example, due to the centering and cyclic constraints, 9 knots will get computed from the input data ``x`` to achieve 7 degrees of freedom. .. note:: This function reproduce the cubic regression splines 'cc' as implemented in the R package 'mgcv' (GAM modelling). c@t|dddS)NrTrrrs r)rz CC.__init__ s#&&t$t&DDDDDr4Nrrr4r)rrsJ(4(33EEEEEr4rc ddl}|ttt jddd|ttjt jddd|ttt jd|ttt jddt jdd |ttt jddt jd  |ttt jdd |ttt jdddS) Nrrdr]r2r\r\r\rrrfr) r?rAr.rrr^r_rrrr`s r)test_crs_errorsrsRMMM MM*b")B--"7"7"?"?AMFFF MM*bddnbimm.C.CF.K.KPQMRRR MM*b")B--000 MM  " IbMM)))44  MM*b")B--A29Q<>i()  # #DC++JC"IcNN ] #t + +y/G4/O/OKK } % - -K NII*1:=1I1IK  ] #v - -$,F= ! NI W  ' ' 4 '(:#;#;<z!cr(x, df=4, constraints='center')c"tSriter data_chunkedsr)z3test_crs_with_specific_constraint..sT,5G5Gr4-q=rrtolatol)patsy.highlevelrrrrr^rr8) rrrr0knots_Rcentering_constraint_Rnew_xresult1new_databuilderresult2r#s @r)!test_crs_with_specific_constraintr1as8MMMMMMMMMM ")B--Ah   G X       H555 6 6Eg .G !CRC&MC233=1LU|Hm+-G-G-G-GG$#WIx88;G ;we# > > >>>>>>r4c.eZdZdZdZdZdZdZeZ dS)TEa>te(s1, .., sn, constraints=None) Generates smooth of several covariates as a tensor product of the bases of marginal univariate smooths ``s1, .., sn``. The marginal smooths are required to transform input univariate data into some kind of smooth functions basis producing a 2-d array output with the ``(i, j)`` element corresponding to the value of the ``j`` th basis function at the ``i`` th data point. The resulting basis dimension is the product of the basis dimensions of the marginal smooths. The usual usage is something like:: y ~ 1 + te(cr(x1, df=5), cc(x2, df=6), constraints='center') to fit ``y`` as a smooth function of both ``x1`` and ``x2``, with a natural cubic spline for ``x1`` marginal smooth and a cyclic cubic spline for ``x2`` (and centering constraint absorbed in the resulting design matrix). :arg constraints: Either a 2-d array defining general linear constraints (that is ``np.dot(constraints, betas)`` is zero, where ``betas`` denotes the array of *initial* parameters, corresponding to the *initial* unconstrained design matrix), or the string ``'center'`` indicating that we should apply a centering constraint (this constraint will be computed from the input data, remembered and re-used for prediction from the fitted model). The constraints are absorbed in the resulting design matrix which means that the model is actually rewritten in terms of *unconstrained* parameters. For more details see :ref:`spline-regression`. Using this function requires scipy be installed. .. note:: This function reproduce the tensor product smooth 'te' as implemented in the R package 'mgcv' (GAM modelling). See also 'Generalized Additive Models', Simon N. Wood, 2006, pp 158-163 .. versionadded:: 0.3.0 c"i|_d|_dSr)rrrs r)rz TE.__init__s  r4c|jd|d}t|drg}|D]@}t |}|jdkrt d||At|}|jdd|jdxx|j dz cc<tj | d}|jdtj |j |jdxx|z cc<dSdS) Nrrr?Each tensor product argument must be a 2-d array or 1-d vector.countrrsum)rrgetr rrLr.rrXrMrrr8r)rrrrargs_2dargrR chunk_sums r)rzTE.memorize_chunksGi**=&**]:S:STT +x 0 0 *G $ $/448q==$5s####$W--B I ! , , , Ig   "(1+ -    bff!fnn55I I (A(A B B B Ie    )     # * *r4c|j}|jd}|`|bt|dr$tj|d|dz }n.tj|}|jdkrt d||_dS)Nrrr8r7rr)rr rrrLr.r)rtmprs r)rzTE.memorize_finishsii . 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