p7]c @ sdZddlmZddlmZmZddlmZddlZ ddl Z ddl m Z ddlmZddlmZd Zd Zd ed Zd ZdZdddddddddZddZddeddZedZdeefdYZdefdYZdefdYZ defdYZ!defd YZ"d!efd"YZ#d#eefd$YZ$d%e$fd&YZ%d'e$fd(YZ&d)e$fd*YZ'd+e$fd,YZ(d-e$fd.YZ)dS(/s Spline and other smoother classes for Generalized Additive Models Author: Luca Puggini Author: Josef Perktold Created on Fri Jun 5 16:32:00 2015 i(tdivision(tABCMetatabstractmethod(twith_metaclassN(tdmatrix(t_get_all_sorted_knots(ttransf_constraintscC s;|d}|j}|j}tj|||}|S(Ni(tmintmaxtnptlinspace(txtdftn_knotstx_mintx_maxtknots((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyt_equally_spaced_knotss    cC sctj|}tjg|jddD]}tj|d|^q(}|j|jddS(NtordertCid(R tasarraytravelt percentiletreshapetshape(R tprobstprobt quantiles((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyt_R_compat_quantile"s 5tallcC syddlm}Wntk r3tdnXtjtj|dt}|jdksgt|j t |}tj|}|jdkr|j ddkr|dddf}n|jdksttj |tj |kstj |tj |kr'tdndt |}t||d|}|d krtj|j d|fdt}|} n|d krtj|j d|fdt} | } n|d krtj|j d|fdt} | } nxt|D]} tj||f} d| | |<| }|dkrh|||| |f|dd|f= %ssAdf=%s with degree=%r implies %s knots, but %s knots were providedRFiitequalsincorrect option for spacings#lower_bound > upper_bound (%r > %r)sknots must be 1 dimensionals1some knot values (%s) fall below lower bound (%r)s1some knot values (%s) fall above upper bound (%r)N(tNoneRRt ValueErrorR(R*R R RRR%tanytarangeR;R'(R R RR.tspacingR=R>RARRRR<R?R@tgridt diff_knotstdiffst lower_knotst upper_knots((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pytget_knots_bsplinessz                       cC s|d}tj|}tj||}tj|}|dddf|}tj|dddf|j|dgf}|S(smadd points to each subinterval defined by knots inserts k_points between each two consecutive knots iNi(R tuniqueRKtdiffRHR;R(Rtk_pointstdxitdxktdxR ((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyt_get_integration_pointss 6iic C sddlm}|j}t|dd}|dkrU|j|d|d|}n|}||dddddf|dddddf|dd } | S( s Approximate integral of cross product of second derivative of smoother This uses scipy.integrate simps to compute an approximation to the integral of the smoother derivative cross-product at knots plus k_points in between knots. i(tsimpsRUiR/t skip_ctransfNtaxisi(tscipy.integrateRZRRYRHt transform( tsmootherRUtintegration_pointsR[R/RZRR td2tcovd2((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyt get_covder2s   Kc C s|rd}nd}t|}tjd||d|f}tjd||d|f}tjd||d|f}xt||dD]x}|||dd||f<|||d|dd||f<||d||d|dd||feZdZdeddddZdZdedZRS(sZB-Spline single smooth component This creates and holds the B-Spline basis function for one component. Parameters ---------- x : array, 1-D underlying explanatory variable for smooth terms. df : int numer of basis functions or degrees of freedom degree : int degree of the spline include_intercept : bool If False, then the basis functions are transformed so that they do not include a constant. This avoids perfect collinearity if a constant or several components are included in the model. constraints : None, string or array Constraints are used to transform the basis functions to satisfy those constraints. `constraints = 'center'` applies a linear transform to remove the constant and center the basis functions. variable_name : None or str The name for the underlying explanatory variable, x, used in for creating the column and parameter names for the basis functions. covder2_kwds : None or dict options for computing the penalty matrix from the second derivative of the spline. knot_kwds : None or list of dict option for the knot selection. By default knots are selected in the same way as in patsy, however the number of knots is independent of keeping or removing the constant. Interior knot selection is based on quantiles of the data and is the same in patsy and mgcv. Boundary points are at the limits of the data range. The available options use with `get_knots_bsplines` are - knots : None or array interior knots - spacing : 'quantile' or 'equal' - lower_bound : None or float location of lower boundary knots, all boundary knots are at the same point - upper_bound : None or float location of upper boundary knots, all boundary knots are at the same point - all_knots : None or array If all knots are provided, then those will be taken as given and all other options will be ignored. iR c K sz||_||_||_t|d|d|||_|dk rK|ni|_tt|j |d|d|dS(NR.R RlRm( R.R R0RRRRHt covder2_kwdsRRR{( RyR R R.R0RlRmRt knot_kwds((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyR{s    cC sUt|j|j|jd|j\}}}t|dt|j}||||fS(NR0R[(R:R RR.R0RctTrueR(RyR3RDR6Rt((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyRos   icC s}|dkr|j}nt||j|jd|d|j}t|dd}|dk ry| ry|j|j}n|S(screate the spline basis for new observations The main use of this stateful transformation is for prediction using the same specification of the spline basis. Parameters ---------- x_new : array observations of the underlying explanatory variable deriv : int which derivative of the spline basis to compute This is an options for internal computation. skip_ctransf : bool whether to skip the constraint transform This is an options for internal computation. Returns ------- basis : ndarray design matrix for the spline basis for given ``x_new`` R/R0RjN( RHR R:RR.R0tgetattrRuRj(Rytx_newR/R[texogRj((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyR^s   N(R|R}R~tFalseRHR{RoR^(((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyRs 3 tUnivariateCubicSplinescB s\eZdZd dddZedZdZdZd dZ dZ d Z RS( siCubic Spline single smooth component Cubic splines as described in the wood's book in chapter 3 tdomainR cC sod|_||_||_|j|dt|_}t|||_tt |j |d|d|dS(Nit initializeRlRm( R.R ttransform_data_methodttransform_dataRR RRRRR{(RyR R RlR^Rm((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyR{s   cC s|j}|dkr|S|tkr|dkrX|jd|_|jd|_nAt|tr|d|_|d|_d|_n t d|j|j|_ n|jdkr||j|j }|St ddS(NRiis-transform should be None, 'domain' or a tuplesincorrect transform_data_method( RRHRRt domain_lowRt domain_uppRqttupleRIt domain_diff(RyR Rttm((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyR s"        cC sD|jddddf}|jdks|ddddfjd|_|ddddfc|j8( RRrR R t design_infoRRHt _get_b_and_dt_get_s(RyR3R<RAtbtdR((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyRos* cC s|d|d }|jd}tj||f}tj||f}||d|dd|d<||dd|d|df<||dd||ddfsi(%Rqtpdt DataFrametcolumnsttolisttSeriestnameRHR RR%tcopyR R*RRfRntboolR0tvariable_namesR,Rrt_make_smoothers_listt smoothersthstacktlistR3RwRttpenalty_matricesRxtextendtmasktarrayRRtappend( RyR RR0tkwargst data_namesR7R_t last_columnR((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyR{sH     /    cC sdS(N((Ry((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyRsc s5tjtfdtjD}|S(screate the spline basis for new observations The main use of this stateful transformation is for prediction using the same specification of the spline basis. Parameters ---------- x_new: array observations of the underlying explanatory variable Returns ------- basis : ndarray design matrix for the spline basis for given ``x_new``. c3 s5|]+}j|jdd|fVqdS(N(RR^(RR7(RyR(s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pys s(R RRR,Rn(RyRR((RyRs;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyR^sN( R|R}R~RHRR{RRR^(((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyRs4tGenericSmootherscB s eZdZdZdZRS(s9generic class for additive smooth components for GAM cC s)||_tt|j|dddS(NR(RRRR{RH(RyR R((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyR{!s cC s|jS(N(R(Ry((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyR%s(R|R}R~R{R(((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyRs tPolynomialSmoothercB s#eZdZddZdZRS(s+additive polynomial components for GAM cC s)||_tt|j|d|dS(NR(tdegreesRRR{(RyR RR((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyR{,s cC sjg}x]t|jD]L}t|jdd|fd|j|d|j|}|j|qW|S(NR.Rm(R,RnRR RRR(RyRtvt uv_smoother((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyR1s N(R|R}R~RHR{R(((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyR)s tBSplinescB s,eZdZeddddZdZRS(sb additive smooth components using B-Splines This creates and holds the B-Spline basis function for several components. Parameters ---------- x : array_like, 1-D or 2-D underlying explanatory variable for smooth terms. If 2-dimensional, then observations should be in rows and explanatory variables in columns. df : int numer of basis functions or degrees of freedom degree : int degree of the spline include_intercept : bool If False, then the basis functions are transformed so that they do not include a constant. This avoids perfect collinearity if a constant or several components are included in the model. constraints : None, string or array Constraints are used to transform the basis functions to satisfy those constraints. `constraints = 'center'` applies a linear transform to remove the constant and center the basis functions. variable_names : None or list of strings The names for the underlying explanatory variables, x used in for creating the column and parameter names for the basis functions. If ``x`` is a pandas object, then the names will be taken from it. knot_kwds : None or list of dict option for the knot selection. By default knots are selected in the same way as in patsy, however the number of knots is independent of keeping or removing the constant. Interior knot selection is based on quantiles of the data and is the same in patsy and mgcv. Boundary points are at the limits of the data range. The available options use with `get_knots_bsplines` are - knots : None or array interior knots - spacing : 'quantile' or 'equal' - lower_bound : None or float location of lower boundary knots, all boundary knots are at the same point - upper_bound : None or float location of upper boundary knots, all boundary knots are at the same point - all_knots : None or array If all knots are provided, then those will be taken as given and all other options will be ignored. Attributes ---------- smoothers : list of univariate smooth component instances basis : design matrix, array of spline bases columns for all components penalty_matrices : list of penalty matrices, one for each smooth term dim_basis : number of columns in the basis k_variables : number of smooth components col_names : created names for the basis columns There are additional attributes about the specification of the splines and some attributes mainly for internal use. Notes ----- A constant in the spline basis function can be removed in two different ways. The first is by dropping one basis column and normalizing the remaining columns. This is obtained by the default ``include_intercept=False, constraints=None`` The second option is by using the centering transform which is a linear transformation of all basis functions. As a consequence of the transformation, the B-spline basis functions do not have locally bounded support anymore. This is obtained ``constraints='center'``. In this case ``include_intercept`` will be automatically set to True to avoid dropping an additional column. cC s_||_||_||_||_|dkr9t}ntt|j|d|d|dS(NRiR0R(RtdfsRRlRRRR{(RyR R R.R0RlRR((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyR{s      cC sg}xt|jD]}|jr2|j|ni}t|jdd|fd|j|d|j|d|j|d|jd|j ||}|j |qW|S(NR R.R0RlRm( R,RnRRR RRR0RlRR(RyRRtkwdsR((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyRs  N(R|R}R~RRHR{R(((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyR<sO t CubicSplinescB s)eZdZddddZdZRS(sadditive smooth components using cubic splines as in Wood 2006. Note, these splines do NOT use the same spline basis as ``Cubic Regression Splines``. RiRcC sA||_||_||_tt|j|d|d|dS(NRlR(RRlR^RRR{(RyR R RlR^R((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyR{s    c C s|g}xot|jD]^}t|jdd|fd|j|d|jd|jd|j|}|j|qW|S(NR RlR^Rm( R,RnRR RRlR^RR(RyRRR((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyRs&  N(R|R}R~RHR{R(((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyRs tCyclicCubicSplinescB s&eZdZdddZdZRS(s6additive smooth components using cyclic cubic regression splines This spline basis is the same as in patsy. Parameters ---------- x : array_like, 1-D or 2-D underlying explanatory variable for smooth terms. If 2-dimensional, then observations should be in rows and explanatory variables in columns. df : int numer of basis functions or degrees of freedom constraints : None, string or array Constraints are used to transform the basis functions to satisfy those constraints. variable_names : None or list of strings The names for the underlying explanatory variables, x used in for creating the column and parameter names for the basis functions. If ``x`` is a pandas object, then the names will be taken from it. cC s2||_||_tt|j|d|dS(NR(RRlRRR{(RyR R RlR((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyR{s  c C ssg}xft|jD]U}t|jdd|fd|j|d|jd|j|}|j|qW|S(NR RlRm(R,RnRR RRlRR(RyRRR((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyRsN(R|R}R~RHR{R(((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyRs(*R~t __future__RtabcRRtstatsmodels.compat.pythonRtnumpyR tpandasRtpatsyRtpatsy.mgcv_cubic_splinesRtstatsmodels.tools.linalgRRRRR:RBRERHRRRYRRcRgRhRRRRRRRRRRR(((s;lib/python2.7/site-packages/statsmodels/gam/smooth_basis.pyt s@    C  ^  (, ohjQ l