[c@`sdZddlmZmZmZmZddlZddlZddlZddl Z ddl m Z m Z ddl ZddlmZmZddlmZdd lmZdd lmZdd lmZdd lmZmZdd lmZyddlm Z e!Z"Wne#k r)e$Z"nXdddddddgZ%egZ&eegZ'ddlm(Z(m)Z)m*Z*de+fdYZ,de,fdYZ-de,e.fdYZ/dej0fdYZ1dZ2ej3e1d e4fd!YZ5ej3e1d"e4fd#YZ6d$e4fd%YZ7ej3e1d&e4fd'YZ8d(e5fd)YZ9d*e5fd+YZ:ej3e1d,e4fd-YZ;dddd.Z=d/Z>d0Z?d1Z@d2ZAd3ZBe"reBe d4d5d6dndS(7u This module implements classes (called Fitters) which combine optimization algorithms (typically from `scipy.optimize`) with statistic functions to perform fitting. Fitters are implemented as callable classes. In addition to the data to fit, the ``__call__`` method takes an instance of `~astropy.modeling.core.FittableModel` as input, and returns a copy of the model with its parameters determined by the optimizer. Optimization algorithms, called "optimizers" are implemented in `~astropy.modeling.optimizers` and statistic functions are in `~astropy.modeling.statistic`. The goal is to provide an easy to extend framework and allow users to easily create new fitters by combining statistics with optimizers. There are two exceptions to the above scheme. `~astropy.modeling.fitting.LinearLSQFitter` uses Numpy's `~numpy.linalg.lstsq` function. `~astropy.modeling.fitting.LevMarLSQFitter` uses `~scipy.optimize.leastsq` which combines optimization and statistic in one implementation. i(tabsolute_importtunicode_literalstdivisiontprint_functionN(treducetwrapsi(tpoly_map_domaint_combine_equivalency_dicti(tQuantity(tAstropyUserWarning(tsix(trange(tSLSQPtSimplex(t leastsquare(titer_entry_pointsuLinearLSQFitteruLevMarLSQFitteruFittingWithOutlierRemovaluSLSQPLSQFitteruSimplexLSQFitteru JointFitteruFitter(tDEFAULT_MAXITERt DEFAULT_EPSt DEFAULT_ACCt ModelsErrorcB`seZdZRS(uBase class for model exceptions(t__name__t __module__t__doc__(((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRAstModelLinearityErrorcB`seZdZRS(u= Raised when a non-linear model is passed to a linear fitter.(RRR(((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyREstUnsupportedConstraintErrorcB`seZdZRS(uE Raised when a fitter does not support a type of constraint. (RRR(((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRIst _FitterMetacB`s eZdZeZdZRS(uD Currently just provides a registry for all Fitter classes. cC`sXtt|j||||}tj| rT|jd rT|jj|n|S(Nu_(tsuperRt__new__tinspectt isabstractt startswithtregistrytadd(tmclstnametbasestmemberstcls((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRVs! (RRRtsetRR(((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyROs c`s"tdfd}|S(u& This is a decorator that can be used to add support for dealing with quantities to any __call__ method on a fitter which may not support quantities itself. This is done by temporarily removing units from all parameters then adding them back once the fitting has completed. c`sV|jdd}t|tp<t|tp<t|t}|j}|sT|r6|jr't|j||j} |j dk rt|tr|j |j dd| d}nt|tr|dk r|j |j dd| d}qn|j d|d|d|}t } t|tr<t } |j} ntj|} t|trlt } |j} ntj|} |dk rt|trt } |j} qtj|} n|dkr||| | |}n||| | | |}| r#|jd|d|d|}n|Stdn||||d||SdS( Nu equivalenciesuxt equivalenciesuytxtytzu8This model does not support being fit to data with units(tpoptNonet isinstanceRt _has_unitst_supports_unit_fittingRtinputstinput_units_equivalenciest input_unitsttotwithout_units_for_datatFalsetTruetvaluetnptasarraytwith_units_from_datatNotImplementedError(tselftmodelR(R)R*tkwargsR'tdata_has_unitstmodel_has_unitsR1tadd_back_unitstxdatatydatatzdatat model_new(tfunc(s7lib/python2.7/site-packages/astropy/modeling/fitting.pytwrapperfsJ   #&     !N(RR,(RFRG((RFs7lib/python2.7/site-packages/astropy/modeling/fitting.pytfitter_unit_support_s QtFittercB`s2eZdZdZdZejdZRS(u Base class for all fitters. Parameters ---------- optimizer : callable A callable implementing an optimization algorithm statistic : callable Statistic function cC`s|dkrtdn|dkr6tdntj|rT||_n'tj|ro||_n tdtj|r||_n ||_dS(NuExpected an optimizer.uExpected a statistic function.u8Expected optimizer to be a callable class or a function.(R,t ValueErrorRtisclasst _opt_methodt isfunctiont _stat_method(R<t optimizert statistic((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyt__init__s    cG`sA|d}|d}t|||j|||dd!}|S(u Function to minimize. Parameters ---------- fps : list parameters returned by the fitter args : list [model, [other_args], [input coordinates]] other_args may include weights or any other quantities specific for a statistic Notes ----- The list of arguments (args) is set in the `__call__` method. Fitters may overwrite this method, e.g. when statistic functions require other arguments. iii(t_fitter_to_model_paramsRN(R<tfpstargsR=tmeastres((s7lib/python2.7/site-packages/astropy/modeling/fitting.pytobjective_functions    cC`stddS(u This method performs the actual fitting and modifies the parameter list of a model. Fitter subclasses should implement this method. u(Subclasses should implement this method.N(R;(R<((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyt__call__s (RRRRQRWtabctabstractmethodRX(((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRIs   tLinearLSQFittercB`sYeZdZdgZdZedddZddZe ddddZ RS(u A class performing a linear least square fitting. Uses `numpy.linalg.lstsq` to do the fitting. Given a model and data, fits the model to the data and changes the model's parameters. Keeps a dictionary of auxiliary fitting information. ufixedcC`s)idd6dd6dd6dd6|_dS(Nu residualsurankusingular_valuesuparams(R,tfit_info(R<((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRQs cC`sq|dkr-tj|j||j}n!tj|j|||j}|jr_||S|d|fSdS(N.(R,R8tarrayt fit_derivt parameterst col_fit_deriv(R=t param_indicesR(R)td((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyt_deriv_with_constraintss  !! cC`s|d krt|drH|jd krH|j|jg|_nt|drx|jd krxddg|_nt||j|jSt|dr|jd kr|j|jg|_nt|dr|jd kr|j|jg|_nt|dr6|j d kr6dd g|_ nt|d rf|j d krfdd g|_ nt||j|j }t||j|j }||fSd S( ud Maps domain into window for a polynomial model which has these attributes. udomainuwindowiiux_domainuy_domainux_windowgg?uy_windowN( R,thasattrtdomaintmintmaxtwindowRtx_domainty_domaintx_windowty_window(R<R=R(R)txnewtynew((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyt_map_domain_window!s" cC`s?|jstdn|js0tdnt|j||j}t|\}} |jdkr|dkrtdnt |||dt |d|j } t |jj} | r6gtt |jD]} | | kr| ^q} tjg| D]} t||j| j^q }nt | dkr| \}}t|drx|j||}n| r|j|| d|}|j|| d|}n|j||j}|j|}|}n| \}}}t|d r|j|||\}}n| r_|j|| d|d |}|j|| d|d |}n|j|||j}|j||}t |d kr|jdkrtjg|D]}|j^qj}q|j}n |j}|j rtj|j}n| rH|j r2tj|j}n||j!|}n|dk rt |d kr||d tj"f}n||}n|dk rJtj|d tj#}t |t |krtdn|jdkr ||ddtj"f9}||ddtj"f}qJ||ddtj"f9}||}n|dkrxt |tj$|j%j&}n||j'd}tj(j)||||\}}}}||j*d<||j*d<||j*d<|j|j}||j*dt fitted_modeltfiltered_weightst filtered_datatn((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRXs:!           N(RRRRQRRR,RX(((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRs    tLevMarLSQFittercB`sbeZdZdddgZdZdZeddee e e dZ e ddZRS( u Levenberg-Marquardt algorithm and least squares statistic. Attributes ---------- fit_info : dict The `scipy.optimize.leastsq` result for the most recent fit (see notes). Notes ----- The ``fit_info`` dictionary contains the values returned by `scipy.optimize.leastsq` for the most recent fit, including the values from the ``infodict`` dictionary it returns. See the `scipy.optimize.leastsq` documentation for details on the meaning of these values. Note that the ``x`` return value is *not* included (as it is instead the parameter values of the returned model). Additionally, one additional element of ``fit_info`` is computed whenever a model is fit, with the key 'param_cov'. The corresponding value is the covariance matrix of the parameters as a 2D numpy array. The order of the matrix elements matches the order of the parameters in the fitted model (i.e., the same order as ``model.param_names``). ufixedutieduboundscC`s_i dd6dd6dd6dd6dd6dd6dd6dd6dd 6|_tt|jdS( Nunfevufvecufjacuipvtuqtfumessageuierru param_jacu param_cov(R,R\RRRQ(R<((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRQms  cG`s{|d}|d}t|||d}|dkrUtj||dd!|Stj|||dd!|SdS(u Function to minimize. Parameters ---------- fps : list parameters returned by the fitter args : list [model, [weights], [input coordinates]] iiiiN(RRR,R8travel(R<RSRTR=RRU((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRWzs     c C`sddlm} t||j} | |ft|||} | jdksS| r\d} n |j} t| \}}| j |j |d| d| d| j d|d|d|d t \}}}}}t | ||jj|||jd <||jd <||jd <|dkr+tjdtnt|t|kr|dk rtj|j || d}t|t|}||||jdRRtp0RR((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRX(s* N( RRRR RvRQRHR,RX(((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRs    tSimplexLSQFittercB`s5eZdZejZdZedddZRS(u Simplex algorithm and least squares statistic. Raises ------ ModelLinearityError A linear model is passed to a nonlinear fitter cC`s,tt|jdtdti|_dS(NRORP(RRRQR RR\(R<((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRQksc K`s~t||jj}t|||}||f|}t|\} } |j|j| ||\} |_t|| |S(uG Fit data to this model. Parameters ---------- model : `~astropy.modeling.FittableModel` model to fit to x, y, z x : array input coordinates y : array input coordinates z : array (optional) input coordinates weights : array (optional) Weights for fitting. For data with Gaussian uncertainties, the weights should be 1/sigma. kwargs : dict optional keyword arguments to be passed to the optimizer or the statistic maxiter : int maximum number of iterations acc : float Relative error in approximate solution equivalencies : list or None, optional and keyword-only argument List of *additional* equivalencies that are should be applied in case x, y and/or z have units. Default is None. Returns ------- model_copy : `~astropy.modeling.FittableModel` a copy of the input model with parameters set by the fitter (RRLRvRzRxRWR\RR( R<R=R(R)R*RR>RRRRR((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRXps$ N( RRRR RvRQRHR,RX(((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyR]s    t JointFittercB`s;eZdZdZdZdZdZdZRS(uH Fit models which share a parameter. For example, fit two gaussians to two data sets but keep the FWHM the same. Parameters ---------- models : list a list of model instances jointparameters : list a list of joint parameters initvals : list a list of initial values cC`s{t||_t||_||_|j|j|_g|jD]}|j^qJ|_t j |j|_ dS(N( Rtmodelstinitvalst jointparamst _verify_inputRxRRyt modeldimsR8RR(R<RtjointparametersRtm((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRQs  "c C`sg}|j|jx||jD]q}g|jD]}|j^q0}|j|}|j}x#|D]}||d}||=qeW|j|q W|S(Nuslice(textendRRR_RRt_param_metrics( R<tfparamsR=tpRt joint_paramst param_metricst param_nametslice_((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRxs"    cG`skt|}g}t|}t|j}|| }||4x|jD]}|j|} ||jd } ||jd4t|jt| } || } || 4g} |j}xy|jD]n}|| kr| j |}| j ||gq||d}|j |j }| j | | | |4qW|j | d | }|j || dqHWtj|S(uP Function to minimize. Parameters ---------- fps : list the fitted parameters - result of an one iteration of the fitting algorithm args : dict tuple of measured and input coordinates args is always passed as a tuple from optimize.leastsq iuslicei(RR{RRRRyt _parametersRRtindexRtstoptstarttevaluateR8R(R<RSRTt lstsqargstfittedRtnumjptjointfitparamsR=RtmargstnumfptmfparamstmparamsRRRRtplentmodelfit((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRWs4        cC`st|jdkr6tdjt|jnt|jjdkrxtdjt|jjnxj|jjD]Y}t|j|t|jkrtdjt|j|t|jqqWdS(NiuExpected >1 models, {} is giveniu1At least two parameters are expected, {} is givenu({} parameter(s) provided but {} expected(R{Rt TypeErrorRRtkeysR(R<tj((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRs  " cG`sddlm}t|td|jkratdjtd|jt|n|j|j|j d|\|j (}|j }t|j }|| }||4x|j D]}|j |}t|j t|} || } || 4g} |j} xy|jD]n} | |krK|j| }| j||gq| | d}|j|j}| j| | | |4qWtj| |_qWdS( uk Fit data to these models keeping some of the parameters common to the two models. i(RcS`s|d|dS(Ni((R(R)((s7lib/python2.7/site-packages/astropy/modeling/fitting.pytsu/Expected {} coordinates in args but {} providedcS`s|d|dS(Ni((R(R)((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRsRTusliceN(RRR{RRRJRRRWRRRRRRRRRRRR8R]R_(R<RTRRRRRR=RRRRRRRRR((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRX s6!          (RRRRQRxRWRRX(((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRs  1 cC`s*tj|dtj}tj|dtj}|dk rWtj|dtj}n|dkr|dkr|j||krtdntj|||j}q|j| |j|d}|j|jko|knstdqn|dkr||f}n|||f}|S(uConvert inputs to float arrays.RriuONumber of data sets (y array is expected to equal the number of parameter sets)u%x, y and z should have the same shapeN(R8R9RR,tshapeRJtrollaxisR(R(R)R*RpRqtz_shapeR((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRz7s"    " cC`st|\}}t|jj}t|jj}td|jjD}|pj|pj|sz||_dSt|}d}|j}xt |j D]\} } | |krqn|| d} || d} t t j | d} |||| !}|j| dkrp|j| \}}|dk rLtj||}n|dk rptj||}qpn||j| <|| 7}qW|rx^t |j D]J\} } |j| r|j| |}|| d} ||j| qsNiusliceushapei(NN(RxR|RR~R}tboundsR_R&Rt enumerateRRtoperatortmulR,R8tfmaxtfmin(R=RSRtfit_param_indicesthas_tiedRt has_boundtoffsetRRR"RRtsizeR~t_mint_maxR7((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRRgs>        cC`sttt|j}t|jjsEt|jjrt|j}|j }xitt |jdddD]E\}}|j|s|j|r||d}||=||=qqWt j ||fS|j|fSdS(uP Convert a model instance's parameter array to an array that can be used with a fitter that doesn't natively support fixed or tied parameters. In particular, it removes fixed/tied parameters from the parameter array. These may be a subset of the model parameters, if some of them are held constant or tied. Niuslice( RR R{RR|R}R~RR_RR R8R](R=RRRRR"R((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRxs * /cC`s"d}ttj|jrBd|krBt|jdnttj|jr~d|kr~t|jdntdtj|jDrd|krt|jdn|jrd |krt|jd n|j rd |krt|jd nd S(u@Make sure model constraints are supported by the current fitter.u(Optimizer cannot handle {0} constraints.ufixedufixed parameterutiedutied parametercs`s!|]}t|dkVqdS(N(NN(ttupleR,(RR((s7lib/python2.7/site-packages/astropy/modeling/fitting.pys suboundsubound parameterueqconsuequalityuineqconsu inequalityN( R|R t itervaluesR}RRRRteqconstineqcons(RvR=tmessage((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRus  $" cC`sr|jstdn|jr4tjdtn!t|dkrUtdnt|||j}|S(uT Check that model and fitter are compatible and return a copy of the model. u%Model does not appear to be fittable.uEModel is linear in parameters; consider using linear fitting methods.iu7Non-linear fitters can only fit one data set at a time.( RsRJRtRRR R{RuRw(R=RvR((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyRs      cC`sx|D]}|j}y|j}WnAtk ri}tjtdjdt|jd|qXt j |stjtdj|qt |t r|j}|t |` u,{type} error occurred in entry point {name}.ttypeR"u0Modeling entry point {0} expected to be a Class.uCModeling entry point {0} expected to extend astropy.modeling.FitterN(R"tloadt ExceptionRRR RRRRRKt issubclassRItglobalst__all__tappend(t entry_pointst entry_pointR"te((s7lib/python2.7/site-packages/astropy/modeling/fitting.pytpopulate_entry_pointss$       tgroupuastropy.modelingR"(CRt __future__RRRRRYRR Rt functoolsRRtnumpyR8tutilsRRtunitsRtutils.exceptionsR texternR textern.six.movesR t optimizersR R RPRt pkg_resourcesRR6tHAS_PKGt ImportErrorR5Rt STATISTICSt OPTIMIZERSRRRRRRRJRtABCMetaRRHt add_metaclasstobjectRIR[RRRRRR,RzRRRxRuRR$(((s7lib/python2.7/site-packages/astropy/modeling/fitting.pyts`"            \FcGD0 7    ,