[c @`s(dZddlmZmZmZmZddlmZddlZ ddl m Z m Z ddl mZddlmZdd lmZmZd d lmZmZd d lmZd d lmZddddddddddddg Zde fdYZdefdYZdefdYZd efd!YZd"efd#YZd$efd%YZ d&efd'YZ!d(efd)YZ"d*efd+YZ#d,efd-YZ$d.efd/YZ%d0efd1YZ&d2e fd3YZ'd4e fd5YZ(dS(6uM This module contains models representing polynomials and polynomial series. i(tabsolute_importtunicode_literalstdivisiontprint_function(t OrderedDictNi(t FittableModeltModel(tShift(t Parameter(tpoly_map_domaintcombi(tindenttcheck_broadcast(trange(tQuantityu Chebyshev1Du Chebyshev2Du Hermite1Du Hermite2Du InverseSIPu Legendre1Du Legendre2Du Polynomial1Du Polynomial2DuSIPuOrthoPolynomialBaseuPolynomialModeltPolynomialBasecB`sAeZdZdZeZeZedZ dZ dZ RS(u Base class for all polynomial-like models with an arbitrary number of parameters in the form of coefficients. In this case Parameter instances are returned through the class's ``__getattr__`` rather than through class descriptors. cC`s|jS(uCoefficient names generated based on the model's polynomial degree and number of dimensions. Subclasses should implement this to return parameter names in the desired format. On most `Model` classes this is a class attribute, but for polynomial models it is an instance attribute since each polynomial model instance can have different parameters depending on the degree of the polynomial and the number of dimensions, for example. (t _param_names(tself((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyt param_names.scC`s>|jr.||jkr.t|ddd|St|dS(Ntdefaultgtmodel(RRtAttributeError(Rtattr((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyt __getattr__>scC`sp|ddkrS|jrS||jkrSt|ddd|}|j||ntt|j||dS(Niu_RgR(RRt__set__tsuperRt __setattr__(RRtvaluetparam((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyRDs((( t__name__t __module__t__doc__RtTruetlineartFalset col_fit_derivtpropertyRRR(((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyRs tPolynomialModelcB`s_eZdZdddddZdZdZedZdZ dZ dZ RS( u Base class for polynomial models. Its main purpose is to determine how many coefficients are needed based on the polynomial order and dimension and to provide their default values, names and ordering. c K`se||_|j|j|_|j|j|_tt|jd|d|d|d||dS(Ntn_modelstmodel_set_axistnametmeta( t_degreet get_num_coefftn_inputst_ordert_generate_coeff_namesRRR%t__init__(RtdegreeR&R'R(R)tparams((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyR/^s  cC`s|j|jgS(N(t _format_reprR0(R((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyt__repr__hscC`s|jd|jfgS(NuDegree(t _format_strR0(R((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyt__str__kscC`s|jS(uDegree of polynomial.(R*(R((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyR0nscC`s^|jdkrtdn|dkr?t|j|}nd}|j||d}|S(uH Return the number of coefficients in one parameter set iu-Degree of polynomial must be positive or nulli(R0t ValueErrorR (Rtndimtnmixedtnumc((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyR+ts cC`s{g}|jd}xTt|D]F}x=t|D]/}|||jkr3|j||fq3q3Wq W|dddS(Nii(R0R tappend(Rtctlencoefftitj((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyt_invlexs cC`s-g}|dkrExt|jD]}|jdj|q"Wnx4t|jdD]}|jdj|dqYWx7td|jdD]}|jdjd|qWxjtd|jD]V}xMtd|jD]9}|||jdkr|jdj||qqWqWt|S(Niuc{0}uc{0}_{1}i(R R-R:tformatR0ttuple(RR7tnamestnR=R>((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyR.s $N( RRRtNoneR/R3R5R$R0R+R?R.(((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyR%Us    tOrthoPolynomialBasec B`seZdZdZdZdddddddddZdZdZdZ dZ d Z d Z d Z d Zd ZdZdZRS(u This is a base class for the 2D Chebyshev and Legendre models. The polynomials implemented here require a maximum degree in x and y. Parameters ---------- x_degree : int degree in x y_degree : int degree in y x_domain : list or None, optional domain of the x independent variable x_window : list or None, optional range of the x independent variable y_domain : list or None, optional domain of the y independent variable y_window : list or None, optional range of the y independent variable **params : dict {keyword: value} pairs, representing {parameter_name: value} uxuyuzc K`s||_||_|j|_||_||_||_||_|j|_ t t |j d|d|d| d| | dS(NR&R'R(R)( tx_degreety_degreeR+R-tx_domainty_domaintx_windowty_windowR.RRRER/( RRFRGRHRJRIRKR&R'R(R)R1((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyR/s       cC`s|j|j|jgS(N(R2RFRG(R((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyR3scC`s%|jd|jfd|jfgS(NuX-DegreeuY-Degree(R4RFRG(R((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyR5s cC`s|jd|jdS(u Determine how many coefficients are needed Returns ------- numc : int number of coefficients i(RFRG(R((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyR+s cC`sg}tj|jd}tj|jd}x2|D]*}x!|D]}|j||fqFWq9Wtj|dddS(Nii(tnptarangeRFRGR:tarray(RR;txvartyvarR>R=((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyR?s  c C`sg}tj|jd}tj|jd}xT|D]L}xC|D];}dj||}||jj|}|j|qFWq9Wtj|dddS(Niuc{0}_{1}i( RLRMRFRGR@RtindexR:RN( Rtcoeffst invlex_coeffsRORPR>R=R(tcoeff((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyt invlex_coeffs  cC`s|j}|dddf|jd|dddf<|jd}|jd}tj||d||f}xLtt|D]8}ddg||||R=((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyR."s !cC`stddS(uTo be implemented by subclassesu Subclasses should implement thisN(tNotImplementedError(RRgRh((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyRa)scG`sv|jdk r*t||j|j}n|jdk rTt||j|j}n|j|}|j|||S(N(RHRDR RJRIRKRURu(RRgRhRRtinvcoeff((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pytevaluate/s cK`satt|j|||\}}|\}}|j|jkrQtdn||f|fS(Nu,Expected input arrays to have the same shape(RREtprepare_inputstshapeR6(RRgRhtkwargstinputst format_info((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyRy7s $ (uxuy(uzN(RRRR|toutputsRDR/R3R5R+R?RUR\RuR.RaRxRy(((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyREs"       t Chebyshev1DcB`seeZdZd Zd Zd ddgd d d d dZdZdZdZ e d Z RS( u Univariate Chebyshev series. It is defined as: .. math:: P(x) = \sum_{i=0}^{i=n}C_{i} * T_{i}(x) where ``T_i(x)`` is the corresponding Chebyshev polynomial of the 1st kind. Parameters ---------- degree : int degree of the series domain : list or None, optional window : list or None, optional If None, it is set to [-1,1] Fitters will remap the domain to this window **params : dict keyword : value pairs, representing parameter_name: value Notes ----- This model does not support the use of units/quantities, because each term in the sum of Chebyshev polynomials is a polynomial in x - since the coefficients within each Chebyshev polynomial are fixed, we can't use quantities for x since the units would not be compatible. For example, the third Chebyshev polynomial (T2) is 2x^2-1, but if x was specified with units, 2x^2 and -1 would have incompatible units. uxuyiic K`sG||_||_tt|j|d|d|d|d||dS(NR&R'R(R)(tdomaintwindowRRR/( RR0RRR&R'R(R)R1((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyR/hs   cG`stj|dtjdtdd}tj|jdf|jd|j}d|d<|jdkrd|}||dscC`s|jd}|jd}i}tj|j|dR((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyRYs  !cC`stj|dtjdtdd}tj|dt|fd|j}|dd|d<|dkrd|}||dR((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyRs$*-$ cC`sg}t|jd}xj|D]b}xY|D]Q}|||jkr-dj||}||jj|}|j|q-q-Wq W|dddS(Niuc{0}_{1}i(R R0R@RRQR:(RRRRSR<R=R>R(RT((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyRUs  c C`s|j}|d}|d}|d}tj|dd}xztt|D]f} || dfdkr||||}tj|ddt}n|||}|| d}qRW|||S(u Multivariate Horner's scheme Parameters ---------- x, y : array coeffs : array of coefficients in inverse lexical order igR]iR(R?RLR`R RWt zeros_likeR"( RRgRhRRR[Rjtr1tr2RlRC((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyRs    cC`sm|jdks3|jjdkr7|jjdkr7dSi|jj|jjd6|jj|jjd6SdS(Niuxuy(R0tc1_0RRDtc0_1tc0_0(R((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyRs3cC`sg}xt|jdD]}x~t|jdD]i}||dkrPq4nt|dj||}|j|j|d|d||d|fq4WqWt|S(Niiuc{0}_{1}uzuxuy(R R0RfR@R:R(R(RRRRR=R>R((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyRs:(uxuy(uzN(RRRR|R~RDR/RyRxRRURR$RR(((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyR[s  ) t Chebyshev2Dc B`sVeZdZdddgdddgdddddZdZdZdZRS(u Bivariate Chebyshev series.. It is defined as .. math:: P_{nm}(x,y) = \sum_{n,m=0}^{n=d,m=d}C_{nm} T_n(x ) T_m(y) where ``T_n(x)`` and ``T_m(y)`` are Chebyshev polynomials of the first kind. Parameters ---------- x_degree : int degree in x y_degree : int degree in y x_domain : list or None, optional domain of the x independent variable y_domain : list or None, optional domain of the y independent variable x_window : list or None, optional range of the x independent variable y_window : list or None, optional range of the y independent variable **params : dict keyword: value pairs, representing parameter_name: value Notes ----- This model does not support the use of units/quantities, because each term in the sum of Chebyshev polynomials is a polynomial in x and/or y - since the coefficients within each Chebyshev polynomial are fixed, we can't use quantities for x and/or y since the units would not be compatible. For example, the third Chebyshev polynomial (T2) is 2x^2-1, but if x was specified with units, 2x^2 and -1 would have incompatible units. iic K`sPtt|j||d|d|d|d|d|d|d| d| | dS( NRHRIRJRKR&R'R(R)(RRR/( RRFRGRHRJRIRKR&R'R(R)R1((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyR/+scC`s|jd}|jd}i}tj|j|d<|j|dR((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyRFs  !cC`stj|dtjdtdd}tj|dt|fd|j}|dd|d<|dkrd|}||dR((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyRs  !cC`stj|dtjdtdd}tj|df|jd|j}|dd|d<|dkr||d((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyR.+s  'cC`s\tj|jd|jdf}xStd|jdD];}dj||d}||jj|||df((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyR7s#$$+cC`stj|dtj}tj|dtj}|jdkrTtj|j}ntj|j}xt|jdD]r}xit|jdD]T}||dkr|||jdkr||||f||||}qqWqzW|S(NRuAii(RLtasarraytfloat64RRVRzR R(RRgRhtcoefRtR=R>((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyRFs'/(uuuv(uwN(RRRR|R~RDR/R3R5RxR+R.RR(((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyRs    tSIPc B`skeZdZd Zd Ziid d iid d d d d ZdZdZe dZ d Z RS( u Simple Imaging Polynomial (SIP) model. The SIP convention is used to represent distortions in FITS image headers. See [1]_ for a description of the SIP convention. Parameters ---------- crpix : list or ndarray of length(2) CRPIX values a_order : int SIP polynomial order for first axis b_order : int SIP order for second axis a_coeff : dict SIP coefficients for first axis b_coeff : dict SIP coefficients for the second axis ap_order : int order for the inverse transformation (AP coefficients) bp_order : int order for the inverse transformation (BP coefficients) ap_coeff : dict coefficients for the inverse transform bp_coeff : dict coefficients for the inverse transform References ---------- .. [1] `David Shupe, et al, ADASS, ASP Conference Series, Vol. 347, 2005 `_ uuuvuxuyc C`s||_||_||_||_||_||_||_||_| |_t |d |_ t |d |_ t |ddd| d| ||_ t |ddd| d| ||_tt|jd| d| d| d | dS( NiiRuAR&R'uBR(R)(t_crpixt_a_ordert_b_ordert_a_coefft_b_coefft _ap_ordert _bp_ordert _ap_coefft _bp_coeffRtshift_atshift_bRtsip1d_atsip1d_bRRR/(Rtcrpixta_ordertb_orderta_coefftb_coefftap_ordertbp_ordertap_coefftbp_coeffR&R'R(R)((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyR/ys$          cC`s.dj|jj|j|j|j|jgS(Nu <{0}({1!r})>(R@t __class__RRRRR(R((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyR3scC`szdj|jjg}xR|j|j|j|jgD]2}|jtt |dd|jdq7Wdj |S(Nu Model: {0}twidthiuu ( R@RRRRRRR:R Rctjoin(RtpartsR((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyR5s %cC`sM|jdk r=|jdk r=t|j|j|j|jStddS(Nu+SIP inverse coefficients are not available.(RRDRt InverseSIPRRRv(R((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pytinversescC`s||jj||jj}|jj||jj}|jj|||jj}|jj|||jj}||fS(N(RRxt param_setsRRR(RRgRhtuRtftg((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyRxs (uuuv(uxuyN( RRRR|R~RDR/R3R5R$RRx(((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyRUs   RcB`sPeZdZd Zd Ziid d d d dZdZdZdZ RS( uu Inverse Simple Imaging Polynomial Parameters ---------- ap_order : int order for the inverse transformation (AP coefficients) bp_order : int order for the inverse transformation (BP coefficients) ap_coeff : dict coefficients for the inverse transform bp_coeff : dict coefficients for the inverse transform uxuyuuuvc C`s||_||_||_||_|jdd|jddtd|jD} td|jD} td|d|| |_td|d|| |_ t t |j d|d|d |d |dS( NuAP_0_0iuBP_0_0cs`s-|]#\}}|jdd|fVqdS(uAP_ucN(treplace(t.0RqR((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pys scs`s-|]#\}}|jdd|fVqdS(uBP_ucN(R(RRqR((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pys sR0R'R&R(R)( RRRRt setdefaulttdicttitemsRtsip1d_aptsip1d_bpRRR/( RRRRRR&R'R(R)tap_coeff_paramstbp_coeff_params((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyR/s&          cC`s"dj|jj|j|jgS(Nu <{0}({1!r})>(R@RRRR(R((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyR3scC`sndj|jjg}xF|j|jgD]2}|jtt|dd|jdq+Wdj|S(Nu Model: {0}Riuu ( R@RRRRR:R RcR(RRR((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyR5s cC`sF|jj|||jj}|jj|||jj}||fS(N(RRxRR(RRgRhtx1ty1((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyRxs(uxuy(uuuvN( RRRR|R~RDR/R3R5Rx(((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyRs  ()Rt __future__RRRRt collectionsRtnumpyRLtcoreRRtfunctional_modelsRt parametersRtutilsR R R R textern.six.movesR tunitsRt__all__RR%RERRRRRRRRRRR(((s:lib/python2.7/site-packages/astropy/modeling/polynomial.pyts8"     7Ijj{i`||ZV