B Ù‹d¶ã@s¬ddlZddlZddlZddlZddlZddlZddlZddlZddlZddl Z ddl m Z ddl mZddlmZddlmZddl mZddlmZdd lmZmZmZdd lmZdd lmZmZd d ddddddddddddddddddd d!gZd"gZ edk rej! "d#¡Z#e$e#dƒd$kr@e$e#dƒd%kr@e%d&ƒ‚e &¡sRe'd'ƒ‚ej(Z)ej*Z*ej+Z+ej,Z,ej-Z-ej.Z.ej/Z/ej0Z0ej1Z1ej2Z2ej3Z3ej4Z4ej5Z5ej6Z6ej7Z7ej8Z8ej9Z9x8ej: ;¡D]*\Zd(¡rÄe=e?ƒe<<e @e<¡qÄWd)d*„ZAe BeA¡n@eCZ)eCZ,eCZ*eCZ+eCZ.eCZ/dZ0dZ1dZ2dZ3dZ4dZ5dZ6dZ7dZ8dZ9d+ZDe Ed,¡ZFd-d.„ZGGd/d„deHƒZIGd0d „d eƒZJGd1d „d ee)ƒZKd2d3„ZLd8d6d„ZMd7d„ZNdS)9éN)Úlog)Úfitsé)Ú docstrings)Ú_wcs)Úunits)Úpossible_filename)ÚAstropyWarningÚAstropyUserWarningÚAstropyDeprecationWarning)Údeprecated_renamed_argument)ÚFITSWCSAPIMixinÚ SlicedFITSWCSÚFITSFixedWarningÚWCSÚ find_all_wcsÚDistortionLookupTableÚSipÚTabprmÚWcsprmÚAuxprmÚWtbarrÚWCSBaseÚvalidateÚWcsErrorÚSingularMatrixErrorÚInconsistentAxisTypesErrorÚInvalidTransformErrorÚInvalidCoordinateErrorÚNoSolutionErrorÚ!InvalidSubimageSpecificationErrorÚ NoConvergenceÚ)NonseparableSubimageCoordinateSystemErrorÚNoWcsKeywordsFoundErrorÚInvalidTabularParametersErrorzWCS.all_world2pixÚ.ééz¦astropy.wcs is built with wcslib {0}, but only versions 5.8 and later on the 5.x series are known to work. 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N)Ú best_solutionÚaccuracyÚniterÚ divergentÚ slow_convcsHtƒj|Ž||_||_||_||_||_|rDt d  t |ƒ¡t ¡dS)NzhFunction received unexpected arguments ({}) these are ignored but will raise an Exception in the future.) ÚsuperÚ__init__rArBrCrDrEÚwarningsÚwarnÚformatÚlistr )ÚselfrArBrCrDrEÚargsÚkwargs)Ú __class__r6r7rGÎs zNoConvergence.__init__)Ú__name__Ú __module__Ú __qualname__Ú__doc__rGÚ __classcell__r6r6)rOr7r!«s!c@seZdZdZdS)rzs The warning raised when the contents of the FITS header have been modified to be standards compliant. N)rPrQrRrSr6r6r6r7rßsc @s„eZdZdZd—dd„Zd d „Zd d „Zd d„Zdd„Zd˜dd„Z e dk rTe j j je _dd„Z d™dd„Z dšdd„Zd›dd„Zdd„Zdd„Zdœd d!„Zdd"d#„Zd$d%„Zdžd&d'„Zd(d)„Zd*d+„Zd,d-„Zd.d/œd0d1„Zd2d3„Zd4 e d5d6¡e d6¡e d7d6¡¡e_d8d9„Z d: e d5d6¡e d6¡e d;d6¡¡e _dd?d@ƒdAdBd.dd.dCœdDdE„ƒZ#dF e d5d6¡e d6¡e dGd6¡¡e#_dHdI„Z$dJ e d5d6¡e d6¡e dGd6¡¡e$_dKdL„Z%dM e dNd6¡e dOd6¡¡e%_dPdQ„Z&dR e dNd6¡e dOd6¡¡e&_dSdT„Z'dU e dNd6¡e dGd6¡¡e'_dVdW„Z(dX e dNd6¡e dOd6¡¡e(_dYdZ„Z)d[ e dNd6¡e dGd6¡¡e)_d\d]„Z*d^d_„Z+dŸd`da„Z,d dbdc„Z-d¡ddde„Z.d¢dfdg„Z/d£dkdl„Z0d¤dmdn„Z1dodp„Z2dqdr„Z3dsdt„Z4dudv„Z5dwdx„Z6dydz„Z7d{d|„Z8d¥d}d~„Z9dd€„Z:dd‚„Z;eeZis_pathZ orig_headerZdict_keyÚ header_stringÚ header_bytesZ est_naxisZ tmp_headerZtmp_header_bytesZ tmp_wcsprmZ header_naxisÚfdr6r6r7rGxsâ                          .        z WCS.__init__cCs@| ¡}t ||j|j|jf|j|j|jf¡|j   |j ¡|S)N) rOrrGrÚcpdis1Úcpdis2r„Údet2im1Údet2im2Ú__dict__Úupdate)rLÚnew_copyr6r6r7Ú__copy__s  z WCS.__copy__c Cs˜ddlm}| ¡}||j|ƒ|_t |||j|ƒ||j|ƒ||j|ƒf||j |ƒ||j |ƒ||j |ƒf¡x&|j   ¡D]\}}|||ƒ|j |<qxW|S)Nr)Údeepcopy)Úcopyr™rOr[rrGrr‘r’r„r“r”r•Úitems)rLÚmemor™r—rYÚvalr6r6r7Ú __deepcopy__#s     zWCS.__deepcopy__cCs t |¡S)a Return a shallow copy of the object. Convenience method so user doesn't have to import the :mod:`copy` stdlib module. .. warning:: Use `deepcopy` instead of `copy` unless you know why you need a shallow copy. )rš)rLr6r6r7rš2s zWCS.copycCs t |¡S)z• Return a deep copy of the object. Convenience method so user doesn't have to import the :mod:`copy` stdlib module. )ršr™)rLr6r6r7r™?sz WCS.deepcopycs¦ˆ ¡}dd„t|jjƒDƒ‰ˆ|j_|j |¡|_|jj|_‡fdd„|jjDƒ}‡fdd„|Dƒ|j_ˆjrˆt‡fdd„|Dƒƒ|_ˆjr¢‡fdd„|Dƒ|_|S)NcSsg|]}tt ¡ƒ‘qSr6)rfÚuuidÚuuid4)Ú.0Úir6r6r7ú PszWCS.sub..cs"g|]}|ˆkrˆ |¡nd‘qS)N)Úindex)r¡Úcname)Ú cname_uuidr6r7r£Yscs$g|]}|dkrdn ˆjj|‘qS)NrW)r„r¥)r¡r¢)rLr6r7r£]scs"g|]}|dkrdnˆj|‘qS)N)Ú pixel_shape)r¡r¢)rLr6r7r£ascs"g|]}|dkrdnˆj|‘qS)N)Ú pixel_bounds)r¡r¢)rLr6r7r£cs) r™Úranger„r[r¥rzr§Útupler¨)rLÚaxesršZkeepr6)r¦rLr7rzHs   zWCS.subcCsÄ|jdkrdS|j ¡}|s dS|jdkr.dSt |¡}xnt|dd…dfƒD]V}t|dd…df|dd…df|kƒ}t|ƒ}x dD]}||krˆ||krˆdSqˆWqNW|j g¡t  dt ¡dS)až Remove SCAMP's PVi_m distortion parameters if SIP distortion parameters are also present. Some projects (e.g., Palomar Transient Factory) convert SCAMP's distortion parameters (which abuse the PVi_m cards) to SIP. However, wcslib gets confused by the presence of both SCAMP and SIP distortion parameters. See https://github.com/astropy/astropy/issues/299. Nrr)éé éé'zURemoved redundant SCAMP distortion parameters because SIP parameters are also present) r„Zget_pvrr0Úasarrayr…ÚmaxZset_pvrHrIr)rLÚpvr¢ÚjsZmax_jÚjr6r6r7Ú _fix_scampjs"    (   zWCS._fix_scampcCsv|jdk rr| ¡|j ||¡}xP| ¡D]D\}}|dkr*|dkrZd|krZt |jj¡sZq*t d  ||¡t ¡q*WdS)a= Perform the fix operations from wcslib, and warn about any changes it has made. Parameters ---------- translate_units : str, optional Specify which potentially unsafe translations of non-standard unit strings to perform. By default, performs none. Although ``"S"`` is commonly used to represent seconds, its translation to ``"s"`` is potentially unsafe since the standard recognizes ``"S"`` formally as Siemens, however rarely that may be used. The same applies to ``"H"`` for hours (Henry), and ``"D"`` for days (Debye). This string controls what to do in such cases, and is case-insensitive. - If the string contains ``"s"``, translate ``"S"`` to ``"s"``. - If the string contains ``"h"``, translate ``"H"`` to ``"h"``. - If the string contains ``"d"``, translate ``"D"`` to ``"d"``. Thus ``''`` doesn't do any unsafe translations, whereas ``'shd'`` does all of them. naxis : int array, optional Image axis lengths. If this array is set to zero or ``None``, then `~astropy.wcs.Wcsprm.cylfix` will not be invoked. Nz No changeZdatfixz 1858-11-17z'{0}' made the change '{1}'.) r„rµrƒr›r0Z count_nonzeroZmjdrefrHrIrJr)rLrdr[ÚfixesrYrr6r6r7rƒ•s& zWCS.fixc Cs|dk r|\}}nV|dkrPy|j\}}Wqhttfk rLt dt¡dSXn| dd¡}| dd¡}|dksx|dkr€tdƒ‚|r®tj ddgd|g||g|dggtj d}n8tj ddgd|dg|d|dg|ddggtj d}|rö|  |d¡S|  |d¡SdS) at Calculates the footprint of the image on the sky. A footprint is defined as the positions of the corners of the image on the sky after all available distortions have been applied. Parameters ---------- header : `~astropy.io.fits.Header` object, optional Used to get ``NAXIS1`` and ``NAXIS2`` header and axes are mutually exclusive, alternative ways to provide the same information. undistort : bool, optional If `True`, take SIP and distortion lookup table into account axes : (int, int), optional If provided, use the given sequence as the shape of the image. Otherwise, use the ``NAXIS1`` and ``NAXIS2`` keywords from the header that was used to create this `WCS` object. center : bool, optional If `True` use the center of the pixel, otherwise use the corner. Returns ------- coord : (4, 2) array of (*x*, *y*) coordinates. The order is clockwise starting with the bottom left corner. Nz4Need a valid header in order to calculate footprint ZNAXIS1ZNAXIS2z#Image size could not be determined.r)r*gà?) r§ÚAttributeErrorrqrHrIr rr/r0ÚarrayZfloat64Ú all_pix2worldÚ wcs_pix2world)rLrXZ undistortr«ÚcenterZnaxis1Znaxis2Zcornersr6r6r7Úcalc_footprintÈs4!       zWCS.calc_footprintcCs2|dkr dSt|tjƒsdSy|d}| |||¡}|Stk rJYnXd}d}d}i} x°td|jdƒD]š} | |t| ƒd¡} | |krœd| | <qp|t| ƒ} | |kr||   ¡} | d krÌ|| =t|tjƒsât d ƒ‚|t| ƒ  ¡}|d }||kr||}||=nd}|d | d ›}| ||krF|d|fj }n|d|fj   ¡}||=|d|fj}| dd¡| dd¡f}| dd¡| dd¡f}| dd¡| dd¡f}t||||ƒ}|| | <n t dt¡x2t|ƒD]}| |d¡râ||=qâWqpd| | <qpW| sdS|  d¡|  d¡fSdS)zp Create a `distortion paper`_ type lookup table for detector to image plane correction. N)NNZAXISCORRÚD2IMDISÚD2IMZD2IMERRrgÚlookupzBAn astropy.io.fits.HDUListis required for Lookup table distortion.z.EXTVERz.AXIS.ÚdÚD2IMARRÚCRPIX1ÚCRPIX2ÚCRVAL1ÚCRVAL2ÚCDELT1gð?ÚCDELT2z*Polynomial distortion is not implemented. r%r))rerrvÚ_read_d2im_old_formatÚKeyErrorr©r[rrfr<rwÚstripr+Ú transposerXrrHrIr r…Ú startswith)rLrXr‡r^ÚaxiscorrZd2imdisr`Úd_kwÚerr_kwÚtablesr¢Úd_errorÚ distortionÚdisÚdpÚ dp_extver_keyÚd_extverÚ dp_axis_keyÚd_dataÚd_headerÚd_crpixÚd_crvalÚd_cdeltÚd_lookuprYr6r6r7r{ sh         zWCS._read_det2im_kwc Cs2t dt¡ddg}ddg}ddg}ddg}y|dj}Wn&tk rNdStk r`dSXt |g¡}|dj} | d} xjt d| dƒD]X} |   dt | ƒd¡|| d<|   d t | ƒd¡|| d<|   d t | ƒd¡|| d<qWt ||||ƒ}|dkr |dfS|d krd|fSt d t ¡dSdS) Nz¦The use of ``AXISCORR`` for D2IM correction has been deprecated.`~astropy.wcs` will read in files with ``AXISCORR`` but ``to_fits()`` will write out files without it.ggð?)rÁr)NNrbrÚCRPIXÚCRVALÚCDELTr)zExpected AXISCORR to be 1 or 2)rHrIr r+rÉr·r0r¸rXr©rrfrr ) rLrXr‡rÍrŒÚcrpixÚcrvalÚcdeltZ d2im_dataZd2im_hdrr[r¢r6r6r7rÈPs6      zWCS._read_d2im_old_formatcsL|jdkr|jdkrdSd‰d‰‡‡‡fdd„}|d|jƒ|d|jƒdS)zq Writes a `distortion paper`_ type lookup table to the given `~astropy.io.fits.HDUList`. Nr½r¾cs„|dkr dSdˆdjˆ›|d›<|dfˆdjˆ›|d›d<t|jjƒdfˆdjˆ›|d›d<xjt|jjƒD]Z}dd d d œ |d |d ›d ¡}|d d|›dfˆdjˆ›|d›d|d d›<qvWtj|jdd}|j}|j ddf|d<|j d df|d<|j ddf|d<|j d df|d<|j ddf|d<|j d df|d<t ˆdjˆ›|d›dƒ|_ ˆ |¡dS)N)ÚLOOKUPz!Detector to image correction typerrÀz$Version number of WCSDVARR extensionz.EXTVERz0Number of independent variables in D2IM functionz.NAXESÚ1stÚ2ndÚ3rd)rr)r¬rÚthzAxis number of the z variable in a D2IM functionz.AXIS.rÁ)Únamez!Coordinate system reference pixelrÂrÃz*Coordinate system value at reference pixelrÄrÅzCoordinate increment along axisrÆrÇ)rXÚlenr+Úshaper©r,rrÚImageHDUrárârãÚintÚverrm)Únumr‹r¢Újthr9rX)rÎr`r2r6r7Ú write_d2is0&"8       z$WCS._write_det2im..write_d2irr))r“r”)rLr2rñr6)rÎr`r2r7Ú _write_det2imts! zWCS._write_det2imr_cCst|ttfƒrdS|dkr$d}d}nd}d}i}xÂtd|jdƒD]¬}|t|ƒ} | |krn|| } || =nd} | |kr„d ||<qD|t|ƒ} | |krê||  ¡} || =| d krÜt|tjƒsÊtd ƒ‚|t|ƒ  ¡} | d }||krú||}||=nd}| d |d›}|||kr,|d|fj }n|d|fj   ¡}||=|d|fj }|  dd¡|  dd¡f}|  dd¡|  dd¡f}|  dd¡|  dd¡f}t||||ƒ}|||<x6t|ƒD]}| | d¡rº||=qºWn t dt¡qDd ||<qDW|sdS|  d¡|  d¡fSd S)zÿ Reads `distortion paper`_ table-lookup keywords and data, and returns a 2-tuple of `~astropy.wcs.DistortionLookupTable` objects. If no `distortion paper`_ keywords are found, ``(None, None)`` is returned. )NNr_ÚDPZCPERRÚDQZCQERRrgNr¿zCan astropy.io.fits.HDUList is required for Lookup table distortion.z.EXTVERz.AXIS.rÀÚWCSDVARRrÂrÃrÄrÅrÆgð?rÇr%z*Polynomial distortion is not implemented. r))rerfrgr©r[r<rrvr/rÊr+rËrXrrr…rÌrHrIr )rLrXr‡r`r^rÎrÏrÐr¢Z d_error_keyrÑrÒrÓrÔrÕrÖr×rØrÙrÚrÛrÜrÝrYr6r6r7r|£sh           zWCS._read_distortion_kwcsV|jdkr|jdkrdSˆdkr&d‰nd‰‡‡‡fdd„}|d|jƒ|d|jƒdS) zi Write out `distortion paper`_ keywords to the given `~astropy.io.fits.HDUList`. Nr_rórôcs’|dkr dSdˆdjˆ›|d›<|dfˆdjˆ›|d›d<t|jjƒdˆ›dfˆdjˆ›|d›d<xpt|jjƒD]`}d d d d œ |d |d ›d¡}|d d|›dˆ›dfˆdjˆ›|d›d|d d›<q~Wtj|jdd}|j}|j ddf|d<|j d df|d<|j ddf|d<|j d df|d<|j ddf|d<|j d df|d<t ˆdjˆ›|d›dƒ|_ ˆ |¡dS)N)räzPrior distortion function typerrÀz$Version number of WCSDVARR extensionz.EXTVERz#Number of independent variables in z functionz.NAXESrårærç)rr)r¬rrèzAxis number of the z variable in a z.AXIS.rõ)réz!Coordinate system reference pixelrÂrÃz*Coordinate system value at reference pixelrÄrÅzCoordinate increment along axisrÆrÇ)rXrêr+rër©r,rrrìrárârãrírîrm)rïrŒr¢rðr9rX)rÎr`r2r6r7Ú write_distús&."8 z,WCS._write_distortion_kw..write_distrr))r‘r’)rLr2r`rör6)rÎr`r2r7Ú_write_distortion_kwís zWCS._write_distortion_kwcCs2x,tdd„ttjt|ƒƒDƒƒD] }||=q WdS)z7 Remove SIP information from a header. css|]}|dk r| ¡VqdS)N)Úgroup)r¡Úmr6r6r7ú sz%WCS._remove_sip_kw..N)r…ÚmapÚSIP_KWÚmatchrK)rLrXrYr6r6r7rys$zWCS._remove_sip_kwcsætˆttfƒrdSdˆkrªˆddkrªdˆkr:tdƒ‚tˆdƒ}t |d|dftj¡}x\t|dƒD]L}xFt||dƒD]2}d|›d|›}|ˆkr„ˆ||||f<ˆ|=q„WqnWtˆdƒ}|dkrRt |d|dftj¡}xjt|dƒD]P}xJt||dƒD]6}d|›d|›}|ˆkrˆ||||f<ˆ|=qWqüWnd}d}ˆd=ˆd=‡‡fd d „td|j dƒDƒ} t d d „| DƒƒrÔd } t   | ¡n*dˆkr̈ddkrÌtdƒ‚nd}d}dˆkr4ˆddkr4dˆkrþtdƒ‚tˆdƒ}t |d|dftj¡} xbt|dƒD]R}xJt||dƒD]6}d|›d|›}|ˆkrHˆ|| ||f<ˆ|=qHWq2Wtˆdƒ}|dkrt |d|dftj¡} xlt|dƒD]R}xJt||dƒD]6}d|›d|›}|ˆkr܈|| ||f<ˆ|=qÜWqÆWnd} d} ˆd=ˆd=n*dˆkrVˆddkrVtdƒ‚nd} d} |dkrŠ|dkrŠ| dkrŠ| dkrŠdSdˆ›ˆksªdˆ›ˆkr²tdƒ‚ˆ  dˆ›¡} ˆ  dˆ›¡}t||| | | |fƒS)z¦ Reads `SIP`_ header keywords and returns a `~astropy.wcs.Sip` object. If no `SIP`_ header keywords are found, ``None`` is returned. NZA_ORDERrZB_ORDERzIA_ORDER provided without corresponding B_ORDER keyword for SIP distortionZA_Ú_ZB_csg|]}ˆd|›ˆ›‘qS)ÚCTYPEr6)r¡Znax)rXrar6r7r£Nsz$WCS._read_sip_kw..css|]}| d¡ VqdS)z-SIPN)Úendswith)r¡Úctypr6r6r7rúOsz#WCS._read_sip_kw..a» Inconsistent SIP distortion information is present in the FITS header and the WCS object: SIP coefficients were detected, but CTYPE is missing a "-SIP" suffix. astropy.wcs is using the SIP distortion coefficients, therefore the coordinates calculated here might be incorrect. If you do not want to apply the SIP distortion coefficients, please remove the SIP coefficients from the FITS header or the WCS object. As an example, if the image is already distortion-corrected (e.g., drizzled) then distortion components should not apply and the SIP coefficients should be removed. While the SIP distortion coefficients are being applied here, if that was indeed the intent, for consistency please append "-SIP" to the CTYPE in the FITS header or the WCS object. zIB_ORDER provided without corresponding A_ORDER keyword for SIP distortionZAP_ORDERZBP_ORDERzKAP_ORDER provided without corresponding BP_ORDER keyword for SIP distortionZAP_ZBP_zKBP_ORDER provided without corresponding AP_ORDER keyword for SIP distortionrÂrÃz.Header has SIP keywords without CRPIX keywords)rerfrgr/rír0Úzerosr1r©r[ÚanyrÚinforr)rLrXrarùÚar¢r´rYÚbÚctypeÚmessageÚapÚbpZcrpix1Zcrpix2r6)rXrar7r}$s”            ( zWCS._read_sip_kwcsZ|jdkriSi‰‡fdd„}|d|jjƒ|d|jjƒ|d|jjƒ|d|jjƒˆS)z[ Write out SIP keywords. Returns a dictionary of key-value pairs. Nc sÄ|dkr dS|jd}|ddkr&dnd}d t|dƒtdƒ|¡}|d|fˆ|›d <d }x^t|ƒD]R}xLt||ƒD]<}|||fd kr||||f|fˆ|›d |d ›d |d ›<q|WqjWdS)Nrr;ÚPzsky to detectorzdetector to skyz%SIP polynomial order, axis {:d}, {:s}ÚArZ_ORDERzSIP distortion coefficientgrþrÀ)rërJÚordr©)rérr.ZtrdirÚcommentr¢r´)Úkeywordsr6r7Ú write_array¥s z&WCS._write_sip_kw..write_arrayr ÚBZAPZBP)rrrr r )rLrr6)rr7Ú _write_sip_kw›s  zWCS._write_sip_kwcCs|jjdkrtdƒ‚|jjdkr(tdƒ‚|jjdkrˆ|jjdkrP|jjdkrP|S|jjdkr~|jjdkr~|dd…ddd…fStd ƒ‚n||jjdks |jjdkr¨td ƒ‚t |j d|jjf¡}|dd…df|dd…|jjf<|dd…df|dd…|jjf<|SdS) NÚRAz[WCS does not have longitude type of 'RA', therefore (ra, dec) data can not be used as inputÚDECz\WCS does not have longitude type of 'DEC', therefore (ra, dec) data can not be used as inputr)rrr;zjWCS does not have longitude and latitude celestial axes, therefore (ra, dec) data can not be used as inputzoWCS does not have both longitude and latitude celestial axes, therefore (ra, dec) data can not be used as input) r„Úlngtypr/Úlattypr[ÚlngÚlatr0rrë)rLÚskyÚoutr6r6r7Ú_denormalize_sky¼s(     zWCS._denormalize_skycCs|jjdkrtdƒ‚|jjdkr(tdƒ‚|jjdkrˆ|jjdkrP|jjdkrP|S|jjdkr~|jjdkr~|dd…ddd…fStd ƒ‚nx|jjdks |jjdkr¨td ƒ‚t |j ddf¡}|dd…|jjf|dd…df<|dd…|jjf|dd…df<|SdS) NrzVWCS does not have longitude type of 'RA', therefore (ra, dec) data can not be returnedrzWWCS does not have longitude type of 'DEC', therefore (ra, dec) data can not be returnedr)rrr;zeWCS does not have longitude and latitude celestial axes, therefore (ra, dec) data can not be returnedzjWCS does not have both longitude and latitude celestial axes, therefore (ra, dec) data can not be returned) r„rr/rr[rrr0Úemptyrë)rLrrr6r6r7Ú_normalize_skyÚs(     zWCS._normalize_skyF)Ú ra_dec_orderc s0‡‡‡‡fdd„}‡‡‡‡fdd„}t|ƒdkr¢y|\}}t |¡}t|ƒ}Wn$tk rrtd ˆj¡ƒ‚YnX|jdksŒt|jƒdkr˜||g|ƒS|||ƒSt|ƒˆjdkr|d d …} |d }yd d „| Dƒ} t|ƒ}Wntk rtd ƒ‚YnX|| |ƒStd ˆjˆjdt|ƒ¡ƒ‚d S)zm A helper function to support reading either a pair of arrays or a single Nx2 array. csâtdd„ˆDƒƒrˆSytjˆŽ‰Wntk r@tdƒ‚YnXt dd„ˆDƒ¡}ˆrlˆdkrlˆ |¡}ˆ||ƒ‰ˆrĈdkrĈ ˆ¡‰ˆdd…df ˆdj¡ˆdd…df ˆdj¡fS‡‡fd d„t ˆjdƒDƒS) NcSsg|]}|jdk‘qS)r)r.)r¡Úxr6r6r7r£þszHWCS._array_converter.._return_list_of_arrays..z5Coordinate arrays are not broadcastable to each othercSsg|]}| |jdf¡‘qS)r)r-r.)r¡rr6r6r7r£sÚinputÚoutputrrcs(g|] }ˆdd…|f ˆdj¡‘qS)Nr)r-rë)r¡r¢)r«r!r6r7r£s) rr0Zbroadcast_arraysr/Zhstackrrr-rër©)r«ÚoriginÚxy)ÚfuncrrLr)r«r!r7Ú_return_list_of_arraysýs"       z4WCS._array_converter.._return_list_of_arrayscsh|jdˆjkr td ˆj¡ƒ‚d|jkr.|SˆrDˆdkrDˆ |¡}ˆ||ƒ}ˆrdˆdkrdˆ |¡}|S)Nr;z@When providing two arguments, the array must be of shape (N, {})rr r!)rër[r/rJrr)r#r"Úresult)r$rrLrr6r7Ú_return_single_arrays       z2WCS._array_converter.._return_single_arrayr)zBWhen providing two arguments, they must be (coords[N][{}], origin)r6rNr;cSsg|]}t |¡‘qSr6)r0r°)r¡rr6r6r7r£2sz(WCS._array_converter..zfWhen providing more than two arguments, they must be a 1-D array for each axis, followed by an origin.zÈWCS projection has {0} dimensions, so expected 2 (an Nx{0} array and the origin argument) or {1} arguments (the position in each dimension, and the origin argument). Instead, {2} arguments were given.) rêr0r°ríÚ ExceptionrqrJr[rë) rLr$rrrMr%r'r#r"r«r6)r$rrLrr7Ú_array_converter÷s6         zWCS._array_convertercOs|j|jdf|ž|ŽS)Nr!)r)Z_all_pix2world)rLrMrNr6r6r7r¹BszWCS.all_pix2worldaÞ Transforms pixel coordinates to world coordinates. Performs all of the following in series: - Detector to image plane correction (if present in the FITS file) - `SIP`_ distortion correction (if present in the FITS file) - `distortion paper`_ table-lookup correction (if present in the FITS file) - `wcslib`_ "core" WCS transformation Parameters ---------- {} For a transformation that is not two-dimensional, the two-argument form must be used. {} Returns ------- {} Notes ----- The order of the axes for the result is determined by the ``CTYPEia`` keywords in the FITS header, therefore it may not always be of the form (*ra*, *dec*). The `~astropy.wcs.Wcsprm.lat`, `~astropy.wcs.Wcsprm.lng`, `~astropy.wcs.Wcsprm.lattyp` and `~astropy.wcs.Wcsprm.lngtyp` members can be used to determine the order of the axes. Raises ------ MemoryError Memory allocation failed. SingularMatrixError Linear transformation matrix is singular. InconsistentAxisTypesError Inconsistent or unrecognized coordinate axis types. ValueError Invalid parameter value. ValueError Invalid coordinate transformation parameters. ValueError x- and y-coordinate arrays are not the same size. InvalidTransformError Invalid coordinate transformation parameters. InvalidTransformError Ill-conditioned coordinate transformation parameters. r[r'zsky coordinates, in degreescs.ˆjdkrtdƒ‚ˆj‡fdd„df|ž|ŽS)Nz#No basic WCS settings were created.csˆj ||¡dS)NÚworld)r„Zp2s)r#Úo)rLr6r7Úóz#WCS.wcs_pix2world..r!)r„r/r))rLrMrNr6)rLr7rº‰s   zWCS.wcs_pix2worlda« Transforms pixel coordinates to world coordinates by doing only the basic `wcslib`_ transformation. No `SIP`_ or `distortion paper`_ table lookup correction is applied. To perform distortion correction, see `~astropy.wcs.WCS.all_pix2world`, `~astropy.wcs.WCS.sip_pix2foc`, `~astropy.wcs.WCS.p4_pix2foc`, or `~astropy.wcs.WCS.pix2foc`. Parameters ---------- {} For a transformation that is not two-dimensional, the two-argument form must be used. {} Returns ------- {} Raises ------ MemoryError Memory allocation failed. SingularMatrixError Linear transformation matrix is singular. InconsistentAxisTypesError Inconsistent or unrecognized coordinate axis types. ValueError Invalid parameter value. ValueError Invalid coordinate transformation parameters. ValueError x- and y-coordinate arrays are not the same size. InvalidTransformError Invalid coordinate transformation parameters. InvalidTransformError Ill-conditioned coordinate transformation parameters. Notes ----- The order of the axes for the result is determined by the ``CTYPEia`` keywords in the FITS header, therefore it may not always be of the form (*ra*, *dec*). The `~astropy.wcs.Wcsprm.lat`, `~astropy.wcs.Wcsprm.lng`, `~astropy.wcs.Wcsprm.lattyp` and `~astropy.wcs.Wcsprm.lngtyp` members can be used to determine the order of the axes. zworld coordinates, in degreescCsÎ| ||¡}|js|S| ¡} | | |¡|} | | 8} tj| | dd} |  ¡} |d} d}d}d}t ¡d}t ¡d}tjddd|sŒxút | ¡| krŠ||krŠ| | |¡|} tj| | dd} |rx| | k}t  |¡rt| | k}t  ||@¡\}|j ddkrt| | k}t  |¡}| |}| ||8<|| |<t  ||@¡\}||}| || |<|d7}d }P| } | | 8} |d7}q’W|rº|dkr¾t  t  | ¡j dd¡\}||}xú|j ddkr¸||kr¸| | ||¡|}tjt |¡dd}| | ¡| |<|| |<|rt|| |k}t  |¡}||}||}| ||8<|| |<t  || k|@¡\}n(| ||8<|| |<t  || k¡\}||}||}|d7}qÀWtj t  | ¡ddtj t  |¡dd@}t  | | k| | k@|B¡\}|j ddkrd}||krRt  | | k| | k@|@¡\}|j ddkrVd}nd}tj||d|dk sx|dk rÊ|sÊ|dkrªtd  |¡| t | ¡||dd ‚n td  |¡| t | ¡|||d ‚| S) Nr)Zaxisr)ÚinvalidÚoverrc)r.r/rTzW'WCS.all_world2pix' failed to converge to the requested accuracy after {:d} iterations.)rArBrCrErDz'WCS.all_world2pix' failed to converge to the requested accuracy. After {:d} iterations, the solution is diverging at least for one input point.)Ú wcs_world2pixÚhas_distortionršÚpix2focr0ÚsumZgeterrZseterrZnanmaxrÚwhererëÚisfiniteÚallZsquarer!rJÚabs)rLr*r"Ú toleranceÚmaxiterÚadaptiveÚdetect_divergenceÚquietZpix0ZpixZdpixÚdnZdnprevZtol2ÚkÚindZinddivZ old_invalidZold_overrDZslowconvÚconvZiconvZdpixgoodZdpixnewZdnnewZiiconvZsubindr.r6r6r7Ú_all_world2pixÎs®R                zWCS._all_world2pixrBr8z4.3g-Cëâ6?é)r8r9r:r;r<cs8ˆjdkrtdƒ‚ˆj‡‡‡‡‡‡fdd„df|ž|ŽS)Nz#No basic WCS settings were created.csˆj|ˆˆˆˆˆdœŽS)N)r8r9r:r;r<)rA)rMrN)r:r;r9r<rLr8r6r7r,asz#WCS.all_world2pix..r )r„r/r))rLr8r9r:r;r<rMrNr6)r:r;r9r<rLr8r7Ú all_world2pixZs  zWCS.all_world2pixa09 all_world2pix(*arg, tolerance=1.0e-4, maxiter=20, adaptive=False, detect_divergence=True, quiet=False) Transforms world coordinates to pixel coordinates, using numerical iteration to invert the full forward transformation `~astropy.wcs.WCS.all_pix2world` with complete distortion model. Parameters ---------- {0} For a transformation that is not two-dimensional, the two-argument form must be used. {1} tolerance : float, optional (default = 1.0e-4) Tolerance of solution. Iteration terminates when the iterative solver estimates that the "true solution" is within this many pixels current estimate, more specifically, when the correction to the solution found during the previous iteration is smaller (in the sense of the L2 norm) than ``tolerance``. maxiter : int, optional (default = 20) Maximum number of iterations allowed to reach a solution. quiet : bool, optional (default = False) Do not throw :py:class:`NoConvergence` exceptions when the method does not converge to a solution with the required accuracy within a specified number of maximum iterations set by ``maxiter`` parameter. Instead, simply return the found solution. Other Parameters ---------------- adaptive : bool, optional (default = False) Specifies whether to adaptively select only points that did not converge to a solution within the required accuracy for the next iteration. Default is recommended for HST as well as most other instruments. .. note:: The :py:meth:`all_world2pix` uses a vectorized implementation of the method of consecutive approximations (see ``Notes`` section below) in which it iterates over *all* input points *regardless* until the required accuracy has been reached for *all* input points. In some cases it may be possible that *almost all* points have reached the required accuracy but there are only a few of input data points for which additional iterations may be needed (this depends mostly on the characteristics of the geometric distortions for a given instrument). In this situation it may be advantageous to set ``adaptive`` = `True` in which case :py:meth:`all_world2pix` will continue iterating *only* over the points that have not yet converged to the required accuracy. However, for the HST's ACS/WFC detector, which has the strongest distortions of all HST instruments, testing has shown that enabling this option would lead to a about 50-100% penalty in computational time (depending on specifics of the image, geometric distortions, and number of input points to be converted). Therefore, for HST and possibly instruments, it is recommended to set ``adaptive`` = `False`. The only danger in getting this setting wrong will be a performance penalty. .. note:: When ``detect_divergence`` is `True`, :py:meth:`all_world2pix` will automatically switch to the adaptive algorithm once divergence has been detected. detect_divergence : bool, optional (default = True) Specifies whether to perform a more detailed analysis of the convergence to a solution. Normally :py:meth:`all_world2pix` may not achieve the required accuracy if either the ``tolerance`` or ``maxiter`` arguments are too low. However, it may happen that for some geometric distortions the conditions of convergence for the the method of consecutive approximations used by :py:meth:`all_world2pix` may not be satisfied, in which case consecutive approximations to the solution will diverge regardless of the ``tolerance`` or ``maxiter`` settings. When ``detect_divergence`` is `False`, these divergent points will be detected as not having achieved the required accuracy (without further details). In addition, if ``adaptive`` is `False` then the algorithm will not know that the solution (for specific points) is diverging and will continue iterating and trying to "improve" diverging solutions. This may result in ``NaN`` or ``Inf`` values in the return results (in addition to a performance penalties). Even when ``detect_divergence`` is `False`, :py:meth:`all_world2pix`, at the end of the iterative process, will identify invalid results (``NaN`` or ``Inf``) as "diverging" solutions and will raise :py:class:`NoConvergence` unless the ``quiet`` parameter is set to `True`. When ``detect_divergence`` is `True`, :py:meth:`all_world2pix` will detect points for which current correction to the coordinates is larger than the correction applied during the previous iteration **if** the requested accuracy **has not yet been achieved**. In this case, if ``adaptive`` is `True`, these points will be excluded from further iterations and if ``adaptive`` is `False`, :py:meth:`all_world2pix` will automatically switch to the adaptive algorithm. Thus, the reported divergent solution will be the latest converging solution computed immediately *before* divergence has been detected. .. note:: When accuracy has been achieved, small increases in current corrections may be possible due to rounding errors (when ``adaptive`` is `False`) and such increases will be ignored. .. note:: Based on our testing using HST ACS/WFC images, setting ``detect_divergence`` to `True` will incur about 5-20% performance penalty with the larger penalty corresponding to ``adaptive`` set to `True`. Because the benefits of enabling this feature outweigh the small performance penalty, especially when ``adaptive`` = `False`, it is recommended to set ``detect_divergence`` to `True`, unless extensive testing of the distortion models for images from specific instruments show a good stability of the numerical method for a wide range of coordinates (even outside the image itself). .. note:: Indices of the diverging inverse solutions will be reported in the ``divergent`` attribute of the raised :py:class:`NoConvergence` exception object. Returns ------- {2} Notes ----- The order of the axes for the input world array is determined by the ``CTYPEia`` keywords in the FITS header, therefore it may not always be of the form (*ra*, *dec*). The `~astropy.wcs.Wcsprm.lat`, `~astropy.wcs.Wcsprm.lng`, `~astropy.wcs.Wcsprm.lattyp`, and `~astropy.wcs.Wcsprm.lngtyp` members can be used to determine the order of the axes. Using the method of fixed-point iterations approximations we iterate starting with the initial approximation, which is computed using the non-distortion-aware :py:meth:`wcs_world2pix` (or equivalent). The :py:meth:`all_world2pix` function uses a vectorized implementation of the method of consecutive approximations and therefore it is highly efficient (>30x) when *all* data points that need to be converted from sky coordinates to image coordinates are passed at *once*. Therefore, it is advisable, whenever possible, to pass as input a long array of all points that need to be converted to :py:meth:`all_world2pix` instead of calling :py:meth:`all_world2pix` for each data point. Also see the note to the ``adaptive`` parameter. Raises ------ NoConvergence The method did not converge to a solution to the required accuracy within a specified number of maximum iterations set by the ``maxiter`` parameter. To turn off this exception, set ``quiet`` to `True`. Indices of the points for which the requested accuracy was not achieved (if any) will be listed in the ``slow_conv`` attribute of the raised :py:class:`NoConvergence` exception object. See :py:class:`NoConvergence` documentation for more details. MemoryError Memory allocation failed. SingularMatrixError Linear transformation matrix is singular. InconsistentAxisTypesError Inconsistent or unrecognized coordinate axis types. ValueError Invalid parameter value. ValueError Invalid coordinate transformation parameters. ValueError x- and y-coordinate arrays are not the same size. InvalidTransformError Invalid coordinate transformation parameters. InvalidTransformError Ill-conditioned coordinate transformation parameters. Examples -------- >>> import astropy.io.fits as fits >>> import astropy.wcs as wcs >>> import numpy as np >>> import os >>> filename = os.path.join(wcs.__path__[0], 'tests/data/j94f05bgq_flt.fits') >>> hdulist = fits.open(filename) >>> w = wcs.WCS(hdulist[('sci',1)].header, hdulist) >>> hdulist.close() >>> ra, dec = w.all_pix2world([1,2,3], [1,1,1], 1) >>> print(ra) # doctest: +FLOAT_CMP [ 5.52645627 5.52649663 5.52653698] >>> print(dec) # doctest: +FLOAT_CMP [-72.05171757 -72.05171276 -72.05170795] >>> radec = w.all_pix2world([[1,1], [2,1], [3,1]], 1) >>> print(radec) # doctest: +FLOAT_CMP [[ 5.52645627 -72.05171757] [ 5.52649663 -72.05171276] [ 5.52653698 -72.05170795]] >>> x, y = w.all_world2pix(ra, dec, 1) >>> print(x) # doctest: +FLOAT_CMP [ 1.00000238 2.00000237 3.00000236] >>> print(y) # doctest: +FLOAT_CMP [ 0.99999996 0.99999997 0.99999997] >>> xy = w.all_world2pix(radec, 1) >>> print(xy) # doctest: +FLOAT_CMP [[ 1.00000238 0.99999996] [ 2.00000237 0.99999997] [ 3.00000236 0.99999997]] >>> xy = w.all_world2pix(radec, 1, maxiter=3, ... tolerance=1.0e-10, quiet=False) Traceback (most recent call last): ... NoConvergence: 'WCS.all_world2pix' failed to converge to the requested accuracy. After 3 iterations, the solution is diverging at least for one input point. >>> # Now try to use some diverging data: >>> divradec = w.all_pix2world([[1.0, 1.0], ... [10000.0, 50000.0], ... [3.0, 1.0]], 1) >>> print(divradec) # doctest: +FLOAT_CMP [[ 5.52645627 -72.05171757] [ 7.15976932 -70.8140779 ] [ 5.52653698 -72.05170795]] >>> # First, turn detect_divergence on: >>> try: # doctest: +FLOAT_CMP ... xy = w.all_world2pix(divradec, 1, maxiter=20, ... tolerance=1.0e-4, adaptive=False, ... detect_divergence=True, ... quiet=False) ... except wcs.wcs.NoConvergence as e: ... print("Indices of diverging points: {{0}}" ... .format(e.divergent)) ... print("Indices of poorly converging points: {{0}}" ... .format(e.slow_conv)) ... print("Best solution:\n{{0}}".format(e.best_solution)) ... print("Achieved accuracy:\n{{0}}".format(e.accuracy)) Indices of diverging points: [1] Indices of poorly converging points: None Best solution: [[ 1.00000238e+00 9.99999965e-01] [ -1.99441636e+06 1.44309097e+06] [ 3.00000236e+00 9.99999966e-01]] Achieved accuracy: [[ 6.13968380e-05 8.59638593e-07] [ 8.59526812e+11 6.61713548e+11] [ 6.09398446e-05 8.38759724e-07]] >>> raise e Traceback (most recent call last): ... NoConvergence: 'WCS.all_world2pix' failed to converge to the requested accuracy. After 5 iterations, the solution is diverging at least for one input point. >>> # This time turn detect_divergence off: >>> try: # doctest: +FLOAT_CMP ... xy = w.all_world2pix(divradec, 1, maxiter=20, ... tolerance=1.0e-4, adaptive=False, ... detect_divergence=False, ... quiet=False) ... except wcs.wcs.NoConvergence as e: ... print("Indices of diverging points: {{0}}" ... .format(e.divergent)) ... print("Indices of poorly converging points: {{0}}" ... .format(e.slow_conv)) ... print("Best solution:\n{{0}}".format(e.best_solution)) ... print("Achieved accuracy:\n{{0}}".format(e.accuracy)) Indices of diverging points: [1] Indices of poorly converging points: None Best solution: [[ 1.00000009 1. ] [ nan nan] [ 3.00000009 1. ]] Achieved accuracy: [[ 2.29417358e-06 3.21222995e-08] [ nan nan] [ 2.27407877e-06 3.13005639e-08]] >>> raise e Traceback (most recent call last): ... NoConvergence: 'WCS.all_world2pix' failed to converge to the requested accuracy. After 6 iterations, the solution is diverging at least for one input point. zpixel coordinatescs.ˆjdkrtdƒ‚ˆj‡fdd„df|ž|ŽS)Nz#No basic WCS settings were created.csˆj ||¡dS)NZpixcrd)r„Zs2p)r#r+)rLr6r7r,³r-z#WCS.wcs_world2pix..r )r„r/r))rLrMrNr6)rLr7r0¯s   zWCS.wcs_world2pixaô Transforms world coordinates to pixel coordinates, using only the basic `wcslib`_ WCS transformation. No `SIP`_ or `distortion paper`_ table lookup transformation is applied. Parameters ---------- {} For a transformation that is not two-dimensional, the two-argument form must be used. {} Returns ------- {} Notes ----- The order of the axes for the input world array is determined by the ``CTYPEia`` keywords in the FITS header, therefore it may not always be of the form (*ra*, *dec*). The `~astropy.wcs.Wcsprm.lat`, `~astropy.wcs.Wcsprm.lng`, `~astropy.wcs.Wcsprm.lattyp` and `~astropy.wcs.Wcsprm.lngtyp` members can be used to determine the order of the axes. Raises ------ MemoryError Memory allocation failed. SingularMatrixError Linear transformation matrix is singular. InconsistentAxisTypesError Inconsistent or unrecognized coordinate axis types. ValueError Invalid parameter value. ValueError Invalid coordinate transformation parameters. ValueError x- and y-coordinate arrays are not the same size. InvalidTransformError Invalid coordinate transformation parameters. InvalidTransformError Ill-conditioned coordinate transformation parameters. cGs|j|jdf|žŽS)N)r)Z_pix2foc)rLrMr6r6r7r2îsz WCS.pix2foca Convert pixel coordinates to focal plane coordinates using the `SIP`_ polynomial distortion convention and `distortion paper`_ table-lookup correction. The output is in absolute pixel coordinates, not relative to ``CRPIX``. Parameters ---------- {} Returns ------- {} Raises ------ MemoryError Memory allocation failed. ValueError Invalid coordinate transformation parameters. Ú2zfocal coordinatescGs|j|jdf|žŽS)N)r)Z _p4_pix2foc)rLrMr6r6r7Ú p4_pix2foc szWCS.p4_pix2focaá Convert pixel coordinates to focal plane coordinates using `distortion paper`_ table-lookup correction. The output is in absolute pixel coordinates, not relative to ``CRPIX``. Parameters ---------- {} Returns ------- {} Raises ------ MemoryError Memory allocation failed. ValueError Invalid coordinate transformation parameters. cGs|j|jdf|žŽS)N)r)Z_det2im)rLrMr6r6r7r‹) sz WCS.det2imaä Convert detector coordinates to image plane coordinates using `distortion paper`_ table-lookup correction. The output is in absolute pixel coordinates, not relative to ``CRPIX``. Parameters ---------- {} Returns ------- {} Raises ------ MemoryError Memory allocation failed. ValueError Invalid coordinate transformation parameters. cGsT|jdkr>t|ƒdkr|dSt|ƒdkr6|dd…Stdƒ‚|j|jjdf|žŽS)Nr)rr¬zWrong number of arguments)rrêrqr)r2)rLrMr6r6r7Ú sip_pix2focF s    zWCS.sip_pix2focaû Convert pixel coordinates to focal plane coordinates using the `SIP`_ polynomial distortion convention. The output is in pixel coordinates, relative to ``CRPIX``. FITS WCS `distortion paper`_ table lookup correction is not applied, even if that information existed in the FITS file that initialized this :class:`~astropy.wcs.WCS` object. To correct for that, use `~astropy.wcs.WCS.pix2foc` or `~astropy.wcs.WCS.p4_pix2foc`. Parameters ---------- {} Returns ------- {} Raises ------ MemoryError Memory allocation failed. ValueError Invalid coordinate transformation parameters. cGsT|jdkr>t|ƒdkr|dSt|ƒdkr6|dd…Stdƒ‚|j|jjdf|žŽS)Nr)rr¬zWrong number of arguments)rrêrqr)Zfoc2pix)rLrMr6r6r7Ú sip_foc2pixo s    zWCS.sip_foc2pixaT Convert focal plane coordinates to pixel coordinates using the `SIP`_ polynomial distortion convention. FITS WCS `distortion paper`_ table lookup distortion correction is not applied, even if that information existed in the FITS file that initialized this `~astropy.wcs.WCS` object. Parameters ---------- {} Returns ------- {} Raises ------ MemoryError Memory allocation failed. ValueError Invalid coordinate transformation parameters. cCs:ddlm}||ƒ}dd„|jjDƒ}dd„t||ƒDƒS)ad Calculate pixel scales along each axis of the image pixel at the ``CRPIX`` location once it is projected onto the "plane of intermediate world coordinates" as defined in `Greisen & Calabretta 2002, A&A, 395, 1061 `_. .. note:: This method is concerned **only** about the transformation "image plane"->"projection plane" and **not** about the transformation "celestial sphere"->"projection plane"->"image plane". Therefore, this function ignores distortions arising due to non-linear nature of most projections. .. note:: This method only returns sensible answers if the WCS contains celestial axes, i.e., the `~astropy.wcs.WCS.celestial` WCS object. Returns ------- scale : list of `~astropy.units.Quantity` A vector of projection plane increments corresponding to each pixel side (axis). See Also -------- astropy.wcs.utils.proj_plane_pixel_scales r)Úproj_plane_pixel_scalescSsg|]}t |¡‘qSr6)ÚuÚUnit)r¡rr6r6r7r£³ sz/WCS.proj_plane_pixel_scales..cSsg|]\}}||‘qSr6r6)r¡ÚvalueÚunitr6r6r7r£´ s)Úastropy.wcs.utilsrHr„ÚcunitÚzip)rLrHÚvaluesrr6r6r7rH” s zWCS.proj_plane_pixel_scalescCs@ddlm}||ƒ}t |jjd¡t |jjd¡}||S)ag For a **celestial** WCS (see `astropy.wcs.WCS.celestial`), returns pixel area of the image pixel at the ``CRPIX`` location once it is projected onto the "plane of intermediate world coordinates" as defined in `Greisen & Calabretta 2002, A&A, 395, 1061 `_. .. note:: This function is concerned **only** about the transformation "image plane"->"projection plane" and **not** about the transformation "celestial sphere"->"projection plane"->"image plane". Therefore, this function ignores distortions arising due to non-linear nature of most projections. .. note:: This method only returns sensible answers if the WCS contains celestial axes, i.e., the `~astropy.wcs.WCS.celestial` WCS object. Returns ------- area : `~astropy.units.Quantity` Area (in the projection plane) of the pixel at ``CRPIX`` location. Raises ------ ValueError Pixel area is defined only for 2D pixels. Most likely the `~astropy.wcs.Wcsprm.cd` matrix of the `~astropy.wcs.WCS.celestial` WCS is not a square matrix of second order. Notes ----- Depending on the application, square root of the pixel area can be used to represent a single pixel scale of an equivalent square pixel whose area is equal to the area of a generally non-square pixel. See Also -------- astropy.wcs.utils.proj_plane_pixel_area r)Úproj_plane_pixel_arear)rMrQrIrJr„rN)rLrQrKrLr6r6r7rQ¶ s* $zWCS.proj_plane_pixel_areacCs<|j||d}tj|d}t |¡}| |¡| |¡|S)a Generate an `~astropy.io.fits.HDUList` object with all of the information stored in this object. This should be logically identical to the input FITS file, but it will be normalized in a number of ways. See `to_header` for some warnings about the output produced. Parameters ---------- relax : bool or int, optional Degree of permissiveness: - `False` (default): Write all extensions that are considered to be safe and recommended. - `True`: Write all recognized informal extensions of the WCS standard. - `int`: a bit field selecting specific extensions to write. See :ref:`relaxwrite` for details. key : str The name of a particular WCS transform to use. This may be either ``' '`` or ``'A'``-``'Z'`` and corresponds to the ``"a"`` part of the ``CTYPEia`` cards. Returns ------- hdulist : `~astropy.io.fits.HDUList` )rZrY)rX)Ú to_headerrZ PrimaryHDUrvròr÷)rLrZrYrXrnr2r6r6r7Úto_fitså s !    z WCS.to_fitscCsät}d}|dkrd}d}|dkr4|t@}|tM}n|}|dkrDtnt}||B}|jdk r”|dk rt|jj}||j_|j |¡}tj  |¡}dddg} x| D]} | |krœ|| =qœWt t dƒd t t d ƒd kr x¼|  ¡D]<\} } | dd …d krÞ| dkrÞt  d| ›dtj›dt¡qÞWnrt t dƒd t t d ƒdkrœxX|  ¡D]B\} } | dd …d krL| dkrLt  d| ›dtj›dt¡qLWnt ¡}|r|jdk r|jdk ràtdd„|jjDƒƒrà|j|ddx"| ¡  ¡D]\} } | || <qîW|s>|jdk r>t|jjƒr>|jdk r>|j|dd}|rÎ|jd|d} g} x*|   ¡D]\} } | |kr`|  | ¡q`Wt| ƒr¤t  d d | ¡¡t¡t|jjƒrÎ|jdk rÎ|j|ddd}|dk rà||j_|S)aà Generate an `astropy.io.fits.Header` object with the basic WCS and SIP information stored in this object. This should be logically identical to the input FITS file, but it will be normalized in a number of ways. .. warning:: This function does not write out FITS WCS `distortion paper`_ information, since that requires multiple FITS header data units. To get a full representation of everything in this object, use `to_fits`. Parameters ---------- relax : bool or int, optional Degree of permissiveness: - `False` (default): Write all extensions that are considered to be safe and recommended. - `True`: Write all recognized informal extensions of the WCS standard. - `int`: a bit field selecting specific extensions to write. See :ref:`relaxwrite` for details. If the ``relax`` keyword argument is not given and any keywords were omitted from the output, an `~astropy.utils.exceptions.AstropyWarning` is displayed. To override this, explicitly pass a value to ``relax``. key : str The name of a particular WCS transform to use. This may be either ``' '`` or ``'A'``-``'Z'`` and corresponds to the ``"a"`` part of the ``CTYPEia`` cards. Returns ------- header : `astropy.io.fits.Header` Notes ----- The output header will almost certainly differ from the input in a number of respects: 1. The output header only contains WCS-related keywords. In particular, it does not contain syntactically-required keywords such as ``SIMPLE``, ``NAXIS``, ``BITPIX``, or ``END``. 2. Deprecated (e.g. ``CROTAn``) or non-standard usage will be translated to standard (this is partially dependent on whether ``fix`` was applied). 3. Quantities will be converted to the units used internally, basically SI with the addition of degrees. 4. Floating-point quantities may be given to a different decimal precision. 5. Elements of the ``PCi_j`` matrix will be written if and only if they differ from the unit matrix. Thus, if the matrix is unity then no elements will be written. 6. Additional keywords such as ``WCSAXES``, ``CUNITia``, ``LONPOLEa`` and ``LATPOLEa`` may appear. 7. The original keycomments will be lost, although `to_header` tries hard to write meaningful comments. 8. Keyword order may be changed. FNT)TFrWrUÚCOMMENTré réGr&)r_ZCQDISZTPDz'WCS contains a TPD distortion model in z . WCSLIB zq is writing this in a format incompatible with current versions - please update to 7.4 or use the bundled WCSLIB.éJzG, which requires WCSLIB 7.4 or later to store in a FITS header (having z).css|]}| d¡ VqdS)z-SIPN)r)r¡rr6r6r7rúˆ sz WCS.to_header..)Úadd_sip)rZrYzYSome non-standard WCS keywords were excluded: {} Use the ``relax`` kwarg to control this.z, )rXÚ log_message)Z WCSHDO_P14Ú WCSHDO_SIPZ WCSHDO_allZ WCSHDO_safer„ÚaltrRrrorxríÚ_parsed_versionr›rHrIrÚ __version__r rrrÚ _fix_ctyperrmrêrJÚjoin)rLrZrYÚ precisionZdisplay_warningZdo_sipÚorig_keyrŽrXZkeys_to_removeÚkwrZ full_headerZ missing_keysr6r6r7rR srK       " "$,    z WCS.to_headercCs„d}|r|rt |¡xhtd|jdƒD]T}d|›|jj› ¡}||kr(|rb|| d¡d}n|| d¡}|||<q(q(q(W|S)a… Parameters ---------- header : `~astropy.io.fits.Header` FITS header. add_sip : bool Flag indicating whether "-SIP" should be added or removed from CTYPE keywords. Remove "-SIP" from CTYPE when writing out a header with relax=False. This needs to be done outside ``to_header`` because ``to_header`` runs twice when ``relax=False`` and the second time ``relax`` is set to ``True`` to display the missing keywords. If the user requested SIP distortion to be written out add "-SIP" to CTYPE if it is missing. a# Inconsistent SIP distortion information is present in the current WCS: SIP coefficients were detected, but CTYPE is missing "-SIP" suffix, therefore the current WCS is internally inconsistent. Because relax has been set to True, the resulting output WCS will have "-SIP" appended to CTYPE in order to make the header internally consistent. However, this may produce incorrect astrometry in the output WCS, if in fact the current WCS is already distortion-corrected. Therefore, if current WCS is already distortion-corrected (eg, drizzled) then SIP distortion components should not apply. In that case, for a WCS that is already distortion-corrected, please remove the SIP coefficients from the header. rrÿz-SIP)rrr©r[r„r[rÊ)rLrXrXrYZ_add_sip_to_ctyper¢rbrr6r6r7r^© s"  zWCS._fix_ctypecCst| |¡ƒS)ze Identical to `to_header`, but returns a string containing the header cards. )rfrR)rLrZr6r6r7Úto_header_stringÜ szWCS.to_header_stringú footprint.regÚgreenr)c Csžd}|p|jj}|dkr&td |¡ƒ‚t|ddb}| |¡| |›d¡| d¡| ¡}|dk r|j|d d | d |›d |d ›d¡WdQRXdS)aj Writes out a `ds9`_ style regions file. It can be loaded directly by `ds9`_. Parameters ---------- filename : str, optional Output file name - default is ``'footprint.reg'`` color : str, optional Color to use when plotting the line. width : int, optional Width of the region line. coordsys : str, optional Coordinate system. If not specified (default), the ``radesys`` value is used. For all possible values, see http://ds9.si.edu/doc/ref/region.html#RegionFileFormat z˜# Region file format: DS9 version 4.0 # global color=green font="helvetica 12 bold select=1 highlite=1 edit=1 move=1 delete=1 include=1 fixed=0 source ) ZPHYSICALZIMAGEZFK4ZB1950ZFK5ZJ2000ZGALACTICZECLIPTICZICRSZLINEARZ AMPLIFIERZDETECTORz_Coordinate system '{}' is not supported. A valid one can be given with the 'coordsys' argument.Úw)ÚmodeÚ zpolygon(Nú,)Úsepz ) # color=z, width=rÀz )r„Zradesysr/rJrlÚwriter¼Útofile)rLÚfilenameÚcolorÚwidthZcoordsysÚcommentsÚfZftprr6r6r7Úfootprint_to_fileã s   zWCS.footprint_to_filec Cs”g}|dk r^t|ttfƒs^xBt d¡D]4}y| |d|›¡Wq&tk rXPYq&Xq&Wt|ƒdkrtddg}nt|ƒdkrŠ| d¡||_dS)Nrrbr) rerfrgÚ itertoolsÚcountrmrÉrêÚ_naxis)rLrXrur[r6r6r7r€ s     zWCS._get_naxiscCstt|ƒƒdS)N)ÚprintÚrepr)rLr6r6r7Úprintwcs sz WCS.printwcsc CsÈdd|j›g}dd dd„t|jƒDƒ¡}ddd g}|jj|jj|jjg}x*t||ƒD]\}}| ||j |Ž¡qZWt |jd ƒrxrt|jƒD]d}d}x:t|jƒD],} |d d t |d ƒd t | d ƒdg¡7}q¨W||7}| |j |jj |Ž¡q”Wd|}| |j |jj Ž¡n†t |jdƒr xvt|jƒD]h}d}x.rÿrßrÞÚpcÚPCrrþrUràÚcdZCDzNAXIS : z rh)r[r_r©r„rrârárOrmrJÚhasattrrfrzrãr|rûru) rLÚ descriptionZsfmtrrPÚkeywordrKr¢Úsr´r6r6r7Ú__repr__# s2 ,.z WCS.__repr__c Cs®|jdkrtdƒ‚dddddœ}ddd d d d d œ}g}xr|jjD]f}i}|dd}|||d<|dd}|||d<|dd}||d<|d} | |d<| |¡q@W|S)aå Similar to `self.wcsprm.axis_types ` but provides the information in a more Python-friendly format. Returns ------- result : list of dict Returns a list of dictionaries, one for each axis, each containing attributes about the type of that axis. Each dictionary has the following keys: - 'coordinate_type': - None: Non-specific coordinate type. - 'stokes': Stokes coordinate. - 'celestial': Celestial coordinate (including ``CUBEFACE``). - 'spectral': Spectral coordinate. - 'scale': - 'linear': Linear axis. - 'quantized': Quantized axis (``STOKES``, ``CUBEFACE``). - 'non-linear celestial': Non-linear celestial axis. - 'non-linear spectral': Non-linear spectral axis. - 'logarithmic': Logarithmic axis. - 'tabular': Tabular axis. - 'group' - Group number, e.g. lookup table number - 'number' - For celestial axes: - 0: Longitude coordinate. - 1: Latitude coordinate. - 2: ``CUBEFACE`` number. - For lookup tables: - the axis number in a multidimensional table. ``CTYPEia`` in ``"4-3"`` form with unrecognized algorithm code will generate an error. Nz.This WCS object does not have a wcsprm object.ZstokesÚ celestialÚspectral)rrr)r¬ZlinearZ quantizedznon-linear celestialznon-linear spectralZ logarithmicZtabular)rrr)r¬ér&ièrUÚcoordinate_typeédÚscalerøÚnumber)r„r·Z axis_typesrm) rLZcoordinate_type_mapZ scale_mapr&Z axis_typeÚ subresultr…r‡rørˆr6r6r7Úget_axis_typesE s4;      zWCS.get_axis_typescCs4|jdd}t ¡}| |¡t|j|j| ¡ffS)z Support pickling of WCS objects. This is done by serializing to an in-memory FITS file and dumping that as a string. T)rZ)rSÚioÚBytesIOZwritetoÚ__WCS_unpickle__rOr•Úgetvalue)rLr2Úbufferr6r6r7Ú __reduce__¦ s   zWCS.__reduce__cCs.tt|jjƒƒ}| |¡| dd„|Dƒ¡S)a¶ Remove an axis from the WCS. Parameters ---------- wcs : `~astropy.wcs.WCS` The WCS with naxis to be chopped to naxis-1 dropax : int The index of the WCS to drop, counting from 0 (i.e., python convention, not FITS convention) Returns ------- `~astropy.wcs.WCS` A new `~astropy.wcs.WCS` instance with one axis fewer cSsg|] }|d‘qS)rr6)r¡r¢r6r6r7r£Ë sz WCS.dropaxis..)rKr©r„r[Úpoprz)rLZdropaxÚindsr6r6r7Údropaxis´ s z WCS.dropaxiscCs>tt|jjƒƒ}||||||<||<| dd„|Dƒ¡S)aß Swap axes in a WCS. Parameters ---------- wcs : `~astropy.wcs.WCS` The WCS to have its axes swapped ax0 : int ax1 : int The indices of the WCS to be swapped, counting from 0 (i.e., python convention, not FITS convention) Returns ------- `~astropy.wcs.WCS` A new `~astropy.wcs.WCS` instance with the same number of axes, but two swapped cSsg|] }|d‘qS)rr6)r¡r¢r6r6r7r£ã sz WCS.swapaxes..)rKr©r„r[rz)rLZax0Zax1r’r6r6r7ÚswapaxesÍ sz WCS.swapaxescCs| tttg¡S)z¾ Reorient the WCS such that the celestial axes are first, followed by the spectral axis, followed by any others. Assumes at least celestial axes are present. )rzÚWCSSUB_CELESTIALÚWCSSUB_SPECTRALZ WCSSUB_STOKES)rLr6r6r7Úreorient_celestial_firstå szWCS.reorient_celestial_firstc CsBt|dƒr$t|ƒ|jjkr$tdƒ‚nt|dƒs4|g}tdd„|DƒƒsPt||ƒS| ¡}|jdk rn|jj   ¡}xžt |ƒD]\}}|j dk r |j dkr t dƒ‚|r¶|jjd|}n|}|j dk rÞ|jdkrÞtd|j|j ƒ}|jdk rœ|j d krh|jj |}|jj|} ||jd |j d d |j d } | |jj |<|jdk rT| ||<| |j |jj|<n4|jj ||j8<|jdk rœ|||j8<ytt |j|¡|ƒ} WnHtk r} z(d t| ƒkrÜ‚t d ||¡t¡Wdd} ~ XYqzX| |j|<qzW|jdk r>t|jj|jj|jj|jj|ƒ|_|S)ao Slice a WCS instance using a Numpy slice. The order of the slice should be reversed (as for the data) compared to the natural WCS order. Parameters ---------- view : tuple A tuple containing the same number of slices as the WCS system. The ``step`` method, the third argument to a slice, is not presently supported. numpy_order : bool Use numpy order, i.e. slice the WCS so that an identical slice applied to a numpy array will slice the array and WCS in the same way. If set to `False`, the WCS will be sliced in FITS order, meaning the first slice will be applied to the *last* numpy index but the *first* WCS axis. Returns ------- wcs_new : `~astropy.wcs.WCS` A new resampled WCS axis Ú__len__z&Must have # of slices <= # of WCS axescss|]}t|tƒVqdS)N)reÚslice)r¡rr6r6r7rú szWCS.slice..Nrz%Reversing an axis is not implemented.r)Nrgð?gà?g@zindices must be integerszQNAXIS{} attribute is not updated because at least one index ('{}') is no integer.) r}rêr„r[r/r6rr™rráÚtolistÚ enumerateÚstepÚNotImplementedErrorÚstartr™ÚstoprãÚbuiltinsr©rurqrfrHrIrJr rrrr r ) rLÚviewZ numpy_orderZwcs_newZ sip_crpixr¢ZiviewZ wcs_indexrárãZcrpZnitemsÚexcr6r6r7r™í sR         &    z WCS.slicecCs | |¡S)N)r™)rLÚitemr6r6r7Ú __getitem__M szWCS.__getitem__cCstd|jj›dƒ‚dS)Nú'z' object is not iterable)rqrOrP)rLr6r6r7Ú__iter__T sz WCS.__iter__cCsVt|jjƒ}|jj}xrZwcsprmsr&rŠr‰r6r6r7rÖ s*;        c CsŽGdd„dtƒ}Gdd„dtƒ}Gdd„dtƒ}t|tjƒrB|}n t |¡}|ƒ}x4t|ƒD]&\}}|||jƒ}| |¡tj dd} t |j t j d d d } Wd QRXxÚ| D]Ò} || jjƒ} | | ¡ybWntk räYnXtj ddŠ} t ¡tjd tdd y$t|j | jjp dt j dd dWn2tk rb} z|  t| ƒ¡Wd d } ~ XYnX|  dd„| Dƒ¡Wd QRXq°Wq^W|S)a Prints a WCS validation report for the given FITS file. Parameters ---------- source : str or file-like or `~astropy.io.fits.HDUList` The FITS file to validate. Returns ------- results : list subclass instance The result is returned as nested lists. The first level corresponds to the HDUs in the given file. The next level has an entry for each WCS found in that header. The special subclass of list will pretty-print the results as a table when printed. c@seZdZdd„Zdd„ZdS)z'validate.._WcsValidateWcsResultcSs ||_dS)N)Ú_key)rLrYr6r6r7rGE sz0validate.._WcsValidateWcsResult.__init__c Ss‚d|jp d›dg}t|ƒrnxZ|D]F}x@t| ¡ƒD]0\}}|dkrJd}nd}| tj||dd¡q4Wq"Wn | d¡d  |¡S) Nz WCS key 'rUz':rz - z )Úinitial_indentÚsubsequent_indentz No issues.rh) rºrêr›Ú splitlinesÚextendÚtextwrapÚwraprmr_)rLr&Úentryr¢Úliner»r6r6r7rH s  z0validate.._WcsValidateWcsResult.__repr__N)rPrQrRrGrr6r6r6r7Ú_WcsValidateWcsResultD srÃc@seZdZdd„Zdd„ZdS)z'validate.._WcsValidateHduResultcSs||_||_t |¡dS)N)Ú _hdu_indexÚ _hdu_namerKrG)rLZ hdu_indexÚhdu_namer6r6r7rG[ sz0validate.._WcsValidateHduResult.__init__cSs`t|ƒr\|jrd|j›d}nd}d|j›|›dg}x|D]}| t|ƒ¡q._WcsValidateHduResult.__repr__N)rPrQrRrGrr6r6r6r7Ú_WcsValidateHduResultZ srÉc@seZdZdd„ZdS)z%validate.._WcsValidateResultscSs6g}x&|D]}t|ƒ}t|ƒr | |¡q Wd |¡S)Nz )rwrêrmr_)rLr&rnÚcontentr6r6r7rm s  z.validate.._WcsValidateResults.__repr__N)rPrQrRrr6r6r6r7Ú_WcsValidateResultsl srËT)ÚrecordF)rZrƒrˆNÚalways)rmrU)rYrZrƒrˆcSsg|]}t|jƒ‘qSr6)rfr)r¡rr6r6r7r£ szvalidate..)rKrerrvrlr›rérmrHrrrXrZ WCSHDR_rejectr„r[Ú__warningregistry__Ú NameErrorÚ resetwarningsr‚rrrrfr¾)ÚsourcerÃrÉrËr2Úresultsr¢rnZ hdu_resultsZ warning_linesZwcsesr„Z wcs_resultsÚer6r6r7r1 sD          &)TNTrWT)OršrŸr‹rsrhÚrer¿rHr Únumpyr0ZastropyrZ astropy.iorrWrrrrIZastropy.utils.compatrZastropy.utils.exceptionsr r r Zastropy.utils.decoratorsr Zwcsapi.fitswcsr rÚ__all__Z__doctest_skip__r]r¨r\ríÚ ImportErrorÚ _sanity_checkÚ RuntimeErrorZ_Wcsrrrrrrrrrrrrrr r"r#r$r•r›rYrrÌÚlocalsrmr8Zset_wtbarr_fitsio_callbackÚobjectrZÚcompilerür@r(r!rrrrrr6r6r6r7ÚsØ           $     4v Y