# Implemented by Duncan Hanson
import numpy as np

import unittest

import healpy as hp

import warnings

# disable new order warnings in tests
warnings.filterwarnings("ignore")

nside_precomputed = 4
lmax_precomputed = 8

galm = np.array(
    [
        -0.60749536999999998 + 0j,
        0.83559932999999997 + 0j,
        -1.0174608599999999 + 0j,
        1.0993299999999999 + 0j,
        -1.0415247299999999 + 0j,
        0.98637741999999995 + 0j,
        -1.2327712799999999 + 0j,
        -0.65081703999999996 + 0j,
        -1.1239971900000001 + 0j,
        0.96501168000000004 - 2.3554313900000001j,
        -0.40474513000000001 - 0.65564383000000004j,
        0.15638859999999999 - 0.23621884000000001j,
        0.28043983 - 0.39658116999999998j,
        -0.26163387999999999 - 0.077809699999999996j,
        0.20287720000000001 - 0.06082216j,
        0.052013629999999998 + 0.073047849999999998j,
        0.68909047999999995 + 0.65423257999999995j,
        0.48747127000000001 + 0.30760153000000001j,
        -0.35432469999999999 - 1.0799235300000001j,
        0.43819587999999998 - 0.22769086999999999j,
        -0.57252002000000002 - 0.13502544j,
        0.63900029000000003 - 0.59585710000000003j,
        -1.16030893 - 0.25760955000000002j,
        0.37504869000000002 + 0.058102309999999997j,
        -0.98924601000000001 - 0.46924109000000003j,
        0.71031016000000002 - 0.90896836000000003j,
        -0.43448922000000001 - 0.12677451000000001j,
        -0.77544904000000003 - 0.25176252999999998j,
        -0.01721661 - 0.94948701000000002j,
        0.85474141000000003 - 0.051103330000000002j,
        -0.60520565999999998 + 0.87760647999999997j,
        -0.77864944000000003 - 0.79208626999999998j,
        -1.08657508 - 0.59487055j,
        0.21367211 - 1.5110769900000001j,
        -0.16784056999999999 + 0.80020639000000005j,
        -1.1339041000000001 - 0.32197503999999999j,
        0.19618954 + 1.08100252j,
        0.43866369 - 0.47475267999999998j,
        0.11857266 - 0.049022839999999998j,
        -0.40366523999999998 + 0.85542658000000005j,
        0.56154870999999995 - 0.77527478999999999j,
        0.48146275999999999 + 0.16245443000000001j,
        -0.68355484 - 0.22983015000000001j,
        -0.061040659999999997 - 0.13420304999999999j,
        0.27255975999999998 - 0.75328077999999998j,
    ]
)

calm = np.array(
    [
        1.0718601933803977 + 0j,
        -1.5182685950801673 + 0j,
        -0.39119975933464429 + 0j,
        -0.6620552667513403 + 0j,
        0.42674481653281382 + 0j,
        1.3799470126677567 + 0j,
        -1.4604721504544589 + 0j,
        -1.1136471151307403 + 0j,
        -1.647392955477013 + 0j,
        0.71919252212426499 - 0.39773236587790972j,
        1.1884542365155342 - 0.02640806030381616j,
        -0.040937417189905477 + 0.41096619318378996j,
        0.19575829981467366 - 0.9285256561788201j,
        -0.81538492817093389 - 0.35929021939020905j,
        0.46870617235542178 - 0.16617809319149193j,
        0.23640105395174835 + 0.20199283448907013j,
        -0.4326244206185022 - 0.59306323217984414j,
        0.70410703555897491 + 1.1105121855564981j,
        -0.25795284664102419 - 1.2596368643912992j,
        -0.32298608901330822 + 0.28961247423501457j,
        0.86075337105780647 + 0.11654277740017273j,
        0.61549312276703594 - 0.10703912813862339j,
        0.18586512296424443 - 0.19025963131317278j,
        -1.0133508690870945 + 0.37723661046981605j,
        0.81779407406185822 + 0.079623471577802724j,
        -0.36878503033040533 - 0.2898255702618146j,
        -0.13864500443953851 + 0.99443154731355876j,
        -0.18473645501235322 - 0.27320195658100321j,
        -0.59576170002379292 + 0.82900875927708351j,
        -0.42589567337148737 - 0.4359073358803493j,
        -1.0071527860797036 + 0.94936616398900131j,
        0.52681818118587864 - 0.14360294581437408j,
        0.92619570387111039 + 0.051664002362596051j,
        0.75431992804310644 - 0.25779974392362176j,
        -0.89919787406938079 + 0.4989749264182417j,
        0.50889483979981087 + 0.80485052548180069j,
        1.0832061738848424 - 0.70024088919678606j,
        -0.81326057995656997 + 1.0871815291974078j,
        0.66115253781072936 - 1.1579428341478799j,
        -0.25669790905903495 + 0.031910894413264487j,
        -0.055840352620168392 - 0.27126620265309953j,
        0.77754873311978667 + 0.1677199540737199j,
        -0.2428367232543345 + 0.058222152917874435j,
        -0.35655343174399751 + 0.28585938716743436j,
        0.44494756551095588 + 0.17931771534010477j,
    ]
)

maps = {
    1: np.array(
        [
            1.1743580943750218 + 1.0162508812596662j,
            -1.7545991014514022 + 3.9632546003544267j,
            3.4755301242047865 + 3.6205268666848651j,
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    ),
    2: np.array(
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            -0.42041547702109927 - 0.6638941892709691j,
            0.17949892445575544 - 0.18716973000962853j,
            0.26430768591955539 - 0.40505260468553134j,
            -0.24063674747596783 - 0.01667629102507856j,
            0.20243814807193189 - 0.061501040558063963j,
            0.074181600901263869 + 0.13110650173965177j,
            0.70925473188372479 + 0.65335194343646219j,
            0.4879926917946677 + 0.31352391256853401j,
            -0.35809352192298388 - 1.0728322735956963j,
            0.4533725297757551 - 0.22559691758977207j,
            -0.60038286724379097 - 0.11246033971793468j,
            0.66825095356633812 - 0.60076635444258042j,
            -1.1946567473464309 - 0.22635664737160516j,
            0.40228588081801298 + 0.068430477904664722j,
            -0.9882729303598855 - 0.46953404636080764j,
            0.71188035470148237 - 0.92234375063488339j,
            -0.42665812492162319 - 0.12577894001454354j,
            -0.76472165401579706 - 0.26752959905101342j,
            -0.0060656639141563051 - 0.93138763769826982j,
            0.89415079943278952 - 0.066507100471720232j,
            -0.61447982075563323 + 0.87348984596560353j,
            -0.78070473872335344 - 0.78753205263021409j,
            -1.1191256017366982 - 0.60047283637051052j,
            0.2133088567364409 - 1.464647765466137j,
            -0.23425203712922088 + 0.80569933612650535j,
            -1.1366303557443924 - 0.32263741303024324j,
            0.2041593807964231 + 1.0927143488558069j,
            0.43611791501355668 - 0.46222719965613662j,
            0.13160849960684828 - 0.025453022150853984j,
            -0.39955107839159809 + 0.85522030725234566j,
            0.55636294499207284 - 0.77063085552936683j,
            0.50643037413406744 + 0.15921955235797908j,
            -0.67794895826681578 - 0.2302258170581491j,
            -0.057766506371200475 - 0.13606392096680481j,
            0.2681214210068823 - 0.75888465889983925j,
        ]
    ),
    2: np.array(
        [
            0.0,
            0.0,
            -1.0146369650118083 + 0j,
            1.11121557988063 + 0j,
            -1.0268187317357511 + 0j,
            0.98244234543551479 + 0j,
            -1.2007880041682084 + 0j,
            -0.69447547017176625 + 0j,
            -1.0726374658022424 + 0j,
            0.0,
            -0.40253474561900393 - 0.65784721719896422j,
            0.15199112969379647 - 0.24330956005348325j,
            0.28523253658954206 - 0.3981266584575725j,
            -0.26845152711149062 - 0.083593980089662734j,
            0.19959571779331189 - 0.057385723112071435j,
            0.048274474287257146 + 0.05571849108314867j,
            0.66612416673860797 + 0.66489298075894143j,
            0.47445092525264315 + 0.33233327925496392j,
            -0.33978651546110278 - 1.0700406529115529j,
            0.42170150945972673 - 0.20638423667056441j,
            -0.5630841470957999 - 0.12922848005411802j,
            0.61971326220555945 - 0.56144750223866158j,
            -1.1423916258591016 - 0.25581299034320437j,
            0.34730218633923393 + 0.10618832232762943j,
            -0.99822733104115735 - 0.4682367163596412j,
            0.70620977727778933 - 0.90938188008554444j,
            -0.44219516027124856 - 0.13493822626962626j,
            -0.78951918570902713 - 0.23576709704052287j,
            -0.014428235772776353 - 0.97751697894267986j,
            0.81909761987552843 - 0.032145061525208574j,
            -0.59959900791799092 + 0.87660510575181094j,
            -0.77968569605966409 - 0.81916479783758211j,
            -1.0543271356804378 - 0.59294085416609699j,
            0.21451468853321071 - 1.575924063487286j,
            -0.097584235980056111 + 0.79606153258991741j,
            -1.1425268084073952 - 0.33343881952558124j,
            0.20815667516194364 + 1.0864812143836942j,
            0.42124636529500581 - 0.49483794628510092j,
            0.12538155362131775 - 0.054095442648732069j,
            -0.40820405930119319 + 0.85936840188813757j,
            0.57774999828224061 - 0.79228000632060525j,
            0.45984172555887304 + 0.1760761108040782j,
            -0.69197600035251772 - 0.22762901382604028j,
            -0.068152714393202821 - 0.13031971412287957j,
            0.28004810987754036 - 0.74648931403104868j,
        ]
    ),
    3: np.array(
        [
            0.0,
            0.0,
            0.0,
            1.1040780794436231 + 0j,
            -1.0554780343915136 + 0j,
            1.003760955073254 + 0j,
            -1.2565856441338645 + 0j,
            -0.62932602562674234 + 0j,
            -1.160067204424214 + 0j,
            0.0,
            0.0,
            0.15865387620507715 - 0.23612586328728333j,
            0.27391824074536975 - 0.40229821680653666j,
            -0.24904217061890843 - 0.066454748333335312j,
            0.19465514972961681 - 0.071603817219522803j,
            0.07585111789946225 + 0.10671255623789123j,
            0.67521859645108184 + 0.63791014584128802j,
            0.0,
            -0.34816350138864738 - 1.084783542403446j,
            0.43615290425078285 - 0.22284828128529358j,
            -0.57324320239356563 - 0.14126286640853886j,
            0.65304426498325374 - 0.6000904287578529j,
            -1.165079833528107 - 0.26540336287320754j,
            0.38879888788337164 + 0.049892403597867507j,
            -0.95196155755809375 - 0.46240128463150965j,
            0.66010872131183373 - 0.89379242001828385j,
            -0.38155334031368932 - 0.11319555736108271j,
            -0.83737598920187895 - 0.23689666124954797j,
            0.036024621196599382 - 0.93058744213774647j,
            0.79480395548872762 - 0.042441974598074916j,
            -0.61480456309191522 + 0.88772972943182071j,
            -0.77889262539414239 - 0.76334259507894808j,
            -1.1118023694151189 - 0.59375535579172312j,
            0.21015147536095025 - 1.4894366921848528j,
            -0.20540486553192566 + 0.80716874886526713j,
            -1.1317123907310076 - 0.32257306660406088j,
            0.18948788955123907 + 1.0757829951402618j,
            0.45816121337749072 - 0.46825028118838685j,
            0.094048425004741185 - 0.062988484577269799j,
            -0.40021838153849576 + 0.85629510171370782j,
            0.54773135746681112 - 0.76849935301866623j,
            0.49872929242448694 + 0.14779843610587595j,
            -0.67415810187311553 - 0.22910004410769433j,
            -0.05652956808223264 - 0.13895923733616072j,
            0.26192691834998399 - 0.75985770223080795j,
        ]
    ),
}

clms = {
    1: np.array(
        [
            0.0,
            -1.5258173689739127 + 0j,
            -0.38321729790014736 + 0j,
            -0.67468807400536313 + 0j,
            0.42460653551185651 + 0j,
            1.3828469966900694 + 0j,
            -1.4606906476867365 + 0j,
            -1.1024802895292889 + 0j,
            -1.6258480748456989 + 0j,
            0.72184388572247027 - 0.40980679076163978j,
            1.155123366597125 - 0.00025652164718847903j,
            -0.046798126366738545 + 0.38718565377077507j,
            0.14209457945669973 - 0.89695521394655509j,
            -0.81580217823771384 - 0.40181448848956358j,
            0.41047881458968138 - 0.1152355464248823j,
            0.25214366009371275 + 0.13596558218505578j,
            -0.48642804026342107 - 0.51921699092205253j,
            0.70318282623713557 + 1.1149229917786518j,
            -0.2620711198443052 - 1.2608592875108899j,
            -0.32886228833465481 + 0.28343506891478615j,
            0.87116700915729073 + 0.12201153895105338j,
            0.61061947387230175 - 0.13255341818790078j,
            0.20682058643208909 - 0.18157727548793343j,
            -1.012535222212142 + 0.35770276797463263j,
            0.82344404513932368 + 0.081123452026155174j,
            -0.36925633394180285 - 0.28239296801331859j,
            -0.13701971130554524 + 1.0015322075605051j,
            -0.17636539799409506 - 0.23987373576395629j,
            -0.61110525471621113 + 0.8387900954265588j,
            -0.38131027712597904 - 0.36432117739386211j,
            -1.0079042770692939 + 0.9484888310663222j,
            0.53963333913487466 - 0.15889892563621916j,
            0.90252874051924248 + 0.047882748600954872j,
            0.77742302026156063 - 0.28243856974519727j,
            -0.9721760087917013 + 0.49058350689687308j,
            0.50365618535953161 + 0.8080725210109363j,
            1.0815686965383575 - 0.70497162383482825j,
            -0.83122125861324603 + 1.0900112211266584j,
            0.63134176691035382 - 1.1506771025986287j,
            -0.25413053864796836 + 0.029385890444217244j,
            -0.056623996602004172 - 0.26225905883112283j,
            0.79047827545371763 + 0.14640251150139555j,
            -0.24482352824373257 + 0.055856847996116454j,
            -0.34090568518036446 + 0.31363733143816142j,
            0.4367718299537125 + 0.17676151335880672j,
        ]
    ),
    2: np.array(
        [
            0.0,
            0.0,
            -0.38326814027750383 + 0j,
            -0.65418849087307329 + 0j,
            0.4365892671577063 + 0j,
            1.3803202920785584 + 0j,
            -1.4916247379419461 + 0j,
            -1.1324277132571721 + 0j,
            -1.718185868626174 + 0j,
            0.0,
            1.1956968215533583 - 0.030205892584907437j,
            -0.046100534504420865 + 0.41807122036767436j,
            0.20782483037951727 - 0.94246433056743517j,
            -0.83529709861832213 - 0.33903347515975163j,
            0.48223350794745773 - 0.1926218400020257j,
            0.21761499886653402 + 0.23961747977479567j,
            -0.41751923193484447 - 0.6353671827291465j,
            0.69260449292859827 + 1.130305228894001j,
            -0.27954119293120033 - 1.2766279639264633j,
            -0.33817969510878398 + 0.30951969744288232j,
            0.83742868793014358 + 0.091212369129396176j,
            0.58571691217352817 - 0.070712873379824182j,
            0.14679306846624376 - 0.21513933832793367j,
            -1.0638029100403115 + 0.41792437931719256j,
            0.8237611915825912 + 0.077755997607020733j,
            -0.37108969890984272 - 0.30238750878485998j,
            -0.14723325508395391 + 0.9932281688841047j,
            -0.19383569442563495 - 0.29295381202435722j,
            -0.60670529686130736 + 0.83380243303561374j,
            -0.45917079393130283 - 0.47912168797908361j,
            -0.99345730695253176 + 0.94820175796661454j,
            0.52649034820916507 - 0.12783909225900825j,
            0.95924022156146393 + 0.055538327979596458j,
            0.75064860942575096 - 0.21370815773918539j,
            -0.84586566942124497 + 0.51342826175108991j,
            0.50395723769037315 + 0.813189467153421j,
            1.1022997429292671 - 0.71579859067105911j,
            -0.81673852639172906 + 1.1007947378391343j,
            0.68458074409331271 - 1.1856051362879017j,
            -0.25008109729217404 + 0.039905637802000099j,
            -0.062189175604629054 - 0.28221196312220687j,
            0.78892563532515847 + 0.20103962113750989j,
            -0.2427808848517484 + 0.05747362398942496j,
            -0.36648874880005772 + 0.26046556342439908j,
            0.46087686583398435 + 0.18234525262036616j,
        ]
    ),
    3: np.array(
        [
            0.0,
            0.0,
            0.0,
            -0.65872355978145192 + 0j,
            0.43111157992422688 + 0j,
            1.3933719902449626 + 0j,
            -1.4337104872664086 + 0j,
            -1.0953871385562564 + 0j,
            -1.592919216965424 + 0j,
            0.0,
            0.0,
            -0.037750501706858508 + 0.4056437707216613j,
            0.19266431434449349 - 0.92413738054154204j,
            -0.80624682077443821 - 0.3750231326847116j,
            0.44820402588981811 - 0.14801697141861184j,
            0.25229035881318124 + 0.17607723506064732j,
            -0.47384685147145073 - 0.54847200740427982j,
            0.0,
            -0.26403005654710615 - 1.2664841194732137j,
            -0.31764611275074489 + 0.29566346120804393j,
            0.85876964582432236 + 0.11833464087123241j,
            0.62548078652733941 - 0.10502140662441077j,
            0.18551399493477491 - 0.18721874018509277j,
            -0.9828066043226521 + 0.38082405462307395j,
            0.80637975865752387 + 0.038495909743214873j,
            -0.37901190842236099 - 0.24290178119622488j,
            -0.15681111690711577 + 0.93523746819782994j,
            -0.19823080090222214 - 0.21435654151321781j,
            -0.61995793538329469 + 0.75489242177728544j,
            -0.4291786442205881 - 0.3647575706316637j,
            -1.036373422481776 + 0.9498490485674238j,
            0.52091939787694486 - 0.16079466106792323j,
            0.90447971944064343 + 0.049384983566628349j,
            0.76161216915691299 - 0.28843184314201131j,
            -0.921447188295894 + 0.49222438394413293j,
            0.50972830882201325 + 0.80496870972031798j,
            1.0799130050305059 - 0.69042579996889542j,
            -0.80230481303668388 + 1.0710316308031511j,
            0.65228711481346291 - 1.1285250709486818j,
            -0.25636616152524505 + 0.027205860798986677j,
            -0.052885291187932219 - 0.26226354597662616j,
            0.76408397668509698 + 0.13719891764968475j,
            -0.24129807401981906 + 0.059572855113709577j,
            -0.35702076334353117 + 0.30851416270921495j,
            0.42377772250897539 + 0.17587202874134827j,
        ]
    ),
}


class TestSpinFunc(unittest.TestCase):
    def setUp(self):
        self.nside = 64
        self.lmax = self.nside

        seed = 12345
        np.random.seed(seed)
        self.mapr = hp.synfast(
            np.ones(self.lmax + 1), self.nside, pixwin=False, fwhm=0.0, sigma=None
        )
        self.mapi = hp.synfast(
            np.ones(self.lmax + 1), self.nside, pixwin=False, fwhm=0.0, sigma=None
        )

        self.almg = hp.synalm(np.ones(self.lmax + 1), self.lmax)
        self.almc = hp.synalm(np.ones(self.lmax + 1), self.lmax)

    def test_der1(self):
        """ compare output of alm2map_der1 with the equivalent spin-1 transform using alm2map_spin """

        m, dt_der1, dp_der1 = hp.alm2map_der1(self.almg, self.nside)

        alm_spin = hp.almxfl(
            self.almg,
            np.array(
                [np.sqrt(l * (l + 1.0)) for l in range(0, self.lmax + 1)]
            ),
            inplace=False,
        )
        dt_spin, dp_spin = hp.alm2map_spin(
            [alm_spin, alm_spin * 0.0], self.nside, 1, self.lmax
        )

        np.testing.assert_array_almost_equal(dt_der1, dt_spin, decimal=8)
        np.testing.assert_array_almost_equal(dp_der1, dp_spin, decimal=8)

    def test_spin0(self):
        m1 = hp.alm2map(self.almg, self.nside, self.lmax)
        m2_r, m2_i = hp.alm2map_spin(
            [-self.almg, 0.0 * self.almg], self.nside, 0, self.lmax
        )

        np.testing.assert_array_almost_equal(m1, m2_r, decimal=8)
        np.testing.assert_array_almost_equal(m1 * 0.0, m2_i, decimal=8)

        a1 = hp.map2alm(m1, lmax=self.lmax)
        a2_g, a2_c = hp.map2alm_spin([m2_r, m2_i], 0, self.lmax)

        np.testing.assert_array_almost_equal(a1, -a2_g, decimal=2)
        np.testing.assert_array_almost_equal(a1 * 0.0, -a2_c, decimal=2)

    def test_alm2map_spin_precomputed(self):
        """ compare alm2map_spin outputs to some precomputed results for spin=1,2,3 """

        for spin in [1, 2, 3]:
            rmap, imap = hp.alm2map_spin(
                [galm, calm], nside_precomputed, spin, lmax_precomputed
            )
            np.testing.assert_array_almost_equal(rmap, maps[spin].real, decimal=7)
            np.testing.assert_array_almost_equal(imap, maps[spin].imag, decimal=7)

    def test_map2alm_spin_spin_precomputed(self):
        """ compare map2alm_spin outputs to some precomputed results for spin=1,2,3 """

        for spin in [1, 2, 3]:
            tglm, tclm = hp.map2alm_spin(
                [maps[spin].real, maps[spin].imag], spin, lmax_precomputed
            )
            np.testing.assert_array_almost_equal(glms[spin], tglm, decimal=7)
            np.testing.assert_array_almost_equal(clms[spin], tclm, decimal=7)

    def test_forward_backward_spin(self):
        """ compare map2alm_spin outputs to alm2map_spin inputs. tolerances are very loose. """
        for spin in [1, 2, 3]:
            tcl = np.ones(self.lmax + 1)
            tcl[0:spin] = 0.0
            almg = hp.almxfl(self.almg, tcl, inplace=False)
            almc = hp.almxfl(self.almc, tcl, inplace=False)

            rmap, imap = hp.alm2map_spin([almg, almc], self.nside, spin, self.lmax)
            tglm, tclm = hp.map2alm_spin([rmap, imap], spin, self.lmax)
            np.testing.assert_allclose(almg, tglm, rtol=1.0e-2, atol=1.0e-2)
            np.testing.assert_allclose(almc, tclm, rtol=1.0e-2, atol=1.0e-2)