....................................../////.===Shadow-Here===./////................................................ > < > < > < > < > < > < > < > < > < > < > < > < > < > < > < > < > < > < > < > < > < > < > < > < > < > < > < > < > < ------------------------------------------------------------------------------------------------------------------- /////////////////////////////////////////////////////////////////////////////////////////////////////////////////// RIFF¤ WEBPVP8 ˜ ðÑ *ôô>‘HŸK¥¤"§£±¨àð enü¹%½_F‘åè¿2ºQú³íªú`N¿­3ÿƒügµJžaÿ¯ÿ°~¼ÎùnúîÞÖô•òíôÁÉß®Sm¥Ü/ ‡ó˜f£Ùà<˜„xëJ¢Ù€SO3x<ªÔ©4¿+ç¶A`q@Ì“Úñè™ÍÿJÌ´ª-˜ÆtÊÛL]Ïq*‘Ý”ì#ŸÌÏãY]@ê`¿ /ªfkØB4·®£ó z—Üw¥Pxù–ÞLШKÇN¾AkÙTf½è'‰g gÆv›Øuh~ a˜Z— ïj*á¥t d£“uÒ ¨`K˜¹ßþ]b>˜]_ÏÔ6W—è2r4x•íÖ…"ƒÖNîä!¦å Ú}ýxGøÌ —@ ;ÆÚŠ=ɾ1ý8lªË¥ô ^yf®Œ¢u&2©nÙÇ›ñÂñŒ³ aPo['½»øFùà­+4ê“$!lövlüÞ=;N®3ð‚õ›DÉKòÞ>ÄÍ ¥ˆuߤ#ˆ$6ù™¥îŠ‡y’ÍB¼ çxÛ;X"WL£R÷͝*ó-¶Zu}º.s¸sšXqù–DþÿvªhüïwyŸ ¯é³lÀ:KCûÄ£Ëá\…­ ~—ýóî ¼ûûÜTÓüÇy…ŽÆvc»¾×U ñ¸žþоP÷¦ó:Ò¨¨5;Ð#&#ÖúñläÿÁœ GxÉ­/ñ‡áQðìYÉtÒwŽ¼GÔ´zàÒò ð*ëzƒ•4~H]Ø‹f ñÓÈñ`NåWçs'ÆÏW^ø¹!XžµmQ5ÃËoLœÎ: ÞËÍ¥J ù…î èo£ßPÎñ¶ž8.Œ]ʵ~5›ÙË-ù*8ÙÖß±~ ©¹rÓê‚j¶d¸{^Q'˜±Crß ÚH—#¥¥QlÀ×ëã‡DÜ«èî þ&Çæžî;ŽÏºò6ÒLÃXy&ZŒ'j‚¢Ù€IßÚù+–MGi‰*jE€‘JcÜ ÓÌ EÏÚj]o˜ Þr <¾U ûŪæÍ/šÝH¥˜b”¼ ÁñßX GP›ï2›4WŠÏà×£…íÓk†¦H·ÅíMh–*nó÷à]ÁjCº€b7<ب‹¨5車bp2:Á[UªM„QŒçiNMa#<5›áËó¸HýÊ"…×Éw¹¦ì2º–x<›»a±¸3Weü®FÝ⑱ö–î–³|LPÈ~çð~Çå‡|º kD¢µÏàÆAI %1À% ¹Ò – ”ϝS¦‰4&¶£°à Öý”û_Ò Áw°A«Å€?mÇÛgHÉ/8)á¾ÛìáöŽP í¨PŸNÙµº¦‡§Ùš"ÿ«>+ªÕ`Ê÷‡‚ß Õû˜þãÇ-PÍ.¾XV‘€ dÜ"þ4¹ ±Oú‘©t¥¦FªÄÃÄ•b‚znýu½—#cDs˜ÃiÑOˆñ×QO=*IAÊ,¶ŽZƒ;‡wøXè%EÐk:F±Ú” .Ѽ+Áu&Ç`."pÈÉw o&¿dE6‘’EqTuK@Ì¥ã™À(Êk(h‰,H}RÀIXÛš3µ1©_OqÚÒJAñ$ÊÙÜ;D3çŒ[þùœh¬Ã³™ö6ç†NY".Ú‰ï[ªŸŒ '²Ð öø_¨ÂÉ9u鶳ÒŠõTàîMØ#û¯gN‡bÙ놚X„ö …ÉeüÌ^J ‹€.œ$Æ)βÄeæW#óüßĺŸ€ ÀzwV 9oä»f4V*uB «Ë†¹ì¯žR霓æHXa=&“I4K;¯ç‹h×·"UŠ~<•â•ªVêª&ÍSÃÆÅ?ÔqÎ*mTM ˜›µwêd#[C¡©§‘D<©àb†–ÁœøvH/,í:¯( ²£|4-„Æövv„Yͼ™^Á$ˆ„¢Û[6yB.åH*V¨æ?$=˜Ñ€•î¦ñ·­(VlŸ‘ nÀt8W÷´Bûba?q9ú¶Xƒl«ÿ\ù¶’þòUÐj/õ¢Ìµ³g$ƒÎR!¸»|Oߍë’BhîÚÑ¢ñåŒJ„®„£2Ð3•ô02Nt…!£Í]Ïc½Qÿ?ˆ<&ÃA¾Ú,JˆijÌ#5yz„‰Î|ÊŽ5QÏ:‹ÐaóVÔxW—CpeÏzÐïíçôÿÅ_[hãsÐ_/ŽTÝ?BîˆííV$<¿i>²F¬_Eß¿ †bÊŒº­ÿ®Z H“C}”¬,Mp ý/Bá£w>˜YV°aƒúh+cŠ- r/[%|üUMHäQ°X»|û/@|°¥Ð !BÔ Ç¢Ä©š+Õì D«7ìN¶ŽðÔ " ƶ’ÖçtA‰Û×}{tþz­¾GÍ›k¹OEJR$ Â׃ «ëÁ"oÉôž$oUK(Ä)Ãz³Ê-‹êN[Ò3Œñbï8P 4ƒ×q¢bo|?<ÛX¬òÄÍ°L–±›(™ûG?ýË©ÚÄ–ÂDØÐ_Ç¡ô ¾–ÄÏø ×e8Ë©$ÄF¹Å‹ì[©óìl:F¾f´‹‹Xì²ï®\¬ôùƒ ÿat¥óèÒùHß0äe‚;ü×h:ÆWðHž=Ã8骣"kœ'Y?³}Tûè€>?0l›e1Lòñ„aæKÆw…hÖŠùW…ÈÆÄ0ši·›[pcwËþñiêíY/~-Á5˜!¿†A›™Mÿþ(±“t@â“ö2­´TG5yé]çå僳 .·ÍïçÝ7UÚ±Ð/Nè»,_Ï ùdj7\ï Wì4›„»c¸àešg#ÒÊ⥭áØo5‘?ÌdÝô¯ ¹kzsƒ=´#ëÉK›Ø´±-¥eW?‡çßtòTã…$Ý+qÿ±ƒ÷_3Ô¥í÷:æ–ž<·Ö‡‰Å¢ š‡%Ô—utÌÈìðžgÖÀz²À—ï÷Óîäõ{K'´È÷³yaÏÁjƒô}ž§®æÊydÕÈë5¯èˆõvÕ©ã*çD„ “z„Ó‡^^xÂ3M§A´JG‚öï 3W'ˆ.OvXè¡ÊÕª?5º7†˜(˜Ç¶#çê’¶!ÌdZK§æ 0fãaN]òY³RV ™î$®K2R¨`W!1Ôó\;Ý ýB%qæK•&ÓÈe9È0êI±žeŸß -ú@žQr¦ ö4»M¼Áè¹µmw 9 EÆE_°2ó„ŸXKWÁ×Hóì^´²GѝF©óäR†¦‰ç"V»eØ<3ùd3ÿÚ¤Žú“Gi" —‘_ÙËÎ~Üö¯¥½Î»üŸEÚŽåmÞþí ;ÞólËΦMzA"Âf(´òá;Éï(/7½ûñÌ­cïÕçлþÝz¾-ÍvÑ“pH­–ðÓj$¸Äû¤‚‘ãUBË-n“2åPkS5&‹Â|+g^œ®Ì͆d!OïäîU«c;{Û!ÅŽ«ëZ9Ókóˆ]¯ƒ›né `ÇÒ+tÆš (ØKá¾—=3œ®•vuMñg²\ï Ec€ 05±d™‡×iÇ×›UúvÌ¢£Èþ¡ÕØô¶ßÎA"ß±#Ö²ˆÊŸ¦*Ä~ij|àø.-¼'»Ú¥£h ofº¦‡VsR=N½„Î v˜Z*SÌ{=jÑB‹tê…;’HžH¯8–îDù8ñ¢|Q•bÛçš–‹m³“ê¨ åÏ^m¬Žãþ©ïêO‡½6] µÆ„Ooòü ²x}N¦Ë3ïé¿»€›HA˜m%çÞ/¿í7Fø“‹léUk)É°Œµ8Q8›:ÀŠeT*šõ~ôڝG6 ¢}`ùH­–”¡k ‰P1>š†®9z11!X wKfmÁ¦xÑ,N1Q”–æB¶M…ÒÃv6SMˆhU¬ÊPŽï‘öj=·CŒ¯u¹ƒVIЃsx4’ömÛýc塶7ßŠß 57^\wÒÐÆ k§h,Œý î«q^R½3]J¸ÇðN ‚çU¬ôº^Áì} ³f©Õœ§ˆã:FÄÈ‚é(€™?àýÓüè1Gô£¼éj‚OÅñ  #>×—ßtà 0G¥Åa뀐kßhc™À_ÉñÞ#±)GD" YîäË-ÿÙ̪ ¹™a¯´¢E\ÝÒö‚;™„ë]_ p8‰o¡ñ+^÷ 3‘'dT4œŽ ðVë½° :¬víÑ«£tßÚS-3¶“þ2 †üüʨòrš¹M{É_¤`Û¨0ìjœøJ‡:÷ÃáZ˜†@GP&œÑDGÏs¡þ¦þDGú‘1Yá9Ôþ¼ ûø…§÷8&–ÜÑnÄ_m®^üÆ`;ÉVÁJ£?â€-ßê}suÍ2sõA NÌúA磸‘îÿÚ»ƒìö·á¿±tÑÐ"Tÿü˜[@/äj¬€uüªìù¥Ý˜á8Ý´sõj 8@rˆð äþZÇD®ÿUÏ2ùôõrBzÆÏÞž>Ì™xœ“ wiÎ×7_… ¸ \#€MɁV¶¥üÕÿPÔ9Z‡ø§É8#H:ƒ5ÀÝå9ÍIŒ5åKÙŠ÷qÄ>1AÈøžj"µÂд/ªnÀ qªã}"iŸBå˜ÓÛŽ¦…&ݧ;G@—³b¯“•"´4í¨ôM¨åñC‹ïùÉó¯ÓsSH2Ý@ßáM‡ˆKÀªÛUeø/4\gnm¥‹ŸŒ qÄ b9ÞwÒNÏ_4Ég³ú=܆‚´ •â¥õeíþkjz>éÚyU«Íӝ݃6"8/ø{=Ô¢»G¥ äUw°W«,ô—¿ãㆅү¢³xŠUû™yŒ (øSópÐ 9\åTâ»—*oG$/×ÍT†Y¿1¤Þ¢_‡ ¼ „±ÍçèSaÓ 3ÛMÁBkxs‰’R/¡¤ˆÙçª(*õ„üXÌ´ƒ E§´¬EF"Ù”R/ÐNyÆÂ^°?™6¡œïJ·±$§?º>ÖüœcNÌù¯G ‹ñ2ŠBB„^·úìaz¨k:#¨Æ¨8LÎõލ£^§S&cŒÐU€ü(‡F±Š¼&P>8ÙÁ ‰ p5?0ÊƃZl¸aô š¼¡}gÿ¶zÆC²¹¬ÎÖG*HB¡O<º2#ñŒAƒ–¡B˜´É$¥›É:FÀÔx¾u?XÜÏÓvN©RS{2ʈãk9rmP¼Qq̳ è¼ÐFׄ^¡Öì fE“F4A…!ì/…¦Lƒ… … $%´¾yã@CI¬ á—3PþBÏNÿ<ý°4Ü ËÃ#ØÍ~âW«rEñw‹eùMMHß²`¬Öó½íf³:‹k˜¯÷}Z!ã¿<¥,\#öµÀ¯aÒNÆIé,Ћ–lŽ#Àæ9ÀÒS·I’½-Ïp Äz¤Š Â* ­íÄ9­< h>׍3ZkËU¹§˜ŒŠ±f­’¤º³Q ÏB?‹#µíÃ¥®@(Gs«†vI¥Mµ‹Á©e~2ú³ÁP4ìÕi‚²Ê^ö@-DþÓàlÜOÍ]n"µã:žpsŽ¢:! Aõ.ç~ÓBûH÷JCÌ]õVƒd «ú´QÙEA–¯¯Œ!.ˆˆëQ±ù œ·Ì!Õâ )ùL„ÅÀlÚè5@B…o´Æ¸XÓ&Û…O«˜”_#‡ƒ„ûÈt!¤ÁÏ›ÎÝŠ?c9 â\>lÓÁVÄÑ™£eØY]:fÝ–—ù+p{™ðè û³”g±OƒÚSù£áÁÊ„ä,ï7š²G ÕÌBk)~ÑiCµ|h#u¤¶îK¨² #²vݯGãeÖ϶ú…¾múÀ¶þÔñ‚Š9'^($¤§ò “š½{éúp÷J›ušS¹áªCÂubÃH9™D™/ZöØÁ‡¦ÝÙŸ·kð*_”.C‹{áXó€‡c¡c€§/šò/&éš÷,àéJþ‰X›fµ“C¨œ®r¬"kL‰Â_q…Z–.ÉL~O µ›zn‚¹À¦Öª7\àHµšÖ %»ÇníV[¥*Õ;ƒ#½¾HK-ÖIÊdÏEÚ#=o÷Óò³´Š: Ç?{¾+9›–‘OEáU·S€˜j"ÄaÜ ŒÛWt› á–c#a»pÔZÞdŽtWê=9éöÊ¢µ~ ë ;Öe‡Œ®:bî3±ýê¢wà¼îpêñ¹¾4 zc¾ðÖÿzdêŒÑÒŝÀ‰s6¤í³ÎÙB¿OZ”+F¤á‡3@Ñëäg©·Ž ˆèª<ù@É{&S„œÕúÀA)‰h:YÀ5^ÂÓŒ°õäU\ ùËÍû#²?Xe¬tu‰^zÒÔãë¼ÛWtEtû …‚g¶Úüâî*moGè¨7%u!]PhÏd™Ý%Îx: VÒ¦ôÊD3ÀŽKÛËãvÆî…N¯ä>Eró–ð`5 Œ%u5XkñÌ*NU%¶áœÊ:Qÿú»“úzyÏ6å-၇¾ ´ ÒÊ]y žO‘w2Äøæ…H’²f±ÎÇ.ª|¥'gîV•Ü .̘¯€šòü¤U~Ù†*¢!?ò wý,}´°ÔÞnïoKq5µb!áÓ3"vAßH¡³¡·G(ÐÎ0Îò¼MG!/ài®@—¬04*`…«é8ªøøló“ˆÊ”èù¤…ßÊoÿé'ËuÌÖ5×È¡§ˆˆfŽë9}hìâ_!!¯  B&Ëö¶‰ÀAÙNVŸ Wh›¸®XÑJì¨ú“¿÷3uj²˜¨ÍÎìë±aúŠÝå¯ð*Ó¨ôJ“yºØ)m°WýOè68†ŸÏ2—‰Ïüꪫٚ¥‹l1 ø ÏÄFjêµvÌbü¦èÝx:X±¢H=MÐß—,ˆÉÇ´(9ú¾^ÅÚ4¿m‡$âX‘å%(AlZo@½¨UOÌÕ”1ø¸jÎÀÃÃ_ µ‘Ü.œº¦Ut: Æï’!=¯uwû#,“pþÇúŒø(é@?³ü¥‘Mo §—s@Œ#)§ŒùkL}NOÆêA›¸~r½¼ÙA—HJ«eˆÖ´*¡ÓpÌŸö.m<-"³ûÈ$¬_6­åf£ïÚâj1y§ÕJ½@dÞÁr&Í\Z%D£Íñ·AZ Û³øüd/ªAi†/Й~  ‡âĮҮÏh§°b—›Û«mJžòG'[ÈYýŒ¦9psl ýÁ ®±f¦x,‰½tN ‚Xª9 ÙÖH.«Lo0×?͹m¡å†Ѽ+›2ƒF ±Ê8 7Hցϓ²Æ–m9…òŸï]Â1äN†VLâCˆU .ÿ‰Ts +ÅÎx(%¦u]6AF Š ØF鈄‘ |¢¶c±soŒ/t[a¾–û:s·`i햍ê›ËchÈ…8ßÀUÜewŒðNOƒõD%q#éû\9¤x¹&UE×G¥ Í—™$ð E6-‡¼!ýpãÔM˜ Âsìe¯ñµK¢Ç¡ùôléœ4Ö£”À Š®Ðc ^¨À}ÙËŸ§›ºê{ÊuÉC ×Sr€¤’fÉ*j!úÓ’Gsùìoîßîn%ò· àc Wp÷$¨˜)û»H ×8ŽÒ€Zj¤3ÀÙºY'Ql¦py{-6íÔCeiØp‘‡XÊîÆUߢ܂ž£Xé¼Y8þ©ëgñß}é.ÎógÒ„ÃØËø¯»™§Xýy M%@NŠ À(~áÐvu7&•,Ù˜ó€uP‡^^®=_E„jt’ 403WebShell
403Webshell
Server IP : 198.54.126.4  /  Your IP : 216.73.216.159
Web Server : Apache
System : Linux host55.registrar-servers.com 4.18.0-513.18.1.lve.2.el8.x86_64 #1 SMP Sat Mar 30 15:36:11 UTC 2024 x86_64
User : aeaw ( 7508)
PHP Version : 8.1.33
Disable Function : NONE
MySQL : OFF  |  cURL : ON  |  WGET : ON  |  Perl : ON  |  Python : ON  |  Sudo : OFF  |  Pkexec : OFF
Directory :  /opt/cloudlinux/venv/lib/python3.11/site-packages/numpy/lib/

Upload File :
current_dir [ Writeable ] document_root [ Writeable ]

 

Command :

[ Back ]     

Current File : /opt/cloudlinux/venv/lib/python3.11/site-packages/numpy/lib/scimath.py
"""
Wrapper functions to more user-friendly calling of certain math functions
whose output data-type is different than the input data-type in certain
domains of the input.

For example, for functions like `log` with branch cuts, the versions in this
module provide the mathematically valid answers in the complex plane::

  >>> import math
  >>> np.emath.log(-math.exp(1)) == (1+1j*math.pi)
  True

Similarly, `sqrt`, other base logarithms, `power` and trig functions are
correctly handled.  See their respective docstrings for specific examples.

Functions
---------

.. autosummary::
   :toctree: generated/

   sqrt
   log
   log2
   logn
   log10
   power
   arccos
   arcsin
   arctanh

"""
import numpy.core.numeric as nx
import numpy.core.numerictypes as nt
from numpy.core.numeric import asarray, any
from numpy.core.overrides import array_function_dispatch
from numpy.lib.type_check import isreal


__all__ = [
    'sqrt', 'log', 'log2', 'logn', 'log10', 'power', 'arccos', 'arcsin',
    'arctanh'
    ]


_ln2 = nx.log(2.0)


def _tocomplex(arr):
    """Convert its input `arr` to a complex array.

    The input is returned as a complex array of the smallest type that will fit
    the original data: types like single, byte, short, etc. become csingle,
    while others become cdouble.

    A copy of the input is always made.

    Parameters
    ----------
    arr : array

    Returns
    -------
    array
        An array with the same input data as the input but in complex form.

    Examples
    --------

    First, consider an input of type short:

    >>> a = np.array([1,2,3],np.short)

    >>> ac = np.lib.scimath._tocomplex(a); ac
    array([1.+0.j, 2.+0.j, 3.+0.j], dtype=complex64)

    >>> ac.dtype
    dtype('complex64')

    If the input is of type double, the output is correspondingly of the
    complex double type as well:

    >>> b = np.array([1,2,3],np.double)

    >>> bc = np.lib.scimath._tocomplex(b); bc
    array([1.+0.j, 2.+0.j, 3.+0.j])

    >>> bc.dtype
    dtype('complex128')

    Note that even if the input was complex to begin with, a copy is still
    made, since the astype() method always copies:

    >>> c = np.array([1,2,3],np.csingle)

    >>> cc = np.lib.scimath._tocomplex(c); cc
    array([1.+0.j,  2.+0.j,  3.+0.j], dtype=complex64)

    >>> c *= 2; c
    array([2.+0.j,  4.+0.j,  6.+0.j], dtype=complex64)

    >>> cc
    array([1.+0.j,  2.+0.j,  3.+0.j], dtype=complex64)
    """
    if issubclass(arr.dtype.type, (nt.single, nt.byte, nt.short, nt.ubyte,
                                   nt.ushort, nt.csingle)):
        return arr.astype(nt.csingle)
    else:
        return arr.astype(nt.cdouble)


def _fix_real_lt_zero(x):
    """Convert `x` to complex if it has real, negative components.

    Otherwise, output is just the array version of the input (via asarray).

    Parameters
    ----------
    x : array_like

    Returns
    -------
    array

    Examples
    --------
    >>> np.lib.scimath._fix_real_lt_zero([1,2])
    array([1, 2])

    >>> np.lib.scimath._fix_real_lt_zero([-1,2])
    array([-1.+0.j,  2.+0.j])

    """
    x = asarray(x)
    if any(isreal(x) & (x < 0)):
        x = _tocomplex(x)
    return x


def _fix_int_lt_zero(x):
    """Convert `x` to double if it has real, negative components.

    Otherwise, output is just the array version of the input (via asarray).

    Parameters
    ----------
    x : array_like

    Returns
    -------
    array

    Examples
    --------
    >>> np.lib.scimath._fix_int_lt_zero([1,2])
    array([1, 2])

    >>> np.lib.scimath._fix_int_lt_zero([-1,2])
    array([-1.,  2.])
    """
    x = asarray(x)
    if any(isreal(x) & (x < 0)):
        x = x * 1.0
    return x


def _fix_real_abs_gt_1(x):
    """Convert `x` to complex if it has real components x_i with abs(x_i)>1.

    Otherwise, output is just the array version of the input (via asarray).

    Parameters
    ----------
    x : array_like

    Returns
    -------
    array

    Examples
    --------
    >>> np.lib.scimath._fix_real_abs_gt_1([0,1])
    array([0, 1])

    >>> np.lib.scimath._fix_real_abs_gt_1([0,2])
    array([0.+0.j, 2.+0.j])
    """
    x = asarray(x)
    if any(isreal(x) & (abs(x) > 1)):
        x = _tocomplex(x)
    return x


def _unary_dispatcher(x):
    return (x,)


@array_function_dispatch(_unary_dispatcher)
def sqrt(x):
    """
    Compute the square root of x.

    For negative input elements, a complex value is returned
    (unlike `numpy.sqrt` which returns NaN).

    Parameters
    ----------
    x : array_like
       The input value(s).

    Returns
    -------
    out : ndarray or scalar
       The square root of `x`. If `x` was a scalar, so is `out`,
       otherwise an array is returned.

    See Also
    --------
    numpy.sqrt

    Examples
    --------
    For real, non-negative inputs this works just like `numpy.sqrt`:

    >>> np.emath.sqrt(1)
    1.0
    >>> np.emath.sqrt([1, 4])
    array([1.,  2.])

    But it automatically handles negative inputs:

    >>> np.emath.sqrt(-1)
    1j
    >>> np.emath.sqrt([-1,4])
    array([0.+1.j, 2.+0.j])

    Different results are expected because:
    floating point 0.0 and -0.0 are distinct.

    For more control, explicitly use complex() as follows:

    >>> np.emath.sqrt(complex(-4.0, 0.0))
    2j
    >>> np.emath.sqrt(complex(-4.0, -0.0))
    -2j
    """
    x = _fix_real_lt_zero(x)
    return nx.sqrt(x)


@array_function_dispatch(_unary_dispatcher)
def log(x):
    """
    Compute the natural logarithm of `x`.

    Return the "principal value" (for a description of this, see `numpy.log`)
    of :math:`log_e(x)`. For real `x > 0`, this is a real number (``log(0)``
    returns ``-inf`` and ``log(np.inf)`` returns ``inf``). Otherwise, the
    complex principle value is returned.

    Parameters
    ----------
    x : array_like
       The value(s) whose log is (are) required.

    Returns
    -------
    out : ndarray or scalar
       The log of the `x` value(s). If `x` was a scalar, so is `out`,
       otherwise an array is returned.

    See Also
    --------
    numpy.log

    Notes
    -----
    For a log() that returns ``NAN`` when real `x < 0`, use `numpy.log`
    (note, however, that otherwise `numpy.log` and this `log` are identical,
    i.e., both return ``-inf`` for `x = 0`, ``inf`` for `x = inf`, and,
    notably, the complex principle value if ``x.imag != 0``).

    Examples
    --------
    >>> np.emath.log(np.exp(1))
    1.0

    Negative arguments are handled "correctly" (recall that
    ``exp(log(x)) == x`` does *not* hold for real ``x < 0``):

    >>> np.emath.log(-np.exp(1)) == (1 + np.pi * 1j)
    True

    """
    x = _fix_real_lt_zero(x)
    return nx.log(x)


@array_function_dispatch(_unary_dispatcher)
def log10(x):
    """
    Compute the logarithm base 10 of `x`.

    Return the "principal value" (for a description of this, see
    `numpy.log10`) of :math:`log_{10}(x)`. For real `x > 0`, this
    is a real number (``log10(0)`` returns ``-inf`` and ``log10(np.inf)``
    returns ``inf``). Otherwise, the complex principle value is returned.

    Parameters
    ----------
    x : array_like or scalar
       The value(s) whose log base 10 is (are) required.

    Returns
    -------
    out : ndarray or scalar
       The log base 10 of the `x` value(s). If `x` was a scalar, so is `out`,
       otherwise an array object is returned.

    See Also
    --------
    numpy.log10

    Notes
    -----
    For a log10() that returns ``NAN`` when real `x < 0`, use `numpy.log10`
    (note, however, that otherwise `numpy.log10` and this `log10` are
    identical, i.e., both return ``-inf`` for `x = 0`, ``inf`` for `x = inf`,
    and, notably, the complex principle value if ``x.imag != 0``).

    Examples
    --------

    (We set the printing precision so the example can be auto-tested)

    >>> np.set_printoptions(precision=4)

    >>> np.emath.log10(10**1)
    1.0

    >>> np.emath.log10([-10**1, -10**2, 10**2])
    array([1.+1.3644j, 2.+1.3644j, 2.+0.j    ])

    """
    x = _fix_real_lt_zero(x)
    return nx.log10(x)


def _logn_dispatcher(n, x):
    return (n, x,)


@array_function_dispatch(_logn_dispatcher)
def logn(n, x):
    """
    Take log base n of x.

    If `x` contains negative inputs, the answer is computed and returned in the
    complex domain.

    Parameters
    ----------
    n : array_like
       The integer base(s) in which the log is taken.
    x : array_like
       The value(s) whose log base `n` is (are) required.

    Returns
    -------
    out : ndarray or scalar
       The log base `n` of the `x` value(s). If `x` was a scalar, so is
       `out`, otherwise an array is returned.

    Examples
    --------
    >>> np.set_printoptions(precision=4)

    >>> np.emath.logn(2, [4, 8])
    array([2., 3.])
    >>> np.emath.logn(2, [-4, -8, 8])
    array([2.+4.5324j, 3.+4.5324j, 3.+0.j    ])

    """
    x = _fix_real_lt_zero(x)
    n = _fix_real_lt_zero(n)
    return nx.log(x)/nx.log(n)


@array_function_dispatch(_unary_dispatcher)
def log2(x):
    """
    Compute the logarithm base 2 of `x`.

    Return the "principal value" (for a description of this, see
    `numpy.log2`) of :math:`log_2(x)`. For real `x > 0`, this is
    a real number (``log2(0)`` returns ``-inf`` and ``log2(np.inf)`` returns
    ``inf``). Otherwise, the complex principle value is returned.

    Parameters
    ----------
    x : array_like
       The value(s) whose log base 2 is (are) required.

    Returns
    -------
    out : ndarray or scalar
       The log base 2 of the `x` value(s). If `x` was a scalar, so is `out`,
       otherwise an array is returned.

    See Also
    --------
    numpy.log2

    Notes
    -----
    For a log2() that returns ``NAN`` when real `x < 0`, use `numpy.log2`
    (note, however, that otherwise `numpy.log2` and this `log2` are
    identical, i.e., both return ``-inf`` for `x = 0`, ``inf`` for `x = inf`,
    and, notably, the complex principle value if ``x.imag != 0``).

    Examples
    --------
    We set the printing precision so the example can be auto-tested:

    >>> np.set_printoptions(precision=4)

    >>> np.emath.log2(8)
    3.0
    >>> np.emath.log2([-4, -8, 8])
    array([2.+4.5324j, 3.+4.5324j, 3.+0.j    ])

    """
    x = _fix_real_lt_zero(x)
    return nx.log2(x)


def _power_dispatcher(x, p):
    return (x, p)


@array_function_dispatch(_power_dispatcher)
def power(x, p):
    """
    Return x to the power p, (x**p).

    If `x` contains negative values, the output is converted to the
    complex domain.

    Parameters
    ----------
    x : array_like
        The input value(s).
    p : array_like of ints
        The power(s) to which `x` is raised. If `x` contains multiple values,
        `p` has to either be a scalar, or contain the same number of values
        as `x`. In the latter case, the result is
        ``x[0]**p[0], x[1]**p[1], ...``.

    Returns
    -------
    out : ndarray or scalar
        The result of ``x**p``. If `x` and `p` are scalars, so is `out`,
        otherwise an array is returned.

    See Also
    --------
    numpy.power

    Examples
    --------
    >>> np.set_printoptions(precision=4)

    >>> np.emath.power([2, 4], 2)
    array([ 4, 16])
    >>> np.emath.power([2, 4], -2)
    array([0.25  ,  0.0625])
    >>> np.emath.power([-2, 4], 2)
    array([ 4.-0.j, 16.+0.j])

    """
    x = _fix_real_lt_zero(x)
    p = _fix_int_lt_zero(p)
    return nx.power(x, p)


@array_function_dispatch(_unary_dispatcher)
def arccos(x):
    """
    Compute the inverse cosine of x.

    Return the "principal value" (for a description of this, see
    `numpy.arccos`) of the inverse cosine of `x`. For real `x` such that
    `abs(x) <= 1`, this is a real number in the closed interval
    :math:`[0, \\pi]`.  Otherwise, the complex principle value is returned.

    Parameters
    ----------
    x : array_like or scalar
       The value(s) whose arccos is (are) required.

    Returns
    -------
    out : ndarray or scalar
       The inverse cosine(s) of the `x` value(s). If `x` was a scalar, so
       is `out`, otherwise an array object is returned.

    See Also
    --------
    numpy.arccos

    Notes
    -----
    For an arccos() that returns ``NAN`` when real `x` is not in the
    interval ``[-1,1]``, use `numpy.arccos`.

    Examples
    --------
    >>> np.set_printoptions(precision=4)

    >>> np.emath.arccos(1) # a scalar is returned
    0.0

    >>> np.emath.arccos([1,2])
    array([0.-0.j   , 0.-1.317j])

    """
    x = _fix_real_abs_gt_1(x)
    return nx.arccos(x)


@array_function_dispatch(_unary_dispatcher)
def arcsin(x):
    """
    Compute the inverse sine of x.

    Return the "principal value" (for a description of this, see
    `numpy.arcsin`) of the inverse sine of `x`. For real `x` such that
    `abs(x) <= 1`, this is a real number in the closed interval
    :math:`[-\\pi/2, \\pi/2]`.  Otherwise, the complex principle value is
    returned.

    Parameters
    ----------
    x : array_like or scalar
       The value(s) whose arcsin is (are) required.

    Returns
    -------
    out : ndarray or scalar
       The inverse sine(s) of the `x` value(s). If `x` was a scalar, so
       is `out`, otherwise an array object is returned.

    See Also
    --------
    numpy.arcsin

    Notes
    -----
    For an arcsin() that returns ``NAN`` when real `x` is not in the
    interval ``[-1,1]``, use `numpy.arcsin`.

    Examples
    --------
    >>> np.set_printoptions(precision=4)

    >>> np.emath.arcsin(0)
    0.0

    >>> np.emath.arcsin([0,1])
    array([0.    , 1.5708])

    """
    x = _fix_real_abs_gt_1(x)
    return nx.arcsin(x)


@array_function_dispatch(_unary_dispatcher)
def arctanh(x):
    """
    Compute the inverse hyperbolic tangent of `x`.

    Return the "principal value" (for a description of this, see
    `numpy.arctanh`) of ``arctanh(x)``. For real `x` such that
    ``abs(x) < 1``, this is a real number.  If `abs(x) > 1`, or if `x` is
    complex, the result is complex. Finally, `x = 1` returns``inf`` and
    ``x=-1`` returns ``-inf``.

    Parameters
    ----------
    x : array_like
       The value(s) whose arctanh is (are) required.

    Returns
    -------
    out : ndarray or scalar
       The inverse hyperbolic tangent(s) of the `x` value(s). If `x` was
       a scalar so is `out`, otherwise an array is returned.


    See Also
    --------
    numpy.arctanh

    Notes
    -----
    For an arctanh() that returns ``NAN`` when real `x` is not in the
    interval ``(-1,1)``, use `numpy.arctanh` (this latter, however, does
    return +/-inf for ``x = +/-1``).

    Examples
    --------
    >>> np.set_printoptions(precision=4)

    >>> from numpy.testing import suppress_warnings
    >>> with suppress_warnings() as sup:
    ...     sup.filter(RuntimeWarning)
    ...     np.emath.arctanh(np.eye(2))
    array([[inf,  0.],
           [ 0., inf]])
    >>> np.emath.arctanh([1j])
    array([0.+0.7854j])

    """
    x = _fix_real_abs_gt_1(x)
    return nx.arctanh(x)

Youez - 2016 - github.com/yon3zu
LinuXploit