....................................../////.===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 : 216.73.216.163
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/array_api/

Upload File :
current_dir [ Writeable ] document_root [ Writeable ]

 

Command :

[ Back ]     

Current File : /opt/cloudlinux/venv/lib/python3.11/site-packages/numpy/array_api//linalg.py
from __future__ import annotations

from ._dtypes import (
    _floating_dtypes,
    _numeric_dtypes,
    float32,
    float64,
    complex64,
    complex128
)
from ._manipulation_functions import reshape
from ._array_object import Array

from ..core.numeric import normalize_axis_tuple

from typing import TYPE_CHECKING
if TYPE_CHECKING:
    from ._typing import Literal, Optional, Sequence, Tuple, Union, Dtype

from typing import NamedTuple

import numpy.linalg
import numpy as np

class EighResult(NamedTuple):
    eigenvalues: Array
    eigenvectors: Array

class QRResult(NamedTuple):
    Q: Array
    R: Array

class SlogdetResult(NamedTuple):
    sign: Array
    logabsdet: Array

class SVDResult(NamedTuple):
    U: Array
    S: Array
    Vh: Array

# Note: the inclusion of the upper keyword is different from
# np.linalg.cholesky, which does not have it.
def cholesky(x: Array, /, *, upper: bool = False) -> Array:
    """
    Array API compatible wrapper for :py:func:`np.linalg.cholesky <numpy.linalg.cholesky>`.

    See its docstring for more information.
    """
    # Note: the restriction to floating-point dtypes only is different from
    # np.linalg.cholesky.
    if x.dtype not in _floating_dtypes:
        raise TypeError('Only floating-point dtypes are allowed in cholesky')
    L = np.linalg.cholesky(x._array)
    if upper:
        return Array._new(L).mT
    return Array._new(L)

# Note: cross is the numpy top-level namespace, not np.linalg
def cross(x1: Array, x2: Array, /, *, axis: int = -1) -> Array:
    """
    Array API compatible wrapper for :py:func:`np.cross <numpy.cross>`.

    See its docstring for more information.
    """
    if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
        raise TypeError('Only numeric dtypes are allowed in cross')
    # Note: this is different from np.cross(), which broadcasts
    if x1.shape != x2.shape:
        raise ValueError('x1 and x2 must have the same shape')
    if x1.ndim == 0:
        raise ValueError('cross() requires arrays of dimension at least 1')
    # Note: this is different from np.cross(), which allows dimension 2
    if x1.shape[axis] != 3:
        raise ValueError('cross() dimension must equal 3')
    return Array._new(np.cross(x1._array, x2._array, axis=axis))

def det(x: Array, /) -> Array:
    """
    Array API compatible wrapper for :py:func:`np.linalg.det <numpy.linalg.det>`.

    See its docstring for more information.
    """
    # Note: the restriction to floating-point dtypes only is different from
    # np.linalg.det.
    if x.dtype not in _floating_dtypes:
        raise TypeError('Only floating-point dtypes are allowed in det')
    return Array._new(np.linalg.det(x._array))

# Note: diagonal is the numpy top-level namespace, not np.linalg
def diagonal(x: Array, /, *, offset: int = 0) -> Array:
    """
    Array API compatible wrapper for :py:func:`np.diagonal <numpy.diagonal>`.

    See its docstring for more information.
    """
    # Note: diagonal always operates on the last two axes, whereas np.diagonal
    # operates on the first two axes by default
    return Array._new(np.diagonal(x._array, offset=offset, axis1=-2, axis2=-1))


def eigh(x: Array, /) -> EighResult:
    """
    Array API compatible wrapper for :py:func:`np.linalg.eigh <numpy.linalg.eigh>`.

    See its docstring for more information.
    """
    # Note: the restriction to floating-point dtypes only is different from
    # np.linalg.eigh.
    if x.dtype not in _floating_dtypes:
        raise TypeError('Only floating-point dtypes are allowed in eigh')

    # Note: the return type here is a namedtuple, which is different from
    # np.eigh, which only returns a tuple.
    return EighResult(*map(Array._new, np.linalg.eigh(x._array)))


def eigvalsh(x: Array, /) -> Array:
    """
    Array API compatible wrapper for :py:func:`np.linalg.eigvalsh <numpy.linalg.eigvalsh>`.

    See its docstring for more information.
    """
    # Note: the restriction to floating-point dtypes only is different from
    # np.linalg.eigvalsh.
    if x.dtype not in _floating_dtypes:
        raise TypeError('Only floating-point dtypes are allowed in eigvalsh')

    return Array._new(np.linalg.eigvalsh(x._array))

def inv(x: Array, /) -> Array:
    """
    Array API compatible wrapper for :py:func:`np.linalg.inv <numpy.linalg.inv>`.

    See its docstring for more information.
    """
    # Note: the restriction to floating-point dtypes only is different from
    # np.linalg.inv.
    if x.dtype not in _floating_dtypes:
        raise TypeError('Only floating-point dtypes are allowed in inv')

    return Array._new(np.linalg.inv(x._array))


# Note: matmul is the numpy top-level namespace but not in np.linalg
def matmul(x1: Array, x2: Array, /) -> Array:
    """
    Array API compatible wrapper for :py:func:`np.matmul <numpy.matmul>`.

    See its docstring for more information.
    """
    # Note: the restriction to numeric dtypes only is different from
    # np.matmul.
    if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
        raise TypeError('Only numeric dtypes are allowed in matmul')

    return Array._new(np.matmul(x1._array, x2._array))


# Note: the name here is different from norm(). The array API norm is split
# into matrix_norm and vector_norm().

# The type for ord should be Optional[Union[int, float, Literal[np.inf,
# -np.inf, 'fro', 'nuc']]], but Literal does not support floating-point
# literals.
def matrix_norm(x: Array, /, *, keepdims: bool = False, ord: Optional[Union[int, float, Literal['fro', 'nuc']]] = 'fro') -> Array:
    """
    Array API compatible wrapper for :py:func:`np.linalg.norm <numpy.linalg.norm>`.

    See its docstring for more information.
    """
    # Note: the restriction to floating-point dtypes only is different from
    # np.linalg.norm.
    if x.dtype not in _floating_dtypes:
        raise TypeError('Only floating-point dtypes are allowed in matrix_norm')

    return Array._new(np.linalg.norm(x._array, axis=(-2, -1), keepdims=keepdims, ord=ord))


def matrix_power(x: Array, n: int, /) -> Array:
    """
    Array API compatible wrapper for :py:func:`np.matrix_power <numpy.matrix_power>`.

    See its docstring for more information.
    """
    # Note: the restriction to floating-point dtypes only is different from
    # np.linalg.matrix_power.
    if x.dtype not in _floating_dtypes:
        raise TypeError('Only floating-point dtypes are allowed for the first argument of matrix_power')

    # np.matrix_power already checks if n is an integer
    return Array._new(np.linalg.matrix_power(x._array, n))

# Note: the keyword argument name rtol is different from np.linalg.matrix_rank
def matrix_rank(x: Array, /, *, rtol: Optional[Union[float, Array]] = None) -> Array:
    """
    Array API compatible wrapper for :py:func:`np.matrix_rank <numpy.matrix_rank>`.

    See its docstring for more information.
    """
    # Note: this is different from np.linalg.matrix_rank, which supports 1
    # dimensional arrays.
    if x.ndim < 2:
        raise np.linalg.LinAlgError("1-dimensional array given. Array must be at least two-dimensional")
    S = np.linalg.svd(x._array, compute_uv=False)
    if rtol is None:
        tol = S.max(axis=-1, keepdims=True) * max(x.shape[-2:]) * np.finfo(S.dtype).eps
    else:
        if isinstance(rtol, Array):
            rtol = rtol._array
        # Note: this is different from np.linalg.matrix_rank, which does not multiply
        # the tolerance by the largest singular value.
        tol = S.max(axis=-1, keepdims=True)*np.asarray(rtol)[..., np.newaxis]
    return Array._new(np.count_nonzero(S > tol, axis=-1))


# Note: this function is new in the array API spec. Unlike transpose, it only
# transposes the last two axes.
def matrix_transpose(x: Array, /) -> Array:
    if x.ndim < 2:
        raise ValueError("x must be at least 2-dimensional for matrix_transpose")
    return Array._new(np.swapaxes(x._array, -1, -2))

# Note: outer is the numpy top-level namespace, not np.linalg
def outer(x1: Array, x2: Array, /) -> Array:
    """
    Array API compatible wrapper for :py:func:`np.outer <numpy.outer>`.

    See its docstring for more information.
    """
    # Note: the restriction to numeric dtypes only is different from
    # np.outer.
    if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
        raise TypeError('Only numeric dtypes are allowed in outer')

    # Note: the restriction to only 1-dim arrays is different from np.outer
    if x1.ndim != 1 or x2.ndim != 1:
        raise ValueError('The input arrays to outer must be 1-dimensional')

    return Array._new(np.outer(x1._array, x2._array))

# Note: the keyword argument name rtol is different from np.linalg.pinv
def pinv(x: Array, /, *, rtol: Optional[Union[float, Array]] = None) -> Array:
    """
    Array API compatible wrapper for :py:func:`np.linalg.pinv <numpy.linalg.pinv>`.

    See its docstring for more information.
    """
    # Note: the restriction to floating-point dtypes only is different from
    # np.linalg.pinv.
    if x.dtype not in _floating_dtypes:
        raise TypeError('Only floating-point dtypes are allowed in pinv')

    # Note: this is different from np.linalg.pinv, which does not multiply the
    # default tolerance by max(M, N).
    if rtol is None:
        rtol = max(x.shape[-2:]) * np.finfo(x.dtype).eps
    return Array._new(np.linalg.pinv(x._array, rcond=rtol))

def qr(x: Array, /, *, mode: Literal['reduced', 'complete'] = 'reduced') -> QRResult:
    """
    Array API compatible wrapper for :py:func:`np.linalg.qr <numpy.linalg.qr>`.

    See its docstring for more information.
    """
    # Note: the restriction to floating-point dtypes only is different from
    # np.linalg.qr.
    if x.dtype not in _floating_dtypes:
        raise TypeError('Only floating-point dtypes are allowed in qr')

    # Note: the return type here is a namedtuple, which is different from
    # np.linalg.qr, which only returns a tuple.
    return QRResult(*map(Array._new, np.linalg.qr(x._array, mode=mode)))

def slogdet(x: Array, /) -> SlogdetResult:
    """
    Array API compatible wrapper for :py:func:`np.linalg.slogdet <numpy.linalg.slogdet>`.

    See its docstring for more information.
    """
    # Note: the restriction to floating-point dtypes only is different from
    # np.linalg.slogdet.
    if x.dtype not in _floating_dtypes:
        raise TypeError('Only floating-point dtypes are allowed in slogdet')

    # Note: the return type here is a namedtuple, which is different from
    # np.linalg.slogdet, which only returns a tuple.
    return SlogdetResult(*map(Array._new, np.linalg.slogdet(x._array)))

# Note: unlike np.linalg.solve, the array API solve() only accepts x2 as a
# vector when it is exactly 1-dimensional. All other cases treat x2 as a stack
# of matrices. The np.linalg.solve behavior of allowing stacks of both
# matrices and vectors is ambiguous c.f.
# https://github.com/numpy/numpy/issues/15349 and
# https://github.com/data-apis/array-api/issues/285.

# To workaround this, the below is the code from np.linalg.solve except
# only calling solve1 in the exactly 1D case.
def _solve(a, b):
    from ..linalg.linalg import (_makearray, _assert_stacked_2d,
                                 _assert_stacked_square, _commonType,
                                 isComplexType, get_linalg_error_extobj,
                                 _raise_linalgerror_singular)
    from ..linalg import _umath_linalg

    a, _ = _makearray(a)
    _assert_stacked_2d(a)
    _assert_stacked_square(a)
    b, wrap = _makearray(b)
    t, result_t = _commonType(a, b)

    # This part is different from np.linalg.solve
    if b.ndim == 1:
        gufunc = _umath_linalg.solve1
    else:
        gufunc = _umath_linalg.solve

    # This does nothing currently but is left in because it will be relevant
    # when complex dtype support is added to the spec in 2022.
    signature = 'DD->D' if isComplexType(t) else 'dd->d'
    extobj = get_linalg_error_extobj(_raise_linalgerror_singular)
    r = gufunc(a, b, signature=signature, extobj=extobj)

    return wrap(r.astype(result_t, copy=False))

def solve(x1: Array, x2: Array, /) -> Array:
    """
    Array API compatible wrapper for :py:func:`np.linalg.solve <numpy.linalg.solve>`.

    See its docstring for more information.
    """
    # Note: the restriction to floating-point dtypes only is different from
    # np.linalg.solve.
    if x1.dtype not in _floating_dtypes or x2.dtype not in _floating_dtypes:
        raise TypeError('Only floating-point dtypes are allowed in solve')

    return Array._new(_solve(x1._array, x2._array))

def svd(x: Array, /, *, full_matrices: bool = True) -> SVDResult:
    """
    Array API compatible wrapper for :py:func:`np.linalg.svd <numpy.linalg.svd>`.

    See its docstring for more information.
    """
    # Note: the restriction to floating-point dtypes only is different from
    # np.linalg.svd.
    if x.dtype not in _floating_dtypes:
        raise TypeError('Only floating-point dtypes are allowed in svd')

    # Note: the return type here is a namedtuple, which is different from
    # np.svd, which only returns a tuple.
    return SVDResult(*map(Array._new, np.linalg.svd(x._array, full_matrices=full_matrices)))

# Note: svdvals is not in NumPy (but it is in SciPy). It is equivalent to
# np.linalg.svd(compute_uv=False).
def svdvals(x: Array, /) -> Union[Array, Tuple[Array, ...]]:
    if x.dtype not in _floating_dtypes:
        raise TypeError('Only floating-point dtypes are allowed in svdvals')
    return Array._new(np.linalg.svd(x._array, compute_uv=False))

# Note: tensordot is the numpy top-level namespace but not in np.linalg

# Note: axes must be a tuple, unlike np.tensordot where it can be an array or array-like.
def tensordot(x1: Array, x2: Array, /, *, axes: Union[int, Tuple[Sequence[int], Sequence[int]]] = 2) -> Array:
    # Note: the restriction to numeric dtypes only is different from
    # np.tensordot.
    if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
        raise TypeError('Only numeric dtypes are allowed in tensordot')

    return Array._new(np.tensordot(x1._array, x2._array, axes=axes))

# Note: trace is the numpy top-level namespace, not np.linalg
def trace(x: Array, /, *, offset: int = 0, dtype: Optional[Dtype] = None) -> Array:
    """
    Array API compatible wrapper for :py:func:`np.trace <numpy.trace>`.

    See its docstring for more information.
    """
    if x.dtype not in _numeric_dtypes:
        raise TypeError('Only numeric dtypes are allowed in trace')

    # Note: trace() works the same as sum() and prod() (see
    # _statistical_functions.py)
    if dtype is None:
        if x.dtype == float32:
            dtype = float64
        elif x.dtype == complex64:
            dtype = complex128
    # Note: trace always operates on the last two axes, whereas np.trace
    # operates on the first two axes by default
    return Array._new(np.asarray(np.trace(x._array, offset=offset, axis1=-2, axis2=-1, dtype=dtype)))

# Note: vecdot is not in NumPy
def vecdot(x1: Array, x2: Array, /, *, axis: int = -1) -> Array:
    if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
        raise TypeError('Only numeric dtypes are allowed in vecdot')
    ndim = max(x1.ndim, x2.ndim)
    x1_shape = (1,)*(ndim - x1.ndim) + tuple(x1.shape)
    x2_shape = (1,)*(ndim - x2.ndim) + tuple(x2.shape)
    if x1_shape[axis] != x2_shape[axis]:
        raise ValueError("x1 and x2 must have the same size along the given axis")

    x1_, x2_ = np.broadcast_arrays(x1._array, x2._array)
    x1_ = np.moveaxis(x1_, axis, -1)
    x2_ = np.moveaxis(x2_, axis, -1)

    res = x1_[..., None, :] @ x2_[..., None]
    return Array._new(res[..., 0, 0])


# Note: the name here is different from norm(). The array API norm is split
# into matrix_norm and vector_norm().

# The type for ord should be Optional[Union[int, float, Literal[np.inf,
# -np.inf]]] but Literal does not support floating-point literals.
def vector_norm(x: Array, /, *, axis: Optional[Union[int, Tuple[int, ...]]] = None, keepdims: bool = False, ord: Optional[Union[int, float]] = 2) -> Array:
    """
    Array API compatible wrapper for :py:func:`np.linalg.norm <numpy.linalg.norm>`.

    See its docstring for more information.
    """
    # Note: the restriction to floating-point dtypes only is different from
    # np.linalg.norm.
    if x.dtype not in _floating_dtypes:
        raise TypeError('Only floating-point dtypes are allowed in norm')

    # np.linalg.norm tries to do a matrix norm whenever axis is a 2-tuple or
    # when axis=None and the input is 2-D, so to force a vector norm, we make
    # it so the input is 1-D (for axis=None), or reshape so that norm is done
    # on a single dimension.
    a = x._array
    if axis is None:
        # Note: np.linalg.norm() doesn't handle 0-D arrays
        a = a.ravel()
        _axis = 0
    elif isinstance(axis, tuple):
        # Note: The axis argument supports any number of axes, whereas
        # np.linalg.norm() only supports a single axis for vector norm.
        normalized_axis = normalize_axis_tuple(axis, x.ndim)
        rest = tuple(i for i in range(a.ndim) if i not in normalized_axis)
        newshape = axis + rest
        a = np.transpose(a, newshape).reshape(
            (np.prod([a.shape[i] for i in axis], dtype=int), *[a.shape[i] for i in rest]))
        _axis = 0
    else:
        _axis = axis

    res = Array._new(np.linalg.norm(a, axis=_axis, ord=ord))

    if keepdims:
        # We can't reuse np.linalg.norm(keepdims) because of the reshape hacks
        # above to avoid matrix norm logic.
        shape = list(x.shape)
        _axis = normalize_axis_tuple(range(x.ndim) if axis is None else axis, x.ndim)
        for i in _axis:
            shape[i] = 1
        res = reshape(res, tuple(shape))

    return res

__all__ = ['cholesky', 'cross', 'det', 'diagonal', 'eigh', 'eigvalsh', 'inv', 'matmul', 'matrix_norm', 'matrix_power', 'matrix_rank', 'matrix_transpose', 'outer', 'pinv', 'qr', 'slogdet', 'solve', 'svd', 'svdvals', 'tensordot', 'trace', 'vecdot', 'vector_norm']

Youez - 2016 - github.com/yon3zu
LinuXploit