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U+,D27999jzQ!q999 77555555333444333444 6 >C DDDA AAAOOOA"b///AAMMMNNNKKKKKKKKKKKK MNNA ;-%,&-%,&-%, ())A %(((A H'''):):):;5 I I I!T!Q1E:::1a 77x!-!-!-..HH x!:!:!:;;H "&(A>>>>>Y,?,?r6c PtdtttzD]x\}}d}|dkrIt d|}t d|\}}t |||}n\t d|}t d|\}}t ||t ||d zz|}||jzd z d tj ||zz}t|d }t||}|||d \} } } || | |d \} } ttd | z tj|d z | zd kzdS)NrrwrT sytrf_lworkr)syconsytrf hetrf_lwork)heconhetrfr.rRrQrr)rbipivrrrd)rrrr/r(rr0rrzr8r rr#rrrcond) rr2rrfunconfunctrfrrrldurr@rconds r4test_sycon_heconr sJJJ~ 566AA U  77)-uEEEJ./AOOOOFGa##E**AA*-uEEEJ./AOOOOFGad1ajjm+33E::A^Q 26!5#9#9#9!9 9Q z1--wqQ777 T16Cd%qAAAqAeGbinnQ!n44455e;a?@@@@-AAr6ctdttD]2\}}d}td|\}}}}t |||}||jzdz }t |||}||jzdz dtj||zz}|||\} } } t| dk||\} } t| dk||| \} } t| dk|| \}} } t| dkt|| d4dS) Nrrw)rsygstsyevdsygvdrrRrgiUMu?r) rrrr(rr0rzr8r rr)rr2rrrrrrBeig_gvdr@rjrrbeigs r4 test_sygstr sJJJ ,,33 U %57I.zs[MMMqr#a&A36A36)9)9::::MMMr6rwrrr/)r8rr_rrr(r#rrr0rrrzrr1r r r6rrrrspacingr)r3rrrr2r tzrzf_lwrrrzrjrrZr&r'rts @@@r4 test_tzrzfr,^sF )   % %C DAq''FF U*+C16888xxA.. 77SXXa^^**51122AAchhq!nnsxx1~~b'88@@GGHHA i,,,au--- C  Ir!!!RaR%y"(Aqs85"A"A"AB C C Irvau---r!!!QRR%y9 : : VAU # # #MMMMMME!HHMMM 263  a1 j%&@&@&@ 55::? ; ;;" F F F F F-FFr6c tjd}ttD]\}}d}|dkrct ||||||dzzt|z|}d}nHt |||t|z|}d}td|\}}}||\} } ||d |} |d | | } t| t| | |d zd krd nd |d | | |} t| t| j | |d zd krd nd |d|tj|tj|f<|d | | |d} t| t| j | |d zd krd nd |d||} |d | | |dd} t| t| | j  j |d zd krd nd dS)z Test for solving a linear system with the coefficient matrix is a triangular array stored in Full Packed (RFP) format. rrrQr.r}rz)trttftfttrtfsmrrRrrrTrVrrrrX)rr3rSr)rr3rN)r8rr_rrrrr r0r(rrrrzr)r3rr2rrrr.r/r0Afpr@rsolnB2s r4 test_tfsmr5s )   % %C'' D D U  77SXXa^^chhq!nnR&77#a&&@AAHHOOAEESXXa^^c!ff,--44U;;AE-.H49;;;udqQ HHQNN ! !% ( (tBQ!$qb! /2Qw!||!! D D D DtBQe,,,!$qvvxxzk1(=(=/2Qw!||!! D D D D).b ")A,, ! $%tBQe#666!$qvvxxzk1(=(=/2Qw!||!! D D D DXXa^^ " "5 ) )tBRu3SAAA!$qb"$(<(<(>(>(@/2Qw!||!! D D D D D? D Dr6c tjd}d\}}}ttD]\}}t d|\}}t |||}|dkrtt||| |} ||| |} t d|\} } nt||||||dzz |} |||t||dzz |} t d|\} } t | ||} || | \}}tj tj |||d d |d fftj ||fd t|D}ttj|}|dkrd nd }dtj|djz}| || | \}}t#|dkt%||| z t'| |d| || || \}}t#|dkt%||j| z t'| |d| || d| \}}t#|dkt%|| |z t'| |d| || d|| \}}t#|dkt%|| |jz t'| |dd S)a This test performs a matrix multiplication with an arbitrary m x n matrix C and a unitary matrix Q without explicitly forming the array. The array data is encoded in the rectangular part of A which is obtained from ?TZRZF. Q size is inferred by m, n, side keywords. r)rwrrrrrR)ormrz ormrz_lworkr.)unmrz unmrz_lworkrNc g|]P}||gddfj|gddfzz QSr#r$r%s r4rWz$test_ormrz_unmrz..s[NNNqr#a&A36A36)9)9::::NNNr6rzr}rwrrrr/rr)rr)rrr)r8rr_rrr(r#rrr0r1r r6rrr(rrrrrrz)r3qmqncnrr2r r)lwork_rzrr}orun_mrz orun_mrz_lw lwork_mrzr*rjrrrtolcqr&r'rts @@@r4test_ormrz_unmrzrEs )   % %CJBB''.!.! U*+C16888x!(B33 77SXXb"%%,,U3344AR  ''..A$45M;@%B%B%B !Hkkchhr2&&"b)9)9")<<DDUKKLLA"b!!DRLLO3;;EBBA$45M;@%B%B%B !Hk#;B77 ax000 C Irvb...111bcc6 ; < < VBe $ $ $NNNNNNE"IINNN 263  QwwCEE#JJO,,,8BQi888D QUU1XX z!}}3RHHHH8BQe9EEED QVVXXZ^^A... 1 C ! ! ! !8BQS BBBD QUU1XX z!}}3RHHHH8BQSYOOOD QUU16688:... 1 C ! ! ! ! ![.!.!r6c |tjd}ttD]\}}d}|dkrF||||||dzz|}d}n+||||}d}td|\}}||\}} t| d k||d \} } t| d k|||d \} } t| d k|||d \} } t| d kt|dz|dzf|} t|dd|dzdf| ddddf<| |dzdzdddfxxt|d|dzd|dzf j z cc<t|dz|dzf|}t|ddd|dzf|ddddf<|d|dzddfxxt||dzd|dzdf j z cc<t|| ddt| | j ddt| |ddt| | j dd|||\}} t| d k||| d \}} t| d k||| |d \}} t| d k||| |d \}} t| d kt|t|t|t|t|t|t|t|dS)z Test conversion routines between the Rectangular Full Packed (RFP) format and Standard Triangular Array (TR) rrrQr.r}rz)r.r/rrrKrNrX)transrrNrRNrF)order)r8rr_rrrr0r(rr rrrzrrreshape)r3rr2rA_fullrIr.r/A_tf_UrjA_tf_LA_tf_U_TA_tf_L_TA_tf_U_mA_tf_L_mA_tr_UA_tr_LA_tr_U_TA_tr_L_Ts r4test_tfttr_trttfrXs )   % %C''1:1: U  77hhq!nnsxx1~~b'88@@GGFFFhhq!nn,,U33FF'(:%HHH uuV}}  uV#...  vf3???$ vf3???$ !A#q!tE222<<1a4551"aaaAa!!!V UadUEQTE\ : ? ? A A CC!A#q!tE222v,,qqq%1a4%x0QQQ!Q$d6ll1a455!Q$%%<8==??AA!&(*:*:2S*:*I*IJJJ!("*--//"3";";Bc";"J"J L L L "&(*:*:2S*:*I*IJJJ!("*--//"3";";Bc";"J"J L L LuQ''  uQS111  q(6DDD$ q(6DDD$ !&$v,,777!(DLL999!&$v,,777!(DLL9999c1:1:r6cvtjd}ttD]\}}d}|dkrD||||||dzz|}n)||||}td|\}}||\}}t|dk||d \} }t|dkt|} t||dzzd z|} t|j | | d d <t|} t||dzzd z|} t|j | | d d <t|| t| | |||\} }t|dk||| d \}}t|dkt| t|t|t|d S) rGrrrQr.)trttptpttrrrrKrHrRN)r8rr_rrrr0r(rrr rrzrrr)r3rr2rrMrZr[A_tp_UrjA_tp_LindsA_tp_U_mA_tp_L_mrTrUs r4test_tpttr_trttpras3 )   % %C'' 8 8 U  77hhq!nnsxx1~~b'88@@GGFFhhq!nn,,U33F'(:%HHH uuV}}  uV#...  AAaC!5111F||~t, AAaC!5111F||~t, !&(333!&(333uQ''  uQS111  !&$v,,777!&$v,,7777A 8 8r6ctjd}ttD]:\}}d}|dkrs||||||dzz|}||jz|t|zz}nF||||}||jz|t|zz}td|\}}}||\}} |||\} } t| dk||| \} } t|} t| | >>@@@@@@@@@BCCL 8111111111 233L ''// U 77CCCEEEEEEEEEGHHAAA:::::::::.s!:::eb!em:::r6rUsyequb) r8rrrr r6rot90r3r(rlog2r0r) desired_log2srr2rrqrrscondrrjrs @r4 test_syequbrs H???@@M'' < < U F2U # # #C!GGbb-- H::::U2q\\:::% H H H RXbgajj ! !!!(%888%vayy5$RWQZZ&&s++];;;; < !,,AudDqBGAJJS ! rd 2bT!V ;<<< 26")B**+++b011AAdGAdG!>!((2<*@*@JJJAudDqBGAJJ I I IJJJJJr6ctjd}d}||}||||dzz}t t D]P\}}|dkrF|||}||}||z}||}n_||||||dzz}||}||z}||}td|}td|} ||d \} } } } | | || | d \}}|dkr*t||||z d (t||||z d RdS) Nrrwr.rRgetc2rgesc2rr*) overwrite_rhsrTr) r8rr_rrrr0r(r)r3rrrrr2rrrrrrjpivrjrr]s r4test_getc2_gesc2rs )   # #C A88A;;L88A;;!R/L'':: U 77AAAL AAAA!Q!22AAL AA 666 666$uQA666D$5Qd!<<<5 77 %l&9&9%&@&@&'gq : : : : : &l&9&9%&@&@&'gq : : : : :+::r6r)rVrUrjobarVjoburTjobvjobrrQjobpc Htjd}|\} } dtj|jz} t |||} t d|} |dk}|dk}|dko| | k}tj| }|dko| o| }|dko|o| o|}|dko|o| o|}|rd}n |s|rd}nd }|dkr$|dkrtt| | |||||| d S| | |||||| \}}}}}}t|||s|d |dz |d | z}t|t| d | |dkr|d d d | f}|rC|rAt|tj |z|jz| | |r>t|j|ztj| | |r>t|j|ztj| | t|d tj| t|dtj|t|dd d Sd S)aTest the lapack routine ?gejsv. This function tests that a singular value decomposition can be performed on the random M-by-N matrix A. The test performs the SVD using ?gejsv then performs the following checks: * ?gejsv exist successfully (info == 0) * The returned singular values are correct * `A` can be reconstructed from `u`, `SIGMA`, `v` * Ensure that u.T @ u is the identity matrix * Ensure that v.T @ v is the identity matrix * The reported matrix rank * The reported number of singular values * If denormalized floats are required Notes ----- joba specifies several choices effecting the calculation's accuracy Although all arguments are tested, the tests only check that the correct solution is returned - NOT that the prescribed actions are performed internally. jobt is, as of v3.9.0, still experimental and removed to cut down number of test cases. However keyword itself is tested externally. rr.gejsvrrRrQr rIr)rrrrjobtrNF)r)r)r8rr_rrr5r(rrrrrrr3rrzidentityr matrix_rank count_nonzero)rr2rrrrrrr3rrr0rrlsvecrsvecl2tran is_complexinvalid_real_jobvinvalid_cplx_jobuinvalid_cplx_jobv exit_statussvarrrrrjsigmas r4test_gejsv_generalr:s B )   # #C DAq %$ $D#D%55A WE 2 2 2E 1HE 1HEai %a1fF##JHUHZMU-=v(>M:MU-=v(>M:  /   qtqyyi4tT4NNNNN',uQ262626262626 (8(8(8$Q4 T;''' &!WtAw&#bqb'1E E3qU#;#;#;$ G G G Gqyyaaa!eH O OBGENN 2QVVXXZ ?NNNN K Q ATJJJJ K Q ATJJJJ q29#8#8#;#; < < < q2#3E#:#: ; ; ; q1 % % % % %5 & &r6cVtd|}|d\}}}}}}t|dt|jdt|jdt|tjdg|tjd|}||\}}}}}}t|dt|jdt|jdt|tjdg|tjd|}||\}}}}}}t|dt|jdt|jdt|tjg|tjtjdd d  |}tj ||j z}| d } ||} t|| d S) z*Test edge arguments return expected statusrrrrrQrQrQrr.rwrN)r(rr1r8rr sinrrLr0asfortranarrayrzrr) r2rrrrrrrjrAcr@s r4test_gejsv_edge_argumentsrs WE 2 2 2E$)599 CAtUDq&!!!&!!!bht5111222 E"""A#(588 CAtUDq&!!!&!!!bht5111222 e$$$A#(588 CAtUDq&!!!&!!!bhr///000 ry~~%%b"--..55e<٬?g٬\m?gJ{/L?g Oe?)gc]Fgꕲ q׿g\m?fc]F)g؁sFڿgZB>?g0L F%?gq= ףp)g?gR!u?guVſg&Sٿ)gǘ?gV-g ^)p?g( )gFx $g6[ ٿgUN@giq?)g1Zd?gOnӿgΈ ?g_vO?)g}?5^Iؿg58EGr?gio?g7[ Acd}td|j}||\}}}} } } t|||t|||t|||dS)z~ This test implements the example found in the NAG manual, f08khf. An example was not found for the complex case. rrrrN)r(r2r) r sva_expectu_expectv_expectr0rrrrrrrjs r4test_gejsv_NAGrs|0 D WAG 4 4 4E#(588 CAtUDJ$////Had++++Had++++++r6c tjd}d}dtj|jz}t |dz f||}t |f||}t |dz f||}|||g}tj|tj|dztj|dz}tj|} || z} td|\} } | |||\} }}}}}t||d t||dt||d tj|d tj|dztj|d z}tj ||}t| D]K\}}||dz }|dd||gf|dd||gf<|dd|fxx|dd|dzf|zz cc<Ld|ddz }}|dd||gf|dd||gf<t|||z| | }| | ||||| \}}t| |t| || |tvr d }|j| z}nd }|j| z}| | ||||||\}}t| || t#t$5| |dd||dddn #1swxYwYt#t$5| ||dd|dddn #1swxYwYt#t$5| |||dddddn #1swxYwYt#t$5| |d |dd|d dddn #1swxYwYd |d <d |d <| |||\}}}}} }!tj||dz d kd||dz ddS)Nrrwr.rQr2r3rgttrfgttrsrrrRrrzr}r1z?gttrf: _d[info-1] is , not the illegal value :0.)r8rr_rrr5rr3rr(r r rrrrzrrrQtestingr)"r2r3rr0durqdldiag_cpyrrrrr_dl_d_dudu2rrjrXrKrBrrb_cpyx_gttrsrb_trans__dl__d__du_du2_ipiv_infos" r4test_gttrf_gttrsr s )   # #C A %$ $D %acV5c B B BB#QD3???A $acV5c B B BB 16688RWWYY/H  RWR__$rwr1~~5A qA AA#$6eDDDLE5$)E"a$4$4!CS#tTr8A;'''q(1+&&&r8A;''' Aa(273??:A qA#11gk111sAh;!!!aX+ !!!Q$1QQQ!V9Q;bAsAqqq3({^Aaaa!SkNAq1u4(((( FFHHEE#r3T155MGTq%   AwT**** #'&&((*q.E#r3T7%HHHMGTAwT**** z " " b"gq" z " " b!CRC&" z " " b!RW z " "## beQrrUBqE"""############### BqE AaD*/%Ar*:*:'D#tT5%Js4!8})-ISPQ]-I-I-IKKKKKsH)M  MM*N  NN+O  OO,"PP!Pz1du, d, dl, du_exp, d_exp, du2_exp, ipiv_exp, b, x)g@rffffff?r)r&rffffff@)333333 @ @r)rrrr)rrrWgC>)rrrX)rRrSrTrUrUg@gffffff@g%@g@g rgffffff&g3@rrUrWrIr )@@???)?rffffff @333333ӿ333333@ffffff ?)???@r )rrrr)rr r!r y~:pffffff?)rrry333333@y@@y333333 @3333332@y333333yffffff-ffffff#@y333333yfffff?@y333333"@y𿚙?yffffff(@r ry@y?@y@@ryrry@c :td|d|df\} } | |||\} } } }}}t||t| |t| |dt||| | | | |||\}}t||dS)Nrrrr)r(r)rrqrdu_expd_expdu2_expipiv_exprrrrrrrrrrjrs r40test_gttrf_gttrs_NAG_f07cdf_f07cef_f07crf_f07csfr'Wsd$$6A1GGLE5$)E"a$4$4!CS#tTC!!!C   BD))))D(###E#r3T155MGTGQr6)r|r{r}c tjd}||||dzz}||dz ||dz dzz}||dz ||dz dzz}tj|tj|dztj|dz}tj|tjr|j|j|j|jf\}}}}||||||||f\}}}}tj ||dkr tj nd}td|f\} } | |||\}}}} } } | |||| | ||\}}td |f\}}||\}}} ||||\}}tj |j d z}t||| dS) NiTfr.rQrr{r)rgtconrrg?r)r8rrr3rrrr0rrrr(rrr)r2rrr3rqrrrrrr)rrrjrCr@rrrrrrs r4 test_gtconr*s, )   ) )C 1  1 b((A AE  SZZA..r1 1B AE  SZZA..r1 1B  RWR__$rwr1~~5A }UBK((8vqvrw7 1b"88E??AHHUOORYYu5E5EryyQVGWGWWLAq"b INN1DCKK"&&QN ? ?E#$6==LE5!&r1b!1!1B2sD$ U2q"c4T : : :FC#$6==LE5U1XXNBd U2u4 ( ( (FC 8E??  $DC4((((((r6))rSrW)rWrSrcrtd|}|\}}|||\}}t|ddS)N geqrfp_lworkrrrr)r2r1r,rrrrjs r4test_geqrfp_lworkr-sM$^EBBBL DAq,a(((KE4qr6z ddtype,dtypecptjd}dtj|jz}d}t |f||dz}t |dz f||}tj|tj|dztjtj|dz}||g}td|} | ||\} } } t||d t||dt| d d | d  tj| dtjtj |z} tj| }t|| |z| jz| t |f||}||z}td|}|| | |\}} t| d d| d  t||| dS)Nrr.rwrTrQrpttrfrrzpttrf: info = z , should be 0)err_msgrpttrszpttrs: info = )r8rr_rrr5r3rrr(r rr rrrz)ddtyper2r3r0rrqrrrr/r_erjrKrrrr1_xs r4test_pttrf_pttrsr5s )   # #C rx" "D A $QD&#66:A#QqSFE377A  RWQ^^#bgbgajj!&<&< >gajj271a==(271b>>9 Hrwwyy{ "  (h < < '1# > > E GAJJA &B 7 GAJJB '"'!Q-- 7 q!Q<r6zdtype,realtyperJctddtj|jz}t d|}d}t ||||\}}}} |||| |\} } } } t | dd| d ttjt|dtj| | |rt| tj | j ztj || t| tj | ztj | j z|| d Sd S) a Tests the ?pteqr lapack routine for all dtypes and compute_z parameters. It generates random SPD matrix diagonals d and e, and then confirms correct eigenvalues with scipy.linalg.eig. With applicable compute_z=2 it tests that z can reform A. rrpteqrrrwrqrrNrJrzinfo = z, should be 0.rN)rr8rrr(rOrrsortr rrzrr3)r2rIrJr0rQrrqrrrNd_pteqre_pteqrz_pteqrrjs r4 test_pteqrrWX s_ HHH # #D ge 4 4 4E A"5(AyAAJAq!Q&+ea1Y&O&O&O#GWgtq8D888999BGDGGAJ'')9)9EEEE&"''"2"2"44bk!nn! # # # # "''"2"22RWW5E5E5GG & & & & & & &&r6ctdtd|}d}t||||\}}}}||dz |||\} } } } | dksJdS)NrrQrrwrTrNrJrrr(rO r2rIrJrQrrqrrrNrTrUrVrjs r4test_pteqr_error_non_spdr\y sy HHH ge 4 4 4E A"5(AyAAJAq!Q',eAE1Y&O&O&O#GWgt !888888r6c Ltdtd|}d}t||||\}}}}tt||dd|||tt|||dd|||r$tt||||dd|dSdS)NrrQrrwrrY)rr(rOrrQ) r2rIrJrQrrqrrrNs r4"test_pteqr_raise_error_wrong_shaper^ s HHH ge 4 4 4E A"5(AyAAJAq!Q*eQssVQ!yIIII*eQ#2#!yIIIINj%A3B39MMMMMMNNr6ctdtd|}d}t||||\}}}}d|d<d|d<|||||\} } } } | dksJdS)NrrQrrwrrYrZr[s r4test_pteqr_error_singularr` s HHH ge 4 4 4E A"5(AyAAJAq!Q AaD AaD&+eAqA&K&K&K#GWgt !888888r6zcompute_z,d,e,d_expect,z_expect)gp= ף@rgq= ףp?r)g\(\ @g ףp= g?)gŏ1w- @gR'?g/n?g&䃞ͪ?)g cZB>?gCl?g:pΈڿg??)gaTR'?gSۿg}гY?g%uο)g\mg٬\m?gAf?gL F%u)gǘgŏ1w-!?g333333?gz6?cnd}td|j}tj|tj|dztj|dz}|||||\}} } } t |||t tj| tj||dS) zb Implements real (f08jgf) example from NAG Manual Mark 26. Tests for correct outputs. rrQrrQrrRrN)r(r2r8r3rr) rJrqrrDz_expectr0rQrNrr3_zrjs r4test_pteqr_NAG_f08jgfrd s D gag 6 6 6E  RWQ]]"RWQ^^3AuqAi@@@BBBt,,,,BF2JJx 0 0t<<<<< " "$$$$$r6ctjg}td|j}t t ||dS)Nrir)r8rr(r2rr)A_emptyris r4#test_geqrfp_errors_with_empty_arrayrx s;hrllG hgm < < .0 s%%%!A%%%r6)rrrr(r#rk)rrrdrr~dlwrlwvals r4test_orcsd_uncsd_lworkr% s JJJ1 A AAK''$$TC C #V , , ,B 2q!Q ' 'ED[[EEuhE %%u%%% & &&&&&&r6c nd\}}}|tvrdnd}|dkrtj|ntj|}t |dz|dzf|\}}t ||||}|dkrd|int tddg|} ||d|d|f|d||df||dd|f||d|dffi| \ } } } } }}}}}}|d ksJt||}t||}tt||t||z ||z }t|||z }t|||z |z }t||z ||z }t||z ||z |z }tj ||f|}|d }t|D] }||||f< t|D]}||||z||zf<t|D]}| |||z|z||z|z|z|z|zf< t|D]}||||z|z|z||z|zf<t|D]}tj |||||z||zf<tj |||||z|z||z|z|zf<tj|| |||z||z|z|z|zf<tj|||||z|z||zf<||z|z}t||d d tj|jz dS)N)rhPrrcsdrrrlrworkrrrg@rP)rr$rvsr%r(r#dictrrrcr8r r6cosrrrr)rrrdrr~Xdrvrrlwvalscs11cs12cs21cs22thetau1u2v1tv2trjrXVHrn11n12n21n22SonerBXcs r4test_orcsd_uncsdr3 sGAq!K''$$TC!Tkk }/@/C/CAucK.? @OOOHC 31a ( (E!$gu  $sG>>>???r:a=)))q*Q-(((r:a=)))q*Q-(((AvD)))) GE9 % %T 1 4U 4 4666 DJqMQWQZ '+>4:a=+>+>12+>+>@@@ DJqMQWQZ '+>4:a=+>+>12+>+>@@@@@r6c tjd}td|\}}d}t |dz f||}t |f||}t |dz f||} tj|dtj|ztj| dz} t |df||} |t vrd nd } |r| jn| | z} |d kr |||| ndgd z\}}}}}}|||| | || ||||| }|\ }}}}}}}}}}|dkr7d|d<d|d<|||| | }|\ }}}}}}}}}}|dks JddS|d krAd|d<d|d<d|d<|||| | |||||| }|\ }}}}}}}}}}|dks JddSdS)NrrrrwrQrrrRrzr}rJrVrrUrz&info should be > 0 for singular matrix)rrrrrr) r8rr_r(r5r3rrrz)r2rrr3rrrrrqrrrrrrrrrrrrrrrrrrr rrrjs r4test_gtsvx_error_singularr sa )   # #C#$6eDDDLE5 A $acV5c B B BB#QD3???A $acV5c B B BB B"'!**$rwr1~~5A#QF%SAAAAK''CCSE! (qA-A!CKKb!RdVAX)D#tUE5b!RUE777I@I=CS$feT4 s{{"2E"aQ'' DMARdD&%tTaxxxAxxxxx BRb E"aQTt#%111 DMARdD&%tTaxxxAxxx xr6ctjd}td|\}}d}t |dz f||}t |f||}t |dz f||} tj|dtj|ztj| dz} t |df||} |t vrd nd } |r| jn| | z} |d kr |||| ndgd z\}}}}}}|d krtt||dd|| | || ||||| tt|||dd| | || ||||| tt|||| dd| || ||||| tt|||| | dd|| ||||| dStt|||| | || |dd|||| tt|||| | || ||dd||| tt|||| | || |||dd|| tt|||| | || ||||dd| dS)NrrrrwrQrrrRrzr}rJrVrUr) r8rr_r(r5r3rrrzrrQr)r2rrr3rrrrrqrrrrrrrrrrrs r4"test_gtsvx_error_incompatible_sizer s. )   # #C#$6eDDDLE5 A $acV5c B B BB#QD3???A $acV5c B B BB B"'!**$rwr1~~5A#QF%SAAAAK''CCSE! (qA-A!CKKb!RdVAX)D#tUE5 s{{j%CRC!Ru$3E 7 7 7 7 j%QssVRu$3E 7 7 7 7 j%Q3B3u$3E 7 7 7 7 iAr1SbS6u$3E 7 7 7 7 7 7 j%QAu$ss)E 7 7 7 7 j%QAu$3ss8E 7 7 7 7 j%QAu$3ss)U < < < < j%QAu$3E#2#JU < < < < < r( 7)H(8?@w)H)H)HHI1)N)Nr6cdSN)NNNrrs r4rr* -?r6c(tjd}dtj|jz}t d|}d}t |f||dz}t |dz f||} tj|tj| dztjtj| dz} t |d f|| } | | z} ||| \} }}| | | g}||| | || | \} }}}}}}t||d t| |dt| |d t|d kd |dt| |tj|dtjtj |z}tj| }t| ||ztj|jz|t!|dr Jd|t|jdkd|jdt|jdkd|jddS)a This tests the ?ptsvx lapack routine wrapper to solve a random system Ax = b for all dtypes and input variations. Tests for: unmodified input parameters, fact options, incompatible matrix shapes raise an error, and singular matrices return info of illegal value. rr.ptsvxrrUrTrQrrRrrrefrzinfo should be 0 but is .rrr)rRrz# but should be ({x_soln.shape[1]},)rN)r8rr_rrr(r5r3rrr rrr rrzrr1)r2rIr df_de_lambdar3r0rrrqrrrrrrrjrrr rrrKrs r4 test_ptsvxr$ s )   # #C %$ $D WE 2 2 2E A#QD(C881. .:::qeAqkk::::::r6c:g|]}t|D]}|Srrrs r4rWz5test_pptrs_pptri_pptrf_ppsv_ppcon.. rr6c6g|]}t|D]}|SrrrVrrs r4rWz5test_pptrs_pptri_pptrf_ppsv_ppcon.. s+<<. s/>>>U1XX>>1>>>>r6)ppsvpptrfpptrspptrippconrrrrrP)rrr)r8rr_rrr5rrzr r6r(rrrrrrrrrr)r2rr3r0rrbrr^aprrrrrulrjaululiaulirbxxvrr rs @r4!test_pptrs_pptri_pptrf_ppsv_ppconr s )   % %C 8E?? s "DGAt#QF%SAAAA#QIUDDDA  Q///%%));;A @::::E!HH:::::::E!HH:::<=>eAqsmm>>>@ 4B'74((($D%u uQ%(((HBq 1E " " "4 (CB!$////a5)))ICq q66$. Dr6FrrrrIrfrPrWrQr r r8rr_rrr5r(rr/rrrrz) r2r3r0rrbr r rrrNd2s r4test_gees_trexcr s )   % %C 8E?? s "D A#QF%SAAAA"#4EBBBKD% T..! 7 7 7FQq Ar A 4B 271::AD9999AEAFFHHJ&==== U1aA  FQq Ar A 271::AD9999AEAFFHHJ&====AdGRad333333r6zt, expect, ifst, ilst)rg)\({Gz?gQ?)r皙rffffff?)rgrg?)rrrr)rlV}gV_?g|?5^?)g?rgV/?g;On?)rrrggj+)y ףp= ? ףp= ׿yRQȿQ?y)\(?п)r@yQ ףp= yq= ףpͿp= ף?)rr @yGz?(\?)rrr@)ry1%Ŀ q?ys??ܵ|ȿyHzG??ܵ?)rryV/?ݓ?yjt?vտ)rrryB>٬?=U?)rrrrcd}td|j}|||||d}t|dd|d}t|||dS) zg This test implements the example found in the NAG manual, f08qfc, f08qtc, f08qgc, f08quc. rr rr)wantqrrN)r(r2rr)rifstilstexpectr0r rs r4test_trexc_NAGr so< D WAG 4 4 4E U1at1 - - -FQq AFAD))))))r6ctjd}tj|jdz}d}t ||g||}t ||g||}t d|\}}|d||dd }t|d d |d } |d } |d } |d} | d| dz } | d| dz }|tvrJt| tj | d |t| tj | d |t| | z| j z|d |t| | z| j z|d ||| | | | dd }t|d d |d } |d } |d} |d} |tvrJt| tj | d |t| tj | d |t| | z| j z|d |t| | z| j z|d |t| d| dz |d |t| d| dz | d |dS)Nrr.rwr)ggestgexcrcdSr#rr s r4rz!test_gges_tgexc..L rr6Fr* overwrite_brrrQrrIrrfrPrWrRrSrr)r2r3r0rrbrr!r"rrrrrNd1rs r4test_gges_tgexcr'A s )   % %C 8E?? s "D A#QF%SAAAA#QF%SAAAA"#4EBBBKD% T..!QEu M M MFQq Aq Ar Ar A 41T7 B 41T7 B 271::AD9999271::AD9999AEAFFHHJ&====AEAFFHHJ&==== U1aAq! $ $FQq Aq Aq Aq A 271::AD9999271::AD9999AEAFFHHJ&====AEAFFHHJ&====AdGag%r====AdGag%r======r6ctjd}tj|jdz}d}t ||g||}t d|\}}}|d|d }t|d d |d } |d } | d } |tvr%t| tj | d |t| | z| j z|d |tj |} d| d<t|| | } |tvr|| | | | }n|| | | | | d}t|d d |d } |d} |tvr%t| tj | d |t| | z| j z|d |t| d| d |dS)Nrr.rwr)r trsen trsen_lworkrcdSr#rr s r4rz!test_gees_trsen..| rr6FrrrrIrfrPrQrVrrliworkrr8rr_rrr5r(rr/rrrrzr r#)r2r3r0rrbr r)r*rrrNrselectrs r4test_gees_trsenr0q s  )   % %C 8E?? s "D A#QF%SAAAA/( 7 7 7D%T..! 7 7 7FQq Ar A 4B 271::AD9999AEAFFHHJ&==== Xa[[FF1I ; 2 2E vq!5111vq!5qBBBQq Aq A 271::AD9999AEAFFHHJ&====AdGRad333333r6z*t, q, expect, select, expect_s, expect_sep)g/$?g QIg~jtx?gJ4?)r58EGrgGr?gyX5;?)rg?߾r1gt?)rrrg yǹ)g؁sF?g_L?gGz?gUN@?)goT?g0*g' gz6>W)g(g&䃞ͪӿgbX9ҿg-!lV?)gb=y?gۊe?rg8EGr?)rg?gQg(\ſ)g ףp= ?gQ?rr)g)\(ܿgQտgQg(\?)rg{GzԿgp= ףg)\(?)rQrrrQg?g(\ @)yqhyfc]F?ڊe׿yMbȿ&S?y&1??п)ry?5^I @yo0*yZd;OͿ~:p?)rryx $(@4@y[ A?&?)rrry?ܵ@St$)y?ܵ꿽R!uy2U0*6[?yV-?=yXy8m4?1%̿)ySt$?\mҿyʡE?S㥛?y~:p cڿyK7A`?[ A?)y:pΈ~jtԿyH}?9#J{yH}? cZy+eXw? -ٿ)y"u? c?y?տN@ayRQȿ{GzĿyh"lxz?EGrǿ)y47 )yS!uq F%u @y yտGx $(?y3ı.n?rh|)yv? F%uyd`TR?I&†ۿyN@?ݓy4@ @ ^)?)ys{ @ o_yH.@|Pk @y 0*?*:Hy]m{?Gz)y) 0[. rr6Fr$rrrQrrIrrfrPrVrirrr.)r2r3r0rrbrr!r9r:rrrrrNr&rr/rs r4test_gges_tgsenr< s )   % %C 8E?? s "D A#QF%SAAAA#QF%SAAAA/( 7 7 7D%T..!QEu M M MFQq Aq Ar Ar A 41T7 B 41T7 B 271::AD9999271::AD9999AEAFFHHJ&====AEAFFHHJ&==== Xa[[FF1I ;1 5 5E1XaZq "E U61aAU 3 3 3FQq Aq Ar Ar A 271::AD9999271::AD9999AEAFFHHJ&====AEAFFHHJ&====AdGag%r====AdGag%r======r6za, b, c, d, e, f, rans, lans)rrrr)rr&rr)rrr&r)rrrg@)rrrr)rrrr)rrg(@)g"rr>)r=rr>r)rrg3@)rrrr&)rrrr)rrrr)rrrr)rrrr)rrrr)rrrr)r?rrr)rrg r)rrr)r@rrr)rrrr)rrr&r)rrrr)rrrr)rr&rr)rrrr)rrrrc |d} td|} | ||||||\} } } }}t|dt| ddtj|jdzdt|d dtj|jdzd t| || d t| || d dS)Nrtgsylrrrr.zSCALE must be 1.0rr0r0rzDIF must be nearly 0zSolution for R is incorrect)r0r0zSolution for L is incorrect)r(rrr8rr)rbrrrqrreranslansr2r0rBroutloutr]difrjs r4test_tgsyl_NAGrI# sH D ge 4 4 4E#(5Aq!Q#:#: D$sDqE3QRXe__-@-D/1111C128E??+>s+B24444D$T9;;;;D$T9;;;;;;r6r)rUrzijob)rrQrRrSrTc x|tjkrdnd}tjd}d\}}t |dd||g||dd||g|d^}}} t |dd||g||dd||g|d^} } } |d d ||g|} |d d ||g|} td | }||| | || | || \}}}}}|dks Jd|dks Jd|dkr/t|ddtj |j dzdn|dks Jd|d kr|dkr!||z|| zz }|| z}||z|| zz }|| z}nq|dkrktj ||ztj ||zz}|| z}|tj | z|tj | zz}d|z| z}t|||ddt|||dddSdS)NgMbP?g|=lOElt/rirwr)outputr rRrBr)rrJrzINFO is non-zerorzSCALE must be non-negativer.zDIF must be 0 for ijob =0rCzDIF must be non-negativerUrzrzlhs1 and rhs1 do not match)r0rr0zlhs2 and rhs2 do not match) r8rrrr!uniformr0r(rrrr)r2rrJr0r3rrrbrqr@rrrrerBrFrGr]rHrjlhs1rhs1lhs2rhs2s r4 test_tgsylrRW s% BJ&&44ED )   0 1 1C DAq#++c21v..55e<<++c21v..55e<<!!!HAq1#++c21v..55e<<++c21v..55e<<!!!HAq1 BAq6""))%00A BAq6""))%00A ge 4 4 4E#(5Aq!Q/44$A$A$A D$sD 1999(999 C<<<5<<< qyySqrx/B3/F ; = = = = =czzz5zzz qyy C<<t8dQh&D7Dt8dQh&D7DD c\\<??T)BLOOd,BBD7D",q//)D2<??,BBD:a > > >dB < > > > > > >yr6mtypercj|dkr|tvrtjdtjd}d\}}|t vrH|||f|||fdzz|}n+|||f|}|dkr ||j zn|| j z}|||f|}|d|d |d f}t|| \} } } | || } | || | \} }}|dksJ| | |||\}}|dksJtj |j }t||z|d|z|zdS)Nrzhetrs not for real dtypes.*M/t|0)rrUrr.rrrtrsrrrr)rbrrrr.r)rrBrCr8rrr/rMr0rzrr(rrr)rSr2rr3rrrrrJrrrVrr rrjrrs r4 test_sy_hetrsrW s }}+-- 0111 )   0 1 1CGAt  [[q!f[ % % !Q (@(@(C C K KE R R KKaVK $ $ + +E 2 2D==ACa!&&((*nA !T ##**511AMMMe...5 =E*5>>>CC Iau % % %Ec!5666OCt 19999cCdau555GAt 19999 (5// CAaCQs++++++r6c|dkr|tvrtjdtjd}d}|||f|||fdzz}tj|tjr|j}| |}|dkr ||j zn|| j z}|d|df}t|| \}}||| \} } } | d ksJ|| | | \} } | d ksJtj |j} tj|}|r>t#tj| tj|d |z| zdSt#tj| tj|d |z| zdS)Nrzhetri not for real dtypes.rUrr.rrrMrrr)rbrrr.r)rrBrCr8rrrrrr0rzrr(rrrrrrr)r2rrSr3rrrJrrMr rrjA_invrrs r4test_sy_he_trirZ s }}+-- 0111 )   0 1 1C A Aq6SZZA//22A }UBK(( F AD==ACa!&&((*nAMMMe=== (EU333HCc!5)))OCt 19999#$e444KE4 19999 (5// C )--  C F 3q59EEEEEE 3q59EEEEEEr6rz uplo, m, n))rXrUrw)rXrwrw)rKrwrU)rKrwrwctjd}|||f|}t d|f\}} |||||} |dkrtj|ntj|}|dkr)tjt||} d|| | f<| ||} t| | ddS) Nl8#q9 r)lantrr)rNr3rXrQ>r) r8rrr0r(rrrrcr) rrNrrr3r2r3rr\rrCrBrs r4 test_lantrr^ s )   1 2 2C A &&u--A#$6==LE5 %ad . . .Cckk rwqzzA s{{ Ic!Qii !Q$ %a..CC4((((((r6c tjd}d\}}}|||f|||fdzz}|tjd|dd|}||z }tj|tjr|j}| |}d|tj ||dz<d|tj || dz <t|||}d|z|zdz} tj | |f|} || |dddf<tj||d kr tjnd } t#d | f\} } | | ||\}}}| |||||| d}t#d |f\}}||d}||| |d}t%||ddS)N2 rwrRrRr.rrwrQrRrr{r)gbcongbtrf)rrgrfrMrrrrr)r8rrrrrrrrr0rrr"r rrrr(r)r2rr3rrfrgrrtmpLDABrMrrbrclu_bandrr@rCrrrrs r4 test_gbconrg s )   , ,CIAr2 Aq6SZZA//22A \\"+aa)<)>LE5uRR((GT1 %TbRG$    C$$6==LE5 q!B %E % % %a (CC1%%%%%%r6c:tjd}d\}}}|||f|||fdzz}tj|tjr|j}||}d|tj||dz<d|tj|| dz <t|||}td|f\}} | ||} |||||} t| | ddS) Nr`rar.rrQ)langbrr]r) r8rrrrrr0rrr"r(r) r2rr3rrfrgrrMrirrrCs r4 test_langbrj s )   , ,CIAr2 Aq6SZZA//22A }UBK(( F A$%Aboaa  !%&Aboa"q!!" 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