ftju-ddlmZddlZddlmZmZmZmZmZm Z ddl Z ddl m Z ddl Zddl mZmZmZmZmZmZmZmZddlmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$ddl%m&Z&ddl'm(Z(dd l)m*Z*m+Z+ddl,m-Z. dd lm/Z0n #e1$rdZ0YnwxYwdd l'm2Z2dd l3m4Z4dd l5m6Z6dxZ7Z8e6dddZ7e6dddZ8ej9ej:gZ;ej<ej=gZ>e;e>zZ?dZ@dZAdZBGddZCGddZDGddZEe jFGde?e jFGdgddZHGdd ZIGd!d"ZJGd#d$ZKGd%d&ZLe jFGde?e jFGd'gd(e jFGd)d*d+ge jFGd,d-d*ge jFGd.d/d0gd1ZMd2ZNd3ZOd4ZPd5ZQGd6d7ZRGd8d9ZSd:ZTd;ZUd<ZVd=ZWd>ZXd?ZYd@ZZdAZ[dBZ\dCZ]dDZ^dEZ_dFZ`dGZaGdHdIZbdJZcdKZddLZedMZfe jFgdNdOPdQZhdRZie jFGdSdTdUge jFGde;e jFGdVejdWe jFGdXejdYe jFGdZejdYe jFGd[dd\ge jFGd]dd\gdhd^Zke jFGde;d_Zle jFGd`dVdaidXdaidZdaid[daidbdaid]daifdcZme jFGddejngdegdfgdggdhgdigdjgejngdkejngdlgdmgdngdogdpgdqgejngdrgdsgdtgdugfgdvZoe jFGde?dwZpe jFGdxejngdyejngdzejngd{ejngd|ejngd}ejngd~ejngdejnddgddgddgddgddggejnddgddgd/dgddgdd\ggf ejngdejngdejngdejngdejngdejngdejngdejnddgddgddgddgddggejnddgddgddgddgddggf gdZqe jFGde?e jFGd'gde jFGd.d/d0gdZre jFGde?e jFGdgddZse jFGdete;e;ze?dZue jFGdete;e;ze?dZve jFGdete;e;ze?dZwe jFGdejngdejngdejngdejngdejndWd0gdadYgddagddgddggejnddgddgd\dgddWgd/dggfejngdejngdejngdejngdejnddgddgddgddggejnddgddgddgddggfgd˄Zxd̄Zye jFGdete?e;e;ze jFGdejd/dτZze jFGdete?e;e;ze jFGdejd/dЄZ{e jFGdete?e;e;ze jFGdejd/dфZ|e jFGdete?e;e;ze jFGdejd/d҄Z}e jFGddejngdԢejngdբejngd֢ejngdעgdآgd٢gdڢgfgdۄZ~e jFGde?e jFGdgdݢdބZd߄Ze jFGdgde jFGdddgdZe jFGdddge jFGdddgdZe jFGde?e jFGdgddZe jFGde?dZe jFGde?e jFGdddNge jFGddd-gdZe jFGde?e jFGddd\ge jFGddd-gdZe jFGde?dze jFGdddNge jFGddd-gdZe jFGdejngdyejngdzejngd{ejnddgddgddgddgddggejnddgddgd/dgddgdd\ggfejngdejngdejngdejnddgddgddgddgddggejnddgddgddgddgddggfgdZe jFGdete?e;e;ze jFGdddfd-dfgdZe jFGdete?e;e;ze jFGdddfd-dfgdZe jFGdete?e;e;ze jFGdddfd-dfgdZe jFGdejngdejngdejndWd0gdadYgddagddgddggejnddgddgd\dgddWgd/dggfejngdejngdejnddgddgddgddggejnddgddgddgddggfgdZe jFGdddNge jFGde?dZe jFGde?dZe jFGdejngdgdgd gd gejngd gd gd gd gdd\fejngdgdgdgdgejngdgdgdgdgd\dYfgdZe jFGde?dZe jFGde?dZe jFGdejngdgdgdgdgejngdgdgd gd!gejngd"gd#gd$gd%gejngd&d'd(fejngd)gd*gd+gd,gejngd-gd.gd/gd0gejngd1gd2gd3gd4gejngd&d5d6fgd7Ze jFGde?d8Ze jFGd9ejngd:gd;gd<gd=gejngd>gd;gd<gd?gejngd@gdAgdBgdCgejngdDgdEgdFgdGgejngdHgdIgdFgdJgejngdKgdLgdMgdNgejngd>gdOgdPgdQgejngdRgdSgdTgdUgfge jFGde;dVZe jFGde;e jFGdWdXe jFGdYgdZd[Ze jFGd\ddge jFGde?e jFGdd]d^Ze jFGd\ddge jFGde?e jFGdd]d_Ze jFGd'ed`e jFGdagdbe jFGd,d-d*ge jFGde?dcZe jFGde?e jFGd'gdddZe jFGd'ed`e jFGde?deZe jFGde;e jFGdfd]dgZdS(i)reduceN) assert_equalassert_array_almost_equalassert_assert_allcloseassert_almost_equalassert_array_equal)raises)eyeoneszeros zeros_liketriutril tril_indices triu_indices) _flapacklapackinvsvdcholeskysolveldlnorm block_diagqreighqz) _to_banded)_compute_lwork) ortho_group unitary_group)_clapack)get_lapack_funcs)get_blas_funcs)CONFIGzBuild Dependenciesblasnameversionc|tvr+|j||j|dzz|S|j||S)N?)COMPLEX_DTYPESrandastype)shapedtyperngs \/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/scipy/linalg/tests/test_lapack.pygenerate_random_dtype_arrayr3+s\ % #(E"4'()/ 7 38U  " "5 ) ))crtjtjdt tj}hd}t }ttD]4}|ds||vr||vr| |5|gks JddS)z%Test that all entries are in the doc.Nzlapack.__doc__ is None>npclapackflapackdivision HAS_ILP64print_functionabsolute_importfind_best_lapack_type_z2Name(s) missing from lapack.__doc__ or ignore_list) r__doc__pytestskipsetsplitlistdir startswithappend)names ignore_listmissingr(s r2test_lapack_documentedrK3s ~ ,--- $$&& ' 'E   KffGF !!$$ ![)@)@E!! NN4 b===N=====r4c.ddlm}ddlm}||ksJdS)Nr)r:)scipy.linalg.blasr:scipy.linalg.lapack)blas_has_ilp64lapack_has_ilp64s r2#test_ilp64_blas_lapack_both_or_nonerQJs>======AAAAAA - - - - - - -r4c&eZdZdZdZdZdZdS)TestFlapackSimplec gdgdgdg}gdgdgdgdg}dD]}tt|d zd}|||\}}}}} t| t| t ||t ||fd t |d d z ft |tjt |||d d \}}}}} t| t| dS) N))) )rUrrga2U0*3?)rXrrgMb`?)r[rUrr)rrUrrsdzcgebalrrU)permutescale) getattrr8rreprrrlenr6r ) selfaa1pfbalohipivscaleinfos r2 test_gebalzTestFlapackSimple.test_gebalRs6 YY 999 -oooollll * *A7D11Ay)*1 &BB$ Hd4jj ) ) ) %b! , , , "bAs1Q4yy{#3 4 4 4 %hA @ @ @)*2q)B)B)B &BB$ Hd4jj ) ) ) ) * *r4cgdgdgdg}dD]K}tt|dzd}|||\}}}t| t|LdS)Nikiifii"iiidgehrd)rbr8rrc)rerfrhrihttaurns r2 test_gehrdzTestFlapackSimple.test_gehrdgs    __ ^^  * *A7D11AyAaDDMBT Hd4jj ) ) ) )  * *r4c tjddgddgg}tjddgddgg}tjdd gd d gg}d }d D]}||||||}}}td|f\} |r|dxxdz cc<d}| |||\} } } t tj|| tj| |z| |z| |||||\} } } t tj|j| tj| |jz| |zd| |||d\} } } t tj|| tj| |z | |zddS)NrUrVrrXrYrZr\r] TfdFD)trsylr+C)tranatranbdecimal)isgn) r6arrayr.r$isupperrdot conjugater~) rerfbctransr0rgb1c1rxrarns r2 test_trsylzTestFlapackSimple.test_trsylrs Hq!fq!f% & & Hq!fq!f% & & Hq"gBx( ) ) = =E%!((5//188E??BB%j2%88FE}} 1 "U2r2..NAud %bfRmmbfQmm&C&+bj 2 2 2#U2r2U%HHHNAud %F2<<>>+Q//"&BLLNN|dvr:tj tjtj|d}t||~dS)Nrqrrrtr Mm1OoIiFfEerrr+)langeFfEeFfrWr[Mm1OoraxisIirU) r6rr.rr$sqrtsumsquareabsrmaxr) rerfr0norm_strrgrvaluerrefs r2 test_langezTestFlapackSimple.test_langes H    OO NN    - -E) - -XXe__==??#tHHHNHHH)*re<<h++v%%}}"#"#'"&26"::)>)>"?"?@@C'sG<<<<4'' fRVBZZ00!U** fRVBF2JJQ%?%?%?@@!T)) fRVBF2JJQ%?%?%?@@ ,,,,1 - - -r4N)__name__ __module__ __qualname__roryrrr4r2rSrSPsP**** * * *===8-----r4rSceZdZdZdZdS) TestLapackc4ttdrdSdSN empty_module)hasattrr8res r2 test_flapackzTestLapack.test_flapack# 7N + +  D  r4c4ttdrdSdSr)rr7rs r2 test_clapackzTestLapack.test_clapackrr4N)rrrrrrr4r2rrs2 r4rc&eZdZdZdZdZdZdS)TestLeastSquaresSolversc ztjd}ttD]\}}d}d}d}|||f|}|||}t d|\} } t| |||} | ||| \} } } t| dk| ||d || \} } } t| dktD]}tj d d gd dgddgg|}tj gd|}t d||f\}}}|j \}}t|j dkr|j d}nd}t||||} |||| \}}} t|ddtj ddg|dtj|jz||\}} } } t!||t"D]}tj dd gddgddgg|}tj gd|}t d||f\}}}|j \}}t|j dkr|j d}nd}t||||} |||| \}}} t|ddtj dd g|dtj|jz||\}} } } t!||dS)!Nr{rU)gels gels_lworkr0lworkrTTCCrr?@@@@ @0@g1@g4@)rrgeqrfrVr祪,-@rtol?@@?@@ @ffffff?ry1@@y4@R ?\j,?W?)r6random default_rng enumerateDTYPESr.r$r r REAL_DTYPESrr/rdrfinfoepsr r,)rer1indr0mnnrhsrgrglsglslwrr>rnrrrlqrr lqr_truths r2 test_gelsz!TestLeastSquaresSolvers.test_gelssi##D))#F++  JCAADQF##**511BA%%e,,B)*@NNNJC#5!Q55ER5111JAq$ DAI   R6#;eDDDJAq$ DAI      / /EC:::'.3555B,,,E:::B&63b"X'?'? #D*e8DAq28}}!!x{#:q!T::E4Be444LCD AcrcFBH.A.@.B38%:%:%:"$BHUOO$7!7 9 9 9 9"'r Iq!Q sI . . . .# / /EHc?$h/$h/18=???B666eDDDB&63b"X'?'? #D*e8DAq28}}!!x{#:q!T::E4Be444LCD AcrcFH&J&J&L+02228:28E??;N8N P P P P"'r Iq!Q sI . . . ./ / /r4c tD]X}tjddgddgddgg|}tjgd|}td ||f\}}|j\}}t |jd kr|jd }nd }||||d \} } } t tj| } | } |||| | d d d \}}}} t|dd tjddg|dtj |j zt|tjddg|dtj |j zZtD]i}tjddgddgddgg|}tjgd|}td ||f\}}|j\}}t |jd kr|jd }nd }||||d \} }} } t tj| } t |}| } |||| || d d d \}}}} t|dd tjddg|dtj |j zt|tjddg|dtj |j zkdS)Nrrrrrrrr)gelsd gelsd_lworkrVrUrFrrrrYN))1)@*@.?rrrrrrrrU.*@_Y@ rr6rr$r/rdintrealrrrr,)rer0rgrrrrrrworkiworkrnr iwork_sizersrankrwork rwork_sizes r2 test_gelsdz"TestLeastSquaresSolvers.test_gelsds  9 9EC:::'.3555B,,,E:::B!12J35r("<"< E;8DAq28}}!!x{!, Aq$ ; ; D% &&EJ$uRUJ%' 7 7 Aq$ AcrcFBH.A.@.B38%:%:%:"$BHUOO$7!7 9 9 9 9 Arx);):)dpts r2 test_gh_2691zTestDpotr.test_gh_2691si##B'' JJFJ # # EE!#JJ)*"?"?"ABBQQQ ]+- . .%Eu#%%%VnfTTrTlVAYU 9K-K,LMNNneDDbDk4011 6)44q&!!  A%3$$C LLQ Q1SPQSS    "%RVBHUOO,,,.CDEEEEBHRZ,@,@,D(D "*!5!5!99 ; ; ; ; ; ;r4N)rrrrKrr4r2r+r+s#;;;;;r4r+ceZdZejdedZejddeDejdddgejdd dgd Zejd gd gd gdgdZ dZ ejdddgdZ dS) TestTbtrsr0cd|tvratjgdgdg|}tjddgddgdd gd d gg|}tjd d gddgddgddgg|}n|tvrdtjgdgdgdg|}tjddgddgddgddgg|}tjddgd d!gd"d#gd$d%gg|}nt d&|d't d(|}|||d)*\}}t |d+t||d+d,-d.S)/zTest real (f07vef) and complex (f07vsf) examples from NAG Examples available from: * https://www.nag.com/numeric/fl/nagdoc_latest/html/f07/f07vef.html * https://www.nag.com/numeric/fl/nagdoc_latest/html/f07/f07vsf.html )p= ףgQ@gHzG@g{Gz?)ggq= ףp@gHzGrrgp= ף0rOg(\+gףp= 0g333333*@g(\gHzG,gQ#rXrUrrWrVr)y ףp= Q@y{Gz@GzyQ?HzGy)\(??)yQ Q @yq= ףpGz@yףp= ?{Gzr)yQ?q= ףp @y)\(zGrryQ! ףp= yףp= 8Gzyp= #/)\h7y\(LHzG @yQHz6@yףp= 3@(\=y{Gz-333333yQ+3@GzT5@y@y?@y?yyt&m=#yi6@Ug$B@y[a^C?b->y-@ji&*!z Datatype z not understood.tbtrsLabruplorh㈵>rr7N)rr6rr, ValueErrorr$rr)rer0rTrx_outrQrrns r2test_nag_example_f07vef_f07vsfz(TestTbtrs.test_nag_example_f07vef_f07vsfs K  4442224 %'''B65/!6* %.!5/+ % &&&A Hq!f!2h !f "g'$) ***EE n $ $KKKFFF:::<!&'''B=.9*N;)>:)>:< % &&&A Hr6l%w/46JK35JKM$) ***EE @@@@AA A '%888%2---4T15qt444444r4z dtype,transc>g|]}dD]}|dkr |tv||fS))Nr~rr)r).0r0rs r2 zTestTbtrs.5sPNNN"'NN6;&+sllu 7K7K %en7K7K7K7Kr4rUUrRr:r\c tjdd\}}td}|dk}||z} || z } t | | dz d} fd| D} fd | D} |dkrtj| | <t j| | d }tj|dzf}t| D]@\}}| |||t|d t|zf<At|f}|||||| \}}t|d |dkrt||z|ddS|dkrt|j|z|ddS|dkr.t|j|z|ddSt%d)Ni)rXrWrVrQrr_rUrc4g|]}t|z Sr)r)r]rrs r2r^z2TestTbtrs.test_random_matrices..Js#888aq3q66z888r4c4g|]}t|fSr)r3)r]widthr0r1s r2r^z2TestTbtrs.test_random_matrices..Ks7+++-eXucBB+++r4dia)formatr)rTrrUrr:r\g-C6 ?rr~rzInvalid trans argument)r6r RandomStater$r=r spsdiagsr rdiagonalrminr3rrr~rrX)rer0rrUr:rkdrQis_upperkukl band_offsets band_widthsbandsrfrTrowkrrrnrr1s ` @@r2test_random_matriceszTestTbtrs.test_random_matrices4s4i##D))  4 666CK (] "WR"q"-- 8888<888 +++++)+++ 3;;///E"I Ie\% 8 8 8XrAvqk5 ) ) -- ; ;FC-.ZZ]]BsC1IIc!A#qkk)) * * (D 5# > >%2UFFF4T1 C<< AE14 0 0 0 0 0 0 c\\ AC!GQT 2 2 2 2 2 2 c\\ ACMMOOa/ > > > > > >566 6r4zuplo,trans,diag)r_r\Invalid)r_rur\)rur\r\c tdtj}tjd}|d}|d}t t ||||||dS)z?Test if invalid values of uplo, trans and diag raise exceptionsrQrr)rXrV)rVrXN)r$r6r@rrrr)rerUrr:rQr1rTrs r2&test_invalid_argument_raises_exceptionz0TestTbtrs.test_invalid_argument_raises_exceptionhso! ;;;i##D)) ZZ   JJv  iAtUDAAAAAr4ctjdt}tjdt}tdt}d|d<|||d\}}t |dd S) aHTest if a matrix with a zero diagonal element is singular If the i-th diagonal of A is zero, ?tbtrs should return `i` in `info` indicating the provided matrix is singular. Note that ?tbtrs requires the matrix A to be stored in banded form. In this form the diagonal corresponds to the last row.rrrXrQr)rrWr_rSN)r6r floatr$r)rerTrrQr>rns r2test_zero_element_in_diagonalz'TestTbtrs.test_zero_element_in_diagonalvswWV5 ) ) ) GAU # # # 6665 %2---4T1r4zldab,n,ldb,nrhs)rYrYrrY)rYrYrWrYctj||ft}tj||ft}tdt}t t |||dS)z2Test ?tbtrs fails correctly if shapes are invalid.rrQNr6r ryr$rr)reldabrldbrrTrrQs r2test_invalid_matrix_shapesz$TestTbtrs.test_invalid_matrix_shapess` WdAYe , , , GS$Ku - - - 666iA.....r4N) rrrr@r(r)rrZrtrwrzrrr4r2rMrMs [Wf--+5+5.-+5Z []NN+1NNNOO [Vc3Z00 [Vc3Z00,7,71010 OO ,7\ [.333333333566BB 66B  [.**1// ///r4rMr)I1OrUr_rRr:r\rrWr{c t|||||}tj|}|||f|||fdzz}|tjd|dd|}||z }tj|tj r|j n|}|dkrtj |ntj |}|dkr+|tj |ddtjfz}||}t!d|f} | ||||\} } |dkr|tj|tj } tjtj|tj } d | | zz }nUtj|d }t!d |f\}}||\}}}|||| \}} d }t+| || dS)Nrr+rr{r_trcon)rrUr:rordrUgecongetrfrr)rDencoder6rrpermutedlogspaceintegers issubdtypefloatingrrrr:r;r.r$linalgrinfrr)r0rrUr:rseedr1AoffsetrrJr>norm_A norm_inv_Aranormrrluipvtrnrs r2 test_trconrs0 5/$//d/A//6688 9 9D )   % %C A #**1a&*"9"9""<B D D D DAq!Q!,,,|||011a|/=CG I I I IAq!QQQ777%1a|44 A A A AAq!QQQ!<<<%1a|44 A A A AAq!QQQ!<<<%1a|44 A A A AAq!QQQQQ!LLL%1a|44 A A A AAq!QRbA>>>%1a|44 A A A As1aA1!<<<1QQ<<> q#=111a4))g   M!ABBE( # #!!""43==??Aabb!!!eHbhqwqz6J6JKK!""aaa%43!!!QRR%"(171:*>*>SIII!!!QRR%!!!Q$5555!QQQ$55555966r4ctdtjd}d}t|||dd}|dks|dksJdSdS) N gesdd_lwork preferredr0ilp64iA%T)r0r/i`DiD)r$r6float32r ) sgesdd_lworkrrs r2 test_sgesdd_lwork_bug_workaroundr&sq $M*5777L A <A&*$ @ @ @E I  )!3!3!3 3  !3!3r4ceZdZejdedZejdeejdddZdS) TestSytrdr0ctjd|}td|f}tt||dS)Nrrsytrdr6r r$rrX)rer0rrs r2test_sytrd_with_zero_dim_arrayz(TestSytrd.test_sytrd_with_zero_dim_arrayCsA HV5 ) ) ) 1$//j%+++++r4rrUrWctj||f|}td|f\}}tjd||dzzdzdz||tj|<||\}}t |d||d|\}} } } }t |dt ||dtj|jzd t | tj |t | d t | d ||| \}} } } }t |dtj ||} tj|j d} | | | | f<tj|j ddz }| | |dz|f<| | ||dzf<tj |||}t|dz D]|}tj||}|d||dzf|d|<d||<tj |||| |tj||zz }tj||}}tj|d }|j|||<tj|jtj||}t || dtj|jzd dS) Nr)r sytrd_lworkrUrVrrrrYrr6rr)r6r r$arangetriu_indices_fromrrrrr:rr/r r=outerrrr~)rer0rrrrrrndataruerxr~rsk2QrIrHi_lowerQTAQs r2 test_sytrdzTestSytrd.test_sytrdJs HaV5 ) ) ) 5t < < { IaAaC!AU 3 3 3 " q ! !""k!nn tT1!&aq > > >aCT1aa(;&;#FFFF271::&&&3S!!!!&au 5 5 5aCT1 M!5 ) ) ) Iagaj ! !!Q$ Yqwqz!| $ $"Q$( "bd(  F1au % % %qs  A%(((A!QqSMAbqbEAaDq!5)))CFRXa^^,CCAq! AA/!R((S\' vac26!Q<<(( aa(;&;#FFFFFFr4N) rrrr@r(r)rrrrr4r2rrBs [Wk22,,32,  [Wk22 [S&))7G7G*)327G7G7Gr4rceZdZejdedZejdee eejdddZ dS) TestHetrd complex_dtypectjd|}td|f}tt||dS)Nrrhetrdr)rerrrs r2test_hetrd_with_zero_dim_arrayz(TestHetrd.test_hetrd_with_zero_dim_arraysA HV= 1 1 1 1$//j%+++++r4zreal_dtype,complex_dtyperrc >tj||f|}td|f\}}tjd||dzzdzdz|dtjd||dzzdzdz|zz|tj|<tj|tjtj|dD]"}|||\}} t| d#t||} ||d| \} } } }} t| dt| |d tj |j zd t| tjtj|t| d t|d ||| \} } } }} t| dtj ||}tj|jdt}| |||f<tj|jddz t}| ||dz|f<| |||dzf<tj|||}t#|dz D]}tj||}| d||dzf|d|<d ||<tj|||||tj|tj|zz }tj||}tj|d}tj|j|||<tjtj|jtj||}t||dtj |j zd dS)Nr)r hetrd_lworkrUrVr+rrUrrrrYrr6rrrr{)r6r r$rr fill_diagonalrr:rr rrrrr/rr r=rrrrr~)rer real_dtyperrrrrr>rnrrrurrxr~rsrrrIrrrQHAQs r2 test_hetrdzTestHetrd.test_hetrds HaV= 1 1 1 5t < < { IaAaC!AZ 8 8 829Q1Q3 1 J???? @ " q ! !" BGBGAJJ//000 " "A!k!1---GAt q ! ! ! !{A..!&aq > > >aCT1aa(<(<(@&@sKKKK27271::..///3S!!!!&au 5 5 5aCT1 M!: . . . Iagaj , , ,!Q$ Yqwqz!|3 / / /"Q$( "bd(  F1a} - - -qs  A-000A!QqSMAbqbEAaDq!=111a&28Arwqzz2223Aq! AA/!R((WQS\**' vbgacllBF1aLL11  !"RXj1155C      r4N) rrrr@r(r)r,rziprrrr4r2rrs [_n==,,>=,  [7 Sn==?? [S&))AA*)??AAAr4rc ttD]_\}}td|\}}t|ddd}|dkrYt jgdgdgd gd gd gd g|}t jgd |}t jddg|}n\t jgdgdgdgdgdgdg}t jdgdgdgdgdgdgg}t jd|}t jgdgdg|}||||||\} } } } } |dkrt jgd} nt jgd} t| | d adS)!N)gglse gglse_lworkrrZrXrV)rrrh)g= ףp=g{Gzg(\ؿ?)zGgHzG?gףp= ӿQ)ffffff@gQ?g?gffffffֿ)rg{Gz?Qg{Gz?)333333?g333333?rg ףp= )g{Gz{Gz?gzG?)grgGz?gHzGgzGg= ףp=?r)yQ?QyQQ?yQ{Gz@y= ףp=?)y\(\￮Gz?y333333RQ?yQzG?yQQ?)yףp= ?q= ףpݿy)\(?{Gz?y)\(?(\ſy(\333333?)yGz?RQ?yRQ?HzGy\(\ ףp= ׿y)\(?ɿ)y(\?RQ?y?{Gz?y(\ſq= ףpݿyQ?q= ףp?)yHzG?Qѿy?QyQ뱿Gz?yp= ף?p= ף?yRQ ףp= ?yffffff?GzyzGGzyQ?ffffff @yp= ף)\(@y(\@Q?)rrr)rrrrr)^"L?\}?rr)y!f?$_Kdy^gŵ翸F @y!f?}dy61ŵe_ @r)rrr$r r6rr r) rr0func func_lworkrrfrrurr>resultrs r2 test_gglsersF'',?,? 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,?,?r4c tjd}ttt zD]\}}d}|dkrPt d|}t d|\}}|||f|}njt d|}t d|\}}|||f|||fd zz|}||j zd z d tj ||zz}t|d }t||} ||| d \} } } || | |d \} } ttd | z tj|d z | zd kdS)Nrr{rX sytrf_lworkr)syconsytrf hetrf_lwork)heconhetrfr+rVrUrr)rfipivrrrh)r6rrrrr,r$r.rr~r rr rrrcond)r1rr0rrfunconfunctrfrrrldur r>rconds r2test_sycon_heconrs )   % %C~ 566AA U  77)-uEEEJ./AOOOOFGQF##++E22AA*-uEEEJ./AOOOOFGQF##cjj!Q&8&8&;;CCEJJA^Q 26!5#9#9#9!9 9Q z1--wqQ777 T16Cd%qAAAqAeGbinnQ!n44455e;a?@@@@-AAr4ctjd}ttD]@\}}d}t d|\}}}}|||f|}||jzdz }|||f|} | | jzdz dtj||zz} ||| \} } } t| dk|| \} } t| dk||| \}} t| dk||\}} } t| dkt|| dBdS) Nrr{)r!sygstsyevdsygvdrrVrgiUMu?r) r6rrrrr$r.r~r rr)r1rr0rr!rrrrBeig_gvdr>rnrrfeigs r2 test_sygstr!s )   % %C ,,33 U %57Irnrrfrs r2 test_hegstr!@s )   % %C//11 U %57I.{s[MMMqr#a&A36A36)9)9::::MMMr4r{rrr6)r6rrfrrr$r rr-r.rrr~rr8r r r=rrrrspacingr)r1rrrr0r&tzrzf_lwrrrzrnrrZr,r-rxs @@@r2 test_tzrzfr2_sF )   % %C DAq''FF U*+C16888xxA.. 77SXXa^^**51122AAchhq!nnsxx1~~b'88@@GGHHA i,,,au--- C  Ir!!!RaR%y"(Aqs85"A"A"AB C C Irvau---r!!!QRR%y9 : : VAU # # #MMMMMME!HHMMM 263  a1 j%&@&@&@ 55::? ; ;;" F F F F F-FFr4c tjd}ttD]\}}d}|dkrct ||||||dzzt|z|}d}nHt |||t|z|}d}td|\}}}||\} } ||d |} |d | | } t| t| | |d zd krd nd |d | | |} t| t| j | |d zd krd nd |d|tj|tj|f<|d | | |d} t| t| j | |d zd krd nd |d||} |d | | |dd} t| t| | j  j |d zd krd nd dS)z Test for solving a linear system with the coefficient matrix is a triangular array stored in Full Packed (RFP) format. rrrUr+rr~)trttftfttrtfsmrrVrrrXrZrrrr_)rr:rWr)rr:rN)r6rrfrrrr-r r.r$rrrr~r)r1rr0rrrr4r5r6Afpr>rsolnB2s r2 test_tfsmr;s )   % %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 Dr4c  tjd}d\}}}ttD]\}}t d|\}}t |||}|dkrvt|||f|} |||f|} t d|\} } nt|||f|||fdzz|} |||f|||fdzz|} 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)r{r$r$r%rrV)ormrz ormrz_lworkr+)unmrz unmrz_lworkrNc g|]P}||gddfj|gddfzz QSr)r*r+s r2r^z$test_ormrz_unmrz..s[NNNqr#a&A36A36)9)9::::NNNr4r~rr{rrrr6rr)rr)rrr)r6rrfrrr$r rr.r8r r=rrr.rrrrrr~)r1qmqncnrr0r&r/lwork_rzrrorun_mrz orun_mrz_lw lwork_mrzr0rnrrrtolcqr,r-rxs @@@r2test_ormrz_unmrzrKs )   % %CJBB''.!.! U*+C16888x!(B33 77SZZR))007788A B8$$++E22A$45M;@%B%B%B !Hkkcjj"b**SZZR-A-A"-DDLLUSSTTARH%% B8(<(Achols r2 test_pftrfrmGsj )   % %C''33 U  77!Q#((1a.."33;;EBBAAFFHHJ3q66)AA!Q''..AAC!CFF("A./J5:<<<ueE!HH T%3-- 4 eAy)) ! !(E2222%33r4c8tjd}ttD]d\}}d}|dkrs||||||dzz|}||jz|t|zz}nF||||}||jz|t|zz}td|\}}}}||\} } ||| \} } ||| \} } t| dk||| \} }t|}t| t||dzdkrd nd fd S) z Test Cholesky factorization of a positive definite Rectangular Full Packed (RFP) format array to find its inverse rrrUr+)pftririr4r5rrrVrXrZrN)r6rrfrrr-r.rr~r r$rrrr)r1rr0rrrorir4r5r8rn A_chol_rfp A_inv_rfpA_inv_rr>Ainvs r2 test_pftrirtbs )   % %C''DD U  77!Q#((1a.."33;;EBBAAFFHHJ3q66)AA!Q''..AAC!CFF("A%57@=B &C&C&C"ueUE!HH T 5C== D%:.. 4 U1i(( 1vv!'4::/2Qw!||!! D D D D D-DDr4ctjd}ttD]\}}d}|dkrs||||||dzz|}||jz|t|zz}nF||||}||jz|t|zz}t|df|}t|dzdf|}t|dz df|}td|\}} } } | |\} } | || \}} ||||\}} t| d ktt||||||||\}} t| d ktt!||||dzd krd nd d S)z Test Cholesky factorization of a positive definite Rectangular Full Packed (RFP) format array and solve a linear system rrrUr+rWrrV)pftrsrir4r5rrXrZrN)r6rrfrrr-r.rr~r r r$rrrrr)r1rr0rrrBf1Bf2rvrir4r5r8rnrpr9s r2 test_pftrsrys' )   % %C''DD U  77!Q#((1a.."33;;EBBAAFFHHJ3q66)AA!Q''..AAC!CFF("A !Qu % % %AaC85)))AaC85)))%57@=B &C&C&C"ueUE!HH T 5C== DU1j#.. d i:s;;;U1j!,, d !%1++t/2Qw!||!! D D D D D7DDr4c tjd}ttD]\}}d}|dkrs||||||dzz|}||jz|t|zz}nF||||}||jz|t|zz}|dkrdnd}tdd |d f| \}}}||\} } ||d|} ||dd | d| } ||| \} } t| t| | j d|zz|dzd krdnddS)zT Test for performing a symmetric rank-k operation for matrix in RFP format. rrrUr+rVrhr4r5frkrrrrXrZrN)r6rrfrrr-r.rr~r r$rrr)r1rr0rrprefixr4r5shfrkr8r>rAfp_outA_outs r2test_sfrk_hfrkrs )   % %C''DD U  77!Q#((1a.."33;;EBBAAFFHHJ3q66)AA!Q''..AAC!CFF("AQwwC.V.../Q5:<<<ueqQ HHQNN ! !% ( (%1b!Q,,5G$$q!%quuQVVXXZ/@/@.@1Q3.F)G)G/2Qw!||!! D D D D D#DDr4c ptjd}ttD]\}}d}|dkrf|dd||f|dd||fdzz|}||jz}nI|dd||f|}||jz|t|zz}dtj |dj z}td | \}}}t||d } t|dd \} } } t||d } ||d| \} }}|| |d \}}}tt!|dt!| | ddfd|dt|dd \}} } ||d \} }}|| |d \}}}tt#|dt#|| ddfd|ddS)zt Test for going back and forth between the returned format of he/sytrf to L and D factors/permutations. rr{rUir+r5r)syconvrrrrF)r hermitianrrNrr6r)r6rrfrrrandintr.rr~r r.rr$r rrrr)r1rr0rrrIrtrf trf_lworklwrRDpermrr rnrfrr_s r2 test_syconvrsk )   % %C''LL U  77S"q!f--S"q!f--b0128&-- AFFHHJAA CaV,,33E::AAC!CFF("A"*UU3ZZ_---!13BIN"P"P"PY Iq 2 2 2!u555 1d Iq 2 2 2#aq333T4VCQ/// 1dQ d1T111W:r&:&:2NNNN!u555 1d#aq///T4VCQ/// 1dQ D47Q$7$7cKKKKK5LLr4ceZdZdZdZdZdS) TestBlockedQRzd Tests for the blocked QR factorization, namely through geqrt, gemqrt, tpqrt and tpmqr. c 2tjd}ttD]\}}d}|dkrD||||||dzz|}n)||||}dtj|djz}td|\}}|||\} } } | d ksJtj | d tj ||z} tj ||| | z| j zz } tj| }t| j | ztj |||d t| |z||d |dkrF||||||dzz|}d }n+||||}d}dD]}d|fD]}|| | |||\}} | d ksJ||kr| j }n| }|dkr||z}n||z}t|||d ||fdkr(|| | |\}} | d ksJt!||t#t$|| | |dt#t$|| | |ddS)NrrrUr+r5r)geqrtgemqrtrrrrr6rr~rRrr\rrrRrRr\rrr7)r6rrfrrr-r.r.rr$rr r~rrrrrr)rer1rr0rrrIrrrftrnrrrr transposerrrqqC c_defaults r2test_geqrt_gemqrtzTestBlockedQR.test_geqrt_gemqrtsDi##D))#F++: A: AJCAQwwXXa^^chhq!nnR&77??FFXXa^^++E22bjs111C,-@NNNME6q!JAq$199992!7!7!77Aq&&&Q);;A A ACHHJJNBF1E,B,B,B!# % % % % AE13R 8 8 8 8QwwXXa^^chhq!nnR&77??FF XXa^^++E22 " 3 3!9-33E$fQ14uEEEGAt19999 ))CHHJJs{{UU#Ar"====e} 22*0&Aq// 4#qyyyy$Y222)3. )VQ13 ? ? ? ? )VQ1C @ @ @ @ @u: A: Ar4c  tjd}ttD]?\}}d}|dkr||||||dzz|}||||||dzz|}nR||||}||||}dtj|djz}td|\}} d |d z|fD]} || |||\} } } }|d ksJttj | d tj |d ttj | | |z dz tj || |z dz tj || |z tj | | |z }}tj tj|||f}tjd |z||| z|jzz }tj tj | tj| f}t%|j|ztjd |z||d t%||ztj tj ||f|d |dkr||||||dzz|}||||||dzz|}d}nT||||}||||}d}dD]}d|fD] }| | | | ||||\}}}|d ksJ||kr|j}n|}|dkr6tj ||fd }tj ||fd }||z}n5tj ||fd}tj ||fd}||z}t%|||d ||fdkr;| | | | ||\}} }|d ksJt||t| | t't(| | | | ||dt't(| | | | ||dAdS)NrrrUr+r5r)tpqrttpmqrtrrrVrrr6rr~rr\rrRrrrrr7)r6rrfrrr-r.r.rr$rrrr<r r~rrrrr)!rer1rr0rrrrIrrlrfrrrnB_pentb_pentrrrrrrrrrrurcdCDqCDr d_defaults! r2test_tpqrt_tpmqrtzTestBlockedQR.test_tpqrt_tpmqrt(sxi##D))#F++O KO KJCAQwwXXa^^chhq!nnR&77??FFXXa^^chhq!nnR&77??FFXXa^^++E22XXa^^++E22bjs111C,-@NNNME6a^@ K@ K %aAq 1 1 1aqyyyyRWQ^^RWQ^^<<<RWQA 22BGAq1uqy4I4IJJJ"$AE!2!2BGAq1u4E4ENBF1E$:$:$:F#CDDF1q5...Q1CCNBGAJJ a0@0@#ABB  Qq1uE0J0J0J%(r3333Ar~rwqzz66J'K'K%(r333377!Q#((1a..*;;CCEJJA!Q#((1a..*;;CCEJJA #II!Q//66A!Q//66A #I&77D"%y!177%+VAq!Q27&9&9&9 1d#qyyyy I-- ! AA !A3;;!#AQ!?!?!?B!#AQ!?!?!?B"#b&CC!#AQ!?!?!?B!#AQ!?!?!?B"$q&C'CcCCCC %=J669?1aA9N9N6Iy$#'19999(A666(A666378iAq!QSIIIIiAq!QcJJJJJA@ KO KO Kr4N)rrrr?rrrr4r2rrsJ <A<A<A|QKQKQKQKQKr4rcptjd}ttD]\}}d}d}t d|}|dkry||||z |d||||z |zz}||j z}n6||||z |}||j z}||\}}} } t|} d| | |z d| |z df<t| dd tj tj jz} d tj tjjz} |d vr| n| }t!||dz dd|dz f| j | zd| ||d \}}} } t#|}d|| |z d| |z df<t| dd tj tj jz} d tj tjjz} |d vr| n| }t!||dz dd|dz f||j zd| dS) Nrr{rVpstrfrrUr+rrrVrWrr6rrfrrr$r-r.rr~rrrrrr@rr)r1rr0rrrrrpivr_crnr_ single_atol double_atolr7rRs r2 test_pstrfr| )   % %C''#P#P U   666 77AaC  ''..chhq!A#6F6F6M6Me6T6T1TTAAFFHHJAAAaC  ''..AACA!E!HH3T GG "#'((C!GHH T1RXbj1155 RXbj1155 !Vmm{{#a%CE*AFFHHJN$OOOO!E!1---3T GG "#'((C!GHH T1RXbj1155 RXbj1155 !Vmm{{#a%CE*A N$OOOOOG#P#Pr4cptjd}ttD]\}}d}d}t d|}|dkry||||z |d||||z |zz}||j z}n6||||z |}||j z}||\}}} } t|} d| | |z d| |z df<t| dd tj tj jz} d tj tjjz} |d vr| n| }t!||dz dd|dz f| j | zd| ||d \}}} } t#|}d|| |z d| |z df<t| dd tj tj jz} d tj tjjz} |d vr| n| }t!||dz dd|dz f||j zd| dS) Nrr{rVpstf2rrUr+rrrrWrr)r1rr0rrrrrrrrnr_rrr7rRs r2 test_pstf2rrr4c tjgdgdgdgdg}tjgdgdgdg}ttD]/\}}|dkr6tjgd gd gd gd g}||}nWtjgd gdgdg|}|tjgdgdgdgdzz }||}t d|}||\}}}} } } |dkr7t |||dddf|z|zddt |||dddf|z|zdd1dS)N)g?rg1w-!?gd`TRۿ)rgsrr)gs?rg2%䃮g,eX)rgsFg%ug??)y/nҿ&?yDioɴ?Af?y o_[ Acп)ysֿAfҿyPkw?JY8y5;NёCl?)yYڊ?1*?y=yXѿ@a+?yhoſFxrV)gЈBgtBgffffff@gٓ)@gg#fDgffffff)gHzG?gQg'Vgp= ף)g(\rgS7нr)gq= ףpgAg(\)g333333gBg333333ÿ)gZ9=gQgֽr)gffffff@gtޅBr.)g(\g Zgq= ףp?)gEop=gQ?gZEqҽr+geequrr rW)r6rrrr.r$r) desired_real desired_cplxrr0rrrrrowcndcolcndamaxrns r2 test_geeqursZ8>>>@@@@@@@@@BCCL 8111111111 233L ''// U 77CCCEEEEEEEEEGHHAAA:::::::::.s!:::eb!em:::r4rYsyequb) r6rrrr r=rot90r:r$rlog2r.r) desired_log2srr0rrurrscondrrnrs @r2 test_syequbrs H???@@M'' < < U F2U # # #C!GGbb-- H::::U2q\\:::% H H H RXbgajj ! !!!(%888%vayy5$RWQZZ&&s++];;;; < !,,AudDqBGAJJS ! rd 2bT!V ;<<< 26")B**+++b011AAdGAdG!>!((2<*@*@JJJAudDqBGAJJ I I IJJJJJr4ctjd}d}||}||||dzz}t t D]P\}}|dkrF|||}||}||z}||}n_||||||dzz}||}||z}||}td|}td|} ||d \} } } } | | || | d \}}|dkr*t||||z d (t||||z d RdS) Nrr{r+rVgetc2rgesc2rr1) overwrite_rhsrXr) r6rrfr-rrr.r$r)r1rrrrr0rrrrrr jpivrnrras r2test_getc2_gesc2rs )   # #C A88A;;L88A;;!R/L'':: U 77AAAL AAAA!Q!22AAL AA 666 666$uQA666D$5Qd!<<<5 77 %l&9&9%&@&@&'gq : : : : : &l&9&9%&@&@&'gq : : : : :+::r4r )rZrYrjobarZjoburXjobvjobrrUjobpc Htjd}|\} } dtj|jz} t |||} t d|} |dk}|dk}|dko| | k}tj| }|dko| o| }|dko|o| o|}|dko|o| o|}|rd}n |s|rd}nd }|dkr$|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. rr5gejsvrrVrUrrPr)rrrrjobtrNF)r0r)r6rrfrrr3r$rrrrrrr:rr~identityr matrix_rank count_nonzero)r r0rrrrrrr1rrr7rrlsvecrsvecl2tran is_complexinvalid_real_jobvinvalid_cplx_jobuinvalid_cplx_jobv exit_statussvarrrrrnsigmas r2test_gejsv_generalr;s B )   # #C DAq %$ $D#D%55A WE 2 2 2E 1HE 1HEai %a1fF##JHUHZMU-=v(>M:MU-=v(>M:  /   qtqyyi4tT4NNNNN',uQ262626262626 (8(8(8$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 & &r4cVtd|}|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 statusrrrrrUrUrUrr5r{rN)r$rr/r6rr sinrrRr.asfortranarrayr~rr) r0rrrrrrrnrAcr>s r2test_gejsv_edge_argumentsrs WE 2 2 2E$)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 $g6[ ٿgUN@giq?)g1Zd?gOnӿgΈ ?g_vO?)g}?5^Iؿg58EGr?gio?g7[ Acd}td|j}||\}}}} } } t|||t|||t|||dS)z~ This test implements the example found in the NAG manual, f08khf. An example was not found for the complex case. r rrrN)r$r0r) r sva_expectu_expectv_expectr7rrrrrrrns r2test_gejsv_NAGrs|0 D WAG 4 4 4E#(588 CAtUDJ$////Had++++Had++++++r4c tjd}d}dtj|jz}t |dz f||}t |f||}t |dz f||}|||g}tj|tj|dztj|dz}||} || z} td|\} } | |||\} }}}}}t||d t||dt||d tj|d tj|dztj|d z}tj ||}t| D]K\}}||dz }|dd||gf|dd||gf<|dd|fxx|dd|dzf|zz cc<Ld|ddz }}|dd||gf|dd||gf<t|||z| | }| | ||||| \}}t| |t| || |tvr d }|j| z}nd }|j| z}| | ||||||\}}t| || t!t"5| |dd||dddn #1swxYwYt!t"5| ||dd|dddn #1swxYwYt!t"5| |||dddddn #1swxYwYt!t"5| |d |dd|d dddn #1swxYwYd |d <d |d <| |||\}}}}} }!tj||dz d kd||dz ddS)Nrr{r5rUr0r1rgttrfgttrsrrrVrr~rr7z?gttrf: _d[info-1] is , not the illegal value :0.)r6rrfrrr3rr:r$r r rrrr~rrrXtestingr)"r0r1rr7durudldiag_cpyrrrrr_dl_d_dudu2r rnr_rRrIrrb_cpyx_gttrsrb_trans__dl__d__du_du2_ipiv_infos" r2test_gttrf_gttrsrs )   # #C A %$ $D %acV5c B B BB#QD3???A $acV5c B B BB 16688RWWYY/H  RWR__$rwr1~~5A 1 A 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-IKKKKKsHMMM NN N!OO O""PPPz1du, d, dl, du_exp, d_exp, du2_exp, ipiv_exp, b, x)g@rffffff?r)r-rffffff@)333333 @ @r)rrrr)rrr[gC>)rrr\)rVrWrXrYrYg@gffffff@g%@g@g rgffffff&g3@rrYr[rPr)@@???)?r"ffffff @333333ӿ333333@ffffff ?)???@r')r"r#r$r%)r&r'r(r'y~:pffffff?)rr r!y333333@y@@y333333 @3333332@y333333yffffff-ffffff#@y333333yfffff?@y333333"@y𿚙?yffffff(@r'ry@y?@y@@r yrr!y@c :td|d|df\} } | |||\} } } }}}t||t| |t| |dt||| | | | |||\}}t||dS)Nrrr r)r$r)rrurdu_expd_expdu2_expipiv_exprrrrrrr r r rnr s r20test_gttrf_gttrs_NAG_f07cdf_f07cef_f07crf_f07csfr.Xsd$$6A1GGLE5$)E"a$4$4!CS#tTC!!!C   BD))))D(###E#r3T155MGTGQr4)rrrc tjd}||||dzz}||dz ||dz dzz}||dz ||dz dzz}tj|tj|dztj|dz}tj|tjr|j|j|j|jf\}}}}||||||||f\}}}}tj ||dkr tj nd}td|f\} } | |||\}}}} } } | |||| | ||\}}td |f\}}||\}}} ||||\}}tj |j d z}t||| dS) NiTfr+rUrrr)rgtconrrg?r)r6rrr:rrrr.rrrr$rrr)r0rrr1rurrrrrr0r r rnrJr>rrrrrrs r2 test_gtconr1s, )   ) )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??  $DC4((((((r4))rWr[)r[rWrcrtd|}|\}}|||\}}t|ddS)N geqrfp_lworkrr rr )r0r/r3rrrrns r2test_geqrfp_lworkr4sM$^EBBBL DAq,a(((KE4qr4z 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)Nrr5r{rXrUrpttrfrrzpttrf: info = z , should be 0)err_msgrpttrszpttrs: info = )r6rrfrrr3r:rrr$r rr rrr~)ddtyper0r1r7rrurrrr6r_ernrRrrrr8_xs r2test_pttrf_pttrsr<s )   # #C rx" "D A $QD&#66:A#QqSFE377A  RWQ^^#bgbgajj!&<&<s A )   % %C WE 2 2 2E#QD&#66:A#QqSFE377A*eQssVQ///*eQ#2#/////r4cd}tjd}td|}t |f||dz}t |dz f||}d|d<d|d<|||\}}} t || dz dd|| dz d t |f||}|||\}}} t | dkd dS) Nr{rr6rrVrUrz?pttrf: _d[info-1] is rz2?pttrf should fail with non-spd matrix, but didn't)r6rrfr$r3rr) r9r0rr1r6rurrr:rns r2'test_pttrf_pttrs_errors_singular_nonSPDr@s A )   # #C WE 2 2 2E#QD&#66:A#QqSFE377A AaD AaD5A;;LBDD1HqS"TAX,SSSUUU $QD&#66A5A;;LBD DAIKLLLLLr4z%d, e, d_expect, e_expect, b, x_expect)rXr{rrY)rrr$r\)rXr]rrU)rgK=UrrrVAg@rr)rB).)y0@0@y2@"?)rBr]rUrX)r'rrIyP@0@y0@y@W@O@yN@PyS@TyQ@Ry,@;yA@.@yr&cd}td|d}|||\}} } t|||t| ||td|d} | || |\} } t| |||jtvr&| || |d\} } t| ||dSdS) Nr r6rrrr8rUr)r$rrr0r,) rurd_expecte_expectrx_expectr7r6rr:rnr8r;s r2test_pttrf_pttrs_NAGrN s4 D WAaD 1 1 1E5A;;LBDBt,,,,Bt,,,, WAaD 1 1 1EuRA&&HBBt,,,, w.  5R!,,,DH4000000! r4ctjd}|dkrt||f||}|tjtj|d|zzz}||jzdz }t|d}t|f||dz}t|dz f||}tj|tj|dztj|dz} || z|jz} |} nt|f||}t|dz f||}|dz}tj|tj|dztj|dz} tj|tj|dztj|dz} ||| | fS)NrrUrXrVr) r6rrfr3r:r rr~r) r0realtyper compute_zr1A_eigvrrurtrirzs r2pteqr_get_d_e_A_zrV9 s )   # #CA~~+QFE3?? ac 1222'1, %[[^ 'h < >gajj271a==(271b>>9 Hrwwyy{ "  (h < < '1# > > E GAJJA &B 7 GAJJB '"'!Q-- 7 q!Q<r4zdtype,realtyperQc|dtj|jz}td|}d}t ||||\}}}} |||| |\} } } } t | dd| dt tjt|dtj| | |rt | tj | j ztj || t | tj | ztj | j z|| d Sd S) a Tests the ?pteqr lapack routine for all dtypes and compute_z parameters. It generates random SPD matrix diagonals d and e, and then confirms correct eigenvalues with scipy.linalg.eig. With applicable compute_z=2 it tests that z can reform A. rpteqrrr{rurrUrQrzinfo = z, should be 0.rN) r6rrr$rVrrsortrrr~rr:)r0rPrQr7rXrrurrrUd_pteqre_pteqrz_pteqrrns r2 test_pteqrr^Y sT # #D ge 4 4 4E A"5(AyAAJAq!Q&+ea1Y&O&O&O#GWgtq8D888999BGDGGAJ'')9)9EEEE&"''"2"2"44bk!nn! # # # # "''"2"22RWW5E5E5GG & & & & & & &&r4ctd|}d}t||||\}}}}||dz |||\} } } } | dksJdS)NrXrr{rXrUrQrr$rV r0rPrQrXrrurrrUr[r\r]rns r2test_pteqr_error_non_spdrcy sn ge 4 4 4E A"5(AyAAJAq!Q',eAE1Y&O&O&O#GWgt !888888r4c .td|}d}t||||\}}}}tt||dd|||tt|||dd|||r$tt||||dd|dSdS)NrXrr{rr`)r$rVrrX) r0rPrQrXrrurrrUs r2"test_pteqr_raise_error_wrong_shapere s ge 4 4 4E A"5(AyAAJAq!Q*eQssVQ!yIIII*eQ#2#!yIIIINj%A3B39MMMMMMNNr4ctd|}d}t||||\}}}}d|d<d|d<|||||\} } } } | dksJdS)NrXrr{rr`rarbs r2test_pteqr_error_singularrg sz ge 4 4 4E A"5(AyAAJAq!Q AaD AaD&+eAqA&K&K&K#GWgt !888888r4zcompute_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. r rXrrUrrYrN)r$r0r6r:rr) rQrurrKz_expectr7rXrUrr:_zrns r2test_pteqr_NAG_f08jgfrk s D gag 6 6 6E  RWQ]]"RWQ^^3AuqAi@@@BBBt,,,,BF2JJx 0 0t<<<<<)r0rlr1rr7rpgqrrrrqr_Arxrnrqqrr A_negativer_rq_negq_rq_negrq_A_negtau_neginfo_negs r2 test_geqrfpr| s )   # #C rx" "D rx" "D x 6 6 6F GE 2 2 2C DAq $QF%SAAAAfQiiOD#t  A  1uuh1vU+++AAArrE  CA & & &q ) CQQQU A . . .q 1AaC&&&&BF171:&&16688:TArwqzz---- BF271::RWQZZ 9 99 : :;;; DAI-aV5cJJJROJJHh"(&"4"4Hgx BF278$$q( ) ) # F271::> " "$$$$$r4ctjg}td|j}t t ||dS)Nrpr)r6rr$r0rr)A_emptyrps r2#test_geqrfp_errors_with_empty_arrayr s;hrllG hgm < < .- s%%%!A%%%r4)r6rrrrr$r rr) rrr1rhrrdlwrlwvals r2test_orcsd_uncsd_lworkr" s )   % %C QA AAK''$$TC C #V , , ,B 2q!Q ' 'ED[[EEuhE %%u%%% & &&& &&&r4c 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)roPrrcsdrrrlrworkrrrg@rW)rr!rvsr"r$r dictrrrjr6r r=cosrrrr)rrrhrrXdrvrrlwvalscs11cs12cs21cs22thetau1u2v1tv2trnr_VHrn11n12n21n22SonerIXcs r2test_orcsd_uncsdr0 sGAq!K''$$TC!Tkk }/@/C/CAucK.? @OOOHC 31a ( (E!$gu  $sG>>>???r:a=)))q*Q-(((r:a=)))q*Q-(((AvD)))) GE9 % %T 1 4U 4 4666 DJqMQWQZ '+>4:a=+>+>12+>+>@@@ DJqMQWQZ '+>4:a=+>+>12+>+>@@@@@r4c tjd}td|\}}d}t |dz f||}t |f||}t |dz f||} tj|dtj|ztj| dz} t |df||} |t vrd nd } |r| jn| | z} |d kr |||| ndgd z\}}}}}}|||| | || ||||| }|\ }}}}}}}}}}|dkr7d|d<d|d<|||| | }|\ }}}}}}}}}}|dks JddS|d krAd|d<d|d<d|d<|||| | |||||| }|\ }}}}}}}}}}|dks JddSdS)Nrrrr{rUrrrVr~rrPrZrr\rz&info should be > 0 for singular matrix)rrrrr r ) r6rrfr$r3r:rrr~)r0rrr1rrrrrurrrrrrrrrrrrrrrrr rrrrrns r2test_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$feT4 s{{"2E"aQ'' DMARdD&%tTaxxxAxxxxx BRb E"aQTt#%111 DMARdD&%tTaxxxAxxx xr4ctjd}td|\}}d}t |dz f||}t |f||}t |dz f||} tj|dtj|ztj| dz} t |df||} |t vrd nd } |r| jn| | z} |d kr |||| ndgd z\}}}}}}|d krtt||dd|| | || ||||| tt|||dd| | || ||||| tt|||| dd| || ||||| tt|||| | dd|| ||||| dStt|||| | || |dd|||| tt|||| | || ||dd||| tt|||| | || |||dd|| tt|||| | || ||||dd| dS)Nrrrr{rUrrrVr~rrPrZr\r) r6rrfr$r3r:rrr~rrXr)r0rrr1rrrrrurrrrrrrrrrrs r2"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$3E#2#JU < < < < < r% 7)H(8?@w)H)H)HHI1)N)Nr4cdSN)NNNrrs r2rr' -?r4c(tjd}dtj|jz}t d|}d}t |f||dz}t |dz f||} tj|tj| dztjtj| dz} t |d f|| } | | z} ||| \} }}| | | g}||| | || | \} }}}}}}t||d t| |dt| |d t|d kd |dt| |tj|dtjtj |z}tj| }t| ||ztj|jz|t!|dr Jd|t|jdkd|jdt|jdkd|jddS)a This tests the ?ptsvx lapack routine wrapper to solve a random system Ax = b for all dtypes and input variations. Tests for: unmodified input parameters, fact options, incompatible matrix shapes raise an error, and singular matrices return info of illegal value. rr5ptsvxrrYrXrUrrVrrrefrzinfo should be 0 but is .rrr)rVrz# but should be ({x_soln.shape[1]},)rN)r6rrfrrr$r3r:rrr rrr rr~rr/)r0rPr df_de_lambdar1r7rrrurrrrrrrnrrrrrrRrs r2 test_ptsvxr! s )   # #C %$ $D WE 2 2 2E A#QD(C881. .:::qeAqkk::::::r4c:g|]}t|D]}|Srrrs r2r^z5test_pptrs_pptri_pptrf_ppsv_ppcon.. rr4c6g|]}t|D]}|Srrr]rrs r2r^z5test_pptrs_pptri_pptrf_ppsv_ppcon.. s+<<. s/>>>U1XX>>1>>>>r4)ppsvpptrfpptrspptrippconrrrrrW)rrr )r6rrfrrr3rr~r r=r$rrrrrrrrrr)r0rr1r7rrfrrdaprrrrrulrnaululiaulirbxxvrrrs @r2!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$. Dr4FrrrrPrmrWr[rUrr r6rrfrrr3r$rr,rrrr~) r0r1r7rrfrrrrrUd2s r2test_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&====AdGRad333333r4zt, 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)rrr yB>٬?=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. r rrr)wantqrrN)r$r0rr)rifstilstexpectr7rrs r2test_trexc_NAGr& so< D WAG 4 4 4E U1at1 - - -FQq AFAD))))))r4ctjd}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)Nrr5r{r)ggestgexcrcdSr)rrs r2rz!test_gges_tgexc..I rr4Fr1 overwrite_brrrUrrPrrmrWr[rVrWrr)r0r1r7rrfrr(r)rrrrrUd1rs r2test_gges_tgexcr.> 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! $ $FQq Aq Aq Aq A 271::AD9999271::AD9999AEAFFHHJ&====AEAFFHHJ&====AdGag%r====AdGag%r======r4ctjd}tj|jdz}d}t ||g||}t d|\}}}|d|d }t|d d |d } |d } | d } |tvr%t| tj | d |t| | z| j z|d |tj |} d| d<t|| | } |tvr|| | | | }n|| | | | | d}t|d d |d } |d} |tvr%t| tj | d |t| | z| j z|d |t| d| d |dS)Nrr5r{r)rtrsen trsen_lworkrcdSr)rrs r2rz!test_gees_trsen..y rr4FrrrrPrmrWrUrZrrliworkrr6rrfrrr3r$rr,rrrr~r r )r0r1r7rrfrr0r1rrrUrselectrs r2test_gees_trsenr7n 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&====AdGRad333333r4z*t, q, expect, select, expect_s, expect_sep)g/$?g QIg~jtx?gJ4?)r58EGrgGr?gyX5;?)rg?߾r8gt?)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)\(?)rUrrrUg?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 $(?y3ı.n?rh|)yv? F%uyd`TR?I&†ۿyN@?ݓy4@ @ ^)?)ys{ @ o_yH.@|Pk @y 0*?*:Hy]m{?Gz)y) 0[ s@` D E) 111E; ; 2 2Ew.  vq!5111vq!5qBBBQq Aq Aw.  1IQi 1IQiFAEAFFHHJ.T::::Ha!e%0000JCe444444r4c*tjd}tj|jdz}d}t ||g||}t ||g||}t d|\}}}|d||dd } t| d d | d } | d } | d } | d} | d| dz }| d| dz }|tvrJt| tj | d |t| tj | d |t| | z| j z|d |t| | z| j z|d |tj |}d |d<t||| | }|d d z|d f}||| | | | |} t| d d | d } | d } | d} | d} |tvrJt| tj | d |t| tj | d |t| | z| j z|d |t| | z| j z|d |t| d| dz |d |t| d| dz |d |dS)Nrr5r{r)r(tgsen tgsen_lworkrcdSr)rrs r2rz!test_gges_tgsen.. rr4Fr+rrrUrrPrrmrWrZrirrr5)r0r1r7rrfrr(r@rArrrrrUr-rr6rs r2test_gges_tgsenrC s )   % %C 8E?? s "D A#QF%SAAAA#QF%SAAAA/( 7 7 7D%T..!QEu M M MFQq Aq Ar Ar A 41T7 B 41T7 B 271::AD9999271::AD9999AEAFFHHJ&====AEAFFHHJ&==== Xa[[FF1I ;1 5 5E1XaZq "E U61aAU 3 3 3FQq Aq Ar Ar A 271::AD9999271::AD9999AEAFFHHJ&====AEAFFHHJ&====AdGag%r====AdGag%r======r4za, b, c, d, e, f, rans, lans)rrrr)rr-rr)rrr-r)rrrg@)rrrr)rrrr)rrg(@)g"rrE)rDrrEr)rrg3@)rrrr-)rrrr)rrrr)rrrr)rrrr)rrrr)rrrr)rFrrr)rrg r)rrr)rGrrr)rrrr)rrr-r)rrrr)rrrr)rr-rr)rrrr)rrrrc |d} td|} | ||||||\} } } }}t|dt| ddtj|jdzdt|d dtj|jdzd t| || d t| || d dS)Nr tgsylrrrr5zSCALE must be 1.0rr7r7rzDIF must be nearly 0zSolution for R is incorrect)r7r7zSolution for L is incorrect)r$rrr6rr)rfrrrurriranslansr0r7rIroutloutradifrns r2test_tgsyl_NAGrP sH D ge 4 4 4E#(5Aq!Q#:#: D$sDqE3QRXe__-@-D/1111C128E??+>s+B24444D$T9;;;;D$T9;;;;;;r4r)r\r~ijob)rrUrVrWrXc x|tjkrdnd}tjd}d\}}t |dd||g||dd||g|d^}}} t |dd||g||dd||g|d^} } } |d d ||g|} |d d ||g|} td | }||| | || | || \}}}}}|dks Jd|dks Jd|dkr/t|ddtj |j dzdn|dks Jd|d kr|dkr!||z|| zz }|| z}||z|| zz }|| z}nq|dkrktj ||ztj ||zz}|| z}|tj | z|tj | zz}d|z| z}t|||ddt|||dddSdS)NgMbP?g|=lOElt/r#ir{r)outputrrVrIr)rrQrzINFO is non-zerorzSCALE must be non-negativer5zDIF must be 0 for ijob =0rJzDIF must be non-negativer\r~rzlhs1 and rhs1 do not match)r7rr7zlhs2 and rhs2 do not match) r6rrrruniformr.r$rrrr)r0rrQr7r1rrrfrur>rrrrirIrMrNrarOrnlhs1rhs1lhs2rhs2s r2 test_tgsylrYT 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 < > > > > > >yr4mtypercj|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)rrYrr+rrrtrsrrr r)rfr rrr5r)rr@rAr6rrr,rTr.r~rr$rrr)rZr0rr1rrrrrHrrr]rrr rnrrs r2 test_sy_hetrsr^ 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++++++r4c0|dkr|tvrtjdtjdkr|t vrtjdt jd}d}|||f|||fdzz}t j |t j r|j }| |}|dkr ||j zn||j z}|d |d f}t|| \}}||| \} } } | d ksJ|| | |\} } | d ksJt j|j} t j|}|r>t)t j| t j|d|z| zdSt)t j| t j|d|z| zdS)Nrzhetri not for real dtypes.z win-arm64z1Test segfaulting on win-arm64 in CI, see gh-23133r\rr+rrrTrrr)rfr rr5r)rr@rA sysconfig get_platformr,r6rrrrrr.r~rr$rrrrrrr)r0rrZr1rrrHrrTrr rnA_invrrs r2test_sy_he_trirc s }}+-- 0111;..5N3J3J GHHH )   0 1 1C A Aq6SZZA//22A }UBK(( F AD==ACa!&&((*nAMMMe=== (EU333HCc!5)))OCt 19999#$e444KE4 19999 (5// C )--  C F 3q59EEEEEE 3q59EEEEEEr4rz uplo, m, n))r_rYr{)r_r{r{)rRr{rY)rRr{r{ctjd}|||f|}t d|f\}} |||||} |dkrtj|ntj|}|dkr)tjt||} d|| | f<| ||} t| | ddS) Nl8#q9 r)lantrr)rUr:r_rU>r) r6rrr.r$rrrrjr) rrUrrr:r0r1rrerrJrIrs r2 test_lantrrg s )   1 2 2C A &&u--A#$6==LE5 %ad . . .Cckk rwqzzA s{{ Ic!Qii !Q$ %a..CC4((((((r4c 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 r{rVrVr+rr{rUrVrrr)gbcongbtrf)rrnrmrTr rrrr)r6rrrrrrrrr.rrrr rrrr$r)r0rr1rrmrnrrtmpLDABrTrrkrllu_bandr r>rJrrrrs r2 test_gbconrp s )   , ,CIAr2 Aq6SZZA//22A \\"+aa)<)>LE5uRR((GT1 %TbRG$    C$$6==LE5 q!B %E % % %a (CC1%%%%%%r4c:tjd}d\}}}|||f|||fdzz}tj|tjr|j}||}d|tj||dz<d|tj|| dz <t|||}td|f\}} | ||} |||||} t| | ddS) Nrirjr+rrU)langbrrfr) r6rrrrrr.rrrr$r) r0rr1rrmrnrrTrrrrrJs r2 test_langbrs s )   , ,CIAr2 Aq6SZZA//22A }UBK(( F A$%Aboaa  !%&Aboa"q!!" BA  B#$6==LE5 %a..C %b"b ! !CC4((((((r4 compute_vctjd}d}|||}||dz |}tj|dtj|ztj|dz}tj|}t d}||||\} } } | dksJttj| tj||rMtj |j } t| tj| z| j z|| d z dSdS) NlJ*Os{Ur{rrUrstevd)rtrrr) r6rrr:reigvalshr$rrZrrr~) r0rtr1rrurrrrvr_r-rnrs r2 test_stevdrxs: )   2 3 3C A 1E ""A 1q5 &&A 2#bgamm3A )  Q  C W % %Eq!y111JAq$ 19999BGAJJ ---@huoo!BGAJJ,ac3h??????@@r4r3) functoolsrr` numpy.testingrrrrrr r@r rnumpyr6r r r rrrrr scipy.linalgrr8rrrrrrrrrrrscipy.linalg._basicrrNr scipy.statsr!r" scipy.sparsesparsergr#r7 ImportErrorr$rMr%scipy.__config__r& blas_provider blas_versionrr@rr complex128r,rr3rKrQrSrrr(r)r rrr+rMrrrrrrrrrrr!r2r;rKr^rgrmrtryrrrrrrrskipifrrr=rrrrrrr.r1r4rr<r>r@rNrVr^rcrergrkr|rrrrrrrrrrrrrrrr&r.r7r>rCrPrYr^rcrDrgrprsrxrr4r2rs$ //////////////// ******!!!!!!!!!!!!!!!!!!!!FFFFFFFFFFFFFFFFFFFFFFFFFFFF******......222222220000000GGG000000,,,,,,######## +,V4V< *+F3I> z2:& , . ~ %***OOO.... ]-]-]-]-]-]-]-]-@        p9p9p9p9p9p9p9p9f&))"B"B"BCCDC*)--------*;;;;;;;;(;;;;;;;;DK/K/K/K/K/K/K/K/^&))11#s,,#s,,q"g&& ) )'&-,-,21*) )F))).'4'4'4T'6'6'6T4448AGAGAGAGAGAGAGAGHLLLLLLLL^.?.?.?bAAA6333>111>FFFD&D&D&DR7!7!7!t7:7:7:t&8&8&8R3336DDD@"D"D"DJDDD4 L L LFUKUKUKUKUKUKUKUKp%P%P%PP%P%P%PP*/*/*/Z < < <DKMMKKMMK$:::>&&!122+..q**q**q**!Q((!Q((b&b&b&)()(+*+*+*/.32b&J+..  /. F(!1+!1+!1+!1+!1+!1+ '1119#28%?%?%?%?%?%?%@%@%@%=%=%=%?%?%?%?%?%? %ABB $28$D$D$DEE#28%G%G%G%F%F%F%E%E%E%H%H%H%G%G%G%G%G%G %IJJ $28%G%G%G%H%H%H%F%F%F%G%G%G%IJJKLMM$ , ,%MM$ , &))XKXK*)XKvL#28$9$9$9::%RX&@&@&@AA%RX&;&;&;<<%RX&9&9&9::%RX&B&B&BCC%RXlll33%RXooo66%RXSz(,d|(+T{(+U|(+T{ ')** &RXAw()2w()2w(*Bx(*Aw '0112&&RX&G&G&GHH%RX'4'4'455&RX&F&F&FGG%RX'A'A'ABB%RX':':':;;%RX&?&?&?@@%RXooo66%RX*'=(3\'B(4i'@(3['A(1:'> '@AA &RX'7(.'7(.'8(/'8(.'7 '9::%%)* * V  W* * V (&))11q"g&&))'&21*))2&))"B"B"BCCDC*)[;6??AA,&,&AA,&^[;6??AA00AA0[;6??AAMMAAM&A""(#5#5#566""(???33""(#4#4#455""(#8#8#899""(QGaVaVb"X%&G$-..""(S!Hq"g2wQ%&G$-.. #"(#3#3#344""(#>#>#>??""(===11""(#5#5#566""(VW$57G%+V$4vv6F$HII""(T5MD$<$%)4L$233 E&11'&1.@)V[;%>??AAeeAhh//&&0/AA&:)V[;%>??AAeeAhh//0/AA)V[;%>??AAeeAhh//NN0/AAN)V[;%>??AAeeAhh//0/AA:#28$;$;$;<<#28$5$5$566#28$D$D$DEE#28%F%F%F%G%G%G%G%G%G%F%F%F%HII J   = =   =&))(@(@(@AA=$=$BA*)=$@...#>#>#>??t -- L L.-@? LD%=11t -- L L.-21 L6**00011 ' '21+* '6**+C+C+*+C\&))t}55#s,,7@7@-,65*)7@t&))1v..#s,,-B-B-,/.*)-B`&(++t}55#s,,-<-<-,65,+-<`#28$9$9$9::#28$?$?$?@@#28$9$9$9::#28c3Z#tsDk&(%[3+%?@@#28b!Wq"g2wR&(!W%.// 0$28$E$E$EFF#28%>%>%>??#28$D$D$DEE#28h %;&1;%?&2H%=&1;%?&/%< %>?? $28ff%57G&,g%6&8I&,f%5%788 9:;;()));;())33v{1<8=,>,>??,NNO ? ?@BCC 1:1: CC??1:h)33v{1<8=,>,>??,NNO ? ?@BCC KK CC??K()33v{1<8=,>,>??,NNO ? ?@BCC "" CC??"J#28$6$6$677#28OOO44#28aWq!fq!fr2h&'W%.//#28c1X2wB&(!Wq"g%788 9 $28$4$4$455#28$?$?$?@@#28h %:&.%9&.%9&.%9%;<<$28fg%6&,f%5&,f%5&,f%5%788 9 :;;" * *#;;" *5$-00&))+=+=*)10+=\&))!4!4*)!4Hbh))))))***)))+,,bh222111111111344 bhJJJKKKHHHHHHJKKbh555555555666 788   0 * *10 * &)),>,>*),>^&))*4*4*)*4Z0bh111111222111344bh000333333111344bh222111333222455bh||| bh666777555555 677bh555666555666 788bh666555555555 677bh|||3'))T55U))T5B&))5>5>*)5>p"bh((((((((((((*++bh((((((((((((*++bh((((((((((((*++bh((((((((((((*++bh((((((((((((*++bh((((((((((((*++bh((((((((((((*++bh((((((((((((*++9,-!.!.D+..;;/.E!.!.F;"+..*--11->->21.-/.->`4,//&))&)),,*)*)0/,.4,//&))&))FF*)*)0/F6m!4!455(E(E(EFF#s,,&)) ) )*)-,FF65 ) &))11!&!&21*)!&Hm!4!455&))))*)65)&+..f--@@.-/.@@@s4A;;BB