g}(+ddlmZddlZddlmZmZmZmZmZm Z ddl Z ddl m Z ddl Zddl mZmZmZmZmZmZmZmZddlmZmZmZddlmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(ddl)m*Z*dd l+m,Z,m-Z-ddl.m/Z0 dd l1m2Z2n #e3$rdZ2YnwxYw dd lm4Z5n #e3$rdZ5YnwxYwdd l)m6Z6dd l7m8Z8ej9ej:gZ;ej<ej=gZ>e;e>zZ?dxZ@ZAe2(e2dddZ@e2dddZAdZBdZCGddZDGddZEGddZFe jGHde?e jGHdgddZIGddZJGd d!ZKGd"d#ZLGd$d%ZMe jGHde?e jGHd&gd'e jGHd(d)d*ge jGHd+d,d)ge jGHd-d.d/gd0ZNd1ZOd2ZPd3ZQd4ZRGd5d6ZSGd7d8ZTd9ZUd:ZVd;ZWd<ZXd=ZYd>ZZd?Z[d@Z\dAZ]dBZ^dCZ_dDZ`dEZadFZbGdGdHZcdIZddJZedKZfdLZge jGhdMdNOdPZidQZje jGHdRdSdTge jGHde;e jGHdUekdVe jGHdWekdXe jGHdYekdXe jGHdZdd[ge jGHd\dd[gdbd]Zle jGHde;d^Zme jGHd_dUd`idWd`idYd`idZd`idad`id\d`ifdbZne jGHdcejogddgdegdfgdggdhgdigejogdjejogdkgdlgdmgdngdogdpgejogdqgdrgdsgdtgfgduZpe jGHde?dvZqe jGHdwejogdxejogdyejogdzejogd{ejogd|ejogd}ejogd~ejoddgddgddgddgddggejoddgddgd.dgddgdd[ggf ejogdejogdejogdejogdejogdejogdejogd~ejoddgddgddgddgddggejoddgddgddgddgddggf gdZre jGHde?e jGHd&gde jGHd-d.d/gdZse jGHde?e jGHdgddZte jGHdeue;e;ze?dZve jGHdeue;e;ze?dZwe jGHdeue;e;ze?dZxe jGHdejogdejogdejogdejogdejodVd/gd`dXgdd`gddgddggejoddgddgd[dgddVgd.dggfejogdejogdejogdejogdejoddgddgddgddggejoddgddgddgddggfgdʄZyd˄Zze jGHdeue?e;e;ze jGHdekd.d΄Z{e jGHdeue?e;e;ze jGHdekd.dτZ|e jGHdeue?e;e;ze jGHdekd.dЄZ}e jGHdeue?e;e;ze jGHdekd.dфZ~e jGHddejogdӢejogdԢejogdբejogd֢gdעgdآgd٢gfgdڄZe jGHde?e jGHdgdܢd݄ZdބZe jGHdgde jGHdddgdZe jGHdddge jGHdddgdZe jGHde?e jGHdgddZe jGHde?dZe jGHde?e jGHdddMge jGHddd,gdZe jGHde?e jGHddd[ge jGHddd,gdZe jGHde?dze jGHdddMge jGHddd,gdZe jGHdejogdxejogdyejogdzejoddgddgddgddgddggejoddgddgd.dgddgdd[ggfejogdejogdejogdejoddgddgddgddgddggejoddgddgddgddgddggfgdZe jGHdeue?e;e;ze jGHdddfd,dfgdZe jGHdeue?e;e;ze jGHdddfd,dfgdZe jGHdeue?e;e;ze jGHdddfd,dfgdZe jGHdejogdejogdejodVd/gd`dXgdd`gddgddggejoddgddgd[dgddVgd.dggfejogdejogdejoddgddgddgddggejoddgddgddgddggfgdZe jGHdddMge jGHde?dZe jGHde?dZe jGHdejogdgdgdgd gejogd gd gd gd gdd[fejogd gdgdgdgejogdgdgdgdgd[dXfgdZe jGHde?dZe jGHde?dZe jGHdejogdgdgdgdgejogdgdgdgd gejogd!gd"gd#gd$gejogd%d&d'fejogd(gd)gd*gd+gejogd,gd-gd.gd/gejogd0gd1gd2gd3gejogd%d4d5fgd6Ze jGHde?d7Ze jGHd8ejogd9gd:gd;gd<gejogd=gd:gd;gd>gejogd?gd@gdAgdBgejogdCgdDgdEgdFgejogdGgdHgdEgdIgejogdJgdKgdLgdMgejogd=gdNgdOgdPgejogdQgdRgdSgdTgfge jGHde;dUZe jGHde;e jGHdVdWe jGHdXgdYdZZe jGHd[ddge jGHde?e jGHdd\d]Ze jGHd&ed^e jGHd_gd`e jGHd+d,d)ge jGHde?daZdS(c)reduceN) assert_equalassert_array_almost_equalassert_assert_allcloseassert_almost_equalassert_array_equal)raises)eyeoneszeros zeros_liketriutril tril_indices triu_indices)randrandintseed) _flapacklapackinvsvdcholeskysolveldlnorm block_diagqreighqz)_compute_lwork) ortho_group unitary_group)CONFIG)_clapack)get_lapack_funcs)get_blas_funcszBuild Dependenciesblasnameversionc|tvr+|j||j|dzz|S|j||S)N?)COMPLEX_DTYPESrastype)shapedtyperngs T/granary/edev/quantum/lib/python3.11/site-packages/scipy/linalg/tests/test_lapack.pygenerate_random_dtype_arrayr41s\ % #(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 r3test_lapack_documentedrL9s ~ ,--- $$&& ' 'E   KffGF !!$$ ![)@)@E!! NN4 b===N=====r5c&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))) )rPrrga2U0*3?)rSrrgMb`?)rVrPrr)rrPrrsdzcgebalrrP)permutescale) getattrr9rreprrrlenr7r ) selfaa1pfbalohipivscaleinfos r3 test_gebalzTestFlapackSimple.test_gebalRs6 YY 999 -oooollll * *A7D11Ay)*1 &BB$ Hd4jj ) ) ) %b! , , , "bAs1Q4yy{#3 4 4 4 %hA @ @ @)*2q)B)B)B &BB$ Hd4jj ) ) ) ) * *r5cgdgdgdg}dD]K}tt|dzd}|||\}}}t| t|LdS)Nikiifii"iiidgehrd)r]r9rr^)r`rarcrdhttauris r3 test_gehrdzTestFlapackSimple.test_gehrdgs    __ ^^  * *A7D11AyAaDDMBT Hd4jj ) ) ) )  * *r5c 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)NrPrQrrSrTrUrWrX TfdFD)trsylr-C)tranatranbdecimal)isgn) r7arrayr/r'isupperrdot conjugatery) r`rabctransr1rbb1c1r{xr\ris r3 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)Nrlrmrorz Mm1OoIiFfEerrr-)langeFfEeFfrRrVMm1OoraxisIirP) r7rr/rr'sqrtsumsquareabsrmaxr) r`rar1norm_strrbrvaluerrefs r3 test_langezTestFlapackSimple.test_langes H    OO NN    - -E) - -XXe__==??#tHHHNHHH)*re<<h++v%%}}"#"#'"&26"::)>)>"?"?@@C'sG<<<<4'' fRVBZZ00!U** fRVBF2JJQ%?%?%?@@!T)) fRVBF2JJQ%?%?%?@@ ,,,,1 - - -r5N)__name__ __module__ __qualname__rjrtrrr5r3rNrNPsP**** * * *===8-----r5rNceZdZdZdZdS) TestLapackc4ttdrdSdSN empty_module)hasattrr9r`s r3 test_flapackzTestLapack.test_flapack# 7N + +  D  r5c4ttdrdSdSr)rr8rs r3 test_clapackzTestLapack.test_clapackrr5N)rrrrrrr5r3rrs2 r5rc&eZdZdZdZdZdZdS)TestLeastSquaresSolversc @tdttD]\}}d}d}d}t|||}t||}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)!NrvrP)gels gels_lworkr1lworkrTTCCrr?@@@@ @0@g1@g4@)rrgeqrfrQr祪,-@rtol?@@?@@ @ffffff?ry1@@y4@R ?\j,?W?)r enumerateDTYPESrr/r'r"r REAL_DTYPESr7rr0r_rfinfoepsr r.)r`indr1mnnrhsrbrglsglslwrr?rirrrlqrr lqr_truths r3 test_gelsz!TestLeastSquaresSolvers.test_gelss T #F++  JCAADa""5))Ba&&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/$h/18=???B666eDDDB&63b"X'?'? #D*e8DAq28}}!!x{#:q!T::E4Be444LCD AcrcFH&J&J&L+02228:28E??;N8N P P P P"'r Iq!Q sI . . . ./ / /r5c tD]X}tjddgddgddgg|}tjgd|}td ||f\}}|j\}}t |jd kr|jd }nd }||||d \} } } t tj| } | } |||| | d d d \}}}} t|dd tjddg|dtj |j zt|tjddg|dtj |j zZtD]i}tjddgddgddgg|}tjgd|}td ||f\}}|j\}}t |jd kr|jd }nd }||||d \} }} } t tj| } t |}| } |||| || d d d \}}}} t|dd tjddg|dtj |j zt|tjddg|dtj |j zkdS)Nrrrrrrrr)gelsd gelsd_lworkrQrPrFrrrrYN))1)@*@.?rrrrrrrrU.*@_Y@ rr7rr'r0r_intrealrrrr.)r`r1rbrrrrrrworkiworkrir iwork_sizersrankrwork rwork_sizes r3 test_gelsdz"TestLeastSquaresSolvers.test_gelsds  9 9EC:::'.3555B,,,E:::B!12J35r("<"< E;8DAq28}}!!x{!, Aq$ ; ; D% &&EJ$uRUJ%' 7 7 Aq$ AcrcFBH.A.@.B38%:%:%:"$BHUOO$7!7 9 9 9 9 Arx);):)"?"?"ABBQQQ ]+- . .%Eu#%%%VnfTTrTlVAYU 9K-K,LMNNneDDbDk4011 6)44q&!! @ @A%3$$C LLQ SVq[$;=>$? @ @ @ @"%RVBHUOO,,,.CDEEEEBHRZ,@,@,D(D "*!5!5!99 ; ; ; ; ; ;r5N)rrrrCrr5r3r#r#s#;;;;;r5r#ceZdZejdedZejddeDejdddgejdd dgd Zejd gd gd gdgdZ dZ ejdddgdZ dS) TestTbtrsr1cd|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= ף0rGg(\+gףp= 0g333333*@g(\gHzG,gQ#rSrPrrRrQr )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$B@y[a^C?b->y-@ji&*!z Datatype z not understood.tbtrsLabruplorh㈵>rr/N)rr7rr. ValueErrorr'rr)r`r1rLrx_outrIrris r3test_nag_example_f07vef_f07vsfz(TestTbtrs.test_nag_example_f07vef_f07vsfs K  4442224 %'''B65/!6* %.!5/+ % &&&A Hq!f!2h !f "g'$) ***EE n $ $KKKFFF:::<!&'''B=.9*N;)>:)>:< % &&&A Hr6l%w/46JK35JKM$) ***EE @@@@AA A '%888%2---4T15qt444444r5z dtype,transc>g|]}dD]}|dkr |tv||fS))Nryr|r|)r).0r1rs r3 zTestTbtrs.3sPNNN"'NN6;&+sllu 7K7K %en7K7K7K7Kr5rMUrJr2rTc 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)rSrRrQrIrrWrPrc4g|]}t|z Sr)r)rUrrs r3rVz2TestTbtrs.test_random_matrices..Hs#888aq3q66z888r5c4g|]}t|fSr)r4)rUwidthr1r2s r3rVz2TestTbtrs.test_random_matrices..Is7+++-eXucBB+++r5dia)formatr)rLrrMrr2rTg-C6 ?rryr|zInvalid trans argument)r7r RandomStater'r5r spsdiagsr rdiagonalrminr4rrryrrP)r`r1rrMr2rkdrIis_upperkukl band_offsets band_widthsbandsrarLrowkrrrirr2s ` @@r3test_random_matriceszTestTbtrs.test_random_matrices2s4i##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 6r5zuplo,trans,diag)rWrTInvalid)rWrmrT)rmrTrTc tdtj}tdd}tdd}t t ||||||dS)z?Test if invalid values of uplo, trans and diag raise exceptionsrIrrSrQN)r'r7r8rrr)r`rMrr2rIrLrs r3&test_invalid_argument_raises_exceptionz0TestTbtrs.test_invalid_argument_raises_exceptionfsR! ;;; !QZZ AJJiAtUDAAAAAr5ctjdt}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.rrrSrIr)rrRrWrKN)r7r floatr'r)r`rLrrIr?ris r3test_zero_element_in_diagonalz'TestTbtrs.test_zero_element_in_diagonalsswWV5 ) ) ) GAU # # # 6665 %2---4T1r5zldab,n,ldb,nrhs)rTrTrrT)rTrTrRrTctj||ft}tj||ft}tdt}t t |||dS)z2Test ?tbtrs fails correctly if shapes are invalid.rrINr7r rqr'rr)r`ldabrldbrrLrrIs r3test_invalid_matrix_shapesz$TestTbtrs.test_invalid_matrix_shapess` WdAYe , , , GS$Ku - - - 666iA.....r5N) rrrrAmark parametrizerrRrlrorrrwrr5r3rErEs [Wf--+5+5.-+5Z []NN+1NNNOO [Vc3Z00 [Vc3Z00,7,71010 OO ,7\ [.333333333566BB 66B  [.**1// ///r5rEr)I1OrMrWrJr2rTrrRrvc tj|||||tjtjdd}|||f|||fdzz}|tjd|dd|}||z }tj|tj r|j n|}|dkrtj |ntj |}|dkr+|tj |ddtjfz}||}t!d|f}|||||\} } |d kr|tj|tj } tjtj|tj } d | | zz } nntj|d }t!d |f\}}||\}}}||||\} } d }t1| | |dS)Nrla$rr-rvrWtrcon)rrMr2rz)ordrPrgecongetrfrr)rrr7 default_rngrpermutedlogspaceintegers issubdtypefloatingrrrr2r3r/r'linalgrinfrrrrr)r1rrMr2rr2Aoffsetr~rBr?norm_A norm_inv_Aranormrrluipvtrirs r3 test_trconrsC K5/$//d/A//000 )  q- @ @ A AC 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$55555966r5ctdtjd}d}t|||dd}|dks|dksJdSdS) N gesdd_lwork preferredr1ilp64iA%T)r(r'i`DiD)r'r7float32r") sgesdd_lworkrrs r3 test_sgesdd_lwork_bug_workaroundr#sq $M*5777L A <A&*$ @ @ @E I  )!3!3!3!3  !3!3r5ceZdZejdedZejdeejdddZdS) TestSytrdr1ctjd|}td|f}tt||dS)Nrrsytrdr7r r'rrP)r`r1rrs r3test_sytrd_with_zero_dim_arrayz(TestSytrd.test_sytrd_with_zero_dim_array@sA HV5 ) ) ) 1$//j%+++++r5rrPrRctj||f|}td|f\}}tjd||dzzdzdz||tj|<||\}}t |d||d|\}} } } }t |dt ||dtj|jzd t | tj |t | d t | d ||| \}} } } }t |dtj ||} tj|j d} | | | | f<tj|j ddz }| | |dz|f<| | ||dzf<tj |||}t|dz D]|}tj||}|d||dzf|d|<d||<tj |||| |tj||zz }tj||}}tj|d }|j|||<tj|jtj||}t || dtj|jzd dS) Nr)r sytrd_lworkrPrQrrrrTrr.rr)r7r r'arangetriu_indices_fromrrrrr2rr0r r5outerrrry)r`r1rrrrrridatarpersryrkk2QrArHi_lowerQTAQs r3 test_sytrdzTestSytrd.test_sytrdGs HaV5 ) ) ) 5t < < { IaAaC!AU 3 3 3 " q ! !""k!nn tT1!&aq > > >aCT1aa(;&;#FFFF271::&&&3S!!!!&au 5 5 5aCT1 M!5 ) ) ) Iagaj ! !!Q$ Yqwqz!| $ $"Q$( "bd(  F1au % % %qs  A%(((A!QqSMAbqbEAaDq!5)))CFRXa^^,CCAq! AA/!R((S\' vac26!Q<<(( aa(;&;#FFFFFFr5N) rrrrArxryrrrrr5r3rr?s [Wk22,,32,  [Wk22 [S&))7G7G*)327G7G7Gr5rceZdZejdedZejdee eejdddZ dS) TestHetrd complex_dtypectjd|}td|f}tt||dS)Nrrhetrdr)r`rrrs r3test_hetrd_with_zero_dim_arrayz(TestHetrd.test_hetrd_with_zero_dim_arraysA HV= 1 1 1 1$//j%+++++r5zreal_dtype,complex_dtyperrc >tj||f|}td|f\}}tjd||dzzdzdz|dtjd||dzzdzdz|zz|tj|<tj|tjtj|dD]"}|||\}} t| d#t||} ||d| \} } } }} t| dt| |d tj |j zd t| tjtj|t| d t|d ||| \} } } }} t| dtj ||}tj|jdt}| |||f<tj|jddz t}| ||dz|f<| |||dzf<tj|||}t#|dz D]}tj||}| d||dzf|d|<d ||<tj|||||tj|tj|zz }tj||}tj|d}tj|j|||<tjtj|jtj||}t||dtj |j zd dS)Nr)r hetrd_lworkrPrQr-rrPrrrrTrr.rrrrv)r7r r'rr fill_diagonalrr2rr"rrrrr0rr r5rrrrry)r`r real_dtyperrrrrr?rirrrprrsryrkrrrArrrQHAQs r3 test_hetrdzTestHetrd.test_hetrds HaV= 1 1 1 5t < < { IaAaC!AZ 8 8 829Q1Q3 1 J???? @ " q ! !" BGBGAJJ//000 " "A!k!1---GAt q ! ! ! !{A..!&aq > > >aCT1aa(<(<(@&@sKKKK27271::..///3S!!!!&au 5 5 5aCT1 M!: . . . Iagaj , , ,!Q$ Yqwqz!|3 / / /"Q$( "bd(  F1a} - - -qs  A-000A!QqSMAbqbEAaDq!=111a&28Arwqzz2223Aq! AA/!R((WQS\**' vbgacllBF1aLL11  !"RXj1155C      r5N) rrrrArxryr.rziprrrr5r3rrs [_n==,,>=,  [7 Sn==?? [S&))AA*)??AAAr5rc 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_lworkrrUrSrQ)rrrc)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?$_Kdy^gŵ翸F @y!f?}dy61ŵe_ @r)rrr'r"r7rr r) rr1func func_lworkrrarrprr?resultrs r3 test_gglsersF'',?,? U+,D27999jzQ!q999 77555555333444333444 6 >C DDDA AAAOOOA"b///AAMMMNNNKKKKKKKKKKKK MNNA ;-%,&-%,&-%, ())A %(((A H'''):):):;5 I I I!T!Q1E:::1a 77x!-!-!-..HH x!:!:!:;;H "&(A>>>>>Y,?,?r5c PtdtttzD]x\}}d}|dkrIt d|}t d|\}}t |||}n\t d|}t d|\}}t ||t ||d zz|}||jzd z d tj ||zz}t|d }t||}|||d \} } } || | |d \} } ttd | z tj|d z | zd kzdS)NrrvrS sytrf_lworkr)syconsytrf hetrf_lwork)heconhetrfr-rQrP)rr)raipivrrrc)rrrr.r'rr/rryr7r rr"rrrcond) rr1rrfunconfunctrfrrrldurr?rconds r3test_sycon_heconr sJJJ~ 566AA U  77)-uEEEJ./AOOOOFGa##E**AA*-uEEEJ./AOOOOFGad1ajjm+33E::A^Q 26!5#9#9#9!9 9Q z1--wqQ777 T16Cd%qAAAqAeGbinnQ!n44455e;a?@@@@-AAr5ctdttD]2\}}d}td|\}}}}t |||}||jzdz }t |||}||jzdz dtj||zz}|||\} } } t| dk||\} } t| dk||| \} } t| dk|| \}} } t| dkt|| d4dS) Nrrv)rsygstsyevdsygvdrrQrgiUMu?r) rrrr'rr/ryr7r rr)rr1rrr r rrBeig_gvdr?rirraeigs r3 test_sygstrsJJJ ,,33 U %57I.xs[MMMqr#a&A36A36)9)9::::MMMr5rvrrr.)r7rr^rrr'r"rrr/rrryrr0r r r5rrrrspacingr)r2rrrr1rtzrzf_lwrrrzrirrZr#r$rss @@@r3 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-FFr5c 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. rrrPr-r|ry)trttftfttrtfsmrrQrrrSrUrrrrW)rr2rRr)rr2rN)r7rr^rrrrr r/r'rrrryr)r2rr1rrrr+r,r-Afpr?rsolnB2s r3 test_tfsmr2~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 Dr5c 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)rvrrrrrQ)ormrz ormrz_lworkr-)unmrz unmrz_lworkrNc g|]P}||gddfj|gddfzz QSr r!r"s r3rVz$test_ormrz_unmrz..s[NNNqr#a&A36A36)9)9::::NNNr5ryr|rvrrrr.rr)rr)rrr)r7rr^rrr'r"rrr/r0r r5rrr%rrrrrry)r2qmqncnrr1rr&lwork_rzrr|orun_mrz orun_mrz_lw lwork_mrzr'rirrrtolcqr#r$rss @@@r3test_ormrz_unmrzrBs )   % %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 $ $ $NNNNNNE"IINNN 263  QwwCEE#JJO,,,8BQi888D QUU1XX z!}}3RHHHH8BQe9EEED QVVXXZ^^A... 1 C ! ! ! !8BQS BBBD QUU1XX z!}}3RHHHH8BQSYOOOD QUU16688:... 1 C ! ! ! ! ![.!.!r5c |tjd}ttD]\}}d}|dkrF||||||dzz|}d}n+||||}d}td|\}}||\}} t| d k||d \} } t| d k|||d \} } t| d k|||d \} } t| d kt|dz|dzf|} t|dd|dzdf| ddddf<| |dzdzdddfxxt|d|dzd|dzf j z cc<t|dz|dzf|}t|ddd|dzf|ddddf<|d|dzddfxxt||dzd|dzdf j z cc<t|| ddt| | j ddt| |ddt| | j dd|||\}} t| d k||| d \}} t| d k||| |d \}} t| d k||| |d \}} t| d kt|t|t|t|t|t|t|t|dS)z Test conversion routines between the Rectangular Full Packed (RFP) format and Standard Triangular Array (TR) rrrPr-r|ry)r+r,rrrJrMrW)transrrMrQNrF)order)r7rr^rrrr/r'rr rrryrrreshape)r2rr1rA_fullrFr+r,A_tf_UriA_tf_LA_tf_U_TA_tf_L_TA_tf_U_mA_tf_L_mA_tr_UA_tr_LA_tr_U_TA_tr_L_Ts r3test_tfttr_trttfrUs )   % %C''1:1: U  77hhq!nnsxx1~~b'88@@GGFFFhhq!nn,,U33FF'(:%HHH uuV}}  uV#...  vf3???$ 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:r5cvtjd}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) rDrrrPr-)trttptpttrrrrJrErQN)r7rr^rrrr/r'rrr rryrrr)r2rr1rrJrWrXA_tp_UriA_tp_LindsA_tp_U_mA_tp_L_mrQrRs r3test_tpttr_trttpr^s3 )   % %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 8r5ctjd}ttD]:\}}d}|dkrs||||||dzz|}||jz|t|zz}nF||||}||jz|t|zz}td|\}}}||\}} |||\} } t| dk||| \} } t|} t| | >>@@@@@@@@@BCCL 8111111111 233L ''// U 77CCCEEEEEEEEEGHHAAA:::::::::.s!:::eb!em:::r5rTsyequb) r7rrrr r5rot90r2r'rlog2r/r) desired_log2srr1rrprrscondrrirs @r3 test_syequbrs H???@@M'' < < U F2U # # #C!GGbb-- H::::U2q\\:::% H H H RXbgajj ! !!!(%888%vayy5$RWQZZ&&s++];;;; < !,,AudDqBGAJJS ! rd 2bT!V ;<<< 26")B**+++b011AAdGAdG!>!((2<*@*@JJJAudDqBGAJJ I I IJJJJJr5ctjd}d}||}||||dzz}t t D]P\}}|dkrF|||}||}||z}||}n_||||||dzz}||}||z}||}td|}td|} ||d \} } } } | | || | d \}}|dkr*t||||z d (t||||z d RdS) Nrrvr-rQgetc2rgesc2rr)) overwrite_rhsrSr) r7rr^rrrr/r'r)r2rrrrr1rrrrrrjpivrirr\s r3test_getc2_gesc2rs )   # #C A88A;;L88A;;!R/L'':: U 77AAAL AAAA!Q!22AAL AA 666 666$uQA666D$5Qd!<<<5 77 %l&9&9%&@&@&'gq : : : : : &l&9&9%&@&@&'gq : : : : :+::r5r)rUrTrjobarUjoburSjobvjobrrPjobpc Htjd}|\} } dtj|jz} t |||} t d|} |dk}|dk}|dko| | k}tj| }|dko| o| }|dko|o| o|}|dko|o| o|}|rd}n |s|rd}nd }|dkr$|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-gejsvrrQrPr rHr)rrrrjobtrNF)r(r)r7rr^rrr4r'rrrrrrr2rryidentityr matrix_rank count_nonzero)rr1rrrrrrr2rrr/rrlsvecrsvecl2tran is_complexinvalid_real_jobvinvalid_cplx_jobuinvalid_cplx_jobv exit_statussvarrrrrisigmas r3test_gejsv_generalr8s 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 & &r5cVtd|}|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 statusrrrrrPrPrPrr-rvrN)r'rr0r7rr sinrrIr/asfortranarrayryrr) r1rrrrrrrirAcr?s r3test_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'r1r) r sva_expectu_expectv_expectr/rrrrrrris r3test_gejsv_NAGrs|0 D WAG 4 4 4E#(588 CAtUDJ$////Had++++Had++++++r5c 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)Nrrvr-rPr1r2rgttrfgttrsrrrQrryr|r.z?gttrf: _d[info-1] is , not the illegal value :0.)r7rr^rrr4rr2rr'r r rrrryrrrPtestingr)"r1r2rr/durpdldiag_cpyrrrrr_dl_d_dudu2rrirWrJrArrb_cpyx_gttrsrb_trans__dl__d__du_du2_ipiv_infos" r3test_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)rrr r)rrrVgC>)rr rW)rQrRrSrTrTg@gffffff@g%@g@g rgffffff&g3@rrTrVrHr )@@???)?rffffff @333333ӿ333333@ffffff ?)???@r)rrrr)rrrry~:pffffff?)rrry333333@y@@y333333 @3333332@y333333yffffff-ffffff#@y333333yfffff?@y333333"@y𿚙?yffffff(@rry@y?@y@@ryrry@c :td|d|df\} } | |||\} } } }}}t||t| |t| |dt||| | | | |||\}}t||dS)Nrrrr)r'r)rrprdu_expd_expdu2_expipiv_exprrrrrrrrrrirs r30test_gttrf_gttrs_NAG_f07cdf_f07cef_f07crf_f07csfr$Usd$$6A1GGLE5$)E"a$4$4!CS#tTC!!!C   BD))))D(###E#r3T155MGTGQr5)r{rzr|c tjd}||||dzz}||dz ||dz dzz}||dz ||dz dzz}tj|tj|dztj|dz}tj|tjr|j|j|j|jf\}}}}||||||||f\}}}}tj| d }td|f\} } | |||\}}}} } } | |||| | ||\}}td |f\}}||\}}} ||||\}}tj |j d z}t||| dS) NiTfr-rPrrr)rgtconrrg?r)r7rrr2rrrr/rrrr'rrr)r1rrr2rprrrrrr&rrrirBr?rrrrrrs r3 test_gtconr's. )   ) )C 1  1 b((A AE  SZZA..r1 1B AE  SZZA..r1 1B  RWR__$rwr1~~5A }UBK((8vqvrw7 1b"88E??AHHUOORYYu5E5EryyQVGWGWWLAq"b F1IIMMqM ! ! % % ' 'E#$6==LE5!&r1b!1!1B2sD$ U2q"c4T : : :FC#$6==LE5U1XXNBd U2u4 ( ( (FC 8E??  $DC4((((((r5))rRrV)rVrRrcrtd|}|\}}|||\}}t|ddS)N geqrfp_lworkrrrr)r1r0r)rrrris r3test_geqrfp_lworkr*sM$^EBBBL DAq,a(((KE4qr5z 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-rvrSrPrpttrfrrzpttrf: info = z , should be 0)err_msgrpttrszpttrs: info = )r7rr^rrr4r2rrr'r rr rrry)ddtyper1r2r/rrprrrr,r_erirJrrrr._xs r3test_pttrf_pttrsr2s )   # #C rx" "D A $QD&#66:A#QqSFE377A  RWQ^^#bgbgajj!&<&< >gajj271a==(271b>>9 Hrwwyy{ "  (h < < '1# > > E GAJJA &B 7 GAJJB '"'!Q-- 7 q!Q<r5zdtype,realtyperGctddtj|jz}t d|}d}t ||||\}}}} |||| |\} } } } t | dd| d ttjt|dtj| | |rt| tj | j ztj || t| tj | ztj | j z|| d Sd S) a Tests the ?pteqr lapack routine for all dtypes and compute_z parameters. It generates random SPD matrix diagonals d and e, and then confirms correct eigenvalues with scipy.linalg.eig. With applicable compute_z=2 it tests that z can reform A. rrpteqrrrvrprrKrGrzinfo = z, should be 0.rN)rr7rrr'rLrrsortr rryrr2)r1rFrGr/rNrrprrrKd_pteqre_pteqrz_pteqrris r3 test_pteqrrTV s_ HHH # #D ge 4 4 4E A"5(AyAAJAq!Q&+ea1Y&O&O&O#GWgtq8D888999BGDGGAJ'')9)9EEEE&"''"2"2"44bk!nn! # # # # "''"2"22RWW5E5E5GG & & & & & & &&r5ctdtd|}d}t||||\}}}}||dz |||\} } } } | dksJdS)NrrNrrvrSrKrGrrr'rL r1rFrGrNrrprrrKrQrRrSris r3test_pteqr_error_non_spdrYw sy HHH ge 4 4 4E A"5(AyAAJAq!Q',eAE1Y&O&O&O#GWgt !888888r5c Ltdtd|}d}t||||\}}}}tt||dd|||tt|||dd|||r$tt||||dd|dSdS)NrrNrrvrrV)rr'rLrrP) r1rFrGrNrrprrrKs r3"test_pteqr_raise_error_wrong_shaper[ s HHH ge 4 4 4E A"5(AyAAJAq!Q*eQssVQ!yIIII*eQ#2#!yIIIINj%A3B39MMMMMMNNr5ctdtd|}d}t||||\}}}}d|d<d|d<|||||\} } } } | dksJdS)NrrNrrvrrVrWrXs r3test_pteqr_error_singularr] s HHH ge 4 4 4E A"5(AyAAJAq!Q AaD AaD&+eAqA&K&K&K#GWgt !888888r5zcompute_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. rrNrrPrrOrN)r'r1r7r2rr) rGrprrAz_expectr/rNrKrr0_zris r3test_pteqr_NAG_f08jgfra s D gag 6 6 6E  RWQ]]"RWQ^^3AuqAi@@@BBBt,,,,BF2JJx 0 0t<<<<< " "$$$$$r5ctjg}td|j}t t ||dS)Nrfr)r7rr'r1rr)A_emptyrfs r3#test_geqrfp_errors_with_empty_arrayru s;hrllG hgm < < .. s%%%!A%%%r5)rrrr'r"rh)rrrcrr{dlwrlwvals r3test_orcsd_uncsd_lworkr# s JJJ1 A AAK''$$TC C #V , , ,B 2q!Q ' 'ED[[EEuhE %%u%%% & &&&&&&r5c 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)rePrrcsdrrrlrworkrrrg@rO)rr#rvsr$r'r"dictrrrbr7r r5cosrrrr)rrrcrr{Xdrvrrlwvalscs11cs12cs21cs22thetau1u2v1tv2trirWVHrn11n12n21n22SonerAXcs r3test_orcsd_uncsdr1 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+>+>@@@@@r5c 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)NrrrrvrPrrrQryr|rGrUrrTrz&info should be > 0 for singular matrix)rrrrrr) r7rr^r'r4r2rrry)r1rrr2rrrrrprrrrrrrrrrrrrrrrrrr rrris r3test_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 xr5ctjd}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)NrrrrvrPrrrQryr|rGrUrTr) r7rr^r'r4r2rrryrrPr)r1rrr2rrrrrprrrrrrrrrrrs r3"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$3E#2#JU < < < < < r& 7)H(8?@w)H)H)HHI1)N)Nr5cdSN)NNNrrs r3rr( -?r5c(tjd}dtj|jz}t d|}d}t |f||dz}t |dz f||} tj|tj| dztjtj| dz} t |d f|| } | | z} ||| \} }}| | | g}||| | || | \} }}}}}}t||d t| |dt| |d t|d kd |dt| |tj|dtjtj |z}tj| }t| ||ztj|jz|t!|dr Jd|t|jdkd|jdt|jdkd|jddS)a This tests the ?ptsvx lapack routine wrapper to solve a random system Ax = b for all dtypes and input variations. Tests for: unmodified input parameters, fact options, incompatible matrix shapes raise an error, and singular matrices return info of illegal value. rr-ptsvxrrTrSrPrrQrrrefrzinfo should be 0 but is .rrr)rQrz# but should be ({x_soln.shape[1]},)rN)r7rr^rrr'r4r2rrr rrr rryrr0)r1rFr df_de_lambdar2r/rrrprrrrrrrirrr rrrJrs r3 test_ptsvxr" s )   # #C %$ $D WE 2 2 2E A#QD(C881. .:::qeAqkk::::::r5c:g|]}t|D]}|Srrrs r3rVz5test_pptrs_pptri_pptrf_ppsv_ppcon.. rr5c6g|]}t|D]}|SrrrUrrs r3rVz5test_pptrs_pptri_pptrf_ppsv_ppcon.. s+<<. s/>>>U1XX>>1>>>>r5)ppsvpptrfpptrspptrippconrrrrrO)rrr)r7rr^rrr4rryr r5r'rrrrrrrrrr)r1rr2r/rrarr[aprrrrrulriaululiaulirbxxvrr rs @r3!test_pptrs_pptri_pptrf_ppsv_ppconr s )   % %C 8E?? s "DGAt#QF%SAAAA#QIUDDDA  Q///%%));;A @::::E!HH:::::::E!HH:::<=>eAqsmm>>>@ 4B'74((($D%u uQ%(((HBq 1E " " "4 (CB!$////a5)))ICq q66$. Dr5FrrrrHrcrOrVrPr r r7rr^rrr4r'rr.rrrry) r1r2r/rrarrrrrKd2s r3test_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&====AdGRad333333r5zt, 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. rrrr)wantqrrN)r'r1rr)rifstilstexpectr/rrs r3test_trexc_NAGr so< D WAG 4 4 4E U1at1 - - -FQq AFAD))))))r5ctjd}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-rvr)ggestgexcrcdSr rr s r3rz!test_gges_tgexc..J r r5Fr) overwrite_brrrPrrHrrcrOrVrQrRrr )r1r2r/rrarrrrrrrrKd1r s r3test_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! $ $FQq Aq Aq Aq A 271::AD9999271::AD9999AEAFFHHJ&====AEAFFHHJ&====AdGag%r====AdGag%r======r5ctjd}tj|jdz}d}t ||g||}t d|\}}}|d|d }t|d d |d } |d } | d } |tvr%t| tj | d |t| | z| j z|d |tj |} d| d<t|| | } |tvr|| | | | }n|| | | | | d}t|d d |d } |d} |tvr%t| tj | d |t| | z| j z|d |t| d| d |dS)Nrr-rvr)rtrsen trsen_lworkrcdSr rr s r3rz!test_gees_trsen..z r r5FrrrrHrcrOrPrUrrliworkrr7rr^rrr4r'rr.rrrryr r")r1r2r/rrarr&r'rrrKr selectrs r3test_gees_trsenr-o s  )   % %C 8E?? s "D A#QF%SAAAA/( 7 7 7D%T..! 7 7 7FQq Ar A 4B 271::AD9999AEAFFHHJ&==== Xa[[FF1I ; 2 2E vq!5111vq!5qBBBQq Aq A 271::AD9999AEAFFHHJ&====AdGRad333333r5z*t, q, expect, select, expect_s, expect_sep)g/$?g QIg~jtx?gJ4?)r58EGrgGr?gyX5;?)rg?߾r.gt?)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)\(?)rPrrrPg?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 $(?y3ı.n?rh|)yv? F%uyd`TR?I&†ۿyN@?ݓy4@ @ ^)?)ys{ @ o_yH.@|Pk @y 0*?*:Hy]m{?Gz)y) 0[. r r5Fr!rrrPrrHrrcrOrUrirrr+)r1r2r/rrarrr6r7rrrrrKr#r r,rs r3test_gges_tgsenr9 s )   % %C 8E?? s "D A#QF%SAAAA#QF%SAAAA/( 7 7 7D%T..!QEu M M MFQq Aq Ar Ar A 41T7 B 41T7 B 271::AD9999271::AD9999AEAFFHHJ&====AEAFFHHJ&==== Xa[[FF1I ;1 5 5E1XaZq "E U61aAU 3 3 3FQq Aq Ar Ar A 271::AD9999271::AD9999AEAFFHHJ&====AEAFFHHJ&====AdGag%r====AdGag%r======r5za, b, c, d, e, f, rans, lans)rrrr)rr%rr)rrr%r)rrrg@)rrrr)rrrr)rrg(@)g"rr;)r:rr;r)rrg3@)rrrr%)rrrr)rrrr)rrrr)rrrr)rrrr)rrrr)r<rrr)r rg r)rrr)r=rrr)rrrr)rrr%r)rrrr)rrrr)rr%rr)rrrr)rrrrc |d} td|} | ||||||\} } } }}t|dt| ddtj|jdzdt|d dtj|jdzd t| || d t| || d dS)Nrtgsylrrrr-zSCALE must be 1.0rr/r-rzDIF must be nearly 0zSolution for R is incorrect)r/r-zSolution for L is incorrect)r'rrr7rr)rarrrprrdranslansr1r/r?routloutr\difris r3test_tgsyl_NAGrF! sH D ge 4 4 4E#(5Aq!Q#:#: D$sDqE3QRXe__-@-D/1111C128E??+>s+B24444D$T9;;;;D$T9;;;;;;r5r)rTryijob)rrPrQrRrSc 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/rirvr)outputr rQr?r)rrGrzINFO is non-zerorzSCALE must be non-negativer-zDIF must be 0 for ijob =0r@zDIF must be non-negativerTryrzlhs1 and rhs1 do not match)r/rr-zlhs2 and rhs2 do not match) r7rrrr!uniformr/r'rrrr)r1rrGr/r2rrrarpr?rrrrdr?rCrDr\rErilhs1rhs1lhs2rhs2s r3 test_tgsylrOU 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 < > > > > > >yr5mtypercf|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)Nr}zhetrs not for real dtypes.l*M/t|0)rrTrr-r|r}r~trsrrrr)rarrr-r)rrArBr7rrr.rJr/ryrr'rrr)rPr1rr2rrrrrIr}r~rRrrrrirrs r3 test_sy_hetrsrS 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!5)))OCt 19999cCda(((GAt 19999 (5// CAaCQs++++++r5rz uplo, m, n))rWrTrv)rWrvrv)rJrvrT)rJrvrvctjd}|||f|}t d|f\}} |||||} |dkrtj|ntj|}|dkr)tjt||} d|| | f<| ||} t| | ddS) Nl8#q9 r)lantrr)rMr2rWrPg>r) r7rrr/r'rrrrbr) rrMrrr2r1r2rrUrrBrArs r3 test_lantrrV s )   1 2 2C A &&u--A#$6==LE5 %ad . . .Cckk rwqzzA s{{ Ic!Qii !Q$ %a..CC4((((((r5r+) functoolsrr numpy.testingrrrrrr rAr rnumpyr7r r r rrrrr numpy.randomrrr scipy.linalgrr9rrrrrrrrrr r!scipy.linalg.lapackr" scipy.statsr#r$ scipy.sparsesparser_scipy.__config__r% ImportErrorr&r8r'scipy.linalg.blasr(rr8rr complex128r.r blas_provider blas_versionr4rLrNrrrxryrrrr#rErrrrrrrrr rrr)r2rBrUr^rdrkrprxrrrrrrskipifrrr5rrrrrr r$r'r*rr2r4r6rDrLrTrYr[r]rarrrurrrrrrrrrrrrrrrr$r-r4r9rFrOrSrErVrr5r3rgs#  //////////////// ******!!!!!!!!!!!!!!!!!!!!-,,,,,,,,,FFFFFFFFFFFFFFFFFFFFFFFFFFFF/.....22222222''''''' FFF0000000GGG000000,,,,,,z2:& , . ~ %##  /08@M./7 BL***OOO.]-]-]-]-]-]-]-]-@        p9p9p9p9p9p9p9p9f&))"B"B"BCCDC*)--------*CCCCCCCC(;;;;;;;;@J/J/J/J/J/J/J/J/\&))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$233 E&11'&1.@)V[;%>??AAeeAhh//&&0/AA&<)V[;%>??AAeeAhh//  0/AA )V[;%>??AAeeAhh// N N0/AA N)V[;%>??AAeeAhh//  0/AA :#28$;$;$;<<#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/,.m!4!455(E(E(EFF#s,,&)) ) )*)-,FF65 ) ) )s$8A??B B  BBB