g<ddlZddlZddlZddlZddlmZmZmZm Z m Z m Z ddl Z ddl m ZddlmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-ddl.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7ddl8m9Z9ddl:m;Z;ddlZ>m?Z?m@Z@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZHmIZImJZJmKZKmLZLmMZMmNZNmOZOmPZPdd lQmRZRdd lSmTZTdd lUmVZVdd lWmXZX ddlYmZZZn #e[$rdZZYnwxYwejdkpej\dvZ]de^fdZ_ejEej`gZaejFejbgZceaeczZddZeGddZfGddZgGddZhGddZiGddZjGddZkGd d!ekZle jmne]d"#e jmod$d%ZpGd&d'ZqGd(d)ZrGd*d+ZsGd,d-ZtGd.d/ZuGd0d1ZvdxZwZxeZ(eZd2d3d4ZweZd2d3d5ZxGd6d7ZyGd8d9ZzGd:d;Z{Gd<d=Z|d>Z}e jmnej\d?kd@#dAZ~dBZdCZe jmddDEdFZGdGdHZdUdIZe jmje jmnejejjdJkdK#dLZdMZe jmdNee^ejEeejFgdOZGdPdQZdRZGdSdTZdS)VN) assert_equalassert_almost_equalassert_array_almost_equalassert_array_equalassert_assert_allclose)raises)eigeigvalslusvdsvdvalscholeskyqrschurrsf2csflu_solve lu_factorsolvediagsvd hessenbergrq eig_bandedeigvals_bandedeigheigvalsh qr_multiplyqzorthordqzsubspace_angleshadamardeigvalsh_tridiagonaleigh_tridiagonal null_spacecdf2rdf LinAlgError) dgbtrfdgbtrszgbtrfzgbtrsdsbevdsbevddsbevxzhbevdzhbevx)norm)_select_function) ortho_group)arraydiagfulllinalgargsortzerosarangefloat32 complex64ravelsqrt iscomplexshapesortsignasarrayisfinitendarrayeye)assert_no_overwrite)matrix)check_free_memory) HAS_ILP64)CONFIG emscripten)wasm32wasm64Fc|tvrdtj||tj||dzz}||jzdz }n-tj||}||jzdz }|r*|t d|ztj|zz }||S)z7Generate random sym/hermitian array of the given size n?) COMPLEX_DTYPESnprandomrandconjTr>rFastype)nposdefdtypeAs T/granary/edev/quantum/lib/python3.11/site-packages/scipy/linalg/tests/test_decomp.py_random_hermitian_matrixr^,s  INN1a 29>>!Q#7#7#< < ^Q  INN1a  WaK ! T!A#YYrvayy   88E??ct|tr|}||dzdz }nLt|tr(t |jdkr|jd}|}nt dtj|}|j t|z|z}d|j |zz}|S)aReturn a random symmetric (Hermitian) matrix. If 'dim_or_eigv' is an integer N, return a NxN matrix, with eigenvalues uniformly distributed on (-1,1). If 'dim_or_eigv' is 1-D real array 'a', return a matrix whose eigenvalues are 'a'. rQrzinput type not supported.?) isinstanceintrTrElenr@ TypeErrorr3rvsrWrVr5) dim_or_eigvrngdimdvhs r]symrandrnBs+s##5 JJsOOA  ! [' * *5 k A % %" 3444A  T!WWq A QSU A Hr_cxeZdZdZdZdZdZej de e e e egdZdS) TestEigValscgdgdgdg}t|}dtdzdz ddtdz dz g}t||dS)NrarQrQ ]rQrr r>rselfawexact_ws r] test_simplezTestEigVals.test_simple^sc YY 999 - AJJd2hhJ>1qbz1n5!!W-----r_c tgdgdgdgdj}|}|j}t|}dt dzdz ddt dz dz g}t ||dS)NrrrtrkrwrxrQr)r4rWcopyr r>rrzs r]test_simple_trzTestEigVals.test_simple_trds 999iii3S 9 9 ; FFHH C AJJd2hhJ>1qbz1n5!!W-----r_cgdgdgdg}t|}dtdzdz ddtdz dz g}t||dS)NrrrQruy@?y"@?yW@@rQrryrzs r]test_simple_complexzTestEigVals.test_simple_complexlsm YY <<< 0 AJJe$a'e$a') "!W-----r_cgdgdgdg}t|d}dtdzdz ddtdz dz g}t||dS) NrrrtF check_finiterwrxrQrryrzs r] test_finitezTestEigVals.test_finitetsj YY 999 - AE * * *d2hhJ>1qbz1n5!!W-----r_dtcrtjd|}t|}|jdksJ|jttjd|jksJt|d}|jdksJ|jttjd|jksJdS)Nrrr[rrQThomogeneous_eigvalsrQr)rSemptyr r@r[rF)r{rr|r}s r] test_emptyzTestEigVals.test_emptyzs HV2 & & & AJJw$w'"&""5"5"566<<<<< A4 0 0 0w&    w'"&""5"5"566<<<<<<r1rrBrangerW r{r|r}rlr~v0v1v2is r]rzTestEig.test_simples8 999iii3 4 41vv1d2hhJ>1qbz1n5 Aq1T"XXaZ<*+ , , ;;;   Aq1T"XXaZ<*+ , , $r((] $r((] $r((]!!W---!"a1gd1T7mm&;<<<!"a1gd1T7mm&;<<<!"a1gd1T7mm&;<<<q A AA %a!AAAqD'k1Q4!!!Q$< @ @ @ @11A&&&1q C CA %acAaaadGmQqT!AAAqD'\ B B B B C Cr_ctddgddgg}t|dd\}}}t|tddgtdD]2}t||dd|fz|||dd|fz3tdD][}t|j|dd|fz|||dd|fz\dS)NrarQr?@y?)r4r rrrVrWr{r|r}vlvrrs r]test_simple_complex_eigzTestEig.test_simple_complex_eigs Aq6B7# $ $+++ 2r!!UD$<%8%8999q C CA %a"QQQT(lAaDAAAqDM B B B Bq < )rrr)rrryrPg|=)tolr)rCrSrFr@r r rrlexsortrrer1onessizeallrD real_if_closer8absimagrA)r{r\B atol_homog rtol_homogrrB0msgr}rwtval1val2rpermpermtlength beta_nonzerowhresw_finwt_fins r]_check_gen_eigzTestEig._check_gen_eigsv =1::wqzzqABB AB A1!Art4442 Q 5 5 52v!QQQ$2v!QQQ$tz!}%% K KA DAJQQQT !+*c K K K K K : AadGQ ' ' ' Bq!!!tHa ( ( (z!}} 2!!!T' Bqqq%xLt$ # % % % %#b''""s2ww ' 'AR1XF1II 4 4c! . . . .!QQQ$1 q, !A|O"4 4Ar 2 Q^^2v2vzTksy|$$ C CAvhs111a4y))** CAAAqD 1%)cCCCC(1++HRLL!b&r%xU;;;;r'6 u====s5zzEJ.//F fk122d VE]!c ; ; ; ;#b''""s2ww ' 'AR1XF1II 4 4cBBBB R$qQ'8"9"9:::::r_c tgdgdgdgdgdg}tgdgdgdgd gd g}tjd 5|||d d ddddS#1swxYwYdS)N)"r)-r*)'/1r)rr)&,r) rrr)r.(r%)rrrrr)rr)r#rrignorerg-a=)rr)r4rSerrstaterr{r\rs r] test_singularzTestEig.test_singulars2 ''''''''''''''' ) * * ''''''''''''''' ) * * [X & & & D D   1U  C C C D D D D D D D D D D D D D D D D D DsA99A=A=cttgd}tgdgdgdf}tgdgdgdf}td}td }t j||g|| gg}t j||g||gg}t jd 5|||ddddS#1swxYwYdS) N)rarrs)rQrr)rrQr)rrrQ)rarr)rrarrrrrsrsrsrr)r5r4r9rFrSblockrr)r{MKDZI3r\rs r] test_falkerzTestEig.test_falkers8 yyy!! " " ;;; [[[9 : : :::zzz9995 6 6 &MM VV Hr1gA2w' ( ( Hq"g1v& ' ' [X & & & & &   1 % % % & & & & & & & & & & & & & & & & & &s7CC"Ccd}tjd5tdD]-}||dzdz \}}|||. ddddS#1swxYwYdS)Ncnd|dzz}d|z}gdgddd|dgddd|gg}gdgdddd| gdd|dgg}||fS) NrQ)rarrr)rrarrr)rrrar)rrrrarar)omegac1c2r\rs r]matricesz)TestEig.test_bad_geneig..matrices&s}eQhB5BQAQ2 AQB3QA Aa4Kr_rrd@)r )rSrrr)r{rkr\rs r]test_bad_geneigzTestEig.test_bad_geneig#s   [X & & & * *3ZZ * *xad3h///1##Aq)))) * * * * * * * * * * * * * * * * * * *s>A%%A),A)ctjd}td|}||dtd|}||||dd|dzz}||d|dd|dzz}|||dS)NrsrrP)rSrT RandomStaternr)r{rir\rs r]test_make_eigvalszTestEig.test_make_eigvals:si##D)) AsOO At$$$ AsOO Aq!!! JJv  CJJv$6$6!6 6 At$$$ JJv  CJJv$6$6!6 6 Aq!!!!!r_cgdgdgdg}t|d\}}dtdzdz ddtdz dz g}td d d tdd z zdz g}tgd }td d d tdd z z dz g}|t|z }|t|z }|t|z }t ||t ||dddft |d zt ||ddd ft |d zt ||dddft |dzt d D]2}t ||dd|fz|||dd|fz3dS)NrrrtFrrwrxrQrrarsrrrr)r r>r4r1rrBrrs r]test_check_finitezTestEig.test_check_finiteHs YY 999 -15)))1d2hhJ>1qbz1n5 Aq1T"XXaZ<*+ , , ;;;   Aq1T"XXaZ<*+ , , $r((] $r((] $r((]!!W---!"a1gd1T7mm&;<<<!"a1gd1T7mm&;<<<!"a1gd1T7mm&;<<<q A AA %a!AAAqD'k1Q4!!!Q$< @ @ @ @ A Ar_ctjddd}ttt |dS)z:Check that passing a non-square array raises a ValueError.rvrsrQN)rSr:reshape assert_raises ValueErrorr )r{r\s r]test_not_square_errorzTestEig.test_not_square_errorYs7 IaLL A & &j#q)))))r_ctd}tjddd}t t t ||t t t ||dS)zOCheck that passing arrays of with different shapes raises a ValueError.rQ"@rsN)rFrSr:rrrr rs r]test_shape_mismatchzTestEig.test_shape_mismatch^sZ FF IcNN " "1a ( (j#q!,,,j#q!,,,,,r_ctjgdgdgdgdgd}tjgdgdgd gd gd}t||\}}tj5}|t d tj|d d sJtj|dd sJ ddddS#1swxYwYdS)N)g(@<@gS@gk@)g0@g@@gT@gl@)g8@D@gV@gm@)r$gL@gZ@go@float64r)@@$@r#)rr&@g=@)r@g*@g?@)r r)g1@gA@z%invalid value encountered in multiplyr'+=r @) rSr4r testingsuppress_warningsfilterRuntimeWarningiscloseany)r{r\rrVsups r] test_gh_11577zTestEig.test_gh_11577fs H/////////0002:C D D D H,,,,,,,,,---/7@ A A A 1ayy1Z ) ) + + 8s JJ~'N O O O:a51115577 7 7 7:a51115577 7 7 7 7  8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8s6A2C66C:=C:rctjd|}t|\}}ttjd|\}}|jdksJ|j|jksJt |tjd|jdksJ|j|jksJt|d\}}|jdksJ|j|jksJ|jdksJ|j|jksJdS)NrrrQrTrr)rSrr rFr@r[r)r{rr|r}rw_nvr_ns r]rzTestEig.test_emptys HV2 & & &A2q+++,, Tw$w#)####BHV,,---x6!!!!x4:%%%%A40002w&    w#)####x6!!!!x4:%%%%%%r_N)rrrr)rrrrrrrrrrrrrrr!r6rrrrdrrSr;rr<rrr_r]rrs2CCC(<<<<<<   AF49H;H;H;H;TDDD" & & &***. " " "AAA"*** ---8888 [TC GR\#RSS&&TS&&&r_rceZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z d Zd ZejdeeejeejgdZdS) TestEigBandedc.|dSN)create_bandmatr{s r] setup_methodzTestEigBanded.setup_methods r_c d}d|_d|_tt|dtt|dz ddztt|dz ddztt|dz ddztt|dz ddz|_tt|dd tt|dz ddzzd tt|dz ddzz tt|dz ddztt|dz ddz|_tt|dtt|dz ddztt|dz d dztt|dz d dztt|dz ddz|_d tt|dztt|dz ddzd tt|dz d dzztt|dz d dztt|dz ddz|_tj |j\}}|j }t|}|||_ |d d |f|_ tj |j\}}|j }t|}|||_|d d |f|_|jdz}t!||ft" |_t!||ft& |_t+|D]P}t|j||j||z dz ||f<t|j||j||z dz ||f<Qd|jz|jzdz}t!||ft" |_t|j|jd|jzd d f<t+|jD]p}t|j|dz|jd|jzdz |z |dz|f<t|j| dz |jd|jzdz|zd|dz |z f<qt!||ft& |_t|j|jd|jzd d f<t+|jD]p}t|j|dz|jd|jzdz |z |dz|f<t|j| dz |jd|jzdz|zd|dz |z f<qdt1|z|_|jdz|_d S)zbCreate the full matrix `self.fullmat` and the corresponding band matrix `self.bandmat`. rQ?rarrrPr&Nrr??)KLKUr5r6sym_matherm_matreal_matcomp_matr7r realr8 w_sym_lin evec_sym_lin w_herm_lin evec_herm_linr9r bandmat_symr bandmat_hermr bandmat_real bandmat_compr:rbc)r{NewevargsLDABrs r]r>zTestEigBanded.create_bandmats T!S\\**tAaC3346:4!T??A6N6NOtAaC3346:4!T??A6N6NO d1dmm,,d4!S>>26667d4!S>>15556 QqS$445 QqS$33 4 d1cll++QqS$4457;D1dOOQ7O7OPQqS#3346:4!T??A6N6NO Da...QqS$445d4!T??A6667 QqS#334 QqS$33 4 DL))B Wr{{Dqqq$wKDM**B Wr{{T(4[ w{ $%888!4)7;;;t F FA.24<.C.CD T!VAXqs] +/3DM1/E/ED d1fQh!m , ,y47"Q&!4)5999*.t}*=*=!DG)QQQ,'tw C CA6:4=!A#6N6ND aik!mQqSU2 38?RT9C9CD aik!mQqs1uW4 5 5"4)7;;;*.t}*=*=!DG)QQQ,'tw C CA6:4=!A#6N6ND aik!mQqSU2 38?RT9C9CD aik!mQqs1uW4 5 5VAYY&F#r_ct|jd\}}}|ddt|f}tt ||jtt |t |jdS)zTCompare dsbev eigenvalues and eigenvectors with the result of linalg.eig.ra compute_vN)r,rSr8rrArOrrPr{r}evecinfoevec_s r] test_dsbevzTestEigBanded.test_dsbevsvd.!<<< 4QQQ ]#!$q''4>:::!#e**c$2C.D.DEEEEEr_ct|jd\}}}|ddt|f}tt ||jtt |t |jdS)zUCompare dsbevd eigenvalues and eigenvectors with the result of linalg.eig.rar^N)r-rSr8rrArOrrPr`s r] test_dsbevdzTestEigBanded.test_dsbevdsvt/1=== 4QQQ ]#!$q''4>:::!#e**c$2C.D.DEEEEEr_c Jt|j\}}t|jddd|dd\}}}}}|ddt |f}t t ||jt t|t|j dS)zUCompare dsbevx eigenvalues and eigenvectors with the result of linalg.eig.rarQr_rN) r@rJr.rSr8rrArOrrPr{rXr}ranumifailrbrcs r] test_dsbevxzTestEigBanded.test_dsbevxsT\""1$*4+;S#q!56a%A%A%A!4eTQQQ ]#!$q''4>:::!#e**c$2C.D.DEEEEEr_ct|jd\}}}|ddt|f}tt ||jtt |t |jdS)zUCompare zhbevd eigenvalues and eigenvectors with the result of linalg.eig.rar^N)r/rTr8rrArQrrRr`s r] test_zhbevdzTestEigBanded.test_zhbevd svt0A>>> 4QQQ ]#!$q''4?;;;!#e**c$2D.E.EFFFFFr_c Jt|j\}}t|jddd|dd\}}}}}|ddt |f}t t ||jt t|t|j dS)zUCompare zhbevx eigenvalues and eigenvectors with the result of linalg.eig.rhrarQriN) r@rKr0rTr8rrArQrrRrjs r] test_zhbevxzTestEigBanded.test_zhbevxsT]##1$*4+rlFrN) rrSrNrrArOrTrQrSlonglong) r{w_symw_hermind1ind2 w_sym_ind w_herm_indv_lowerv_upper w_sym_val w_herm_vals r]test_eigvals_bandedz!TestEigBanded.test_eigvals_bandedsKt/00 !$u++t~>>> 122!$v,,@@@{1~~"4#3*-T4LJJJ !$y//"&.d1f"= ? ? ?#D$5+.dD\KKK !$z"2"2"&/$tAv+"> @ @ @.&/.&/"4#3*-Wg @ @ @t/eDDD !$u++t~>>>>>r_c t|j\}}|ddt|jf}t t ||jt t|t|jt|j \}}|ddt|jf}t t ||j t t|t|j d}d}t|jd||f\} } t t | |j||dzt t| t|jdd||dzft|j d||f\} } t t | |j ||dzt t| t|j dd||dzf|j|dz } |j|dz}t|jd| |f\}}t t ||j||dzt t|t|jdd||dzf|j |dz } |j |dz}t|j d| |f\}}t t ||j ||dzt t|t|j dd||dzft|jd \}}|ddt|jf}t t ||jt t|t|jdS) zXCompare eigenvalues and eigenvectors of eig_banded with those of linalg.eig. NrQrvrrsrarvrlFr) rrSr8rNrrArOrrPrTrQrR)r{rxevec_sym evec_sym_ry evec_herm evec_herm_rzr{r| evec_sym_indr} evec_herm_indr~rr evec_sym_valr evec_herm_vals r]test_eig_bandedzTestEigBanded.test_eig_bandedFs%T%566xQQQ 3 334 !$u++t~>>>!#i..#d6G2H2HIII&t'899 qqq'&+"6"667 !$v,,@@@!#j//3t7I3J3JKKK",T-=47;?,#H#H#H < "$y//"&.d1f"= ? ? ?!#l"3"3"%d&74Q;&G"H"H J J J%/t/@69=A4L%J%J%J! M "$z"2"2"&/$tAv+"> @ @ @!#m"4"4"%d&8DaK&H"I"I K K K.&/.&/",T-=47;BG:L#N#N#N < "$y//"&.d1f"= ? ? ?!#l"3"3"%d&74Q;&G"H"H J J J/$'&0/$'&0$.t/@69=Dg @ @ @!#m"4"4"%d&8DaK&H"I"I K K K%T%5EJJJxQQQ 3 334 !$u++t~>>>!#i..#d6G2H2HIIIIIr_ct|j\}}t|j|j|j\}}}t |d|jzddf}t|j|jzD]3}|t |d|jzdz |z |dz|f|dzz }4t|jd\}} } t|| dS)zZCompare dgbtrf LU factorisation with the LU factorisation result of linalg.lu.rQNrar permute_l) r@rLr(rUrHrIr5rr r r{rrX lu_symm_bandipivrburp_linl_linu_lins r] test_dgbtrfzTestEigBanded.test_dgbtrfT]##1#)$*;TWdg#N#N dD ail+ , ,tw()) ? ?A l1TW9Q;q=!A#a%#78!A#>> >AA !<<<ue!!U+++++r_ct|j\}}t|j|j|j\}}}t |d|jzddf}t|j|jzD]3}|t |d|jzdz |z |dz|f|dzz }4t|jd\}} } t|| dS)zZCompare zgbtrf LU factorisation with the LU factorisation result of linalg.lu.rQNrarr) r@rMr*rVrHrIr5rr rrs r] test_zgbtrfzTestEigBanded.test_zgbtrfrr_ct|j|j|j\}}}t ||j|j|j|\}}t j|j|j}t||dS)zhCompare dgbtrs solutions for linear equation system A*x = b with solutions of linalg.solve.N) r(rUrHrIr)rr7rrLrr{rrrbyy_lins r] test_dgbtrszTestEigBanded.test_dgbtrssm$*$*;TWdg#N#N dDtwFF4 T]DF33!!U+++++r_ct|j|j|j\}}}t ||j|j|j|\}}t j|j|j}t||dS)zhCompare zgbtrs solutions for linear equation system A*x = b with solutions of linalg.solve.N) r*rVrHrIr+rWr7rrMrrs r] test_zgbtrszTestEigBanded.test_zgbtrssm$*$*;TWdg#N#N dDtw$GG4 T]DG44!!U+++++r_rctjd|}t|\}}ttjddgddgg|\}}|jdksJ|j|jksJ|jdksJ|j|jksJt|d}|jdksJ|j|jksJdS)NrrrrarT eigvals_only)rSrrr4r@r[)r{ra_bandr}rlr8v_ns r]rzTestEigBanded.test_emptys&+++&!!1bhAA'7rBBBCCSw$w#)####w&    w#)#### vD 1 1 1w$w#)######r_N)rrrr@r>rdrfrmrorqrrrrrrrrrrdrrSr;rr<rrr_r]r;r;s-M$M$M$bFFFFFF F F FGGG G G G(?(?(?T8J8J8Jt , , , , , ,,,,,,, [TC GR\#RSS$$TS$$$r_r;c2eZdZdZdZdZdZdZdZdS)TestEigTridiagonalc.|dSr=) create_trimatr?s r]r@zTestEigTridiagonal.setup_methods r_cd}t|d|_t|dz d|_t|jt|jdzt|jdz|_t j|j\}}|j}t|}|||_ |dd|f|_ dS)z>Create the full matrix `self.fullmat`, `self.d`, and `self.e`.rBrCrarDrN) r6rker5full_matr7r rNr8r}ra)r{rXrYrZr[s r]rz TestEigTridiagonal.create_trimats aac4dfTVR(8(884??J DM**B Wr{{Dqqq$wK r_cttt|j|jddtt t|j|jdztt t|j|jdttt|j|jdttt|j|jdd dS) zTest error conditions.NrrPrC lapack_driverfoorrrrs)rrr#rkrrfr?s r]test_degeneratez"TestEigTridiagonal.test_degenerates j"6ss LLLi!5tvtv{KKKi!5tvtv$& ( ( ( (j"6$) + + + + j"6 w 8 8 8 8 8 8r_c "dD]@}t|j|j|}tt ||jAdD],}t tt|j|j|dd-dD]}t|j|jddt|jd z f| }tt ||jd }d }t|j|jd||f| }tt ||j||d z|j|d z }|j|d z}t|j|jd||f| }tt ||j||d zdS)z>Compare eigenvalues of eigvalsh_tridiagonal with those of eig.)sterfstevstebzstemrautor)rrrrrrtrurrrrrartrurrQrvrvrlN) r#rkrrrAr}rrre) r{driverr}w_indrzr{r~rw_vals r]test_eigvalsh_tridiagonalz,TestEigTridiagonal.test_eigvalsh_tridiagonalsB 7 7F$TVTV6JJJA %d1ggtv 6 6 6 6' / /F *&:DFDF(.s'- / / / / /1 H HF(s!S[[]9K$&&&E &d5kk46 : : :DD(s$$&&&E &d5kk46$tAv+3F G G GfTlV+GfTlV+G(s'79K$&&&E &d5kk46$tAv+3F G G G G+ H Hr_c nttt|j|jddD]}t|j|j|\}}|ddt |f}t t||jt t|t|j ttt|j|jdddd D]}d }t|jd z }t|j|jd||f| \}}t t||jt t|t|j d }d}t|j|jd||f| \}}t t||j||d zt t|t|j dd||d zf|j|dz }|j|dz}t|j|jd||f| \}}t t||j||d zt t|t|j dd||d zfdS)zWCompare eigenvalues and eigenvectors of eigh_tridiagonal with those of eig. rr)rrrrNrrrrrrrarrQrvrvrl) rrr$rkrr8rrAr}rrare) r{rr}rarcrzr{r~rs r]test_eigh_tridiagonalz(TestEigTridiagonal.test_eigh_tridiagonals j"2DFDF$+ - - - -8 B BF&tvtvVLLLGAtGAJJ'E %d1ggtv 6 6 6 %c%jj#di.. A A A Aj"2DFDF$*3V M M M M0 F FFDtv;;q=D&s$$&&&GAt &d1ggtv 6 6 6 %c$iiTY @ @ @DD&s$$&&&GAt &d1ggtvd46k/B C C C %c$ii&)$)AAAtDF{N*C&D&D F F FfTlV+GfTlV+G&s'79K$&&&GAt &d1ggtvd46k/B C C C %c$ii&)$)AAAtDF{N*C&D&D F F F F3 F Fr_ctjdg}tjg}t||d}|jdksJt ||t||dd\}}|jdksJ|jdksJt ||t |td ggt||d d \}}|jd ksJ|jd ksJ|jdksJdS)z See gh-20075rETrrarrrsrQrCrl)rrrrrN)rSr4r$ndimrrr@)r{r|rxr4s r]test_eigh_tridiagonal_1x1z,TestEigTridiagonal.test_eigh_tridiagonal_1x1/s HdV   HRLL Q 5 5 5v{{{{11SvFFF1v{{{{v{{{{152$==)))1SwGGG1v{{{{w$w&      r_N) rrrr@rrrrrrr_r]rrsv     8 8 8 H H HD(F(F(FT!!!!!r_rceZdZdZdZdZdZdZdZe j de e j dd d Z e j dd d Ze j d d e j dddZdZe j deeejeejgdZdS)TestEighcDtjddS)Nr)rSrTseedr?s r] setup_classzTestEigh.setup_classCs tr_c Lttttjddgttttjddgtjddgttttjddgtjddgttttjddgtjddgdttttjddgtjddgddgddgttttjddgtjddgddgttttjddgtjddgd dgttttjddgtjddgddgttttjddgtjddgddg ttttjddgd ttttjddgdd ttttjddgtjddgd ttttjddgtjddgdddgttttjddgtjddgdddgdS)NrarQrs)type)subset_by_valuesubset_by_indexrrrrwrongrgvxevrgvd)rr)rrrrSrr?s r]test_wrong_inputszTestEigh.test_wrong_inputsFs j$A888j$A!QIIIj$A!QIIIj$A!Q     j$A!Q'(!fq!f F F F F j$A!Q'(!f . . . . j$A!Q')1g / / / / j$A!Q'(!f . . . . j$A!Q'(!f . . . . j$AHHHHj$AeLLLLj$A!Q" $ $ $ $ j$A!Q"QF < < < <j$A!Q"QF < < < < < >***w$w#)######r_N)rrrrrrrrrrrrrrrrrrdrrSr;rr<rrr_r]rrBs$<$<$itfB????j#vUCCCCCCr_cgdgdgdg}dD]}t|||j\}}}t|j|zt dt|j|zt dt |jd|jdf|jj}tt|D]}|||||f<t||z|z|dS)NrrrarrsrtTF full_matricesrrsr r rrrWrFr9r@r[charrrer{r|r rsvhsigmars r]rzTestSVD_GESDD.test_simples YY III .* 9 9M1M)-);===HAq" %acAgs1vv 6 6 6 %bdRiQ 8 8 8171:rx{3QW\BBE3q66]] # #dad %a%i"na 8 8 8 8 9 9r_cgdgdgdg}dD]}t|||j\}}}t|j|zt dt|j|zt dt |jd|jdf|jj}tt|D]}|||||f<t||z|z|dS)Nrrrtr r rsrrrs r]test_simple_singularz"TestSVD_GESDD.test_simple_singulars YY 999 -* 9 9M1M)-);===HAq" %acAgs1vv 6 6 6 %bdRiQ 8 8 8171:rx{3QW\BBE3q66]] # #dad %a%i"na 8 8 8 8 9 9r_cgdgdg}dD]}t|||j\}}}t|j|zt |jdt |jd|jdf|jj}tt|D]}|||||f<t||z|z|dS)Nrrrrurvr r r r rrrWrFr@r9r[rrrers r]test_simple_underdetz"TestSVD_GESDD.test_simple_underdets YY "* 9 9M1M)-);===HAq" %acAgs171: ? ? ?171:rx{3QW\BBE3q66]] # #dad %a%i"na 8 8 8 8 9 9r_cddgddgddgg}dD]}t|||j\}}}t|j|zt |jdt|j|zt dt |jd|jdf|jj}tt|D]}|||||f<t||z|z|dS) NrarQrrursr r rrrs r]test_simple_overdetz!TestSVD_GESDD.test_simple_overdetsVaVaV $* 9 9M1M)-);===HAq" %acAgs171: ? ? ? %bdRiQ 8 8 8171:rx{3QW\BBE3q66]] # #dad %a%i"na 8 8 8 8 9 9r_c tjd}d}d}tdD](}|||g|||gfD]}dD]}t |||j\}}} t |j|zt|j dt | | jzt| j dt|j d| j df|j j } tt|D]}||| ||f<t || z| z|*dS) Nrrrrsr r rar)rSrTrrr rrrWrFr@r9r[rre) r{rirYmrr|r rrrrs r] test_randomzTestSVD_GESDD.test_randomsqi##D))  q A AAjj!Q((#**aV*<*<= A A%2AAM"1M151C E E EHAq"-acAgs171:GGG-b24iRXa[9I9IJJJ!171:rx{";QW\JJE"3q66]]++&'dad -a%i"na@@@@A A A Ar_cPgdgdgdg}dD]}t|||j\}}}t|j|zt |jdt|j|zt |jdt|jd|jdf|jj }tt|D]}|||||f<t||z|z|dS)Nrr)ray@rsrtr r rar) r rrrVrWrFr@r9r[rrrers r]rz!TestSVD_GESDD.test_simple_complexs YY III .* 9 9M1M)-);===HAq" %affhhj1nc!'!*oo F F F %bggiikB&6BHQK8H8H I I I171:rx{3QW\BBE3q66]] # #dad %a%i"na 8 8 8 8 9 9r_c tjd}d}d}tdD];}dD]4}|||g|||gfD]}|d|t |jzz}t |||j\}}} t| j |zt|jdt|jd| jd f|j j} tt|D]}||| ||f<t|| z| z|6=dS) Nrrrrsr rPr rar)rSrTrrlistr@r rrrVrWrFr9r[rre) r{rirYrrr r|rrrrs r]test_random_complexz!TestSVD_GESDD.test_random_complex si##D))  q A AA!. A A **aV,,cjj!Q.@.@A A AABszz$qw--8888A"1M151C E E EHAq"-affhhj1n.1!'!*oo??? "171:rx{";QW\JJE"3q66]]++&'dad -a%i"na@@@@ A A A Ar_ctjd}gd}|D]f}tjtjtjtjfD]5}|j||}t||j 6gdS)Nr))rr)r2)<rr) rSrTrr;r%r< complex128rUrXr r)r{risizesszrr|s r]test_crash_1580zTestSVD_GESDD.test_crash_15804si##D))/// 9 9Bz2:r|R]K 9 9CHbM((,,AT%788888 9 9 9r_cgdgdgdg}t|d|j\}}}t|j|zt dt|j|zt dt |jd|jdf|jj}tt|D]}|||||f<t||z|z|dS)Nrrr rtF)rrrsrr)r{r|rrrrrs r]rzTestSVD_GESDD.test_check_finite=s YY III .quD>s1vv  AA$E!Q$KK!!e)b.!44444r_crtjgdgdgdgdg}t||jdS)N)K}\UU?vWUU?r,rhrhrh)rhr,r-r,rhrh)rhrhr,r-r,rh)rhrhrhr,r-r,r)rSr4r r)r{rs r] test_gh_5039zTestSVD_GESDD.test_gh_5039Gs^ H = = = = = = = = = = = = ? @ @ AT/000000r_z64-bit LAPACK requiredreasonctdtjddgtj}d|d<t |d\}}}t |d d t |d |dzd dS) NihB)free_mbralrrFr rrCr)rIrSr9r;r r)r{r\rrrs r]test_large_matrixzTestSVD_GESDD.test_large_matrixXs %(((( HaZrz 2 2 2%q...1b!c"""$"U)+S11111r_rrrarQrYr[ctj||f|}t||}|jj}|dvr|n|}t |\}} } t|j||ft|j|t| j|ft| jtj|t| j||ft| j|t |d\}} } t|j||ft|j|t| j|ft| jtj|t| j||ft| j|t |d} t| j|ft| jtj|dS)NrFDFr3 compute_uv) rSr9minr[rlowerr rr@) r{rrYr[r|rdchar real_dcharrrrls r]test_shape_dtypezTestSVD_GESDD.test_shape_dtypebs HaV5 ) ) ) 1II &+tmmU[[]]] a&&1aQWq!f%%%QWe$$$QWqd###QWbhz22333QWq!f%%%QWe$$$au---1aQWq!f%%%QWe$$$QWqd###QWbhz22333QWq!f%%%QWe$$$ e $ $ $QWqd###QWbhz2233333r_rrrYrrrctjd|}t|\}}}tj||f|}t|\} } } t | tj|t | tjdt | tj|| j|jksJ| j|jksJ| j|jksJt|d\} } } t | tj|dft | tjdt | tjd|f| j|jksJ| j|jksJ| j|jksJt|d} t | tjd| j|jksJdS)NrsrrFr3rr8)rSrFr rrrr[) r{rrrYa0u0s0rr|rrrls r]rzTestSVD_GESDD.test_emptysVAR WW B HaV2 & & &a&&1a2;q>>***28D>>***2;q>>***w"(""""w"(""""w"(""""au---1a28QF++,,,28D>>***28QF++,,,w"(""""w"(""""w"("""" e $ $ $28D>>***w"(""""""r_N)rrrrrrrrrrrr"r)rr.rrskipifrJslowr4rrr>rdrrSr;rr<rrr_r]rrsMDDD 9 9 9 9 9 9 9 9 9 9 9 9AAA 9 9 9AAA(999555111" [I .FGG [22HG2 [S))),, [S))),, [Wf--44.--,-,44 [TC GR\#RSS [Z)A)A)ABB##CBTS###r_rceZdZdZdS) TestSVD_GESVDgesvdN)rrrrrr_r]rHrHsMMMr_rHzout of memory in WASMr/rBctjdtj}tt5t |ddddS#1swxYwYdS)N)iir)rSrr%rrr )dfs r]test_svd_gesdd_nofegfaultrLs  w}BJ///B z " " BsAAAceZdZejdeeej e ej gdZ dZ dZdZdZdZdZd Zejjd Zd S) TestSVDValsrcXggtjdtjdfD]~}tj||}t |}t |tjdt tjd|}|j|jksJdS)NrrrsrrrQ)rSrrr4rrrFr[)r{rr|rrDs r]rzTestSVDVals.test_emptysrx''8 ' 'A"%%%A A BHQKK ( ( (,,,--B7bh&&&&&  ' 'r_cgdgdgdg}t|}tt|dkt|d|dcxko |dkncdS)NrrrtrsrrarQrrrer{r|rs r]rzTestSVDVals.test_simplesy YY 999 - AJJA! !!$$$$!$$$$%%%%%r_cgdgdg}t|}tt|dkt|d|dkdS)NrrrrQrrarRrSs r]rz TestSVDVals.test_simple_underdetsW YY " AJJA! !! r_cddgddgddgg}t|}tt|dkt|d|dkdS)NrarQrrursrrRrSs r]rzTestSVDVals.test_simple_overdets]VaVaV $ AJJA! !! r_cgdgdgdg}t|}tt|dkt|d|dcxko |dkncdS)Nrr)rar@rtrsrrarQrRrSs r]rzTestSVDVals.test_simple_complexsy YY YYY / AJJA! !!$$$$!$$$$%%%%%r_cgdgdg}t|}tt|dkt|d|dkdS)Nrr)ry@rvrQrrarRrSs r]test_simple_underdet_complexz(TestSVDVals.test_simple_underdet_complexsW YY # AJJA! !! r_cddgddgddgg}t|}tt|dkt|d|dkdS)NrarQrrurWrrRrSs r]test_simple_overdet_complexz'TestSVDVals.test_simple_overdet_complexs]VaVb!W % AJJA! !! r_cgdgdgdg}t|d}tt|dkt|d|dcxko |dkncdS) NrrrtFrrsrrarQrRrSs r]rzTestSVDVals.test_check_finites YY 999 - AE * * *A! !!$$$$!$$$$%%%%%r_ctjdtjdd}t |dS)Nrii )rSrTrrUrr{r|s r]test_crash_2609zTestSVDVals.test_crash_2609s: t INN4 & & r_N)rrrrrrrdrrSr;rr<rrrrrrYr[rrFr_rr_r]rNrNs [TC GR\#RSS''TS'&&&   &&&   &&&  [r_rNceZdZdZdS) TestDiagSVDcZttgdddgdgdgdgdS)Nrarrrsr)rrr?s r]rzTestDiagSVD.test_simplesK!')))Q":":#,99iii"C E E E E Er_N)rrrrrr_r]raras(EEEEEr_raceZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z d Zd ZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZdZ dZ!d Z"d!Z#d"Z$d#Z%d$Z&d%Z'd&Z(d'Z)d(Z*d)Z+d*Z,d+Z-d,Z.d-Z/d.Z0d/Z1d0Z2d1Z3d2Z4d3Z5d4Z6e7j89d5gd6e7j89d7gd6e7j89d8d9d:ge7j89d;e:d<Z;e7j89d=gd>d?Zs JAAA/ 0 0Q&&&1a QLLqu#2#''(((!!#'3q66222!!a%111a4111AaaadGB!!R(((!!R(((((r_cddgddgddgg}t|d\}}t|j|ztdt||z|t |jdt |jd dS) NrirQrwrurseconomicmodersrQrQrQrrrWrFrr@rms r]test_simple_tall_ezTestQR.test_simple_tall_eJsVaVaV $!*%%%1!!#'3q66222!!a%+++QWf%%%QWf%%%%%r_ctjddgddgddgg}t|dd\}}}tt |}t tj|d d|dd kt|j|ztdt||z|dd|ft|dd|fd \}}t||t||dS) NrirQrwrursTrr{rrarrr|r}s r]test_simple_tall_e_pivotingz"TestQR.test_simple_tall_e_pivotingSs JAAA/ 0 0QJ7771a QLLqu#2#''(((!!#'3q66222!!a%111a4111AaaadG*---B!!R(((!!R(((((r_cddgddgddgg}t|d\}}ddg}t||d \}}t||z|t||tgd }t||d d \}}t||ddz|t|t dd \}}t||dS) NrirQrwrursrrrarrarQrT overwrite_crrrr4rFrrs r]test_simple_tall_leftzTestQR.test_simple_tall_left_sVaVaV $!*%%%1 FQ6**B!!a%,,,!!R((( )))  Q6t<<<B!!ae)R000As1vvv..A!"a(((((r_c(ddgddgddgg}t|dd\}}}d dg}t||d d\}}}t||t||z|t|t dd d\}}}t||dS) NrirQrwrursrTrr{rar)rrrrrF)r{r|rnrorrsrtkpvts r]test_simple_tall_left_pivotingz%TestQR.test_simple_tall_left_pivotinglsVaVaV $ T::: 1d F!!Q55 At4&&&!!a%,,,!!SVVVT:: At!"a(((((r_cddgddgddgg}t|d\}}gd}t||\}}t||z|t||t|td\}}t||dS) NrirQrwrursrrrrrqr{r|rnrorscqrus r]test_simple_tall_rightzTestQR.test_simple_tall_rightvsVaVaV $!*%%%1 IIQ""B!!a%,,,!!R(((As1vv&&A!"a(((((r_cddgddgddgg}t|dd\}}}gd }t||d \}}}t||z|t|tdd \}}}t||dS) NrirQrwrursTrrrrrzrqr{r|rnrorrsrs r]test_simple_tall_right_pivotingz&TestQR.test_simple_tall_right_pivotingsVaVaV $Dz::: 1d II!!Q666 At!!a%,,,!!SVVd;;; At!"a(((((r_cgdgdg}t|\}}t|j|ztdt||z|t |jdt |jddS)NrirQrurjrQrrQrsrrms r]test_simple_fatzTestQR.test_simple_fats} YY "!uu1!!#'3q66222!!a%+++QWf%%%QWf%%%%%r_cVtjgdgdg}t|d\}}}tt |}t tj|dd|ddkt|j|ztdt||z|dd|ft|j dt|j d t|dd|f\}}t||t||dS) NrrjTrzrarrQrr rSrCrrr5rrrrWrFrr@r}s r]test_simple_fat_pivotingzTestQR.test_simple_fat_pivotings J 999- . .Q&&&1a QLLqu#2#''(((!!#'3q66222!!a%111a4111QWf%%%QWf%%%AaaadGB!!R(((!!R(((((r_cgdgdg}t|d\}}t|j|ztdt||z|t |jdt |jddS)NrhrQrwrurrrQrrrrms r]test_simple_fat_ezTestQR.test_simple_fat_es YY "!*%%%1!!#'3q66222!!a%+++QWf%%%QWf%%%%%r_c\tjgdgdg}t|dd\}}}tt |}t tj|dd|ddkt|j|ztdt||z|dd|ft|j d t|j d t|dd|fd \}}t||t||dS) NrhrTrrrarrQrrrrr}s r]test_simple_fat_e_pivotingz!TestQR.test_simple_fat_e_pivotings J 999- . .QJ7771a QLLqu#2#''(((!!#'3q66222!!a%111a4111QWf%%%QWf%%%AaaadG*---B!!R(((!!R(((((r_cgdgdg}t|d\}}ddg}t||d\}}t||z|t||t|tdd\}}t||dS)NrhrrrrarQrrqrrs r]test_simple_fat_leftzTestQR.test_simple_fat_lefts YY "!*%%%1 FQ6**B!!a%,,,!!R(((As1vvv..A!"a(((((r_cgdgdg}t|dd\}}}ddg}t||dd\}}}t||z|t|tddd\}}}t||dS) NrhrrTrrarQrrqrs r]test_simple_fat_left_pivotingz$TestQR.test_simple_fat_left_pivotings YY " T::: 1d F!!Q55 At!!a%,,,!!SVVVT:: At!"a(((((r_cgdgdg}t|d\}}ddg}t||\}}t||z|t||t|td\}}t||dS)NrhrrrrarQrqrs r]test_simple_fat_rightzTestQR.test_simple_fat_rights YY "!*%%%1 FQ""B!!a%,,,!!R(((As1vv&&A!"a(((((r_cgdgdg}t|dd\}}}ddg}t||d\}}}t||z|t|tdd\}}}t||dS) NrhrTrrrarQrzrqrs r]test_simple_fat_right_pivotingz%TestQR.test_simple_fat_right_pivotings YY "Dz::: 1d F!!Q666 At!!a%,,,!!SVVd;;; At!"a(((((r_cgdgdgdg}t|\}}t|j|zt dt||z|dSNrs@@rururQy@@rsrQrrs)rrrVrWrFrms r]rzTestQR.test_simple_complexsg \\<<< 3!uu1!!&&((*q.#a&&999!!a%+++++r_cgdgdgdg}t|\}}gd}t||d\}}t||z|t|tdd\}}t||dS)NrrrrarQrrrsrqr{r|rnrorsrts r]test_simple_complex_leftzTestQR.test_simple_complex_lefts \\<<< 3!uu1 LLAq&))A!!a%,,,As1vvv..A!!R(((((r_cgdgdgdg}t|\}}gd}t||\}}t||z|t|td\}}t||dS)Nrrrrrsrqrs r]test_simple_complex_rightz TestQR.test_simple_complex_rights \\<<< 3!uu1 LLAq!!A!!a%,,,As1vv&&A!!R(((((r_cddgddgddgg}t|d\}}d d g}t||d \}}t||z|t||tgd }t||d d \}}t||ddz|t|t dd \}}t||dS)Nriy@@rQrwy@@rsrrra@@rrTrrrrs r]test_simple_tall_complex_leftz$TestQR.test_simple_tall_complex_leftsYAq *!*%%%1 IQ6**B!!a%,,,!!R((( )))  Q6t<<<B!!ae)R000As1vvv..A!"a(((((r_cgdgdgdg}t|\}}gd}t||dd\}}t||z|dS)NrrrrrT conjugaterrrrVrs r]"test_simple_complex_left_conjugatez)TestQR.test_simple_complex_left_conjugatesn \\<<< 3!uu1 LLAq&D999A!!&&((Q,33333r_cddgddgddgg}t|d\}}ddg}t||d d \}}t||z|dS) NrsrrurrQrrrarTrrrs r]'test_simple_complex_tall_left_conjugatez.TestQR.test_simple_complex_tall_left_conjugate suYD Aq6 *!*%%%1 IAq&D999A!!&&((Q,33333r_cgdgdgdg}t|\}}tjgd}t||d\}}t ||z|dS)NrrrrTr)rrSr4rrrVrs r]#test_simple_complex_right_conjugatez*TestQR.test_simple_complex_right_conjugatesv \\<<< 3!uu1 H\\\ " "AqD111A!!affhh,33333r_c"tgdgdgdg}t|d\}}}tt|}t t j|dd|ddkt|j |ztdt||z|dd|ft|dd|f\}}t||t||dS) NrrrTrzrarrs) r4rrr5rrSrrrVrWrFr}s r]test_simple_complex_pivotingz#TestQR.test_simple_complex_pivotings <<<yyy9 : :Q&&&1a QLLqu#2#''(((!!&&((*q.#a&&999!!a%111a4111AaaadGB!!R(((!!R(((((r_ctgdgdgdg}t|d\}}}gd}t||dd\}}}t||z|dS)NrrrTrzrrr4rrrrs r]!test_simple_complex_left_pivotingz(TestQR.test_simple_complex_left_pivoting"sv <<<yyy9 : :D))) 1d LL!!Q55 At!!a%,,,,,r_ctgdgdgdg}t|d\}}}gd}t||d\}}}t||z|dS)NrrrTrzrrrs r]"test_simple_complex_right_pivotingz)TestQR.test_simple_complex_right_pivoting)sw <<<yyy9 : :D))) 1d LL!!Q666 At!!a%,,,,,r_c.tjd}d}tdD]c}|||g}t |\}}t |j|zt|t ||z|ddSNrrrQrSrTrrrrrWrFr{rirYrr|rnros r]rzTestQR.test_random0si##D)) q 0 0A Aq6""Aa55DAq %acAgs1vv 6 6 6 %a!eQ / / / /  0 0r_ctjd}d}tdD]}|||g}t |\}}||g}t ||d\}}t ||z|t |t|d\}}t ||dS)NrrrQrrSrTrrrrrrF r{rirYrr|rnrorsrts r]test_random_leftzTestQR.test_random_left9si##D)) q - -A Aq6""Aa55DAq A3A1f--EB %a!eR 0 0 03q66622EB %a , , , , - -r_ctjd}d}tdD]}|||g}t |\}}||g}t ||\}}t ||z|t |t|\}}t ||dSrr r{rirYrr|rnrorsrs r]test_random_rightzTestQR.test_random_rightEsi##D)) q - -A Aq6""Aa55DAq A3A1%%EB %a!eR 0 0 03q66**EB %a , , , , - -r_c btjd}d}tdD]}|||g}t |d\}}}t t |}ttj|dd|ddkt|j |zt|t||z|dd|ft |dd|f\} } t|| t|| dS)NrrrQTrzrar rSrTrrrrr5rrrrWrF r{rirYrr|rnror~rkrrus r]test_random_pivotingzTestQR.test_random_pivotingQsi##D)) q - -A Aq6""AT***GAq!DGG A BF1QRR5AcrcF?++ , , , %acAgs1vv 6 6 6 %a!eQqqq!tW 5 5 5!!!Q$[[FB %a , , , %a , , , , - -r_c2tjd}d}d}tdD]c}|||g}t |\}}t |j|zt|t ||z|ddSNrrrQrr{rirrYrr|rnros r]test_random_tallzTestQR.test_random_tall_si##D))  q 0 0A Aq6""Aa55DAq %acAgs1vv 6 6 6 %a!eQ / / / /  0 0r_ctjd}d}d}tdD]}|||g}t |d\}}||g}t ||d\} }t ||z| t |t|d\} }t | |dS)NrrrrQrrrr) r{rirrYrr|rnrorsrts r]test_random_tall_leftzTestQR.test_random_tall_leftjsi##D))  q - -A Aq6""Aaj)))DAq A3A1f--EB %a!eR 0 0 03q66622EB %b! , , , , - -r_ctjd}d}d}tdD]}|||g}t |d\}}||g}t ||\} }t ||z| t |t|\} }t | |dSNrrrrQrrr) r{rirrYrr|rnrorsrs r]test_random_tall_rightzTestQR.test_random_tall_rightxsi##D))  q - -A Aq6""Aaj)))DAq A3A1%%EB %a!eR 0 0 03q66**EB %b! , , , , - -r_c ftjd}d}d}tdD]}|||g}t |d\}}}t t |} ttj| dd| ddkt|j |zt|t||z|dd|ft |dd|f\} } t|| t|| dS) NrrrrQTrzrarr r{rirrYrr|rnror~rkrrus r]test_random_tall_pivotingz TestQR.test_random_tall_pivotings$i##D))  q - -A Aq6""AT***GAq!DGG A BF1QRR5AcrcF?++ , , , %acAgs1vv 6 6 6 %a!eQqqq!tW 5 5 5!!!Q$[[FB %a , , , %a , , , , - -r_ctjd}d}d}tdD]}|||g}t |d\}}t |j|zt|t ||z|t|j ||ft|j ||fdSr) rSrTrrrrrWrFrr@rs r]test_random_tall_ezTestQR.test_random_tall_esi##D))  q * *A Aq6""Aaj)))DAq %acAgs1vv 6 6 6 %a!eQ / / / 1a& ) ) ) 1a& ) ) ) )  * *r_c tjd}d}d}tdD]/}|||g}t |dd\}}}t t |} ttj| dd| dd kt|j |zt|t||z|dd|ft|j ||ft|j ||ft |dd|fd \} } t|| t|| 1dS) NrrrrQTrrrarr)rSrTrrrrr5rrrrWrFrr@rs r]test_random_tall_e_pivotingz"TestQR.test_random_tall_e_pivotingsYi##D))  q - -A Aq6""AT ;;;GAq!DGG A BF1QRR5AcrcF?++ , , , %acAgs1vv 6 6 6 %a!eQqqq!tW 5 5 5 1a& ) ) ) 1a& ) ) )!!!Q$j111FB %a , , , %a , , , , - -r_c2tjd}d}d}tdD]c}|||g}t |\}}t |j|zt|t ||z|ddSNrrrrQrrs r]test_random_trapzTestQR.test_random_trapsi##D))  q 0 0A Aq6""Aa55DAq %acAgs1vv 6 6 6 %a!eQ / / / /  0 0r_c ftjd}d}d}tdD]}|||g}t |d\}}}t t |} ttj| dd| ddkt|j |zt|t||z|dd|ft |dd|f\} } t|| t|| dS) NrrrrQTrzrarrrs r]test_random_trap_pivotingz TestQR.test_random_trap_pivotings$i##D))  q - -A Aq6""AT***GAq!DGG A BF1QRR5AcrcF?++ , , , %acAgs1vv 6 6 6 %a!eQqqq!tW 5 5 5!!!Q$[[FB %a , , , %a , , , , - -r_ctjd}d}tdD]}|||gd|||gzz}t |\}}t |j|zt|t ||z|dSNrrrQrP) rSrTrrrrrVrWrFrs r]r"zTestQR.test_random_complexsi##D)) q 0 0A Aq6""R Aq6(:(:%::Aa55DAq %affhhj1nc!ff = = = %a!eQ / / / /  0 0r_ctjd}d}tdD]}|||gd|||gzz}t |\}}||gd||gzz}t ||d\}}t ||z|t |t|d\}}t ||dS)NrrrQrPrrrs r]test_random_complex_leftzTestQR.test_random_complex_leftsi##D)) q - -A Aq6""R Aq6(:(:%::Aa55DAq A3"SZZ__"44A1f--EB %a!eR 0 0 03q66622EB %a , , , , - -r_ctjd}d}tdD]}|||gd|||gzz}t |\}}||gd||gzz}t ||\}}t ||z|t |t|\}}t ||dSrrrs r]test_random_complex_rightz TestQR.test_random_complex_rightsi##D)) q - -A Aq6""R Aq6(:(:%::Aa55DAq A3"SZZ__"44A1%%EB %a!eR 0 0 03q66**EB %a , , , , - -r_c tjd}d}tdD]+}|||gd|||gzz}t |d\}}}t t |}ttj|dd|ddkt| j |zt|t||z|dd|ft |dd|f\} } t|| t|| -dS) NrrrQrPTrzrar) rSrTrrrrr5rrrrVrWrFrs r]test_random_complex_pivotingz#TestQR.test_random_complex_pivotingsAi##D)) q - -A Aq6""R Aq6(:(:%::AT***GAq!DGG A BF1QRR5AcrcF?++ , , , %affhhj1nc!ff = = = %a!eQqqq!tW 5 5 5!!!Q$[[FB %a , , , %a , , , , - -r_cgdgdgdg}t|d\}}t|j|ztdt||z|dSNrhrjrkFrrsrlrms r]rzTestQR.test_check_finitesf YY 999 -!%(((1!!#'3q66222!!a%+++++r_cgdgdgdg}t|d\}}t|d\}}t||t||t|d\}}t||t||t|d\}} t||t| |ttt|fdd ittt|fdd idS) Nrhrjrk)lworkrsrBrrrrQ)rrr Exception) r{r|rnrorruq3r3q4r4s r] test_lworkzTestQR.test_lworks  YY 999 -!4   1AQB!"a(((!"a(((ARB!"a(((!"a(((ARB!"a(((!"a((( iaTGQ<888iaTGQ<88888r_rr5rYr{FTr[cbt||}tj||f|}t||^}}} t |j||ft |j|t |j||ft |j|t| |rdndksJ|r9| \} t | j|ft | jtjt|d|^}} t |j||ft |j|t| |rdndksJ|r9| \} t | j|ft | jtjt|d|^}}} t |j||ft |j|t |j||ft |j|t| |rdndksJ|r9| \} t | j|ft | jtjt|d|^\} } }} t | j||ft | j|t | j|ft | j|t |j||ft |j|t| |rdndksJ|r;| \} t | j|ft | jtjdSdS) Nrrzrarrorrraw) r:rSr9rrr@r[reint32) r{rrYr{r[rr|rnrootherr~rtaus r]r>zTestQR.test_shape_dtypes< 1II HaV5 ) ) )!h/// 1uQWq!f%%%QWe$$$QWq!f%%%QWe$$$5zz82aa3333  ,BA 1$ ' ' ' "( + + +qsX666 EQWq!f%%%QWe$$$5zz82aa3333  ,BA 1$ ' ' ' "( + + +!*x@@@ 1uQWq!f%%%QWe$$$QWq!f%%%QWe$$$5zz82aa3333  ,BA 1$ ' ' ' "( + + + "158 D D D cASYA'''SY&&&SY%%%SY&&&QWq!f%%%QWe$$$5zz82aa3333  ,BA 1$ ' ' ' "( + + + + + , ,r_r?r@c&t||}tj||f}t|\}}t |tj|t |tj||ft|d\}}}t |tj|t |tj||ft |tj|t|d\}t |tj||ft|d\}}t |tj||ft |tj||ft|d\\}} }t |tj||ft | tj|ft |tj||fdS)NTrzrorrr)r:rSrrrrr:) r{rrYrr|rnror~rrs r]rzTestQR.test_emptyOs 1II HaV  !uu12;q>>***28QF++,,,Q&&&1a2;q>>***28QF++,,,29Q<<((( ___28QF++,,,!*%%%128QF++,,,28QF++,,,15))) cARXq!f--...RXqd^^,,,28QF++,,,,,r_c4tjd}tjd}t||\}}t|tjdtjd}tjd}t||\}}t|tjdtjd}tjd}t||\}}t|tjddS)Nrrr)rSrrr)r{r|rsrros r]test_multiply_emptyzTestQR.test_multiply_emptyis HV   HV  Aq!!ABHV,,--- HV   HV  Aq!!ABHV,,--- HV   HV  Aq!!ABHV,,-----r_N)>rrrrrvrxrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr"r r r rrrrrrr>rrrr_r]reres,,, )))))) ) ) )------,,, ) ) ),,, ) ) )&&& ) ) ) ) ) ))))))))))&&& ) ) )&&& ) ) ))))))))))))),,, )))))) ) ) )444444444 ) ) )------000 - - - - - - - - - 0 0 0 - - - - - ---- * * *---$000 - - -000 - - - - - - - - -,,, 9990 [S))),, [S))),, [Z%77 [Wf--.,.,.-87-,-,.,` [Z)A)A)ABB--CB-2.....r_rec|eZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z d Zd ZejdgdejdgdejdedZejdgddZdS)TestRQcgdgdgdg}t|\}}t||jztdt||z|dSrgrrrWrFr{r|rorns r]rzTestRQ.test_simple{s_ YY 999 -!uu1!!ac'3q66222!!a%+++++r_cgdgdgdg}t|\}}t|d}t||dS)Nrhrjrkror)rr)r{r|rornrus r]test_rz TestRQ.test_rsN YY 999 -!uu1 ___!!R(((((r_c.tjd}d}tdD]c}|||g}t |\}}t ||jzt|t ||z|ddSrrSrTrrrrrWrFr{rirYrr|rorns r]rzTestRQ.test_randomsi##D)) q 0 0A Aq6""Aa55DAq %a!#gs1vv 6 6 6 %a!eQ / / / /  0 0r_cgdgdg}t|\}}t|j|ztdt||z|dS)Nrhrjrsr#r$s r]rzTestRQ.test_simple_traprr_cddgddgddgg}t|\}}t|j|ztdt||z|dSrr#r$s r]rzTestRQ.test_simple_talls_VaVaV $!uu1!!#'3q66222!!a%+++++r_cgdgdg}t|\}}t||jztdt||z|dS)Nrrjrsr#r$s r]rzTestRQ.test_simple_fatsY YY "!uu1!!ac'3q66222!!a%+++++r_cgdgdgdg}t|\}}t||jzt dt||z|dSr)rrrVrWrFr$s r]rzTestRQ.test_simple_complexsg \\<<< 3!uu1!!affhhj.#a&&999!!a%+++++r_c2tjd}d}d}tdD]c}|||g}t |\}}t ||jzt|t ||z|ddSrr(r{rirrYrr|rorns r]rzTestRQ.test_random_talli##D))  q 0 0A Aq6""Aa55DAq %a!#gs1vv 6 6 6 %a!eQ / / / /  0 0r_c2tjd}d}d}tdD]c}|||g}t |\}}t ||jzt|t ||z|ddSrr(r/s r]rzTestRQ.test_random_trapr0r_ctjd}d}d}tdD]}|||g}t |d\}}t ||jzt|t ||z|t|j ||ft|j ||fdS)NrrrrQrr) rSrTrrrrrWrFrr@r/s r]test_random_trap_economicz TestRQ.test_random_trap_economicsi##D))  q * *A Aq6""Aaj)))DAq %a!#gs1vv 6 6 6 %a!eQ / / / 1a& ) ) ) 1a& ) ) ) )  * *r_ctjd}d}tdD]}|||gd|||gzz}t |\}}t ||jzt|t ||z|dSr) rSrTrrrrrVrWrFr)s r]r"zTestRQ.test_random_complexsi##D)) q 0 0A Aq6""R Aq6(:(:%::Aa55DAq %a!&&((*nc!ff = = = %a!eQ / / / /  0 0r_ctjd}d}d}tdD]}|||gd|||gzz}t |d\}}t ||jzt|t ||z|t|j ||ft|j ||fdS)NrrrrQrPrr) rSrTrrrrrVrWrFrr@r/s r]test_random_complex_economicz#TestRQ.test_random_complex_economicsi##D))  q * *A Aq6""R Aq6(:(:%::Aaj)))DAq %a!&&((*nc!ff = = = %a!eQ / / / 1a& ) ) ) 1a& ) ) ) )  * *r_cgdgdgdg}t|d\}}t||jztdt||z|dSrr#r$s r]rzTestRQ.test_check_finitesf YY 999 -!%(((1!!ac'3q66222!!a%+++++r_rr5rYr[c|t||}tj||f|}t|\}}t |j||ft |j||ft |j|t |j|t|d}t |j||ft |j|t|d\}}t |j||ft |j|t |j||ft |j|dS)Nrrorr)r:rSr9rrr@r[)r{rrYr[rr|rorns r]r>zTestRQ.test_shape_dtypes+ 1II HaV5 ) ) )!uu1QWq!f%%%QWq!f%%%QWe$$$QWe$$$ qsOOOQWq!f%%%QWe$$$!*%%%1QWq!f%%%QWe$$$QWq!f%%%QWe$$$$$r_r?r@c$t||}tj||f}t|\}}t |tj||ft |tj|t|d}t |tj||ft|d\}}t |tj||ft |tj||fdS)Nrorr)r:rSrrrr)r{rrYrr|rorns r]rzTestRQ.test_emptys 1II HaV  !uu128QF++,,,2;q>>*** qsOOO28QF++,,,!*%%%128QF++,,,28QF++,,,,,r_N)rrrrr&rrrrrrrr3r"r6rrrrrr>rrr_r]r!r!zs},,, ))) 000,,, ,,, ,,, ,,, 000000 * * *000 * * *,,,  [S))),, [S))),, [Wf--%%.--,-,%( [Z)A)A)ABB - -CB - - -r_r!c eZdZdZdZejddej d dej ddgfdej ddej d dgfd ddej dej d gfd ej dej d ddgfd ej ddej d dgfgd Z d Z dZ ejde eejeejgdZejdd d gejdddgejdejejejejgdZejdddgejdejejejejgdZdS) TestSchurct||z|jz|||dt||jztjt |z dd|ddS)Nz&Schur decomposition does not match 'a'rrzu is not unitary)rrVrWrSrFre)r{r|trrrs r] check_schurzTestSchur.check_schur sA *ADt H J J J J AFFHHJA7 2 4 4 4 4 4 4r_c gdgdgdg}t|\}}||||ddt|d\}}ttjt t |o-tjt t |||||ddt||\}}||||dddS)Nri rsrjrBrsrvr++<rrr)rr>rrSr3r=r?r)r{r|r=rtczctc2zc2s r]rzTestSchur.test_simples ZZJJJ /Qxx1 Aqu5999q)$$BuYr]]++,,Mimm8L8L1M1MNNN BU;;;2r??S C5u=====r_zsort, expected_diaglhprQrbrhpiucoucc|dkS)Nrhr)rs r]zTestSchur.&s AHr_cgdgdgdgdg}t||\}}}||||ddttj||d t d |dS) Nr'rrCrDgg rDrCr @g@rTr'rF @rAr+rCrD-q=rrQ)rr>rrSr5r)r{rA expected_diagr|r=rsdims r] test_sortzTestSchur.test_sort s   " " "       !14((( 1d Aqu5999 M>>>>Qr_cgdgdgdgdg}ttt|dttt|ddS)NrQrRrSrV unsupportedrXra)rrrr^s r]test_sort_errorszTestSchur.test_sort_errors4sc    " " "       ! j%????j%333333r_cgdgdgdg}t|d\}}t||z|jz|dS)Nr@rjrBFr)rrrVrW)r{r|r=rs r]rzTestSchur.test_check_finite<sY ZZJJJ /QU+++1!!a%!&&((*"4a88888r_rctjd|}t|\}}ttjd|\}}t |tjdt |tjd|j|jksJ|j|jksJt|d\}}}t |tjdt |tjdt |d|j|jksJ|j|jksJdS)NrrrQrIrXr)rSrrrFrr[r)r{rr|r=rt0z0r\s r]rzTestSchur.test_emptyAs/ HV2 & & &Qxx1rvar***++B28F++,,,28F++,,,w"(""""w"(""""15))) 1d28F++,,,28F++,,,T1w"(""""w"(""""""r_rAoutputrNrr[ctjddgddgg}t||||d}|dkr|dks n|dksJdSdS)N皙?rrQrArerrLr)rSrCrrX)r{rArer[r\r\s r]test_gh_13137_sort_strz TestSchur.test_gh_13137_sort_strRsl Jb As8, - -QXXe__4???C EMMtqyyytqyyyyyyyyr_ctjddgddgg}|dko|tjtjhvd fd }t ||||d}r|dks n|dksJdSdS) NrgrrQrNcr7tj|rJ|tj|sJ||dzz}ntj|sJ|J|}|jdkS)NrPr)rS iscomplexobjisrealr)rrrall_reals r]rAz1TestSchur.test_gh_13137_sort_custom..sortysu ?1-----}1}}}"Hq)))))yyy6E> !r_rhrrar=)rSrCr;r%rrX)r{rer[r\rAr\rns @r]test_gh_13137_sort_customz#TestSchur.test_gh_13137_sort_customhs Jb As8, - -6>Ge BJ/G&G " " " " " "QXXe__4???C$3tqyyy$!))))))yyr_N)rrrr>rrrrrSr>r]r`rrdrr;rr<rr%r&rirorr_r]r;r; s444>>> [ 7271::+tWRWQZZ5 6 '"'!**cGBGAJJ;5 6 $WRWQZZ'"'!**5 6 '"'!**wrwqzzk45 6  wrwqzz3 TB C  E   444999  [TC GR\#RSS##TS#  [VeU^44 [X ':;; [Wrz2:')|R]'DEE99EE<;549$ [X ':;; [Wrz2:')|R]'DEE44EE<;444r_r;ceZdZdZdZdZdZdZdZdZ dZ e j d eeeeegd Zd S) TestHessenbergcgdgdgdg}gdgdgdg}t|d\}}t|j|z|z|t||d dS) Nikiif"ir gbgsE@g㥛 cg(m̀gkwc@gfjWrg&S?g,eX@racalc_qrdecimalrrrWr{r|h1rmrns r]rzTestHessenberg.test_simples    __ ^^ .--...!!!#!A&&&1!!#'A+q111!!R333333r_cgdgdgdg}t|d\}}t|j|z|z|dS)Nrs)ruyf@rw)y;r ryrar})rrrVrWr{r|rmrns r]rz"TestHessenberg.test_simple_complexsc       __ !A&&&1!!&&((*q.1"4a88888r_cgdgdgdgdgdgdgdg}t|d \}}t|j|z|z|dS) N)rarQrsrrurvr)rrQrsrrvrrQ)rrQrQrsrrsrQ)rrrQrirrrQ)rrsrarQrrarQ)rrarQrsrrar)rrrrrrarQrar}rrs r] test_simple2zTestHessenberg.test_simple2s " " " " " " " " " " " " " " " " " " " " "  $!A&&&1!!#'A+q11111r_ctjd}d|d<t|d\}}t|j|z|z|dS)NrsrQ)rrrar})rSrFrrrWrs r] test_simple3zTestHessenberg.test_simple3sN F1II%!A&&&1!!#'A+q11111r_ctjd}d}tdD]H}|||g}t |d\}}t |j|z|z|IdS)NrrrQrar})rSrTrrrrrWr{rirYrr|rmrns r]rzTestHessenberg.test_randomsi##D)) q 6 6A Aq6""Aa***DAq %acAgk1 5 5 5 5 6 6r_cRtjd}d}tdD]u}|||gd|||gzz}t |d\}}t |j|z|z|vdS)NrrrQrPrar})rSrTrrrrrVrWrs r]r"z"TestHessenberg.test_random_complexsi##D)) q = =A Aq6""R Aq6(:(:%::Aa***DAq %affhhj1nq&8! < < < < = =r_cgdgdgdg}gdgdgdg}t|dd \}}t|j|z|z|t||d dS) Nrsrtrxrzr{r|raF)r~rrrrrs r]rz TestHessenberg.test_check_finites    __ ^^ .--...!!!#!AE:::1!!#'A+q111!!R333333r_c>ddgddgg}t|d\}}t|tjdt||ddgdd gg}t|d\}}t|tjdt||dS) NrQrarrAr}y@ry@@y(@)rrrSrF)r{r|rmrnrh2rs r]test_2x2zTestHessenberg.test_2x2sVaW !A&&&1!!RVAYY///!!Q'''D\D%= )Aa(((B!"bfQii000!"a(((((r_rctjd|}t|}|jdksJ|jttjd|jksJt|d\}}t|d\}}|jdksJ|j|jksJ|jdksJ|j|jksJdS)NrrrsTr})rSrrr@r[rF)r{rr|rmrnh3rs r]rzTestHessenberg.test_emptys HV2 & & & qMMw&    w*RVAR%8%8%899?????!D)))1Ad+++Bw&    w"(""""w&    w"(""""""r_N)rrrrrrrrr"rrrrrrdrr;rr<rrr_r]rqrqs 4 4 4999 2 2 2222 666=== 4 4 4 ) ) ) [TC)#LMM # #NM # # #r_rqzBuild Dependenciesblasnameversionc8eZdZdZdZdZdZdZdZdZ dS) TestQZctjd}d}|||gt}|||gt}t ||\}}}}t ||z|jz|dt ||z|jz|dt ||jzt|dt ||jzt|dttj t|dkdS)N90rurr) rSrTrrXr;rrrWrFrrr5 r{rirYr\rAABBQrs r]test_qz_singlezTestQZ.test_qz_singlesi##E**  JJ1v   % %g . . JJ1v   % %g . .!Qxx B1!!b&13,1====!!b&13,1====!!ac'3q661====!!ac'3q661====tBxx1}%%&&&&&r_c2tjd}d}|||g}|||g}t||\}}}}t ||z|jz|t ||z|jz|t ||jzt |t ||jzt |ttjt|dkdS)Nrrur rSrTrrrrWrFrrr5rs r]test_qz_doublezTestQZ.test_qz_doublesi##E**  JJ1v   JJ1v  !Qxx B1!!b&13,222!!b&13,222!!ac'3q66222!!ac'3q66222tBxx1}%%&&&&&r_ctjd}d}|||gd|||gzz}|||gd|||gzz}t||\}}}}t ||z|jz|t ||z|jz|t ||jzt|t ||jzt|ttj t|dkttj t|j dkdS)NrrurPr) rSrTrrrrVrWrFrrr5rrs r]test_qz_complexzTestQZ.test_qz_complex sji##E**  JJ1v  CJJ1v$6$6!6 6 JJ1v  CJJ1v$6$6!6 6!Qxx B1!!b&16688:"5q999!!b&16688:"5q999!!affhhj.#a&&999!!affhhj.#a&&999tBxx1}%%&&&tBxx})**+++++r_c tjd}d}|||gd|||gzzt}|||gd|||gzzt}t ||\}}}}t ||z|jz|dt ||z|jz|dt ||jzt|dt ||jzt|dttj t|dkttj t|j dkdS)NrrurPrr)rSrTrrXr<rrrVrWrFrrr5rrs r]test_qz_complex64zTestQZ.test_qz_complex64 si##E**  ZZA  "SZZA%7%7"7 7 ? ? J J ZZA  "SZZA%7%7"7 7 ? ? J J!Qxx B1!!b&16688:"5q!DDDD!!b&16688:"5q!DDDD!!affhhj.#a&&!DDDD!!affhhj.#a&&!DDDDtBxx1}%%&&&tBxx})**+++++r_c6tjd}d}|||g}|||g}t||d\}}}}||z|jz} t | j|t | jd||z|jz} t | j|t | jdt ||jzt|t ||jzt|ttj t|dkdS)Nrrur)rer) rSrTrrrVrWrrNrrFrrr5) r{rirYr\rrrrraabbs r]test_qz_double_complexzTestQZ.test_qz_double_complex sJi##E**  JJ1v   JJ1v  !Qy111 B1 Vaffhhj !"'1---!"'1--- Vaffhhj !"'1---!"'1---!!affhhj.#a&&999!!affhhj.#a&&999tBxx1}%%&&&&&r_ctjgdgdgdgdg}tjgdgdgdgdg}ttt||d dS) N)333333@)@@Ag@333333@5@gGg@)rrErW)皙@rTGrT)rCrCrFrC)rCrgr)rCr&rUrC)rrrUr'c|dkS)Nrr)araibetas r]rOz,TestQZ.test_qz_double_sort..H s bAgr_rX) rSr4rrrrrrWr)r{r\rrrrrr\s r]test_qz_double_sortzTestQZ.test_qz_double_sort0 s H------,,,,,,. / / H++++++++++++- . . j"a1M1MNNNN F Fr_c6tjd}d}|||g}|||g}t||d\}}}}t ||z|jz|t ||z|jz|t ||jzt |t ||jzt |ttjt|dkdS)NrruFrrrrs r]rzTestQZ.test_check_finite si##E**  JJ1v   JJ1v  !QU333 B1!!b&13,222!!b&13,222!!ac'3q66222!!ac'3q66222tBxx1}%%&&&&&r_N) rrrrrrrrrrrr_r]rrs ' ' ' ' ' ' , , , , , ,''' 5F5F5FF ' ' ' ' 'r_rcfeZdZedZdZdZdZdZdZ dZ dZ d Z d Z d Zd Zd S) TestOrdQZc6tjgdgdgdgdg}tjgdgdgdgdg}tjgd gd gd gd g}tjgd gdgdgdg}tjgdgdgdgdg}tjgdgdgdgdg}tjd}tjddg}tjddg} ||||| g|_||||| g|_dS)N)y56yJ@@Iy@A_@y@?)yq= ףpݿQy By/@M@y%)y333333@yC@1y Q)@y )y@@y,@fffffE@y@@Gy3@@)y?y?333333?yy)y?333333yy@y333333 )y?y333333@?yy)rPy333333@yy@)rrrrJr)rrrrW)rg:@rrT)rarQra)rarsr)rarsrs)rarsrr)rrCrr)r'r'r&r*)r*r'rCr)rhr'r-r*)r-r(rTr()r*r*r&r )r rCrTrT)rrCr'r*rQrra)rSr4rFr5r\r) clsA1B1A2B2A3B3A4B4A5s r]rzTestOrdQZ.setup_class sX$$$&&&%%%''' ())XDDDDDDDDDDDDFGG X///.........011 X}}}$}}$}}$}}&''X'''''''''''')**X)))''''''''')** VAYY WaV__WaV__RR$RR$r_ctjd5fdt|j|jD}dddn #1swxYwYt |S)Nraiserc:g|]\}}t||S)rX)r ).0AiBirAs r] z'TestOrdQZ.qz_decomp.. s,NNNB5Rd+++NNNr_)rSrzipr\rtuple)r{rArets ` r] qz_decompzTestOrdQZ.qz_decomp s [W % % % O ONNNN#dfdf:M:MNNNC O O O O O O O O O O O O O O OSzzs'A  AAc *tj|j} t||jz| t| | jz| t||z|| zt||z|| zt tj|dtj|jt tj|dtj|jt|jdD]{} | dkr|| | dz fdkr| |jddz kr|| dz| fdkrt|| | dz| | dzf|| | dz| | dzf\} } | dj dkr | ddg} || | dz|| | dzz }|dj dkr |ddg}t| ||| dkr>|| dkr2t|| | fdt|| | fd#|| dkrt|| | fdIt|| | f|| | fz || || z }t|}d}t|jdD]H} |tj|| gtj|| g}|s|rJ|}IdS)NrrrrarQT)rSrFr@rrWrVrtrilr9rr rrrr2r4)r{r\rrArralpharrrIdrevals_tmpsortfunlastsortcursorts r]checkzTestOrdQZ.check s VQW !!achhjj."555!!achhjj."555!!b&!a%000!!b&!a%000272r??BHRX,>,>???272r??BHRX,>,>???qwqz"" M MA1uu1a!e8))28A;?""r!a%(|q'8'8r!AE'1QU7"23R!a%1q58H5IJJq8=1$$!1a&MEAa!eGnT!AE']2q6;??q!f+C)%55558q==T!W\\ AqD1--- AqD1----!W\\ AqD1----'1a4AqD(958DG;KLLLL"4((qwqz""  Agbhaz22BHd1gY4G4GHHG #""""HH   r_c||}t||j|jD]\}}}|j|||g|RdSr=)rrr\rr)r{rArretirrs r] check_allzTestOrdQZ.check_all scnnT""TVTV44 , ,LD"b DJr2t +d + + + + + , ,r_c0|ddS)NrIrr?s r]test_lhpzTestOrdQZ.test_lhp  ur_c0|ddS)NrKrr?s r]test_rhpzTestOrdQZ.test_rhp rr_c0|ddS)NrLrr?s r]test_iuczTestOrdQZ.test_iuc rr_c0|ddS)NrMrr?s r]test_ouczTestOrdQZ.test_ouc rr_c6d}||dS)Nctj|t}|dk}d||<||||z jdk||<|SNrrFrS empty_likeboolrrroutnonzeros r]rAz TestOrdQZ.test_ref..sort M-...CAvG!CMgJqz171.sort* rr_rrs r]test_cefzTestOrdQZ.test_cef( rr_c>t|jd|jdd}|j|jd|jddg|Rt|jd|jdd}|j|jd|jddg|RdS)NrarQrIrX)r r\rr)r{rs r]test_diff_input_typeszTestOrdQZ.test_diff_input_types3 sDF1Itvayu555 46!9dfQi55555DF1Itvayu555 46!9dfQi5555555r_cvtjd}tjddg}dddgfdddgfdddgfdddgfg}tjd}tjd d g}dd d gfdd d gfdd d gfdd d gfg}tjd}tjdd g}ddtjgfddtjgfdtjdgfg} tjd} tjdd g} ddtjgfddtjgfdtjdgfg} tjd dg} tjd dg}ddtjgfddtjgfg}|||| | g}|||| |g}||| | |g}t |||D]\}}}|D]\}}t |||\}}}}}}|d k}|d k}tj|}tj|||z<tj|||z<||||z ||<t||dS)NrQrrbrIrJrKrLrMy?y??yٿɿ?rrarX) rSrFr5rnanrr rr)r{rr expected1rr expected2rr expected3rr expected4rB5 expected5r\rexpectedrr expectedisortstrexpected_eigvalsrrrazerobzerors r]test_sort_explicitzTestOrdQZ.test_sort_explicit: sVAYY Wb#Y  dAY'aY'dAY'aY') VAYY Wgz* + +k>:;nk:;k>:;nk:;= VAYY WaV__c26]+c26]+bfc]+- VAYY Wb!W  dBF^,dBF^,bfd^,. WaV__ WaX  a[)a[)+ RR  RR y)Y J!$Q8!4!4 5 5 BI-6 5 5))*/BW*E*E*E'1eT1a!M%((#%6%%- $&F5&5.!!5&M$v,65&  0!4444 5 5 5r_N)rrr classmethodrrrrrrrrrrrrrr_r]rr s4%4%[4%l ,,,\,,,       666-5-5-5-5-5r_rc~eZdZejddZejjdZdS)TestOrdQZWorkspaceSizerucTtjd}d}tjtjfD]j}|||f|}|||f|}t ||dd}ktjtjfD]j}|||f|}|||f|}t ||dd}kdS)Nrc||kSr=rrrs r]rOz7TestOrdQZWorkspaceSize.test_decompose..t UT\r_rNrhc||kSr=rrs r]rOz7TestOrdQZWorkspaceSize.test_decompose..z rr_r) rSrTrr;r%rXr r&r<)r{rirXddtyper\rrs r]test_decomposez%TestOrdQZWorkspaceSize.test_decomposek s*i##E** z2:. % %F Aq6""))&11A Aq6""))&11Aa!A!A#%%%AA}bl3 ( (F Aq6""))&11A Aq6""))&11Aa!A!A&(((AA ( (r_ctjd}d}tjtjtjtjfD]o}|||f|}|||f|}t||d\}}}} } } pdS)NrrrMrX) rSrTrr;r%r&r<rXr ) r{rirXrr\rSrWrrUr4s r]test_decompose_oucz)TestOrdQZWorkspaceSize.test_decompose_ouc} si##E** z2:r}blK > >F Aq6""))&11A Aq6""))&11A&+Aqu&=&=&= #Aq%q!! > >r_N) rrrrr fail_slowrrFrrr_r]rrj s_ [1(((" [>>>>>r_rceZdZdZdS)TestDatacopiedc ddlm}tddgddgg}t| |}|}G fdd}G fdd }|}|}|d f d f|d f|d f|d f|d ffD]=\} } t| } t || | | t|  >dS) Nr) _datacopiedrarQrsceZdZdfd ZdS)-TestDatacopied.test_datacopied..Fake1NcSr=r)r{r[rr\s r] __array__z7TestDatacopied.test_datacopied..Fake1.__array__ sr_)NN)rrrr&r\sr]Fake1r$ s3        r_r(ceZdZjZdS)-TestDatacopied.test_datacopied..Fake2N)rrr__array_interface__r'sr]Fake2r* s"#"7   r_r,FTr)scipy.linalg._decompr"rHrCtolistrrrepr) r{r"rLM2r(r,F1F2itemstatusarrr\s @r]test_datacopiedzTestDatacopied.test_datacopied sV444444 QFQF# $ $ AJJ HHJJ VVXX           8 8 8 8 8 8 8 8 8 8UWW UWWZ!UaY %[2u+E{D - -LD&$--C S$//!%d - - - - - - -r_N)rrrr7rr_r]r r  s#-----r_r ctdtj}tj|jddt }d|_t|dt|jdd S) z4Check linalg works with non-aligned memory (float32)irrQroffsetcountr[rBrBT overwrite_aN) r:rSuint8 frombufferdatar;r@r rWr|rs r]test_aligned_mem_floatrC si s"(###A afQcAAAAAGtr_ppc64lezcrashes on ppc64lectdtj}tj|jddt }d|_t|dt|jdd S) z4Check linalg works with non-aligned memory (float64)i$rrrr9r<Tr=N) r:rSr?r@rArr@r rWrBs r]test_aligned_memrF si s"(###A afQc???AAGtr_ctdtj}tj|jddt }d|_t|dt|jdd S) z>Check that complex objects don't need to be completely alignediHrrirr9r<Tr=N) r9rSr?r@rArr@r rWrBs r]test_aligned_mem_complexrH si d"(###A afQcAAAAAGtr_cbt|}tt|D]}|dd}t||tjrt j||j||jj zdztj }t j |j d||j||j}||j |_ |||d<|||<||i|t||j dkr||j||<||i|dS)Nrirrr9.ra)r!rrercrSrEr9rr[itemsizer?r@rAr@rW)funcr[kwargsrr|rs r]check_lapack_misalignedrM s) ::D 3t99   # # G adBJ ' ' #!A$)AaDJ$779JJJBrwq! %&qTZ111BtzBHdBsGAaD D! v   1Q4:""tv!a"6""" # #r_z0Ticket #1152, triggers a segfault in rare cases.)runr0ctjdt}tjd}d|_tjdtj}tj|jddt}d|_tjd}t|\}}t|ftd ft|ftd ft|ftd ft|ftd ft||f|ftd ft||ftdd ft |ftd ft |ftd ft |ftd ft"|ftft"|ftd ft$|ftd ft&|ftd ft(|ftd ft*|ftd ft,|ftd ffD]\}}}t/|||dS) NrBrrr<i Nrr9Tr=) overwrite_b)r>rP)rSrFrr:r@r?r@rArrr dictr r rrr rrrrrrrM) rRrrLUpivrKr[rLs r]test_lapack_misalignedrU s+ rA #AAG %rx(((A afQc???AAG  AllGB 1$... / qdDT222 3 !t--- . dt444 5 S 1~t'='='= > QFDTtDDD E 1$... / 1$... / 1$... / qdDFF # qdDT222 3 tTd333 4 !t--- . !t--- . !t555 6 QD$4000 1!!44tV$ dF3333%44r_cneZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z d Zd ZdZdZdZdS) TestOverwritec`ttdgttddgdSNr)rGr r?s r]test_eigzTestOverwrite.test_eig s/C&***C&&!122222r_c`ttdgttddgdSrY)rGrr?s r] test_eighzTestOverwrite.test_eigh s/D6(+++D66"233333r_c2ttdgdSNr)rGrr?s r]rzTestOverwrite.test_eig_banded J11111r_c2ttdgdSrY)rGr r?s r] test_eigvalszTestOverwrite.test_eigvals GfX.....r_c2ttdgdSrY)rGrr?s r] test_eigvalshzTestOverwrite.test_eigvalsh sHvh/////r_c2ttdgdSr^)rGrr?s r]rz!TestOverwrite.test_eigvals_banded sNVH55555r_c2ttdgdSrY)rGrr?s r]test_hessenbergzTestOverwrite.test_hessenberg r_r_c2ttdgdSrY)rGrr?s r]test_lu_factorzTestOverwrite.test_lu_factor sIx00000r_ctjgdgdgdg}t|tfddgdS)Nrrr)rriric$t|Sr=)r)rxlus r]rOz-TestOverwrite.test_lu_solve.. shsA&6&6r_)rs)rSr4rrG)r{rrls @r] test_lu_solvezTestOverwrite.test_lu_solve sR HiiiIII6 7 7ll6666?????r_c2ttdgdSrY)rGr r?s r]test_luzTestOverwrite.test_lu! B)))))r_c2ttdgdSrY)rGrr?s r]test_qrzTestOverwrite.test_qr$ rpr_c2ttdgdSrY)rGrr?s r]test_rqzTestOverwrite.test_rq' rpr_c2ttdgdSrY)rGrr?s r] test_schurzTestOverwrite.test_schur* sEF8,,,,,r_cZtddgtjtjgdS)Nc"t|dS)Nr)rr|s r]rOz2TestOverwrite.test_schur_complex... seAy&9&9r_r)dtypes)rGrSr;r%r?s r]test_schur_complexz TestOverwrite.test_schur_complex- s999F8$&J #; = = = = = =r_cVttdgtddgdS)Nrc$t|dS)NrIr)r rys r]rOz(TestOverwrite.test_svd..3 sc!7&C&C&Cr_)rGr r?s r]test_svdzTestOverwrite.test_svd1 s0C&***CCfXNNNNNr_c2ttdgdSrY)rGrr?s r] test_svdvalszTestOverwrite.test_svdvals5 rbr_N)rrrrZr\rrardrrgrirmrorrrtrvr{r~rrr_r]rWrW s 333444222///000666222111@@@ *********---===OOO/////r_rWctj|dft|}tj|j}d|z}t |}t|j|dft|| |t |j }t|jdt|| ||dkr|stj d}||d|d|z}|d||dz|d|zz}||}t |d }t|j|dft |d }t|j|d fdSdSdS) NrQrrrar,rQraru-C6?MbP?rcondư>rv)rSrrrXrrrrr@rmeanrWrTrrU)rYr[skip_bigXrrYris r] _check_orthr9 s Ae$$$++E22A (5// C *C QA1a&!!!Aqvvxxc**** QS A&!!!Aqvvxxc****1uuXui##A&& HHQNNSXXa^^ + sxx1~~%A6 6 HHUOO $   QWq!f%%% $   QWq%j))))) uuur_riz"test only on 64-bit, else too slowcd} t|tjddS#t$r}t d|d}~wwxYw)NiT)rz.memory error perhaps caused by orth regression)rrSr% MemoryErrorAssertionError)rYrs r]test_orth_memory_efficiencyrT sb AArzD111111  <   s" A<Actjtjtjtjg}gd}t j||D]\}}t||dS)NrarQrsrBr)rSr;r%r<r& itertoolsproductr)rzr'rrYs r] test_orthre s`j"*blBM BF   E"6511AArr_rctjd|}tjd|}t|}|jt|jksJ|jdksJdSNrrrQ)rSrrFrr[r@)rr|rBoas r]test_orth_emptyrk si r"""A    B aB 8tBxx~ % % % % 8v      r_cReZdZdZejdeee j e e j gdZ ejdddgejdddgejdd d gd Zd S) TestNullSpacectjd}tjtjtjtjg}gd}tj||D] \}}tj d|f|}tj |j }d|z}t|} t| j||dz ft|| zd|t|j} t| jdt|j| zd||d|dzz|}t|} t| j||dz |dzz ft|| zd||d krtjd}||d |d |z}|d ||dz|d|zz}||}t|d } t| j||d z ft|d } t| j||dz fdS)NrarrQrrrr,rrurrrrrv)rSrTrr;r%r<r&rrrrrr%rr@rrWrandnrUrX) r{rirzr'rrYrrrrs r]test_null_spacezTestNullSpace.test_null_spacev sAi##A&&*bj", F"""&vu55 2 2EBAb)))A(2,,"C*C1 A 1ac( + + + AE13 / / / /13A & ) ) ) AC!GQS 1 1 1 1 !ad(A&&A1 A 1a!eadl"3 4 4 4 AE13 / / / /1uui++A..HHQNNSXXa^^3sxx1~~-A>>HHRLLq---QWq!a%j111q---QWq!a%j111; 2 2r_rctjd|}tjd|}t|}|jdksJ|jt|jksJdSr)rSrrFr%r@r[)r{rr|rBnsas r]test_null_space_emptyz#TestNullSpace.test_null_space_empty sj HV2 & & & VAR mmyF""""yJrNN0000000r_r>TFrrrrIc4tjd}d}|d|dzz|f}t ||||}t ||zdtj|jj dzdS) Nl'YeNrBrarQ)r>rrrrr,) rSrT default_rngstandard_normalr%rrrr[r)r{r>rrrirYrrs r]test_null_space_optionsz%TestNullSpace.test_null_space_options si##$;<<    QT1 . . qvvxx[|%2 4 4 4Aqrx'8'8'>::: A AOAq))28D>>::: A AOAq))28D>>:::::r_cbeZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z d Zd ZdZdS) TestCDF2RDFc.tjd||S)Nz...ij,...jk->...ik)rSeinsum)r{r|rs r]matmulzTestCDF2RDF.matmul sy-q!444r_cvt||||||dSr=)rr)r{r}rlrs r]assert_eig_validzTestCDF2RDF.assert_eig_valid s@! KK1   KK1       r_ctjd}tjdtjd}}t||\}}||||dS)Nrr)rSrr&rr{rr}rlwrrs r]test_single_array0x0realz$TestCDF2RDF.test_single_array0x0real s[ HV  x{{BHV,,1AB b"a(((((r_ctjddgddgg}tj|\}}t ||\}}||||dS)NrarQrsrrSr4r7r r&rrs r]test_single_array2x2_realz%TestCDF2RDF.test_single_array2x2_real sd Hq!fq"g& ' 'y}}Q1AB b"a(((((r_ctjddgddgg}tj|\}}t ||\}}||||dS)NrarQrrrs r]test_single_array2x2_complexz(TestCDF2RDF.test_single_array2x2_complex sd Hq!fr1g& ' 'y}}Q1AB b"a(((((r_ctjgdgdgdg}tj|\}}t ||\}}||||dS)Nrrrtrrs r]test_single_array3x3_realz%TestCDF2RDF.test_single_array3x3_real sj HiiiIII6 7 7y}}Q1AB b"a(((((r_ctjgdgdgdg}tj|\}}t ||\}}||||dSNrr)rrru)rrrrrs r]test_single_array3x3_complexz(TestCDF2RDF.test_single_array3x3_complex sj HiiiJJJ7 8 8y}}Q1AB b"a(((((r_cDtddD]}tjdtjd||}tj|\}}t||\}}||||dS)Nrariɚ;r) rrSrTrrUr7r r&rr{rrr}rlrrs r]test_random_1d_stacked_arraysz)TestCDF2RDF.test_random_1d_stacked_arrays sq! - -A INN9 % % % sAq))A9==##DAqQ]]FB  ! !"b! , , , ,  - -r_ctddD]p}tjdd||}tj|\}}t ||\}}||||qdS)NrarrB)rrSrTrUr7r r&rrs r]test_random_2d_stacked_arraysz)TestCDF2RDF.test_random_2d_stacked_arrays( sq! - -A r2q!,,A9==##DAqQ]]FB  ! !"b! , , , ,  - -r_ctjdtjd}}ttt ||dS)Nr)rQ)rSrr4rrr&r{r}rls r]test_low_dimensionality_errorz)TestCDF2RDF.test_low_dimensionality_error0 s5x||RXd^^1j'1a00000r_ctjdtjddd}}ttt ||dS)NrsrvrQrSr:rrrr&rs r]rz!TestCDF2RDF.test_not_square_error4 sEy||RYq\\11!Q771j'1a00000r_ctjgdgdgdg}tj|\}}t t t ||dSrrSr4r7r rrr&r{rr}rls r]test_swapped_v_w_errorz"TestCDF2RDF.test_swapped_v_w_error9 sU HiiiJJJ7 8 8y}}Q1j'1a00000r_ctjdtjddd}}ttt ||dS)Nrsrrrrs r]test_non_associated_errorz%TestCDF2RDF.test_non_associated_error? sEy||RYr]]221a881j'1a00000r_ctjgdgdgdg}tj|\}}t t t ||tjgdgdgdggdgdgdgg}tj|\}}t t t ||dS)Nrrr)rQruy@rrs r]test_not_conjugate_pairsz$TestCDF2RDF.test_not_conjugate_pairsD s HiiiLLL9 : :y}}Q1j'1a000 H YY <<< 0 YY <<< 0   y}}Q1j'1a00000r_N)rrrrrrrrrrrrrrrrrrr_r]rr s555   )))))) ))) ))) ))) ------111111 111 111 1 1 1 1 1r_r)F)rplatformsysnumpyrS numpy.testingrrrrrrrr r scipy.linalgr r r r rrrrrrrrrrrrrrrrrrr r!r"r#r$r%r&r'scipy.linalg.lapackr(r)r*r+r,r-r.r/r0scipy.linalg._miscr1scipy.linalg._decomp_qzr2 scipy.statsr3r4r5r6r7r8r9r:r;r<r=r>r?r@rArBrCrDrErFscipy.linalg._testutilsrGscipy.sparse._sputilsrHscipy._lib._testutilsrIscipy.linalg.blasrJscipy.__config__rK ImportErrormachineIS_WASMrr^r% REAL_DTYPESr&rRrrnrprr;rrrrHrrErrLrNrarer!r;rq blas_provider blas_versionrrrr rCrFrHrMxfailrUrWrrFr[intprJrrrrdrrrrrrr_r]rsn  5555555555555555 ******NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNAAAAAAAAAAAAAAAAAAAAAA$#####444444######;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;877777((((((333333''''''''''''' FFF << ' U+;8+;+=+=AU+U(-E    z2:& , . ~ %    4'='='='='='='='=TO&O&O&O&O&O&O&O&ff$f$f$f$f$f$f$f$P ~!~!~!~!~!~!~!~!BJ$J$J$J$J$J$J$J$XM#M#M#M#M#M#M#M#^M G$;<<r=<;;;;;;;;|EEEEEEEEE .E .E .E .E .E .E .E .PN-N-N-N-N-N-N-N-b}4}4}4}4}4}4}4}4@Y#Y#Y#Y#Y#Y#Y#Y#x $#  /08@M./7 BLp'p'p'p'p'p'p'p'fG5G5G5G5G5G5G5G5T>>>>>>>><--------6   $H$&&)3/11  11    ###$uLNN44NN4@5/5/5/5/5/5/5/5/p****6HBHRW%%.2?AA  AA  UBJNOOPO8B8B8B8B8B8B8B8BvB;B;B;J[1[1[1[1[1[1[1[1[1[1sCC'&C'