a Re!@s"ddlZddlmZddlmZmZmZmZmZm Z ddl Z ddl m Z ddl Zddl mZmZmZmZmZmZmZmZddlmZmZmZddlmZmZmZm 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.Z/zdd l0m1Z1Wne2ydZ1Yn0zdd lm3Z4Wne2y:dZ4Yn0dd l(m5Z5dd l6m7Z7ej8ej9gZ:ej;ejdZ?Z@e1dure1dddZ?e1dddZ@ddZAddZBGdddZCGdddZDGdddZEe jFGde>e jFGdgddd ZHGd!d"d"ZIGd#d$d$ZJGd%d&d&ZKGd'd(d(ZLd)d*ZMd+d,ZNd-d.ZOd/d0ZPGd1d2d2ZQGd3d4d4ZRd5d6ZSd7d8ZTd9d:ZUd;d<ZVd=d>ZWd?d@ZXdAdBZYdCdDZZdEdFZ[dGdHZ\dIdJZ]dKdLZ^dMdNZ_dOdPZ`GdQdRdRZadSdTZbdUdVZcdWdXZddYdZZee jFjfd[d\d]d^d_Zgd`daZhe jFGdbdcddge jFGde:e jFGdeeidfe jFGdgeidhe jFGdieidhe jFGdjddkge jFGdlddkgdpdmdnZje jFGde:dodpZke jFGdqdedridgdrididridjdridsdridldrifdtduZle jFGdvemgdwgdxgdygdzgd{gd|gemgd}emgd~gdgdgdgdgdgemgdgdgdgdgfgddZne jFGde>ddZoe jFGdemgdemgdemgdemgdemgdemgdemgdemddgddgddgddgddggemddgddgddgddgddkggf emgdemgdemgdemgdemgdemgdemgdemddgddgddgddgddggemddgddgddgddgddggf gddZpe jFGde>e jFGdgdddZqe jFGdere:e:e>ddĄZse jFGdere:e:e>ddƄZte jFGdere:e:e>ddȄZue jFGdemgdʢemgdˢemgd̢emgd͢emdfdgdrdhgddrgddgddggemddgddgdkdgddfgddggfemgd֢emgdעemgdآemgd٢emddgddgddgddggemddgddgddgddggfgddZvddZwe jFGdere>e:e:e jFGdeidddZxe jFGdere>e:e:e jFGdeidddZye jFGdere>e:e:e jFGdeidddZze jFGdere>e:e:e jFGdeidddZ{e jFGddemgdemgdemgdemgdgdgdgdgfgddZ|e jFGde>e jFGdgdddZ}ddZ~e jFGdgde jFGdddgddZe jFGdd d ge jFGdddgd d Ze jFGd e>e jFGdgdddZe jFGd e>ddZe jFGde>e jFGddd[ge jFGdddgddZe jFGde>e jFGdddkge jFGdddgddZe jFGde>de jFGddd[ge jFGdddgddZe jFGdemgdemgdemgdemddgddgddgddgddggemddgddgddgddgddkggfemgdemgdemgdemddgddgddgddgddggemddgddgddgddgddggfgd d!Ze jFGdere>e:e:e jFGd"dd#d$fdd%d$fgd&d'Ze jFGdere>e:e:e jFGd"dd(d$fdd)d$fgd*d+Ze jFGdere>e:e:e jFGd"dd,d$fdd-d$fgd.d/Ze jFGd0emgdʢemgdˢemdfdgdrdhgddrgddgddggemddgddgdkdgddfgddggfemgd֢emgdעemddgddgddgddggemddgddgddgddggfgd1d2Ze jFGd3dd[ge jFGde>d4d5Ze jFGde>d6d7Ze jFGd8emgd9gd:gd;gd<gemgd=gd>gd?gd<gddkfemgd@gdAgdBgdCgemgdDgdEgdFgdGgdkdhfgdHdIZe jFGde>dJdKZe jFGde>dLdMZe jFGdNemgdOgdPgdQgdRgemgdSgdTgdUgdVgemgdWgdXgdYgdZgemgd[d\d]femgd^gd_gd`gdagemgdbgdcgddgdegemgdfgdggdhgdigemgd[djdkfgdldmZe jFGde>dndoZdS(qN)reduce) assert_equalassert_array_almost_equalassert_assert_allcloseassert_almost_equalassert_array_equal)raises)eyeoneszeros zeros_liketriutril tril_indices triu_indices)randrandintseed) _flapacklapackinvsvdcholeskysolveldlnorm block_diagqreigh)_compute_lwork) ortho_group unitary_group)CONFIG)_clapack)get_lapack_funcs)get_blas_funcszBuild DependenciesZblasnameversioncCs<|tvr*tjj|tjj|d|Stjj||S)N?)COMPLEX_DTYPESnprandomrastype)shapedtyper0R/var/www/sunrise/env/lib/python3.9/site-packages/scipy/linalg/tests/test_lapack.pygenerate_random_dtype_array1s r2cCsvtjdurtdttj}hd}t}ttD](}|ds8||vr8||vr8| |q8|gksrJddS)z%Test that all entries are in the doc.Nzlapack.__doc__ is None>divisionZ HAS_ILP64Zfind_best_lapack_typeabsolute_importclapackflapackprint_function_z2Name(s) missing from lapack.__doc__ or ignore_list) r__doc__pytestskipsetsplitlistdir startswithappend)namesZ ignore_listmissingr'r0r0r1test_lapack_documented9s    rDc@s,eZdZddZddZddZddZd S) TestFlapackSimplec Csgdgdgdg}gdgdgdgdg}dD]}tt|d d}|durTq6||\}}}}} t| t| t||t||fd t|d d ft|tt|||d d d \}}}}} t| t| q6dS) N))) )rFrrga2U0*3?)rIrrgMb`?)rLrFrr)rrFrrZsdzcZgebalrrF)Zpermutescale) getattrr6rreprrrlenr+r ) selfaa1pfbalohiZpivscaleinfor0r0r1 test_gebalLs" zTestFlapackSimple.test_gebalcCs\gdgdgdg}dD]<}tt|dd}|dur8q||\}}}t| t|qdS)Nikiifii"iiidZgehrd)rPr6rrQ)rSrTrVrWZhttaur[r0r0r1 test_gehrdaszTestFlapackSimple.test_gehrdc Cs\tddgddgg}tddgddgg}tdd gd d gg}d }d D] }||||||}}}td|f\} |r|dd7<d}| |||\} } } tt|| t| || || |||||d\} } } tt|j| t| |j| |dd| |||dd\} } } tt|| t| || |ddqJdS)NrFrGrrIrJrKrMrN TfdFD)trsylr)C)ZtranaZtranbdecimal)Zisgn) r+arrayr-r%isupperrdot conjugaterg) rSrTbctransr/rUb1Zc1rixrOr[r0r0r1 test_trsylls. ""zTestFlapackSimple.test_trsylc Cstgdgdgdg}dD]}dD]}||}|rN|dd7<td|f\}|||}|d vr|d vr|d }nd }tttt|}t |||q(|d vrt t|}nH|dvrt tjt|dd}n$|dvr t tjt|dd}t ||q(q dS)Nr]r^r`rhZ Mm1OoIiFfEerrr))langeZFfEeZFfrHrLZMmZ1OorZaxisZIirF) r+rnr-ror%sqrtsumZsquareabsrmaxr) rSrTr/Znorm_strrUryvaluerlrefr0r0r1 test_langes2   zTestFlapackSimple.test_langeN)__name__ __module__ __qualname__r\rcrwrr0r0r0r1rEJs rEc@seZdZddZddZdS) TestLapackcCsttdr dSNZ empty_module)hasattrr6rSr0r0r1 test_flapacks zTestLapack.test_flapackcCsttdr dSr)rr5rr0r0r1 test_clapacks zTestLapack.test_clapackN)rrrrrr0r0r0r1rsrc@s,eZdZddZddZddZddZd S) TestLeastSquaresSolverscCsztdttD]\}}d}d}d}t|||}t||}td|d\}} t| |||} |||| d\} } } t| dk|||d || d \} } } t| dkqtD]}t j d d gd dgddgg|d}t j gd|d}td||f\} }}|j \}}t |j dkr|j d}nd}t||||} | ||| d\}}} t |ddt j ddg|ddt |jd||\}} } } t||qtD]}t j dd gddgddgg|d}t j gd|d}td||f\} }}|j \}}t |j dkr|j d}nd}t||||} | ||| d\}}} t |ddt j dd g|ddt |jd||\}} } } t||qdS)!NrdrF)gels gels_lworkr/lworkrZTTCCrtr?@@@@ @0@g1@g4@)rrgeqrfrGrm祪,-@rtol?@@?@@ @ffffff?ry1@@y4@R ?\j,?W?)r enumerateDTYPESrr-r%r r REAL_DTYPESr+rnr.rRrfinfoepsrr*)rSindr/mnnrhsrUruZglsZglslwrr8r[rrrZlqrrvZ lqr_truthr0r0r1 test_gelss           z!TestLeastSquaresSolvers.test_gelsc Cs8tD] }tjddgddgddgg|d}tjgd|d}td ||f\}}|j\}}t|jd krr|jd }nd }||||d \} } } tt| } | } |||| | d d d \}}}} t|dd tjddg|ddt |j dt|tjddg|ddt |j dqt D]}tjddgddgddgg|d}tjgd|d}td ||f\}}|j\}}t|jd kr|jd }nd }||||d \} }} } tt| } t|}| } |||| || d d d \}}}} t|dd tjddg|ddt |j dt|tjddg|ddt |j dqdS)Nrrrrrrrr)gelsd gelsd_lworkrGrFrmFrrrrYN))1)@*@.?rrrrrrrrU.*@_Y@ rr+rnr%r.rRintrealrrrr*)rSr/rUrurrrrrworkiworkr[rZ iwork_sizervsrankZrworkZ rwork_sizer0r0r1 test_gelsds               z"TestLeastSquaresSolvers.test_gelsdcCs$tD]}tjddgddgddgg|d}tjgd|d}td ||f\}}|j\}}t|jd krr|jd }nd }||||d \} } tt| } |||d | d d \} } }}} } t| dd tjddg|ddt |j dt|tjddg|ddt |j dqt D] }tjddgddgddgg|d}tjgd|d}td ||f\}}|j\}}t|jd kr|jd }nd }||||d \} } tt| } |||d | d d \} } }}} } t| dd tjddg|ddt |j dt|tjddg|ddt |j dqdS)Nrrrrrrrr)gelss gelss_lworkrGrFrmFrrrrrrrrrrrrrrrrr)rSr/rUrurrrrrrr[rvrvrrr0r0r1 test_gelss9s           z"TestLeastSquaresSolvers.test_gelssc Cs0tD] }tjddgddgddgg|d}tjgd|d}td ||f\}}|j\}}t|jd krr|jd }nd }||||d t|j\} } tt | } tj |jd d ftj d} |||| t|j| d d \} }}}} t |ddtjddg|ddt|jdqt D]}tjddgddgddgg|d}tjgd|d}td ||f\}}|j\}}t|jd kr|jd }nd }||||d t|j\} } tt | } tj |jd d ftj d} |||| t|j| d d \} }}}} t |ddtjddg|ddt|jdqdS)Nrrrrrrrr)gelsyrrGrFrdFrmrrrrrrrrrrrr)rr+rnr%r.rRrrrrr int32rr*)rSr/rUrurZ gelsy_lworkrrrrr[rZjptvrrvjrr0r0r1 test_gelsyrsr         z"TestLeastSquaresSolvers.test_gelsyN)rrrrrrrr0r0r0r1rsD<9rr/r.)rHrI)rJrGrcCs2td|d}|\}}|||d\}}t|ddS)N geqrf_lworkrrrrr%r)r/r.rrrrr[r0r0r1test_geqrf_lworks rc@seZdZddZdS)TestRegressionc CstD]}tjd|d}tdg|g\}tt||dd||\}}}}|tvrtdg|g\}tt||dd|dd||dd|ddq|tvrtd g|g\} tt| |dd|dd| |dd|ddqdS) N)i,rGrgerqfrGrorgrqrFungrq)rr+r r% assert_raises Exceptionrr*) rSr/rTrZrqrbrr[rrr0r0r1test_ticket_1645szTestRegression.test_ticket_1645N)rrrrr0r0r0r1rsrc@seZdZddZdS) TestDpotrc CsdD]}dD]}tjdtjjdd}||j}td|f\}}||||d\}}|||d} |rtt| tt |q tt | t t |q qdS)N)TF*)rHrH)size)potrfZpotri)cleanr) r+r,rnormalrprgr%rrrr) rSlowerrrvrTZdpotrfZdpotrirsr[Zdptr0r0r1 test_gh_2691s  zTestDpotr.test_gh_2691N)rrrrr0r0r0r1rsrc@seZdZddZdS) TestDlasd4c Csltgd}tgd}ttt|ddtdt|dff|ddtjff}t|ddddd}t|}t |ddd|d|t |gf}t |ddddf}t d |f}g} t d|D]4} || ||} | | dt| d dkd | qt| ddd} ttt|  d ft|| d ttjjd ttjjddS)N)r@rr)g(\@g@g333333皙rrmrFF) full_matrices compute_uv overwrite_aZ check_finiterlasd4rHzcLAPACK root finding dlasd4 failed to find the singular value %izThere are NaN rootsdatolr)r+rnhstackZvstackdiagr rRZnewaxisr concatenaterr%rangerAranyisnanrrfloat64r) rSZsigmasZm_vecMZSMZit_lenZsgmZmvcrrootsiresr0r0r1test_sing_val_updates4 *  zTestDlasd4.test_sing_val_updateN)rrrrr0r0r0r1rsrc@seZdZejdeddZejdddeDejddd gejd d dgd d ZejdgdgdgdgddZ ddZ ejdddgddZ dS) TestTbtrsr/cCs2|tvrptjgdgdg|d}tjddgddgdd gd d gg|d}tjd d gddgddgddgg|d}n|tvrtjgdgdgdg|d}tjddgddgddgddgg|d}tjddgd d!gd"d#gd$d%gg|d}ntd&|d'td(|d}|||d)d*\}}t|d+t||d+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= ף0rg(\+gףp= 0g333333*@g(\gHzG,gQ#rIrFrmrHrGr)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$B@y[a^C?b->y-@ji&*!z Datatype z not understood.tbtrsLabrruplorh㈵>rrN)rr+rnr* ValueErrorr%rr)rSr/rrrZx_outrrvr[r0r0r1test_nag_example_f07vef_f07vsfs\         z(TestTbtrs.test_nag_example_f07vef_f07vsfz dtype,transcCs.g|]&}dD]}|dkr |tvs ||fq qS))Nrgrjrj)r).0r/rtr0r0r1 -s zTestTbtrs.rUrrrcsztdd\}}tdd}|dk}||} || } t| | dd} fdd | D} fd d | D} |dkrtjd| | <tj| | d d }t|df}t| D].\}}| |||t |d t |f<qt |f}||||||d\}}t |d |dkr.t|||ddnH|dkrNt|j||ddn(|dkrnt|j||ddntddS)Ni)rIrHrGrrrrFrmcsg|]}t|qSr0)r}rrvrr0r1rAz2TestTbtrs.test_random_matrices..csg|]}t|fqSr0)r2)rwidthrr0r1rBsZdia)formatr)rrrrrtrrg-C6 ?rrgrjzInvalid trans argument)rr%rr+r spsZdiagsr rZdiagonalr~minr2rrrgHr)rSr/rtrrrZkdrZis_upperZkuklZ band_offsetsZ band_widthsZbandsrTrrowkrrrvr[r0)r/rr1test_random_matrices,s6   (    zTestTbtrs.test_random_matriceszuplo,trans,diag)rrInvalid)rrr)rrrcCs:tdtjd}tdd}tdd}tt||||||dS)z?Test if invalid values of uplo, trans and diag raise exceptionsrrrIrGN)r%r+rrrr)rSrrtrrrrrr0r0r1&test_invalid_argument_raises_exception_s  z0TestTbtrs.test_invalid_argument_raises_exceptioncCsPtjdtd}tjdtd}tdtd}d|d<|||dd\}}t|dd S) aHTest if a matrix with a zero diagonal element is singular If the i-th diagonal of A is zero, ?tbtrs should return `i` in `info` indicating the provided matrix is singular. Note that ?tbtrs requires the matrix A to be stored in banded form. In this form the diagonal corresponds to the last row.rrrIrr)rmrHrrN)r+r floatr%r)rSrrrrr8r[r0r0r1test_zero_element_in_diagonalls  z'TestTbtrs.test_zero_element_in_diagonalzldab,n,ldb,nrhs)rJrJrrJ)rJrJrHrJcCsBtj||ftd}tj||ftd}tdtd}tt|||dS)z2Test ?tbtrs fails correctly if shapes are invalid.rrNr+r rr%rr)rSZldabrZldbrrrrrr0r0r1test_invalid_matrix_shapes|s z$TestTbtrs.test_invalid_matrix_shapesN) rrrr:mark parametrizerrrrrrr0r0r0r1rs.  -- rcCsdD]}td|d}td|}td|}t|r>|d9}|||\}}}t|dt|dt|rt|d tt|tktt|tkqt|d qdS) NrhlartgrrHrIr)333333?ry皙?) r%r+rn iscomplexobjrrtypecomplexr)r/rrWgcsZsnrr0r0r1 test_lartgs        r%c CsdD]}d}d}tdd|}tdd|}dt|jd }|dvr^td |d }d}n td |d }|d 9}|d 9}d }t|||||gdgdg|dt|||||ddgddd||gg|dt|||||dddgd||ddgg|dt|||||ddddgd||ddgg|dt|||||ddddgdd|d|gg|dt|||||dddddd gd||d|gg|dt|||||ddddgdd|d|gg|d|||||ddd\}} t||ut| |ut|gd|dt| gd|dqdS)NrhrrrIrHrdrFfdrotryr)y@)rJrJrJrJ)rrrrrrGr )rJrJrHrHr)offxoffy)rHrHrJrJ)incxr*r)rJrHrJrH)r)incyr)r)r+r*r,r)rHrHrJrHr)r+r,r)Z overwrite_xZ overwrite_y)r+fullrZ precisionr&r%rr) r/rsrurrr'rWrTrrr0r0r1test_rotsV      r/c Cstjdtjd}|j|}tjddtjd}|j|}dD]b}tddg|d\}}|dvr|}n|}||jd d |d |d dd f\}}}t |ddd f} |d | d <|| d <t |d dd f} d| d <|| d d<|| | |d dddft |jd |d dddf<|| ||ddd dft |jd dd|ddd df<t |ddd f| ddt |d ddf| ddqTdS)Nr)rIrIr)rhlarfglarfrZFDrrFrFrrGrxrRsiderr() r+r,rrgrpconjr%copyr.r rqr r) Za0Za0jr/r0r1rTalpharvrbexpectedrr0r0r1test_larfg_larfs*     ,  >>r:cCs>tdtjdd}d}t|||ddd}|dks:|dks:JdS) NZ gesdd_lwork preferredr/Zilp64iA%T)rri`DiD)r%r+float32r )Z sgesdd_lworkrrr0r0r1 test_sgesdd_lwork_bug_workaroundsr>c@sFeZdZejdeddZejdeejddddZdS) TestSytrdr/cCs*tjd|d}td|f}tt||dS)Nrxrsytrdr+r r%rr)rSr/Ar@r0r0r1test_sytrd_with_zero_dim_arrays z(TestSytrd.test_sytrd_with_zero_dim_arrayrrFrHcCstj||f|d}td|f\}}tjd||ddd|d|t|<||\}}t|d||d|d\}} } } }t|dt||dt|jdd t| t |t| d t| d |||d \}} } } }t|dtj ||d} t|j d} | | | | f<t|j dd}| | |d|f<| | ||df<tj |||d}t |dD]h}tj||d}|d||df|d|<d||<tj |||d| |t||}t||}q^t|d }|j|||<t|jt||}t|| dt|jdd dS) Nr)r@ sytrd_lworkrFrGrrrrJrrrrm)r+r r%arangetriu_indices_fromrrrrrr r.r routerrprrg)rSr/rrBr@rErr[dataraerbrgrk2Qrrri_lowerZQTAQr0r0r1 test_sytrds@         $ zTestSytrd.test_sytrdN) rrrr:rrrrCrPr0r0r0r1r?s     r?c@sLeZdZejdeddZejdee eejddddZ d S) TestHetrd complex_dtypecCs*tjd|d}td|f}tt||dS)NrxrhetrdrA)rSrRrBrSr0r0r1test_hetrd_with_zero_dim_arrayTs z(TestHetrd.test_hetrd_with_zero_dim_arrayzreal_dtype,complex_dtyperrDc Cstj||f|d}td|f\}}tjd||ddd|ddtjd||ddd|d|t|<t|tt|dD]}|||d\}} t| dqt ||} ||d| d \} } } }} t| dt | |d t |j d d t | tt|t | d t |d ||| d\} } } }} t| dtj ||d}tj|jdtd}| |||f<tj|jddtd}| ||d|f<| |||df<tj|||d}t|dD]n}tj||d}| d||df|d|<d ||<tj|||d||t|t|}t||}qt|d}t|j|||<tt|jt||}t ||dt |j d d dS)Nr)rS hetrd_lworkrFrGr))rrFrrrFrJrrrGrrmrd)r+r r%rHrIZ fill_diagonalrrrr rrrr r.rr rrJr6rprrg)rSrZ real_dtyperRrBrSrUrvr8r[rrKrarLrbrgrrMrNrrrrOZQHAQr0r0r1 test_hetrd[sR "         zTestHetrd.test_hetrdN) rrrr:rrr*rTziprrWr0r0r0r1rQSs   rQc CsbttD]R\}}td|d\}}t|dddd}|dkrtjgdgdgd gd gd gd g|d}tjgd |d}tjddg|d}n^tgdgdgdgdgdgdg}tdgdgdgdgdgdgg}tjd|d}tjgdgdg|d}||||||d\} } } } } |dkr@tgd} ntgd} t| | dd qdS)!N)ZgglseZ gglse_lworkrrKrIrG)rrrV)g= ףp=g{Gzg(\ؿ?)zGgHzG?gףp= ӿQ)ffffff@gQ?g?gffffffֿ)rZg{Gz?Qg{Gz?)333333?g333333?r^g ףp= )g{Gz{Gz?gzG?)gr[gGz?gHzGgzGg= ףp=?rG)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?)rrGrG)rGrrGrar)^"L?\}?rbrc)y!f?$_Kdy^gŵ翸F @y!f?}dy61ŵe_ @rk)rrr%r r+rnr r) rr/func func_lworkrrTrsrarrr8resultr9r0r0r1 test_gglsesL    rgc Cs tdtttD]\}}d}|dkrXtd|d}td|d\}}t|||}n:td|d}td|d\}}t||t||d |}||jd d t j ||d}t |d }t ||}|||d d \} } } || | |d d \} } t td | t jj|d d| d kqdS)NrrdrI sytrf_lworkr)ZsyconsytrfZ hetrf_lwork)ZheconZhetrfr)rGrF)rr)rTipivanormrrV)rrrr*r%rr-r6rgr+r rr rr}linalgcond) rr/rreZfunconZfunctrfrBrkrldurjr8rcondr0r0r1test_sycon_hecons   $  rqcCstdttD]\}}d}td|d\}}}}t|||}||jd}t|||}||jddtj||d}|||\} } } t | dk||\} } t | dk||| \} } t | dk|| \}} } t | dkt || ddqdS) Nrrd)rsygstsyevdsygvdrrGr-C6?r) rrrr%rr-rgr+r rr)rr/rrrrrsrtrBBeig_gvdr8r[rrrTeigr0r0r1 test_sygsts&      rycCs,tdttD]\}}d}td|d\}}}}t|||dt|||}||jd}t|||dt|||}||jddtj ||d}|||\} } } t | dk||\} } t | dk||| \} } t | dk|| \}} } t | dkt || dd qdS) Nrrd)rhegstheevdhegvdrr)rGrrur) rrr*r%rr-r6rgr+r rr)rr/rrrzr{r|rBrvrwr8r[rrrTrxr0r0r1 test_hegst s&$$$     r}c sntdd\}}ttD]N\}}td|d\}}t|||}|dkr\tt|||}n"tt||t||d|}tt ||j |||d\}} t | dkt |d d d |ft j|||f|df} t t j||d|d d |d fft j||dfd d t|D} tt j| } t| | |t||dd t |d jddqd S)z This test performs an RZ decomposition in which an m x n upper trapezoidal array M (m <= n) is factorized as M = [R 0] * Z where R is upper triangular and Z is unitary. r)rdtzrzfZ tzrzf_lworkrrGr)rrNc sDg|]<}||gddfj|gddfqSNrgrpr6rZIdVrbr0r1rHr ztest_tzrzf..rdrrGr)rrrr%r rrr-rrrgrr+rr r rrrprr spacingr) rrrr/rtzrzf_lwrrBrzr[r3rZr0rr1 test_tzrzf,s*  " 0( rc CstdttD]\}}d}|dkrVtt||t||dt||}d}n tt||t||}d}td|d\}}}||\}} t|d |} |d || } t| t | | |d d krd nd d|d || |d} t| t | j | |d d kr d nd d|d|t |t |f<|d || |dd} t| t | j | |d d krhd nd dtd||} |d || |ddd} t| t | | j  j |d d krd nd dqdS)z Test for solving a linear system with the coefficient matrix is a triangular array stored in Full Packed (RFP) format. rrrFr)rjrg)trttftfttrtfsmrrGrmrrIrKrkrtrr)rtrrHr3)rtrr5N)rrrrrr r-r%rrr6rgr+rH) rr/rrBrtrrrAfpr8rvsolnZB2r0r0r1 test_tfsmNs>*   rc stdd\}}}ttD]^\}}td|d\}}t|||}|dkr~tt|||}t|||} td|d\} } nPtt||t||d|}t||t||d|} td|d\} } t| ||} |||d \} }t tj ||d| d d |d fftj ||dfd d t |D}t tj |}|dkrVd nd}dt|dj}| | | | d \}}t|dkt|| | t| |dd| | | || d\}}t|dkt||j | t| |dd| | | d| d\}}t|dkt|| |t| |dd| | | d|| d\}}t|dkt|| |jt| |ddqd S)a This test performs a matrix multiplication with an arbitrary m x n matric 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)rdr~r~rrrG)ZormrzZ ormrz_lworkr))ZunmrzZ unmrz_lworkrNc sDg|]<}||gddfj|gddfqSrrrrr0r1rr z$test_ormrz_unmrz..rgrjrdrrrGrrr3)r5r)r5rtr)rrrr%r rrr-r+rr rrrprrrrr r6rg)ZqmqnZcnrr/rrZlwork_rzrBrjZorun_mrzZ orun_mrz_lwZ lwork_mrzrr[rrNrttolZcqr0rr1test_ormrz_unmrzwsT    "  (     rc CstdttD]\}}d}|dkrJt||t||d|}d}nt|||}d}td|d\}}||\}}t|d k||d d \} }t|d k|||d d \} }t|d k|||d d \} }t|d kt|d|df|d} t|dd|ddf| ddddf<| |dddddft|d|dd|df j 7<t|d|df|d} t |ddd|df| ddddf<| d|dddft ||dd|ddf j 7<t || j dddt | | j j dddt | | j dddt | | j j ddd|||\}}t|d k||| d d \}}t|d k||| |d d \}}t|d k||| |d d \}}t|d kt |t|t |t|t |t |t |t |qdS)z Test conversion routines between the Rectengular Full Packed (RFP) format and Standard Triangular Array (TR) rrrFr)rjrg)rrrrrrr)transrrrGNrmF)order)rrrrr-r%rr rr6rgrrreshape)rr/rA_fullrrrZA_tf_Ur[ZA_tf_LZA_tf_U_TZA_tf_L_TZA_tf_U_mZA_tf_L_mA_tr_UA_tr_LZA_tr_U_TZA_tr_L_Tr0r0r1test_tfttr_trttfsV     ,F,B    rcCsttdttD]\\}}d}|dkrFt||t||d|}nt|||}td|d\}}||\}}t|dk||dd \}}t|dkt|} t||dd |d} t |j | | d d <t |} t||dd |d} t |j | | d d <t || t || |||\} }t|dk|||dd \} }t|dkt | t |t | t |qd S) rrrrFr))trttptpttrrrrrrGN)rrrrr-r%rrr rrgrrr)rr/rrrrZA_tp_Ur[ZA_tp_LindsZA_tp_U_mZA_tp_L_mrrr0r0r1test_tpttr_trttps2        rc CstdttD]\}}d}|dkr^t||t||d|}||j|t|}n&t|||}||j|t|}td|d\}}}||\}}|||\} }t |dk||| \} } t |} t | | qdS) zk Test Cholesky factorization of a positive definite Rectengular Full Packed (RFP) format array rrrFr))pftrfrrrrN) rrrrr-r6rgr r%rrr) rr/rrBrrrrr[Z Achol_rfpZA_chol_rr8ZAcholr0r0r1 test_pftrfs"   rcCs tdttD]\}}d}|dkr^t||t||d|}||j|t|}n&t|||}||j|t|}td|d\}}}}||\}} |||\} } ||| \} } t | dk||| \} } t |}t | t ||ddkrd nd d qd S) z Test Cholesky factorization of a positive definite Rectengular Full Packed (RFP) format array to find its inverse rrrFr))pftrirrrrrrGrIrKrkN) rrrrr-r6rgr r%rrrr)rr/rrBrrrrrr[ A_chol_rfpZ A_inv_rfpZA_inv_rr8ZAinvr0r0r1 test_pftri/s(   rcCs`tdttD]H\}}d}|dkr`t||t||d|}||j|t|}n&t|||}||j|t|}t|df|d}t|ddf|d}t|ddf|d}t d|d\}}} } | |\} } ||| \} } ||| |\}} t | d kt t ||| |||| |\}} t | d kt t||||dd krRd nd d qd S)z Test Cholesky factorization of a positive definite Rectengular Full Packed (RFP) format array and solve a linear system rrrFr)rHrrG)pftrsrrrrrIrKrkN)rrrrr-r6rgr r r%rrrrr)rr/rrBrvZBf1ZBf2rrrrrr[rrr0r0r1 test_pftrsOs0    rc Cs4tdttD]\}}d}|dkr`t||t||d|}||j|t|}n&t|||}||j|t|}|dkrdnd}tdd d |f|d \}}}||\}} t j |d|} ||dd | d|} ||| \} } t | t | | j d||dd kr&dnddqdS)zT Test for performing a symmetric rank-k operation for matrix in RFP format. rrrFr)rGrhrrz{}frkrrmrrIrKrkN)rrrrr-r6rgr r%r r+r,rrrp) rr/rrBprefixrrZshfrkrr8rjZAfp_outZA_outr0r0r1test_sfrk_hfrkts*    rcCstdttD]\}}d}|dkr`tdd||ftdd||fd|}||j}n,tdd||f|}||j|t|}dt |dj }t d |d \}}}t ||dd }t |dd d \} } } t ||dd }||d|d\} } }|| | dd \}}}tt|dt| | ddfd|ddt |dd d \}} } ||dd \} } }|| | dd \}}}tt|dt|| ddfd|ddqdS)zt Test for going back and forth between the returned format of he/sytrf to L and D factors/permutations. rrdrFir)rr)syconvrirhrrVF)rZ hermitianrFrmNrGrr)rrrrr-r6rgr r+rrr%r rrrr)rr/rrBrrZtrfZ trf_lworklwrDpermrorjr[rTrLrr0r0r1 test_syconvs4 (rc@s eZdZdZddZddZdS) TestBlockedQRzd Tests for the blocked QR factorization, namely through geqrt, gemqrt, tpqrt and tpmqr. c Cs>tdttD]&\}}d}|dkrFt||t||d|}nt|||}dt|dj}td|d\}}|||\}} } | d ksJt |d tj ||d} tj ||d| | | j } t |} t| j | tj ||d|d d t| | ||d d |dkr@t||t||d|}d }nt|||}d}dD]}d|fD]}||| |||d\}} | d ksJ||kr| j }n| }|dkr||}n||}t|||d d ||fdkrd||| |\}} | d ksJt||qdqXtt||| |ddtt||| |ddqdS)NrrrFr)rr)geqrtgemqrtrrrmrGrrjrgrr3rr5rtrrrrBr4r)rrrrr-r+rrr%rr rgr6rrrrr)rSrr/rrBrrrrTtr[rrNr3rj transposer5rtrsqZqC c_defaultr0r0r1test_geqrt_gemqrtsN          zTestBlockedQR.test_geqrt_gemqrtc CstdttD]\}}d}|dkrdt||t||d|}t||t||d|}n t|||}t|||}dt|dj}td|d\}}d |d |fD]} || |||\} } } } | d ksJt t | d t |d t t | | |dt || |dt || |t | | |}}t tj ||d|f}tj d ||d|| |j}t t | t| f}t|j|tj d ||d|d d t||t t ||f|d d |dkr2t||t||d|}t||t||d|}d}n$t|||}t|||}d}dD]}d|fD]}|| | | ||||d\}}} | d ksJ||kr|j}n|}|dkrtj ||fd d}tj ||fd d}||}n,tj ||fdd}tj ||fdd}||}t|||d d ||fdkrh|| | | ||\}}} | d ksXJt ||t ||qhqZtt|| | | ||ddtt|| | | ||ddqqdS)NrrrFr)rr)tpqrttpmqrtrrrGrmrGrrjrgrrrrrzrrBr4r)rrrrr-r+rrr%rrrrr rgr6r rrr) rSrr/rrBrvrrrlrTrrrr[ZB_pentZb_pentrrNr3rjrrr5rtrsrarZcdZCDZqCDrZ d_defaultr0r0r1test_tpqrt_tpmqrtsp  *"$        zTestBlockedQR.test_tpqrt_tpmqrtN)rrrr9rrr0r0r0r1rs>rcCstdttD]\}}d}d}td|d}|dkrrt||||dt||||}||j}nt||||}||j}||\}}}} t|} d| ||d||df<t | dd t t j j } d t t jj } |d vr| n| } t||ddd|df| j| d| d ||dd \}}}} t|}d|||d||df<t | dd t t j j } d t t jj } |d vr| n| } t||ddd|df||jd| d qdS) NrrdrGpstrfrrFr)rGrrGrrVrrrr%rr-r6rgrrr+rr=rrrr)rr/rr$rrBrspivr_cr[r single_atol double_atolrrr0r0r1 test_pstrfJs4 ,  2 rcCstdttD]\}}d}d}td|d}|dkrrt||||dt||||}||j}nt||||}||j}||\}}}} t|} d| ||d||df<t | dd t t j j } d t t jj } |d vr| n| } t||ddd|df| j| d| d ||dd \}}}} t|}d|||d||df<t | dd t t j j } d t t jj } |d vr| n| } t||ddd|df||jd| d qdS) NrrdrGpstf2rrFr)rGrrrrVr)rr/rr$rrBrsrrr[rrrrrr0r0r1 test_pstf2rs4 ,  2 rc CsZtgdgdgdgdg}tgdgdgdg}ttD] \}}|dkrtgd gd gd gd g}||}nNtjgd gdgdg|d}|tgdgdgdgd7}||}td|d}||\}}}} } } |dkr*t|||dddf||dddqFt|||dddf||dddqFdS)N)g?rg1w-!?gd`TRۿ)rgsrara)gs?rag2%䃮g,eX)ragsFg%ug??)y/nҿ&?yDioɴ?Af?y o_[ Acп)ysֿAfҿyPkw?JY8y5;NёCl?)yYڊ?1*?y=yXѿ@a+?yhoſFxrG)gЈBgtBgffffff@gٓ)@gg#fDgffffff)gHzG?gQg'Vgp= ף)g(\r]gS7нr)gq= ףpgAg(\)g333333gBg333333ÿ)gZ9=gQgֽr)gffffff@gtޅBr)g(\g Zgq= ףp?)gEop=gQ?gZEqҽr)geequrrur)r+rnrrr-r%r) desired_real desired_cplxrr/rBrr$rsZrowcndZcolcndamaxr[r0r0r1 test_geequsN            rc stgd}ttD]\}}tjd|d}||dkr:dndtjfddtd d D|d}|tt|7}td |d}||\}}}} t t | t |qdS) N) rrrrrrrmrmrrrdrrGrr)csg|]}d|qS)rr0rr8r0r1rr ztest_syequb..rJsyequb) r+rnrrr rZrot90rr%rlog2r-r) Z desired_log2srr/rBrarrscondrr[r0rr1 test_syequbs" rTz.Failing on some OpenBLAS version, see gh-12276)reasonc Cstdgddgdtjtdddd}t|\}}}}t|dtt|d d gdd gd gdtdtt d d d}d|d<d|d<tj | tj dd\}}}}t|dtt|gddS)NrGrJirNrF)rr)rrGrarrKirJrJy0@)rJrrV) rrmrmrrrrrmrmrr) r+rr rZzheequbrrrr}rHZcheequbr- complex64)rBrrrr[r0r0r1 test_heequbs2 (  rcCs<tjdd}tj|}tj|tj|d}ttD]\}}|dkr|tj||}||}||}||}n٬?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 $g6[ ٿgUN@giq?)g1Zd?gOnӿgΈ ?g_vO?)g}?5^Iؿg58EGr?gio?g7[ Ac CsTd}td|jd}||\}}}} } } t|||dt|||dt|||ddS)z~ This test implements the example found in the NAG manual, f08khf. An example was not found for the complex case. rurrr(N)r%r/r) rBZ sva_expectZu_expectZv_expectrrrr.rrrr[r0r0r1test_gejsv_NAGs rc! Cstdd}dt|j}t|df|d}t|f|d}t|df|d}|||g}t|t|dt|d}tj|}||} t d|d\} } | |||\} } }}}}t ||dt ||dt ||d t| dt|dt|d }tj ||d}t | D]f\}}||d}|dd||gf|dd||gf<|dd|f|dd|df|7<q&d|dd}}|dd||gf|dd||gf<t ||||d | }| | | |||| \}}t | |t |||d |tvr&d }|j|}nd }|j|}| | | |||||d \}}t |||d tt$| |dd||Wdn1s0Ytt$| ||dd|Wdn1s0Ytt$| |||ddWdn1s0Ytt,| |d|dd|dWdn1sV0Yd|d<d|d<| |||\}}}}}} tj||ddkd||ddS)NrrdrrFrrmgttrfgttrsrrGr(rgrjrz3?gttrf: _d[info-1] is {}, not the illegal value :0.)rr+rrr2r7rr,rr%rr rrrrgr6rrrZtestingrr )!r/rrduradldiag_cpyrBrvrrrr_dl_d_dudu2rjr[rrrrrZb_cpyx_gttrsrtZb_transZ__dlZ__dZ__duZ_du2Z_ipiv_infor0r0r1test_gttrf_gttrssf" $ $0$    4 4 4 < rz1du, d, dl, du_exp, d_exp, du2_exp, ipiv_exp, b, x)g@raffffff?r)rr\gffffff@)333333 @ @rg)r\rrr)rrrLgC>)rmrrM)rGrHrIrJrJg@gffffff@g%@g@g rgffffff&g3@rrJrLrHrr)@@???)?rffffff @333333ӿ333333@ffffff ?)???@r)rrrr)rrrry~:pffffff?)r r ry333333@y@@y333333 @3333332@y333333yffffff-ffffff#@y333333yfffff?@y333333"@y𿚙?yffffff(@rr y@y?@y@@r yr ry@c Cstd|d|df\} } | |||\} } } }}}t||t| |t| |ddt||| | | | |||\}}t||dS)Nrrrur()r%r)rrarZdu_expZd_expZdu2_expZipiv_exprrrvrrrrrrrjr[rr0r0r10test_gttrf_gttrs_NAG_f07cdf_f07cef_f07crf_f07csf's2   r))rHrL)rLrHrcCs2td|d}|\}}|||d\}}t|ddS)N geqrfp_lworkrrrr)r/r.rrrrr[r0r0r1test_geqrfp_lworkfs rz ddtype,dtypecCs`tddt|j}d}t|f|d}t|df|}t|t|dtt|d}||g}td|d}|||\} } } t ||d t ||dt | d d | d d t| dtt |} t| } t || | | j|d t|f|}||}td|d}|| | |\}} t | d d| d d t |||d dS)NrrrdrIrFrmpttrfrrzpttrf: info = z , should be 0)err_msgr(pttrszpttrs: info = )rr+rrr2rr6r7r%rrr rrqrg)ddtyper/rrrarLrBrrr_er[rrrvrrr_xr0r0r1test_pttrf_pttrsos*(    rcCs`d}td|d}t|f|d}t|df|}tt||dd|tt|||dddS)NrdrrrGrFrm)r%r2rr)rr/rrrarLr0r0r1*test_pttrf_pttrs_errors_incompatible_shapes  r c Csd}td|d}t|f|d}t|df|}d|d<d|d<|||\}}}t||ddd||dt|f|}|||\}}}t|dkddS) NrdrrrGrFrz3?pttrf: _d[info-1] is {}, not the illegal value :0.z2?pttrf should fail with non-spd matrix, but didn't)r%r2rr r) rr/rrrarLrrr[r0r0r1'test_pttrf_pttrs_errors_singular_nonSPDs   r!z%d, e, d_expect, e_expect, b, x_expect)rIrdrrJ)rr r~rM)rIrNrrF)r gK=Urr`rdrGAg@rmr)r#).)y0@0@y2@"?)r#rNrFrI)rr r*yP@0@y0@y@W@O@yN@PyS@TyQ@Ry,@;yA@.@yrc Csd}td|dd}|||\}} } t|||dt| ||dtd|dd} | || |\} } t| ||d|jtvr| || |dd\} } t| ||ddS) Nrurrrr(rrFrV)r%rr6r/r*) rarLd_expectZe_expectrrZx_expectrrrrr[rrr0r0r1test_pttrf_pttrs_NAGs r,c Cs|dkrt||f|}|tt|d|}||jd}t|d}t|f|d}t|df|}t|t|dt|d}|||j} |} nht|f|}t|df|}|d}t|t|dt|d} t|t|dt|d} ||| | fS)NrFrIrGrm)r2r+rr r6rgr) r/realtyper compute_zZA_eigZvrrarLZtrirBzr0r0r1pteqr_get_d_e_A_zs  " ""r0zdtype,realtyper.cCstddt|j}td|d}d}t||||\}}}} |||| |d\} } } } t| dd| d ttt |dt| |d |rt| t | j t ||d t| t | t | j ||d d 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. rrpteqrrrdrarLr/r.rzinfo = z, should be 0.r(N)rr+rrr%r0rrsortrr6rgrr)r/r-r.rr1rrarLrBr/d_pteqre_pteqrz_pteqrr[r0r0r1 test_pteqr s  "r7c CsZtdtd|d}d}t||||\}}}}||d|||d\} } } } | dksVJdS)Nrr1rrdrIr/r.rrr%r0 r/r-r.r1rrarLrBr/r4r5r6r[r0r0r1test_pteqr_error_non_spd+ s  r;c Cstdtd|d}d}t||||\}}}}tt||dd|||dtt|||dd||d|rtt||||dd|ddS)Nrr1rrdrmr8)rr%r0rr) r/r-r.r1rrarLrBr/r0r0r1"test_pteqr_raise_error_wrong_shape: s r<c Csftdtd|d}d}t||||\}}}}d|d<d|d<|||||d\} } } } | dksbJdS)Nrr1rrdrr8r9r:r0r0r1test_pteqr_error_singularI s r=zcompute_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?c Csxd}td|jd}t|t|dt|d}|||||d\}} } } t|||dtt| t||ddS) zb Implements real (f08jgf) example from NAG Manual Mark 26. Tests for correct outputs. rur1rrFrmr2r(N)r%r/r+rrr}) r.rarLr+Zz_expectrr1r/rrZ_zr[r0r0r1test_pteqr_NAG_f08jgfX s "r> matrix_size)r)rLrKrKrKc Cstjddt|j}dt|j}td|d}td|d}|\}}t||f|d}||\} } } t| } ||krtj||f|d} | | ddd|f<|| | |dd}n"|| ddd|f| |dd}t || ||d t t |j d|| j ||d t | t| |d ttt| ttt| kt| dkt||f|dd }t|\}}||\}}}ttt|dkott| dkdS) NrrgeqrfprZorgqr)rbrrrrrm)r+r,rrrr%r2rr rr r.r6rgrallrrRrr)r/r?rrrBZgqrrrrBZqr_Arbr[r$ZqqrrZ A_negativeZr_rq_negZq_rq_negZrq_A_negZtau_negZinfo_negr0r0r1 test_geqrfpq s6    "(  rDcCs(tg}td|jd}tt||dS)NrBr)r+rnr%r/rr)ZA_emptyrBr0r0r1#test_geqrfp_errors_with_empty_array s rEdriver)ZevZevdZevrZevxpfxsyhec Csd}|dkrtnt}t||d|dd}t||d|dd}z t||ddt||ddWn:ty}z"td|||WYd}~n d}~00dS) NrH_lworkrrrFrV({}_lwork raised unexpected exception: {}rr*r%r rr:Zfailr rGrFrr/Zsc_dlwZdz_dlwrLr0r0r1test_standard_eigh_lworks srOgvZgvxc Csd}|dkrtnt}t||d|dd}t||d|dd}z t||ddt||ddWn:ty}z"td |||WYd}~n d}~00dS) NrJrHrKrrrFrrrLrMrNr0r0r1test_generalized_eigh_lworks srQdtype_r)rFrdrrcCsxtdtd|}||}|tvr&dnd}|d}t||d}t||||}|dkrX|n|f}tdd|DstJdS) Nrrorun csd_lworkrcSsg|] }|dkqSrr0rr0r0r1r r z*test_orcsd_uncsd_lwork..)rrrr%r rC)rRrrVrrGdlwrlwvalr0r0r1test_orcsd_uncsd_lwork s  rXc Csd\}}}|tvrdnd}|dkr,t|nt|}t|d|df|d\}}t||||}|dkrpd|inttddg|} ||d|d|f|d||df||dd|f||d|dffi| \ } } } } }}}}}}|d ksJt||}t||}t t ||t ||||}t |||}t ||||}t ||||}t |||||}t j ||f|d}|d }t |D]}||||f<qt |D]}||||||f<qt |D]0}| ||||||||||f<qt |D]&}|||||||||f<qt |D]}t |||||||f<t ||||||||||f<t || ||||||||f<t ||||||||f<q>|||}t||d d t |jd dS)N)rAPrSrTcsdrUrrZlrworkrrrGg@r)rr!Zrvsr"r%r dictrXrrr+r rcosrrrr)rRrrVrrGXdrvrVrWZlwvalsZcs11Zcs12Zcs21Zcs22thetau1u2Zv1tZv2tr[rZVHr$Zn11Zn12Zn21Zn22SZonerZXcr0r0r1test_orcsd_uncsd sJ T      . $ *,& rd trans_boolFfactrrc Cstddt|j}td|d\}}d}t|df|d}t|f|d}t|df|d} t|dt|t| d} t|df|d} |r|tvrd qd nd } |r| j n| | } | | | | g}|d kr|||| nd gd\}}}}}}|||| | || |||||d }|\ }}}}}}}}}}t |dkd|dt ||dt ||dt | |dt | |dt | ||dt t|ddud|t |jd| jdkd|jd| jdt |jd| jdkd|jd| jdd S)aS These tests uses ?gtsvx to solve a random Ax=b system for each dtype. It tests that the outputs define an LU matrix, that inputs are unmodified, transposal options, incompatible shapes, singular matrices, and singular factorizations. It parametrizes DTYPES and the 'fact' value along with the fact related inputs. rrgtsvxrrrdrFrmrGrgrjrrNrKrfrtdlfdfdufrrjrz?gtsvx info = z, should be zerorHr(__len__Trcond should be scalar but is z!ferr.shape is {} but shoud be {},z!berr.shape is {} but shoud be {},)rr+rrr%r2rrr6rgr7rrrrr.r ) r/rerfrrhrrrrarrBrvrtrrZ inputs_cpydlf_df_duf_du2f_ipiv_info_ gtsvx_outrjrkrldu2frjx_solnrpferrberrr[r0r0r1 test_gtsvx sB "rzc Cstdtd|d\}}d}t|df|d}t|f|d}t|df|d}t|dt|t|d} t|df|d} |tvrdnd } |r| jn| | } |d kr||||ndgd \} }}}}}||||| || | ||||d }|\ }}}}}}}}}}|d krZd|d<d|d<||||| }|\ }}}}}}}}}}|dksJdnh|d krd|d<d|d<d|d<||||| || ||||d }|\ }}}}}}}}}}|dksJddS)NrrgrrdrFrmrGrgrjrrKrirrz&info should be > 0 for singular matrix)rfrjrkrlrrj)rr%r2r+rrr6rg)r/rerfrhrrrrarrBrvrtrrrorprqrrrsrtrurjrkrlrvrjrwrprxryr[r0r0r1test_gtsvx_error_singularS s>"  r{cCs0tdtd|d\}}d}t|df|d}t|f|d}t|df|d}t|dt|t|d} t|df|d} |tvrdnd } |r| jn| | } |d kr||||ndgd \} }}}}}|d krtt ||dd||| || | ||||d tt |||dd|| || | ||||d tt ||||dd| || | ||||d tt ||||| dd|| | ||||d ntt ||||| || | dd||||d tt ||||| || | |dd|||d tt ||||| || | ||dd||d tt ||||| || | |||dd|d dS)NrrgrrdrFrmrGrgrjrrKrri) rr%r2r+rrr6rgrrr)r/rerfrhrrrrarrBrvrtrrrorprqrrrsrtr0r0r1"test_gtsvx_error_incompatible_size sZ" r|z du,d,dl,b,xc CsBtd|jd}|||||}|\ }}} } } } } }}}t|| dS)Nrhrr%r/r)rrarrrrvrhrurjrkrlrvrjrwrprxryr[r0r0r1test_gtsvx_NAG sr~zfact,df_de_lambdacCstd|jd||SNrrr%r/rarLr0r0r1 srcCsdSN)NNNr0rr0r0r1r r cCstddt|j}td|d}d}t|f|d}t|df|}t|t|dtt|d} t|d f|d} | | } |||\} } }||| g}|||| || | d \} } }}}}}t ||d t ||dt | |d t |d kd |d t | |t| dtt |}t| }t | ||t|j|dt|drxJd|t |jdkd|j| jdt |jdkd|j| 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. rrptsvxrrJrIrFrmrGrfrkefrzinfo should be 0 but is .r(rmrn)rGz#ferr.shape is {} but shoud be ({},)z#berr.shape is {} but shoud be ({},)N)rr+rrr%r2rr6r7rrrr rrgrr.r )r/r-rf df_de_lambdarrrrarLrBrwrrrkrr[rrvrprxryrrr0r0r1 test_ptsvx s> (     rcCstd|jd||Srrrr0r0r1r scCsdSrr0rr0r0r1r r c Cstdtd|d}d}t|f|d}t|df|}t|t|dtt|d}t|df|d} || } |||\} } } tt||dd|| || | d tt|||dd| || | d tt|||| dd|| | d dS) NrrrrJrIrFrmrGr) rr%r2r+rr6rrr)r/r-rfrrrrarLrBrwrrrkrr[r0r0r1test_ptsvx_error_raise_errors s (  rcCstd|jd||Srrrr0r0r1r2 scCsdSrr0rr0r0r1r4 r cCsltdtd|d}d}t|f|d}t|df|}t|t|dtt|d}t|df|d} || } |||\} } } |d krd |d <|||\} } } |||| \} } }}}}} | d kr| |ksJt|f|}|||| \} } }}}}} | d kr| |kshJnP|||\} } } d | d <d | d <|||| || | d \} } }}}}} | d kshJdS) NrrrrJrIrFrmrGrrrHr)rr%r2r+rr6)r/r-rfrrrrarLrBrwrrrkrr[rvrprxryr0r0r1test_ptsvx_non_SPD_singular. s0 (   rzd,e,b,xc Cs6td|jd}||||\}}}}} } } t||dS)Nrrr}) rarLrrrvrrkrZx_ptsvxrprxryr[r0r0r1test_ptsvx_NAGZ srrcstdt|jd}d\}tg|d}t|g|d}|j|tj|d|d}|rfddtDfddtDf}n0d dtd d Dd dtd d Df}||}t d |d d\}} } } } | ||d\} }t |dt ||d|}t | |d|d| | |d\}}t |dt ||}t ||d|d| | ||d\}}t |dt||}t ||d|d||||d\}}t |dt ||d|dtj|d }| |||d\}}t |dttd |tjj|d d|d kdS)Nrr)rdrIrrcs g|]}t|D]}|qqSr0rryrvr r0r1r r z5test_pptrs_pptri_pptrf_ppsv_ppcon..cs g|]}t|D]}|qqSr0rrr r0r1r r cSsg|]}t|D]}|qqSr0rrr0r0r1r r rFcSs"g|]}t|D] }|dqqSrrrr0r0r1r r )ppsvpptrfpptrspptrippconr;r<rVrr)rkrrl)rr+rrr2r6rgr rr%rrrrrrmrrr}rn)r/rrrrTrrrZaprrrrrulr[ZaulZuliZaulirvbxZxvrkrpr0r r1!test_pptrs_pptri_pptrf_ppsv_ppconx sL$       rc Cs0tdt|jd}d}t||g|d}td|d\}}|dd|dd }t|d d |d }|d }|d } |tvrt|t |d |dt||| j |d |d|||dd}t|d d |d }|d}|tvrt|t |d |dt||| j |d |dt|d| d |ddS)Nrrrdr)geestrexccSsdSrr0rvr0r0r1r r z!test_gees_trexc..Frrmrrr@rrLrFrrx) rr+rrr2r%rr*rrr6rg) r/rrrTrrrfrr/d2r0r0r1test_gees_trexc s*rzt, expect, ifst, ilst)rg)\({Gz?gQ?)rG皙rYffffff?)rGgrg?)rGrGrGr)rlV}gV_?g|?5^?)g?rgV/?g;On?)rGrGrggj+)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?)rrrrcCsLd}td|jd}|||||dd}t|dd|d}t|||ddS) zg This test implements the example found in the NAG manual, f08qfc, f08qtc, f08qgc, f08quc. rurrr)Zwantqrmr(N)r%r/rr)rZifstZilstexpectrrrfr0r0r1test_trexc_NAG s rcCs>|tjkr.tjdkr.tdkr.tdkr.tdtdt |j d}d}t ||g|d}t ||g|d}t d |d\}}|d d ||d d d }t |dd|d}|d} |d} |d} |d| d} |d| d} |tvrt|t|d|dt| t| d|dt| || j|d|dt| | | j|d|d||| | | dd}t |dd|d}|d} |d} |d} |tvrt|t|d|dt| t| d|dt| || j|d|dt| | | j|d|dt|d| d| d|dt|d| d| d|ddS)Ndarwinopenblas 0.3.21.dev8gges[float32] broken for OpenBLAS on macOS, see gh-16949rrrdr)ggestgexccSsdSrr0rr0r0r1r r z!test_gges_tgexc..FrZ overwrite_brmrrFrrrxr@rrLrGrHr)r+r=sysplatform blas_provider blas_versionr:xfailrrrr2r%rr*rrr6rg)r/rrrTrrrrrfrrrr/d1rr0r0r1test_gges_tgexc sR   rc Csttdt|jd}d}t||g|d}td|d\}}}|dd|dd }t|d d |d }|d } |d } |tvrt|t |d |dt| || j |d |dt |} d| d<t || |} |tvr|| || | d}n|| || | | dd}t|d d |d }|d} |tvr>t|t |d |dt| || j |d |dt|d| d |ddS)Nrrrdr)rtrsen trsen_lworkcSsdSrr0rr0r0r1r8 r z!test_gees_trsen..Frrmrrr@rrFrKrrZliworkrx)rr+rrr2r%rr*rrr6rgr r ) r/rrrTrrrrfrr/rselectrr0r0r1test_gees_trsen- s8    rz*t, q, expect, select, expect_s, expect_sep)g/$?g QIg~jtx?gJ4?)rG58EGrgGr?gyX5;?)rGg?߾rgt?)rGrGrGg 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(\?)rYg{GzԿgp= ףg)\(?)rFrrrFg?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 $(?y3ı.n?rh|)yv? F%uyd`TR?I&†ۿyN@?ݓy4@ @ ^)?)ys{ @ o_yH.@|Pk @y 0*?*:Hy]m{?Gz)y) 0[.FrrmrrFrrrxr@rrKrir r)r+r=rrrrr:rrrrr2r%rr*rrr6rgr r )r/rrrTrrrrrrfrrrr/rrrrr0r0r1test_gges_tgsen s^     r)r)r functoolsrZ numpy.testingrrrrrrr:r rnumpyr+r r r r rrrrZ numpy.randomrrrZ scipy.linalgrr6rrrrrrrrrrZscipy.linalg.lapackr Z scipy.statsr!r"Z scipy.sparsesparser Zscipy.__config__r# ImportErrorr$r5r%Zscipy.linalg.blasr&r=rrrZ complex128r*rrrr2rDrErrrrrrrrrr%r/r:r>r?rQrgrqryr}rrrrrrrrrrrrrrrZskipifrrrrrrrnrrrrrXrr r!r,r0r7r;r<r=r>rDrErOrQrXrdrzr{r|r~rrrrrrrrrrrr0r0r0r1s`   (4         ` t    **DO1")::) %#((-  e  #        \                  +     /                             @   . : 00             4    %          . $     7 -      *!