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from scipy.linalg import svd; a = np.zeros([9537, 9537], dtype=np.float32); svd(a))stdoutstderr2g?rzCode apparently failed: ) subprocessPopensys executablePIPEZSTDOUTrtimesleepZpoll returncodeZ terminaterr6readdecode)rRrr@r-r-r. test_sgesdd_lwork_bug_workarounds"   rCc@sFeZdZejdeddZejdeejddddZdS) TestSytrdr,cC*tjd|d}td|f}tt||dS)Nrsrsytrdr(r r$rr)rOr,ArFr-r-r.test_sytrd_with_zero_dim_array z(TestSytrd.test_sytrd_with_zero_dim_arrayrrBrDcCstj||f|d}td|f\}}tjd||ddd|d|t|<||\}}t|d||d|d\}} } } }t|dt||dt|jdd t| t |t| d t| d |||d \}} } } }t|dtj ||d} t|j d} | | | | f<t|j dd}| | |d|f<| | ||df<tj |||d}t |dD]3}tj||d}|d||df|d|<d||<tj |||d| |t||}t||}qt|d }|j|||<t|jt||}t|| dt|jdd dS) Nr)rF sytrd_lworkrBrCrrrrFrrrrh)r(r r$arangetriu_indices_fromrrrrrr r+r routerrkrrb)rOr,rrHrFrLrrVdatar\er]rbrk2Qrrr i_lowerZQTAQr-r-r. test_sytrds@        $  zTestSytrd.test_sytrdN) r|r}r~r4rrrrIrWr-r-r-r.rDs     rDc@sLeZdZejdeddZejdee eejddddZ d S) TestHetrd complex_dtypecCrE)NrsrhetrdrG)rOrYrHrZr-r-r.test_hetrd_with_zero_dim_arrayUrJz(TestHetrd.test_hetrd_with_zero_dim_arrayzreal_dtype,complex_dtyperrKc Cstj||f|d}td|f\}}tjd||ddd|ddtjd||ddd|d|t|<t|tt|dD]}|||d\}} t| dqFt ||} ||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]6}tj||d}| d||df|d|<d ||<tj|||d||t|t|}t||}qt|d}t|j|||<tt|jt||}t ||dt |j d d dS)Nr)rZ hetrd_lworkrBrCr&)rrBrrrMrFrrrNrrhr_)r(r r$rOrPZ fill_diagonalrrrr rrrr r+rr rrQr1rkrrb)rOrZ real_dtyperYrHrZr\rqr2rVrrRr\rSr]rbrrTrUrrr rVZQHAQr-r-r. test_hetrd\sR "          zTestHetrd.test_hetrdN) r|r}r~r4rrr'r[ziprr^r-r-r-r.rXTs   rXc Cs^ttD]\}}td|d\}}t|dddd}|dkrHtjgdgdgd gd gd gd g|d}tjgd |d}tjddg|d}n/tgdgdgdgdgdgdg}tdgdgdgdgdgdgg}tjd|d}tjgdgdg|d}||||||d\} } } } } |dkrtgd} ntgd} t| | dd qdS)!N)ZgglseZ gglse_lworkrrGrErC)rrrR)g= ףp=g{Gzg(\ؿg?)zGgHzG?gףp= ӿQ)ffffff@gQ?g?gffffffֿ)r`g{Gz?Qg{Gz?)333333?g333333?rdg ףp= )g{Gz{Gz?gzG?)gragGz?gHzGgzGg= ףp=?rN)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?)rrNrN)rNrrNrgr)^"L?\}?rhri)y!f?$_Kdy^gŵ翸F @y!f?}dy61ŵe_ @rf)rrr$r r(rir r) rr,func func_lworkrrPrnr\rmr2resultr4r-r-r. test_gglsesN   rmc CstdtttD]\}}d}|dkr+td|d}td|d\}}t|||}ntd|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 kq dS)Nrr_rE sytrf_lworkr)ZsyconsytrfZ hetrf_lwork)ZheconZhetrfr&rCrB)rr)rPipivanormrrR)rrrr'r$rr*r1rbr(r rr rrwlinalgcond) rr,rrkZfunconZfunctrfrHrqrldurpr2rcondr-r-r.test_sycon_hecons"  $  *rwcCstdttD]r\}}d}td|d\}}}}t|||}||jd}t|||}||jddtj||d}|||\} } } t | dk||\} } t | dk||| \} } t | dk|| \}} } t | dkt || ddqdS) Nrr_)rsygstsyevdsygvdrrCr-C6?r) rrrr$rr*rbr(r rr)rr,rrrxryrzrHBeig_gvdr2rVrmrPeigr-r-r. test_sygsts(      rcCs*tdttD]\}}d}td|d\}}}}t|||dt|||}||jd}t|||dt|||}||jddtj ||d}|||\} } } t | dk||\} } t | dk||| \} } t | dk|| \}} } t | dkt || dd qdS) Nrr_)rhegstheevdhegvdrr&rCrr{r) rrr'r$rr*r1rbr(r rr)rr,rrrrrrHr|r}r2rVrmrPr~r-r-r. test_hegsts($$$     rc sltdd\}}ttD]\}}td|d\}}t|||}|dkr-tt|||}ntt||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 jddq d 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)r_tzrzfZ tzrzf_lworkrrCr&rrNc Dg|]}||gddfj|gddfqSNrbrkr1rZIdVr]r-r.rIDztest_tzrzf..r_rrNr)rrrr$r rrr*rrrbrr(rr r rrrkrr spacingr) rrrr,rtzrzf_lwrrHrzrVr.rzZr-rr. test_tzrzf-s, " 0( rc CstdttD]\}}d}|dkr*tt||t||dt||}d}ntt||t||}d}td|d\}}}||\}} t|d |} |d || } t| t | | |d d krfd nd d|d || |d} t| t | j | |d d krd nd d|d|t |t |f<|d || |dd} t| t | j | |d d krd nd dtd||} |d || |ddd} t| t | | j  j |d d krd nd dqdS)z Test for solving a linear system with the coefficient matrix is a triangular array stored in Full Packed (RFP) format. rrrBr&rerb)trttftfttrtfsmrrCrhrrErGrfrorr)rorrDr.)rorr0N)rrrrrr r*r$rrr1rbr(rO) rr,rrHrorrrAfpr2r|solnZB2r-r-r. test_tfsmOs@*  rc s~tdd\}}}ttD].\}}td|d\}}t|||}|dkr?tt|||}t|||} td|d\} } n(tt||t||d|}t||t||d|} td|d\} } t| ||} |||d \} }t tj ||d| d d |d fftj ||dfd d t |D}t tj |}|dkrd 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| |ddq d 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)r_rrrrrC)ZormrzZ ormrz_lworkr&)ZunmrzZ unmrz_lworkrNc rrrrrr-r.rrz$test_ormrz_unmrz..rbrer_rrrNrrr.)r0r)r0ror)rrrr$r rrr*r(rr rrrkrrrrr r1rb)ZqmZqnZcnrr,rrZlwork_rzrHreZorun_mrzZ orun_mrz_lwZ lwork_mrzrrVrzrUrotolZcqr-rr.test_ormrz_unmrzxsV   " (     rc CstdttD]t\}}d}|dkr%t||t||d|}d}n t|||}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) rrrBr&rerb)rrrrrrr)transrrrCNrhF)Zorder)rrrrr*r$rr rr1rbrrreshape)rr,rA_fullrrrZA_tf_UrVZA_tf_LZA_tf_U_TZA_tf_L_TZA_tf_U_mZA_tf_L_mA_tr_UA_tr_LZA_tr_U_TZA_tr_L_Tr-r-r.test_tfttr_trttfsX     ,F,B    rcCsrtdttD]\}}d}|dkr"t||t||d|}nt|||}td|d\}}||\}}t|dk||dd \}}t|dkt|} t||dd |d} t |j | | d d <t |} t||dd |d} t |j | | d d <t || t || |||\} }t|dk|||dd \} }t|dkt | t |t | t |qd S) rrrrBr&)trttptpttrrrrrrCN)rrrrr*r$rrr rrbrrr)rr,rrrrZA_tp_UrVZA_tp_LindsZA_tp_U_mZA_tp_L_mrrr-r-r.test_tpttr_trttps4        rc CstdttD]f\}}d}|dkr/t||t||d|}||j|t|}nt|||}||j|t|}td|d\}}}||\}}|||\} }t |dk||| \} } t |} t | | qdS) zk Test Cholesky factorization of a positive definite Rectengular Full Packed (RFP) format array rrrBr&)pftrfrrrrN) rrrrr*r1rbr r$rrr) rr,rrHrrrrrVZ Achol_rfpZA_chol_rr2ZAcholr-r-r. test_pftrfs$   rcCs tdttD]z\}}d}|dkr/t||t||d|}||j|t|}nt|||}||j|t|}td|d\}}}}||\}} |||\} } ||| \} } t | dk||| \} } t |}t | t ||ddkr~d nd d qd S) z Test Cholesky factorization of a positive definite Rectengular Full Packed (RFP) format array to find its inverse rrrBr&)pftrirrrrrrCrErGrfN) rrrrr*r1rbr r$rrrr)rr,rrHrrrrrrV A_chol_rfpZ A_inv_rfpZA_inv_rr2ZAinvr-r-r. test_pftri0s*   rcCs\tdttD]\}}d}|dkr/t||t||d|}||j|t|}nt|||}||j|t|}t|df|d}t|ddf|d}t|ddf|d}t d|d\}}} } | |\} } ||| \} } ||| |\}} t | d kt t ||| |||| |\}} t | d kt t||||dd krd nd d qd S)z Test Cholesky factorization of a positive definite Rectengular Full Packed (RFP) format array and solve a linear system rrrBr&rDrrC)pftrsrrrrrErGrfN)rrrrr*r1rbr r r$rrrrr)rr,rrHr|ZBf1ZBf2rrrrrrVrrr-r-r. test_pftrsPs2    rc Cs0tdttD]\}}d}|dkr/t||t||d|}||j|t|}nt|||}||j|t|}|dkrHdnd}tdd d |f|d \}}}||\}} t j |d|} ||dd | d|} ||| \} } t | t | | j d||dd krdnddqdS)zT Test for performing a symmetric rank-k operation for matrix in RFP format. rrrBr&rCrhrrz{}frkrrhrrErGrfN)rrrrr*r1rbr r$rr(r)rrrk) rr,rrHprefixrrZshfrkrr2reZAfp_outZA_outr-r-r.test_sfrk_hfrkus,  rcCstdttD]\}}d}|dkr/tdd||ftdd||fd|}||j}ntdd||f|}||j|t|}dt |dj }t d |d \}}}t ||dd }t |dd d \} } } t ||dd }||d|d\} } }|| | dd \}}}tt|dt| | ddfd|ddt |dd d \}} } ||dd \} } }|| | dd \}}}tt|dt|| ddfd|ddqdS)zt Test for going back and forth between the returned format of he/sytrf to L and D factors/permutations. rr_rBir&rr)syconvrornrr]F)rZ hermitianrMrhNrNrr)rrrrr*r1rbr r(rrr$r rrrr)rr,rrHrrZtrfZ trf_lworklwrDZpermrurprVrPrSrr-r-r. test_syconvs6 (*rc@s eZdZdZddZddZdS) TestBlockedQRzd Tests for the blocked QR factorization, namely through geqrt, gemqrt, tpqrt and tpmqr. c Cs.tdttD] \}}d}|dkr#t||t||d|}nt|||}dt|dj}td|d\}}|||\}} } | d ksKJt |d tj ||d} tj ||d| | | j } t |} t| j | tj ||d|d d t| | ||d d |dkrt||t||d|}d }n t|||}d}dD]T}d|fD]M}||| |||d\}} | d ksJ||kr| j }n| }|dkr||}n||}t|||d d ||fdkr||| |\}} | d ksJt||qqtt||| |ddtt||| |ddqdS)NrrrBr&rr)geqrtgemqrtrrrhrNrrerbrr.rr0rorrrrHr/r)rrrrr*r(rrr$rr rbr1rrrrr)rOrr,rrHrrrrPtrVrrUr.re transposer0rornqZqC c_defaultr-r-r.test_geqrt_gemqrtsT           zTestBlockedQR.test_geqrt_gemqrtc CstdttD]\}}d}|dkr2t||t||d|}t||t||d|}nt|||}t|||}dt|dj}td|d\}}d |d |fD]t} || |||\} } } } | d ksoJt t | d t |d t t | | |dt || |dt || |t | | |}}t tj ||d|f}tj d ||d|| |j}t t | t| f}t|j|tj d ||d|d d t||t t ||f|d d |dkrt||t||d|}t||t||d|}d}nt|||}t|||}d}dD]}d|fD]}|| | | ||||d\}}} | d ksJJ||krU|j}n|}|dkrstj ||fd d}tj ||fd d}||}ntj ||fdd}tj ||fdd}||}t|||d d ||fdkr|| | | ||\}}} | d ksJt ||t ||q3q-tt|| | | ||ddtt|| | | ||ddq[qdS)NrrrBr&rr)tpqrttpmqrtrrrCrhrNrrerbrrrrrurrHr/r)rrrrr*r(rrr$rrrrr rbr1r rrr) rOrr,rrHr|rrrlrPrmrrVZB_pentZb_pentrrUr.rerrr0rornr\rZcdZCDZqCDrZ d_defaultr-r-r.test_tpqrt_tpmqrtsx  *"$         zTestBlockedQR.test_tpqrt_tpmqrtN)r|r}r~r3rrr-r-r-r.rs >rcCtdttD]\}}d}d}td|d}|dkr8t||||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) Nrr_rCpstrfrrBr&rNrrCrr]rrrr$rr*r1rbrrr(rfloat32rrrr)rr,rr rrHrnpivr_crVr single_atol double_atolrrr-r-r. test_pstrfK6 ,  2 4rcCr) Nrr_rCpstf2rrBr&rNrrrr]r)rr,rr rrHrnrrrVrrrrrr-r-r. test_pstf2srrc CsVtgdgdgdgdg}tgdgdgdg}ttD]\}}|dkrBtgd gd gd gd g}||}n'tjgd gdgdg|d}|tgdgdgdgd7}||}td|d}||\}}}} } } |dkrt|||dddf||dddq#t|||dddf||dddq#dS)N)g?rg1w-!?gd`TRۿ)rgsrgrg)gs?rgg2%䃮g,eX)rggsFg%ug??)y/nҿ&?yDioɴ?Af?y o_[ Acп)ysֿAfҿyPkw?JY8y5;NёCl?)yYڊ?1*?y=yXѿ@a+?yhoſFxrC)gЈBgtBgffffff@gٓ)@gg#fDgffffff)gHzG?gQg'Vgp= ף)g(\rcgS7нr)gq= ףpgAg(\)g333333gBg333333ÿ)gZ9=gQgֽr)gffffff@gtޅBr)g(\g Zgq= ףp?)gEop=gQ?gZEqҽr&geequrr{r)r(rirrr*r$r) desired_real desired_cplxrr,rHrr rnZrowcndZcolcndamaxrVr-r-r. test_geequsP           rc stgd}ttD]I\}}tjd|d}||dkrdndtjfddtd d D|d}|tt|7}td |d}||\}}}} t t | t |q dS) N) rrrrrrrhrhrrr_rrCrr&csg|]}d|qS)rr-rr3r-r.rrztest_syequb..rFsyequb) r(rirrr rZrot90rr$rlog2r*r) Z desired_log2srr,rHr\rrscondrrVr-rr. 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)NrCrFirJrB)rr&rrNrgrrGyirFrFy0@)rFrr]) rrhrhrrrrrhrhrr) r(rr rZzheequbrrrrwrOZcheequbr* complex64)rHrrrrVr-r-r. test_heequbs2 (  rcCs:tjdd}tj|}tj|tj|d}ttD]z\}}|dkr>tj||}||}||}||}ntj||tj||d}||}||}||}td|d}td|d}||dd \} } } } || || | dd \} }|dkrt||| |d d q t||| |d d q dS) Nrr_r&rCgetc2rgesc2r)r)Z overwrite_rhsrErf) r(r)rrrrr*r$r)rrrrr,rHrmrrZlurpZjpivrVrqrKr-r-r.test_getc2_gesc2s4           rr)rGrFrjobarGjoburEjobvjobrrBjobpc Cstd|\}} dt|j} t||} td|d} |dk} |dk}|dko*|| k}t| }|dko9| o9| }|dkoD|oA| oD|}|dkoO| oL| oO|}|rUd}n |sY|r\d}nd }|dkrt|dkrttt| | |||||| d S| | ||||||d \}}}}}}t |||s |d |d|d | }t |t | d d | d|dkr|d d d | f}| r|rt |t || j| | d| rt | j|t| | d|rt | j|t| | dt |d tj| t |dt|t |dd d Sd S)aTest the lapack routine ?gejsv. This function tests that a singular value decomposition can be performed on the random M-by-N matrix A. The test performs the SVD using ?gejsv then performs the following checks: * ?gejsv exist successfully (info == 0) * The returned singular values are correct * `A` can be reconstructed from `u`, `SIGMA`, `v` * Ensure that u.T @ u is the identity matrix * Ensure that v.T @ v is the identity matrix * The reported matrix rank * The reported number of singular values * If denormalized floats are required Notes ----- joba specifies several choices effecting the calculation's accuracy Although all arguments are tested, the tests only check that the correct solution is returned - NOT that the prescribed actions are performed internally. jobt is, as of v3.9.0, still experimental and removed to cut down number of test cases. However keyword itself is tested externally. rrgejsvrrCrBrrr)rrrrjobtrNF)rr$)rr(rrr/r$rrrrrrrr1rbidentityrsZ matrix_rankZ count_nonzero)rr,rrrrrrrrrrHrZlsvecZrsvecZl2tranZ is_complexZinvalid_real_jobvZinvalid_cplx_jobuZinvalid_cplx_jobvZ exit_statussvar)rrrrVZsigmar-r-r.test_gejsv_general sV!    "rc CsXtd|d}|d\}}}}}}t|dt|jdt|jdt|tjdg|dtjd|d}||\}}}}}}t|dt|jdt|jdt|tjdg|dtjd|d}||\}}}}}}t|dt|jdt|jdt|tjg|dttdd d  |}t ||j }| d } ||} t || d S) z*Test edge arguments return expected statusrrrrrBrBrBr-rr_rHN)r$rr+r(rir sinrOrr*Zasfortranarrayrbr2r) r,rrr)rrrrVrHZAcr2r-r-r.test_gejsv_edge_argumentsvs.           rkwargsrJrcCs2tjdtd}tdtd}tt||fi|dS)z-Test invalid job arguments raise an Exception)rCrCrrNr)rrHrr-r-r. test_gejsv_invalid_job_argumentss rzA,sva_expect,u_expect,v_expect)g)\(@gp= ףgffffff?g ףp= )gQ?gQgGz?g(\)gQ޿gQgGz?gzGʿ)gQ?gQ?gHzG?g)\(?)ggq= ףp@g333333rb)ףp= ?g(\reg(\)g cZB#@gI.!v @g?ܵ?rf)gC?g=yX5gc=yXga4?)gB`"?g:pΈҞgʡE?gn4@?)g[B>٬?g٬\m?gJ{/L?g Oe?)gc]Fgꕲ q׿g\m?gfc]F)g؁sFڿgZB>?g0L F%?gq= ףp)g?gR!u?guVſg&Sٿ)gǘ?gV-g ^)p?g( )gFx $g6[ ٿgUN@giq?)g1Zd?gOnӿgΈ ?g_vO?)g}?5^Iؿg58EGr?gio?g7[ Ac CsTd}td|jd}||\}}}} } } t|||dt|||dt|||ddS)z~ This test implements the example found in the NAG manual, f08khf. An example was not found for the complex case. r{rrr$N)r$r,r) rHZ sva_expectZu_expectZv_expectrrrr)rrrrVr-r-r.test_gejsv_NAGs rc! Cstdd}dt|j}t|df|d}t|f|d}t|df|d}|||g}t|t|dt|d}tj|}||} t d|d\} } | |||\} } }}}}t ||dt ||dt ||d t| dt|dt|d }tj ||d}t | D]2\}}||d}|dd||gf|dd||gf<|dd|f|dd|df|7<qd|dd}}|dd||gf|dd||gf<t ||||d | }| | | |||| \}}t | |t |||d |tvrd }|j|}n d }|j|}| | | |||||d \}}t |||d tt| |dd||Wdn 1sIwYtt| ||dd|Wdn 1shwYtt| |||ddWdn 1swYtt| |d|dd|dWdn 1swYd|d<d|d<| |||\}}}}}} tj||ddkd||ddS)Nrr_rrBrrhgttrfgttrsrrCr$rbrerz3?gttrf: _d[info-1] is {}, not the illegal value :0.)rr(rrr/r2rr)rr$rr rrrrbr1rrrZtestingrr)!r,rrdur\dldiag_cpyrHrqrmrr_dl_d_dudu2rprVrrrrrZb_cpyx_gttrsroZb_transZ__dlZ__dZ__duZ_du2Z_ipiv_infor-r-r.test_gttrf_gttrssl" $ $.$       rz1du, d, dl, du_exp, d_exp, du2_exp, ipiv_exp, b, x)g@rgffffff?r)rrbgffffff@)333333 @ @rg)rbrrr )r r rHgC>)rhrrI)rCrDrErFrFg@gffffff@g%@g@g rgffffff&g3@rrFrHrDrr)@@???)?rffffff @333333ӿ333333@ffffff ?)???@r)rrrr)rrrry~:pffffff?)rrry333333@y@@y333333 @3333332@y333333yffffff-ffffff#@y333333yfffff?@y333333"@y𿚙?yffffff(@rry@y?@y@@ryrry@c Cstd|d|df\} } | |||\} } } }}}t||t| |t| |ddt||| | | | |||\}}t||dS)Nrrr{r$)r$r)rr\rZdu_expZd_expZdu2_expZipiv_exprmrqrrrrrrrprVrr-r-r.0test_gttrf_gttrs_NAG_f07cdf_f07cef_f07crf_f07csf(s2   r))rDrH)rHrDrcCr)N geqrfp_lworkrrrr)r,r+rrrrrVr-r-r.test_geqrfp_lworkgrrz ddtype,dtypecCs\tddt|j}d}t|f|d}t|df|}t|t|dtt|d}||g}td|d}|||\} } } t ||d t ||dt | d d | d t| dtt |} t| } t || | | j|d t|f|}||}td |d}|| | |\}} t | d d | d t |||d dS)Nrrr_rErBrhpttrfrrzpttrf: info = {}, should be 0)err_msgr$pttrszpttrs: info = {}, should be 0)rr(rrr/rr1r2r$rrrr rrlrb)ddtyper,rrr\rSrHrrr_erVrrrqrmr_xr-r-r.test_pttrf_pttrsps*(    r"cCs`d}td|d}t|f|d}t|df|}tt||dd|tt|||dddS)Nr_rrrCrBrh)r$r/rr)rr,rrr\rSr-r-r.*test_pttrf_pttrs_errors_incompatible_shapes  r#c Csd}td|d}t|f|d}t|df|}d|d<d|d<|||\}}}t||ddd||dt|f|}|||\}}}t|dkddS) Nr_rrrCrBrz3?pttrf: _d[info-1] is {}, not the illegal value :0.z2?pttrf should fail with non-spd matrix, but didn't)r$r/rrr) rr,rrr\rSrr rVr-r-r.'test_pttrf_pttrs_errors_singular_nonSPDs  r$z%d, e, d_expect, e_expect, b, x_expect)rEr_rrF)rr rrI)rErJrrB)r gK=Urrfr_rCAg@rhr)r&).)y0@0@y2@"?)r&rJrBrE)rrr-yP@0@y0@y@W@O@yN@PyS@TyQ@Ry,@;yA@.@yrc Csd}td|dd}|||\}} } t|||dt| ||dtd|dd} | || |\} } t| ||d|jtvrQ| || |dd\} } t| ||ddSdS) Nr{rrrr$rrBr])r$rr1r,r') r\rSd_expectZe_expectrmZx_expectrrrr rVrr!r-r-r.test_pttrf_pttrs_NAGs r/c Cs|dkrUt||f|}|tt|d|}||jd}t|d}t|f|d}t|df|}t|t|dt|d}|||j} |} n4t|f|}t|df|}|d}t|t|dt|d} t|t|dt|d} ||| | fS)NrBrErCrh)r/r(rr r1rbr) r,realtyper compute_zZA_eigZvrr\rSZtrirHzr-r-r.pteqr_get_d_e_A_zs  " "" r3zdtype,realtyper1cCstddt|j}td|d}d}t||||\}}}} |||| |d\} } } } t| dd| tt t |dt | |d |rkt| t | j t ||d t| t| t | j ||d d Sd S) a Tests the ?pteqr lapack routine for all dtypes and compute_z parameters. It generates random SPD matrix diagonals d and e, and then confirms correct eigenvalues with scipy.linalg.eig. With applicable compute_z=2 it tests that z can reform A. rrpteqrrr_r\rSr2r1rzinfo = {}, should be 0.r$N)rr(rrr$r3rrrsortrr1rbrr)r,r0r1rr4rr\rSrHr2d_pteqre_pteqrz_pteqrrVr-r-r. test_pteqr s   " r:c CsZtdtd|d}d}t||||\}}}}||d|||d\} } } } | dks+JdS)Nrr4rr_rEr2r1rrr$r3 r,r0r1r4rr\rSrHr2r7r8r9rVr-r-r.test_pteqr_error_non_spd, s  r>c Cstdtd|d}d}t||||\}}}}tt||dd|||dtt|||dd||d|rEtt||||dd|ddSdS)Nrr4rr_rhr;)rr$r3rr) r,r0r1r4rr\rSrHr2r-r-r."test_pteqr_raise_error_wrong_shape; s  r?c Csftdtd|d}d}t||||\}}}}d|d<d|d<|||||d\} } } } | dks1JdS)Nrr4rr_rr;r<r=r-r-r.test_pteqr_error_singularJ 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. r{r4rrBrhr5r$N)r$r,r(rrrw) r1r\rSr.Zz_expectrr4r2rr Z_zrVr-r-r.test_pteqr_NAG_f08jgfY s "rA matrix_size)r)rHrGrGrGc Cstjddt|j}dt|j}td|d}td|d}|\}}t||f|d}||\} } } t| } ||kr[tj||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)r]rrrrrh)r(r)rrrr$r/rr rr r+r1rbrallrrNrr)r,rBrrrEZgqrrrrHZqr_Ar]rVr ZqqrrZ A_negativeZr_rq_negZq_rq_negZrq_A_negZtau_negZinfo_negr-r-r. test_geqrfpr s6    "(  rGcCs(tg}td|jd}tt||dS)NrEr)r(rir$r,rr)ZA_emptyrEr-r-r.#test_geqrfp_errors_with_empty_array s rHdriver)ZevZevdZevrZevxpfxsyhec Csd}|dkrtnt}t||d|dd}t||d|dd}zt||ddt||ddWdStyQ}ztd|||WYd}~dSd}~ww) NrK_lworkrrrBr]({}_lwork raised unexpected exception: {}rr'r$r rr4ZfailrrJrIrr,Zsc_dlwZdz_dlwrSr-r-r.test_standard_eigh_lworks s rRgvZgvxc Csd}|dkrtnt}t||d|dd}t||d|dd}zt||ddt||ddWdStyQ}ztd |||WYd}~dSd}~ww) NrMrKrNrrrBrrrOrPrQr-r-r.test_generalized_eigh_lworks s rTdtype_r)rBr_rrcCsxtdtd|}||}|tvrdnd}|d}t||d}t||||}|dkr,|n|f}tdd|Ds:JdS) Nrrorun csd_lworkrcSsg|]}|dkqSrr-rr-r-r.r sz*test_orcsd_uncsd_lwork..)rrrr$r rF)rUrrRrrJdlwrlwvalr-r-r.test_orcsd_uncsd_lwork s  r[c Csd\}}}|tvr dnd}|dkrt|nt|}t|d|df|d\}}t||||}|dkr8d|inttddg|} ||d|d|f|d||df||dd|f||d|dffi| \ } } } } }}}}}}|d ks|Jt||}t||}t t ||t ||||}t |||}t ||||}t ||||}t |||||}t j ||f|d}|d }t |D]}||||f<qt |D] }||||||f<qt |D]}| ||||||||||f<qt |D]}|||||||||f<qt |D]N}t |||||||f<t ||||||||||f<t || ||||||||f<t ||||||||f<q|||}t||d d t |jd dS)N)rDPrVrWZcsdrXrrZlrworkrrrNg@r)rr!Zrvsr"r$r dictr_rr r(r rZcosrrrr)rUrrRrrJXZdrvrYrZZlwvalsZcs11Zcs12Zcs21Zcs22ZthetaZu1Zu2Zv1tZv2trVrZVHr Zn11Zn12Zn21Zn22SZonerZXcr-r-r.test_orcsd_uncsd sJ T      , $ *,&  ra trans_boolFfactrrc Cstddt|j}td|d\}}d}t|df|d}t|f|d}t|df|d} t|dt|t| d} t|df|d} |rR|tvrPd nd nd } |r[| j n| | } | | | | g}|d krw|||| nd gd\}}}}}}|||| | || |||||d }|\ }}}}}}}}}}t |dkd |t ||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. rrgtsvxrrr_rBrhrCrbrerrNrGrcrodlfdfdufrrprz ?gtsvx info = {}, should be zerorDr$__len__T rcond should be scalar but is {}z!ferr.shape is {} but shoud be {},z!berr.shape is {} but shoud be {},)rr(rrr$r/rrr1rbr2rrrrrr+) r,rbrcrrerrrr\rrHrqrormZ inputs_cpydlf_df_duf_du2f_ipiv_info_ gtsvx_outrgrhridu2frpx_solnrvferrberrrVr-r-r. test_gtsvx sB "rwc Cstdtd|d\}}d}t|df|d}t|f|d}t|df|d}t|dt|t|d} t|df|d} |tvrFdnd } |rO| jn| | } |d kr]||||ndgd \} }}}}}||||| || | ||||d }|\ }}}}}}}}}}|d krd|d<d|d<||||| }|\ }}}}}}}}}}|dksJddS|d krd|d<d|d<d|d<||||| || ||||d }|\ }}}}}}}}}}|dksJddSdS)Nrrdrr_rBrhrCrbrerrGrfrrz&info should be > 0 for singular matrix)rcrgrhrirrp)rr$r/r(rrr1rb)r,rbrcrerrrr\rrHrqrormrlrmrnrorprqrrrgrhrirsrprtrvrurvrVr-r-r.test_gtsvx_error_singularT sB" rxcCs0tdtd|d\}}d}t|df|d}t|f|d}t|df|d}t|dt|t|d} t|df|d} |tvrFdnd } |rO| jn| | } |d kr]||||ndgd \} }}}}}|d krtt ||dd||| || | ||||d tt |||dd|| || | ||||d tt ||||dd| || | ||||d tt ||||| dd|| | ||||d dStt ||||| || | dd||||d tt ||||| || | |dd|||d tt ||||| || | ||dd||d tt ||||| || | |||dd|d dS)Nrrdrr_rBrhrCrbrerrGrrf) rr$r/r(rrr1rbrrr)r,rbrcrerrrr\rrHrqrormrlrmrnrorprqr-r-r."test_gtsvx_error_incompatible_size sZ"  ryz du,d,dl,b,xc CsBtd|jd}|||||}|\ }}} } } } } }}}t|| dS)Nrerr$r,r)rr\rrmrqrerrrgrhrirsrprtrvrurvrVr-r-r.test_gtsvx_NAG sr{zfact,df_de_lambdacCtd|jd||SNrrr$r,r\rSr-r-r. rcCdSN)NNNr-rr-r-r.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 |t | |t| dtt |}t| }t| ||t|j|d t|drJd |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. rrptsvxrrFrErBrhrCrcrhefrzinfo should be 0 but is {}.r$rjrk)rCz#ferr.shape is {} but shoud be ({},)z#berr.shape is {} but shoud be ({},)N)rr(rrr$r/rr1r2rrrrr rrbrr+)r,r0rc df_de_lambdarrrr\rSrHrtrmrhrrVrrqrvrurvrrr-r-r. test_ptsvx s> (      rcCr|r}r~rr-r-r.r rcCrrr-rr-r-r.r rc 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) NrrrrFrErBrhrCr) rr$r/r(rr1rrr)r,r0rcrrrr\rSrHrtrmrhrrVr-r-r.test_ptsvx_error_raise_errors s (  $rcCr|r}r~rr-r-r.r2 rcCrrr-rr-r-r.r4 rcCsftdtd|d}d}t|f|d}t|df|}t|t|dtt|d}t|df|d} || } |||\} } } |d krd |d <|||\} } } |||| \} } }}}}} | d kri| |kskJt|f|}|||| \} } }}}}} | d kr| |ksJdS|||\} } } d | d <d | d <|||| || | d \} } }}}}} | d ksJdS) NrrrrFrErBrhrCrrrDr)rr$r/r(rr1)r,r0rcrrrr\rSrHrtrmrhrrVrqrvrurvr-r-r.test_ptsvx_non_SPD_singular. s0 (  rzd,e,b,xc Cs6td|jd}||||\}}}}} } } t||dS)Nrrrz) r\rSrmrqrrhrZx_ptsvxrvrurvrVr-r-r.test_ptsvx_NAGZ srrcstdt|jd}d\}tg|d}t|g|d}|j|tj|d|d}|rKfddtDfddtDf}nd 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)r_rErrcs g|] }t|D]}|q qSr-rryrqrr-r.r  z5test_pptrs_pptri_pptrf_ppsv_ppcon..cs g|] }t|D]}|q qSr-rrrr-r.r rcSsg|] }t|D]}|qqSr-rrr-r-r.r srBcSs"g|] }t|D]}|dqqSrrrr-r-r.r s")ppsvpptrfpptrspptrippconZ preferred)r,Zilp64r]rr)rqrrr)rr(rrr/r1rbr rr$rrrrrrsrrrwrt)r,rrrrPrmrZaprrrrrZulrVZaulZuliZaulirqZbxZxvrqrvr-rr.!test_pptrs_pptri_pptrf_ppsv_ppconx sL$       ,rcCs tdt|jd}d}t||g|d}t||g|d}td|d\}}|dd||ddd }t|d d |d }|d } |d } |d} |d| d} |d| d} |tvrrt|t |d |dt| t | d |dt| || j |d |dt| | | j |d |d||| | | dd }t|d d |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)Nrrr_r)ggestgexccSsdSrr-)rqr-r-r.r rz!test_gges_tgexc..F)rZ overwrite_brhrrBrrrsrCrrGrCrDr) rr(rrr/r$rr'rrr1rb)r,rrrPrmrrrlrrrr2Zd1Zd2r-r-r.test_gges_tgexc s@ rr)r;r9r> functoolsrZ numpy.testingrrrrrrr4r rZnumpyr(r r r r rrrrZ numpy.randomrrrZ scipy.linalgrr1rrrrrrrrrrZscipy.linalg.lapackr Z scipy.statsr!r"Z scipy.sparseZsparser r#r0 ImportErrorr$Zscipy.linalg.blasr%rrrrZ complex128r'rr/r?rArrrrrrrrrr!r*r5ZxslowrCrDrXrmrwrrrrrrrrrrrrrrrrrZskipifrrrrrrrirrrrr_r"r#r$r/r3r:r>r?r@rArGrHrRrTr[rarwrxryr{rrrrrrr-r-r-r.s   (4       `  t   ** "DO1")::) %#((-   e #        \                   +    /                            @   . :0 0            3     %         .