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In this form the diagonal corresponds to the last row.)rFrG)r+rGrr)rgrFr)rrlrN)r'r floatr$r)rQrrlrr4rYr,r,r-test_zero_element_in_diagonalfs  z'TestTbtrs.test_zero_element_in_diagonalzldab,n,ldb,nrhs)rHrHrrH)rHrHrFrHcCsBtj||ftd}tj||ftd}tdtd}tt|||dS)z2Test ?tbtrs fails correctly if shapes are invalid.)r+rN)r'r rr$rr)rQZldabrZldbrrrlrr,r,r-test_invalid_matrix_shapesvs z$TestTbtrs.test_invalid_matrix_shapesN) r{r|r}r6mark parametrizerrrrrrr,r,r,r-rs.. rcCsxdD]}td|d}td|}td|}t|r@|d9}|||\}}}t|dt|dt|rt|d tt|tktt|tkqt|d qWdS) Nrclartg)r+rFrGy?g333333?g@yg?) r$r'rh iscomplexobjrrtypecomplexr)r+rrUgcsZsnrr,r,r- test_lartgs         rc CsHx@dD]6}d}d}tdd|}tdd|}dt|jd }|dkrbtd |d }d}n td |d }|d 9}|d 9}d }t|||||ddddgddddgg|dt|||||ddddddgdd||gg|dt|||||dddddddg||ddgg|dt|||||ddddddddg||ddgg|dt|||||ddddddddgd|d|gg|dt|||||dddddd ddddg||d|gg|dt|||||ddddddddgd|d|gg|d|||||ddd\}} t||kt| |kt|ddddg|dt| ddddg|dqWdS)Nrcg333333?g?rGrFr_rDfdrot)r+yy?y@rHr)rrE)r)offxoffy)incxrr)rincyr)rrrrrr)rrr)Z overwrite_xZ overwrite_y)r'fullrZ precisionr%r$rr) r+rmrurrrrUrRrlr,r,r-test_rots@    rc Cstjdtjd}|j|}tjddtjd}|j|}xldD]b}tddg|d\}}|dkr|}n|}||jd d |d |d dd f\}}}t |ddd f} |d | d <|| d <t |d dd f} d| d <|| d d<|| | |d dddft |jd |d dddf<|| ||ddd dft |jd dd|ddd df<t |ddd f| ddt |d ddf| ddqXWdS)Ni)rGrGy?rclarfglarf)r+ZFDrrD)rDrrE)rrg?R)sidegh㈵>)r) r'r(rrbrjconjr$copyr*r rkr r) Za0Za0jr+rrrRalpharpr]expectedrr,r,r-test_larfg_larfs*    ,  >>rcCsrtjtjddgtjtjd}x:tdD]"}td| dk r&|j }Pq&Wd}| t |dd|j dS)Nz-czfimport numpy as np; from scipy.linalg import svd; a = np.zeros([9537, 9537], dtype=np.float32); svd(a))stdoutstderr2g?rzCode apparently failed: ) subprocessPopensys executablePIPESTDOUTrtimesleeppoll returncode terminaterrread)rTrr r,r,r- test_sgesdd_lwork_bug_workarounds    rc@sFeZdZejdeddZejdeejddddZdS) TestSytrdr+cCs*tjd|d}td|f}tt||dS)N)rr)r+sytrd)r'r r$rr)rQr+Arr,r,r-test_sytrd_with_zero_dim_arrays z(TestSytrd.test_sytrd_with_zero_dim_arrayr)rDrFcCstj||f|d}td|f\}}tjd||ddd|d|t|<||\}}t|d||d|d\}} } } }t|dt||dt|jdd t| t |t| d t| d |||d \}} } } }t|dtj ||d} t|j d} | | | | f<t|j dd}| | |d|f<| | ||df<tj |||d}xxt |dD]h}tj||d}|d||df|d|<d||<tj |||d| |t||}t||}q`Wt|d }|j|||<t|jt||}t|| dt|jdd dS) N)r+)r sytrd_lworkrDrEr)rrrHg?)rrg)rrg)r'r r$arangetriu_indices_fromrrrrrr r*r routerrjrrb)rQr+rrrrrrYdatar\er]rbrk2Qrrri_lowerZQTAQr,r,r- test_sytrds<*       $ zTestSytrd.test_sytrdN) r{r|r}r6rrrrrr,r,r,r-rs rc@sLeZdZejdeddZejdee eejddddZ d S) TestHetrd complex_dtypecCs*tjd|d}td|f}tt||dS)N)rr)r+hetrd)r'r r$rr)rQrrrr,r,r-test_hetrd_with_zero_dim_arrayUs z(TestHetrd.test_hetrd_with_zero_dim_arrayzreal_dtype,complex_dtyper)rDrFc Cstj||f|d}td|f\}}tjd||ddd|ddtjd||ddd|d|t|<t|tt|x&dD]}|||d\}} t| dqWt ||} ||d| d \} } } }} t| dt | |d t |j d d t | tt|t | d t |d ||| d\} } } }} t| dtj ||d}tj|jdtd}| |||f<tj|jddtd}| ||d|f<| |||df<tj|||d}x~t|dD]n}tj||d}| d||df|d|<d ||<tj|||d||t|t|}t||}qWt|d}t|j|||<tt|jt||}t ||dt |j d d dS)N)r+)r hetrd_lworkrDrEy?)rrD)rr)rrrHg?)rrg)rrgr_)r'r r$rrZ fill_diagonalrrrr rrrr r*rr rrrrjrrb)rQrZ real_dtyperrrr!rpr4rYrrr\rr]rbrrrrrrrZQHAQr,r,r- test_hetrd\sH0        zTestHetrd.test_hetrdN) r{r|r}r6rrr&r ziprr"r,r,r,r-rTs rc CsxttD]\}}td|d\}}t|dddd}|dkrtjddd d gd d d dgddddgd dddgddddgddddgg|d}tjddddd d!g|d}tjd"d"g|d}nvtd#d$d%d&gd'd(d)d*gd+d,d-d.gd/d0d1d2gd3d4d5d6gd7d8d9d:gg}td;gdgd?gd@gg}tjd|d}tjdAd"dBd"gd"dAd"dBgg|d}||||||dC\} } } } } |dkrtdDdEdDdEg} ntdFdGdHdIg} t| | ddJq WdS)KN)ZgglseZ gglse_lwork)r+rIrGrE)rrrTg= ףp=g{Gzg(\ؿg?gzGgHzG?gףp= ӿgQgffffff@gQ?g?gffffffֿg{Gz?gQg{Gz?g333333?g333333?g ףp= g{Gzg{Gz?gzGg?ggGz?gHzGgzGg= ףp=?gyQ?QyQQ?yQ{Gz@y= ףp=?y\(\￮Gz?y333333RQ?yQzG?yQQ?yףp= ?q= ףpݿy)\(?{Gz?y)\(?(\ſy(\333333?yGz?RQ?yRQ?HzGy\(\ ףp= ׿y)\(?ɿy(\?RQ?y?{Gz?y(\ſq= ףpݿyQ?q= ףp?yHzG?Qѿy?QyQ뱿Gz?yp= ף?p= ף?yRQ ףp= ?yffffff?GzyzGGzyQ?ffffff @yp= ף)\(@y(\@Q?g?g)rg^"L?g\}?y!f?$_Kdy^gŵ翸F @y!f?}dy61ŵe_ @)rf)rrr$r r'rhr r) rr+func func_lworkrrRrmr\rlr4resultrr,r,r- test_gglsesL          "  r'c Cs&tdxtttD]\}}d}|dkr\td|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 kqWdS)Nir_rG sytrf_lwork)r+)ZsyconsytrfZ hetrf_lwork)ZheconZhetrfy?rErD)rr)rRipivanormr)rT)rrrr&r$rr)rrbr'r rr rrvlinalgZcond) rr+rr%ZfunconZfunctrfrr+rldur*r4rcondr,r,r-test_sycon_hecons   $  r/cCstdxttD]\}}d}td|d\}}}}t|||}||jd}t|||}||jddtj||d}|||\} } } t | dk||\} } t | dk||| \} } t | dk|| \}} } t | dkt || ddqWdS) Nir_)rsygstsyevdsygvd)r+rErg-C6?)r) rrrr$rr)rbr'r rr)rr+rrr0r1r2rBeig_gvdr4rYrlrReigr,r,r- test_sygsts$      r6cCs2tdx"ttD]\}}d}td|d\}}}}t|||dt|||}||jd}t|||dt|||}||jddtj ||d}|||\} } } t | dk||\} } t | dk||| \} } t | dk|| \}} } t | dkt || dd qWdS) Nir_)rhegstheevdhegvd)r+y?rErg-C6?)r) rrr&r$rr)rrbr'r rr)rr+rrr7r8r9rr3r4r4rYrlrRr5r,r,r- test_hegsts$$$$     r:c sttdd\}}x\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 jddqWd 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. i)r_)tzrzf tzrzf_lwork)r+rEy?)rrNc sDg|]<}||gddfj|gddfqS)N)rbrjr)rrp)IdVr]r,r-rIsztest_tzrzf..r_g?g)rr)rrrr$r rrr)rrrbrr'rr r rrrjrr spacingr) rrrr+r<tzrzf_lwrrrzrYrryZr,)r>r?r]r- test_tzrzf-s&  " 0( rDc CstdxttD]\}}d}|dkrZtt||t||dt||}d}n tt||t||}d}td|d\}}}||\}} t|d |} |d || } t| t | | |d d krd nd d|d || |d} t| t | j | |d d krd nd d|d|t |t |f<|d || |dd} t| t | j | |d d krld nd dtd||} |d || |ddd} t| t | | j  j |d d krd nd dqWdS)z Test for solving a linear system with the coefficient matrix is a triangular array stored in Full Packed (RFP) format. irrDy?rerb)trttftfttrtfsm)r+rErgrrGrI)rf)rng?r)rnrrFr)rnrrN)rrrrrr r)r$rrrrbr'r) rr+rrrnrErFrGAfpr4r3solnZB2r,r,r- test_tfsmOs4*  rJc stdd\}}}xlttD]^\}}td|d\}}t|||}|dkrtt|||}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 |}|dkrZd 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| |ddqWd 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. i)r_r;r;)r<r=)r+rE)ZormrzZ ormrz_lworky?)ZunmrzZ unmrz_lwork)rNc sDg|]<}||gddfj|gddfqS)N)rbrjr)rrp)r>r?r]r,r-rsz$test_ormrz_unmrz..rbrer_g?rg)rr)rnrr)rr)rrnr)rrrr$r rrr)r'rr rrrjr@rrrr rrb)ZqmqnZcnrr+r<rAZlwork_rzrreZorun_mrzZ orun_mrz_lwZ lwork_mrzrBrYryrrntolZcqr,)r>r?r]r-test_ormrz_unmrzxsJ   "  (     rMc CstdxttD]\}}d}|dkrNt||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 |qWdS)zz Test conversion routines between the Rectengular Full Packed (RFP) format and Standard Triangular Array (TR) irrDy?rerb)rErF)r+rr)rr)transrrrENrgF)order)rrrrr)r$rr rrrbrrZreshape)rr+rA_fullrNrErFZA_tf_UrYZA_tf_LZA_tf_U_TZA_tf_L_TZA_tf_U_mZA_tf_L_mA_tr_UA_tr_LZA_tr_U_TZA_tr_L_Tr,r,r-test_tfttr_trttfsR     ,F,B    rTcCsztdxjttD]\\}}d}|dkrJt||t||d|}nt|||}td|d\}}||\}}t|dk||dd \}}t|dkt|} t||dd |d} t |j | | d d <t |} t||dd |d} t |j | | d d <t || t || |||\} }t|dk|||dd \} }t|dkt | t |t | t |qWd S) zz Test conversion routines between the Rectengular Full Packed (RFP) format and Standard Triangular Array (TR) irrDy?)trttptpttr)r+rr)rrEN)rrrrr)r$rrr rrbrrr)rr+rrQrUrVZA_tp_UrYZA_tp_LZindsZA_tp_U_mZA_tp_L_mrRrSr,r,r-test_tpttr_trttps2        rWc CstdxttD]\}}d}|dkr`t||t||d|}||j|t|}n&t|||}||j|t|}td|d\}}}||\}}|||\} }t |dk||| \} } t |} t | | qWdS) zk Test Cholesky factorization of a positive definite Rectengular Full Packed (RFP) format array irrDy?)pftrfrErF)r+rN) rrrrr)rrbr r$rrr) rr+rrrXrErFrHrYZ Achol_rfpZA_chol_rr4ZAcholr,r,r- test_pftrfs   rYcCstdxttD]\}}d}|dkrbt||t||d|}||j|t|}n&t|||}||j|t|}td|d\}}}}||\}} |||\} } ||| \} } t | dk||| \} } t |}t | t ||ddkrd nd d qWd S) z Test Cholesky factorization of a positive definite Rectengular Full Packed (RFP) format array to find its inverse irrDy?)pftrirXrErF)r+rrErGrI)rfN) rrrrr)rrbr r$rrrr)rr+rrrZrXrErFrHrY A_chol_rfpZ A_inv_rfpZA_inv_rr4ZAinvr,r,r- test_pftri0s$   r\cCsftdxVttD]H\}}d}|dkrdt||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 krVd nd d qWd S)z Test Cholesky factorization of a positive definite Rectengular Full Packed (RFP) format array and solve a linear system irrDy?rF)r+rE)pftrsrXrErFrrGrI)rfN)rrrrr)rrbr r r$rrrrr)rr+rrr3ZBf1ZBf2r]rXrErFrHrYr[rIr,r,r- test_pftrsPs,    r^c Cs:tdx*ttD]\}}d}|dkrdt||t||d|}||j|t|}n&t|||}||j|t|}|dkrdnd}tdd d |f|d \}}}||\}} t j |d|} ||dd | d|} ||| \} } t | t | | j d||dd kr*dnddqWdS)zT Test for performing a symmetric rank-k operation for matrix in RFP format. irrDy?rErhrErFz{}frk)r+rgrrGrI)rfN)rrrrr)rrbr r$rr'r(rrrj) rr+rrprefixrErFZshfrkrHr4reZAfp_outZA_outr,r,r-test_sfrk_hfrkus$   racCstdxttD]\}}d}|dkrdtdd||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|ddqWdS)zt Test for going back and forth between the returned format of he/sytrf to L and D factors/permutations. ir_rDiy?rg?)syconvr)r()r+)rF)rZ hermitian)rrrgNg)rrr)rrrrr)rrbr r'r@rr$r rrrr)rr+rrrLrcZtrfZ trf_lworklwrDZpermr-r*rYrRrrr,r,r- test_syconvs,(rfc@s eZdZdZddZddZdS) TestBlockedQRzd Tests for the blocked QR factorization, namely through geqrt, gemqrt, tpqrt and tpmqr. c CsLtdxrr rbrrrrrr)rQrr+rrrLrhrirRtrYrrrre transposerrnrmqZqC c_defaultr,r,r-test_geqrt_gemqrtsL          zTestBlockedQR.test_geqrt_gemqrtc CstdxttD]\}}d}|dkrht||t||d|}t||t||d|}n t|||}t|||}dt|dj}td|d\}}x d |d |fD]} || |||\} } } } | d kst t t | d t |d t t | | |dt || |dt || |t | | |}}t tj||d|f}tjd ||d|| |j}t t | t| f}t|j|tjd ||d|d d t||t t ||f|d d |dkr:t||t||d|}t||t||d|}d}n$t|||}t|||}d}x&dD]}xd|fD]}|| | | ||||d\}}} | d kst ||kr|j}n|}|dkrtj ||fd d}tj ||fd d}||}n,tj ||fdd}tj ||fdd}||}t|||d d ||fdkrx|| | | ||\}}} | d ksht t ||t ||qxWqfWtt|| | | ||ddtt|| | | ||ddqWqWdS)NirrDy?rg?)tpqrttpmqrt)r+rrErgg)rrrerb)rrr)rrnr)rs)rrr)r)rn)rrrrr)r'r@rr$r>rrrrr rbrr rrr) rQrr+rrr3rLrorplrRrlrjrYZB_pentZb_pentrrrrererkrrnrmr\rlZcdZCDZqCDrmZ d_defaultr,r,r-test_tpqrt_tpmqrtsj  *"$        zTestBlockedQR.test_tpqrt_tpmqrtN)r{r|r}r5rnrrr,r,r,r-rgs>rgcCstdxttD]\}}d}d}td|d}|dkrvt||||dt||||}||j}nt||||}||j}||\}}}} t|} d| ||d||df<t | dd t t j j } d t t jj } |d kr| n| } t||ddd|df| j| d| d ||dd \}}}} t|}d|||d||df<t | dd t t j j } d t t jj } |d kr| n| } t||ddd|df||jd| d qWdS) Nir_rEpstrf)r+rDy?gi)rrE)rr)r)rrrr$rr)rrbrrr'rfloat32rrrr)rr+rrrsrrmpivr_crYr single_atol double_atolrrr,r,r- test_pstrfKs4 ,  2 rycCstdxttD]\}}d}d}td|d}|dkrvt||||dt||||}||j}nt||||}||j}||\}}}} t|} d| ||d||df<t | dd t t j j } d t t jj } |d kr| n| } t||ddd|df| j| d| d ||dd \}}}} t|}d|||d||df<t | dd t t j j } d t t jj } |d kr| n| } t||ddd|df||jd| d qWdS) Nir_rEpstf2)r+rDy?gi)rrE)rr)r)rrrr$rr)rrbrrr'rrtrrrr)rr+rrrzrrmrurvrYrrwrxrrr,r,r- test_pstf2ss4 ,  2 r{c Cstddddgddddgdddd gdd d d gg}td ddgdddgdddgg}x6ttD](\}}|dkrtddddgddddgdd d!d"gd#d$d%d&gg}||}nZtjd'd(d)gd*d+d,gd-d.d/gg|d0}|td1d2d3gd4d5d6gd7d8d9ggd:7}||}td;|d0}||\}}}} } } |dkr`t|||dddf||dq`t|||dddf||dq`WdS)?Ng?g?g1w-!?gd`TRۿgsggs?g2%䃮g,eXgsFg%ug??y/nҿ&?yDioɴ?Af?y o_[ AcпysֿAfҿyPkw?JY8y5;NёCl?yYڊ?1*?y=yXѿ@a+?yhoſFxrEgЈBgtBgffffff@gٓg@gg#fDgffffffgHzG?gQg'Vgp= ףg(\gQgS7нg?gq= ףpgAg(\g333333gBg333333ÿgZ9=gQgֽ)r+gffffff@gtޅBgg(\g Zgq= ףp?gEop=gQ?gZEqҽy?geequrg-C6?)rr)r'rhrrr)r$r) desired_real desired_cplxrr+rr|rrmZrowcndZcolcndamaxrYr,r,r- test_geequsD             rc stddddddddddg }xttD]\}}tjd|d}||dkrLdnd tjfd d td d D|d}|tt|7}td|d}||\}}}} t t | t |q(WdS)Nrrgrrr_)r+rEg?y?csg|]}d|qS)g@r,)rrp)rr,r-rsztest_syequb..rHsyequb) r'rhrrr rZrot90rr$rlog2r)r) Z desired_log2srr+rr\rrscondrrYr,)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|dddddd dddddg dS)NrErHirLrD)ry?rggrrIyi)rHrHy0@)rHr)rrrg) r'rr rZzheequbrrrrvrZcheequbr) complex64)rrrrrYr,r,r- test_heequbs2 (  rcCsBtjdd}tj|}tj|tj|d}xttD]\}}|dkrtj||}||}||}||}n٬?g٬\m?gJ{/L?g Oe?gc]Fgꕲ q׿g\m?gfc]Fg؁sFڿgZB>?g0L F%?gq= ףpg?gR!u?guVſg&Sٿgǘ?gV-g ^)p?g( gFx $g6[ ٿgUN@giq?g1Zd?gOnӿgΈ ?g_vO?g}?5^Iؿg58EGr?gio?g7[ Ac CsTd}td|jd}||\}}}} } } t|||dt|||dt|||ddS)z~ This test implements the example found in the NAG manual, f08khf. An example was not found for the complex case. g-C6?r)r+)rN)r$r+r) rZ sva_expectZu_expectZv_expectrrrrrrrrYr,r,r-test_gejsv_NAGs rc! Cs`tdd}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}xrt | D]f\}}||d}|dd||gf|dd||gf<|dd|f|dd|df|7<q(Wd|dd}}|dd||gf|dd||gf<t ||||d | }| | | |||| \}}t | |t |||d |tkr*d }|j|}nd }|j|}| | | |||||d \}}t |||d tt| |dd||WdQRXtt| ||dd|WdQRXtt| |||ddWdQRXtt"| |d|dd|dWdQRXd|d<d|d<| |||\}}}}}} tj||ddkd||ddS)Nrr_rrD)r+rg)gttrfgttrsrrE)rrbre)rnz3?gttrf: _d[info-1] is {}, not the illegal value :0.)rr'rrr.rrr(rr$rr rrrrbrrrrZtestingrr)!r+rrdur\dldiag_cpyrrprlrr_dl_d_dudu2r*rYrrrrruZb_cpyx_gttrsrnZb_transZ__dlZ__dZ__duZ_du2Z_ipiv_infor,r,r-test_gttrf_gttrssb" $ $2$       &rz1du, d, dl, du_exp, d_exp, du2_exp, ipiv_exp, b, xg@ggffffff?g @g@gggffffff@g333333 @g @g@grrJigC>rgrKrErFrHg@gffffff@gg%@g@g g333333?gffffff&g3@rrry@y@?y?y?y?yffffff @y333333ӿ333333@yffffff ?y?y??y@y~:pffffff?y333333@y@@y333333 @3333332@y333333yffffff-ffffff#@y333333yfffff?@y333333"@y𿚙?yffffff(@y@y?@y@@yy@c Cstd|d|df\} } | |||\} } } }}}t||t| |t| |ddt||| | | | |||\}}t||dS)N)rrrg-C6?)r)r$r)rr\rZdu_expZd_expZdu2_expZipiv_exprlrprrrrrrr*rYrr,r,r-0test_gttrf_gttrs_NAG_f07cdf_f07cef_f07crf_f07csf s2   r)rFrJ)rJrFcCs2td|d}|\}}|||d\}}t|ddS)N geqrfp_lwork)r+)rrr)r$r)r+r*rrrrrYr,r,r-test_geqrfp_lwork_s 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 t| dtt |} t| } t || | | j|d t|f|}||}td |d}|| | |\}} t | d d | d t |||d dS)Nrrr_rGrDrgpttrf)r+rzpttrf: info = {}, should be 0)err_msg)rpttrszpttrs: info = {}, should be 0)rr'rrr.rrrr$rrrr rrkrb)ddtyper+rrr\rrrrr_erYrrerprlr_xr,r,r-test_pttrf_pttrshs*(    rcCs`d}td|d}t|f|d}t|df|}tt||dd|tt|||dddS)Nr_r)r+rErDrg)r$r.rr)rr+rrr\rr,r,r-*test_pttrf_pttrs_errors_incompatible_shapes  rc Csd}td|d}t|f|d}t|df|}d|d<d|d<|||\}}}t||ddd||dt|f|}|||\}}}t|dkddS) Nr_r)r+rErDrz3?pttrf: _d[info-1] is {}, not the illegal value :0.z2?pttrf should fail with non-spd matrix, but didn't)r$r.rrr) rr+rrr\rrrrYr,r,r-'test_pttrf_pttrs_errors_singular_nonSPDs  rz%d, e, d_expect, e_expect, b, x_expectr_rr;gK=UAg@).y0@0@y2@"y?yP@0@y0@y@W@O@yN@PyS@TyQ@Ry,@;yA@.@yc Csd}td|dd}|||\}} } t|||dt| ||dtd|dd} | || |\} } t| ||d|jtkr| || |dd\} } t| ||ddS) Ng-C6?rr)r+)rrrD)r)r$rrr+r&) r\rd_expectZe_expectrlZx_expectrrrrrYrrr,r,r-test_pttrf_pttrs_NAGs rc 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)NrDrGrErg)r.r'rr rrbr) r+realtyper compute_zZA_eigZvrr\rZtrirzr,r,r-pteqr_get_d_e_A_zs  " ""rzdtype,realtypercCstddt|j}td|d}d}t||||\}}}} |||| |d\} } } } t| dd| tt t |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. ripteqr)r+r_)r\rrrrzinfo = {}, should be 0.)rN)rr'rrr$rrrrsortrrrbrr)r+rrrrrr\rrrd_pteqre_pteqrz_pteqrrYr,r,r- test_pteqr s  "rc CsZtdtd|d}d}t||||\}}}}||d|||d\} } } } | dksVtdS)Nrr)r+r_rG)rrr)rr$rr>) r+rrrrr\rrrrrrrYr,r,r-test_pteqr_error_non_spd$ s  rc Cstdtd|d}d}t||||\}}}}tt||dd|||dtt|||dd||d|rtt||||dd|ddS)Nrr)r+r_rg)rr)rr$rrr) r+rrrrr\rrrr,r,r-"test_pteqr_raise_error_wrong_shape3 s rc Csftdtd|d}d}t||||\}}}}d|d<d|d<|||||d\} } } } | dksbtdS)Nrr)r+r_r)rr)rr$rr>) r+rrrrr\rrrrrrrYr,r,r-test_pteqr_error_singularB s rzcompute_z,d,e,d_expect,z_expectgp= ף@g@gq= ףp?g\(\ @g ףp= g?gŏ1w- @gR'?g/n?g&䃞ͪ?g cZB>?gCl?g:pΈڿg??gaTR'?gSۿg}гY?g%uοg\mg٬\m?gAf?gL F%ugǘgŏ1w-!?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. g-C6?r)r+rDrg)r\rrr)rN)r$r+r'rrrv) rr\rrZz_expectrrrrrZ_zrYr,r,r-test_pteqr_NAG_f08jgfQ s "r matrix_size)rJrI)rIrIc Cstjddt|j}dt|j}td|d}td|d}|\}}t||f|d}||\} } } t| } ||krtj||f|d} | | ddd|f<|| | |dd}n"|| ddd|f| |dd}t || ||d t t |j d|| j ||d t | t| |d ttt| ttt| kt| dkt||f|dd }t|\}}||\}}}ttt|dkott| dkdS) Nrrgeqrfp)r+Zorgqr)r]rr)r)rrrg)r'r(rrrr$r.rr rr r*rrbrallrrPrr)r+rrrrZgqrrrrZqr_Ar]rYrZqqrrlZ A_negativeZr_rq_negZq_rq_negZrq_A_negZtau_negZinfo_negr,r,r- test_geqrfpj s2    "(  rcCs(tg}td|jd}tt||dS)Nr)r+)r'rhr$r+rr)ZA_emptyrr,r,r-#test_geqrfp_errors_with_empty_array s rdriverZevZevdZevrZevxpfxsyhec Csd}|dkrtnt}t||d|dd}t||d|dd}y t||ddt||ddWn8tk r}ztd|||Wdd}~XYnXdS) Nir_lworkr)r+rD)rz({}_lwork raised unexpected exception: {})rr&r$r rr6failr)rrrr+sc_dlwdz_dlwrr,r,r-test_standard_eigh_lworks srgvZgvxc Csd}|dkrtnt}t||d|dd}t||d|dd}y t||ddt||ddWn8tk r}ztd |||Wdd}~XYnXdS) Nirrr)r+rDr)rz({}_lwork raised unexpected exception: {})rr&r$r rr6rr)rrrr+rrrr,r,r-test_generalized_eigh_lworks srdtype_rricCsxtdtd|}||}|tkr&dnd}|d}t||d}t||||}|dkrX|n|f}tdd|DsttdS) Nirorun csd_lwork)r+cSsg|] }|dkqS)rr,)rrpr,r,r-r sz*test_orcsd_uncsd_lwork..)rrrr$r rr>)rrrTrlrdlwrdlwvalr,r,r-test_orcsd_uncsd_lwork s  rc Csd\}}}|tkrdnd}|dkr,t|nt|}t|d|df|d\}}t||||}|dkrpd|inttddg|} ||d|d|f|d||df||dd|f||d|dff| \ } } } } }}}}}}|d kstt ||}t ||}t t ||t ||||}t |||}t ||||}t ||||}t |||||}t j ||f|d}|d }xt |D]}||||f<qWx&t |D]}||||||f<qWxrrr'r rcossinrrr)rrrTrlrXdrvrrZlwvalsZcs11Zcs12Zcs21Zcs22thetau1u2Zv1tZv2trYrZVHrZn11Zn12Zn21Zn22SZonerZXcr,r,r-test_orcsd_uncsd sB  f   0&*,( r trans_boolFfactrOrc Cstddt|j}td|d\}}d}t|df|d}t|f|d}t|df|d} t|dt|t| d} t|df|d} |r|tkrd qd nd } |r| j n| | } | | | | g}|d kr|||| nd gd\}}}}}}|||| | || |||||d }|\ }}}}}}}}}}t |dkd |t ||dt ||dt | |dt | |dt| ||dt t|ddk d |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. rr)gtsvxr)r+r_rDrgrErbrerrONrI)rrndlfdfdufrr*rz ?gtsvx info = {}, should be zerorF)r__len__Tz rcond should be scalar but is {}z!ferr.shape is {} but shoud be {},z!berr.shape is {} but shoud be {},)rr'rrr$r.rrrrbrrrrrrr*) r+rrrrrrrr\rrrprnrlZ inputs_cpydlf_df_duf_du2f_ipiv_info_ gtsvx_outrrrdu2fr*x_solnr.ferrberrrYr,r,r- test_gtsvx s8 "*  rc Cstdtd|d\}}d}t|df|d}t|f|d}t|df|d}t|dt|t|d} t|df|d} |tkrdnd } |r| jn| | } |d kr||||ndgd \} }}}}}||||| || | ||||d }|\ }}}}}}}}}}|d krZd|d<d|d<||||| }|\ }}}}}}}}}}|dkstdnh|d krd|d<d|d<d|d<||||| || ||||d }|\ }}}}}}}}}}|dkstddS)Nr)rr)r+r_rDrgrErbrerOrI)rrnrrrrr*rrz&info should be > 0 for singular matrix)rrrrrr*) rr$r.r'rrrrbr>)r+rrrrrrr\rrrprnrlrrrrrrrrrrrr*rr.rrrYr,r,r-test_gtsvx_error_singularL s8"*    rcCs0tdtd|d\}}d}t|df|d}t|f|d}t|df|d}t|dt|t|d} t|df|d} |tkrdnd } |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)Nr)rr)r+r_rDrgrErbrerOrIr)rrnrrrrr*) rr$r.r'rrrrbrrr)r+rrrrrrr\rrrprnrlrrrrrrr,r,r-"test_gtsvx_error_incompatible_size sH"*      rz du,d,dl,b,xc CsBtd|jd}|||||}|\ }}} } } } } }}}t|| dS)Nr)r+)r$r+r)rr\rrlrprrrrrrr*rr.rrrYr,r,r-test_gtsvx_NAG srzfact,df_de_lambdacCstd|jd||S)Nr)r+)r$r+)r\rr,r,r- srcCsdS)N)NNNr,)r\rr,r,r-r cCstddt|j}td|d}d}t|f|d}t|df|}t|t|dtt|d} t|d f|d} | | } |||\} } }||| g}|||| || | d \} } }}}}}t ||d t ||dt | |d t |d kd |t | |t| dtt |}t| }t| ||t|j|d t|drvtd |t |jdkd |j| jdt |jdkd |j| jddS)a This tests the ?ptsvx lapack routine wrapper to solve a random system Ax = b for all dtypes and input variations. Tests for: unmodified input parameters, fact options, incompatible matrix shapes raise an error, and singular matrices return info of illegal value. rrptsvx)r+rHrGrDrgrE)rrefrzinfo should be 0 but is {}.)rrz rcond should be scalar but is {})rEz#ferr.shape is {} but shoud be ({},)z#berr.shape is {} but shoud be ({},)N)rr'rrr$r.rrrrrrrr rrbrr>r*)r+rr df_de_lambdarr rr\rrrrlrr rYrrpr.rrrrer,r,r- test_ptsvx s6 (    r cCstd|jd||S)Nr)r+)r$r+)r\rr,r,r-r scCsdS)N)NNNr,)r\rr,r,r-r r c Cstdtd|d}d}t|f|d}t|df|}t|t|dtt|d}t|df|d} || } |||\} } } tt||dd|| || | d tt|||dd| || | d tt|||| dd|| | d dS) Nrr )r+rHrGrDrgrE)rrr ) rr$r.r'rrrrr)r+rrr r rr\rrrrlrr rYr,r,r-test_ptsvx_error_raise_errors s (  rcCstd|jd||S)Nr)r+)r$r+)r\rr,r,r-r* scCsdS)N)NNNr,)r\rr,r,r-r, r cCsltdtd|d}d}t|f|d}t|df|}t|t|dtt|d}t|df|d} || } |||\} } } |d krd |d <|||\} } } |||| \} } }}}}} | d kr| |kstt|f|}|||| \} } }}}}} | d kr| |kshtnP|||\} } } d | d <d | d <|||| || | d \} } }}}}} | d kshtdS) Nrr )r+rHrGrDrgrErrrF)rrr )rr$r.r'rrr>)r+rrr r rr\rrrrlrr rYrpr.rrr,r,r-test_ptsvx_non_SPD_singular& s. (   rzd,e,b,xc Cs6td|jd}||||\}}}}} } } t||dS)Nr )r+)r$r+r) r\rrlrpr rr Zx_ptsvxr.rrrYr,r,r-test_ptsvx_NAGR sr)r)rrr functoolsrZ numpy.testingrrrrrrr6r rnumpyr'r r r r rrrrZ numpy.randomrrrZ scipy.linalgrr2rrrrrrrrrrZscipy.linalg.lapackr Z scipy.statsr!r"Z scipy.sparsesparserr#r0 ImportErrorr$Zscipy.linalg.blasr%rtrrrZ complex128r&rr.rBobjectrCr~rrrrrrrrrrrZxslowrrrr'r/r6r:rDrJrMrTrWrYr\r^rarfrgryr{rrZskipifrrrrrrrhrrrrr#rrrrrrrrrrrrrrrrrrrrr rrrr,r,r,r-s   ((        ` t   **#DO1")::) %#((- e           ]           0   "    " " " " * (A &&, / (; (1(1         $4  $  $& "