K i(ddlmZddlZddlej j ZejZejZ ejZ ejZ ejZ e gdgdgdgZgdZe gdgd gd gd gZgd Ze gd gdgdgdgdgZgdZe gdgdgdgdgdgZgdZe gdgdgdgZe gdgdgdgZgdZe d d!gd"d gd#d$ggZgd%Ze gd&gd'gd(gd)gZgd*Ze gd+gd,gd-gZgd.Ze gd/gd0gd1gZgd2Z d3Z!d4Z"d5Z#d6Z$d7Z%d8Z&d9Z'd:Z(d;Z)d<Z*e+d=d>Z,d?Z-d@Z.dAZ/dBZ0dCZ1y)D)divisionN)*))rr)rrr)r)rr r)rrr )rrr )rrr )rrr r )rrr r r)rrrrr )r rrr)rrr i)rrr )rrrr2)gQx$@g= ףp=ggQ롿gGz@)gNbX9gRQ?g(\@g(\B!gHzG?)gRQgQ?g rпgp= ף"@gE)g)\#@g(\@g@1g;On?g\(8@)gQ"g33333sA@gp= ףS@gQ?g33333sP@)gfffff!@g ףp=4@gGz@ffffff@gףp= 7M@)rrr )r rr)rri)g ?gZB>@gr3܀o@)gsFZ*o@g#GGge,i9@)g}.AgR#@g(~Ƅ.)g7@gQ/gQ@rgrr r)rrr )rrr)r rr)r r r )rrr )rrrr )r rr )rrr )r r g@) g/)??@r)g@g@g@)g@g @g"@)?rrc"tj}t}t|\}}t |||}t ||}|gdk(sJ|Dcgc]}t |dc}gdk(sJtj}t}t|\}}t |||}t ||}|gdk(sJ|Dcgc]}t |dc}gdk(sJtd}|j}t|d||k7sJycc}wcc}w) N)rrrr)g-P@grhA@g(mUg^ \^v@g+6CV@)rrr r)gw]@g_DP@gIϘ}X?gRxgE9rr) overwrite) A3copyb3 LU_decompL_solveU_solveroundA4b4 randmatrix)Abpyxibaks ^/mnt/ssd/data/python-lab/Trading/venv/lib/python3.12/site-packages/mpmath/tests/test_linalg.pytest_LU_decompr/Hs  A A Q.coeffts\ q" BA HHaQ@1bAEAI&@ A BayAsA r )gRmX.@g8hi\?g5Żڌ^?g?g A8C?vIh%<=ctd|z|}td|zddd}|jd}t|dddf|zt|d|dfz}|S)Nrr rminmaxc4tdtz|zS)Ny?)exppir+s r.z9test_householder..hilbert_cmplx..sc"RT'!)nr:r)hilbertr&applydiag)rBr'vs r. hilbert_cmplxz'test_householder..hilbert_cmplxsc AaCN qsA21 - GG, - 1Q3LN4"1"Q$= (r:r)mpdpsA8b8 householderextendrAmpfr#normr?r@residualinfr)r'r(Hr)r+rr*rD residualsrefresrBresrSresiduals_cmplx refres_cmplxs r.test_householderrecs BF rqAVAq\*JAq!Q  %j#f+s6{A. 3" #C(=$>s5zJ C& ',@(A  " 3$ %c*@&A ! "# ## # R234 44 4 aR $6 66 6 AI F 1a[2 !H 1. 1a 1I 1Ia$ d8Aq!,a01 2'0 0sE#rN 05# ## # y!F6N2C 86 AA AOL 1b\G !  * 1atAqz*D!AdqsdF)Q!AaC%!A1EF G '&*>> Dv MM M) 1s Jcltd}t|\}}}t||z||zz ddksJy)NrrgV瞯<)r&lur5)r'PLUs r.test_factorizationrks;1 AeGAq! 1qsA  '' 'r:c tttttttt dksJttt tt ttt dksJtttttttt dksJttttttdtt dksJttt tt tdtt dksJttttttdtddksJtttttttddksJttttttdtddksJy)Ng|=?go@rrg333333@) r[r\A6lu_solveb6r]A7b7rVrWqr_solveA10b10r:r. test_solverws> Xb"-r2C 86 AA A Xb"-r2C 83 >> > Xb"-r2C 8J FF F Xb"-a0"5s ;f DD D Xb"-a0"5s ;c AA A Xb"-a0"5q 9S @@ @ hsC0#6 :V CC C hsC03S91 = FF Fr:c tddgddgddgg}tdtzdt g}tt|t |||dksJy) Nry@ry@rrrg|a2U?)rArCr[r\ro)r'r(s r.test_solve_overdet_complexrysWB!R1a&)*AAq1"~A HQNA. /& 88 8r:cdt_ddgddgg}ttd}ddg}d|d |d d|d |d d |d |d d |d |d fD]%t j t tffd 'y) Nr<rg333333?g?g?rrz lu_solve(z, )z qr_solve(ctSN)eval)r,sr.rNztest_singular..s tAwr:)rTrUreprzerospytestraisesZeroDivisionError ValueError)r'Br(r,s @r. test_singularrsx BF seR[!A U1XA AA$%q)A+F$%q)A+FHH (*5GHr:cftjtjttjgdgdgdgk(sJtj tt }tj tjt|t tjdk(sJy)N)rrr)rrr)r grmr) fpcholeskyrAA9cholesky_solveb9r[r\r]rMs r. test_choleskyrsm ;;ryy} %Iy/3Z)[ [[ [ "b!A 772;;r1b)266 2a 77 7r:cpttdk(sJtttddk(sJtttdk(sJttt dk(sJtt dk(sJtttdk(sJttddk(sJy) Nrri*iCirr) detr1r#r2rr$r3rnrrvr:r.test_detrs r7a<< R"  "" " R>T !! ! R>W $$ $ r7a<< R>X %% % uQx=A  r:cdt_tddgddgg}t|dt dk(sJt|dt dk(sJt|d t d k(sJy) Nr<g6?gꕲ q?ga2U0*?gBiq?ct|dS)Nrr5rMs r.rNztest_cond..s U1QZr:z327065209.73817754c"t|tSr})r5r]rMs r.rNztest_cond..s U1S\r:ct|dS)NFrrMs r.rNztest_cond..s U1S\r:z249729266.80008656)rTrUrAcondrZr's r. test_condrsv BF 66"234A ' (C0D,E EE E ) *c2F.G GG G ) *c2F.G GG Gr:rchtdd}ttt||z ddksJy)Nrrgj7֖6)r&r5r4rs r.test_precisionrs12rA $q(! ,v 55 5r:ctdt_dt_tjgdgdgdg}tjgd}tj ||}|dj dksJ|dj dksJ|d j dksJd |dvsJd |dvsJd |d vsJy) Nr<)z0.1z0.3z1.0)z7.1z5.5z4.8)z3.2z4.4z5.6)4z0.6z0.5rrErrgiE'n@gFxlbO*g'ɮ@)rTrUivrArodelta)ar(cs r.test_interval_matrixrs BF BF &':;NOPA #$A AqA Q4::   Q4::   Q4::   $! ,, , $! ,, , $! ,, ,r:ctd}t|}|jt|k(sJd|d<|jJy)Nr)rr)r&r _LU)r'LUs r. test_LU_cachersA1 A 1B 55IaL  AcF 55==r:ctddd}tdddd}t||tdddd z}t|||}tt |||d tt |||d ksJy) Nrg#B ;g@xDrGrrigh㈵gh㈵>r)r&roimprove_solutionr[r\)r'r(x1x2s r.test_improve_solutionrsw1%T*A1aU-A !Q*Qu%@ @B !R #B B"A &hq"a.@!)D DD Dr:c 2tdD]}d}d}||zt_d}d}td|dz}t|}t|Dcgc] }t |c}}t |dkr%t |} t| }t |dkr% |z } | dz|z| z} | dz|z| z} |t_t| d} ||zt_| | z } |t_t| tjdrJdt_ycc}w) Nrr<rrg{Gz?r pade)method) r?rTrUrQrKabsr&rexpmr[r]ae)r,rUextradmNdgrr+expama1e2e1ds r. test_exp_paders 1X"u   1QqS\ HR(SV()"gn1 AQB"gn bD UQY] UT\A  "V $u GAs|q!!!1"2BF#)sD c dt_d}d}d}d}td}tddD]M}d}d }t |d z}t |t z}t |t z} tt|| } tt|| } tj| | } |rpd}d } td| D]\}td| D]K}t |||z t zz}t |||z t zz}t||| ||f<M^nRd }d } td| D]?}td| D].}t |||z t zz}t|| ||f<0At| ||\}}td}t| ||zz }||ksJ| d k(rVtt| |j|zz }||ksJtt| ||jzz }||ksJ| d k(stt| |j|j!zz }||ksJtt| |j!|jzz }||krNJy)Nr<irr Fz0.0rrfullrcomplexTreal)edpsz1.0E-11)rTrUrZxrangeboolnintrandintrIrHrAmpcqrr[r6T conjugate)lowlimituplimitmaxmflgzerokexdpsmodenum1num2rrBr'dtyperCr,valval2QRmaxnormn1s r.test_qrrs BFHG D C u:D Ab\<!1q5kDK DK  D$  D$  IIaN CEAa[ ,!,Ax78+;TV*CCDCGH,rs     LL ** **nn && Y          ! ! ! ! !  #$  3 3 3 3 3  56 & \    / / 9 ;<' aYV!W  Y     \    $  ,6 5Nn( G9 H8 H "66 -E8D!r: