K ic ddlmZddlZddlmZddlmZddlmZddl m Z ddl m Z ddl mZdd lmZdd lmZdd lmZdd lmZdd lmZmZddlmZddlmZddlmZddl m!Z!ddl"m#Z#m$Z$ddl%m&Z&ddl'm(Z(m)Z)m*Z*m+Z+ddl,m-Z-ddl.m/Z/ddl0m1Z1ddl2m3Z3ddl4m5Z5m6Z6ddl m7Z7ddl8m9Z9m:Z:ddl;mZ>m?Z?ddl@mAZAddlBmCZCmDZDdd lEmFZFmGZGmHZHmIZIdd!l'mJZJed"\ZKZLZMZNed#\ ZOZPZQZRZSZTZUZVZWZXZYZZZ[d$Z\d%Z]d&Z^d'Z_d(Z`d)Zad*Zbd+Zcd,Zdd-Zed.ZfeCd/Zgd0ZheCd1ZieCd2ZjeCd3Zkd4Zld5Zmd6Znd7Zod8Zpd9Zqd:Zrd;Zsd<Ztd=Zud>Zvd?Zwd@ZxdAZydBZzdCZ{dDZ|dEZ}dFZ~dGZdHZeCdIZdJZdKZdLZdMZdNZdOZdPZdQZdRZdSZdTZdUZdVZdWZdXZdYZdZZeCd[Zd\ZeCd]Zd^ZeCd_Zd`ZdaZdbZy)c)reduceN)add) MatrixSolve)Add)Tuple)UnevaluatedExpr)Function)Mul)Pow)Eq)S)Symbolsymbols)sympify)exp)sqrt) Piecewise)cossin)Matrix)InverseMatAddMatMul Transpose)CRootOf)Ocse)signsimp)Idx IndexedBase count_ops)sub_presub_post)meijerg)cse_maincse_opts)subsets)XFAILraises)MutableDenseMatrixMutableSparseMatrixImmutableDenseMatrixImmutableSparseMatrix) MatrixSymbolzw,x,y,zzx:13cXtjd}ttj|ddt ddDcgc]}t d|zc}k(sJtjd}ttj|ddt ddDcgc]}t d|zc}k(sJtj}ttj|ddt ddDcgc]}t d|zc}k(sJycc}wcc}wcc}w)Ny)prefixr zy%szx%s)r'numbered_symbolslist itertoolsisliceranger)nsis c/mnt/ssd/data/python-lab/Trading/venv/lib/python3.12/site-packages/sympy/simplify/tests/test_cse.pytest_numbered_symbolsr>+s#  " "# .B     Ar 38B<@auqy)@ AA A  " "# .B     B 49"bMBq *B CC C  " " $B     Ar 38B<@auqy)@ AA A ACAsD#D"D'c|tzSN)r2exprs r=opt1rC9s !8Oc|tzSr@)zrAs r=opt2rG=s 6MrDctjttdfgttzk(sJtjtdtfgtk(sJtjtdgtk(sJtjttt fgttzk(sJtjttdft dfgttzt zk(sJyN)NN)r'preprocess_for_csexrCr2rGrFrDr=test_preprocess_for_cserMAs  & &qD$<. 9QU BB B  & &qD$<. 9Q >> >  & &q<. 9Q >> >  & &qD$<. 9QU BB B  & & T4L4, ' )-.UAI 66 6rDctjttdfgtk(sJtjtdtfgttzk(sJtjtdgtk(sJtjttt fgtt zk(sJtjtdtfdt fgtt ztzk(sJyrI)r'postprocess_for_cserKrCr2rGrFrLrDr=test_postprocess_for_cserPJs  ' 'T4L> :a ?? ?  ' 'T4L> :a!e CC C  ' 'L> :a ?? ?  ' 'T4L> :ac AA A  ' ' T4L4, ' ),-aC!G 44 4rDcttttzdt ttz}t |g\}}|t ttzfgk(sJ|t t t dzzgk(sJt dg\}\}t|dk(r|dk(sJt dg\}\}t|dk(r|dk(sJy)N*r?)rr rKr2rrx0lenesubstsreducedsubst42red42 subst_halfred_halfs r=test_cse_singler_Ts CAqM4A;'A1#hOFG r1q5k] "" " tBx"a%'( (( (RD GXe w<1 ", ,!3%jJ  z?a HO3 3OrDcttttzdt ttz}t |\}}|t ttzfgk(sJ|t t t dzzgk(sJt tdgg\}}t|dtsJt d\}\}t|dk(r|dk(sJt d\}\}t|dk(r|dk(sJy)NrRrrSrT) rr rKr2rrrUr isinstancerVrWs r=test_cse_single2rcas CAqM4A;'A!fOFG r1q5k] "" " tBx"a%'( (( (&1#-(OFG gaj& )) )BGXe w<1 ", ,!#hJ  z?a HO3 3OrDc ttt}t|g\}}|gk(sJ|ttzgk(sJt dtdfdgtt dtdfdgtz}t|g|gfk(sJy)N)rarR))ra)rrKr2rr&)rXrYrZeqs r=test_cse_not_possiblerips Aq A1#hOFG R<< q1ug   &1a&$A . &1a&$A . /B r7rB4j  rDc&ttttztzdt ttztz}t |g\}}|tttztzfgk(sJ|t ttdzzgk(sJyNrR)rr wrKr2rrrU)rXrYrZs r=test_nested_substitutionrm|sq C!aOT!A#']+A1#hOFG r1Q37m_ $$ $ tBx"a%'( (( (rDcttz ttz ztttz ttz zz}t |gt j t jfg\}}|tttz ttz zfgk(sJ|t tt zgk(sJttz ttz ztttz ttz zz}t |gt j t jfg\}}|tttz ttz zfgk(sJ|tttzgk(sJddtz z}|tz | dzz d|z tz z }t |t j t jfggdgfk(sJt ttztztzttz tz zttzdzz tttzftttzfgttz ttzztdzz gfk(sJy)N optimizationsrarRrrg) rKr2rFrrr(r$r%rUrlx1)rXrYrZns r=test_subtraction_optrts QQ#q1uq1uo..A X--x/@/@ABDOFG rAEAE?+, ,, , sS"X~& && & a%!a%3QxQ/00A X--x/@/@ABDOFG rAEAE?+, ,, , rCG|n $$ $ QqSA !aR!G ac!eA q("2"2H4E4E!F G H aS    QQQ+a!eaZ7 8 q1u+AE{ #q2vR&8Q&>%?@ AA ArDcttztz}ttztz}t ||g\}}|t ttzfgk(sJ|t tzt tzgk(sJttztztzttzg}t |\}}t t |\}}||k(sJ|ttt zzt gk(sJttztzttztztzttzg}t |\}}t t |\}}||k(sJ|tttzt gk(sJttz ttz zttz ttz g}t |\}}t t |\}}|t t fttt zftt tzfgk(sJ|t t ftt tzfttt zfgk(sJ|ttzttgk(sJttztztztztzttztzg}t |t ttzfgttzt ztztztt zgfk(sJt ttzttztzgt ttzfgt tt zgfk(sJt ttzttzggttzttzgfk(sJt ttztttzzttztzdzgt ttzfgt tt zdt tzzgfk(sJy)Nrg) rKr2rFrlrrUreversedrrx2)e1e2rYrZlrsubsts_s r=test_multiple_expressionsr}s a%B a%B2r(mOFG r1q5k] "" " r!tRTl "" " 1QAaCA!fOFGXa[!JGQ W   q1R4xn $$ $ 1Q!A 1Q3A!fOFGXa[!JGQ W   r262& && & a%!a%!a%Q'A!fOFGXa[!JGQ rA2hQV r26l; ;; ; QBx"b1fAF|< << < r"ub"o %% % 1q1q1 ac!e$A q6AaCykAEBJNQ$6"#=> >> > Aq1uqy! "QU }r1r6l&C CC C Aq1u~ 2Aq1u~"6 66 6 !Q1Wac!eai( ) qs)r1r61r!t8,- .. .rDctdd\}}}||z|z||zg}t|g|fk(sJ||z|z||zg}t|t||zfgt|ztgfk(sJyNA B CF commutative)rrrUABCrzs r=test_non_commutative_csers}g51GAq! 1Q! A q6b!W   1Q! A q6AaCykBqD":. .. .rDctdd\}}}||z|z||zg}t|g|fk(sJ||z|z||zg}t|g|fk(sJ||z||z|zg}t|g|fk(sJyrrrrs r=test_bypass_non_commutativesrsg51GAq! 1Q! A q6b!W   1Q! A q6b!W   1ac!e A q6b!W  rDctdd\}}}tdd}||z|||zzg}t||||zfg|||zgfk(sJy)NrFrrUr)rrrrUrzs r=test_non_commutative_orderrs^g51GAq! 5 )B 1a1gA q6AaCykB":. .. .rDcNtttdzzttzzgtttzfgttztzgfk(sJtttzdtztzgtttzfgtttzgfk(sJttdtzztzt zttzdzftttzfgttztzt ztdzgfk(sJtttztzt zttz zttzz tttzfgttzt zttz ztz gfk(sJt d\}}}}}}}}||dzz|z|zd|z|z|z|z||z|z|dzzf}t|t||zft||zfg||z|ztzdtztz||z|ztzgfk(sJy)NrRraza, b, c, d, f, g, j, mre)rrKr2rUrlrFrrr) abcdfgjmexprss r=test_issue_10228rs !Q$1 ~ R1I;A "< << < AqsQw r1q5k]RRL$A AA A AaC! aQ+ , a!e Q QQ/11 11 1 QQQ'!a%0 1 a!e a!a!e,R/062 22 2$%=>Aq!Q1a q!tVAXaZ1QqAaCE!Q$J /E u: acR1I1Qr1R47AaCE"H =  rDctttdzzttzztttzfgttztzgfk(sJyrk)rrKr2rUrLrDr= test_powersrs> qAv!| 2qs)r!tbyk : :: :rDcttttz z tttz z zdgttz ttz z gfk(sJy)Nbasicro)rrlrKr2rFrLrDr=test_issue_4498rsG q!a%y1a!e9$G < q1uq1uo    rDcttdztdzztdzztdzzdttdzfgttdztztzdzzgfk(sJy)NrfrergrRrrora)rrKrUrLrDr=test_issue_4020rsd q!tad{QT!AqD( @!Q$ZL2q!tax"}q012 3 44 4rDcttttzttzz tttzfgtttz gfk(sJyr@)rrrKrUrLrDr=test_issue_4203rs> s1a4yA~ RAJ<#b'"*"> >> >rDcttt dzzttdz zzd}t|dgdgfk(sJy)NrarrroT)r rKr)rXs r=test_issue_6263rs@ 1qb1f:1q5 !1%A q (R$L 88 8rDctd}tdd}t||dzz||dz|dzz zzdd}|j}t|t|Dchc]}|jc}k(sJycc}w)NrrUT)realrRrerq)rr free_symbolsrVname)rrKcse_exprfreer<s r=test_issue_25043rs| A4 A1QT6Aq!tad{O+,R04H  D t9T2QVV23 33 32sA= c Lddlm}td}td}t||tt tt fd||tt tt fdz\}\}|gk(sJ|||tt tt fd||tt tt fdzk(sJt||tt tt fdtt zf||tt tt fdtt zfz\}\}|t tt zfgk(sJ|||tt tt fdt f||tt tt fdt fzk(sJy)Nr)Subsrrrra)sympy.core.functionrr rrKr2rU)rrrname_valrBs r=test_dont_cse_tuplesrsa( A A Qq!Wq!ff% qAwA ' ()Hgt r>> D1a1a&&11Q7QFF+, -- - Qq!Wq!fq!a%j) qAwAAE + ,-Hgt QU } $$ $ 4!Q!Q!R1 Qq!Wq!fq"g&' '' 'rDc tdtdzz tdzzttdzfgtdtz zgfk(sJttdzddtdzz ztdzz zttdzftdtz fgtttdzzzgfk(sJtdtdzz ddtdzz ztdzzzttdzftdtz fgttdzztzgfk(sJtt dtdzz t dtdzz zttdzfgt tt tzgfk(sJtt tdzt tdzzttdzfgt tt tzgfk(sJtt dtdzzz ttdzz t z zttdzfgt tdzz ttt zz zgfk(sJtttdztdzt dtdzz zzttdzfgtt dtz zttzgfk(sJtddtdzz ztdzz ttdzfgttdzzgfk(sJttdt zztdt zzzttdt zzfgtdtz zgfk(sJy)NrarR) rrKrUrrrrr2rFrrLrDr=test_pow_invpowrs qAv1}  q!t*QrT {# $$ $ q!tq1QT6z1a4'' ( q!t*r1R4j !BR!V$4#56 77 7 qAvQq!tVQT)) * q!t*r1R4j !BQK"$4#56 77 7 s1QT6{S1a4[( ) q2w-3r7SW,-. // / s1a4y3q!t9$ % q!t*B#b')*+ ,, , q!ad(|a1fQh& ' q!t*26 Q1X-./ 00 0 s1a4y1a4AadF ++ , q!t*3qt9 s2w./0 11 1 AadF AqD ! q2w-2rAv;-( )) ) q1Q3x!bd)# $ q1Q3x. B2I;' (( (rDctdzttdztdzz zttdzz}t |t tt dzt dz t dztdzzgtjttdzftt dzfttfttdzfgttttz zttzt dz ttzggk(sJy)NrarR postprocess) rKrr2rrr rFr' cse_separaterUrwrrrhs r=test_postprocessr,s a%#q1uq1uo& &QU 3B Bq!a%L!a%!a%!a%9)) + q1u+AE{QGb!a%[ 9 c"R%j3r7 "AE2b51 3 33 3rDclddlm}m}td}td}t ||t j zd|z|d|z|z dzttdz d|zdzz|d|z|z ttz||dz ttz||z|d|z|z dzzttttdz d|zdzzz||ttz|d|z|z ttz||z|d|z|z dzzttttdz d|zdzzz||dz ttz|d|z|z dzttz||z|d|z|z dzzttdz d|zdzz||ttz|d|z|z dzttz||z|d|z|z dzzddt j tdz | dzd|z|zd|zf}t|}td|zft| tzfttdzft|dz ftttft|ttft tdz dtz z||z|tzft"t |ttzft$||tft&t |ttzfg ||t j zt|ttt"ztt"zt$zttzt&zt$t&zddt j tdz t t t fgf}||k(sJy)Nr)rrrGrRrar) sympy.abcrrr rr HalfrrFrrUrrrwx3x4x5x6x7x8x9)rrrrtranss r=test_issue_4499r4sZ A A AJ!Q!a! d1gai2a4!8-DQqs H 7F.a!eT!W%.&&'d.++,QqS1Wq[>.: QabdQh''!T!W 5a!a Q7 1 !a! n %&*1gtAwqyBqD1H.E&EaA QG'1Q37Q;Q('))*1'../!a! n'= abdQh!T!W -a!a!  Q/ 1 !a! n %&'AFFAaC!aA 1  A AA acR!bMBQ<"a!er47m aBi21B/!4QrU:;b"Qr2Y,=O a2h"b2rl+ - QZQBrE2b58RU2Xr"u Q!bS2#s , -  .C !8O8rDc&ttdzdtdzzz dz d}t|g|gfk(sJtt t t z t ztz t z t tt zztz t z k(sJy)NrerfrRra)rrKrr%r$r2rF)rs r=test_issue_6169rLs{1qAv !1%A q6b1#Y   GaR!VQJNQ./ 0QBAJNQ4F FF FrDcd}td|f}td|f}td|dz }||dz||z ||dz||z z }d||dz||z z }t||g\}}t|dkDsJy)Nrfr2)shaperKr<rar)r!r rrV)len_yr2rKr<expr1expr2 replacements reduced_exprss r=test_cse_IndexedrTs ECx(ACx(A CqA qsVAaD[1QqS6!A$; 'E q1vad{OE"%uen"5L- | q  rDctddd}t|g|gfk(sJtdd}td||}t|g|gfk(sJt|d|dzg|d|dzgfk(sJt|d|d z|d|d z|d zzt|d|d zfgt|d ztzgfk(sJy) NrrgrsT)integerrr)rrr)rrR)r0rrrU)rrsrs r=test_cse_MatrixSymbolr`sS!QA q6b1#Y  T"AS!QA q6b1#Y   qtad{ QqT!A$YK0 00 0 qvaf}qvaf}QsV33 42qwqw:O9PSUVWX\V]S]`bSbRc8d dd drDcHtddd}tddd}|j|zj|z|z}|j|z|z|z}t||g\}}t |dkDsJt||z|g\}}|sJt|dz||dzzg\}}|sJy)Nrrgr2rarrR)r0TIrrV)rr2rrrrs r=test_cse_MatrixExprrmsS!QAS!QA SSUIIMA E SSUaK!OE"%uen"5L- | q  "%uu}e&<"=L- <"%q!tQAX&6"7L-  2.35), (C392, True)), True))zGPiecewise((2.05*C390**(-1.03), C390 < 0.5), (2.5*C390**(-0.625), True))C391ggv?C390gɥ:?C392raraPiecewise((Symbol('ON'), Equality(Symbol('mode'), Symbol('ON'))), (Piecewise((Piecewise((Symbol('OFF'), StrictLessThan(Symbol('x'), Symbol('threshold'))), (Symbol('ON'), true)), Equality(Symbol('mode'), Symbol('AUTO'))), (Symbol('OFF'), true)), true)))rrrrrV) C393rsub ss_answer substitutionsnew_eqnpair cse_answerrBs r=test_issue_7840rs  - D Q D 99VD !D CCKCK #IIM'. GLL-DGLL.%J  "" "  : D !YM7 1:   }  !! !rDc *ttttfD]z}|ddtt zdddg}t tt z|g}ttt zfgt|tdgddgggf}||k(sJt|dd|rzJy)NrRrrarq) r,r-r.r/rKr2rrUrb)clsrresrs r=test_issue_8891rs"$7 "79+ 1q1uaA& '1q5!*oQU }r3Q!Q'8#9:;czz#a&*c*** +rDc Dtd\}}}}}}||z|z|z|z||z|dzz|z||z|dzz|zg}t|\}}td|DrJddlm} ddlm} td} tdDcgc]'}ttd Dcgc] }| |  c})} }t| d D]t}t|}t|\}}td |DrJt|D]0} tt|D]}||j| ||<2||k(rtJtdDcgc]*}ttd Dcgc] }| | ddc},} }t| d D]}t|}t|\}}td |DrJt|D]0} tt|D]}||j| ||<2||Dcgc] }| | c}k(rJycc}wcc}wcc}wcc}wcc}w) Nz a b f k l irRc3VK|]!}|jD]}|j#ywr@argsis_Mul.0rr<s r= z#test_issue_11230..s$771188787')r)choice) expand_mulza:mrfrgc3VK|]!}|jD]}|j#ywr@rrs r=rz#test_issue_11230..$;AAFF;qqxx;x;rc3VK|]!}|jD]}|j#ywr@)ris_Addrs r=rz#test_issue_11230..r r)rranysympy.core.randomrrrr:r r)r7rvrVrr)rrrkrzr<pRrrrsexris r=test_issue_11230rs/}-Aq!Q1 1QqAaC1HQJ!AqD +A q6DAq7Q777 7).A7.check..s5a1)5)rr#rVsum)rhrrs r=checkztest_issue_11577..checksJ2w1||~ FS5155 5 aL  rDrfrRrera)rKr2rrUrr)rrhs r=test_issue_11577rs AadQT!V ad "B r7 adb!A#Y!Q$Bq.2b5"8!9; ;; ; "I Aq1uqj1a!e9 $B r7 a!e 1RU QrT)*, ,, , "IrDcLtdztdzg}t|g|fk(sJy)Nrgre)rKrrs r=test_hollow_rejectionr s) a%QB r7r2h  rDcttdtzdttdzzzzttdtzdttdzzzzg}t |\}}t d|DsJdt |tf\}}t d|DrJdt d |DsJd y) Nrgrarfc3FK|]\}}t|jvywr@r2rrr|rs r=rz"test_cse_ignore..s:CqC$$$:!z&cse failed to identify any term with yignorec3FK|]\}}t|jvywr@r r!s r=rz"test_cse_ignore..s>VQ1(((>r"z,Sub-expressions containing y must be ignoredc3RK|]\}}|ttdzz dk(!yw)rarN)rrKr!s r=rz"test_cse_ignore..s&;&!SsT!a%[ A%;s%'z4cse failed to identify sqrt(x + 1) as sub-expression)rr2rrKrr )rsubst1red1subst2red2s r=test_cse_ignorer+s VQqS1T!A#Y;& 'Q1qac{1B)C DEu:LFD :6: :dv>>n@nn > ;F; ;s=ss ;rDcBtttztt zttttztt zg}t |tf\}}|Dcgc]}|j t|}}||k(sJycc}w)Nr#)rlrrKrFr2rrrv)rzrYrZrXrls r=test_cse_ignore_issue_15002r.s~ #a&aR As1v c1"g A!QD)OFG,3 4q!&&&! " 4B 4 7N7 5s1!Bcttdz}td|z d|z z g\\\}}\}||k(r|d|z d|z z k(sJy|| k(r|d|zd|zz k(sJyd|d| d|}J|)NrarqzExpected common subexpression z or z, instead got )rrKr)xp1rUueredmsgs r=test_cse_unevaluatedr4$s !a% Cb3h1s7345JXb" SyrBw1r6**** trBw1r6****.se4v^B4PcurDcd\}}td|z}t|Dcgc]5}ttt|Dcgc]}||d||zzzc}7}}}|d|dzj dk(sJt |\}}t |dkDsJdt|D]8\}}|jt|||z j dk(r8Jycc}wcc}}w)N)rgr5zx:%drqrraz!exprs[0] == -exprs[2], i.e. a CSE) rr:rrsimplifyrrV enumeraterrv) nexprsntermsrKr<rrsubstr2rXs r=test_cse__performancer;1sNFF Av   suV}=!QqT21+%=> E  !HuQx  ) ) +q 00 0UJE3 u:>>>>>#D1x'%(2<<>!CCCD > sC,C' C,'C,c ttzdtztzttztzdtztztzg}t|\}}dt |t d|Dzt |zk\sJy)NrRrgrc3BK|]\}}|jywr@r")rrvs r=rz#test_issue_12070..Bs!BDAq!++-!Br)rKr2rFrrVrr#)rr:r2s r=test_issue_12070r??sq UAEAIq1uqy!a%!)a- 8EUJE3 Uc!BE!BBB3  !! !rDcntdtdzztdzzz }t|dd}||k(sJy)NrRrar)rKr2r)rhcse_eqs r=test_issue_13000rCFs9 Bq!tGadN B WQZ]F R<r<s r=test_cse_release_variablesrUVsq= BBB EAI>1 AA!a AEAI>1 1qAE C s 5 6DAq FaQK"rAvk"R1qMBr2r6lRJRJR2t*r1g/24RR0DFFF1IIK/DAq!Q/A/ a(166!9( (( ( 0(s< E5E5E;c*d}|tgtfk(sJ|dgdfk(sJtg}tttfD]}|||g||fk(rJ|t |gt |fk(sJtdi}||g|fk(sJy)Nct|dS)NF)r7r)rKs r=ztest_cse_list..hs S'rDrKra)rKr7tuplesetr)_cseitrrs r= test_cse_listr]gs 'D 7r1g   9S !! ! BE3 *AbE{r1R5k)))* r E2J/ // / AA 7r1g  rDcZtddd}t| |z|z | |z|z k(sJy)NrrR)r0r)rs r=test_issue_18991r_ss7S!QA QBFQJ A26A: -- -rDcFtdddg}t|g|fk(sJy)NrarRFrH)r r)rs r=test_unevaluated_Mulraxs) QE "#A q6b!W  rDcttdjdd}t|}t |}|gt|gfk(sJyNA:4rR)r.rreshaperrrrKrs r="test_cse_matrix_expression_inverserg}sHWU^,44Q:A A1vH WQZL) )) )rDcttdjdd}ttd}tt ||}t |}|g|gfk(sJyNrdrRzb:2)r.rrerrrrrrKrs r=)test_cse_matrix_expression_matmul_inverserksXWU^,44Q:AWU^,Awqz1A1vH QCy  rDcttdjdd}ttj |}t |}|g|gfk(sJyrcr.rrerr NegativeOnerrfs r=test_cse_matrix_negate_matrixrosJWU^,44Q:Aq}}a A1vH QCy  rDcttdjdd}ttdjdd}ttj ||}t |}|g|gfk(sJyNrdrRzB:4rmrrrKrs r=+test_cse_matrix_negate_matmul_not_extractedrssgWU^,44Q:AWU^,44Q:Aq}}a#A1vH QCy  rDc8ttdjdd}ttdjdd}ttj t||}t |}|gttj ||gfk(sJyrqrmrrs r='test_cse_matrix_nested_matmul_collapsedruszWU^,44Q:AWU^,44Q:Aq}}fQl+A1vH VAMM1a89: :: :rDcttdjdd}ttt|}t |}|g|gfk(sJyrc)r.rrerrrfs r=0test_cse_matrix_optimize_out_single_argument_mulrwsMWU^,44Q:AvfQi !A1vH QCy  rDc ttdjdd}tt t t |t t |t ||}t |}|gt d|gfk(sJyNrdrRre)r.rrerrrrfs r=9test_cse_matrix_optimize_out_single_argument_mul_combinedrzlWU^,44Q:AvfVAY'(&*;VAYJA1vH VAq\N+ ++ +rDc ttdjdd}tttt|}t |}|g|gfk(sJyrc)r.rrerrrfs r=0test_cse_matrix_optimize_out_single_argument_addr}sRWU^,44Q:AvfVAY'()A1vH QCy  rDc ttdjdd}tt t t |t t |t ||}t |}|gtd|gfk(sJyry)r.rrerrrrfs r=9test_cse_matrix_optimize_out_single_argument_add_combinedrr{rDcttdjdd}ttd}t||}t |}|g|gfk(sJyri)r.rrerrrjs r='test_cse_matrix_expression_matrix_solversTWU^,44Q:AWU^,AAqA1vH QCy  rDc tttdjdd}ttd}tt tt ||t ||}t |}tddd}tt t||||}||t |fg|gfk(sJy)NzX:4rRzy:2rU)r.rrerrrrr0)Xr2rrrUreduced_expr_expecteds r=!test_cse_matrix_matrix_expressionrsWU^,44Q:AWU^,AwvilA./1qAA1vH dAq !B"76"a=#92qA "il+,/D.EF FF FrDcd}ttd|}ttd||zj||}ttd||zj||}ttd||zj||}ttd|}t|t |t |t t|t ||t |tt ||t tj|}t|t tj|t |t t|t ||t |||}t||g}td||} td||} | t |f| t t|t ||| fg} t|t || | tt ||t tj|t|t tj|| | ||g} || | fk(sJy ) aKalman Filter example from Matthew Rocklin's SciPy 2013 talk. Talk titled: "Matrix Expressions and BLAS/LAPACK; SciPy 2013 Presentation" Video: https://pyvideo.org/scipy-2013/matrix-expressions-and-blaslapack-scipy-2013-pr.html Notes ===== Equations are: new_mu = mu + Sigma*H.T * (R + H*Sigma*H.T).I * (H*mu - data) = MatAdd(mu, MatMul(Sigma, Transpose(H), Inverse(MatAdd(R, MatMul(H, Sigma, Transpose(H)))), MatAdd(MatMul(H, mu), MatMul(S.NegativeOne, data)))) new_Sigma = Sigma - Sigma*H.T * (R + H*Sigma*H.T).I * H * Sigma = MatAdd(Sigma, MatMul(S.NegativeOne, Sigma, Transpose(H)), Inverse(MatAdd(R, MatMul(H*Sigma*Transpose(H)))), H, Sigma)) rRzmu:zSigma:zH:zR:zdata:rUrrN) r.rrerrrrr rnrr0) NmuSigmaHrdatanew_mu new_SigmarrUrrreplacements_expectedreduced_exprs_expecteds r=test_cse_matrix_kalman_filterrs:$ A gA3i0 1B 6!a%)9!: ; C CAq IEWr!a%\23;;AqAAWr!a%\23;;AqAA %s 4 5D BuilGF1fQPUW`abWcFdrCrGrMrPr_rcrirmrtr}rrrrrrrrrrrrrrrrrrrrrrrrrrrrr+r.r4r;r?rCrFrJrUr]r_rargrkrorsrurwrzr}rrrrrLrDr=rsh2'+( $"/&69:?'II+ ',3)51--.553Y  1a8?5BBBBBS# A64 4 4 !)A*.<////  ;; 4 ?9 4',(*30G ! e  C <<""J+"/J* t  D! ! / )" .  *!!!;;!,,!,,!G%GrD