ёiSSKJr SSKrSSKrSSKrSSKrSSKJrJr SSK r SSK r SSK J r SSKJrJr SSKJr SSKJr S S KJrJr S S KJrJrJr S S KJrJr \(a SS K J!r! SSK J"r" /r#S*Sjr$S+Sjr%S,Sjr&S-Sjr'S.Sjr(S/Sjr)S0Sjr*S1Sjr+S2Sjr,S3Sjr-S4Sjr.S5Sjr/S6Sjr0S7Sjr1"SS5r2S8Sjr3S9S jr4S:S!jr5"S"S#\5r6S;S$jr7SS'jr:S>S(jr;S?S)jrksa| B | ++eR C#hG l "" ")),7 /011H J  s8s7| #> #r(c XS/[U5-n[R"SU5nUbUR5UR 5pT[R"SU5nU(aT[ [ XE5SSS2[ UR5UR 55SSS25H upxXU'M [R"[ U5[ U[U555n O[[ [U555n U Hn URX5X*'M U$)a Build an inverse map of dimension indices. Three conditions must hold for the result to be meaningful. First, no duplicate letter labels in each label string. Second, the number of dots in dimout_labels >= that in in_labels. Third, dots are contiguous in each label string. Parameters ---------- in_labels: The dimension labels to map to out_labels: The dimension labels to map from Returns ------- The inverse map from out_labels to in_labels. The length of the inverse map equals that of out_labels. -1 is filled if there's no matching input dimension for a specific label. Examples -------- in_labels = 'ij..', out_labels = '..ji' inv_map = [2, 3, 1, 0] in_labels = 'ij..', out_labels = '..kji' inv_map = [2, 3, -1, 1, 0] rz\.+N) rresearchstartendziprange itertoolschainiterr) in_labels out_labelsinv_maprrBrCsaxdimitis r& build_viewrRs8dS_$G &*%A}WWYs IIfi ( e!$B$'qwwy!%%')B4R4)H"  __U5\5c*o+F G %J( ) ^^JM2  Nr(c[SRU5RSS55n//pT[S/UQU5H;upgXg:wa$UR U5 UR S5 M.US==S- ss'M= Ub"[ XU5 URSSU-5nO'SU-SRS[XE555-n[ [U55SSS2H/n XIU;dM URU 5 URU 5 M1 SRU5n X-n UV s/sHn [X5PM n n [U5n UnXX4$s sn f)a Build the global view, which is a layout of all dimension labels plus an index table that maps from the layout to the dimensions in each operand. In the global view, the dimensions are arranged such that output ones are put on the left and contraction ones are put on the right. Parameters ---------- nop_labels: The input full label strings of all input operands rhs: The equation right hand side n_bcast_dims: The maximum number of broadcast dimensions Returns ------- A tuple of g_labels, g_view, g_nout, g_count g_labels: the layout of all labels in a string g_view: the index table g_nout: the number of output dimensions g_count: the counter array for dimension contractions rrr rNrc3:# UHupUS:XdM Uv M g7f)r N).0lr#s r& $build_global_view..s4 ,$!QAA,s  ) r8joinrrDappendr>rErpoprR)r2r9r;concatlabelscountab g_labels_outrQ g_labels_sumg_labelsg_viewg_noutg_counts r&build_global_viewrhsM@BGGJ'//R8 9FESN6NF+ 6 MM!  LLO "INI , S,/{{5# *<= \)BGG4 f,4 -  3u: tt $ 9 $ JJqM IIaL% 776?L*H/9 :z!j%zF :  FG V ,, ;s.Ec l/n/n[X5H0upVURUVs/sHowS:aXgOSPM sn5 M2 [U6Vs/sHn[U5S1- PM n n[U 5V V s/sHup[ U 5S:dMU PM n n n U (aSXSS35eU V s/sH$n [ U 5S:aU R 5OSPM& n n UVVs/sH#oVs/sHoS:=(d US:HPM snPM% nnnX4$s snfs snfs sn n fs sn fs snfs snnf)a The global shape is the shape of all dimensions rearranged and broadcasting to the global view. It's a reference data structure for einsum planning. Parameters ---------- g_view: the global view op_shapes: the shapes of the all operands Returns ------- g_shape: the global shape vector g_masks: list of shape masks for each operand. A dimension's shape mask is a boolean indicating whether its size > 1, in other words, it's not squeezable rr zInvalid operands: label rz- corresponds to non-broadcastable dimensions.)rDr[r6 enumeraterr\)rerd op_shapes view_shapesg_masksviewop_shaperO sizes_per_ax g_set_shaperNsizes non_bcastableg_shape view_shaperMs r&build_global_shapervsh,$&K "Gf0M2XHM1<MN1584E#4ELLQC4E# &k22yrc%j1n2 "8!,<#=">?7 8  BMMc%j1nuyy{!3GMBMAL::.:aQ !r' :.   +N#N /s5D D7D D 4+D&& D0/D+ D0+D0cfURSS5n[U5[[U55:$)z/ Returns True if there is any duplicate label. rr)rrr6)r^s r&has_duplicated_labelsrx/s,^^C $F v;S[) ))r(c6[U5(aS5eX4$)a Merges dimensions with duplicate labels. For those dimensions with duplicate labels, merge them into one dimension which represents the diagonal elements. This requires the dimensions with duplicate labels are equal sized. Examples -------- 'ijj...i' would be merged into 'ij...' z#Duplicate labels are not supported.)rx)r^r"s r& diagonalizerz7s)%V,,- , ?r(PlancH^SU3nU4SjnXT/XB4nURU5 g)z Add reduce to the plan opc>[XTS9$)Nkeepdim paddle_sum)vardimsrs r&plan_reduce..Rs *S@r(Nadd_step)planr} reduce_dimsrvarnamefsteps ` r& plan_reducerJs- 2$iG@A i -DMM$r(cNSU3SU3/nSnXCUS4nURU5 g)Nr}c[U5U-$Nr)var1var2s r&r"plan_scalar_prod..Ys:d+d2r(r r)rop1op2varnamesrrs r&plan_scalar_prodrWs7SE bJ'H2A  #DMM$r(c  ^^SU3SU3pU4SjX#45upUVs/sHoUS:dM UPM nnUVs/sHoUS:dM UPM nn[R"U 5n XU-U -n[R"U 5n U UU-U -nU4SjX#45unn[R"[UU5VVs/sHunnU(aUOSPM snn5n[R"[UU5VVs/sHunnU(aUOSPM snn5n[R"UU5n[ [ UUXxU 45unnnnn[ U[R"[ U55:g5(a%[U /U [U54nURU5 [ U[R"[ U55:g5(a%[U /U [U54nURU5 UU-S:Ga.US:Ga'S[R"UU45;Ga /[UU5Q[R"UU5P[R"UU 5Pn /[UU5Q[R"UU5P[R"UU 5Pn![U /U U 4nURU5 [U /U U!4nURU5 [X/U SS4nURU5 [UXg-U-5n"[U /U U"4nURU5 GOUUs=:Xa Us=:XaS:Xa"O O[X/U SS4nURU5 GOlU(a:[[UU-UU-U-55n#[ U /U U#4nURU5 U(a4[[UUU-55n#[ U /U U#4nURU5 US:Xa["X/U 4nURU5 GOUU-S:Xa{US:Xau[ U /U S /4nURU5 [ U /U S/4nURU5 [X/U 4nURU5 [$U /U SS /4nURU5 GOIUU-S:XGaS[R"UU UU 45;a['UU UU :H5(de[U /U /[UU5QSP[R"UU 5P4nURU5 [U /U /[UU5QSP[R"UU 5P4nURU5 [X/U SS4nURU5 [$U /U SS /4nURU5 O<["X/U 4nURU5 [[U*S55n$[)XU$SS 9 Xg-U-Hn%UU%S:=(d UU%S:HUU%'M U Hn%SUU%'M [[ U 55Hn%SU U%'M Sn&Xg-U-Hn%U&U&S-sU U%'n&M [U 5TU'g s snfs snfs snnfs snnf) z plan matmul r}c3.># UH nTUv M g7frrU)rVr}res r&rXplan_matmul..rs:z&*zrc3.># UH nTUv M g7frrU)rVr} g_supportss r&rXr|s>:R*R.:rr rFTrN)nparrayrDmaximumr0ranyarangerr/r concatenateprodrr rErrrallr)'rrerrrrtIJ1J2Krrop1_viewop2_viewidxI1I2op1_dimsop2_dimsop1_maskop2_maskrMm op1_vshape op2_vshapevshapei1i2j1j2kr op1_shape op2_shaper fillrrNrOs' ` ` r& plan_matmulr_sD"cUr#Z$:z:H 1#smq0#B 1 1#smq0#B 1xx!HR! $Hxx!HR! $H>C:>HhS(5KL5KTQ1q=5KLMJS(5KL5KTQ1q=5KLMJ ZZ J /FC"b"!!45BBA 8ryyX/ /004&$X6 d 8ryyX/ /004&$X6 d R! E bnnj*%=> > *Q-  GGJrN #  GGJqM "  *Q-  GGJrN #  GGJqM " i/ di/ d|T5$6 dVAFRK()e+ d r Q ! |T5$6 d b2grBw|45DtfdD0D MM$  b"r'*+DtfdD0D MM$  6d\4/D MM$  "W\a1ftfdRD0D MM$ tfdRD0D MM$ D<-D MM$ TFD2r(2D MM$  "W\b ]JqM *)  z!} 1 566 66A$z!}%AqA"''*Q-*@A D MM$ A$z!}%AqA"''*Q-*@A D MM$ D<ud:D MM$ TFD2r(2D MM$ d\4/D MM$ uaR|,K ; >frkbzA~9r)9  CM" # Cfrkq cx.F3KE 2 1MLs! YY Y YY! Y' c XXpXBXCp[U5n U [U5- n S/U -U-n[[U55///4unnnn[[X|5XSXS5HunnnUS:gUS:g:wa,US:waUR U5 M,UR U5 M?US:wdMG[ U U5[ U U5-nUU :a)UUU:Xa UR U5 UU==U-ss'MUR U5 UU==[ US- S5-ss'M XSUSS&[XX#XEUUUU5 g)z! Plan various kinds of summation rNrr )rr/rErDr[intmaxr)rrerrrrtrgn_bcastrrrrndimnoutr_rrrrrNdim1dim2folds r&plan_summationrsQ fkh#*/h x=D #g, D C$J Eg'R3LAq"b ghx0(82DD$ BJDBJ 'rz "  " RZx|$s8B<'88DTzdeBi/ b T!  b S1-- !&uGAJc QBJr(c//p![U5H/up4US:aURU5 MURU5 M1 [S[U555(a/nX4$)Nrc3.# UH upX:Hv M g7frrU)rVrQrOs r&rXrearrange..2s 2/18/)rjr[r)axespermrrNrOs r& rearranger*s[R$T? 7 KKO KK  #  2)D/ 222 :r(c^ [U5n[U5Vs/sHnSU3PM snm [[U5U5H]upE[U5upgT UnU(a[U/X4n UR U 5 U(dMB[ U/X4n UR U 5 M_ U 4Sjn U T S4n UR U 5 gs snf)z Plan broadcast across r}c d>SRT5n[U[[TU555$)Nz * )rZevaldictrD)argsexprrs r&rplan_broadcast..fLs*zz(#D$s8T2344r(N)rrErDrrrr) rr1nop_axesnoprQop_axesrrrrrrs @r&plan_broadcastr8s h-C"'*-*Q"QC*-H%*h/ w' qk seS.D MM$  4seS.D MM$ 05 h DMM$%.sB?cD\rSrSrSrS SjrSrS SjrS SjrSr Sr g ) r{iTc 0Ul/Ulgrenvsteps)selfs r&__init__ Plan.__init__Us r(c:URRU5 gr)rr[)rrs r&r Plan.add_stepYs $r(cBXR;aURU$S$rr)rrs r&get_var Plan.get_var\s$+xx$7txx ATAr(c X RU'grr)rrrs r&set_var Plan.set_var_sr(chSnURHtp#pE[[XB/UQUQ755 M! U$r)rprintreprrresr in_varnames out_varnamers r&show Plan.showbs926** .AK $ <3= r(cSnURH=tp#pEU"/[URU5QUQ76nU(dM,URXA5 M? U$r)rr0rrrs r&execute Plan.executehsO26** .AK;S{3;d;C{ [.3= r(rN)returnNone) __name__ __module__ __qualname____firstlineno__rrrrrr__static_attributes__rUr(r&r{r{Ts! B  r(c [U5n[US5nU[U5- n[5n [U5V s/sHn SU 3PM n n [[ U R X55 U(d[ XU5 U $[X5Hdup[XSXS5VVs/sH!up[US-=(a U(+5PM# nnn[U5Hun nXJ==U-ss'M Mf [[U5X5Hupn/n[XSUUSU5H'unnnURU(aUS:XaUOS5 M) [[SU55nU(a [XUSS9 [U5H1upX-nUU=(a US:HUU'XJ==US:XaSOS-ss'M3 M [U5HCn U S:XaM [X:S- 5(d[XS- U 5 M1[XU S- XX$U5 ME [!S X6S- US55(deUSn [S [U SU555(aU Vs/sH nUS:dM UPM nn[#U5U:wa$SUS- 3n[$U/UU4nU R'U5 Sn/n[U 5HunnUS:wdMUUS-sU U'nM [U SU5HunnUS:XdMURU5 M! U(a$SUS- 3n[(U/UU4nU R'U5 XSVs/sH nUS:wdM UPM nnU(a$SUS- 3n[*U/UU4nU R'U5 U $s sn fs snnfs snfs snf) zF Plans the actual execution steps. Results ------- the execution plan rr}Nr rc US:$)NrrU)xs r&rplan_einsum..sAFr(Trc3.# UH o(+v M g7frrU)rVmaskeds r&rXplan_einsum..sC(Bfzz(Brc3.# UH upX:gv M g7frrU)rVrNrOs r&rXrs ;$:29$:r)rr{rEr/r0rrrDrrjr[filterrrrrrr8rrrr)r1rertrrgrrrrrrQop_namesrnsupportdrM down_countr_mask to_reducerOrrrNrrrunsqueeze_dims squeeze_dimss r& plan_einsumrqs h-C vay>D #g, D 6D"'*-*Q"QC*H-T\\8 ./ tv. V0 DK8 8 Q#U $8  "*-HAu J% J. 1U3Z<  "%d5k4;"H C   V S D#I6"2I>?  d ;i(DABBx-Q"WDH JqBw!A -J)= 3Z 6 &:!e$%% Tq5! , a!eQGg 7B C 7(;DE(BC C CC C ":D ;Id5Dk$: ;;;#0tsaxt0 $<4 37)nGwi$6D MM$ t_EBBw #S1W R#%tET{+EBBw%%b), 37)nGwi.@D MM$ #';<;C#)C;L<sQwi. 7L8 d KC. z1$=s#M6'(M; N*N3 NNc r^ SnSn/n[[S5[S55Vs1sHn[U5iM snm [UR S5U5H[upx[ UR 5[ URSS55- n [XI5nUHnT RU5 M M] [UR S5U5HupxSU;akURS5n U[ UR 5[ URSS55- - n [U[U 5V s/sHoU -PM sn S9nURU5 M SRU 4S j[U555nUb$URSU5nURSU5nXU4$s snfs sn f) zM we replace ... as unused variables to simplify the EinsumOp implementation. Nrr`zr*rr)axisc3D># UHnTR5v M g7fr)r\)rV_unused_variabless r&rX#replace_ellipsis..sO!/3355s )rEordchrrDr.rr rrdiscardindexrr[rZ) left_equationr9r1ellipsis_stringsmax_ndim new_operandsr#equr"r$start_unsqueeze_idxto_squeeze_numrQrs @r&replace_ellipsisr&s H!#L(-c#hC(AB(A1A(ABM//4h? GMM"SUB)?%@@x'A  $ $Q '@ M//4h?  C<"%))E"2 %GMM"SUB)?%@@N 7<^7LM7L!--7LMG G$@wwOuXOO#%--e5EF kk%!12 | ++1CNs F/8F4 c URSS5n[U5nUS:d SU35eUR5RS5tp4[U5S:dS5e[ X15nU(aUSOSnUc [ U5n[URS 55[U5:Xd/S [U5S [URS 55S 35eS U;a S U;aS5e[ X4/UQ76up4nX4XV4$)z? check equation / raise error, default right labels generation  rrz:Required at least one operand in Einsum API, but received ->r+Invalid equation: multiple `->` were found.Nr*r+r,r-rr5)rrlowerr.r3 rhs_inferencer&)equationr1rlhsr9r^r"s r& preprocessr/ s' R(H h-C 7 DSEJ7  &&t,IC s8a<FFF< # (F#a&TC {C  syy~ #h- / 6s8}oF3())I K /  c!1> 2.cBBCl V ))r(c \rSrSr%S\S'Srg)Shapedi0 list[int]r rUN)rrrr__annotations__rrUr(r&r1r10s r(r1cjSURS55nSSjn[[XCX!55nU$)z this shape is just used for operands planning. may differ with the original shape. for example: ... is replaced by 1 -1 is replaced by 1 Results ------- list of shape c3@# UHoR5v M g7fr)strip)rVrs r&rX#parse_fake_shape..Bs<(;1WWYY(;sr*c[UR5[U5:Xd)S[UR5S[U535e[[XR55VVVs/sH unupEUPM nnnn[ [ [ U55nSU;a!URURS5S5 [U5$s snnnf)z 1. ori_label is the original labels, not aligned by '....' 2. if the '...' is evaluated to empty list, there is no '.' in label zClength of shape and length of label must be the same, but received z != rr ) rr rjrDr/r0absinsertrr1) ori_labellabelr}rQrWrMfakess r& fake_shape$parse_fake_shape..fake_shapeDs 288}E * QRUVXV^V^R_Q``dehineodp q *%.c%.B$CD$Cyq&1$CDSe_% )  LL-q 1e} Es.C)r;strr<r@r}rrr1)r.r/r0)r-r1r^ origin_labelsr>outs r&parse_fake_shaperC4s4=s(;TRU5S:H=(a US;$)Nr )rr*)get)keycnts r&is_freerhs_inference..is_freeWs wws|q :S %::r(rr) collectionsCounterrZr r8elements)r.rIr9rHs @r&r,r,VsQ;   c "CC<%RC ws||~(>?@ @C Jr(cSSjn[R"U5nU"U5nUc [U5nURSU5nURSU5nUS-U-U4$)z+ 1. gen rhs if rhs is None 2. '...' -> 'A' c[UR55n[RH nX!;dM Us $ [ S5e)NzSYou have used all `a` - `z`, there can't find a unused char for einsum optimization)r6rMstringascii_lowercase ValueError)counterusedr#s r&get_used_label2gen_equation_for_opteinsum..get_used_labelfsA7##%&''A}( a  r(rr))rr@)rKrLr,r)r.r9rUrHbroadcast_labels r&gen_equation_for_opteinsumrX`sf     c "C$S)O {C  ++e_ -C ++e_ -C : _ ,,r(c[U5n[U/UQ76up4pVUS::a[US-U-/UQ76$[X6U5n[ X45up[ R "U/UQ7SS06upUn U Hfn U tupn nnX:dS5eU RU5U RU5/nURU S5nU R[U/UQ765 Mh [U 5S:XdS[U 5S 35eU S $) z einsum v2 implementation. 1. Implement C++ EinsumOp. 2. V2 create the EinsumOp to calculate, so just a little verify work in python. 3. V2 use opt_einsum.contract_path to optimize the multivariable einsum. rr) einsum_callTzUAssume the first var_idx is smaller than the second_idx. opt_einsum can guarantee it.rr z1There must be one elements in list, but received rr) rr/ gen_einsum_oprCrX opt_einsum contract_pathr\rr[)r-r1n_opr.r9r^r"shapes opt_equationrWrconsvar_listpathr`raeq__var_ss r& einsum_v2rgxs" x=D%/%D8%D"Cf qyS4Z#-= == c 8F$>s$H!L&&|OfO$OGAH!2u c ua(,,q/2 ZZ / b1512 x=A  ;CM?!L  A;r(c[5(a[R"X5S$S[U5s=::a S::dS5e S5eUHn[ USSS/S5 M [ US [ S5 [S0[5D6nURUSRS 9n0nXS '[[U55Vs/sHnURUSRS 9PM! nn[[U55Vs/sHnURUSRS 9PM! nnURSS U0XGUS .US 9 U$s snfs snf)z EinsumOp Python Interface: rr rz&Only support two operands in EinsumOp.dtypefloat32float64einsumr-)riOperands)Out InnerCacheXShape)typeinputsoutputsattrs)rl) r rrlrr rr@r locals"create_variable_for_type_inferencerirE append_op) r-r1inphelperrBrtrQcachesxshapes r&r[r[su }}X033CM&Q&P(PP&P(PP&C $Wy)4h  8Zh72277hqk>O>O7P$j3x=) )  5 5HQK` or omitted. In the latter case, the output labels will be inferred from the input labels. - Inference of output labels - Broadcasting label `...`, if present, is put on the leftmost position. - Free labels are reordered alphabetically and put after `...`. - On explicit output labels - If broadcasting is enabled, then `...` must be present. - The output labels can be an empty, an indication to output as a scalar the sum over the original output. - Non-input labels are invalid. - Duplicate labels are invalid. - For any dummy label which is present for the output, it's promoted to a free label. - For any free label which is not present for the output, it's lowered to a dummy label. - Examples - '...ij, ...jk', where i and k are free labels, j is dummy. The output label string is '...ik' - 'ij -> i', where i is a free label and j is a dummy label. - '...ij, ...jk -> ...ijk', where i, j and k are all free labels. - '...ij, ...jk -> ij', an invalid equation since `...` is not present for the output. **The summation rule** The summation procedure can be outlined as follows, although the actual steps taken may vary significantly due to implementation specific optimization. - Step 1: preparation for broadcasting, that is, transposing and unsqueezing the input operands to have each resulting dimension identically labeled across all the input operands. - Step 2: broadcasting multiply all the resulting operands from step 1. - Step 3: reducing dummy labeled dimensions. - Step 4: transposing the result tensor to match the output labels. **On trace and diagonal** The trace and diagonal are planned yet unimplemented features. Args: equation (`str`): The summation terms using the Einstein summation notation. operands (`list|Tensor`): The input tensors over which to compute the Einstein summation. The number of operands should equal the number of input terms in the equation. Returns: result (`Tensor`), the result tensor. Examples: .. code-block:: python >>> import paddle >>> paddle.seed(102) >>> x = paddle.rand([4]) >>> y = paddle.rand([5]) >>> # sum >>> print(paddle.einsum('i->', x)) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 1.81225157) >>> # dot >>> print(paddle.einsum('i,i->', x, x)) Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True, 1.13530672) >>> # outer >>> print(paddle.einsum("i,j->ij", x, y)) Tensor(shape=[4, 5], dtype=float32, place=Place(cpu), stop_gradient=True, [[0.26443148, 0.05962684, 0.25360870, 0.21900642, 0.56994802], [0.20955276, 0.04725220, 0.20097610, 0.17355499, 0.45166403], [0.35836059, 0.08080698, 0.34369346, 0.29680005, 0.77240014], [0.00484230, 0.00109189, 0.00464411, 0.00401047, 0.01043695]]) >>> A = paddle.rand([2, 3, 2]) >>> B = paddle.rand([2, 2, 3]) >>> # transpose >>> print(paddle.einsum('ijk->kji', A)) Tensor(shape=[2, 3, 2], dtype=float32, place=Place(cpu), stop_gradient=True, [[[0.50882483, 0.56067896], [0.84598064, 0.36310029], [0.55289471, 0.33273944]], [[0.04836850, 0.73811269], [0.29769155, 0.28137168], [0.84636718, 0.67521429]]]) >>> # batch matrix multiplication >>> print(paddle.einsum('ijk, ikl->ijl', A,B)) Tensor(shape=[2, 3, 3], dtype=float32, place=Place(cpu), stop_gradient=True, [[[0.36321065, 0.42009076, 0.40849245], [0.74353045, 0.79189068, 0.81345987], [0.90488225, 0.79786193, 0.93451476]], [[0.12680580, 1.06945944, 0.79821426], [0.07774551, 0.55068684, 0.44512171], [0.08053084, 0.80583858, 0.56031936]]]) >>> # Ellipsis transpose >>> print(paddle.einsum('...jk->...kj', A)) Tensor(shape=[2, 2, 3], dtype=float32, place=Place(cpu), stop_gradient=True, [[[0.50882483, 0.84598064, 0.55289471], [0.04836850, 0.29769155, 0.84636718]], [[0.56067896, 0.36310029, 0.33273944], [0.73811269, 0.28137168, 0.67521429]]]) >>> # Ellipsis batch matrix multiplication >>> print(paddle.einsum('...jk, ...kl->...jl', A,B)) Tensor(shape=[2, 3, 3], dtype=float32, place=Place(cpu), stop_gradient=True, [[[0.36321065, 0.42009076, 0.40849245], [0.74353045, 0.79189068, 0.81345987], [0.90488225, 0.79786193, 0.93451476]], [[0.12680580, 1.06945944, 0.79821426], [0.07774551, 0.55068684, 0.44512171], [0.08053084, 0.80583858, 0.56031936]]]) rNFLAGS_new_einsum1z!At least one operand is expected.r(rr)rr*c3B# UHoRS5v M g7f)rN)r_)rVrMs r&rXeinsum..ns8Zwws||Zs)osrenvironrFrgrr+rr.r3r/rDr0rzrrhrvr rr)r-r1rrr.r9r2r;rdrerfrgr}rtrrresults r&rlrls9x 2::>>,c 233-H-- h-C 77777 ((b177=IC s8a<FFF<#a&TCc,J Sj%K LMJ 8Z88L,):)%Hf-h7h88h7G 'w D\\^F M8s>D; )r!r@r"rrr@)r!r@r1Sequence[Tensor]rz list[str])r9r@r: Sequence[str]r;rrr)rIr@rJr@rr2)r2rr9 str | Noner;rrz4tuple[str, list[list[int]], int, list[Tensor | int]])relist[list[int]]rdr@rkzSequence[list[int]]rz"tuple[list[int], list[list[bool]]])r^r@rbool)r^r@r"rrztuple[str, Tensor]) rr{r}rrr2rrrr)rr{rrrrrr)rr{rerrrrrrlist[list[bool]]rtr2rr2rr2rr2rr2rr)rr{rerrrrrrrrtr2rglist[Tensor | int]rrrr)rr2rztuple[list[int], list[int]])rr{r1rrrrr)r1rrerrtr2rrrgrrrrr{)rr@r9r@r1rrztuple[str, str, list[Tensor]])r-r@r1rrz(tuple[str, str, list[str], list[Tensor]])r-r@r1rr^rrz list[Shaped])r.r@rr@)r.r@r9rrztuple[str, str])r-r@r1rrr)r-r@r1rrz Tensor | None)= __future__rrKrFr@rPtypingrrnumpyrr\paddlerbase.data_feederrr base.frameworkr base.layer_helperr linalgr r manipulationrrrmathrrrcollections.abcrr__all__r'r3r>rRrhrvrxrzrrrrrrr{rr&r/r1rCr,rXrgr[rlrUr(r&rs# ,C3+%55 ( "J<2 )9< <2j<-<-$.<->A<-9<-~/ /'*/7J/'/d*&    &/ :>   W! 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