Vpf UddlmZddlmZmZddlZddlmZmZm Z ddl Z ddl m Z m Z mZddlmZddlmZddlmZdd lmZdd lmZdd lmZdd lmZdd lmZddlmZmZmZmZddlm Z m!Z!ddl"m#Z#ddl$m%Z%ddl&m'Z'ddl&m(Z(ddl&m)Z)ddl&m*Z+ddl&m,Z,ddl-m.Z.ddl/m0Z0ddl1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;ddlZ>m?Z?m@Z@mAZAmBZBejCeDe?ZEe>ZFdZGdZHdZIdZJdZKe e e4d ZLejMd!ZNed"ZOejPGd#d$e eOZQd%ZRejSd&ZTe ejMd'(d)ZUGd*d+ejVZWdtd2ZXe ejMd'(dud6ZYejZ[e0j\eWd7Z]d8Z^e^ej_e]<d9Z`e)jae]e`d:Zbebe'jce]<ejPGd;dZfd?Zgd@Zhe ejMd'(dAZiejSdBZjdvdCZkdvdDZlGdEdFejmZnendGZoe ejMd'(dwdHZpdIZqdJZrdKZsejtdLZud'eu_veuwereuxeseuen_ye)jaeue)jzerd'MdxdUZ{e{e'j|eu<dxdVZ}e}e(j~eu<e e}de(jeu<e,jeue'je(je'j<e)jae'je'jdWZe7GdXdYZdyd\Zdzd_Ze=d`ZdaZdbZd{ddZdeZdfZdgZejVdhZd'e_veweeeee'jce<e,jee)jaee)jzed'MejVdiZdjedk<d'e_vdlZewee)jaeeedmdedidndoZe eedpqZdrZejVdsZdS)|) annotations)CallableSequenceN)update_wrapperreducepartial)AnyGenericTypeVar)config)core)custom_api_util)custom_transpose)dtypes)effects) linear_util)traceback_util)stop_gradient_p SymbolicZeroZerozeros_like_aval)argnums_partialflatten_fun_nokwargs)raise_to_shaped)UnexpectedTracerError)ad)batching)mlir) partial_eval)xla not_mapped)lax) tree_flattentree_unflattentree_maptreedef_is_leaf treedef_tupleregister_pytree_node_class tree_leavestree_flatten_with_pathkeystrtreedef_children)cachesafe_zipsafe_map split_list Unhashableunzip2ct|trd}tj|j|i|}||jrtd|jS)NcdSNargskwargss [/var/www/html/nettyfy-visnx/env/lib/python3.11/site-packages/jax/_src/custom_derivatives.pyz!_resolve_kwargs..>s$z4keyword arguments could not be resolved to positions) isinstancerinspect signaturebindapply_defaultsr: TypeErrorr9)funr9r:bas r;_resolve_kwargsrF;spW' & &C"w"D3F33"Y J K KK 7Nr=c@tj||\}}}\||fSr6)petrace_to_jaxpr_dynamic)rDin_avalsjaxpr_constss r;_initial_style_jaxprrNFs'23AA%FB r=cNtjtj|Sr6)rH close_jaxprconvert_constvars_jaxpr)rKs r; _close_jaxprrRJs 2599 : ::r=c8ttj||Sr6)rr add_tangents)rLxxss r; _sum_tangentsrWMs Q ' ''r=c6ttj|Sr6)r&r from_valuerUs r;_zeros_like_pytreer[Ps $/1 % %%r=cbt|tjrtj|S|Sr6)r>r TracerrrArZs r;_stop_gradientr^Ss,4;   " "" Hr=c'Kt||}|ifV}t|\}}d|D}|||ffVdS)NcZg|](}tjtj|)Sr7r rget_aval.0rUs r; z)_flatten_fun_nokwargs..`s-HHH!t#DM!$4$455HHHr=)r%r$)in_tree args_flatpy_argsansans_flatans_tree ans_avalss r;_flatten_fun_nokwargsrm[se 7I . .'rk##C(((HHHxHHH)8Y'''''''r= ReturnValueceZdZUdZded<ded<dZded<d Zd ed < ddd Zej Z dddZ ddZ e jddZdS) custom_jvpaSet up a JAX-transformable function for a custom JVP rule definition. This class is meant to be used as a function decorator. Instances are callables that behave similarly to the underlying function to which the decorator was applied, except when a differentiation transformation (like :py:func:`jax.jvp` or :py:func:`jax.grad`) is applied, in which case a custom user-supplied JVP rule function is used instead of tracing into and performing automatic differentiation of the underlying function's implementation. There are two instance methods available for defining the custom JVP rule: :py:func:`~jax.custom_jvp.defjvp` for defining a *single* custom JVP rule for all the function's inputs, and for convenience :py:func:`~jax.custom_jvp.defjvps`, which wraps :py:func:`~jax.custom_jvp.defjvp`, and allows you to provide separate definitions for the partial derivatives of the function w.r.t. each of its arguments. For example:: @jax.custom_jvp def f(x, y): return jnp.sin(x) * y @f.defjvp def f_jvp(primals, tangents): x, y = primals x_dot, y_dot = tangents primal_out = f(x, y) tangent_out = jnp.cos(x) * x_dot * y + jnp.sin(x) * y_dot return primal_out, tangent_out For a more detailed introduction, see the tutorial_. .. _tutorial: https://jax.readthedocs.io/en/latest/notebooks/Custom_derivative_rules_for_Python_code.html Callable[..., ReturnValue]rDtuple[int, ...]nondiff_argnumsNz5Callable[..., tuple[ReturnValue, ReturnValue]] | NonejvpFboolsymbolic_zerosr7cBt||||_||_dSr6)rrDrsselfrDrss r;__init__zcustom_jvp.__init__s)4DH*Dr=.Callable[..., tuple[ReturnValue, ReturnValue]]returnc"||_||_|S)ahDefine a custom JVP rule for the function represented by this instance. Args: jvp: a Python callable representing the custom JVP rule. When there are no ``nondiff_argnums``, the ``jvp`` function should accept two arguments, where the first is a tuple of primal inputs and the second is a tuple of tangent inputs. The lengths of both tuples are equal to the number of parameters of the ``custom_jvp`` function. The ``jvp`` function should produce as output a pair where the first element is the primal output and the second element is the tangent output. Elements of the input and output tuples may be arrays or any nested tuples/lists/dicts thereof. symbolic_zeros: boolean, indicating whether the rule should be passed objects representing static symbolic zeros in its tangent argument in correspondence with unperturbed values; otherwise, only standard JAX types (e.g. array-likes) are passed. Setting this option to ``True`` allows a JVP rule to detect whether certain inputs are not involved in differentiation, but at the cost of needing special handling for these objects (which e.g. can't be passed into jax.numpy functions). Default ``False``. Returns: None. Examples: @jax.custom_jvp def f(x, y): return jnp.sin(x) * y @f.defjvp def f_jvp(primals, tangents): x, y = primals x_dot, y_dot = tangents primal_out = f(x, y) tangent_out = jnp.cos(x) * x_dot * y + jnp.sin(x) * y_dot return primal_out, tangent_out )rtrv)ryrtrvs r;defjvpzcustom_jvp.defjvpsRDH(D Jr=jvps!Callable[..., ReturnValue] | Nonecljrtdfd}|dS)aConvenience wrapper for defining JVPs for each argument separately. This convenience wrapper cannot be used together with ``nondiff_argnums``. Args: *jvps: a sequence of functions, one for each positional argument of the ``custom_jvp`` function. Each function takes as arguments the tangent value for the corresponding primal input, the primal output, and the primal inputs. See the example below. Returns: None. Examples: @jax.custom_jvp def f(x, y): return jnp.sin(x) * y f.defjvps(lambda x_dot, primal_out, x, y: jnp.cos(x) * x_dot * y, lambda y_dot, primal_out, x, y: jnp.sin(x) * y_dot) z/Can't use ``defjvps`` with ``nondiff_argnums``.ctfdt|D}ttg|R}|fS)Nc2g|]\}}|r ||gRnSr7r7)rdtrt primal_outprimalszeross r;rez3custom_jvp.defjvps..jvp..sK===$a;>H##a6g66665===r=)r[zipr&rW)rtangentsall_tangents_out tangent_outrrrrys` @@r;rtzcustom_jvp.defjvps..jvps~4>j ,,e======(+Hd(;(;===]JJ9IJJJk  $$r=N)rsrCr~)ryrrts`` r;defjvpszcustom_jvp.defjvpssY. I G H HH%%%%%% KKr=r9r r:rnct|jdt|j}|jsd|d}t |t|jdt|j}t |j||jrt|jtfdtDfdttD}ttj|j|d\}}fd|jD} ttj|j| } n4tj|j}}tj|j} t!|\} } t#|| \} }t%| ||| |\}}t'j| |g| Rd |ji}tj||\}\}}t/||S) N__name__z'No JVP defined for custom_jvp function z using defjvp.c3HK|]\}}|vrt|n|VdSr6)r^)rdirUrss r; z&custom_jvp.__call__..sR00q!)*_(<(<>!$$$!000000r=cg|]}|v| Sr7r7rdrrss r;rez'custom_jvp.__call__..s#NNNAQo5M5Ma5M5M5Mr=Frequire_static_args_hashablec g|] }| Sr7r7rdrr9s r;rez'custom_jvp.__call__..s;;;T!W;;;r=rv)getattrrDstrrtAttributeErrorrFrssettuple enumeraterangelenrlu wrap_init _add_argsr$rm _flatten_jvpcustom_jvp_call_prArvmerge_linear_auxr%)ryr9r: primal_namemsgjvp_name diff_argnumsf_dyn_args static_argsrtrgrfflat_fun out_type1flat_jvp out_type2out_flatrLout_treerss ` @r;__call__zcustom_jvp.__call__s)$(JDH >>K 8 Qk Q Q Qc 3  $(JDH >>H 48T6 2 2D  #D011o 0000(00000dNNNNs4yy!1!1NNNl$R\$(%;%;\4BGIIIlb(;;;;d&:;;;k bl48,,k : :cc\$(++T(b L " "c%h//Iw/G<<Hi&sK7'022Hi %hJ9JJJ595HJJH*9i@@A}! (H - --r=r7rDrqrsrrF)rtr{rvrur|r{)rrr9r r:r r|rn)r __module__ __qualname____doc____annotations__rtrvrzr forward_attr __getattr__r~rr api_boundaryrr7r=r;rprpgs##H"!!!""""?C#CCCC.35+++++ ,+%*+++++Z""""H......r=rpcPt|td|DS)Nc34K|]}t|VdSr6)r2rdargs r;rz_add_args.. s(CCZ__CCCCCCr=) _add_args_r)f extra_argss r;rr s) AuCC CCCCC D DDr=c/VKtd|D}||z}||fVVdS)Nc3$K|] }|jV dSr6)valrs r;rz_add_args_..s$33SW333333r=)r)rr9r:all_argss r;rr sI33 33333*4(       r=T) use_eq_storec'TKt|t|dzg\}}t||}t||}||fifV} t| tt frt| dkrd|d|d| d} t | | \} } t| \} }t| \}}d| D}||krd|d|d|d|d } t | |}n#tj $rd}YnwxYw|2|\}}t|d |D}t|d |D}||krfd|d|d |d t| ddd|dt| ddd }t |tttj||sed|d|d |dt| ddd|dt| dd }t |d| D}d|D}||krt|dkrR||c\}\}d} t | ||d} dt%||D}t | d|| |z||ffVdS)NzCustom JVP rule  for function zd must produce a pair (list or tuple of length two) representing primal and tangent outputs, but got .cZg|](}tjtj|)Sr7rarcs r;rez _flatten_jvp..!-NNNQ$&t}Q'7'788NNNr=z[ must produce primal and tangent outputs with equal container (pytree) structures, but got z and z respectively.c6g|]}|Sr7 str_shortrdas r;rez _flatten_jvp.., )N)N)NA!++--)N)N)Nr=c6g|]}|Sr7rrs r;rez _flatten_jvp..- )O)O)OA!++--)O)O)Or=z must produce a pair (list or tuple of length two) where the first element represents the primal output (equal in value to the output of the custom_jvp-decorated function z, and in particular of the same container/pytree structure), but instead the JVP rule output's first element had container/pytree structure: 'z) while the custom_jvp-decorated function , had output container/pytree structure: z, and in particular with leaves of the same shape/dtype), but instead the JVP rule output's first element had shapes/dtypes of: " had output shapes/dtypes of: cTg|]%}ttj|d&SF) weak_typerr rbrcs r;rez _flatten_jvp..Js?,,,&dmA&6&6%HHH,,,r=cg|]T}t|tur#ttj|dn|jUSr)typerrr rbavalstrip_weak_typerdrs r;rez _flatten_jvp..Lsf...q''55't}Q'7'75IIII;<6;Q;Q;S;S...r=zuCustom JVP rule must produce primal and tangent outputs with equal shapes and dtypes, but got {} and {} respectively.zaCustom JVP rule must produce primal and tangent outputs with equal shapes and dtypes, but got: {}c3K|]9\}}||k d|d|V:dS)z primal z for tangent Nr)rdav1av2s r;rz_flatten_jvp..Xs\RRc3cSjj Fcmmoo E ECMMOO E EFPjjjRRr= )r1rr%r>listrrCr$rStoreExceptionrreplaceallmapr typematchformatrrjoin)rrrfmaybe_out_typer9 primals_in tangents_in py_primals py_tangentspair_outrpy_primals_outpy_tangents_out primals_outr tangents_out out_tree2 primal_avals out_type_ out_tree_ primal_avals_ty_treety_tree_mprimal_avals_outtangent_avals_outrr disagreementss r;rrsW&tc$ii1n-=>>*kgz22*w 44+ ,b0 0 0( HtUm , ,H 0B0B >h > >k > >2: > > >C C..$,!./&~66+x(99, NN+NNN,  Kh K Kk K K"* K K1: K K KC C..!>##yy ,,,III,(I}h)N)N)N)N)NOOGi)O)O)O)O)OPPHH 8h 8 8k 8 8 8 8MM))#r22 8 87B 8 8MM))#r22 8 8 8a aLL s4><?? @ @  7h 7 7k 7 7 7 7MM))#r22 7 77B 7 7MM))#r22 7 7a aLL,,*,,,.. ,...*** !!'):nfsfsHc cjj#--//BB C CC5cRR.0ABBRRRm cjj=!9!9:: ; ;;l"X|$<<<<<<.jvp..s# 7 7 7T!WW $ 7 7 7r=c>g|]}t|tu|Sr7r4rs r;rez)lift_jvp..jvp..s(KKKatAwwl/J/J/J/J/Jr=cg|]I\}}|r3ttj|nt JSr7)rr rbat_least_vspacenext)rdpznz_out_tangents_s r;rez)lift_jvp..jvp..sa===15Lq!1!1!A!A!C!CDDD"#344===r=)divmodrr eval_jaxprr1iterrr8)rVnraggedrrr jvp_jaxpr jvp_consts out_zerosnonzero_tangentsout out_primalsnz_out_tangents out_tangentsr;r&r%s @r;rtzlift_jvp..jvps's2ww""IAv:a<("Qz\]]*;XG 7 7h 7 7 7E'6'>$Iz9KK8KKK /)Z M' Mr r]_tracerrdrUrs r;rez&process_env_traces..H>>>Q*Q "<"<>MQX^e%;%;%;%;%;r=c|jjSr6rLrrZs r;r<z$process_env_traces.. qx~r=key) maxrLmainwith_cur_sublevelrrr"appendr) primitiverrr9rtodorrir cur_todos ` r;r r sRx$ $ >>>>$>>>G 55 6 6 6cc JO - - / /E u & &D++E4EEND(KK  eDkkr=custom_jvp_callc~~~tj|j}|rtd||j|jfS)Nz'Effects not supported in `custom_jvp`: r"custom_derivatives_allowed_effects filter_not_inNotImplementedError out_avals)rLr$r&r%rvrJdisallowed_effectss r;_custom_jvp_call_typecheckrcsaAOOPZPbccH F2DFF H HH  z1 11r=c~~~tj|j}tj|j|j|j|j|g|Rd|ji\}}| ||S)Ndim_var_values) r _ir_constsrM jaxpr_subcompmodule_contextrK name_stack tokens_inreset_tokens_out) ctxr$r&r%rvr9rMrEtokenss r;!_custom_jvp_call_mlir_translationrnsz> ?:, - -&"3#5z7G#&>3=&M$(MMM9<9KMM+#vV *r=cH~tj|jd|j||Sr6)r backward_passrKrM)r+rKr9ctrLs r;_custom_jvp_call_transposerrs" %+tU\4 D DDr=cZeZdZdZ dddZejZ dddZe j ddZ dS) custom_vjpaSet up a JAX-transformable function for a custom VJP rule definition. This class is meant to be used as a function decorator. Instances are callables that behave similarly to the underlying function to which the decorator was applied, except when a reverse-mode differentiation transformation (like :py:func:`jax.grad`) is applied, in which case a custom user-supplied VJP rule function is used instead of tracing into and performing automatic differentiation of the underlying function's implementation. There is a single instance method, :py:func:`~jax.custom_vjp.defvjp`, which may be used to define the custom VJP rule. This decorator precludes the use of forward-mode automatic differentiation. For example:: @jax.custom_vjp def f(x, y): return jnp.sin(x) * y def f_fwd(x, y): return f(x, y), (jnp.cos(x), jnp.sin(x), y) def f_bwd(res, g): cos_x, sin_x, y = res return (cos_x * g * y, sin_x * g) f.defvjp(f_fwd, f_bwd) For a more detailed introduction, see the tutorial_. .. _tutorial: https://jax.readthedocs.io/en/latest/notebooks/Custom_derivative_rules_for_Python_code.html r7rDrqrsrrclt||||_||_d|_d|_d|_dSNF)rrDrsfwdbwdrvrxs r;rzzcustom_vjp.__init__s?4DH*D>BDH6:DHDr=Frw&Callable[..., tuple[ReturnValue, Any]]rxCallable[..., tuple[Any, ...]]rvrur|Nonec0||_||_||_dS)a Define a custom VJP rule for the function represented by this instance. Args: fwd: a Python callable representing the forward pass of the custom VJP rule. When there are no ``nondiff_argnums``, the ``fwd`` function has the same input signature as the underlying primal function. It should return as output a pair, where the first element represents the primal output and the second element represents any "residual" values to store from the forward pass for use on the backward pass by the function ``bwd``. Input arguments and elements of the output pair may be arrays or nested tuples/lists/dicts thereof. bwd: a Python callable representing the backward pass of the custom VJP rule. When there are no ``nondiff_argnums``, the ``bwd`` function takes two arguments, where the first is the "residual" values produced on the forward pass by ``fwd``, and the second is the output cotangent with the same structure as the primal function output. The output of ``bwd`` must be a tuple of length equal to the number of arguments of the primal function, and the tuple elements may be arrays or nested tuples/lists/dicts thereof so as to match the structure of the primal input arguments. symbolic_zeros: boolean, determining whether to indicate symbolic zeros to the ``fwd`` and ``bwd`` rules. Enabling this option allows custom derivative rules to detect when certain inputs, and when certain output cotangents, are not involved in differentiation. If ``True``: * ``fwd`` must accept, in place of each leaf value ``x`` in the pytree comprising an argument to the original function, an object (of type ``jax.custom_derivatives.CustomVJPPrimal``) with two attributes instead: ``value`` and ``perturbed``. The ``value`` field is the original primal argument, and ``perturbed`` is a boolean. The ``perturbed`` bit indicates whether the argument is involved in differentiation (i.e., if it is ``False``, then the corresponding Jacobian "column" is zero). * ``bwd`` will be passed objects representing static symbolic zeros in its cotangent argument in correspondence with unperturbed values; otherwise, only standard JAX types (e.g. array-likes) are passed. Setting this option to ``True`` allows these rules to detect whether certain inputs and outputs are not involved in differentiation, but at the cost of special handling. For instance: * The signature of ``fwd`` changes, and the objects it is passed cannot be output from the rule directly. * The ``bwd`` rule is passed objects that are not entirely array-like, and that cannot be passed to most ``jax.numpy`` functions. * Any custom pytree nodes involved in the primal function's arguments must accept, in their unflattening functions, the two-field record objects that are given as input leaves to the ``fwd`` rule. Default ``False``. Returns: None. Examples: @jax.custom_vjp def f(x, y): return jnp.sin(x) * y def f_fwd(x, y): return f(x, y), (jnp.cos(x), jnp.sin(x), y) def f_bwd(res, g): cos_x, sin_x, y = res return (cos_x * g * y, sin_x * g) f.defvjp(f_fwd, f_bwd) N)rwrxrv)ryrwrxrvs r;defvjpzcustom_vjp.defvjps!^DHDH(Dr=r9r r:rnct|jdt|j}|jr|jsd|d}t |t|jdt|j}t |j|tjj r9|j rtdt|j|j|jS|j r|j D]}t|t|j fdtt!D}t#t%j|j|d\}} fd|j D} t#t%j|j|d\} } t)t%j|j| } nMt%j|j} }t%j|jt%j|j} } t+| \}}d |D}t-||\}}t/| |j||||\}}t3| |||j}t7j|||g|R||jd }t%j||\} \}} t=||S) Nrz'No VJP defined for custom_vjp function z using defvjp.z2nondiff_argnums not implemented for new custom_vjpcg|]}|v| Sr7r7rs r;rez'custom_vjp.__call__..[s#OOOQa6N6Nq6N6N6Nr=Frc g|] }| Sr7r7rs r;rez'custom_vjp.__call__..^s===1tAw===r=cZg|](}tjtj|)Sr7rarcs r;rez'custom_vjp.__call__..fs-LLLQ$&t}Q'7'788LLLr= out_treesrv)rrDrrwrxrrFr %enable_custom_vjp_by_custom_transposevaluersr`custom_vjp_by_custom_transpose_check_for_tracersrrrrrrrr$rm _flatten_fwdrv _flatten_bwdrcustom_vjp_call_prArr%)ryr9r:rrfwd_namer dyn_argnumsrrrrwrLrxrgrfrJrout_typeflat_fwdrflat_bwdrrrss ` @r;rzcustom_vjp.__call__Js$(JDH >>K 8 48 Qk Q Q Qc 3  txS]];;H 48T6 2 2D 390 B! @BB B I +DHdh I I4 PP  B%BBA'9$q''B'B'B'Bd233OOOO%D "2"2OOO &r|DH'='={'+%QQQ H====(<===  dh!7!7d>CEEEQ TX.. <<|DH--tH<))2<+A+AS'11iLL)LLLh0W==h(d.A;)17HFFh c7Hi@@Mh"'(HL)2LL>G7;7JLLLh,XyAAa(A Hh / //r=Nrrr)rwryrxrzrvrur|r{r) rrrrrzrrrr}rrrr7r=r;rtrtsF35      ,+ %*Q)Q)Q)Q)Q)f$0$0$0$0$0$0r=rtc(eZdZUdZded<ded<dS)CustomVJPPrimalzHPrimal to a ``custom_vjp``'s forward rule when ``symbolic_zeros`` is setr rru perturbedN)rrrrrr7r=r;rrqs(PP ***/////r=rc(d}t||S)a Strips away perturbation information from forward rule arguments. This is a helper function for user with the ``symbolic_zeros`` option to the ``defvjp`` method of a ``custom_vjp``-decorated function. In ``symbolic_zeros`` mode, the custom forward rule receives arguments whose pytree leaves are records with a ``value`` attribute that carries the primal argument. This is a way to convert such argument trees back to their original form, replacing each such record with its carried value at each leaf. czt|turtdt||jS)Nzunexpected leaf type )rrrCr)leafs r;rz,custom_vjp_primal_tree_values..values8 Dzz(( :d4jj:: ; ;; :r=)r&)treers r;custom_vjp_primal_tree_valuesrws# %  r=ct|D]-}t|tjrd}t |.dS)NaFound a JAX Tracer object passed as an argument to a custom_vjp function in a position indicated by nondiff_argnums as non-differentiable. Tracers cannot be passed as non-differentiable arguments to custom_vjp functions; instead, nondiff_argnums should only be used for arguments that can't be or contain JAX tracers, e.g. function-valued arguments. In particular, array-valued arguments should typically not be indicated as nondiff_argnums.)r*r>r r]r)rUrrs r;rrsR!nn ' 'd$ $$'Nc "# & &&' ' 'r=c'|K|r-dt|ddd|dddD}n |ddd}t||}|ifV}t|ttfrt |dkr!d|d|d|d|d|d }t ||\} } t| \} } t| \} } d | D}|}n#tj $rd}YnwxYw|2|\}}t| d |D}t|d |D}|| krfd|d|d |dt| ddd|dt| ddd }t |tttj||sed|d|d |dt| ddd|dt| dd }t |g| | R| | ffVdS)Nc4g|]\}}t||Sr7)r)rdrUr:s r;rez _flatten_fwd..s& I I IdaOAq ! ! I I Ir=rrzCustom VJP fwd rule rz must produce a pair (list or tuple of length two) where the first element represents the primal output (equal to those of the custom_vjp-decorated function z) and the second element represents residuals (i.e. values stored from the forward pass for use on the backward pass), but instead of a pair the fwd rule z produced rcZg|](}tjtj|)Sr7rarcs r;rez _flatten_fwd..rr=c6g|]}|Sr7rrs r;rez _flatten_fwd..rr=c6g|]}|Sr7rrs r;rez _flatten_fwd..rr=z must produce a pair (list or tuple of length two) where the first element represents the primal output (equal to the output of the custom_vjp-decorated function z) and the second element represents residuals (i.e. values stored from the forward pass for use on the backward pass), but instead the fwd rule output's first element had container/pytree structure: rrz) while the custom_vjp-decorated function rz) and the second element represents residuals (i.e. values stored from the forward pass for use on the backward pass), but instead the fwd rule output's first element had shapes/dtypes of: r)rr%r>rrrrCr$rrrrrrr r)rvrrrfrr9rhrrrresrrres_treerrrrrrrs r;rrs? I Ic$sss)T!$Q$Z.H.H I I IDD !9D 7D ) )'B;  ( HtUm , ,H 0B0B M( M M+ M M-8 M M .6  M M BJ  M M MC C.. .#&~66+xs##-#xNN+NNN,!>##yy ,,,III,(I}h)N)N)N)N)NOOGi)O)O)O)O)OPPHH 8( 8 8+ 8 8 8 8MM))#r22 8 87B 8 8MM))#r22 8 8 8a aLL s4><?? @ @  7( 7 7+ 7 7 7 7MM))#r22 7 77B 7 7MM))#r22 7 7a aLL# x2222222s C##C76C7c'&K|\}}t||j|jzksJt||jg\}}t||}t||} || fifV} t | t r.appendsg\!__Q'((JyQ]$*,---- !z)*** Hr=c |duSr6r7rZs r;r<z_flatten_bwd..s dr=)is_leafa(Custom VJP bwd rule must produce an output with the same container (pytree) structure as the args tuple of the primal function, and in particular must produce a tuple of length equal to the number of arguments to the primal function, but got bwd output structure {} for primal input structure {}.zCustom VJP bwd rule produced a SymbolicZero with a shape/dtype that does not match the corresponding input tangent shape/dtype: at outputz" the SymbolicZero had shape/dtype z/ while the corresponding input had shape/dtype zG. Consider just returning a None here instead of a SymbolicZero object.z}Custom VJP bwd rule must produce an output with the same shape/dtypes as the args tuple of the primal function, but at outputz0 the bwd rule produced an output of shape/dtype z* corresponding to an input of shape/dtype r)rrr1r%r>rr-robjectr3r+ ValueErrorr&r$rCrrr7rWrrrr typecompatrr,rrb_temporary_dtype_exception_temporary_shape_exceptionr)rfrJrr9rrrcts_outpy_res py_cts_out py_cts_indummykeypathsrLrWin_tree2rresultskprrqa_rrs @@r;rrs y{{(H Th)H,?? ? ? ? ?D8#6"788,#w (C ( (&h00*Z(",,,) 4  !S^^s;KG;T;T7U7U%U%Ui  I $ 688*w/A"A B B%-e44Q788+(A+       = i ' '  VY/B/BCCCCC ===y))KAx 9C CJJx11 2 2<= 'x;77ib!R TzzQ!++---- nnT!++--..//// b\ ! ! _Q..00-" @ @!"::,,..78kkmm oo nnT"']]####oa//11r9J9J3J2KK-a44-a44>r >>.b11;;==>>./[[]] >>> oo nnR-----s '0EAFc(t|tjrwt|tjr]|j|jkoLt j|jtjp(t j|jtjj SdSrv) r>r ShapedArrayshaper issubdtypedtypeextendednpinexactrrs r;rrsx4#$$=B8H)I)I= Grx  <  rx 9 9;  qw (9 : := r=c$tjjSr6)r custom_vjp_disable_shape_checkrrs r;rrs  . 44r=c,eZdZUded<dZdZdZdS)CustomVJPCallPrimitivecore.Primitive initial_stylec Lttj|}tj|}t |||o|jd\}}t ||o|j|\}} t|j|} fd} ||||| | ||} tj || \} }| r-tj |ttj| S|\}}t|tj |ttj| S)NFc|Sr6r7)r9rxs r;r<z-CustomVJPCallPrimitive.bind..)s dr=r) rr r r r rprocess_env_traces_fwdrprocess_custom_vjp_callrrr_apply_bwd_transform)ryrDrwrxrrvr9rrrrbwd_rfstr bwd_transforms ` r;rAzCustomVJPCallPrimitive.bind!s/ t % %D#D))I- T90%99C1 9 ()55C)&--G # # # #D  , ,T3T77@.DrNr=c|jjSr6rPrZs r;r<z(process_env_traces_fwd..GrQr=rR) rTrLrUrVrr post_process_custom_vjp_call_fwdrWr) rrr9rrYbwd_transformsrrir rZ bwd_xforms ` r;rr>sRx$ $. %>>>>$>>>G 55 6 6 6cc JO - - / /E u & &D % F FtY W WD(IKK)$$$ % uT{{E.112222222r=cft|}|r||}||Sr6)rr()todosrx todos_lists r;rrRs=E{{* *..  3  C  *r=c0tj||Sr6)r r)) fun_jaxprr9rLs r;_custom_vjp_call_jaxpr_implrXs % 9 % %t ,,r=ctj|j}|rtd||j|jfS)Nz'Effects not supported in `custom_vjp`: r])rrL__rbs r;$_custom_vjp_call_jaxpr_abstract_evalr[sXAOOPYPabbH F2DFF H HH  i/ //r=custom_vjp_call_jaxpr)r.rcore.ClosedJaxprfwd_jaxpr_thunk/Callable[..., tuple[core.Jaxpr, Sequence[Any]]]rxrrvct||g\}} t||g\} } td| Drtjd| D} || \} }|\}}t j| |g| R}t||jg\}}d|D}ttj| } ttj | | } tj j g|| R|j|||d}ttj j ||}ttj||}||fS)Nc3BK|]}t|tuVdSr6rrrs r;rz-_custom_vjp_call_jaxpr_jvp..qs-11a 111111r=c:g|]}t|tuSr7rrs r;rez._custom_vjp_call_jaxpr_jvp..ss# 1 1 11477$  1 1 1r=cPg|]#}ttj|$Sr7rrcs r;rez._custom_vjp_call_jaxpr_jvp..xs*FFFQt}Q//00FFFr=)num_resrxrarv)r1anyrCustomVJPExceptionr r=rrinstantiate_zerosreplace_float0s custom_lin_prAr#tie_precast_to_float0)rrrrr%rxrrvrLr9 consts_dotargs_dotr fwd_jaxpr fwd_constsrres_and_primals_outrr avals_outrs r;_custom_vjp_call_jaxpr_jvprksv w - -'!T#Hzl;;*h11j11111"  ! !! 1 1 1 1 1%)/51)Z +!X :EEEE 3h6I5JKK#{FF+FFF) %x 0 0(#T8 4 4(%: : ::'2.:::,SY^[,??,R(+|DD, l ""r=c dt||D}d|D} t| |g\} tj|| d\}}d|D}gtjfd}dD}fd}tj| ||}tj|||||| | d}rd n|}||fS) Ncbg|],\}}|tur|dkrtj||dn|-Sr)r"rmoveaxis)rdrUrs r;rez/_custom_vjp_call_jaxpr_vmap..sS 1 1 1Q)*(;(;Q( Aq! $ $ $ 1 1 1r=c g|] }|tu Sr7r!)rdrs r;rez/_custom_vjp_call_jaxpr_vmap..s555#555r=Fc$g|] }|rdntSrr!rdbs r;rez/_custom_vjp_call_jaxpr_vmap..s!;;;!A%qq:;;;r=c tj|}tj|d \}} d|D|j|jfS)NFc$g|] }|rdntSrr!rs r;rezP_custom_vjp_call_jaxpr_vmap..batched_fwd_jaxpr_thunk..s!BBB1,aa*BBBr=)r ClosedJaxprr batch_jaxprrWrKrM) rrbatched_fwd_jaxpr out_batched args_batched axis_name axis_sizer main_type out_dims2spmd_axis_names r;batched_fwd_jaxpr_thunkz<_custom_vjp_call_jaxpr_vmap..batched_fwd_jaxpr_thunksv //5"9:I%-%99lE9n&&"{BBkBBBCCC  "$5$< <.s!CCC1,aa*CCCr=cdSrr7)r sr;r<z-_custom_vjp_call_jaxpr_vmap..s 1r=)rrrxr%rrvr) rr1rrrH_memoizebatch_custom_vjp_bwdcustom_vjp_call_jaxpr_prA)rr r r r9in_dimsrrr%rxrrv in_batchedrLbatched_fun_jaxprr out_dims1rfwd_args_batched fwd_out_dims batched_bwd batched_outsout_dimsr r s```` ` @@r;_custom_vjp_call_jaxpr_vmaprsu  1 1 w// 1 1 1$65W555*zJ<88/!\#+#7Jy.$$ [<;{;;;));==========;=DClCCC%%%%,- 9i/?+)- (-;yQQQ,' 5Yq\\I( x r=chtfd}fd}d}||||S)a Convenience function for defining custom VJP rules (aka custom gradients). While the canonical way to define custom VJP rules is via ``jax.custom_vjp``, the ``custom_gradient`` convenience wrapper follows TensorFlow's ``tf.custom_gradient`` API. The difference here is that ``custom_gradient`` can be used as a decorator on one function that returns both the primal value (representing the output of the mathematical function to be differentiated) and the VJP (gradient) function. See https://www.tensorflow.org/api_docs/python/tf/custom_gradient. If the mathematical function to be differentiated has Haskell-like signature ``a -> b``, then the Python callable ``fun`` should have the signature ``a -> (b, CT b --o CT a)`` where we use ``CT x`` to denote a cotangent type for ``x`` and the ``--o`` arrow to denote a linear function. See the example below. That is, ``fun`` should return a pair where the first element represents the value of the mathematical function to be differentiated and the second element is a function to be called on the backward pass of reverse-mode automatic differentiation (i.e. the "custom gradient" function). The function returned as the second element of the output of ``fun`` can close over intermediate values computed when evaluating the function to be differentiated. That is, use lexical closure to share work between the forward pass and the backward pass of reverse-mode automatic differentiation. However, it cannot perform Python control flow which depends on the values of the closed-over intermediate values or its cotangent arguments; if the function includes such control flow, an error is raised. Args: fun: a Python callable specifying both the mathematical function to be differentiated and its reverse-mode differentiation rule. It should return a pair consisting of an output value and a Python callable that represents the custom gradient function. Returns: A Python callable that accepts the same arguments as ``fun`` and returns the output value specified by the first element of ``fun``'s output pair. For example: >>> @jax.custom_gradient ... def f(x): ... return x ** 2, lambda g: (g * x,) ... >>> print(f(3.)) 9.0 >>> print(jax.grad(f)(3.)) 3.0 An example with a function on two arguments, so that the VJP function must return a tuple of length two: >>> @jax.custom_gradient ... def f(x, y): ... return x * y, lambda g: (g * y, g * x) ... >>> print(f(3., 4.)) 12.0 >>> print(jax.grad(f, argnums=(0, 1))(3., 4.)) (Array(4., dtype=float32, weak_type=True), Array(3., dtype=float32, weak_type=True)) c|i|\}}|Sr6r7)r9r:rirLrDs r; wrapped_funz$custom_gradient..wrapped_funs S$ !& ! !FC Jr=c |i|\}}t|f\}}ttj||\}}d|D}t j||\}} } \|t |||| fS)NcZg|](}tj|)Sr7r rbr7rcs r;rez0custom_gradient..fwd..s.FFFq!!1133FFFr=)r$rrrrHrI Residuals) r9r:rirulerjrrfrlrKrLrMrDs r;rwzcustom_gradient..fwdsT$V$$IC%sf--Hh(d););XFFMD'FFXFFFI4T9EEE1fb  %Hf== ==r=c|\}}}}t|f\}}||krt|d|tj||g|R}t ||}t |r|f}|S)Nz != )r$rCr r=r%r') rctsrKrfrrMcts_flatrrs r;rxzcustom_gradient..bwds'*$E7Hf&v..Hi9I.L.L.L.L$M$MMoeV7h777GWg..Gw g Nr=)rtr})rDr!rwrxs` r;custom_gradientr*soz:>>>>>S# r=c6eZdZdZdZdZedZdS)r%c>||_||_||_||_dSr6)rKrfrrM)ryrKrfrrMs r;rzzResiduals.__init__s"DJDLDMDKKKr=cPt|j|j|j|jfSr6)r>rKrfrrMrys r;__iter__zResiduals.__iter__s! T\4=$+F G GGr=c8|j|j|j|jffSr6)rMrKrfrr.s r;r$zResiduals.tree_flattens ;T\4=A AAr=c*|\}}}|||||Sr6r7)clsauxrMrKrfrs r;r%zResiduals.tree_unflattens$"E7H 3ugx 0 00r=N)rrrrzr/r$ classmethodr%r7r=r;r%r% s` HHHBBB11;111r=r%rDtuple[Callable, list[Any]]ct|\}}ttt|}tjjrt|||St|||S)a Closure conversion utility, for use with higher-order custom derivatives. To define custom derivatives such as with ``jax.custom_vjp(f)``, the target function ``f`` must take, as formal arguments, all values involved in differentiation. If ``f`` is a higher-order function, in that it accepts as an argument a Python function ``g``, then values stored away in ``g``'s closure will not be visible to the custom derivative rules, and attempts at AD involving these values will fail. One way around this is to convert the closure by extracting these values, and to pass them as explicit formal arguments across the custom derivative boundary. This utility carries out that conversion. More precisely, it closure-converts the function ``fun`` specialized to the types of the arguments given in ``example_args``. When we refer here to "values in the closure" of ``fun``, we do not mean the values that are captured by Python directly when ``fun`` is defined (e.g. the Python objects in ``fun.__closure__``, if the attribute exists). Rather, we mean values encountered during the execution of ``fun`` on ``example_args`` that determine its output. This may include, for instance, arrays captured transitively in Python closures, i.e. in the Python closure of functions called by ``fun``, the closures of the functions that they call, and so forth. The function ``fun`` must be a pure function. Example usage:: def minimize(objective_fn, x0): converted_fn, aux_args = closure_convert(objective_fn, x0) return _minimize(converted_fn, x0, *aux_args) @partial(custom_vjp, nondiff_argnums=(0,)) def _minimize(objective_fn, x0, *args): z = objective_fn(x0, *args) # ... find minimizer x_opt ... return x_opt def fwd(objective_fn, x0, *args): y = _minimize(objective_fn, x0, *args) return y, (y, args) def rev(objective_fn, res, g): y, args = res y_bar = g # ... custom reverse-mode AD ... return x0_bar, *args_bars _minimize.defvjp(fwd, rev) Args: fun: Python callable to be converted. Must be a pure function. example_args: Arrays, scalars, or (nested) standard Python containers (tuples, lists, dicts, namedtuples, i.e., pytrees) thereof, used to determine the types of the formal arguments to ``fun``. This type-specialized form of ``fun`` is the function that will be closure converted. Returns: A pair comprising (i) a Python callable, accepting the same arguments as ``fun`` followed by arguments corresponding to the values hoisted from its closure, and (ii) a list of values hoisted from the closure. ) r$rr abstractifyr check_tracer_leaksr_closure_convert_for_avals __wrapped__)rD example_args flat_argsrfrJs r;closure_convertr=sf|$L11)W 3{I.. / /( $> % 1 1#w I II %c7H = ==r=rUr ctj|}t|tjsdSt|tjrG|j}|tjupt|ddtj k St|tj s+td|DSdS)NFrc3:K|]\}}t|VdSr6)_maybe_perturbed)rdnameattrs r;rz#_maybe_perturbed..rs/FF*$%%FFFFFFr=T)r r r>r]rHDynamicJaxprTracerrr7abstract_tokenrrfloat0r JVPTracerr _contents)rUvspaces r;r@r@bs oa! At{ # #  5!R*++ V # # % %F$--@..&-? AA a & & FF FFF F FF 4r=c ttj|\} tj||\ }}\ t t |\\} t|  fd}||fS)Nct| z }t||g\}} |}tt|\}} |ksJt j |g|R}t |Sr6)rr1r$rr r=r%) args_hconstsnum_argsr9hoisted_constsrMrrrclosure_constsrfrKmerger%rs r; converted_funz1_closure_convert_for_avals..converted_funs<  :-H%lXJ??D. U>> 2 2F%eDkk22Hh h    uf8x888H (H - --r=)rrrrHrIpartition_listr@r) rDrfrJr! out_pvalsrMrMrPrNrKrOr%rs ` @@@@@r;r9r9vs.r|C/@/@'JJ+x!#!:;!Q!Q%FB XZZ(,:;KV,T,T)">>E>""*..........  &&r=c@ggffd|Dfd}|fS)Ncng|]1}||p |2Sr7)rW)rdeltchoicerEs r;rez"partition_list..sA F F F33vvc{{  " "3 ' ' 666#;; F F Fr=cdt|t|cfdDS)Nc6g|]}t|rnSr7)r8)rdsndi1i2s r;rez1partition_list..merge..s* 5 5 5Ds" # # 5 5 5r=)r>)l1l2rZr[whichs @@r;rOzpartition_list..merges9 "XXtBxxFB 5 5 5 5 5u 5 5 55r=r7)rVlstrOrEr^s` @@r;rQrQsO B# F F F F F# F F F%66666 er=cNtjtj|Sr6rarZs r;r7r7s dmA.. / //r= fun_transposec rt|\}}t|\}}t||f}ttj||\} } t t |} t t |} t| g| | R\} }t| } t tj | j }t|| f}ttj||\}}t|g| |R\}}t|}||krtd|d|dtjg||||R| |t|t|t|d}t!| |S)ak Call a linear function, with a custom implementation for its transpose. The `Haskell-like type signatures`_ of ``fun`` and ``fun_transpose`` are: .. code-block:: haskell fun :: r -> a -o b fun_transpose :: r -> b -o a where the ``-o`` arrow indicates a linear function, ``r`` is the residual input type and ``a`` is the linear input type. The functions ``fun`` and ``fun_transpose`` are coupled as transposes of one another. Specifically, the transpose of a ``linear_call`` primitive is another ``linear_call`` to ``fun_transpose``, with ``fun`` as its custom transposition. For example: >>> def f(r, x): ... return x / r >>> def t(r, t): ... return t / r >>> def div_add(x, denom): ... return x + linear_call(f, t, denom, x) >>> def transpose(f, x_example): ... def transposed(y): ... x, = jax.linear_transpose(f, x_example)(y) ... return x ... return transposed >>> div_add(9., 3.) Array(12., dtype=float32, weak_type=True) >>> transpose(partial(div_add, denom=3.), 1.)(18.) # custom Array(24., dtype=float32, weak_type=True) >>> transpose(lambda x: x + x / 3., 1.)(18.) # reference Array(24., dtype=float32, weak_type=True) The above definition of ``f`` illustrates the purpose of a residual argument: division is linear in one of its inputs (the dividend ``x``) but not the other (the divisor ``r``). As another example: >>> def custom_id(x): ... def f(_, x): return x ... def t(_, t): return 7. ... return linear_call(f, t, (), x) >>> custom_id(1.) 1.0 >>> transpose(custom_id, 1.)(1.) 7.0 >>> transpose(transpose(custom_id, 1.), 1.)(1.) 1.0 >>> transpose(transpose(transpose(custom_id, 1.), 1.), 1.)(1.) 7.0 Args: fun: a Python callable specifying a linear function. It should take two arguments: one of "residual" inputs (type ``r``), i.e. inputs in which the function is not necessarily linear, and one of "linear" inputs (type ``a``). It should return output whose components are linear in the linear input (type ``b``). fun_transpose: a Python callable specifying a structurally linear function that is the transpose of ``fun`` with respect to its linear inputs. Its first argument is the same residual inputs (``r``) as ``fun``. Its second argument is of type ``b``. Finally, its output is of type ``a`` and each of its component are linear in its second argument (the ``b`` inputs). residual_args: Argument in which ``fun`` and ``fun_transpose`` are not necessarily linear. Not involved in transposition. linear_args: Argument in which ``fun`` and ``fun_transpose`` are linear and with respect to which the two are transposes. Returns: The call result, i.e. ``fun(residual_args, linear_args)``. .. _Haskell-like type signatures: https://wiki.haskell.org/Type_signature zYtranspose output pytree structure must match that of linear inputs, got output structure z and input structure rcallee transposenum_callee_constsnum_transpose_constsr)r$r(rrrrr7rNrRr rrarC linear_call_prArr%)rDra residual_args linear_args operands_resr operands_linlin_tree f_in_treerr res_avals lin_avalsf_jaxprf_constsra t_in_treer t_out_treet_jaxprt_constsrEs r; linear_callrwsl( 66,' 44,Xx011)$R\#%6%6 BB+!X+|,,)+|,,)*1.F .FI.F.FGG'8  ! !'$&(9::)Xxxzz233)&r|M'B'BINN-!Z*1.F .FI.F.FGG'8  ! !'Z\\X  + *  + +' + + + , ,,  6H 6x 6, 6 6 6")%,-0]]03H #&|#4#4  6 6 6#  C ( ((r=cl~t||||g\}}}} tj|jdg||| RS)Nr7)r1r r=rK) rdrerfrgrr9rMrLrkrls r;_linear_call_implrysS*4  4g >+@+@'&!\< r QF Q\ QL Q Q QQr=c t||||g\}}} } t|j||g\} } } td| DsJtd| DsJdt|| D}t jg||| |R||t |t |t | d} dg||z|zz| zS)Nc3>K|]}tj|VdSr6ris_undefined_primalrcs r;rz._linear_call_transpose_rule..s- A AqR #A & & A A A A A Ar=c3@K|]}tj| VdSr6r|rcs r;rz._linear_call_transpose_rule..s0 A Aq'** * A A A A A Ar=cbg|],\}}t|turt|n|-Sr7)rrr)rdrqrs r;rez/_linear_call_transpose_rule..!sI + + + R $Bxx4//   R + + +r=rc)r1rJrrrhrAr)r(rdrerfrgrr9rrrvrkrlrL cts_avalsrs r;_linear_call_transpose_rulersA4>  4g >4@4@0(HlL/9;;/!Q  A AL A A A A AAAA A AL A A A A AAAA + +#y)) + + +#   : :8 :l :S : :&/)/14X47MM'*<'8'8  : : :' $';;gE F PPr=cLttj|djS)Nrd)rr rrar8s r;_linear_call_abstract_evalr-s T !6(#3#= > >>r=rw unreachabler unreachable_pc~||r6r7)raexc_typemessagerLs r;unreachable_implr>sr=c|Sr6r7)rarLrs r;r<r<LsIr=rarrc|ttj|}t|\}}t|\}}t j||||d}t ||S)aFail when evaluated concretely (but allow for staging). This function allows one to assert an impossibility of evaluation. It can be used to guarantee that evaluation does not "reach" a certain point in the sense that it does not execute, but it can nonetheless be staged out by JAX without error. Args: *args: The arbitrary pytree of arguments to the function. out_avals: Optional specification of the output types of this function invocation from the point of view of staging. If ``None``, these are chosen as equal to types of input arguments. exc_type: Optional constructor for the Python exception raised if evaluated. message: Optional string message for the Python exception raised if evaluated. Nr)r&r rbr$rrAr%) rarrr9rgrfout_avals_flatrrEs r;rrNso(--I#D)))W))44.(I$,g ? ? ?# # & &&r=zAcan't apply forward-mode autodiff (jvp) to a custom_vjp function.)rrcNt|}|jfd}|S)Nc|\}}td|}ttt|}||||||fS)NcNtj|Sr6r$)os r;r<z=custom_vjp_by_custom_transpose..jvp..xst}Q'7'7'G'G'I'Ir=)ra)r&rr disallow_jvp def_transpose)rrr residuals tan_out_typestan_fnrxrws r;rtz+custom_vjp_by_custom_transpose..jvpuslc7mOD)II4PPM glmLLL M MF   y(;; ;;r=)rpr~)rDrwrxrts `` r;rrrs@3#:<<<<<:< *r=custom_jvp_call_jaxpr)r%r/r&rr|r0)rr/rru)r|ru)rr/) rrrrr%r/rxrrrrvru)rDrr|r5)rUr r|ru)rDrrar) __future__rcollections.abcrr dataclasses functoolsrrrr?typingr r r jax._srcr r rjax._src.custom_transposerrrrrrjax._src.ad_utilrrrrjax._src.api_utilrr jax._src.corerjax._src.errorsrjax._src.interpretersrrrrrHr jax._src.interpreters.batchingr" jax._src.laxr#jax._src.tree_utilr$r%r&r'r(r)r*r+r,r- jax._src.utilr.r/r0r1r2r3register_exclusion__file__rrrFrNrRrWr[r^transformation_with_auxrmrnregister_custom_decorator_typerprtransformationrr Primitiver r*r r^add_typeInOutFeedEffectrrccustom_typechecksrnregister_loweringrrprimitive_transposesrt dataclassrrrrrrr CallPrimitiverrrrrr AxisPrimitiverr.def_impldef_effectful_abstract_evalr lower_funrprimitive_jvpsrspmd_axis_primitive_batchersaxis_primitive_batchers register_initial_style_primitiveraise_custom_vjp_error_on_jvpprimitive_batchersrr*r%r=r@r9rQr7rwryrrrhdef_abstract_evalrrrrCrrrcustom_jvp_call_jaxpr_pr7r=r;rs #""""""........5555555555(((((((((($$$$$$666666&&&&&&######::::::::::::CCCCCCCC))))))111111$$$$$$******&&&&&&444444%%%%%%555555################"!(+++   ;;;(((&&& (   (((gm$$ /`.`.`.`.`.%`.`.0/`.DEEE!!!   #$777H=H=87H=T"""""T^"""@    &  #$77787"*33C4GHHH**+<==222-G()   (*KLLL EEE.H)* /f0f0f0f0f0%f0f00/f0P  $ ' ' '  #$77793938793v>>>B5555CCCCCT/CCC<+*+<== #$777333873&   ---000-$,-DEE+/( !<===334XYYY'>$.$181818999####0.H)*$ $ $ $ L  %&=>C>C>C>J('' '&000 u)u)u)u)nRRRQQQ.???}-- !%  ()))  :;;;)D &$$]333}ndn'.'.'./// !/} = = ====!%  '((( }&6777 E EFFF!% %'''''<w  OQQQ    )$.)@AAr=