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docs update
2024-01-17 17:15:29 -08:00
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sig-object<63>eh%]<5D>h']<5D>h)]<5D><>module<6C><65>mlx.nn<6E>jh<06>fullname<6D>h<EFBFBD>uh+hCh<1D>{/Users/awnihannun/repos/mlx/python/mlx/nn/layers/positional_encoding.py:docstring of mlx.nn.layers.positional_encoding.RoPE<50>hKhh@hhubh<00> desc_content<6E><74><EFBFBD>)<29><>}<7D>(hhh]<5D>(h <09> paragraph<70><68><EFBFBD>)<29><>}<7D>(h<05>*Implements the rotary positional encoding.<2E>h]<5D>h<16>*Implements the rotary positional encoding.<2E><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj"hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j h<1D>{/Users/awnihannun/repos/mlx/python/mlx/nn/layers/positional_encoding.py:docstring of mlx.nn.layers.positional_encoding.RoPE<50>hKhjhhubj!)<29><>}<7D>(h<05><>The traditional implementation rotates consecutive pairs of elements in the
feature dimension while the default implementation rotates pairs with
stride half the feature dimensions for efficiency.<2E>h]<5D>h<16><>The traditional implementation rotates consecutive pairs of elements in the
feature dimension while the default implementation rotates pairs with
stride half the feature dimensions for efficiency.<2E><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj1hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j hj0hKhjhhubj!)<29><>}<7D>(h<05>yFor more details see `RoFormer: Enhanced Transformer with Rotary Position
Embedding <https://arxiv.org/abs/2104.09864>`_.<2E>h]<5D>(h<16>For more details see <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj?hhhNhNubh <09> reference<63><65><EFBFBD>)<29><>}<7D>(h<05>c`RoFormer: Enhanced Transformer with Rotary Position
Embedding <https://arxiv.org/abs/2104.09864>`_<>h]<5D>h<16>=RoFormer: Enhanced Transformer with Rotary Position
Embedding<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjIhhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>name<6D><65>=RoFormer: Enhanced Transformer with Rotary Position Embedding<6E><67>refuri<72><69> https://arxiv.org/abs/2104.09864<EFBFBD>uh+jGhj?ubh <09>target<65><74><EFBFBD>)<29><>}<7D>(h<05># <https://arxiv.org/abs/2104.09864><3E>h]<5D>h}<7D>(h!]<5D><><roformer-enhanced-transformer-with-rotary-position-embedding<6E>ah#]<5D>h%]<5D><>=roformer: enhanced transformer with rotary position embedding<6E>ah']<5D>h)]<5D><>refuri<72>jZuh+j[<00>
referenced<EFBFBD>Khj?ubh<16>.<2E><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj?hhhNhNubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j hj0hKhjhhubh <09>
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Parameters<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jhj|hhlhKubh <09>
field_body<EFBFBD><EFBFBD><EFBFBD>)<29><>}<7D>(hhh]<5D>h <09> bullet_list<73><74><EFBFBD>)<29><>}<7D>(hhh]<5D>(h <09> list_item<65><6D><EFBFBD>)<29><>}<7D>(hhh]<5D>j!)<29><>}<7D>(h<05><>dims (intint) -- The feature dimensions to be rotated. If the input feature
is larger than dims then the rest is left unchanged.<2E>h]<5D>(h<00>literal_strong<6E><67><EFBFBD>)<29><>}<7D>(h<05>dims<6D>h]<5D>h<16>dims<6D><73><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubh<16> (<28><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubh<62>)<29><>}<7D>(hhh]<5D>(h<>)<29><>}<7D>(h<05>int<6E>h]<5D>h<00>literal_emphasis<69><73><EFBFBD>)<29><>}<7D>(h<05>int<6E>h]<5D>h<16>int<6E><74><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> condition<6F>h<EFBFBD>uh+h<>hj<>ubh<62>)<29><>}<7D>(h<05>int<6E>h]<5D>j<EFBFBD>)<29><>}<7D>(h<05>int<6E>h]<5D>h<16>int<6E><74><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> condition<6F>h<EFBFBD>uh+h<>hj<>ubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> refdomain<69><6E>py<70><79> refexplicit<69><74><EFBFBD>reftype<70>j<00> reftarget<65>j<EFBFBD><00> refspecific<69><63><EFBFBD> py:module<6C>j<00>py:class<73>h<EFBFBD>uh+h<>hj<>ubh<16>)<29><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubh<16> – <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubh<16>oThe feature dimensions to be rotated. If the input feature
is larger than dims then the rest is left unchanged.<2E><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j hj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubj<62>)<29><>}<7D>(hhh]<5D>j!)<29><>}<7D>(h<05><>traditional (boolbool, optionaloptional) -- If set to True choose the traditional
implementation which is slightly less efficient. Default: False.<2E>h]<5D>(j<>)<29><>}<7D>(h<05> traditional<61>h]<5D>h<16> traditional<61><6C><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjhhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hjubh<16> (<28><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjhhhNhNubh<62>)<29><>}<7D>(hhh]<5D>(h<>)<29><>}<7D>(h<05>bool<6F>h]<5D>j<EFBFBD>)<29><>}<7D>(h<05>bool<6F>h]<5D>h<16>bool<6F><6C><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj3hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj/ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> condition<6F>h<EFBFBD>uh+h<>hj,ubh<62>)<29><>}<7D>(h<05>bool<6F>h]<5D>j<EFBFBD>)<29><>}<7D>(h<05>bool<6F>h]<5D>h<16>bool<6F><6C><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjLhhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hjHubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> condition<6F>h<EFBFBD>uh+h<>hj,ubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> refdomain<69>j<EFBFBD><00> refexplicit<69><74><EFBFBD>reftype<70>j<00> reftarget<65>jNj<><00>j<EFBFBD>jj<>h<>uh+h<>hjubj<62>)<29><>}<7D>(h<05>, <20>h]<5D>h<16>, <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjkhhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hjubh<62>)<29><>}<7D>(hhh]<5D>(h<>)<29><>}<7D>(h<05>optional<61>h]<5D>j<EFBFBD>)<29><>}<7D>(h<05>optional<61>h]<5D>h<16>optional<61><6C><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj|ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> condition<6F>h<EFBFBD>uh+h<>hjyubh<62>)<29><>}<7D>(h<05>optional<61>h]<5D>j<EFBFBD>)<29><>}<7D>(h<05>optional<61>h]<5D>h<16>optional<61><6C><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> condition<6F>h<EFBFBD>uh+h<>hjyubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> refdomain<69>j<EFBFBD><00> refexplicit<69><74><EFBFBD>reftype<70>j<00> reftarget<65>j<EFBFBD>j<><00>j<EFBFBD>jj<>h<>uh+h<>hjubh<16>)<29><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjhhhNhNubh<16> – <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjhhhNhNubh<16>`If set to True choose the traditional
implementation which is slightly less efficient. Default: <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjhhhNhNubh <09>literal<61><6C><EFBFBD>)<29><>}<7D>(h<05> ``False``<60>h]<5D>h<16>False<73><65><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hjhhhNhNubh<16>.<2E><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjhhhNhNubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j hjubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubj<62>)<29><>}<7D>(hhh]<5D>j!)<29><>}<7D>(h<05><>base (floatfloat, optionaloptional) -- The base used to compute angular frequency for
each dimension in the positional encodings. Default: 10000.<2E>h]<5D>(j<>)<29><>}<7D>(h<05>base<73>h]<5D>h<16>base<73><65><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubh<16> (<28><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubh<62>)<29><>}<7D>(hhh]<5D>(h<>)<29><>}<7D>(h<05>float<61>h]<5D>j<EFBFBD>)<29><>}<7D>(h<05>float<61>h]<5D>h<16>float<61><74><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjhhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hjubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> condition<6F>h<EFBFBD>uh+h<>hj<>ubh<62>)<29><>}<7D>(h<05>float<61>h]<5D>j<EFBFBD>)<29><>}<7D>(h<05>float<61>h]<5D>h<16>float<61><74><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjhhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hjubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> condition<6F>h<EFBFBD>uh+h<>hj<>ubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> refdomain<69>j<EFBFBD><00> refexplicit<69><74><EFBFBD>reftype<70>j<00> reftarget<65>jj<><00>j<EFBFBD>jj<>h<>uh+h<>hj<>ubj<62>)<29><>}<7D>(h<05>, <20>h]<5D>h<16>, <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubh<62>)<29><>}<7D>(hhh]<5D>(h<>)<29><>}<7D>(h<05>optional<61>h]<5D>j<EFBFBD>)<29><>}<7D>(h<05>optional<61>h]<5D>h<16>optional<61><6C><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjQhhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hjMubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> condition<6F>h<EFBFBD>uh+h<>hjJubh<62>)<29><>}<7D>(h<05>optional<61>h]<5D>j<EFBFBD>)<29><>}<7D>(h<05>optional<61>h]<5D>h<16>optional<61><6C><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjjhhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hjfubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> condition<6F>h<EFBFBD>uh+h<>hjJubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> refdomain<69>j<EFBFBD><00> refexplicit<69><74><EFBFBD>reftype<70>j<00> reftarget<65>jlj<><00>j<EFBFBD>jj<>h<>uh+h<>hj<>ubh<16>)<29><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubh<16> – <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubh<16>dThe base used to compute angular frequency for
each dimension in the positional encodings. Default: <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubj<62>)<29><>}<7D>(h<05> ``10000``<60>h]<5D>h<16>10000<30><30><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>hhhNhNubh<16>.<2E><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j hj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubj<62>)<29><>}<7D>(hhh]<5D>j!)<29><>}<7D>(h<05>\scale (floatfloat, optionaloptional) -- The scale used to scale the positions. Default: 1.0.<2E>h]<5D>(j<>)<29><>}<7D>(h<05>scale<6C>h]<5D>h<16>scale<6C><65><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubh<16> (<28><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubh<62>)<29><>}<7D>(hhh]<5D>(h<>)<29><>}<7D>(h<05>float<61>h]<5D>j<EFBFBD>)<29><>}<7D>(h<05>float<61>h]<5D>h<16>float<61><74><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> condition<6F>h<EFBFBD>uh+h<>hj<>ubh<62>)<29><>}<7D>(h<05>float<61>h]<5D>j<EFBFBD>)<29><>}<7D>(h<05>float<61>h]<5D>h<16>float<61><74><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> condition<6F>h<EFBFBD>uh+h<>hj<>ubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> refdomain<69>j<EFBFBD><00> refexplicit<69><74><EFBFBD>reftype<70>j<00> reftarget<65>j<EFBFBD>j<><00>j<EFBFBD>jj<>h<>uh+h<>hj<>ubj<62>)<29><>}<7D>(h<05>, <20>h]<5D>h<16>, <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubh<62>)<29><>}<7D>(hhh]<5D>(h<>)<29><>}<7D>(h<05>optional<61>h]<5D>j<EFBFBD>)<29><>}<7D>(h<05>optional<61>h]<5D>h<16>optional<61><6C><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hjubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> condition<6F>h<EFBFBD>uh+h<>hjubh<62>)<29><>}<7D>(h<05>optional<61>h]<5D>j<EFBFBD>)<29><>}<7D>(h<05>optional<61>h]<5D>h<16>optional<61><6C><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj9hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj5ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> condition<6F>h<EFBFBD>uh+h<>hjubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> refdomain<69>j<EFBFBD><00> refexplicit<69><74><EFBFBD>reftype<70>j<00> reftarget<65>j;j<><00>j<EFBFBD>jj<>h<>uh+h<>hj<>ubh<16>)<29><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubh<16> – <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubh<16>0The scale used to scale the positions. Default: <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubj<62>)<29><>}<7D>(h<05>``1.0``<60>h]<5D>h<16>1.0<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjdhhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>hhhNhNubh<16>.<2E><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j hj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj|ubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jzhjwubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+juhjhhhNhNubh.)<29><>}<7D>(hhh]<5D>h}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>entries<65>]<5D>(h:<3A>*_cos_sin_theta_key (mlx.nn.RoPE attribute)<29><>mlx.nn.RoPE._cos_sin_theta_key<65>hNt<4E>auh+h-hjhhhNhNubh?)<29><>}<7D>(hhh]<5D>(hD)<29><>}<7D>(h<05>_cos_sin_theta_key<65>h]<5D>h<EFBFBD>)<29><>}<7D>(hj<>h]<5D>h<16>_cos_sin_theta_key<65><79><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>(h<>h<EFBFBD>eh%]<5D>h']<5D>h)]<5D>hjhkuh+hhj<>hhhj0hKubah}<7D>(h!]<5D>j<EFBFBD>ah#]<5D>(jjeh%]<5D>h']<5D>h)]<5D>jjjh<>j<00>RoPE._cos_sin_theta_key<65>uh+hChj0hKhj<>hhubj)<29><>}<7D>(hhh]<5D>(j!)<29><>}<7D>(h<05>6Cached key for the precomputed cosine and sine values.<2E>h]<5D>h<16>6Cached key for the precomputed cosine and sine values.<2E><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j hj0hKhj<>hhubjv)<29><>}<7D>(hhh]<5D>j{)<29><>}<7D>(hhh]<5D>(j<>)<29><>}<7D>(h<05>type<70>h]<5D>h<16>Type<70><65><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jhj<>hj0hKubj<62>)<29><>}<7D>(h<05>tuple<6C>h]<5D>j!)<29><>}<7D>(hj<>h]<5D>h<EFBFBD>)<29><>}<7D>(hhh]<5D>(h<>)<29><>}<7D>(h<05>tuple<6C>h]<5D>h <09>emphasis<69><73><EFBFBD>)<29><>}<7D>(h<05>tuple<6C>h]<5D>h<16>tuple<6C><65><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> condition<6F>h<EFBFBD>uh+h<>hj<>ubh<62>)<29><>}<7D>(h<05>tuple<6C>h]<5D>h<16>tuple<6C><65><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> condition<6F>h<EFBFBD>uh+h<>hj<>ubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><> refdomain<69><6E>py<70><79> refexplicit<69><74><EFBFBD>reftype<70>j<00> reftarget<65><74>tuple<6C>j<EFBFBD><00>j<EFBFBD>jj<>h<>uh+h<>hj<>hhhNhNubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j hj0hKhj<>ubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+j<>hj<>ubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jzhj0hKhj<>hhubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+juhj<>hhhNhNubeh}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D>uh+jhj<>hhhj0hKubeh}<7D>(h!]<5D>h#]<5D>(j#<00> attribute<74>eh%]<5D>h']<5D>h)]<5D><>domain<69>j#<00>objtype<70>jI<00>desctype<70>jI<00>noindex<65><78>uh+h>hhhjhNhNubh.)<29><>}<7D>(hhh]<5D>h}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>entries<65>]<5D>(h:<3A>,_cos_sin_th
hhhhhh,hKubah}<7D>(h!]<5D>h#]<5D>h%]<5D>h']<5D>h)]<5D><>source<63>h,uh+h<01>current_source<63>N<EFBFBD> current_line<6E>N<EFBFBD>settings<67><73>docutils.frontend<6E><64>Values<65><73><EFBFBD>)<29><>}<7D>(hN<> generator<6F>N<EFBFBD> datestamp<6D>N<EFBFBD> source_link<6E>N<EFBFBD>
source_url<EFBFBD>N<EFBFBD> toc_backlinks<6B><73>entry<72><79>footnote_backlinks<6B>K<01> sectnum_xform<72>K<01>strip_comments<74>N<EFBFBD>strip_elements_with_classes<65>N<EFBFBD> strip_classes<65>N<EFBFBD> report_level<65>K<02>
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