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refdomainjUreftypejW reftargetfloat refspecific py:moduleopengen.constraints.ball_infpy:classNuh+jEhjubah}(h!]h#]hah%]h']h)]uh+hhjsubh)}(h h]h }(hhhjhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhjsubh)}(h=h]h=}(hhhjhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhjsubh)}(h h]h }(hhhjhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhjsubh)}(h1.0h]h1.0}(hhhjhhhNhNubah}(h!]h#]jah%]h']h)]support_smartquotesuh+hhjsubeh}(h!]h#]h%]h']h)]hhuh+hhj:ubeh}(h!]h#]h%]h']h)]hhuh+hhjhhhjhKubeh}(h!]jah#](jjeh%]h']h)]jopengen.constraints.ball_infjWhjj.jj j.jj.uh+h|hjhKhjhhubj)}(hhh](j)}(h=Bases: :py:class:`~opengen.constraints.constraint.Constraint`h](hBases: }(hBases: hjhhhNhNubjF)}(h6:py:class:`~opengen.constraints.constraint.Constraint`h]j)}(hjh]h Constraint}(hhhjhhhNhNubah}(h!]h#](jpypy-classeh%]h']h)]uh+jhjubah}(h!]h#]h%]h']h)]refdocj refdomainj'reftypeclass refexplicitrefwarnjj jj.j)opengen.constraints.constraint.Constraintuh+jEh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/ball_inf.py:docstring of opengen.constraints.ball_infhKhjubeh}(h!]h#]h%]h']h)]uh+jh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/ball_inf.py:docstring of opengen.constraints.ball_inf.BallInfhKhj hhubj)}(h5Norm-ball of norm infinity translated by given vectorh]h5Norm-ball of norm infinity translated by given vector}(hjChjAhhhNhNubah}(h!]h#]h%]h']h)]uh+jh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/ball_inf.py:docstring of opengen.constraints.ball_inf.BallInfhKhj hhubj)}(h-Centered inf-ball around given point, that ish]h-Centered inf-ball around given point, that is}(hjRhjPhhhNhNubah}(h!]h#]h%]h']h)]uh+jhjOhKhj hhubj)}(h]:math:`\mathcal{B}_{\infty}(x_0, r) = \{x\in{\rm I\!R}^n {}:{} \|x - x_0\|_{\infty} \leq 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refdomainpy refexplicitreftypejW reftargetfloatj<jjjj.uh+jEhjubah}(h!]h#]h%]h']h)]uh+jhjubah}(h!]h#]h%]h']h)]uh+jShjubeh}(h!]h#]h%]h']h)]uh+j>hjubeh}(h!]h#]h%]h']h)]uh+j9hjhhhNhNubeh}(h!]h#]h%]h']h)]uh+jhjhhhjhKubeh}(h!]h#](jmethodeh%]h']h)]jjjjjjjjjuh+hwhhhj hNhNubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hs:is_compact() (opengen.constraints.ball_inf.BallInf method)/opengen.constraints.ball_inf.BallInf.is_compacthNtauh+hWhj hhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/ball_inf.py:docstring of opengen.constraints.ball_inf.BallInf.is_compacthNubhx)}(hhh](h})}(hBallInf.is_compact()h](h)}(h is_compacth]h is_compact}(hhhjhhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhjhhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/ball_inf.py:docstring of opengen.constraints.ball_inf.BallInf.is_compacthKubh)}(h()h]h}(h!]h#]h%]h']h)]hhuh+hhjhhhjhKubeh}(h!]jah#](jjeh%]h']h)]jopengen.constraints.ball_infjWj.jBallInf.is_compactjj BallInf is_compactjBallInf.is_compact()uh+h|hjhKhjhhubj)}(hhh]j)}(hWhether the set is compacth]hWhether the set is compact}(hjhjhhhNhNubah}(h!]h#]h%]h']h)]uh+jhjhKhjhhubah}(h!]h#]h%]h']h)]uh+jhjhhhjhKubeh}(h!]h#](pymethodeh%]h']h)]jj*jj+jj+jjjuh+hwhhhj hjhNubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hs9is_convex() (opengen.constraints.ball_inf.BallInf method).opengen.constraints.ball_inf.BallInf.is_convexhNtauh+hWhj hhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/ball_inf.py:docstring of opengen.constraints.ball_inf.BallInf.is_convexhNubhx)}(hhh](h})}(hBallInf.is_convex()h](h)}(h is_convexh]h is_convex}(hhhjEhhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhjAhhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/ball_inf.py:docstring of opengen.constraints.ball_inf.BallInf.is_convexhKubh)}(h()h]h}(h!]h#]h%]h']h)]hhuh+hhjAhhhjShKubeh}(h!]j;ah#](jjeh%]h']h)]jopengen.constraints.ball_infjWj.jBallInf.is_convexjjdBallInf is_convexjBallInf.is_convex()uh+h|hjShKhj>hhubj)}(hhh]j)}(hWhether the set is convexh]hWhether the set is convex}(hjohjmhhhNhNubah}(h!]h#]h%]h']h)]uh+jhj=hKhjjhhubah}(h!]h#]h%]h']h)]uh+jhj>hhhjShKubeh}(h!]h#](pymethodeh%]h']h)]jjjjjjjjjuh+hwhhhj hj=hNubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hs7project() (opengen.constraints.ball_inf.BallInf method),opengen.constraints.ball_inf.BallInf.projecthNtauh+hWhj 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pointh](j])}(hjah]hu}(hhhjhhhNhNubah}(h!]h#]h%]h']h)]uh+j\hjubh – }(hhhjhhhNhNubh given point}(h given pointhjhhhNhNubeh}(h!]h#]h%]h']h)]uh+jhjubah}(h!]h#]h%]h']h)]uh+jShjubeh}(h!]h#]h%]h']h)]uh+j>hjubj?)}(hhh](jD)}(hReturnsh]hReturns}(hhhj2hhhNhNubah}(h!]h#]h%]h']h)]uh+jChj/hjhKubjT)}(hhh]j)}(hprojection of u onto this seth](hprojection of }(hprojection of hjChhhNhNubj3 )}(h`u`h]hu}(hhhjLhhhNhNubah}(h!]h#]h%]h']h)]uh+j2 hjChhhNhNubh onto this set}(h onto this sethjChhhNhNubeh}(h!]h#]h%]h']h)]uh+jhj@ubah}(h!]h#]h%]h']h)]uh+jShj/ubeh}(h!]h#]h%]h']h)]uh+j>hjubeh}(h!]h#]h%]h']h)]uh+j9hjhhhNhNubeh}(h!]h#]h%]h']h)]uh+jhjhhhjhKubeh}(h!]h#](pymethodeh%]h']h)]jjjjjjjjjuh+hwhhhj hNhNubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hs6radius (opengen.constraints.ball_inf.BallInf property)+opengen.constraints.ball_inf.BallInf.radiushNtauh+hWhj hhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/ball_inf.py:docstring of opengen.constraints.ball_inf.BallInf.radiushNubhx)}(hhh](h})}(hBallInf.radiush](h)}(h5[<#text: 'property'>, >]h](hproperty}(hhhjhhhNhNubh)}(h h]h }(hhhjhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhjubeh}(h!]h#]h%]h']h)]hhuh+hhjhhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/ball_inf.py:docstring of opengen.constraints.ball_inf.BallInf.radiushKubh)}(hradiush]hradius}(hhhjhhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhjhhhjhKubeh}(h!]jah#](jjeh%]h']h)]jopengen.constraints.ball_infjWj.jBallInf.radiusjjBallInfradiusjjuh+h|hjhKhjhhubj)}(hhh]j)}(hReturns the radius of the ballh]hReturns the radius of the ball}(hjhjhhhNhNubah}(h!]h#]h%]h']h)]uh+jhjhKhjhhubah}(h!]h#]h%]h']h)]uh+jhjhhhjhKubeh}(h!]h#](pypropertyeh%]h']h)]jjjjjjjjjuh+hwhhhj hjhNubeh}(h!]h#]h%]h']h)]uh+jhjhhhjhKubeh}(h!]h#](pyclasseh%]h']h)]jjjjjjjjjuh+hwhhhjhNhNubeh}(h!](j#opengen-constraints-ball-inf-moduleeh#]h%]#opengen.constraints.ball_inf moduleah']h)]uh+h hh hhhh,hKubh )}(hhh](h)}(h$opengen.constraints.cartesian moduleh]h$opengen.constraints.cartesian module}(hj hj hhhNhNubah}(h!]h#]h%]h']h)]uh+hhjhhhh,hK ubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hd%module; opengen.constraints.cartesian$module-opengen.constraints.cartesianhNtauh+hWhjhhhNhNubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hs9CartesianProduct (class in opengen.constraints.cartesian).opengen.constraints.cartesian.CartesianProducthNtauh+hWhjhhhNhNubhx)}(hhh](h})}(htCartesianProduct(segments: ~typing.List[int], constraints: ~typing.List[~opengen.constraints.constraint.Constraint])h](h)}(h2[<#text: 'class'>, >]h](hclass}(hhhj:hhhNhNubh)}(h h]h }(hhhjBhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhj:ubeh}(h!]h#]h%]h']h)]hhuh+hhj6hhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/cartesian.py:docstring of opengen.constraints.cartesian.CartesianProducthKubh)}(hopengen.constraints.cartesian.h]hopengen.constraints.cartesian.}(hhhjWhhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhj6hhhjVhKubh)}(hCartesianProducth]hCartesianProduct}(hhhjehhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhj6hhhjVhKubh)}(hbsegments: ~typing.List[int], constraints: ~typing.List[~opengen.constraints.constraint.Constraint]h](h)}(hsegments: List[int]h](h)}(hsegmentsh]hsegments}(hhhj{hhhNhNubah}(h!]h#]hah%]h']h)]uh+hhjwubj#)}(h:h]h:}(hhhjhhhNhNubah}(h!]h#]j/ah%]h']h)]uh+j"hjwubh)}(h h]h }(hhhjhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhjwubh)}(h List[int]h](jF)}(hhh]hList}(hhhjhhhNhNubah}(h!]h#]h%]h']h)] refdomainjUreftypeobj reftarget typing.List refspecific py:moduleopengen.constraints.cartesianpy:classNuh+jEhjubj#)}(h[h]h[}(hhhjhhhNhNubah}(h!]h#]j/ah%]h']h)]uh+j"hjubjF)}(hhh]hint}(hhhjhhhNhNubah}(h!]h#]h%]h']h)] refdomainjUreftypejW reftargetint refspecific py:modulejpy:classNuh+jEhjubj#)}(h]h]h]}(hhhjhhhNhNubah}(h!]h#]j/ah%]h']h)]uh+j"hjubeh}(h!]h#]hah%]h']h)]uh+hhjwubeh}(h!]h#]h%]h']h)]hhuh+hhjsubh)}(hconstraints: List[Constraint]h](h)}(h constraintsh]h constraints}(hhhjhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhjubj#)}(h:h]h:}(hhhj hhhNhNubah}(h!]h#]j/ah%]h']h)]uh+j"hjubh)}(h h]h }(hhhjhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhjubh)}(hList[Constraint]h](jF)}(hhh]hList}(hhhj-hhhNhNubah}(h!]h#]h%]h']h)] refdomainjUreftypej reftarget typing.List refspecific py:modulejpy:classNuh+jEhj)ubj#)}(h[h]h[}(hhhjAhhhNhNubah}(h!]h#]j/ah%]h']h)]uh+j"hj)ubjF)}(hhh]h Constraint}(hhhjOhhhNhNubah}(h!]h#]h%]h']h)] refdomainjUreftypejW reftarget)opengen.constraints.constraint.Constraint refspecific py:modulejpy:classNuh+jEhj)ubj#)}(h]h]h]}(hhhjchhhNhNubah}(h!]h#]j/ah%]h']h)]uh+j"hj)ubeh}(h!]h#]hah%]h']h)]uh+hhjubeh}(h!]h#]h%]h']h)]hhuh+hhjsubeh}(h!]h#]h%]h']h)]hhuh+hhj6hhhjVhKubeh}(h!]j1ah#](jjeh%]h']h)]jopengen.constraints.cartesianjWhjjgjjjgjjguh+h|hjVhKhj3hhubj)}(hhh](j)}(h=Bases: :py:class:`~opengen.constraints.constraint.Constraint`h](hBases: }(hBases: hjhhhNhNubjF)}(h6:py:class:`~opengen.constraints.constraint.Constraint`h]j)}(hjh]h Constraint}(hhhjhhhNhNubah}(h!]h#](jpypy-classeh%]h']h)]uh+jhjubah}(h!]h#]h%]h']h)]refdocj refdomainjreftypeclass refexplicitrefwarnjjjjgj)opengen.constraints.constraint.Constraintuh+jEh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/cartesian.py:docstring of opengen.constraints.cartesianhKhjubeh}(h!]h#]h%]h']h)]uh+jh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/cartesian.py:docstring of opengen.constraints.cartesian.CartesianProducthKhjhhubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hsB__init__() (opengen.constraints.cartesian.CartesianProduct method)7opengen.constraints.cartesian.CartesianProduct.__init__hNtauh+hWhjhhhNhNubhx)}(hhh](h})}(h}CartesianProduct.__init__(segments: ~typing.List[int], constraints: ~typing.List[~opengen.constraints.constraint.Constraint])h](h)}(h__init__h]h__init__}(hhhjhhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhjhhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/cartesian.py:docstring of opengen.constraints.cartesian.CartesianProduct.__init__hKubh)}(hbsegments: ~typing.List[int], constraints: ~typing.List[~opengen.constraints.constraint.Constraint]h](h)}(hsegments: List[int]h](h)}(hsegmentsh]hsegments}(hhhjhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhjubj#)}(h:h]h:}(hhhjhhhNhNubah}(h!]h#]j/ah%]h']h)]uh+j"hjubh)}(h h]h }(hhhjhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhjubh)}(h List[int]h](jF)}(hhh]hList}(hhhjhhhNhNubah}(h!]h#]h%]h']h)] refdomainjUreftypej reftarget typing.List refspecific py:modulejpy:classjguh+jEhjubj#)}(h[h]h[}(hhhj-hhhNhNubah}(h!]h#]j/ah%]h']h)]uh+j"hjubjF)}(hhh]hint}(hhhj;hhhNhNubah}(h!]h#]h%]h']h)] refdomainjUreftypejW reftargetint refspecific py:modulejpy:classjguh+jEhjubj#)}(h]h]h]}(hhhjOhhhNhNubah}(h!]h#]j/ah%]h']h)]uh+j"hjubeh}(h!]h#]hah%]h']h)]uh+hhjubeh}(h!]h#]h%]h']h)]hhuh+hhjubh)}(hconstraints: List[Constraint]h](h)}(h constraintsh]h constraints}(hhhjmhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhjiubj#)}(h:h]h:}(hhhj{hhhNhNubah}(h!]h#]j/ah%]h']h)]uh+j"hjiubh)}(h h]h }(hhhjhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhjiubh)}(hList[Constraint]h](jF)}(hhh]hList}(hhhjhhhNhNubah}(h!]h#]h%]h']h)] refdomainjUreftypej reftarget typing.List refspecific py:modulejpy:classjguh+jEhjubj#)}(h[h]h[}(hhhjhhhNhNubah}(h!]h#]j/ah%]h']h)]uh+j"hjubjF)}(hhh]h Constraint}(hhhjhhhNhNubah}(h!]h#]h%]h']h)] refdomainjUreftypejW reftarget)opengen.constraints.constraint.Constraint refspecific py:modulejpy:classjguh+jEhjubj#)}(h]h]h]}(hhhjhhhNhNubah}(h!]h#]j/ah%]h']h)]uh+j"hjubeh}(h!]h#]hah%]h']h)]uh+hhjiubeh}(h!]h#]h%]h']h)]hhuh+hhjubeh}(h!]h#]h%]h']h)]hhuh+hhjhhhjhKubeh}(h!]jah#](jjeh%]h']h)]jopengen.constraints.cartesianjWjgjCartesianProduct.__init__jjCartesianProduct__init__jCartesianProduct.__init__()uh+h|hjhKhjhhubj)}(hhh](j)}(hCartesian producth]hCartesian product}(hjhjhhhNhNubah}(h!]h#]h%]h']h)]uh+jh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/cartesian.py:docstring of opengen.constraints.cartesian.CartesianProduct.__init__hKhjhhubj)}(h4:math:`X = X_1 \times X_1 \times \ldots \times X_s.`h]j)}(h4:math:`X = X_1 \times X_1 \times \ldots \times X_s.`h]h,X = X_1 \times X_1 \times \ldots \times X_s.}(hhhjhhhNhNubah}(h!]h#]h%]h']h)]uh+jhjubah}(h!]h#]h%]h']h)]uh+jhjhKhjhhubj)}(hXConstruct a Cartesian product of constraints by providing a list of sets and their dimensions as follows: an `n`-dimensional vector `x` can be partitioned into subvectors as :math:`x = (x_{[1]}, x_{[2]}, ..., x_{[s]})`, where each :math:`x_{[i]}` has dimension :math:`m_i`.h](hmConstruct a Cartesian product of constraints by providing a list of sets and their dimensions as follows: an }(hmConstruct a Cartesian product of constraints by providing a list of sets and their dimensions as follows: an hj'hhhNhNubj3 )}(h`n`h]hn}(hhhj0hhhNhNubah}(h!]h#]h%]h']h)]uh+j2 hj'ubh-dimensional vector }(h-dimensional vector hj'hhhNhNubj3 )}(h`x`h]hx}(hhhjChhhNhNubah}(h!]h#]h%]h']h)]uh+j2 hj'ubh' can be partitioned into subvectors as }(h' can be partitioned into subvectors as hj'hhhNhNubj)}(h,:math:`x = (x_{[1]}, x_{[2]}, ..., x_{[s]})`h]h$x = (x_{[1]}, x_{[2]}, ..., x_{[s]})}(hhhjVhhhNhNubah}(h!]h#]h%]h']h)]uh+jhj'ubh, where each }(h, where each hj'hhhNhNubj)}(h:math:`x_{[i]}`h]hx_{[i]}}(hhhjihhhNhNubah}(h!]h#]h%]h']h)]uh+jhj'ubh has dimension }(h has dimension hj'hhhNhNubj)}(h :math:`m_i`h]hm_i}(hhhj|hhhNhNubah}(h!]h#]h%]h']h)]uh+jhj'ubh.}(h.hj'hhhNhNubeh}(h!]h#]h%]h']h)]uh+jhjhKhjhhubj)}(hXJFor example consider the 5-dimensional vector :math:`x = (x_0, x_1, x_2, x_3, x_4)`, which can be partitioned into :math:`x_{[1]} = (x_0, x_1)` and :math:`x_{[2]} = (x_2, x_3, x_4)`. We can associate with :math:`x_{[1]}` the indices [0, 1] and with :math:`x_{[2]}` the indices [2, 3, 4]. The *segment ids* are the indices 1 and 4.h](h.For example consider the 5-dimensional vector }(h.For example consider the 5-dimensional vector hjhhhNhNubj)}(h%:math:`x = (x_0, x_1, x_2, x_3, x_4)`h]hx = (x_0, x_1, x_2, x_3, x_4)}(hhhjhhhNhNubah}(h!]h#]h%]h']h)]uh+jhjubh , which can be partitioned into }(h , which can be partitioned into hjhhhNhNubj)}(h:math:`x_{[1]} = (x_0, x_1)`h]hx_{[1]} = (x_0, x_1)}(hhhjhhhNhNubah}(h!]h#]h%]h']h)]uh+jhjubh and }(h and hjhhhNhNubj)}(h!:math:`x_{[2]} = (x_2, x_3, x_4)`h]hx_{[2]} = (x_2, x_3, x_4)}(hhhjhhhNhNubah}(h!]h#]h%]h']h)]uh+jhjubh. We can associate with }(h. We can associate with hjhhhNhNubj)}(h:math:`x_{[1]}`h]hx_{[1]}}(hhhjhhhNhNubah}(h!]h#]h%]h']h)]uh+jhjubh the indices [0, 1] and with }(h the indices [0, 1] and with hjhhhNhNubj)}(h:math:`x_{[2]}`h]hx_{[2]}}(hhhjhhhNhNubah}(h!]h#]h%]h']h)]uh+jhjubh the indices [2, 3, 4]. The }(h the indices [2, 3, 4]. The hjhhhNhNubh emphasis)}(h *segment ids*h]h segment ids}(hhhjhhhNhNubah}(h!]h#]h%]h']h)]uh+jhjubh are the indices 1 and 4.}(h are the indices 1 and 4.hjhhhNhNubeh}(h!]h#]h%]h']h)]uh+jhjhK hjhhubh definition_list)}(hhh]h definition_list_item)}(hXaExample: In this example we shall define the set :math:`X = \mathcal{B}_{1.5} \times R \times {\rm I\!R}^{5}`, where :math:`\mathcal{B}_{1.5}` is a Euclidean ball of dimension 2 with radius 1.5, :math:`R` is a 3-dimensional rectangle with :math:`x_{\min} = (-1, -2, -3)` and :math:`x_{\max} = (0, 10, -1)`. Here the segments are `[1, 4, 9]`. >>> ball = og.constraints.Ball2(None, 1.5) >>> rect = og.constraints.Rectangle(xmin=[-1,-2,-3], xmax=[0, 10, -1]) >>> free = og.constraints.NoConstraints() >>> segment_ids = [1, 4, 9] >>> my_set = og.constraints.CartesianProduct(segment_ids, [ball, rect, free]) h](h term)}(hExample:h]hExample:}(hj'hj%hhhNhNubah}(h!]h#]h%]h']h)]uh+j#hjhKhjubh definition)}(hhh](j)}(hXPIn this example we shall define the set :math:`X = \mathcal{B}_{1.5} \times R \times {\rm I\!R}^{5}`, where :math:`\mathcal{B}_{1.5}` is a Euclidean ball of dimension 2 with radius 1.5, :math:`R` is a 3-dimensional rectangle with :math:`x_{\min} = (-1, -2, -3)` and :math:`x_{\max} = (0, 10, -1)`. Here the segments are `[1, 4, 9]`.h](h(In this example we shall define the set }(h(In this example we shall define the set hj8hhhNhNubj)}(h<:math:`X = \mathcal{B}_{1.5} \times R \times {\rm I\!R}^{5}`h]h4X = \mathcal{B}_{1.5} \times R \times {\rm I\!R}^{5}}(hhhjAhhhNhNubah}(h!]h#]h%]h']h)]uh+jhj8ubh , where }(h , where hj8hhhNhNubj)}(h:math:`\mathcal{B}_{1.5}`h]h\mathcal{B}_{1.5}}(hhhjThhhNhNubah}(h!]h#]h%]h']h)]uh+jhj8ubh5 is a Euclidean ball of dimension 2 with radius 1.5, }(h5 is a Euclidean ball of dimension 2 with radius 1.5, hj8hhhNhNubj)}(h :math:`R`h]hR}(hhhjghhhNhNubah}(h!]h#]h%]h']h)]uh+jhj8ubh% is a 3-dimensional rectangle with }(h% is a 3-dimensional rectangle with hj8hhhNhNubj)}(h:math:`x_{\min} = (-1, -2, -3)`h]hx_{\min} = (-1, -2, -3)}(hhhjzhhhNhNubah}(h!]h#]h%]h']h)]uh+jhj8ubh and }(h and hj8hhhNhNubj)}(h:math:`x_{\max} = (0, 10, -1)`h]hx_{\max} = (0, 10, -1)}(hhhjhhhNhNubah}(h!]h#]h%]h']h)]uh+jhj8ubh. Here the segments are }(h. Here the segments are hj8hhhNhNubj3 )}(h `[1, 4, 9]`h]h [1, 4, 9]}(hhhjhhhNhNubah}(h!]h#]h%]h']h)]uh+j2 hj8ubh.}(hjhj8hhhNhNubeh}(h!]h#]h%]h']h)]uh+jhjhKhj5ubh doctest_block)}(hX>>> ball = og.constraints.Ball2(None, 1.5) >>> rect = og.constraints.Rectangle(xmin=[-1,-2,-3], xmax=[0, 10, -1]) >>> free = og.constraints.NoConstraints() >>> segment_ids = [1, 4, 9] >>> my_set = og.constraints.CartesianProduct(segment_ids, [ball, rect, free])h]hX>>> ball = og.constraints.Ball2(None, 1.5) >>> rect = og.constraints.Rectangle(xmin=[-1,-2,-3], xmax=[0, 10, -1]) >>> free = og.constraints.NoConstraints() >>> segment_ids = [1, 4, 9] >>> my_set = og.constraints.CartesianProduct(segment_ids, [ball, rect, free])}(hhhjubah}(h!]h#]doctestah%]h']h)]hhuh+jhj5ubeh}(h!]h#]h%]h']h)]uh+j3hjubeh}(h!]h#]h%]h']h)]uh+jhjhKhjubah}(h!]h#]h%]h']h)]uh+jhjhhhjhNubj:)}(hhh]j?)}(hhh](jD)}(h Parametersh]h Parameters}(hhhjhhhNhNubah}(h!]h#]h%]h']h)]uh+jChjhjhKubjT)}(hhh]jq )}(hhh](jv )}(hhh]j)}(hsegments -- ids of 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compact}(hj'hj'hhhNhNubah}(h!]h#]h%]h']h)]uh+jhj'hKhj'hhubah}(h!]h#]h%]h']h)]uh+jhj'hhhj'hKubeh}(h!]h#](pymethodeh%]h']h)]jj'jj'jj'jjjuh+hwhhhj#$hj'hNubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hs=is_convex() (opengen.constraints.finite_set.FiniteSet method)2opengen.constraints.finite_set.FiniteSet.is_convexhNtauh+hWhj#$hhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/finite_set.py:docstring of opengen.constraints.finite_set.FiniteSet.is_convexhNubhx)}(hhh](h})}(hFiniteSet.is_convex()h](h)}(h is_convexh]h is_convex}(hhhj'hhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhj'hhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/finite_set.py:docstring of opengen.constraints.finite_set.FiniteSet.is_convexhKubh)}(h()h]h}(h!]h#]h%]h']h)]hhuh+hhj'hhhj(hKubeh}(h!]j'ah#](jjeh%]h']h)]jopengen.constraints.finite_setjWj#jFiniteSet.is_convexjj( FiniteSet is_convexjFiniteSet.is_convex()uh+h|hj(hKhj'hhubj)}(hhh]j)}(hWhether the set is convexh]hWhether the set is convex}(hj(hj(hhhNhNubah}(h!]h#]h%]h']h)]uh+jhj'hKhj(hhubah}(h!]h#]h%]h']h)]uh+jhj'hhhj(hKubeh}(h!]h#](pymethodeh%]h']h)]jj2(jj3(jj3(jjjuh+hwhhhj#$hj'hNubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hs:points (opengen.constraints.finite_set.FiniteSet property)/opengen.constraints.finite_set.FiniteSet.pointshNtauh+hWhj#$hhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/finite_set.py:docstring of opengen.constraints.finite_set.FiniteSet.pointshNubhx)}(hhh](h})}(hFiniteSet.pointsh](h)}(h5[<#text: 'property'>, >]h](hproperty}(hhhjM(hhhNhNubh)}(h h]h }(hhhjU(hhhNhNubah}(h!]h#]hah%]h']h)]uh+hhjM(ubeh}(h!]h#]h%]h']h)]hhuh+hhjI(hhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/finite_set.py:docstring of opengen.constraints.finite_set.FiniteSet.pointshKubh)}(hpointsh]hpoints}(hhhjj(hhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhjI(hhhji(hKubeh}(h!]jC(ah#](jjeh%]h']h)]jopengen.constraints.finite_setjWj#jFiniteSet.pointsjj~( FiniteSetpointsjj(uh+h|hji(hKhjF(hhubj)}(hhh]j)}(hList of points of this seth]hList of points of this set}(hj(hj(hhhNhNubah}(h!]h#]h%]h']h)]uh+jhjE(hKhj(hhubah}(h!]h#]h%]h']h)]uh+jhjF(hhhji(hKubeh}(h!]h#](pypropertyeh%]h']h)]jj(jj(jj(jjjuh+hwhhhj#$hjE(hNubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hs;project() (opengen.constraints.finite_set.FiniteSet method)0opengen.constraints.finite_set.FiniteSet.projecthNtauh+hWhj#$hhhNhNubhx)}(hhh](h})}(hFiniteSet.project(u)h](h)}(hprojecth]hproject}(hhhj(hhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhj(hhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/finite_set.py:docstring of opengen.constraints.finite_set.FiniteSet.projecthKubh)}(hjah]h)}(huh]h)}(huh]hu}(hhhj(hhhNhNubah}(h!]h#]hah%]h']h)]uh+hhj(ubah}(h!]h#]h%]h']h)]hhuh+hhj(ubah}(h!]h#]h%]h']h)]hhuh+hhj(hhhj(hKubeh}(h!]j(ah#](jjeh%]h']h)]jopengen.constraints.finite_setjWj#jFiniteSet.projectjj( FiniteSetprojectjFiniteSet.project()uh+h|hj(hKhj(hhubj)}(hhh](j)}(h"Project a given point onto the seth]h"Project a given point onto the set}(hj(hj(hhhNhNubah}(h!]h#]h%]h']h)]uh+jh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/finite_set.py:docstring of opengen.constraints.finite_set.FiniteSet.projecthKhj(hhubj:)}(hhh](j?)}(hhh](jD)}(h Parametersh]h Parameters}(hhhj )hhhNhNubah}(h!]h#]h%]h']h)]uh+jChj)hj(hKubjT)}(hhh]j)}(hu -- given pointh](j])}(hjah]hu}(hhhj )hhhNhNubah}(h!]h#]h%]h']h)]uh+j\hj)ubh – }(hhhj)hhhNhNubh given point}(h given pointhj)hhhNhNubeh}(h!]h#]h%]h']h)]uh+jhj)ubah}(h!]h#]h%]h']h)]uh+jShj)ubeh}(h!]h#]h%]h']h)]uh+j>hj)ubj?)}(hhh](jD)}(hReturnsh]hReturns}(hhhjK)hhhNhNubah}(h!]h#]h%]h']h)]uh+jChjH)hj(hKubjT)}(hhh]j)}(hprojection of u onto this seth](hprojection of }(hprojection of hj\)hhhNhNubj3 )}(h`u`h]hu}(hhhje)hhhNhNubah}(h!]h#]h%]h']h)]uh+j2 hj\)hhhNhNubh onto this set}(h onto this sethj\)hhhNhNubeh}(h!]h#]h%]h']h)]uh+jhjY)ubah}(h!]h#]h%]h']h)]uh+jShjH)ubeh}(h!]h#]h%]h']h)]uh+j>hj)ubeh}(h!]h#]h%]h']h)]uh+j9hj(hhhNhNubeh}(h!]h#]h%]h']h)]uh+jhj(hhhj(hKubeh}(h!]h#](pymethodeh%]h']h)]jj)jj)jj)jjjuh+hwhhhj#$hNhNubeh}(h!]h#]h%]h']h)]uh+jhj#hhhj#hKubeh}(h!]h#](pyclasseh%]h']h)]jj)jj)jj)jjjuh+hwhhhjn#hNhNubeh}(h!](j#%opengen-constraints-finite-set-moduleeh#]h%]%opengen.constraints.finite_set moduleah']h)]uh+h hh hhhh,hK0ubh )}(hhh](h)}(h$opengen.constraints.halfspace moduleh]h$opengen.constraints.halfspace module}(hj)hj)hhhNhNubah}(h!]h#]h%]h']h)]uh+hhj)hhhh,hK8ubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hd%module; opengen.constraints.halfspace$module-opengen.constraints.halfspacehNtauh+hWhj)hhhNhNubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hs2Halfspace (class in opengen.constraints.halfspace)'opengen.constraints.halfspace.HalfspacehNtauh+hWhj)hhhNhNubhx)}(hhh](h})}(h'Halfspace(normal_vector, offset: float)h](h)}(h2[<#text: 'class'>, >]h](hclass}(hhhj)hhhNhNubh)}(h h]h }(hhhj)hhhNhNubah}(h!]h#]hah%]h']h)]uh+hhj)ubeh}(h!]h#]h%]h']h)]hhuh+hhj)hhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/halfspace.py:docstring of opengen.constraints.halfspace.HalfspacehKubh)}(hopengen.constraints.halfspace.h]hopengen.constraints.halfspace.}(hhhj*hhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhj)hhhj*hKubh)}(h Halfspaceh]h Halfspace}(hhhj*hhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhj)hhhj*hKubh)}(hnormal_vector, offset: floath](h)}(h normal_vectorh]h)}(h normal_vectorh]h normal_vector}(hhhj)*hhhNhNubah}(h!]h#]hah%]h']h)]uh+hhj%*ubah}(h!]h#]h%]h']h)]hhuh+hhj!*ubh)}(h offset: floath](h)}(hoffseth]hoffset}(hhhjA*hhhNhNubah}(h!]h#]hah%]h']h)]uh+hhj=*ubj#)}(h:h]h:}(hhhjO*hhhNhNubah}(h!]h#]j/ah%]h']h)]uh+j"hj=*ubh)}(h h]h }(hhhj]*hhhNhNubah}(h!]h#]hah%]h']h)]uh+hhj=*ubh)}(hfloath]jF)}(hhh]hfloat}(hhhjo*hhhNhNubah}(h!]h#]h%]h']h)] refdomainjUreftypejW reftargetfloat refspecific py:moduleopengen.constraints.halfspacepy:classNuh+jEhjk*ubah}(h!]h#]hah%]h']h)]uh+hhj=*ubeh}(h!]h#]h%]h']h)]hhuh+hhj!*ubeh}(h!]h#]h%]h']h)]hhuh+hhj)hhhj*hKubeh}(h!]j)ah#](jjeh%]h']h)]jopengen.constraints.halfspacejWhjj*jj*j*jj*uh+h|hj*hKhj)hhubj)}(hhh](j)}(h=Bases: :py:class:`~opengen.constraints.constraint.Constraint`h](hBases: }(hBases: hj*hhhNhNubjF)}(h6:py:class:`~opengen.constraints.constraint.Constraint`h]j)}(hj*h]h Constraint}(hhhj*hhhNhNubah}(h!]h#](jpypy-classeh%]h']h)]uh+jhj*ubah}(h!]h#]h%]h']h)]refdocj refdomainj*reftypeclass refexplicitrefwarnjj*jj*j)opengen.constraints.constraint.Constraintuh+jEh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/halfspace.py:docstring of opengen.constraints.halfspacehKhj*ubeh}(h!]h#]h%]h']h)]uh+jh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/halfspace.py:docstring of opengen.constraints.halfspace.HalfspacehKhj*hhubj)}(hHalfspace constrainth]hHalfspace constraint}(hj*hj*hhhNhNubah}(h!]h#]h%]h']h)]uh+jh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/halfspace.py:docstring of opengen.constraints.halfspace.HalfspacehKhj*hhubj)}(hA halfspace is a set of the form :math:`H = \{c^\intercal x \leq b\}`, where `c` is a given vector and `b` is a constant scalar.h](h!A halfspace is a set of the form }(h!A halfspace is a set of the form hj*hhhNhNubj)}(h$:math:`H = \{c^\intercal x \leq b\}`h]hH = \{c^\intercal x \leq b\}}(hhhj*hhhNhNubah}(h!]h#]h%]h']h)]uh+jhj*ubh, where }(h, where hj*hhhNhNubj3 )}(h`c`h]hc}(hhhj*hhhNhNubah}(h!]h#]h%]h']h)]uh+j2 hj*ubh is a given vector and }(h is a given vector and hj*hhhNhNubj3 )}(h`b`h]hb}(hhhj+hhhNhNubah}(h!]h#]h%]h']h)]uh+j2 hj*ubh is a constant scalar.}(h is a constant scalar.hj*hhhNhNubeh}(h!]h#]h%]h']h)]uh+jhj*hKhj*hhubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hs;__init__() (opengen.constraints.halfspace.Halfspace method)0opengen.constraints.halfspace.Halfspace.__init__hNtauh+hWhj*hhhNhNubhx)}(hhh](h})}(h0Halfspace.__init__(normal_vector, offset: float)h](h)}(h__init__h]h__init__}(hhhj>+hhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhj:+hhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/halfspace.py:docstring of opengen.constraints.halfspace.Halfspace.__init__hKubh)}(hnormal_vector, offset: floath](h)}(h normal_vectorh]h)}(h normal_vectorh]h normal_vector}(hhhjU+hhhNhNubah}(h!]h#]hah%]h']h)]uh+hhjQ+ubah}(h!]h#]h%]h']h)]hhuh+hhjM+ubh)}(h offset: floath](h)}(hoffseth]hoffset}(hhhjm+hhhNhNubah}(h!]h#]hah%]h']h)]uh+hhji+ubj#)}(h:h]h:}(hhhj{+hhhNhNubah}(h!]h#]j/ah%]h']h)]uh+j"hji+ubh)}(h h]h }(hhhj+hhhNhNubah}(h!]h#]hah%]h']h)]uh+hhji+ubh)}(hfloath]jF)}(hhh]hfloat}(hhhj+hhhNhNubah}(h!]h#]h%]h']h)] refdomainjUreftypejW reftargetfloat refspecific py:modulej*py:classj*uh+jEhj+ubah}(h!]h#]hah%]h']h)]uh+hhji+ubeh}(h!]h#]h%]h']h)]hhuh+hhjM+ubeh}(h!]h#]h%]h']h)]hhuh+hhj:+hhhjL+hKubeh}(h!]j5+ah#](jjeh%]h']h)]jopengen.constraints.halfspacejWj*jHalfspace.__init__jj+ Halfspace__init__jHalfspace.__init__()uh+h|hjL+hKhj7+hhubj)}(hhh](j)}(h>Construct a new halfspace :math:`H = \{c^\intercal x \leq b\}`h](hConstruct a new halfspace }(hConstruct a new halfspace hj+hhhNhNubj)}(h$:math:`H = \{c^\intercal x \leq b\}`h]hH = \{c^\intercal x \leq b\}}(hhhj+hhhNhNubah}(h!]h#]h%]h']h)]uh+jhj+ubeh}(h!]h#]h%]h']h)]uh+jh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/halfspace.py:docstring of opengen.constraints.halfspace.Halfspace.__init__hKhj+hhubj:)}(hhh]j?)}(hhh](jD)}(h Parametersh]h Parameters}(hhhj+hhhNhNubah}(h!]h#]h%]h']h)]uh+jChj+hjL+hKubjT)}(hhh]jq )}(hhh](jv )}(hhh]j)}(hnormal_vector -- vector ch](j])}(h normal_vectorh]h normal_vector}(hhhj,hhhNhNubah}(h!]h#]h%]h']h)]uh+j\hj ,ubh – }(hhhj ,hhhNhNubhvector }(hvector hj ,hhhNhNubj3 )}(h`c`h]hc}(hhhj&,hhhNhNubah}(h!]h#]h%]h']h)]uh+j2 hj ,hhhNhNubeh}(h!]h#]h%]h']h)]uh+jhj,ubah}(h!]h#]h%]h']h)]uh+ju hj,ubjv )}(hhh]j)}(hoffset -- parameter bh](j])}(hoffseth]hoffset}(hhhjG,hhhNhNubah}(h!]h#]h%]h']h)]uh+j\hjC,ubh – }(hhhjC,hhhNhNubh parameter }(h parameter hjC,hhhNhNubj3 )}(h`b`h]hb}(hhhj^,hhhNhNubah}(h!]h#]h%]h']h)]uh+j2 hjC,hhhNhNubeh}(h!]h#]h%]h']h)]uh+jhj@,ubah}(h!]h#]h%]h']h)]uh+ju hj,ubeh}(h!]h#]h%]h']h)]uh+jp hj,ubah}(h!]h#]h%]h']h)]uh+jShj+ubeh}(h!]h#]h%]h']h)]uh+j>hj+ubah}(h!]h#]h%]h']h)]uh+j9hj+hhhNhNubeh}(h!]h#]h%]h']h)]uh+jhj7+hhhjL+hKubeh}(h!]h#](pymethodeh%]h']h)]jj,jj,jj,jjjuh+hwhhhj*hNhNubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hshj,ubah}(h!]h#]h%]h']h)]uh+j9hj,hhhNhNubeh}(h!]h#]h%]h']h)]uh+jhj,hhhj,hKubeh}(h!]h#](pymethodeh%]h']h)]jj+-jj,-jj,-jjjuh+hwhhhj*hNhNubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hsCdistance_squared() (opengen.constraints.halfspace.Halfspace method)8opengen.constraints.halfspace.Halfspace.distance_squaredhNtauh+hWhj*hhhNhNubhx)}(hhh](h})}(hHalfspace.distance_squared(u)h](h)}(hdistance_squaredh]hdistance_squared}(hhhjE-hhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhjA-hhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/halfspace.py:docstring of opengen.constraints.halfspace.Halfspace.distance_squaredhKubh)}(hjah]h)}(huh]h)}(huh]hu}(hhhj[-hhhNhNubah}(h!]h#]hah%]h']h)]uh+hhjW-ubah}(h!]h#]h%]h']h)]hhuh+hhjT-ubah}(h!]h#]h%]h']h)]hhuh+hhjA-hhhjS-hKubeh}(h!]j<-ah#](jjeh%]h']h)]jopengen.constraints.halfspacejWj*jHalfspace.distance_squaredjj{- Halfspacedistance_squaredjHalfspace.distance_squared()uh+h|hjS-hKhj>-hhubj)}(hhh](j)}(h,Squared distance of a given point to the seth]h,Squared distance of a given point to the set}(hj-hj-hhhNhNubah}(h!]h#]h%]h']h)]uh+jh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/halfspace.py:docstring of opengen.constraints.halfspace.Halfspace.distance_squaredhKhj-hhubj:)}(hhh](j?)}(hhh](jD)}(h Parametersh]h Parameters}(hhhj-hhhNhNubah}(h!]h#]h%]h']h)]uh+jChj-hjS-hKubjT)}(hhh]j)}(hu -- given pointh](j])}(hjah]hu}(hhhj-hhhNhNubah}(h!]h#]h%]h']h)]uh+j\hj-ubh – }(hhhj-hhhNhNubh given point}(h given 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Constraint}(hhhjU6hhhNhNubah}(h!]h#](jpypy-classeh%]h']h)]uh+jhjQ6ubah}(h!]h#]h%]h']h)]refdocj refdomainj_6reftypeclass refexplicitrefwarnjjC6jj5j)opengen.constraints.constraint.Constraintuh+jEh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/rectangle.py:docstring of opengen.constraints.rectanglehKhjH6ubeh}(h!]h#]h%]h']h)]uh+jh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/rectangle.py:docstring of opengen.constraints.rectangle.RectanglehKhjE6hhubj)}(hA Rectangle (Box) constrainth]hA Rectangle (Box) constraint}(hj{6hjy6hhhNhNubah}(h!]h#]h%]h']h)]uh+jh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/rectangle.py:docstring of opengen.constraints.rectangle.RectanglehKhjE6hhubj)}(hA set of the formh]hA set of the form}(hj6hj6hhhNhNubah}(h!]h#]h%]h']h)]uh+jhj6hKhjE6hhubj)}(hY:math:`X = \{x\in{\mathrm{I\!R}}^n {}:{} x_{\mathrm{min}} \leq x \leq x_{\mathrm{max}}\}`h]j)}(hY:math:`X = \{x\in{\mathrm{I\!R}}^n {}:{} x_{\mathrm{min}} \leq x \leq x_{\mathrm{max}}\}`h]hQX = \{x\in{\mathrm{I\!R}}^n {}:{} x_{\mathrm{min}} \leq x \leq x_{\mathrm{max}}\}}(hhhj6hhhNhNubah}(h!]h#]h%]h']h)]uh+jhj6ubah}(h!]h#]h%]h']h)]uh+jhj6hKhjE6hhubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hs;__init__() (opengen.constraints.rectangle.Rectangle method)0opengen.constraints.rectangle.Rectangle.__init__hNtauh+hWhjE6hhhNhNubhx)}(hhh](h})}(hRectangle.__init__(xmin, xmax)h](h)}(h__init__h]h__init__}(hhhj6hhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhj6hhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/rectangle.py:docstring of opengen.constraints.rectangle.Rectangle.__init__hKubh)}(h xmin, xmaxh](h)}(hxminh]h)}(hxminh]hxmin}(hhhj6hhhNhNubah}(h!]h#]hah%]h']h)]uh+hhj6ubah}(h!]h#]h%]h']h)]hhuh+hhj6ubh)}(hxmaxh]h)}(hxmaxh]hxmax}(hhhj6hhhNhNubah}(h!]h#]hah%]h']h)]uh+hhj6ubah}(h!]h#]h%]h']h)]hhuh+hhj6ubeh}(h!]h#]h%]h']h)]hhuh+hhj6hhhj6hKubeh}(h!]j6ah#](jjeh%]h']h)]jopengen.constraints.rectanglejWj5jRectangle.__init__jj7 Rectangle__init__jRectangle.__init__()uh+h|hj6hKhj6hhubj)}(hhh](j)}(h%Construct a new instance of Rectangleh]h%Construct a new instance of Rectangle}(hj7hj7hhhNhNubah}(h!]h#]h%]h']h)]uh+jh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/rectangle.py:docstring of opengen.constraints.rectangle.Rectangle.__init__hKhj7hhubj:)}(hhh](j?)}(hhh](jD)}(h Parametersh]h Parameters}(hhhj07hhhNhNubah}(h!]h#]h%]h']h)]uh+jChj-7hj6hKubjT)}(hhh]jq )}(hhh](jv )}(hhh]j)}(h$xmin -- minimum bounds (can be None)h](j])}(hxminh]hxmin}(hhhjK7hhhNhNubah}(h!]h#]h%]h']h)]uh+j\hjG7ubh – }(hhhjG7hhhNhNubhminimum bounds (can be 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hj7hhhNhNubj)}(h``xmin``h]hxmin}(hhhj8hhhNhNubah}(h!]h#]h%]h']h)]uh+jhj7hhhNhNubh and }(h and hj7hhhNhNubj)}(h``xmax``h]hxmax}(hhhj&8hhhNhNubah}(h!]h#]h%]h']h)]uh+jhj7hhhNhNubh is }(h is hj7hhhNhNubj)}(h``None``h]hNone}(hhhj98hhhNhNubah}(h!]h#]h%]h']h)]uh+jhj7hhhNhNubeh}(h!]h#]h%]h']h)]uh+jhj7ubah}(h!]h#]h%]h']h)]uh+ju hj7ubjv )}(hhh]j)}(h>Exception -- if xmin and xmax are both not None and not a listh](jF)}(hhh]j])}(h Exceptionh]h Exception}(hhhj]8hhhNhNubah}(h!]h#]h%]h']h)]uh+j\hjZ8ubah}(h!]h#]h%]h']h)] refdomainj8 refexplicitreftypej8 reftargetj_8j<jj7jj5uh+jEhjV8ubh – }(hhhjV8hhhNhNubhif }(hif hjV8hhhNhNubj)}(h``xmin``h]hxmin}(hhhj~8hhhNhNubah}(h!]h#]h%]h']h)]uh+jhjV8hhhNhNubh and }(h and hjV8hhhNhNubj)}(h``xmax``h]hxmax}(hhhj8hhhNhNubah}(h!]h#]h%]h']h)]uh+jhjV8hhhNhNubh are both not }(h are both not hjV8hhhNhNubj)}(h``None``h]hNone}(hhhj8hhhNhNubah}(h!]h#]h%]h']h)]uh+jhjV8hhhNhNubh and not a list}(h and not a listhjV8hhhNhNubeh}(h!]h#]h%]h']h)]uh+jhjS8ubah}(h!]h#]h%]h']h)]uh+ju hj7ubjv )}(hhh]j)}(h7Exception -- if xmin and xmax have incompatible lengthsh](jF)}(hhh]j])}(h Exceptionh]h Exception}(hhhj8hhhNhNubah}(h!]h#]h%]h']h)]uh+j\hj8ubah}(h!]h#]h%]h']h)] refdomainj8 refexplicitreftypej8 reftargetj8j<jj7jj5uh+jEhj8ubh – }(hhhj8hhhNhNubhif }(hif hj8hhhNhNubj)}(h``xmin``h]hxmin}(hhhj8hhhNhNubah}(h!]h#]h%]h']h)]uh+jhj8hhhNhNubh and }(h and hj8hhhNhNubj)}(h``xmax``h]hxmax}(hhhj9hhhNhNubah}(h!]h#]h%]h']h)]uh+jhj8hhhNhNubh have incompatible lengths}(h have incompatible lengthshj8hhhNhNubeh}(h!]h#]h%]h']h)]uh+jhj8ubah}(h!]h#]h%]h']h)]uh+ju hj7ubjv )}(hhh]j)}(h8Exception -- if xmin(i) > xmax(i) for some i (empty set)h](jF)}(hhh]j])}(h Exceptionh]h Exception}(hhhj*9hhhNhNubah}(h!]h#]h%]h']h)]uh+j\hj'9ubah}(h!]h#]h%]h']h)] refdomainj8 refexplicitreftypej8 reftargetj,9j<jj7jj5uh+jEhj#9ubh – }(hhhj#9hhhNhNubhif }(hif hj#9hhhNhNubj)}(h``xmin(i) > xmax(i)``h]hxmin(i) > xmax(i)}(hhhjK9hhhNhNubah}(h!]h#]h%]h']h)]uh+jhj#9hhhNhNubh for some }(h for some 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to this rectanglehj ;hhhNhNubeh}(h!]h#]h%]h']h)]uh+jhj;ubah}(h!]h#]h%]h']h)]uh+jShj:ubeh}(h!]h#]h%]h']h)]uh+j>hj:ubeh}(h!]h#]h%]h']h)]uh+j9hj:hhhNhNubeh}(h!]h#]h%]h']h)]uh+jhj_:hhhjt:hKubeh}(h!]h#](pymethodeh%]h']h)]jjH;jjI;jjI;jjjuh+hwhhhjE6hNhNubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hsGidx_bound_finite_all() (opengen.constraints.rectangle.Rectangle method)hj;ubah}(h!]h#]h%]h']h)]uh+j9hj;hhhNhNubeh}(h!]h#]h%]h']h)]uh+jhj[;hhhjp;hKubeh}(h!]h#](pymethodeh%]h']h)]jj;jj;jj;jjjuh+hwhhhjE6hNhNubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hsIidx_infinite_only_xmax() (opengen.constraints.rectangle.Rectangle method)>opengen.constraints.rectangle.Rectangle.idx_infinite_only_xmaxhNtauh+hWhjE6hhhNhNubhx)}(hhh](h})}(h"Rectangle.idx_infinite_only_xmax()h](h)}(hidx_infinite_only_xmaxh]hidx_infinite_only_xmax}(hhhj;hhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhj;hhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/rectangle.py:docstring of opengen.constraints.rectangle.Rectangle.idx_infinite_only_xmaxhKubh)}(h()h]h}(h!]h#]h%]h']h)]hhuh+hhj;hhhj<hKubeh}(h!]j;ah#](jjeh%]h']h)]jopengen.constraints.rectanglejWj5j Rectangle.idx_infinite_only_xmaxjj< Rectangleidx_infinite_only_xmaxj"Rectangle.idx_infinite_only_xmax()uh+h|hj<hKhj;hhubj)}(hhh](j)}(h@Coordinates at which ``xmax`` is infinity and ``xmin`` is finiteh](hCoordinates at which }(hCoordinates at which hj<hhhNhNubj)}(h``xmax``h]hxmax}(hhhj%<hhhNhNubah}(h!]h#]h%]h']h)]uh+jhj<ubh is infinity and }(h is infinity and hj<hhhNhNubj)}(h``xmin``h]hxmin}(hhhj8<hhhNhNubah}(h!]h#]h%]h']h)]uh+jhj<ubh is finite}(h is finitehj<hhhNhNubeh}(h!]h#]h%]h']h)]uh+jh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/rectangle.py:docstring of opengen.constraints.rectangle.Rectangle.idx_infinite_only_xmaxhKhj<hhubj:)}(hhh]j?)}(hhh](jD)}(hReturnsh]hReturns}(hhhjX<hhhNhNubah}(h!]h#]h%]h']h)]uh+jChjU<hj<hKubjT)}(hhh]j)}(hlist of 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Rectangleidx_infinite_only_xminj"Rectangle.idx_infinite_only_xmin()uh+h|hj<hKhj<hhubj)}(hhh](j)}(hFCoordinates at which ``xmin`` is minus infinity and ``xmax`` is finiteh](hCoordinates at which }(hCoordinates at which hj<hhhNhNubj)}(h``xmin``h]hxmin}(hhhj<hhhNhNubah}(h!]h#]h%]h']h)]uh+jhj<ubh is minus infinity and }(h is minus infinity and hj<hhhNhNubj)}(h``xmax``h]hxmax}(hhhj<hhhNhNubah}(h!]h#]h%]h']h)]uh+jhj<ubh is finite}(h is finitehj<hhhNhNubeh}(h!]h#]h%]h']h)]uh+jh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/rectangle.py:docstring of opengen.constraints.rectangle.Rectangle.idx_infinite_only_xminhKhj<hhubj:)}(hhh]j?)}(hhh](jD)}(hReturnsh]hReturns}(hhhj=hhhNhNubah}(h!]h#]h%]h']h)]uh+jChj=hj<hKubjT)}(hhh]j)}(hlist of coordinatesh]hlist of coordinates}(hlist of coordinateshj"=hhhNhNubah}(h!]h#]h%]h']h)]uh+jhj=ubah}(h!]h#]h%]h']h)]uh+jShj=ubeh}(h!]h#]h%]h']h)]uh+j>hj =ubah}(h!]h#]h%]h']h)]uh+j9hj<hhhNhNubeh}(h!]h#]h%]h']h)]uh+jhj<hhhj<hKubeh}(h!]h#](pymethodeh%]h']h)]jjL=jjM=jjM=jjjuh+hwhhhjE6hNhNubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hs=is_compact() (opengen.constraints.rectangle.Rectangle method)2opengen.constraints.rectangle.Rectangle.is_compacthNtauh+hWhjE6hhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/rectangle.py:docstring of opengen.constraints.rectangle.Rectangle.is_compacthNubhx)}(hhh](h})}(hRectangle.is_compact()h](h)}(h is_compacth]h is_compact}(hhhjg=hhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhjc=hhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/rectangle.py:docstring of opengen.constraints.rectangle.Rectangle.is_compacthKubh)}(h()h]h}(h!]h#]h%]h']h)]hhuh+hhjc=hhhju=hKubeh}(h!]j]=ah#](jjeh%]h']h)]jopengen.constraints.rectanglejWj5jRectangle.is_compactjj= Rectangle is_compactjRectangle.is_compact()uh+h|hju=hKhj`=hhubj)}(hhh]j)}(hWhether the set is compacth]hWhether the set is compact}(hj=hj=hhhNhNubah}(h!]h#]h%]h']h)]uh+jhj_=hKhj=hhubah}(h!]h#]h%]h']h)]uh+jhj`=hhhju=hKubeh}(h!]h#](pymethodeh%]h']h)]jj=jj=jj=jjjuh+hwhhhjE6hj_=hNubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hsjj>jj>jjjuh+hwhhhjE6hj=hNubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hs=is_orthant() (opengen.constraints.rectangle.Rectangle method)2opengen.constraints.rectangle.Rectangle.is_orthanthNtauh+hWhjE6hhhNhNubhx)}(hhh](h})}(hRectangle.is_orthant()h](h)}(h is_orthanth]h is_orthant}(hhhj>hhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhj>hhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/rectangle.py:docstring of opengen.constraints.rectangle.Rectangle.is_orthanthKubh)}(h()h]h}(h!]h#]h%]h']h)]hhuh+hhj>hhhj(>hKubeh}(h!]j>ah#](jjeh%]h']h)]jopengen.constraints.rectanglejWj5jRectangle.is_orthantjj9> Rectangle is_orthantjRectangle.is_orthant()uh+h|hj(>hKhj>hhubj)}(hhh](j)}(h$Whether this rectangle is an orthanth]h$Whether this rectangle is an orthant}(hjD>hjB>hhhNhNubah}(h!]h#]h%]h']h)]uh+jh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/rectangle.py:docstring of opengen.constraints.rectangle.Rectangle.is_orthanthKhj?>hhubj)}(hAn orthant is a rectangle whose projection on every coordinate is an interval of the form :math:`[0, \infty)` or :math:`(-\infty, 0]`.h](h[An orthant is a rectangle whose projection on every coordinate is an interval of the form }(h[An orthant is a rectangle whose projection on every coordinate is an interval of the form hjQ>hhhNhNubj)}(h:math:`[0, \infty)`h]h [0, \infty)}(hhhjZ>hhhNhNubah}(h!]h#]h%]h']h)]uh+jhjQ>ubh or }(h or hjQ>hhhNhNubj)}(h:math:`(-\infty, 0]`h]h (-\infty, 0]}(hhhjm>hhhNhNubah}(h!]h#]h%]h']h)]uh+jhjQ>ubh.}(hjhjQ>hhhNhNubeh}(h!]h#]h%]h']h)]uh+jhjP>hKhj?>hhubj:)}(hhh]j?)}(hhh](jD)}(h Return typeh]h Return type}(hhhj>hhhNhNubah}(h!]h#]h%]h']h)]uh+jChj>hj(>hKubjT)}(hhh]j)}(hbooleanh]jF)}(hhh]hboolean}(hhhj>hhhNhNubah}(h!]h#]h%]h']h)] refdomainpy refexplicitreftypejW reftargetbooleanj<jj9>jj5uh+jEhj>ubah}(h!]h#]h%]h']h)]uh+jhj>ubah}(h!]h#]h%]h']h)]uh+jShj>ubeh}(h!]h#]h%]h']h)]uh+j>hj>ubah}(h!]h#]h%]h']h)]uh+j9hj?>hhhNhNubeh}(h!]h#]h%]h']h)]uh+jhj>hhhj(>hKubeh}(h!]h#](j>methodeh%]h']h)]jj>jj>jj>jjjuh+hwhhhjE6hNhNubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hs:project() (opengen.constraints.rectangle.Rectangle method)/opengen.constraints.rectangle.Rectangle.projecthNtauh+hWhjE6hhhNhNubhx)}(hhh](h})}(hRectangle.project(u)h](h)}(hprojecth]hproject}(hhhj>hhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhj>hhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/rectangle.py:docstring of opengen.constraints.rectangle.Rectangle.projecthKubh)}(hjah]h)}(huh]h)}(huh]hu}(hhhj?hhhNhiNubah}(h!]h#]hah%]h']h)]uh+hhj>ubah}(h!]h#]h%]h']h)]hhuh+hhj>ubah}(h!]h#]h%]h']h)]hhuh+hhj>hhhj>hKubeh}(h!]j>ah#](jjeh%]h']h)]jopengen.constraints.rectanglejWj5jRectangle.projectjj#? RectangleprojectjRectangle.project()uh+h|hj>hKhj>hhubj)}(hhh](j)}(h"Project a given point onto the seth]h"Project a given point onto the set}(hj.?hj,?hhhNhNubah}(h!]h#]h%]h']h)]uh+jh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/rectangle.py:docstring of opengen.constraints.rectangle.Rectangle.projecthKhj)?hhubj:)}(hhh](j?)}(hhh](jD)}(h Parametersh]h Parameters}(hhhjA?hhhNhNubah}(h!]h#]h%]h']h)]uh+jChj>?hj>hKubjT)}(hhh]j)}(hu -- given pointh](j])}(hjah]hu}(hhhjV?hhhNhNubah}(h!]h#]h%]h']h)]uh+j\hjR?ubh – }(hhhjR?hhhNhNubh given point}(h given pointhjR?hhhNhNubeh}(h!]h#]h%]h']h)]uh+jhjO?ubah}(h!]h#]h%]h']h)]uh+jShj>?ubeh}(h!]h#]h%]h']h)]uh+j>hj;?ubj?)}(hhh](jD)}(hReturnsh]hReturns}(hhhj?hhhNhNubah}(h!]h#]h%]h']h)]uh+jChj~?hj>hKubjT)}(hhh]j)}(hprojection of u onto this seth](hprojection of }(hprojection of hj?hhhNhNubj3 )}(h`u`h]hu}(hhhj?hhhNhNubah}(h!]h#]h%]h']h)]uh+j2 hj?hhhNhNubh onto this set}(h onto this sethj?hhhNhNubeh}(h!]h#]h%]h']h)]uh+jhj?ubah}(h!]h#]h%]h']h)]uh+jShj~?ubeh}(h!]h#]h%]h']h)]uh+j>hj;?ubeh}(h!]h#]h%]h']h)]uh+j9hj)?hhhNhNubeh}(h!]h#]h%]h']h)]uh+jhj>hhhj>hKubeh}(h!]h#](pymethodeh%]h']h)]jj?jj?jj?jjjuh+hwhhhjE6hNhNubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hs7xmax (opengen.constraints.rectangle.Rectangle property),opengen.constraints.rectangle.Rectangle.xmaxhNtauh+hWhjE6hhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/rectangle.py:docstring of opengen.constraints.rectangle.Rectangle.xmaxhNubhx)}(hhh](h})}(hRectangle.xmaxh](h)}(h5[<#text: 'property'>, >]h](hproperty}(hhhj?hhhNhNubh)}(h h]h }(hhhj?hhhNhNubah}(h!]h#]hah%]h']h)]uh+hhj?ubeh}(h!]h#]h%]h']h)]hhuh+hhj?hhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/rectangle.py:docstring of opengen.constraints.rectangle.Rectangle.xmaxhKubh)}(hxmaxh]hxmax}(hhhj@hhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhj?hhhj@hKubeh}(h!]j?ah#](jjeh%]h']h)]jopengen.constraints.rectanglejWj5jRectangle.xmaxjj@ Rectanglexmaxjj@uh+h|hj@hKhj?hhubj)}(hhh]j)}(h Maximum boundh]h Maximum bound}(hj%@hj#@hhhNhNubah}(h!]h#]h%]h']h)]uh+jhj?hKhj @hhubah}(h!]h#]h%]h']h)]uh+jhj?hhhj@hKubeh}(h!]h#](pypropertyeh%]h']h)]jj:@jj;@jj;@jjjuh+hwhhhjE6hj?hNubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hs7xmin (opengen.constraints.rectangle.Rectangle property),opengen.constraints.rectangle.Rectangle.xminhNtauh+hWhjE6hhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/rectangle.py:docstring of opengen.constraints.rectangle.Rectangle.xminhNubhx)}(hhh](h})}(hRectangle.xminh](h)}(h5[<#text: 'property'>, >]h](hproperty}(hhhjU@hhhNhNubh)}(h h]h }(hhhj]@hhhNhNubah}(h!]h#]hah%]h']h)]uh+hhjU@ubeh}(h!]h#]h%]h']h)]hhuh+hhjQ@hhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/rectangle.py:docstring of opengen.constraints.rectangle.Rectangle.xminhKubh)}(hxminh]hxmin}(hhhjr@hhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhjQ@hhhjq@hKubeh}(h!]jK@ah#](jjeh%]h']h)]jopengen.constraints.rectanglejWj5jRectangle.xminjj@ Rectanglexminjj@uh+h|hjq@hKhjN@hhubj)}(hhh]j)}(h Minimum boundh]h Minimum bound}(hj@hj@hhhNhNubah}(h!]h#]h%]h']h)]uh+jhjM@hKhj@hhubah}(h!]h#]h%]h']h)]uh+jhjN@hhhjq@hKubeh}(h!]h#](pypropertyeh%]h']h)]jj@jj@jj@jjjuh+hwhhhjE6hjM@hNubeh}(h!]h#]h%]h']h)]uh+jhj5hhhj5hKubeh}(h!]h#](pyclasseh%]h']h)]jj@jj@jj@jjjuh+hwhhhj5hNhNubeh}(h!](j5$opengen-constraints-rectangle-moduleeh#]h%]$opengen.constraints.rectangle moduleah']h)]uh+h hh hhhh,hKHubh )}(hhh](h)}(h"opengen.constraints.simplex moduleh]h"opengen.constraints.simplex module}(hj@hj@hhhNhNubah}(h!]h#]h%]h']h)]uh+hhj@hhhh,hKPubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hd#module; opengen.constraints.simplex"module-opengen.constraints.simplexhNtauh+hWhj@hhhNhNubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hs.Simplex (class in opengen.constraints.simplex)#opengen.constraints.simplex.SimplexhNtauh+hWhj@hhhNhNubhx)}(hhh](h})}(hSimplex(alpha: float = 1.0)h](h)}(h2[<#text: 'class'>, >]h](hclass}(hhhj@hhhNhNubh)}(h h]h }(hhhj@hhhNhNubah}(h!]h#]hah%]h']h)]uh+hhj@ubeh}(h!]h#]h%]h']h)]hhuh+hhj@hhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/simplex.py:docstring of opengen.constraints.simplex.SimplexhKubh)}(hopengen.constraints.simplex.h]hopengen.constraints.simplex.}(hhhjAhhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhj@hhhjAhKubh)}(hSimplexh]hSimplex}(hhhjAhhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhj@hhhjAhKubh)}(halpha: float = 1.0h]h)}(halpha: float = 1.0h](h)}(halphah]halpha}(hhhj5AhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhj1Aubj#)}(h:h]h:}(hhhjCAhhhNhNubah}(h!]h#]j/ah%]h']h)]uh+j"hj1Aubh)}(h h]h }(hhhjQAhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhj1Aubh)}(hfloath]jF)}(hhh]hfloat}(hhhjcAhhhNhNubah}(h!]h#]h%]h']h)] refdomainjUreftypejW reftargetfloat refspecific py:moduleopengen.constraints.simplexpy:classNuh+jEhj_Aubah}(h!]h#]hah%]h']h)]uh+hhj1Aubh)}(h h]h }(hhhj~AhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhj1Aubh)}(h=h]h=}(hhhjAhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhj1Aubh)}(h h]h }(hhhjAhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhj1Aubh)}(h1.0h]h1.0}(hhhjAhhhNhNubah}(h!]h#]jah%]h']h)]support_smartquotesuh+hhj1Aubeh}(h!]h#]h%]h']h)]hhuh+hhj-Aubah}(h!]h#]h%]h']h)]hhuh+hhj@hhhjAhKubeh}(h!]j@ah#](jjeh%]h']h)]jopengen.constraints.simplexjWhjj!AjjAj!Ajj!Auh+h|hjAhKhj@hhubj)}(hhh](j)}(h=Bases: :py:class:`~opengen.constraints.constraint.Constraint`h](hBases: }(hBases: hjAhhhNhNubjF)}(h6:py:class:`~opengen.constraints.constraint.Constraint`h]j)}(hjAh]h Constraint}(hhhjAhhhNhNubah}(h!]h#](jpypy-classeh%]h']h)]uh+jhjAubah}(h!]h#]h%]h']h)]refdocj refdomainjAreftypeclass refexplicitrefwarnjjAjj!Aj)opengen.constraints.constraint.Constraintuh+jEh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/simplex.py:docstring of opengen.constraints.simplexhKhjAubeh}(h!]h#]h%]h']h)]uh+jh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/simplex.py:docstring of opengen.constraints.simplex.SimplexhKhjAhhubj)}(hSimplex constrainth]hSimplex constraint}(hjBhjAhhhNhNubah}(h!]h#]h%]h']h)]uh+jh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/simplex.py:docstring of opengen.constraints.simplex.SimplexhKhjAhhubj)}(hA set of the formh]hA set of the form}(hjBhjBhhhNhNubah}(h!]h#]h%]h']h)]uh+jhj BhKhjAhhubj)}(hX:math:`X = \left\{x \in \mathrm{I\!R}^n : \sum_{i=1}^{n} x_i = \alpha, x \geq 0\right\}`h]j)}(hX:math:`X = \left\{x \in \mathrm{I\!R}^n : \sum_{i=1}^{n} x_i = \alpha, x \geq 0\right\}`h]hPX = \left\{x \in \mathrm{I\!R}^n : \sum_{i=1}^{n} x_i = \alpha, x \geq 0\right\}}(hhhj BhhhNhNubah}(h!]h#]h%]h']h)]uh+jhjBubah}(h!]h#]h%]h']h)]uh+jhj BhKhjAhhubj)}(h,where :math:`\alpha` is a positive constant.h](hwhere }(hwhere hj4BhhhNhNubj)}(h:math:`\alpha`h]h\alpha}(hhhj=BhhhNhNubah}(h!]h#]h%]h']h)]uh+jhj4Bubh is a positive constant.}(h is a positive constant.hj4BhhhNhNubeh}(h!]h#]h%]h']h)]uh+jhj BhKhjAhhubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hs7__init__() (opengen.constraints.simplex.Simplex method),opengen.constraints.simplex.Simplex.__init__hNtauh+hWhjAhhhNhNubhx)}(hhh](h})}(h$Simplex.__init__(alpha: float = 1.0)h](h)}(h__init__h]h__init__}(hhhjkBhhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhjgBhhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/simplex.py:docstring of opengen.constraints.simplex.Simplex.__init__hKubh)}(halpha: float = 1.0h]h)}(halpha: float = 1.0h](h)}(halphah]halpha}(hhhjBhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhj~Bubj#)}(h:h]h:}(hhhjBhhhNhNubah}(h!]h#]j/ah%]h']h)]uh+j"hj~Bubh)}(h h]h }(hhhjBhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhj~Bubh)}(hfloath]jF)}(hhh]hfloat}(hhhjBhhhNhNubah}(h!]h#]h%]h']h)] refdomainjUreftypejW reftargetfloat refspecific py:modulejApy:classj!Auh+jEhjBubah}(h!]h#]hah%]h']h)]uh+hhj~Bubh)}(h h]h }(hhhjBhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhj~Bubh)}(h=h]h=}(hhhjBhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhj~Bubh)}(h h]h }(hhhjBhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhj~Bubh)}(h1.0h]h1.0}(hhhjBhhhNhNubah}(h!]h#]jah%]h']h)]support_smartquotesuh+hhj~Bubeh}(h!]h#]h%]h']h)]hhuh+hhjzBubah}(h!]h#]h%]h']h)]hhuh+hhjgBhhhjyBhKubeh}(h!]jbBah#](jjeh%]h']h)]jopengen.constraints.simplexjWj!AjSimplex.__init__jjCSimplex__init__jSimplex.__init__()uh+h|hjyBhKhjdBhhubj)}(hhh](j)}(h$Constructor for a Simplex constrainth]h$Constructor for a Simplex constraint}(hj 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pointhjDhhhNhNubeh}(h!]h#]h%]h']h)]uh+jhjDubah}(h!]h#]h%]h']h)]uh+jShjDubeh}(h!]h#]h%]h']h)]uh+j>hjDubj?)}(hhh](jD)}(hReturnsh]hReturns}(hhhjDhhhNhNubah}(h!]h#]h%]h']h)]uh+jChjDhjBDhKubjT)}(hhh]j)}(hsquared distanceh]hsquared distance}(hsquared distancehjDhhhNhNubah}(h!]h#]h%]h']h)]uh+jhjDubah}(h!]h#]h%]h']h)]uh+jShjDubeh}(h!]h#]h%]h']h)]uh+j>hjDubj?)}(hhh](jD)}(h Return typeh]h Return type}(hhhjDhhhNhNubah}(h!]h#]h%]h']h)]uh+jChjDhjBDhKubjT)}(hhh]j)}(hfloath]jF)}(hhh]hfloat}(hhhj EhhhNhNubah}(h!]h#]h%]h']h)] refdomainpy refexplicitreftypejW reftargetfloatj<jjjDjj!Auh+jEhjEubah}(h!]h#]h%]h']h)]uh+jhjEubah}(h!]h#]h%]h']h)]uh+jShjDubeh}(h!]h#]h%]h']h)]uh+j>hjDubeh}(h!]h#]h%]h']h)]uh+j9hjpDhhhNhNubeh}(h!]h#]h%]h']h)]uh+jhj-DhhhjBDhKubeh}(h!]h#](jEmethodeh%]h']h)]jjEjj@Ejj@Ejjjuh+hwhhhjAhNhNubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hs9is_compact() (opengen.constraints.simplex.Simplex 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is convex (`True`)h](hWhether the set is convex (}(hWhether the set is convex (hjEhhhNhNubj3 )}(h`True`h]hTrue}(hhhjEhhhNhNubah}(h!]h#]h%]h']h)]uh+j2 hjEubh)}(hjt7hjEhhhNhNubeh}(h!]h#]h%]h']h)]uh+jhjEhKhjEhhubah}(h!]h#]h%]h']h)]uh+jhjEhhhjEhKubeh}(h!]h#](pymethodeh%]h']h)]jjFjjFjjFjjjuh+hwhhhjAhjEhNubhX)}(hhh]h}(h!]h#]h%]h']h)]entries](hs6project() (opengen.constraints.simplex.Simplex method)+opengen.constraints.simplex.Simplex.projecthNtauh+hWhjAhhhNhNubhx)}(hhh](h})}(hSimplex.project(y)h](h)}(hprojecth]hproject}(hhhj3FhhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhj/Fhhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/simplex.py:docstring of opengen.constraints.simplex.Simplex.projecthKubh)}(hyh]h)}(hyh]h)}(hyh]hy}(hhhjJFhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhjFFubah}(h!]h#]h%]h']h)]hhuh+hhjBFubah}(h!]h#]h%]h']h)]hhuh+hhj/FhhhjAFhKubeh}(h!]j*Fah#](jjeh%]h']h)]jopengen.constraints.simplexjWj!AjSimplex.projectjjjFSimplexprojectjSimplex.project()uh+h|hjAFhKhj,Fhhubj)}(hhh](j)}(h\Computes the projection of a given point :math:`y\in{\rm I\!R}^n` onto the current simplex.h](h)Computes the projection of a given point }(h)Computes the projection of a given point hjsFhhhNhNubj)}(h:math:`y\in{\rm I\!R}^n`h]hy\in{\rm I\!R}^n}(hhhj|FhhhNhNubah}(h!]h#]h%]h']h)]uh+jhjsFubh onto the current simplex.}(h onto the current simplex.hjsFhhhNhNubeh}(h!]h#]h%]h']h)]uh+jh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/simplex.py:docstring of opengen.constraints.simplex.Simplex.projecthKhjpFhhubj:)}(hhh](j?)}(hhh](jD)}(h Parametersh]h Parameters}(hhhjFhhhNhNubah}(h!]h#]h%]h']h)]uh+jChjFhjAFhKubjT)}(hhh]j)}(hYy -- given point; must be a list of numbers (float, int) or a numpy n-dim array (ndarray)h](j])}(hjDFh]hy}(hhhjFhhhNhNubah}(h!]h#]h%]h']h)]uh+j\hjFubh – }(hhhjFhhhNhNubhLgiven point; must be a list of numbers (float, int) or a numpy n-dim array (}(hLgiven point; must be a list of numbers (float, int) or a numpy n-dim array (hjFhhhNhNubj3 )}(h `ndarray`h]hndarray}(hhhjFhhhNhNubah}(h!]h#]h%]h']h)]uh+j2 hjFhhhNhNubh)}(hjt7hjFhhhNhNubeh}(h!]h#]h%]h']h)]uh+jhjFubah}(h!]h#]h%]h']h)]uh+jShjFubeh}(h!]h#]h%]h']h)]uh+j>hjFubj?)}(hhh](jD)}(hReturnsh]hReturns}(hhhjFhhhNhNubah}(h!]h#]h%]h']h)]uh+jChjFhjAFhKubjT)}(hhh]j)}(hAthe projection point in {\rm I\!R}^n as a numpy array of float64sh](hthe projection point in }(hthe projection point in hjFhhhNhNubj)}(h:math:`{\rm I\!R}^n`h]h {\rm I\!R}^n}(hhhjGhhhNhNubah}(h!]h#]h%]h']h)]uh+jhjFhhhNhNubh as a numpy array of float64s}(h as a numpy array of float64shjFhhhNhNubeh}(h!]h#]h%]h']h)]uh+jhjFubah}(h!]h#]h%]h']h)]uh+jShjFubeh}(h!]h#]h%]h']h)]uh+j>hjFubeh}(h!]h#]h%]h']h)]uh+j9hjpFhhhNhNubeh}(h!]h#]h%]h']h)]uh+jhj,FhhhjAFhKubeh}(h!]h#](pymethodeh%]h']h)]jj, >]h](hclass}(hhhjGhhhNhNubh)}(h h]h }(hhhjGhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhjGubeh}(h!]h#]h%]h']h)]hhuh+hhjGhhh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/soc.py:docstring of opengen.constraints.soc.SecondOrderConehKubh)}(hopengen.constraints.soc.h]hopengen.constraints.soc.}(hhhjGhhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhjGhhhjGhKubh)}(hSecondOrderConeh]hSecondOrderCone}(hhhjGhhhNhNubah}(h!]h#](hheh%]h']h)]hhuh+hhjGhhhjGhKubh)}(ha: float = 1.0h]h)}(ha: float = 1.0h](h)}(hah]ha}(hhhjGhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhjGubj#)}(h:h]h:}(hhhjGhhhNhNubah}(h!]h#]j/ah%]h']h)]uh+j"hjGubh)}(h h]h }(hhhjGhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhjGubh)}(hfloath]jF)}(hhh]hfloat}(hhhjGhhhNhNubah}(h!]h#]h%]h']h)] refdomainjUreftypejW reftargetfloat refspecific py:moduleopengen.constraints.socpy:classNuh+jEhjGubah}(h!]h#]hah%]h']h)]uh+hhjGubh)}(h h]h }(hhhjHhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhjGubh)}(h=h]h=}(hhhj#HhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhjGubh)}(h h]h }(hhhj1HhhhNhNubah}(h!]h#]hah%]h']h)]uh+hhjGubh)}(h1.0h]h1.0}(hhhj?HhhhNhNubah}(h!]h#]jah%]h']h)]support_smartquotesuh+hhjGubeh}(h!]h#]h%]h']h)]hhuh+hhjGubah}(h!]h#]h%]h']h)]hhuh+hhjGhhhjGhKubeh}(h!]jGah#](jjeh%]h']h)]jopengen.constraints.socjWhjjGjj`HjGjjGuh+h|hjGhKhjGhhubj)}(hhh](j)}(h=Bases: :py:class:`~opengen.constraints.constraint.Constraint`h](hBases: }(hBases: hjeHhhhNhNubjF)}(h6:py:class:`~opengen.constraints.constraint.Constraint`h]j)}(hjpHh]h Constraint}(hhhjrHhhhNhNubah}(h!]h#](jpypy-classeh%]h']h)]uh+jhjnHubah}(h!]h#]h%]h']h)]refdocj refdomainj|Hreftypeclass refexplicitrefwarnjj`HjjGj)opengen.constraints.constraint.Constraintuh+jEh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/soc.py:docstring of opengen.constraints.sochKhjeHubeh}(h!]h#]h%]h']h)]uh+jh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/soc.py:docstring of opengen.constraints.soc.SecondOrderConehKhjbHhhubj)}(hFA Second-Order Cone given by :math:`C = \{u = (x, r): a\|x\| \leq r\}`h](hA Second-Order Cone given by }(hA Second-Order Cone given by hjHhhhNhNubj)}(h):math:`C = \{u = (x, r): a\|x\| \leq r\}`h]h!C = \{u = (x, r): a\|x\| \leq r\}}(hhhjHhhhNhNubah}(h!]h#]h%]h']h)]uh+jhjHubeh}(h!]h#]h%]h']h)]uh+jh/Users/3054363/Documents/Development/OpEn/open-codegen/venv/lib/python3.8/site-packages/opengen/constraints/soc.py:docstring of opengen.constraints.soc.SecondOrderConehKhjbHhhubj)}(hgSecond-order cones are used in conic optimisation to describe inequalities that 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