o o hc@sdZddlmZmZddlmZddlmZddlm Z m Z m Z ddl m Z ddlmZmZddlmZdd lmZgd ZGd d d eeZGd ddeZGdddeZdS)aLActivation dynamics for musclotendon models. Musculotendon models are able to produce active force when they are activated, which is when a chemical process has taken place within the muscle fibers causing them to voluntarily contract. Biologically this chemical process (the diffusion of :math:`\textrm{Ca}^{2+}` ions) is not the input in the system, electrical signals from the nervous system are. These are termed excitations. Activation dynamics, which relates the normalized excitation level to the normalized activation level, can be modeled by the models present in this module. )ABCabstractmethod)cached_property)Symbol)FloatIntegerRational)tanh)MutableDenseMatrixzeros) _NamedMixin)dynamicsymbols)ActivationBase FirstOrderActivationDeGroote2016ZerothOrderActivationc@seZdZdZddZeeddZeddZ edd Z ed d Z ed d Z eeddZ eeddZeeddZeeddZeeddZeeddZeeddZeeddZeeddZed d!Zd"d#Zd$d%Zd&S)'ra Abstract base class for all activation dynamics classes to inherit from. Notes ===== Instances of this class cannot be directly instantiated by users. However, it can be used to created custom activation dynamics types through subclassing. cCs.t||_td||_td||_dS)z#Initializer for ``ActivationBase``.e_a_N)strnamer _e_aselfrry/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/sympy/physics/biomechanics/activation.py__init__,s zActivationBase.__init__cCdS)zOAlternate constructor that provides recommended defaults for constants.Nrclsrrrr with_defaults4szActivationBase.with_defaultscC|jS)zDynamic symbol representing excitation. Explanation =========== The alias ``e`` can also be used to access the same attribute. rrrrr excitation; zActivationBase.excitationcCr )zDynamic symbol representing excitation. Explanation =========== The alias ``excitation`` can also be used to access the same attribute. r!r"rrreGr$zActivationBase.ecCr )zDynamic symbol representing activation. Explanation =========== The alias ``a`` can also be used to access the same attribute. rr"rrr activationSr$zActivationBase.activationcCr )zDynamic symbol representing activation. Explanation =========== The alias ``activation`` can also be used to access the same attribute. r&r"rrra_r$zActivationBase.acCr):Order of the (differential) equation governing activation.Nrr"rrrorderkszActivationBase.ordercCr)Ordered column matrix of functions of time that represent the state variables. Explanation =========== The alias ``x`` can also be used to access the same attribute. Nrr"rrr state_varsq zActivationBase.state_varscCr)Ordered column matrix of functions of time that represent the state variables. Explanation =========== The alias ``state_vars`` can also be used to access the same attribute. Nrr"rrrxr-zActivationBase.xcCr)Ordered column matrix of functions of time that represent the input variables. Explanation =========== The alias ``r`` can also be used to access the same attribute. Nrr"rrr input_varsr-zActivationBase.input_varscCr)Ordered column matrix of functions of time that represent the input variables. Explanation =========== The alias ``input_vars`` can also be used to access the same attribute. Nrr"rrrrr-zActivationBase.rcCr)zOrdered column matrix of non-time varying symbols present in ``M`` and ``F``. Only symbolic constants are returned. If a numeric type (e.g. ``Float``) has been used instead of ``Symbol`` for a constant then that attribute will not be included in the matrix returned by this property. This is because the primary use of this property attribute is to provide an ordered sequence of the still-free symbols that require numeric values during code generation. Explanation =========== The alias ``p`` can also be used to access the same attribute. Nrr"rrr constantszActivationBase.constantscCr)aOrdered column matrix of non-time varying symbols present in ``M`` and ``F``. Only symbolic constants are returned. If a numeric type (e.g. ``Float``) has been used instead of ``Symbol`` for a constant then that attribute will not be included in the matrix returned by this property. This is because the primary use of this property attribute is to provide an ordered sequence of the still-free symbols that require numeric values during code generation. Explanation =========== The alias ``constants`` can also be used to access the same attribute. Nrr"rrrpr6zActivationBase.pcCr)<Ordered square matrix of coefficients on the LHS of ``M x' = F``. Explanation =========== The square matrix that forms part of the LHS of the linear system of ordinary differential equations governing the activation dynamics: ``M(x, r, t, p) x' = F(x, r, t, p)``. Nrr"rrrMzActivationBase.McCr)1Ordered column matrix of equations on the RHS of ``M x' = F``. Explanation =========== The column matrix that forms the RHS of the linear system of ordinary differential equations governing the activation dynamics: ``M(x, r, t, p) x' = F(x, r, t, p)``. Nrr"rrrFr:zActivationBase.FcCr)z Explanation =========== The solution to the linear system of ordinary differential equations governing the activation dynamics: ``M(x, r, t, p) x' = F(x, r, t, p)``. Nrr"rrrrhss zActivationBase.rhscCs(t|t|kr dS|j|jkrdSdS)z'Equality check for activation dynamics.FT)typer)rotherrrr__eq__s  zActivationBase.__eq__cCs|jjd|jdS)z.Default representation of activation dynamics.()) __class____name__rr"rrr__repr__ szActivationBase.__repr__N)rD __module__ __qualname____doc__r classmethodrrpropertyr#r%r'r(r*r,r/r1r3r5r7r9r<r=r@rErrrrr sZ                      rcseZdZdZfddZeddZeddZedd Z ed d Z ed d Z eddZ eddZ eddZeddZeddZddZZS)raSimple zeroth-order activation dynamics mapping excitation to activation. Explanation =========== Zeroth-order activation dynamics are useful in instances where you want to reduce the complexity of your musculotendon dynamics as they simple map exictation to activation. As a result, no additional state equations are introduced to your system. They also remove a potential source of delay between the input and dynamics of your system as no (ordinary) differential equations are involed. cst||j|_dS)zInitializer for ``ZerothOrderActivation``. Parameters ========== name : str The name identifier associated with the instance. Must be a string of length at least 1. N)superrrrrrCrrrs zZerothOrderActivation.__init__cCs||S)aAlternate constructor that provides recommended defaults for constants. Explanation =========== As this concrete class doesn't implement any constants associated with its dynamics, this ``classmethod`` simply creates a standard instance of ``ZerothOrderActivation``. An implementation is provided to ensure a consistent interface between all ``ActivationBase`` concrete classes. rrrrrr0sz#ZerothOrderActivation.with_defaultscCr)r)rrr"rrrr*@zZerothOrderActivation.ordercC tddS)aOrdered column matrix of functions of time that represent the state variables. Explanation =========== As zeroth-order activation dynamics simply maps excitation to activation, this class has no associated state variables and so this property return an empty column ``Matrix`` with shape (0, 1). The alias ``x`` can also be used to access the same attribute. rr r"rrrr,E z ZerothOrderActivation.state_varscCrN)aOrdered column matrix of functions of time that represent the state variables. Explanation =========== As zeroth-order activation dynamics simply maps excitation to activation, this class has no associated state variables and so this property return an empty column ``Matrix`` with shape (0, 1). The alias ``state_vars`` can also be used to access the same attribute. rrOrPr"rrrr/VrQzZerothOrderActivation.xcC t|jgS)aOrdered column matrix of functions of time that represent the input variables. Explanation =========== Excitation is the only input in zeroth-order activation dynamics and so this property returns a column ``Matrix`` with one entry, ``e``, and shape (1, 1). The alias ``r`` can also be used to access the same attribute. Matrixrr"rrrr1g z ZerothOrderActivation.input_varscCrR)aOrdered column matrix of functions of time that represent the input variables. Explanation =========== Excitation is the only input in zeroth-order activation dynamics and so this property returns a column ``Matrix`` with one entry, ``e``, and shape (1, 1). The alias ``input_vars`` can also be used to access the same attribute. rSr"rrrr3xrUzZerothOrderActivation.rcCrN)aNOrdered column matrix of non-time varying symbols present in ``M`` and ``F``. Only symbolic constants are returned. If a numeric type (e.g. ``Float``) has been used instead of ``Symbol`` for a constant then that attribute will not be included in the matrix returned by this property. This is because the primary use of this property attribute is to provide an ordered sequence of the still-free symbols that require numeric values during code generation. Explanation =========== As zeroth-order activation dynamics simply maps excitation to activation, this class has no associated constants and so this property return an empty column ``Matrix`` with shape (0, 1). The alias ``p`` can also be used to access the same attribute. rrOrPr"rrrr5 zZerothOrderActivation.constantscCrN)aVOrdered column matrix of non-time varying symbols present in ``M`` and ``F``. Only symbolic constants are returned. If a numeric type (e.g. ``Float``) has been used instead of ``Symbol`` for a constant then that attribute will not be included in the matrix returned by this property. This is because the primary use of this property attribute is to provide an ordered sequence of the still-free symbols that require numeric values during code generation. Explanation =========== As zeroth-order activation dynamics simply maps excitation to activation, this class has no associated constants and so this property return an empty column ``Matrix`` with shape (0, 1). The alias ``constants`` can also be used to access the same attribute. rrOrPr"rrrr7rVzZerothOrderActivation.pcCstgS)aOrdered square matrix of coefficients on the LHS of ``M x' = F``. Explanation =========== The square matrix that forms part of the LHS of the linear system of ordinary differential equations governing the activation dynamics: ``M(x, r, t, p) x' = F(x, r, t, p)``. As zeroth-order activation dynamics have no state variables, this linear system has dimension 0 and therefore ``M`` is an empty square ``Matrix`` with shape (0, 0). )rTr"rrrr9szZerothOrderActivation.McCrN)aOrdered column matrix of equations on the RHS of ``M x' = F``. Explanation =========== The column matrix that forms the RHS of the linear system of ordinary differential equations governing the activation dynamics: ``M(x, r, t, p) x' = F(x, r, t, p)``. As zeroth-order activation dynamics have no state variables, this linear system has dimension 0 and therefore ``F`` is an empty column ``Matrix`` with shape (0, 1). rrOrPr"rrrr<s zZerothOrderActivation.FcCrN)aOrdered column matrix of equations for the solution of ``M x' = F``. Explanation =========== The solution to the linear system of ordinary differential equations governing the activation dynamics: ``M(x, r, t, p) x' = F(x, r, t, p)``. As zeroth-order activation dynamics have no state variables, this linear has dimension 0 and therefore this method returns an empty column ``Matrix`` with shape (0, 1). rrOrPr"rrrr=s zZerothOrderActivation.rhs)rDrFrGrHrrIrrJr*r,r/r1r3r5r7r9r<r= __classcell__rrrLrrs0           rcs6eZdZdZ   d0fdd ZeddZeddZej d dZed d Z ed d Z e j dd Z eddZ eddZ e j ddZ eddZeddZeddZeddZeddZeddZed d!Zed"d#Zed$d%Zed&d'Zd(d)Zed*d+Zd,d-Zd.d/ZZS)1raAFirst-order activation dynamics based on De Groote et al., 2016 [1]_. Explanation =========== Gives the first-order activation dynamics equation for the rate of change of activation with respect to time as a function of excitation and activation. The function is defined by the equation: .. math:: \frac{da}{dt} = \left(\frac{\frac{1}{2} + a0}{\tau_a \left(\frac{1}{2} + \frac{3a}{2}\right)} + \frac{\left(\frac{1}{2} + \frac{3a}{2}\right) \left(\frac{1}{2} - a0\right)}{\tau_d}\right) \left(e - a\right) where .. math:: a0 = \frac{\tanh{\left(b \left(e - a\right) \right)}}{2} with constant values of :math:`tau_a = 0.015`, :math:`tau_d = 0.060`, and :math:`b = 10`. References ========== .. [1] De Groote, F., Kinney, A. L., Rao, A. V., & Fregly, B. J., Evaluation of direct collocation optimal control problem formulations for solving the muscle redundancy problem, Annals of biomedical engineering, 44(10), (2016) pp. 2922-2936 Ncs"t|||_||_||_dS)aInitializer for ``FirstOrderActivationDeGroote2016``. Parameters ========== activation time constant : Symbol | Number | None The value of the activation time constant governing the delay between excitation and activation when excitation exceeds activation. deactivation time constant : Symbol | Number | None The value of the deactivation time constant governing the delay between excitation and activation when activation exceeds excitation. smoothing_rate : Symbol | Number | None The slope of the hyperbolic tangent function used to smooth between the switching of the equations where excitation exceed activation and where activation exceeds excitation. The recommended value to use is ``10``, but values between ``0.1`` and ``100`` can be used. N)rKractivation_time_constantdeactivation_time_constantsmoothing_rate)rrrXrYrZrLrrrs  z)FirstOrderActivationDeGroote2016.__init__cCs&td}td}td}|||||S)awAlternate constructor that will use the published constants. Explanation =========== Returns an instance of ``FirstOrderActivationDeGroote2016`` using the three constant values specified in the original publication. These have the values: :math:`tau_a = 0.015` :math:`tau_d = 0.060` :math:`b = 10` z0.015z0.060z10.0)r)rrtau_atau_dbrrrr8sz.FirstOrderActivationDeGroote2016.with_defaultscCr )zDelay constant for activation. Explanation =========== The alias ```tau_a`` can also be used to access the same attribute. _tau_ar"rrrrXNr$z9FirstOrderActivationDeGroote2016.activation_time_constantcCRt|drdt|d|jd}t||dur$td|j|_dS||_dS)Nr_z2Can't set attribute `activation_time_constant` to * as it is immutable and already has value .tau_a_)hasattrreprr_AttributeErrorrr)rr[msgrrrrXZ (cCr )zDelay constant for activation. Explanation =========== The alias ``activation_time_constant`` can also be used to access the same attribute. r^r"rrrr[e z&FirstOrderActivationDeGroote2016.tau_acCr )zDelay constant for deactivation. Explanation =========== The alias ``tau_d`` can also be used to access the same attribute. _tau_dr"rrrrYrr$z;FirstOrderActivationDeGroote2016.deactivation_time_constantcCr`)Nrkz4Can't set attribute `deactivation_time_constant` to rarbtau_d_)rdrerkrfrr)rr\rgrrrrY~rhcCr )zDelay constant for deactivation. Explanation =========== The alias ``deactivation_time_constant`` can also be used to access the same attribute. rjr"rrrr\riz&FirstOrderActivationDeGroote2016.tau_dcCr )zSmoothing constant for the hyperbolic tangent term. Explanation =========== The alias ``b`` can also be used to access the same attribute. _br"rrrrZr$z/FirstOrderActivationDeGroote2016.smoothing_ratecCsNt|drd|d|jd}t||dur"td|j|_dS||_dS)Nrnz(Can't set attribute `smoothing_rate` to rarbb_)rdrnrfrr)rr]rgrrrrZs (cCr )zSmoothing constant for the hyperbolic tangent term. Explanation =========== The alias ``smoothing_rate`` can also be used to access the same attribute. rmr"rrrr]riz"FirstOrderActivationDeGroote2016.bcCr)r)rOrr"rrrr*rMz&FirstOrderActivationDeGroote2016.ordercCrR)r+rTrr"rrrr, z+FirstOrderActivationDeGroote2016.state_varscCrR)r.rpr"rrrr/rqz"FirstOrderActivationDeGroote2016.xcCrR)r0rSr"rrrr1rqz+FirstOrderActivationDeGroote2016.input_varscCrR)r2rSr"rrrr3rqz"FirstOrderActivationDeGroote2016.rcC4|j|j|jg}dd|D}|rt|StddS)r4cSg|]}|js|qSr is_number.0crrr z>FirstOrderActivationDeGroote2016.constants..rrOr_rkrnrTr rr5symbolic_constantsrrrr5z*FirstOrderActivationDeGroote2016.constantscCrr)aOrdered column matrix of non-time varying symbols present in ``M`` and ``F``. Explanation =========== Only symbolic constants are returned. If a numeric type (e.g. ``Float``) has been used instead of ``Symbol`` for a constant then that attribute will not be included in the matrix returned by this property. This is because the primary use of this property attribute is to provide an ordered sequence of the still-free symbols that require numeric values during code generation. The alias ``constants`` can also be used to access the same attribute. cSrsrrtrvrrrryrzz6FirstOrderActivationDeGroote2016.p..rrOr{r|rrrr7r~z"FirstOrderActivationDeGroote2016.pcCsttdgS)r8rO)rTrr"rrrr9s z"FirstOrderActivationDeGroote2016.McCrR)r;rT_da_eqnr"rrrr<-s z"FirstOrderActivationDeGroote2016.FcCrR)aOrdered column matrix of equations for the solution of ``M x' = F``. Explanation =========== The solution to the linear system of ordinary differential equations governing the activation dynamics: ``M(x, r, t, p) x' = F(x, r, t, p)``. rr"rrrr=<s z$FirstOrderActivationDeGroote2016.rhscCsttdd}|t|j|j|j}|tdd|j}|||j|}||||j}|||j|j}|S)NrO)rr rnrrr_rk)rHALFa0a1a2a3activation_dynamics_equationrrrrJs z(FirstOrderActivationDeGroote2016._da_eqncCsLt|t|kr dS|j|j|j|jf}|j|j|j|jf}||kr$dSdS)z8Equality check for ``FirstOrderActivationDeGroote2016``.FT)r>rr[r\r])rr? self_attrs other_attrsrrrr@Tsz'FirstOrderActivationDeGroote2016.__eq__c Cs.|jjd|jd|jd|jd|jd S)z7Representation of ``FirstOrderActivationDeGroote2016``.rAz, activation_time_constant=z, deactivation_time_constant=z, smoothing_rate=rB)rCrDrr[r\r]r"rrrrE^sz)FirstOrderActivationDeGroote2016.__repr__)NNN)rDrFrGrHrrIrrJrXsetterr[rYr\rZr]r*r,r/r1r3r5r7r9r<r=rrr@rErWrrrLrrsb'                      rN)rHabcrr functoolsrsympy.core.symbolrsympy.core.numbersrrr%sympy.functions.elementary.hyperbolicr sympy.matrices.denser rTr !sympy.physics.biomechanics._mixinr sympy.physics.mechanicsr __all__rrrrrrrs     pd