This class implements the nonlinear continuum mechanics as described in [5] . More...

Detailed Description

This class implements the nonlinear continuum mechanics as described in [5] .

Definition at line 19 of file Dynamics.m.

Public Member Functions
	Dynamics (sys)

function	configUpdated ()

function	prepareSimulation (colvec< double > mu)

function fx =	evaluateCoreFun (colvec< double > x,double t)
	Actual method used to evaluate the dynamical sytems' core function. More...

function fx =	evaluateComponentSet (integer nr,colvec< double > x,double t)
	Computes the full or reduced component functions of the given point set. More...

function fx =	evaluateComponentSetMulti (integer nr,matrix< double > x,rowvec< double > t,matrix< double > mu)
	Computes the full component functions of the given point set. More...

function res =	test_Jacobian (matrix< double > y,double t,colvec< double > mu)
	Overrides the random argument jacobian test as restrictions on the possible x values (detF = 1) hold. More...

function copy =	clone ()
	Create new instance. More...

function	setSystem (sys)

function copy =	project (V, W)

function [ SPK , SPg , SPalpha , SPLamDot ] =	computeSparsityPattern ()
	Computes all sorts of patterns simultaneously. More...

Public Member Functions inherited from dscomponents.ACompEvalCoreFun
	ACompEvalCoreFun (sys)

function fx =	evaluateComponentSet (integer nr,colvec< double > x,double t)
	Computes the full or reduced component functions of the given point set. More...

function fx =	evaluateComponentSetMulti (integer nr,matrix< double > x,rowvec< double > t,matrix< double > mu)
	Computes the full component functions of the given point set. More...

function dfx =	evaluateComponentSetGradientsAt (integer nr,colvec< double > x,double t)
	Computes the full/reduced gradients of all component functions of the given point set. More...

function J =	evaluateJacobianSet (integer nr,colvec< double > x,double t)
	Returns the jacobian entries of the point set that have been specified using setPointSet's argument jpd. More...

function J =	evaluateJacobianSetMulti (integer nr,matrix< double > x,rowvec< double > t,colvec< double > mu)
	Returns the jacobian entries at multiple locations/times/parameters of the point set that have been specified using setPointSet's argument jpd. More...

function	setPointSet (nr, pts, jpd)
	Parameters: pts: A row vector with the desired points jpd: ("Jacobian Partial Derivatives") A cell array of size equal to the number of points. Each cell contains the indices for which the partial derivatives of the corresponding component function will be computed when calling evaluateJacobianSet. More...

function target =	project (V, W, target)

function copy =	clone (copy)
	The interface method with returns a copy of the current class instance. More...

function res =	test_ComponentEvalMatch (xsize)
	Tests if the local implementation of evaluateComponents matches the full evaluation. More...

Public Member Functions inherited from dscomponents.ACoreFun
	ACoreFun (sys)

function	setSystem (sys)

function target =	project (V, W, target)
	Sets the protected \(\vV,\vW\) matrices that can be utilized on core function evaluations after projection. More...

function fx =	evaluate (x, t)
	Evaluates the f-approximation. Depending on a possible projection and the CustomProjection-property the function either calls the inner evaluation directly which assumes \(f = f^r(z)\) or projects the reduced state variable z into the original space and evaluates the function there, so via \(f = V'f(Vz)\). More...

function fx =	evaluateMulti (colvec< double > x,double t,colvec< double > mu)
	Evaluates this function on multiple locations and maybe multiple times and parameters. More...

function	prepareSimulation (colvec< double > mu)
	A method that allows parameter-dependent computations to be performed before a simulation using this parameter starts. More...

function J =	getStateJacobian (x, t)
	Default implementation of jacobian matrix evaluation via finite differences. More...

function J =	getStateJacobianImpl (colvec< double > x,double t)
	Default implementation of state jacobians. uses finite differences. More...

function copy =	clone (copy)
	The interface method with returns a copy of the current class instance. More...

function [ matrix< double > J , dx ] =	getStateJacobianFD (x, t,rowvec< integer > partidx)
	Implementation of jacobian matrix evaluation via finite differences. More...

function res =	test_MultiArgEval (mudim)
	Convenience function that tests if a custom MultiArgumentEvaluation works as if called with single arguments. More...

function logical res =	test_Jacobian (matrix< double > xa,rowvec< double > ta,matrix< double > mua)
	Tests the custom provided jacobian matrix against the default finite difference computed one. More...

Public Member Functions inherited from KerMorObject
	KerMorObject ()
	Constructs a new KerMor object. More...

function	display ()
	disp(object2str(this)); More...

function bool =	eq (B)
	Checks equality of two KerMor objects. More...

function bool =	ne (B)
	Checks if two KerMorObjects are different. More...

function cn =	getClassName ()
	Returns the simple class name of this object without packages. More...

Public Member Functions inherited from DPCMObject
	DPCMObject ()
	Creates a new DPCM object. More...

	DPCMObject ()

Public Member Functions inherited from general.AProjectable
function handle target =	project (matrix< double > V,matrix< double > W,handle target)
	Returns a NEW INSTANCE of the projected object that does not rely on data of the old one via references (everything must be copied to ensure separability of reduced(=projected) versions and full versions, unless. More...

function copy =	clone (copy)
	The interface method with returns a copy of the current class instance. More...

Public Attributes
	b1cf = 5.316372204148964
	Cross-fibre markert part [MPa] = [N/mm²]. More...

	d1cf = 0.014991843974911
	[-] More...

function_handle	alpha = @("t")0
	The activation of the muscle at time t [-]. More...

	ComputeUnassembled = false
	% Unassembled stuff More...

	Sigma
	Sigma assembly matrix. More...

	idx_uv_bc_glob_unass
	The indices of any dirichlet value in the unassembled vector duvw. More...

	fDim_unass

	num_dv_unass

	idx_v_elems_unass

	ForceLengthFun
	% Force length function fields More...

	ForceLengthFunDeriv

	APExp

	AnisoPassiveMuscle

	AnisoPassiveMuscleDeriv

	AnisoPassiveTendon

	AnisoPassiveTendonDeriv

	lambda_dot_pos
	Helper variable for fullmodels.muscle.model. More...

	lambda_dot

	nfibres

	LastBCResiduals
	Prepared arguments for APExpansion muprep;. More...

	nfevals

	nJevals

	RampTime
	Helper value for QuickReleaseTests (or others) that use a function handle with certain alpha ramp time for different simulations. Used in getSimCacheExtra to uniquely identify a simulation in the cache. More...

Public Attributes inherited from dscomponents.ACompEvalCoreFun
	PointSets

Public Attributes inherited from dscomponents.ACoreFun
logical	TimeDependent = true
	Flag that indicates if the ACoreFun is (truly) time-dependent. More...

	CustomProjection = false
	Set this property if the projection process is customized by overriding the default project method. More...

sparse< logical >	JSparsityPattern = "[]"
	Sparsity pattern for the jacobian matrix. More...

integer	xDim = "[]"
	The current state space dimension of the function's argument \(x\). More...

integer	fDim = "[]"
	The current output dimension of the function. More...

models.BaseFirstOrderSystem	System
	The system associated with the current ACoreFun. More...

colvec< double >	mu = "[]"
	The current model parameter mu for evaluations. Will not be persisted as only valid for runtime during simulations. More...

	Vcache

	Wcache

Public Attributes inherited from DPCMObject
	WorkspaceVariableName = ""
	The workspace variable name of this class. Optional. More...

	ID = "[]"
	An ID that allows to uniquely identify this DPCMObject (at least within the current MatLab session/context). More...

	PropertiesChanged = "[]"
	The Dictionary containing all the property settings as key/value pairs. More...

Public Attributes inherited from handle
	addlistener
	Creates a listener for the specified event and assigns a callback function to execute when the event occurs. More...

	notify
	Broadcast a notice that a specific event is occurring on a specified handle object or array of handle objects. More...

	delete
	Handle object destructor method that is called when the object's lifecycle ends. More...

	disp
	Handle object disp method which is called by the display method. See the MATLAB disp function. More...

	display
	Handle object display method called when MATLAB software interprets an expression returning a handle object that is not terminated by a semicolon. See the MATLAB display function. More...

	findobj
	Finds objects matching the specified conditions from the input array of handle objects. More...

	findprop
	Returns a meta.property objects associated with the specified property name. More...

	fields
	Returns a cell array of string containing the names of public properties. More...

	fieldnames
	Returns a cell array of string containing the names of public properties. See the MATLAB fieldnames function. More...

	isvalid
	Returns a logical array in which elements are true if the corresponding elements in the input array are valid handles. This method is Sealed so you cannot override it in a handle subclass. More...

	eq
	Relational functions example. See details for more information. More...

	transpose
	Transposes the elements of the handle object array. More...

	permute
	Rearranges the dimensions of the handle object array. See the MATLAB permute function. More...

	reshape
	hanges the dimensions of the handle object array to the specified dimensions. See the MATLAB reshape function. More...

	sort
	ort the handle objects in any array in ascending or descending order. More...

Public Attributes inherited from general.AProjectable
	V
	The \(V\) matrix of the biorthogonal pair \(V,W\). More...

	W
	The \(W\) matrix of the biorthogonal pair \(V,W\). More...

Protected Member Functions
function fx =	evaluateComponents (rowvec< integer > pts,rowvec< integer > ends, unused1, unused2,matrix< double > x, unused3)
	This is the template method that actually evaluates the components at given points and values. More...

function dfx =	evaluateComponentPartialDerivatives (rowvec< integer > pts,rowvec< integer > ends,rowvec< integer > idx,rowvec< integer > deriv,rowvec< integer > self,colvec< double > x,double t, dfxsel)
	Computes specified partial derivatives of \(f\) of the components given by pts and the selected partial derivatives by dfxsel. More...

Protected Member Functions inherited from dscomponents.ACompEvalCoreFun
function matrix < double > dfx =	evaluateComponentGradientsAt (rowvec< integer > pts,rowvec< integer > ends,rowvec< integer > idx,rowvec< integer > self,colvec< double > x,double t)
	Default implementation of gradient computation via finite differences. More...

function dfx =	evaluateComponentPartialDerivatives (rowvec< integer > pts,rowvec< integer > ends,rowvec< integer > idx,rowvec< integer > deriv,rowvec< integer > self,colvec< double > x,double t, dfxsel)
	Computes specified partial derivatives of \(f\) of the components given by pts and the selected partial derivatives by dfxsel. More...

function dfx =	evaluateComponentPartialDerivativesMulti (pts, ends, idx, deriv, self,colvec< double > x,double t,colvec< double > mu, dfxsel)
	Multi-argument evaluation method for partial derivatives. Not used so far in KerMor, this is "legacy code" to keep around if needed at any stage as default finite difference-implementation. More...

function fx =	evaluateComponentsMulti (pts, ends, idx, self,colvec< double > x,double t,colvec< double > mu)

virtual function fx =	evaluateComponents (rowvec< integer > pts,rowvec< integer > ends,rowvec< integer > idx,rowvec< integer > self,matrix< double > x,rowvec< double > t,colvec< double > mu)
	This is the template method that actually evaluates the components at given points and values. More...

Protected Member Functions inherited from KerMorObject
function	checkType (obj, type)
	Object typechecker. More...

Protected Member Functions inherited from DPCMObject
function	registerProps (varargin)
	Call this method at any class that defines DPCM observed properties. More...

function	registerProps (varargin)

Additional Inherited Members
Static Protected Member Functions inherited from dscomponents.ACompEvalCoreFun
static function obj =	loadobj (obj, from)

Static Protected Member Functions inherited from dscomponents.ACoreFun
static function obj =	loadobj (obj, from)

Static Protected Member Functions inherited from DPCMObject
static function obj =	loadobj (obj, from)
	Re-register any registered change listeners! More...

static function obj =	loadobj (obj, from)

Static Protected Member Functions inherited from general.AProjectable
static function obj =	loadobj (obj, from)

Protected Attributes inherited from dscomponents.ACompEvalCoreFun
matrix< double >	S = {""}
	The x-component selection matrices (precomputed on setting PointSet/AltPointSet). �S� is passed to the function evaluating the components of �� or its derivatives. More...

Constructor & Destructor Documentation

models.muscle.Dynamics.Dynamics ( sys )

Definition at line 201 of file Dynamics.m.

Member Function Documentation

function copy = models.muscle.Dynamics.clone ( )

Create new instance.

Definition at line 339 of file Dynamics.m.

function [ SPK , SPg , SPalpha , SPLamDot ] = models.muscle.Dynamics.computeSparsityPattern ( )

Computes all sorts of patterns simultaneously.

Definition at line 20 of file computeSparsityPattern.m.

References k.

Referenced by configUpdated().

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function models.muscle.Dynamics.configUpdated ( )

Definition at line 212 of file Dynamics.m.

References computeSparsityPattern(), dscomponents.ACoreFun.fDim, dscomponents.ACoreFun.JSparsityPattern, nfibres, and dscomponents.ACoreFun.xDim.

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function dfx = models.muscle.Dynamics.evaluateComponentPartialDerivatives	(	rowvec< integer >	pts,
		rowvec< integer >	ends,
		rowvec< integer >	idx,
		rowvec< integer >	deriv,
		rowvec< integer >	self,
		colvec< double >	x,
		double	t,
			dfxsel
	)

protected

Computes specified partial derivatives of \(f\) of the components given by pts and the selected partial derivatives by dfxsel.

See Also: setPointSet

Parameters

pts	The components of \(f\) for which derivatives are required
ends	At the \(i\)-th entry it contains the last position in the \(\vx\) vector that indicates an input value relevant for the \(i\)-th point evaluation, i.e. \(f_i(\vx) = f_i(\vx(ends(i-1){:}ends(i)));\)
idx	The indices of \(\vx\)-entries in the global \(\vx\) vector w.r.t the \(i\)-th point, e.g. \(xglobal(i-1:i+1) = \vx(ends(i-1):ends(i))\)
deriv	The indices within \(\vx\) that derivatives are required for.
self	The positions in the \(\vx\) vector that correspond to the \(i\)-th output dimension, if applicable (usually \(f_i\) depends on \(x_i\), but not necessarily)
x	The state space location \(\vx\)
t	The corresponding times \(t\) for the state \(\vx\)
dfxsel	A derivative selection matrix. Contains the mapping for each row of x to the output points pts. As deriv might contain less than `size(x,1)` values, use
mu	The corresponding parameter \(\mu\) for the state \(\vx\)
dfxsel(,deriv)'	to select the mapping for the actually computed derivatives.

Return values

dfx	A column vector with `numel(deriv)` rows containing the derivatives at all specified pts i with respect to the coordinates given by `idx(ends(i-1):ends(i))`

Definition at line 429 of file Dynamics.m.

function fx = models.muscle.Dynamics.evaluateComponents	(	rowvec< integer >	pts,
		rowvec< integer >	ends,
			unused1,
			unused2,
		matrix< double >	x,
			unused3
	)

protected

This is the template method that actually evaluates the components at given points and values.

Attention: This method must be able to handle vector-arguments for \(\vx,t,\vmu\)!

Parameters

pts	The components of \(\vf\) for which derivatives are required
ends	At the \(i\)-th entry it contains the last position in the \(\vx\) vector that indicates an input value relevant for the \(i\)-th point evaluation, i.e. \(f_i(\vx) = f_i(\vx(ends(i-1)+1{:}ends(i)));\)
unused1	Marked as "~" in original m-file.
unused2	Marked as "~" in original m-file.
x	A matrix \(\vX\) with the state space locations \(\vx_i\) in its columns. In rows end(i-1)+1:end(i) it contains the states relevant to evaluate the i-th component of ��. States occur multiply in �� if different components of �� depend on these states.
unused3	Marked as "~" in original m-file.
idx	The indices of \(\vx\)-entries in the global \(\vx\) vector w.r.t the \(i\)-th point, e.g. \(xglobal(i-1:i+1) = \vx(ends(i-1):ends(i))\)
self	The positions in the \(\vx\) vector that correspond to the \(i\)-th output dimension, if applicable (usually \(f_i\) depends on \(x_i\), but not necessarily)
t	The corresponding times \(t_i\) for each state \(\vx_i\)
mu	The corresponding parameters \(\mu_i\) for each state \(\vx_i\), as column matrix

Return values

fx	A matrix with pts-many component function evaluations \(f_i(\vx)\) as rows and as many columns as \(\vX\) had.

Definition at line 391 of file Dynamics.m.

function fx = models.muscle.Dynamics.evaluateComponentSet	(	integer	nr,
		colvec< double >	x,
		double	t
	)

Computes the full or reduced component functions of the given point set.

See Also: PointSet

Parameters

nr	The number of the PointSet to use.
x	The state space location \(\vx\)
t	The corresponding times \(t\) for the state \(\vx\)

Definition at line 271 of file Dynamics.m.

References dscomponents.ACoreFun.evaluate(), dscomponents.ACompEvalCoreFun.PointSets, and general.AProjectable.V.

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function fx = models.muscle.Dynamics.evaluateComponentSetMulti	(	integer	nr,
		matrix< double >	x,
		rowvec< double >	t,
		matrix< double >	mu
	)

Computes the full component functions of the given point set.

See Also: PointSet

Parameters

nr	The number of the PointSet to use.
x	The state space locations \(\vx\)
t	The corresponding times \(t\) for the state \(\vx\)
mu	The corresponding parameters \(\mu\). Can be a single parameter or as many as the size of x

Definition at line 288 of file Dynamics.m.

References dscomponents.ACoreFun.evaluateMulti(), and dscomponents.ACompEvalCoreFun.PointSets.

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function fx = models.muscle.Dynamics.evaluateCoreFun	(	colvec< double >	x,
		double	t
	)

virtual

Actual method used to evaluate the dynamical sytems' core function.

Subclasses might implement this method and set the flag CustomProjection appropriately. However, for speed reasons, if both are true one might as well override the evaluate member directly as it basically cares for the cases when one of the flags is not true. In that case it is still important to set both flags to true as some components rely on them.

Parameters

x	The state variable vector \(\vx(t)\)
t	The current time(s) \(t \in [0, T]\)

Implements dscomponents.ACoreFun.

Definition at line 266 of file Dynamics.m.

function models.muscle.Dynamics.prepareSimulation ( colvec< double > mu )

Definition at line 229 of file Dynamics.m.

References alpha, AnisoPassiveMuscle, AnisoPassiveMuscleDeriv, AnisoPassiveTendon, AnisoPassiveTendonDeriv, dscomponents.ACoreFun.mu, nfevals, and nJevals.

function copy = models.muscle.Dynamics.project	(	V,
		W
	)

Definition at line 366 of file Dynamics.m.

function models.muscle.Dynamics.setSystem ( sys )

Definition at line 356 of file Dynamics.m.

function res = models.muscle.Dynamics.test_Jacobian	(	matrix< double >	y,
		double	t,
		colvec< double >	mu
	)

Overrides the random argument jacobian test as restrictions on the possible x values (detF = 1) hold.

Currently the tests using viscosity are commented out as we assume linear damping, which is extracted as extra \(A(t,\mu)\) part in the models' system

Parameters

y	The output variable vector \(\vy(t) = \vC(t,\vmu)\vx(t),~t=0\ldots T\) (general notation)
t	The current time(s) \(t \in [0, T]\)
mu	The currently used parameter \(\vmu\). Set to \([]\) if not used.

Definition at line 308 of file Dynamics.m.

References models.BaseSecondOrderSystem.getX0(), and models.BaseFirstOrderSystem.Model.

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Member Data Documentation

models.muscle.Dynamics.alpha = @("t")0

The activation of the muscle at time t [-].

Default: @(t)0 @(t)0

Definition at line 46 of file Dynamics.m.

Referenced by prepareSimulation().

models.muscle.Dynamics.AnisoPassiveMuscle

Definition at line 100 of file Dynamics.m.

Referenced by prepareSimulation().

models.muscle.Dynamics.AnisoPassiveMuscleDeriv

Definition at line 102 of file Dynamics.m.

Referenced by prepareSimulation().

models.muscle.Dynamics.AnisoPassiveTendon

Definition at line 104 of file Dynamics.m.

Referenced by prepareSimulation().

models.muscle.Dynamics.AnisoPassiveTendonDeriv

Definition at line 106 of file Dynamics.m.

Referenced by prepareSimulation().

models.muscle.Dynamics.APExp

Definition at line 98 of file Dynamics.m.

models.muscle.Dynamics.b1cf = 5.316372204148964

Cross-fibre markert part [MPa] = [N/mm²].

Default: 5.316372204148964

Definition at line 30 of file Dynamics.m.

models.muscle.Dynamics.ComputeUnassembled = false

% Unassembled stuff

Default: false

Note: This property has custom functionality when its value is changed.

Definition at line 57 of file Dynamics.m.

models.muscle.Dynamics.d1cf = 0.014991843974911

[-]

Default: 0.014991843974911

Definition at line 38 of file Dynamics.m.

models.muscle.Dynamics.fDim_unass

Definition at line 79 of file Dynamics.m.

models.muscle.Dynamics.ForceLengthFun

% Force length function fields

Definition at line 86 of file Dynamics.m.

models.muscle.Dynamics.ForceLengthFunDeriv

Definition at line 93 of file Dynamics.m.

models.muscle.Dynamics.idx_uv_bc_glob_unass

The indices of any dirichlet value in the unassembled vector duvw.

Definition at line 72 of file Dynamics.m.

models.muscle.Dynamics.idx_v_elems_unass

Definition at line 83 of file Dynamics.m.

models.muscle.Dynamics.lambda_dot

Definition at line 121 of file Dynamics.m.

models.muscle.Dynamics.lambda_dot_pos

Helper variable for fullmodels.muscle.model.

Note: This property has non-standard access specifiers: SetAccess = Protected, GetAccess = Public; Matlab documentation of property attributes.

Definition at line 111 of file Dynamics.m.

models.muscle.Dynamics.LastBCResiduals

Prepared arguments for APExpansion muprep;.

Note: This property has the MATLAB attribute Transient set to true.; This property has non-standard access specifiers: SetAccess = Private, GetAccess = Public; Matlab documentation of property attributes.

Definition at line 129 of file Dynamics.m.

models.muscle.Dynamics.nfevals

Definition at line 142 of file Dynamics.m.

Referenced by prepareSimulation().

models.muscle.Dynamics.nfibres

Definition at line 124 of file Dynamics.m.

Referenced by configUpdated().

models.muscle.Dynamics.nJevals

Definition at line 144 of file Dynamics.m.

Referenced by prepareSimulation().

models.muscle.Dynamics.num_dv_unass

Definition at line 81 of file Dynamics.m.

models.muscle.Dynamics.RampTime

Helper value for QuickReleaseTests (or others) that use a function handle with certain alpha ramp time for different simulations. Used in getSimCacheExtra to uniquely identify a simulation in the cache.

Note: This property has the MATLAB attribute Transient set to true.; Matlab documentation of property attributes.

Definition at line 149 of file Dynamics.m.

models.muscle.Dynamics.Sigma

Sigma assembly matrix.

Definition at line 65 of file Dynamics.m.

The documentation for this class was generated from the following files:

+models/+muscle/@Dynamics/Dynamics.m
+models/+muscle/@Dynamics/computeSparsityPattern.m

Detailed Description

Public Member Functions

Public Attributes

Protected Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation