Reference documentation for deal.II version 9.3.3

#include <deal.II/differentiation/ad/ad_helpers.h>
Public Types  
using  scalar_type = typename HelperBase< ADNumberTypeCode, ScalarType >::scalar_type 
using  ad_type = typename HelperBase< ADNumberTypeCode, ScalarType >::ad_type 
Public Member Functions  
Constructor / destructor  
EnergyFunctional (const unsigned int n_independent_variables)  
virtual  ~EnergyFunctional ()=default 
Dependent variables  
void  register_energy_functional (const ad_type &energy) 
scalar_type  compute_energy () const 
void  compute_residual (Vector< scalar_type > &residual) const override 
virtual void  compute_linearization (FullMatrix< scalar_type > &linearization) const override 
Independent variables  
void  register_dof_values (const std::vector< scalar_type > &dof_values) 
void  register_dof_values (const VectorType &values, const std::vector<::types::global_dof_index > &local_dof_indices) 
const std::vector< ad_type > &  get_sensitive_dof_values () const 
Operations specific to taped mode: Reusing tapes  
void  set_dof_values (const std::vector< scalar_type > &dof_values) 
void  set_dof_values (const VectorType &values, const std::vector<::types::global_dof_index > &local_dof_indices) 
Interrogation of internal information  
std::size_t  n_independent_variables () const 
std::size_t  n_dependent_variables () const 
void  print (std::ostream &stream) const 
void  print_values (std::ostream &stream) const 
void  print_tape_stats (const typename Types< ad_type >::tape_index tape_index, std::ostream &stream) const 
Operations specific to taped mode: Recording tapes  
virtual void  reset (const unsigned int n_independent_variables=::numbers::invalid_unsigned_int, const unsigned int n_dependent_variables=::numbers::invalid_unsigned_int, const bool clear_registered_tapes=true) 
bool  is_recording () const 
Types< ad_type >::tape_index  active_tape_index () const 
bool  is_registered_tape (const typename Types< ad_type >::tape_index tape_index) const 
void  set_tape_buffer_sizes (const typename Types< ad_type >::tape_buffer_sizes obufsize=64 *1024 *1024, const typename Types< ad_type >::tape_buffer_sizes lbufsize=64 *1024 *1024, const typename Types< ad_type >::tape_buffer_sizes vbufsize=64 *1024 *1024, const typename Types< ad_type >::tape_buffer_sizes tbufsize=64 *1024 *1024) 
bool  start_recording_operations (const typename Types< ad_type >::tape_index tape_index, const bool overwrite_tape=false, const bool keep_independent_values=true) 
void  stop_recording_operations (const bool write_tapes_to_file=false) 
void  activate_recorded_tape (const typename Types< ad_type >::tape_index tape_index) 
bool  recorded_tape_requires_retaping (const typename Types< ad_type >::tape_index tape_index) const 
bool  active_tape_requires_retaping () const 
void  clear_active_tape () 
Static Public Member Functions  
Operations specific to tapeless mode  
static void  configure_tapeless_mode (const unsigned int n_independent_variables, const bool ensure_persistent_setting=true) 
Drivers and taping  
TapedDrivers< ad_type, scalar_type >  taped_driver 
TapelessDrivers< ad_type, scalar_type >  tapeless_driver 
void  activate_tape (const typename Types< ad_type >::tape_index tape_index, const bool read_mode) 
Independent variables  
std::vector< scalar_type >  independent_variable_values 
std::vector< ad_type >  independent_variables 
std::vector< bool >  registered_independent_variable_values 
std::vector< bool >  registered_marked_independent_variables 
void  reset_registered_independent_variables () 
void  set_sensitivity_value (const unsigned int index, const scalar_type &value) 
void  mark_independent_variable (const unsigned int index, ad_type &out) const 
void  finalize_sensitive_independent_variables () const 
void  initialize_non_sensitive_independent_variable (const unsigned int index, ad_type &out) const 
unsigned int  n_registered_independent_variables () const 
Dependent variables  
std::vector< ad_type >  dependent_variables 
std::vector< bool >  registered_marked_dependent_variables 
void  reset_registered_dependent_variables (const bool flag=false) 
unsigned int  n_registered_dependent_variables () const 
void  register_dependent_variable (const unsigned int index, const ad_type &func) 
A helper class that facilitates the implementation of a generic (incremental) variational formulation from which the computation of the residual vector, as well as its linearization, is automated. This class would typically be used to derive the residual vector and tangent matrix (defined on the level of a cell), or a linearized system of equations, starting from a scalar energy functional.
An example of its usage in the case of a residual and tangent computations might be as follows (in this case we'll compute the linearization of a finitestrain hyperelastic solid from a stored/strain energy density function):
In most use cases, and in particular in the code example shown above, the number of independent variables equals the number of dofs_per_cell
for the used finite element.
Definition at line 1218 of file ad_helpers.h.
using Differentiation::AD::EnergyFunctional< ADNumberTypeCode, ScalarType >::scalar_type = typename HelperBase<ADNumberTypeCode, ScalarType>::scalar_type 
Type definition for the floating point number type that is used in, and results from, all computations.
Definition at line 1225 of file ad_helpers.h.
using Differentiation::AD::EnergyFunctional< ADNumberTypeCode, ScalarType >::ad_type = typename HelperBase<ADNumberTypeCode, ScalarType>::ad_type 
Type definition for the autodifferentiation number type that is used in all computations.
Definition at line 1232 of file ad_helpers.h.
Differentiation::AD::EnergyFunctional< ADNumberTypeCode, ScalarType >::EnergyFunctional  (  const unsigned int  n_independent_variables  ) 
The constructor for the class.
[in]  n_independent_variables  The number of independent variables that will be used in the definition of the functions that it is desired to compute the sensitivities of. In the computation of \(\Psi(\mathbf{X})\), this will be the number of inputs \(\mathbf{X}\), i.e., the dimension of the domain space. 
Definition at line 798 of file ad_helpers.cc.

virtualdefault 
Destructor
void Differentiation::AD::EnergyFunctional< ADNumberTypeCode, ScalarType >::register_energy_functional  (  const ad_type &  energy  ) 
Register the definition of the total cell energy \(\Psi(\mathbf{X})\).
[in]  energy  A recorded function that defines the total cell energy. This represents the single dependent variable from which both the residual and its linearization are to be computed. 
Definition at line 807 of file ad_helpers.cc.
EnergyFunctional< ADNumberTypeCode, ScalarType >::scalar_type Differentiation::AD::EnergyFunctional< ADNumberTypeCode, ScalarType >::compute_energy 
Evaluation of the total scalar energy functional for a chosen set of degree of freedom values, i.e.
\[ \Psi(\mathbf{X}) \vert_{\mathbf{X}} \]
The values at the evaluation point \(\mathbf{X}\) are obtained by calling CellLevelBase::set_dof_values().
Definition at line 819 of file ad_helpers.cc.

overridevirtual 
Evaluation of the residual for a chosen set of degree of freedom values. Underlying this is the computation of the gradient (first derivative) of the scalar function \(\Psi\) with respect to all independent variables, i.e.
\[ \mathbf{r}(\mathbf{X}) = \frac{\partial\Psi(\mathbf{X})}{\partial\mathbf{X}} \Big\vert_{\mathbf{X}} \]
The values at the evaluation point \(\mathbf{X}\) are obtained by calling CellLevelBase::set_dof_values().
[out]  residual  A Vector object, for which the value for each entry represents the residual value for the corresponding local degree of freedom. The output residual vector has a length corresponding to n_independent_variables . 
Implements Differentiation::AD::CellLevelBase< ADNumberTypeCode, double >.
Definition at line 873 of file ad_helpers.cc.

overridevirtual 
Compute the linearization of the residual vector around a chosen set of degree of freedom values. Underlying this is the computation of the Hessian (second derivative) of the scalar function \(\Psi\) with respect to all independent variables, i.e.
\[ \frac{\partial\mathbf{r}(\mathbf{X})}{\partial\mathbf{X}} = \frac{\partial^{2}\Psi(\mathbf{X})}{\partial\mathbf{X} \otimes \partial\mathbf{X}} \Big\vert_{\mathbf{X}} \]
The values at the evaluation point \(\mathbf{X}\) are obtained by calling CellLevelBase::set_dof_values().
[out]  linearization  A FullMatrix representing the linearization of the residual vector. The output linearization matrix has dimensions corresponding to n_independent_variables \(\times\)n_independent_variables . 
Implements Differentiation::AD::CellLevelBase< ADNumberTypeCode, double >.
Definition at line 938 of file ad_helpers.cc.

inherited 
Register the complete set of independent variables \(\mathbf{X}\) that represent the local degree of freedom values.
[in]  dof_values  A vector field associated with local degree of freedom values on the current finite element. These define the values of all independent variables. When considering taped AD numbers with branching functions, to avoid potential issues with branch switching it may be a good idea to choose these values close or equal to those that will be later evaluated and linearized around. 
scalar_type
. Depending on the selected ADNumberTypeCode
, this may or may not correspond with the ScalarType
prescribed as a template argument.Definition at line 905 of file ad_helpers.cc.

inherited 
Register the complete set of independent variables \(\mathbf{X}\) that represent the local degree of freedom values.
[in]  values  A global field from which the values of all independent variables will be extracted. This typically will be the solution vector around which point a residual vector is to be computed and around which linearization is to occur. When considering taped AD numbers with branching functions, to avoid potential issues with branch switching it may be a good idea to choose these values close or equal to those that will be later evaluated and linearized around. 
[in]  local_dof_indices  A vector of degree of freedom indices from which to extract the local degree of freedom values. This would typically obtained by calling cell>get_dof_indices() . 

inherited 
Return the complete set of degree of freedom values as represented by autodifferentiable numbers. These are the independent variables \(\mathbf{X}\) about which the solution is linearized.
This function indicates to the AD library that implements the autodifferentiable number type that operations performed on these numbers are to be tracked so they are considered "sensitive" variables. This is, therefore, the set of variables with which one would then perform computations, and based on which one can then extract both the value of the function and its derivatives with the member functions below. The values of the components of the returned object are initialized to the values set with register_independent_variable().
Definition at line 952 of file ad_helpers.cc.

inherited 
Set the values for the independent variables \(\mathbf{X}\), i.e., the linearization point.
[in]  dof_values  A vector field associated with local degree of freedom values on the current finite element. These define the values of all independent variables. 
scalar_type
. Depending on the selected ADNumberTypeCode
, this may or may not correspond with the ScalarType
prescribed as a template argument.keep_independent_values
flag has been set when HelperBase::start_recording_operations() is called then the tape is immediately usable after creation, and the values of the independent variables set by register_dof_values() are those at which the function is to be evaluated. In this case, a separate call to this function is not strictly necessary. Definition at line 981 of file ad_helpers.cc.

inherited 
Set the values for the independent variables \(\mathbf{X}\), i.e., the linearization point.
[in]  values  A vector field from which the values of all independent variables is to be extracted. 
[in]  local_dof_indices  A vector of degree of freedom indices from which to extract the local degree of freedom values. This would typically obtained by calling cell>get_dof_indices() . 
keep_independent_values
flag has been set when HelperBase::start_recording_operations() is called then the tape is immediately usable after creation, and the values of the independent variables set by register_dof_values() are those at which the function is to be evaluated. In this case, a separate call to this function is not strictly necessary.

inherited 
Return the number of independent variables that this object expects to work with. This is the dimension of the domain space.
Definition at line 226 of file ad_helpers.cc.

inherited 
Return the number of dependent variables that this object expects to operate on. This is the dimension of the image space.
Definition at line 233 of file ad_helpers.cc.

inherited 
Print the status of all queryable data. Exactly what is printed and its format depends on the ad_type
, as is determined by the ADNumberTypeCode
template parameter.
[in]  stream  The output stream to which the values are to be written. 
Definition at line 244 of file ad_helpers.cc.

inherited 
Print the values currently assigned to the independent variables.
[in]  stream  The output stream to which the values are to be written. 
Definition at line 253 of file ad_helpers.cc.

inherited 
Print the statistics regarding the usage of the tapes.
[in]  tape_index  The index of the tape to get the statistics of. 
[out]  stream  The output stream to which the values are to be written. 
ad_type
is a taped autodifferentiable number. Definition at line 266 of file ad_helpers.cc.

staticinherited 
Prespecify the number of independent_variables
to be used in tapeless mode.
Although this function is called internally in the HelperBase constructor, there may be occasions when ADOLC tapeless numbers (adtl::adoubles
) are created before an instance of this class is created. This function therefore allows one to declare at the earliest possible instance how many directional derivatives will be considered in tapeless mode.
ensure_persistent_setting
set to true
when the ad_type
is an ADOLC tapeless number, calling this function leaves the set number of directional derivatives in a persistent state. It will therefore not be possible to further modify the number of directional derivatives to be tracked by adtl::adoubles
's during course of the program's execution. Definition at line 295 of file ad_helpers.cc.

virtualinherited 
Reset the state of the helper class.
When an instance of an HelperBase is stored as a class member object with the intention to reuse its instance, it may be necessary to reset the state of the object before use. This is because, internally, there is error checking performed to ensure that the correct autodifferentiable data is being tracked and used only when appropriate. This function clears all member data and, therefore, allows the state of all internal flags to be safely reset to their initial state.
In the rare case that the number of independent or dependent variables has changed, this can also reconfigured by passing in the appropriate arguments to the function.
[in]  n_independent_variables  The number of independent variables that will be used in the definition of the functions that it is desired to compute the sensitivities of. In the computation of \(\mathbf{f}(\mathbf{X})\), this will be the number of inputs \(\mathbf{X}\), i.e., the dimension of the domain space. 
[in]  n_dependent_variables  The number of scalar functions to be defined that will have a sensitivity to the given independent variables. In the computation of \(\mathbf{f}(\mathbf{X})\), this will be the number of outputs \(\mathbf{f}\), i.e., the dimension of the image space. 
[in]  clear_registered_tapes  A flag that indicates the that list of registered_tapes must be cleared. If set to true then the data structure that tracks which tapes have been recorded is cleared as well. It is then expected that any preexisting tapes be rerecorded. 
Reimplemented in Differentiation::AD::PointLevelFunctionsBase< dim, ADNumberTypeCode, ScalarType >, and Differentiation::AD::PointLevelFunctionsBase< dim, ADNumberTypeCode, double >.
Definition at line 341 of file ad_helpers.cc.

inherited 
Return whether or not this class is tracking calculations performed with its marked independent variables.
Definition at line 352 of file ad_helpers.cc.

inherited 
Return the tape index which is currently activated for recording or reading.
Definition at line 359 of file ad_helpers.cc.

inherited 
Return whether or not a tape number has already been used or registered.
Definition at line 366 of file ad_helpers.cc.

inherited 
Set the buffer sizes for the next active tape.
This function must be called before start_recording_operations() for it to have any influence on the memory allocated to the next recorded tape.
[in]  obufsize  ADOLC operations buffer size 
[in]  lbufsize  ADOLC locations buffer size 
[in]  vbufsize  ADOLC value buffer size 
[in]  tbufsize  ADOLC Taylor buffer size 
Definition at line 395 of file ad_helpers.cc.

inherited 
Enable recording mode for a given tape. The use of this function is mandatory if the autodifferentiable number is a taped type. However, for the purpose of developing generic code, it can also be safely called for tapeless autodifferentiable numbers.
The operations that take place between this function call and that of stop_recording_operations() are recorded to the tape and can be replayed and reevaluated as necessary.
The typical set of operations to be performed during this "recording" phase (between the calls to start_recording_operations() and stop_recording_operations() ) are:
keep
flag is set to true
then these represent precisely the point about which the function derivatives are to be computed. If the keep
flag is set to false
then these only represent dummy values, and the point at which the function derivatives are to be computed must be set by calling set_independent_variables() again.[in]  tape_index  The index of the tape to be written 
[in]  overwrite_tape  Express whether tapes are allowed to be overwritten. If true then any existing tape with a given tape_index will be destroyed and a new tape traced over it. 
[in]  keep_independent_values  Determines whether the numerical values of all independent variables are recorded in the tape buffer. If true, then the tape can be immediately used to perform computations after recording is complete. 
Definition at line 451 of file ad_helpers.cc.

inherited 
Disable recording mode for a given tape. The use of this function is mandatory if the autodifferentiable number is a taped type. However, for the purpose of developing generic code, it can also be safely called for tapeless autodifferentiable numbers.
Definition at line 468 of file ad_helpers.cc.

inherited 
Select a prerecorded tape to read from.
[in]  tape_index  The index of the tape to be read from. 
Definition at line 480 of file ad_helpers.cc.

inherited 
Return a flag that, when true
, indicates that the retaping of the dependent function is necessary for a reliable computation to be performed on a tape with the given tape_index
. This may be necessary if a sign comparison within branched operations yields different results to those computed at the original tape evaluation point.
This issue, known as "branch switching", can be clarified by means of a trivial, contrived example:
During taping, the conditional statement may be either true
or false
, and the result (with its sensitivities) returned by this function. The AD library doesn't just record the parse tree of the operations applied on the branch chosen at the time to taping, but also checks that the condition continues to be satisfied. For some other evaluation of the tape (i.e. for some different inputs x
and y
), the other branch of the conditional check may be chosen. The result of following this code path has not been recorded on the tape, and therefore cannot be evaluated. In such a case, the underlying AD library will be able to tell you that it is necessary to rerecord the tape at the new evaluation point in order to resolve the new code branch. This function can be used to find out whether this is so.
For the output of this function to be meaningful, it must be called after activate_recorded_tape() is called and the new evaluation point for the tape (i.e. values of the independent variables) have been set and subsequently used (i.e. in the determination of the values or derivatives of the dependent variables).
Definition at line 523 of file ad_helpers.cc.

inherited 
Return a flag that, when true
, indicates that the retaping of the dependent function is necessary for a reliable computation to be performed on the currently active tape. This may be necessary if a sign comparison within branched operations yields different results to those computed at the original tape evaluation point.
This issue, known as "branch switching", can be clarified by means of a trivial, contrived example:
During taping, the conditional statement may be either true
or false
, and the result (with its sensitivities) returned by this function. The AD library doesn't just record the parse tree of the operations applied on the branch chosen at the time to taping, but also checks that the condition continues to be satisfied. For some other evaluation of the tape (i.e. for some different inputs x
and y
), the other branch of the conditional check may be chosen. The result of following this code path has not been recorded on the tape, and therefore cannot be evaluated. In such a case, the underlying AD library will be able to tell you that it is necessary to rerecord the tape at the new evaluation point in order to resolve the new code branch. This function can be used to find out whether this is so.
For the output of this function to be meaningful, it must be called after activate_recorded_tape() is called and the new evaluation point for the tape (i.e. values of the independent variables) have been set and subsequently used (i.e. in the determination of the values or derivatives of the dependent variables).
Definition at line 566 of file ad_helpers.cc.

inherited 
Clears and removes the currently active tape.
This is typically only necessary when branch switching is detected on the original tape at evaluation point. This state can be checked using the active_tape_requires_retaping() function.
Definition at line 576 of file ad_helpers.cc.

protectedinherited 
Select a tape to record to or read from.
This function activates a tape, but depending on whether read_mode
is set, the tape is either taken as previously written to (and put into readonly mode), or cleared for (re)taping.
[in]  tape_index  The index of the tape to be written to/read from. 
[in]  read_mode  A flag that marks whether or not we expect to read data from a preexisting tape. 
Definition at line 619 of file ad_helpers.cc.

protectedinherited 
Reset the boolean vector registered_independent_variable_values
that indicates which independent variables we've been manipulating for the current set of operations.
Definition at line 666 of file ad_helpers.cc.

protectedinherited 
Set the actual value of the independent variable \(X_{i}\).
[in]  index  The index in the vector of independent variables. 
[in]  value  The value to set the index'd independent variable to. 
Definition at line 675 of file ad_helpers.cc.

protectedinherited 
Initialize an independent variable \(X_{i}\) such that subsequent operations performed with it are tracked.
[in]  index  The index in the vector of independent variables. 
[out]  out  An autodifferentiable number that is ready for use in computations. The operations that are performed with it are recorded on the tape and will be considered in the computation of dependent variable values. 
Definition at line 696 of file ad_helpers.cc.

protectedinherited 
Finalize the state of the independent variables before use.
This step and the storage of the independent variables is done separately because some derived classes may offer the capability to add independent variables in a staggered manner. This function is to be triggered when these values are considered finalized and we can safely initialize the sensitive equivalents of those values.
Definition at line 709 of file ad_helpers.cc.

protectedinherited 
Initialize an independent variable \(X_{i}\).
[out]  out  An autodifferentiable number that is ready for use in standard computations. The operations that are performed with it are not recorded on the tape, and so should only be used when not in recording mode. 
[in]  index  The index in the vector of independent variables. 
Definition at line 721 of file ad_helpers.cc.

protectedinherited 
The number of independent variables that have been manipulated within a set of operations.
Definition at line 729 of file ad_helpers.cc.

protectedinherited 
Reset the boolean vector registered_marked_dependent_variables
that indicates which independent variables have been manipulated by the current set of operations. All entries in the vector are set to the value of the flag
.
Definition at line 764 of file ad_helpers.cc.

protectedinherited 
The number of dependent variables that have been registered.
Definition at line 770 of file ad_helpers.cc.

protectedinherited 
Register the definition of the index'th dependent variable \(f(\mathbf{X})\).
[in]  index  The index of the entry in the global list of dependent variables that this function belongs to. 
[in]  func  The recorded function that defines a dependent variable. 
Definition at line 784 of file ad_helpers.cc.

protectedinherited 
An object used to help manage stored tapes.
In the event that the ad_type
is a tapeless AD type, then the object constructed here is, effectively, a dummy one.
Definition at line 592 of file ad_helpers.h.

protectedinherited 
An object used to help manage tapeless data structures.
In the event that the ad_type
is a taped AD type, then the object constructed here is, effectively, a dummy one.
Definition at line 600 of file ad_helpers.h.

mutableprotectedinherited 
A set of independent variables \(\mathbf{X}\) that differentiation will be performed with respect to.
The gradients and Hessians of dependent variables will be computed at these finite values.
Definition at line 636 of file ad_helpers.h.

mutableprotectedinherited 
A set of sensitive independent variables \(\mathbf{X}\) that differentiation will be performed with respect to.
The gradients and Hessians of dependent variables will be computed using these configured AD numbers. Note that only reversemode AD requires that the sensitive independent variables be stored.
Definition at line 646 of file ad_helpers.h.

protectedinherited 
A list of registered independent variables that have been manipulated for a given set of operations.
Definition at line 652 of file ad_helpers.h.

mutableprotectedinherited 
A list of registered independent variables that have been extracted and their sensitivities marked.
Definition at line 658 of file ad_helpers.h.

protectedinherited 
The set of dependent variables \(\mathbf{f}(\mathbf{X})\) of which the derivatives with respect to \(\mathbf{X}\) will be computed.
The gradients and Hessians of these dependent variables will be computed at the values \(\mathbf{X}\) set with the set_sensitivity_value() function.
ad_type
so that we can use them to compute function values and directional derivatives in the case that tapeless numbers are used Definition at line 750 of file ad_helpers.h.

protectedinherited 
A list of registered dependent variables.
Definition at line 755 of file ad_helpers.h.