Reference documentation for deal.II version 9.4.1
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#include <deal.II/differentiation/ad/ad_helpers.h>

[legend]

## Public Types

using scalar_type = typename HelperBase< ADNumberTypeCode, ScalarType >::scalar_type

## Public Member Functions

Constructor / destructor
PointLevelFunctionsBase (const unsigned int n_independent_variables, const unsigned int n_dependent_variables)

virtual ~PointLevelFunctionsBase ()=default

Operations specific to taped mode: Reusing tapes
void set_independent_variables (const std::vector< scalar_type > &values)

template<typename ValueType , typename ExtractorType >
void set_independent_variable (const ValueType &value, const ExtractorType &extractor)

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
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)

## Static Public Attributes

static constexpr unsigned int dimension = dim

## Independent variables

std::vector< boolsymmetric_independent_variables

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) override

void register_independent_variables (const std::vector< scalar_type > &values)

template<typename ValueType , typename ExtractorType >
void register_independent_variable (const ValueType &value, const ExtractorType &extractor)

const std::vector< ad_type > & get_sensitive_variables () const

template<typename ExtractorType >
internal::Extractor< dim, ExtractorType >::template tensor_type< ad_typeget_sensitive_variables (const ExtractorType &extractor) const

void set_sensitivity_value (const unsigned int index, const bool symmetric_component, const scalar_type &value)

bool is_symmetric_independent_variable (const unsigned int index) const

unsigned int n_symmetric_independent_variables () const

## 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

std::vector< scalar_typeindependent_variable_values

std::vector< boolregistered_independent_variable_values

std::vector< boolregistered_marked_independent_variables

## 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)

std::vector< boolregistered_marked_dependent_variables

## Detailed Description

A base helper class that facilitates the evaluation of point-wise defined functions. This is the point-wise counterpart of the CellLevelBase class, and was conceived for computations at a continuum point, or quadrature point, rather than for finite-element level calculations. That being said, the interface to this and the derived classes are sufficiently generic that the dependent function(s) and their argument(s), that are the independent variables, can be interpreted in any manner that the user may choose.

As it offers a field-based interface, this class would typically be used to compute the derivatives of a constitutive law defined at a quadrature point; however, it may also be used in other contexts, such as to compute the linearization of a set of local nonlinear equations.

Warning
ADOL-C does not support the standard threading models used by deal.II, so this class should not be embedded within a multithreaded function when using ADOL-C number types. It is, however, suitable for use in both serial and MPI routines.

Definition at line 2641 of file ad_helpers.h.

## ◆ scalar_type

Type definition for the floating point number type that is used in, and results from, all computations.

Definition at line 2655 of file ad_helpers.h.

Type definition for the auto-differentiation number type that is used in all computations.

Definition at line 2662 of file ad_helpers.h.

## ◆ PointLevelFunctionsBase()

 Differentiation::AD::PointLevelFunctionsBase< dim, ADNumberTypeCode, ScalarType >::PointLevelFunctionsBase ( const unsigned int n_independent_variables, const unsigned int n_dependent_variables )

The constructor for the class.

Parameters
 [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.

Definition at line 1154 of file ad_helpers.cc.

virtualdefault

Destructor

## ◆ reset()

 void Differentiation::AD::PointLevelFunctionsBase< dim, ADNumberTypeCode, ScalarType >::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 )
overridevirtual

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 auto-differentiable 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.

Parameters
 [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 re-recorded.
Note
This also resets the active tape number to an invalid number, and deactivates the recording mode for taped variables.

Definition at line 1168 of file ad_helpers.cc.

## ◆ register_independent_variables()

 void Differentiation::AD::PointLevelFunctionsBase< dim, ADNumberTypeCode, ScalarType >::register_independent_variables ( const std::vector< scalar_type > & values )

Register the complete set of independent variables $$\mathbf{X}$$.

Parameters
 [in] values A field that defines 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 differentiated around.
Note
The input value type must correspond to this class's scalar_type. Depending on the selected ADNumberTypeCode, this may or may not correspond with the ScalarType prescribed as a template argument.
For taped AD numbers, this operation is only valid in recording mode.

Definition at line 1219 of file ad_helpers.cc.

## ◆ register_independent_variable()

template<typename ValueType , typename ExtractorType >
 void Differentiation::AD::PointLevelFunctionsBase< dim, ADNumberTypeCode, ScalarType >::register_independent_variable ( const ValueType & value, const ExtractorType & extractor )

Register the subset of independent variables $$\mathbf{A} \subset \mathbf{X}$$.

Parameters
 [in] value A field that defines a number of 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 differentiated around. [in] extractor An extractor associated with the input field variables. This effectively defines which components of the global set of independent variables this field is associated with.
Note
The input value type must correspond to this class's scalar_type. Depending on the selected ADNumberTypeCode, this may or may not correspond with the ScalarType prescribed as a template argument.
The input extractor must correspond to the input ValueType. So, for example, if a value is a rank-1 tensor (i.e. of type Tensor<1,dim,scalar_type>), then the extractor must be an FEValuesExtractors::Vector or FEValuesExtractors::Tensor<1>.
This function may be repeatedly used until a call to finalize_sensitive_independent_variables() or get_sensitive_variables() is made.
For taped AD numbers, this operation is only valid in recording mode.

## ◆ get_sensitive_variables() [1/2]

Return the complete set of independent variables as represented by auto-differentiable numbers. These are the independent variables $$\mathbf{X}$$ at which the dependent values are evaluated and differentiated.

This function indicates to the AD library that implements the auto-differentiable 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().

Returns
An array of auto-differentiable type numbers.
Note
For taped AD numbers, this operation is only valid in recording mode.

Definition at line 1245 of file ad_helpers.cc.

## ◆ get_sensitive_variables() [2/2]

template<typename ExtractorType >
 internal::Extractor< dim, ExtractorType >::template tensor_type< ad_type > Differentiation::AD::PointLevelFunctionsBase< dim, ADNumberTypeCode, ScalarType >::get_sensitive_variables ( const ExtractorType & extractor ) const

## ◆ set_independent_variables()

 void Differentiation::AD::PointLevelFunctionsBase< dim, ADNumberTypeCode, ScalarType >::set_independent_variables ( const std::vector< scalar_type > & values )

Set the values for the independent variables $$\mathbf{X}$$.

Parameters
 [in] values A vector that defines the values of all independent variables.
Note
The input value type must correspond to this class's scalar_type. Depending on the selected ADNumberTypeCode, this may or may not correspond with the ScalarType prescribed as a template argument.
If the 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_independent_variables() 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 1295 of file ad_helpers.cc.

## ◆ set_independent_variable()

template<typename ValueType , typename ExtractorType >
 void Differentiation::AD::PointLevelFunctionsBase< dim, ADNumberTypeCode, ScalarType >::set_independent_variable ( const ValueType & value, const ExtractorType & extractor )

Set the values for a subset of independent variables $$\mathbf{A} \subset \mathbf{X}$$.

Parameters
 [in] value A field that defines the values of a number of independent variables. [in] extractor An extractor associated with the input field variables. This effectively defines which components of the global set of independent variables this field is associated with.
Note
The input value type must correspond to this class's scalar_type. Depending on the selected ADNumberTypeCode, this may or may not correspond with the ScalarType prescribed as a template argument.
The input extractor must correspond to the input ValueType. So, for example, if a value is a rank-1 tensor (i.e. of type Tensor<1,dim,scalar_type>), then the extractor must be an FEValuesExtractors::Vector or FEValuesExtractors::Tensor<1>.
If the 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_independent_variable() are those at which the function is to be evaluated. In this case, a separate call to this function is not strictly necessary.

## ◆ set_sensitivity_value() [1/2]

 void Differentiation::AD::PointLevelFunctionsBase< dim, ADNumberTypeCode, ScalarType >::set_sensitivity_value ( const unsigned int index, const bool symmetric_component, const scalar_type & value )
protected

Set the actual value of the independent variable $$X_{i}$$.

Parameters
 [in] index The index in the vector of independent variables. [in] symmetric_component Mark whether this index relates to a component of a field that has a symmetric counterpart (e.g. if index represents an off-diagonal entry in a symmetric tensor). [in] value The value to set the index'd independent variable to.

Definition at line 1273 of file ad_helpers.cc.

## ◆ is_symmetric_independent_variable()

 bool Differentiation::AD::PointLevelFunctionsBase< dim, ADNumberTypeCode, ScalarType >::is_symmetric_independent_variable ( const unsigned int index ) const
protected

Return whether the index'th independent variables is one for which we must take into account symmetry when extracting their gradient or Hessian values.

Definition at line 1191 of file ad_helpers.cc.

## ◆ n_symmetric_independent_variables()

protected

Return the number of independent variables that have been marked as being components of a symmetric field.

Definition at line 1205 of file ad_helpers.cc.

## ◆ n_independent_variables()

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 241 of file ad_helpers.cc.

## ◆ n_dependent_variables()

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 262 of file ad_helpers.cc.

## ◆ print()

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.

Parameters
 [in] stream The output stream to which the values are to be written.

Definition at line 309 of file ad_helpers.cc.

## ◆ print_values()

inherited

Print the values currently assigned to the independent variables.

Parameters
 [in] stream The output stream to which the values are to be written.

Definition at line 359 of file ad_helpers.cc.

## ◆ print_tape_stats()

 void Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::print_tape_stats ( const typename Types< ad_type >::tape_index tape_index, std::ostream & stream ) const
inherited

Print the statistics regarding the usage of the tapes.

Parameters
 [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.
Note
This function only produces meaningful output when ad_type is a taped auto-differentiable number.

Definition at line 373 of file ad_helpers.cc.

## ◆ configure_tapeless_mode()

 void Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::configure_tapeless_mode ( const unsigned int n_independent_variables, const bool ensure_persistent_setting = true )
staticinherited

Pre-specify 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 ADOL-C 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.

Warning
With ensure_persistent_setting set to true when the ad_type is an ADOL-C 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 448 of file ad_helpers.cc.

## ◆ is_recording()

inherited

Return whether or not this class is tracking calculations performed with its marked independent variables.

Definition at line 271 of file ad_helpers.cc.

## ◆ active_tape_index()

inherited

Return the tape index which is currently activated for recording or reading.

Definition at line 284 of file ad_helpers.cc.

## ◆ is_registered_tape()

inherited

Return whether or not a tape number has already been used or registered.

Definition at line 296 of file ad_helpers.cc.

## ◆ set_tape_buffer_sizes()

 void Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::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 )
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.

Note
This function only has an effect when using ADOL-C numbers. As stated by the ADOL-C manual, it may be desirable to create a file ".adolcrc" in the program run directory and set the buffer size therein. Alternatively, this function can be used to override the settings for any given tape, or can be used in the event that no ".adolcrc" file exists. The default value for each buffer is set at 64 megabytes, a heuristically chosen value thought to be appropriate for use within the context of finite element analysis when considering coupled problems with multiple vector-valued fields discretised by higher order shape functions, as well as complex constitutive laws.
Parameters
 [in] obufsize ADOL-C operations buffer size [in] lbufsize ADOL-C locations buffer size [in] vbufsize ADOL-C value buffer size [in] tbufsize ADOL-C Taylor buffer size

Definition at line 559 of file ad_helpers.cc.

## ◆ start_recording_operations()

 bool Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::start_recording_operations ( const typename Types< ad_type >::tape_index tape_index, const bool overwrite_tape = false, const bool keep_independent_values = true )
inherited

Enable recording mode for a given tape. The use of this function is mandatory if the auto-differentiable number is a taped type. However, for the purpose of developing generic code, it can also be safely called for tapeless auto-differentiable 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:

• Definition of some independent variables via register_independent_variable() or register_independent_variables(). These define the branch of operations tracked by the tape. If the 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.
• Extraction of a set of independent variables of auto-differentiable type using get_sensitive_variables(). These are then tracked during later computations.
• Defining the dependent variables via register_dependent_variable() or register_dependent_variables(). These are the functions that will be differentiated with respect to the independent variables.
Parameters
 [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.
Note
During the recording phase, no value(), gradient(), hessian(), or jacobian() operations can be performed.
The chosen tape index must be greater than Numbers<ad_type>::invalid_tape_index and less than Numbers<ad_type>::max_tape_index.

Definition at line 578 of file ad_helpers.cc.

## ◆ stop_recording_operations()

 void Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::stop_recording_operations ( const bool write_tapes_to_file = false )
inherited

Disable recording mode for a given tape. The use of this function is mandatory if the auto-differentiable number is a taped type. However, for the purpose of developing generic code, it can also be safely called for tapeless auto-differentiable numbers.

Note
After this function call, the tape is considered ready for use and operations such as value(), gradient() or hessian() can be executed.
For taped AD numbers, this operation is only valid in recording mode.

Definition at line 643 of file ad_helpers.cc.

## ◆ activate_recorded_tape()

inherited

Select a pre-recorded tape to read from.

Parameters
 [in] tape_index The index of the tape to be read from.
Note
The chosen tape index must be greater than Numbers<ad_type>::invalid_tape_index and less than Numbers<ad_type>::max_tape_index.

Definition at line 474 of file ad_helpers.cc.

## ◆ recorded_tape_requires_retaping()

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:

{
if (x < y)
return y;
else
return x*z;
}

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 re-record 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 484 of file ad_helpers.cc.

## ◆ active_tape_requires_retaping()

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:

{
if (x < y)
return y;
else
return x*z;
}

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 re-record 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 497 of file ad_helpers.cc.

## ◆ clear_active_tape()

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 510 of file ad_helpers.cc.

## ◆ activate_tape()

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 read-only mode), or cleared for (re-)taping.

Parameters
 [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.
Note
The chosen tape index must be greater than Numbers<ad_type>::invalid_tape_index and less than Numbers<ad_type>::max_tape_index.

Definition at line 522 of file ad_helpers.cc.

## ◆ reset_registered_independent_variables()

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 82 of file ad_helpers.cc.

## ◆ set_sensitivity_value() [2/2]

 void Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::set_sensitivity_value ( const unsigned int index, const scalar_type & value )
protectedinherited

Set the actual value of the independent variable $$X_{i}$$.

Parameters
 [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 105 of file ad_helpers.cc.

## ◆ mark_independent_variable()

protectedinherited

Initialize an independent variable $$X_{i}$$ such that subsequent operations performed with it are tracked.

Note
Care must be taken to mark each independent variable only once.
The order in which the independent variables are marked defines the order of all future internal operations. They must be manipulated in the same order as that in which they are first marked. If not then, for example, ADOL-C won't throw an error, but rather it might complain nonsensically during later computations or produce garbage results.
Parameters
 [in] index The index in the vector of independent variables. [out] out An auto-differentiable 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 142 of file ad_helpers.cc.

## ◆ finalize_sensitive_independent_variables()

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 181 of file ad_helpers.cc.

## ◆ initialize_non_sensitive_independent_variable()

protectedinherited

Initialize an independent variable $$X_{i}$$.

Parameters
 [out] out An auto-differentiable 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 204 of file ad_helpers.cc.

## ◆ n_registered_independent_variables()

protectedinherited

The number of independent variables that have been manipulated within a set of operations.

Definition at line 230 of file ad_helpers.cc.

## ◆ reset_registered_dependent_variables()

 void Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::reset_registered_dependent_variables ( const bool flag = false )
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 93 of file ad_helpers.cc.

## ◆ n_registered_dependent_variables()

protectedinherited

The number of dependent variables that have been registered.

Definition at line 250 of file ad_helpers.cc.

## ◆ register_dependent_variable()

protectedinherited

Register the definition of the index'th dependent variable $$f(\mathbf{X})$$.

Parameters
 [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.
Note
Each dependent variable must only be registered once.

Definition at line 679 of file ad_helpers.cc.

## ◆ dimension

staticconstexpr

Type definition for the dimension of the associated input and output tensor types.

Definition at line 2649 of file ad_helpers.h.

## ◆ symmetric_independent_variables

private

The independent variables for which we must take into account symmetry when extracting their gradient or Hessian values.

Definition at line 2921 of file ad_helpers.h.

## ◆ taped_driver

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.

## ◆ tapeless_driver

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.

## ◆ independent_variable_values

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.

## ◆ independent_variables

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 reverse-mode AD requires that the sensitive independent variables be stored.

Definition at line 646 of file ad_helpers.h.

## ◆ registered_independent_variable_values

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.

## ◆ registered_marked_independent_variables

mutableprotectedinherited

A list of registered independent variables that have been extracted and their sensitivities marked.

Definition at line 658 of file ad_helpers.h.

## ◆ dependent_variables

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.

Note
These are stored as an 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.
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