Reference documentation for deal.II version Git 3ff8e288d2 2020-02-20 17:30:00 +0100

#include <deal.II/differentiation/ad/ad_helpers.h>

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## Public Types

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

## Public Member Functions

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

virtual ~CellLevelBase ()=default

Independent variables
void register_dof_values (const std::vector< scalar_type > &dof_values)

template<typename VectorType >
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)

template<typename VectorType >
void set_dof_values (const VectorType &values, const std::vector<::types::global_dof_index > &local_dof_indices)

Dependent variables
virtual void compute_residual (Vector< scalar_type > &residual) const =0

virtual void compute_linearization (FullMatrix< scalar_type > &linearization) const =0

HelperBase (const unsigned int n_independent_variables, const unsigned int n_dependent_variables)

virtual ~HelperBase ()=default

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

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 void configure_tapeless_mode (const unsigned int n_independent_variables, const bool ensure_persistent_setting=true)

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

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< scalar_typeindependent_variable_values

std::vector< bool > registered_independent_variable_values

std::vector< bool > registered_marked_independent_variables

std::vector< bool > registered_marked_dependent_variables

## Detailed Description

A general helper class that facilitates the evaluation of a vector of functions, as well as its first derivatives (their Jacobian). This class would typically be used to compute the linearization of a set of local nonlinear equations, but can also be used as the basis of the linearization of the residual vector defined on the level of a finite element (for example, in order to compute the Jacobian matrix necessary in Newton-type solvers for nonlinear problems).

Note
When using the cell-level taped AD methods in 3d and/or with higher order elements, it is incredibly easy to exceed the tape buffer size. The reason for this is two-fold:
1. there are many independent variables (the local degrees-of-freedom) to take the derivatives with respect to, and
2. the expressions for the dependent variables (each being a component of the residual vector) in terms of all of the independent variables are lengthy, especially when non-trivial constitutive laws are considered. These buffer variables dictate the amount of memory allocated to a tape before it is written to file (at a significant performance loss). Therefore for ADOL-C taped AD numbers, it may be desirable to create a file ".adolcrc" in the program run directory and set the buffer size therein (as is suggested by the ADOL-C manual). For example, the following settings increase the default buffer size by 128 times:
"OBUFSIZE" "67108864"
"LBUFSIZE" "67108864"
"VBUFSIZE" "67108864"
"TBUFSIZE" "67108864"
Note that the quotation marks are mandatory. An alternative approach that allows for run-time decision making is to use the HelperBase::set_tape_buffer_sizes() function before starting taping (as done via the HelperBase::start_recording_operations() function).
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 840 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 848 of file ad_helpers.h.

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

Definition at line 855 of file ad_helpers.h.

## ◆ CellLevelBase()

 Differentiation::AD::CellLevelBase< ADNumberTypeCode, ScalarType >::CellLevelBase ( 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 719 of file ad_helpers.cc.

virtualdefault

Destructor

## ◆ register_dof_values() [1/2]

 void Differentiation::AD::CellLevelBase< ADNumberTypeCode, ScalarType >::register_dof_values ( const std::vector< scalar_type > & dof_values )

Register the complete set of independent variables $$\mathbf{X}$$ that represent the local degree of freedom values.

Parameters
 [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.
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 730 of file ad_helpers.cc.

## ◆ register_dof_values() [2/2]

template<typename VectorType >
 void Differentiation::AD::CellLevelBase< ADNumberTypeCode, ScalarType >::register_dof_values ( const VectorType & values, const std::vector<::types::global_dof_index > & local_dof_indices )

Register the complete set of independent variables $$\mathbf{X}$$ that represent the local degree of freedom values.

Parameters
 [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().
Note
For taped AD numbers, this operation is only valid in recording mode.

## ◆ get_sensitive_dof_values()

Return the complete set of degree of freedom values as represented by auto-differentiable numbers. These are the independent variables $$\mathbf{X}$$ about which the solution is linearized.

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 representing the local degree of freedom values.
Note
For taped AD numbers, this operation is only valid in recording mode.

Definition at line 753 of file ad_helpers.cc.

## ◆ set_dof_values() [1/2]

 void Differentiation::AD::CellLevelBase< ADNumberTypeCode, ScalarType >::set_dof_values ( const std::vector< scalar_type > & dof_values )

Set the values for the independent variables $$\mathbf{X}$$, i.e., the linearization point.

Parameters
 [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.
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_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 778 of file ad_helpers.cc.

## ◆ set_dof_values() [2/2]

template<typename VectorType >
 void Differentiation::AD::CellLevelBase< ADNumberTypeCode, ScalarType >::set_dof_values ( const VectorType & values, const std::vector<::types::global_dof_index > & local_dof_indices )

Set the values for the independent variables $$\mathbf{X}$$, i.e., the linearization point.

Parameters
 [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().
Note
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_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.

## ◆ compute_residual()

 virtual void Differentiation::AD::CellLevelBase< ADNumberTypeCode, ScalarType >::compute_residual ( Vector< scalar_type > & residual ) const
pure virtual

Compute the value of the residual vector field $$\mathbf{r}(\mathbf{X})$$.

Parameters
 [out] residual A Vector object with the value for each component of the vector field evaluated at the point defined by the independent variable values.
Note
The size of the residual vector is determined by the derived classes, as it depends on the order of the dependent variable(s) derivative(s) that it represents. Code examples that show how to use this interface will be provided in the documentation of the derived classes.

## ◆ compute_linearization()

$\frac{\partial\mathbf{r}(\mathbf{X})}{\partial\mathbf{X}}$
The dimensions of the linearization matrix is determined by the derived classes, as it depends on the order of the dependent variable(s) derivative(s) that it represents. Code examples that show how to use this interface will be provided in the documentation of the derived classes.