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Reference documentation for deal.II version 9.1.1
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Reference documentation for deal.II version 9.1.1
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#include <deal.II/differentiation/ad/ad_helpers.h>
Public Types | |
| using | scalar_type = typename AD::NumberTraits< ScalarType, ADNumberTypeCode >::scalar_type |
| using | ad_type = typename AD::NumberTraits< ScalarType, ADNumberTypeCode >::ad_type |
Public Member Functions | |
Constructor / destructor | |
| HelperBase (const unsigned int n_independent_variables, const unsigned int n_dependent_variables) | |
| virtual | ~HelperBase ()=default |
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 base helper class that facilitates the evaluation of the derivative(s) of a number of user-defined dependent variables \(\mathbf{f}(\mathbf{X})\) with respect to a set of independent variables \(\mathbf{X}\), that is \(\dfrac{d^{i} \mathbf{f}(\mathbf{X})}{d \mathbf{X}^{i}}\).
This class is templated on the floating point type scalar_type of the number that we'd like to differentiate, as well as an enumeration indicating the ADNumberTypeCode . The ADNumberTypeCode dictates which auto-differentiation library is to be used, and what the nature of the underlying auto-differentiable number is. Refer to the Automatic and symbolic differentiation module for more details in this regard.
For all of the classes derived from this base class, there are two possible ways that the code in which they are used can be structured. The one approach is effectively a subset of the other, and which might be necessary to use depends on the nature of the chosen auto-differentiable number.
When "tapeless" numbers are employed, the most simple code structure would be of the following form:
Note that since the specialized classes interpret the independent variables in different ways, above represents only an outline of the steps taken to compute derivatives. More specific examples are outlined in the individual classes that specialize this base class.
When "taped" numbers are to be used, the above code should be wrapped by a few more lines of code to manage the taping procedure:
The second approach outlined here is more general than the first, and will work equally well for both taped and tapeless auto-differentiable numbers.
Definition at line 172 of file ad_helpers.h.
| using Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::scalar_type = typename AD::NumberTraits<ScalarType, ADNumberTypeCode>::scalar_type |
Type definition for the floating point number type that is used in, and results from, all computations.
Definition at line 180 of file ad_helpers.h.
| using Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::ad_type = typename AD::NumberTraits<ScalarType, ADNumberTypeCode>::ad_type |
Type definition for the auto-differentiation number type that is used in all computations.
Definition at line 187 of file ad_helpers.h.
| Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::HelperBase | ( | const unsigned int | n_independent_variables, |
| const unsigned int | n_dependent_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 \(\mathbf{f}(\mathbf{X})\), 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 38 of file ad_helpers.cc.
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virtualdefault |
Destructor
| std::size_t Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::n_independent_variables | ( | ) | const |
Return the number of independent variables that this object expects to work with. This is the dimension of the domain space.
Definition at line 245 of file ad_helpers.cc.
| std::size_t Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::n_dependent_variables | ( | ) | const |
Return the number of dependent variables that this object expects to operate on. This is the dimension of the image space.
Definition at line 266 of file ad_helpers.cc.
| void Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::print | ( | std::ostream & | stream | ) | const |
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 313 of file ad_helpers.cc.
| void Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::print_values | ( | std::ostream & | stream | ) | const |
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 368 of file ad_helpers.cc.
| void Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::print_tape_stats | ( | const typename Types< ad_type >::tape_index | tape_index, |
| std::ostream & | stream | ||
| ) | const |
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 auto-differentiable number. Definition at line 382 of file ad_helpers.cc.
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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.
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 457 of file ad_helpers.cc.
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virtual |
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.
| [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. |
Reimplemented in Differentiation::AD::PointLevelFunctionsBase< dim, ADNumberTypeCode, ScalarType >.
Definition at line 399 of file ad_helpers.cc.
| bool Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::is_recording | ( | ) | const |
Return whether or not this class is tracking calculations performed with its marked independent variables.
Definition at line 275 of file ad_helpers.cc.
| Types< typename HelperBase< ADNumberTypeCode, ScalarType >::ad_type >::tape_index Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::active_tape_index | ( | ) | const |
Return the tape index which is currently activated for recording or reading.
Definition at line 288 of file ad_helpers.cc.
| bool Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::is_registered_tape | ( | const typename Types< ad_type >::tape_index | tape_index | ) | const |
Return whether or not a tape number has already been used or registered.
Definition at line 300 of file ad_helpers.cc.
| 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, |
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| const typename Types< ad_type >::tape_buffer_sizes | vbufsize = 64 * 1024 * 1024, |
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| const typename Types< ad_type >::tape_buffer_sizes | tbufsize = 64 * 1024 * 1024 |
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| ) |
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 | 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 568 of file ad_helpers.cc.
| bool Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::start_recording_operations | ( | const typename Types< ad_type >::tape_index | tape_index, |
| const bool | overwrite_tape = false, |
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| const bool | keep_independent_values = true |
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| ) |
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:
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 587 of file ad_helpers.cc.
| void Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::stop_recording_operations | ( | const bool | write_tapes_to_file = false | ) |
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.
Definition at line 652 of file ad_helpers.cc.
| void Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::activate_recorded_tape | ( | const typename Types< ad_type >::tape_index | tape_index | ) |
Select a pre-recorded tape to read from.
| [in] | tape_index | The index of the tape to be read from. |
Definition at line 483 of file ad_helpers.cc.
| bool Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::recorded_tape_requires_retaping | ( | const typename Types< ad_type >::tape_index | tape_index | ) | const |
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 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 493 of file ad_helpers.cc.
| bool Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::active_tape_requires_retaping | ( | ) | const |
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 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 506 of file ad_helpers.cc.
| void Differentiation::AD::HelperBase< ADNumberTypeCode, ScalarType >::clear_active_tape | ( | ) |
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 519 of file ad_helpers.cc.
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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.
| [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 531 of file ad_helpers.cc.
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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.
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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 109 of file ad_helpers.cc.
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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 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 146 of file ad_helpers.cc.
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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 185 of file ad_helpers.cc.
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Initialize an independent variable \(X_{i}\).
| [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 209 of file ad_helpers.cc.
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The number of independent variables that have been manipulated within a set of operations.
Definition at line 234 of file ad_helpers.cc.
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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 96 of file ad_helpers.cc.
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The number of dependent variables that have been registered.
Definition at line 254 of file ad_helpers.cc.
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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 688 of file ad_helpers.cc.
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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 594 of file ad_helpers.h.
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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 602 of file ad_helpers.h.
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mutableprotected |
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 638 of file ad_helpers.h.
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mutableprotected |
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 648 of file ad_helpers.h.
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A list of registered independent variables that have been manipulated for a given set of operations.
Definition at line 654 of file ad_helpers.h.
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mutableprotected |
A list of registered independent variables that have been extracted and their sensitivities marked.
Definition at line 660 of file ad_helpers.h.
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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 752 of file ad_helpers.h.
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A list of registered dependent variables.
Definition at line 757 of file ad_helpers.h.
1.8.14