Description language¶
Identifier conventions¶
Identifiers whose names start with the pattern <letters> are special. The following special variable names are supported:
Internal names¶
<p>NAME
This variable contains persistent state. (that survives from one step to the next)
<cond>NAME
This variable is used by a conditional. May not be re-defined.
<dt>
The time increment for the present time step.
Its value at the beginning of a step indicates the step size to be used. If a time step of this size cannot be completed, FailStep must be issued.
This variable contains persistent state. (that survives from one step to the next)
<t>
Base time of current time step.
The integrator code is responsible for incrementing <t> at the end of a successful step.
This variable contains persistent state. (that survives from one step to the next)
User-controlled values¶
<state>NAME
State identifier under user (=scheme writer) control
This variable contains persistent state. (that survives from one step to the next)
<ret_time_id>COMPONENT_ID
<ret_time>COMPONENT_ID
<ret_state>COMPONENT_ID
For targets that are incapable of returning state mid-step, these variables are used to store computed state.
See dagrt.function_registry
for interpretation of function names. The
function namespace and the variable namespace are distinct. No user-defined
identifiers should start with dagrt_.
Statements¶
Assignment Statements¶
These statements perform updates to the execution state, i.e. the variables.
- class dagrt.language.AssignImplicit(assignees, solve_variables, expressions, other_params, solver_id, **kwargs)[source]¶
- assignees¶
A tuple of strings. The names of the variables to assign with the results of solving for solve_variables
- solve_variables¶
A tuple of strings, the names of the variables being solved for
- expressions¶
A tuple of expressions, which represent the left hand sides of a system of (possibly nonlinear) equations. The solver will attempt to find a simultaneous root of the system.
- other_params¶
A dictionary used to pass extra arguments to the solver, for instance a starting guess
- solver_id¶
An identifier for the solver that is to be used to solve the system. This identifier is intended to match information about solvers which is supplied by the user.
- class dagrt.language.Assign(assignee=None, assignee_subscript=None, expression=None, loops=None, **kwargs)[source]¶
- loops¶
A list of triples (identifier, start, end) that the assignment should be carried out inside of these loops. No ordering of loop iterations is implied. The loops will typically be nested outer-to-inner, but a target may validly use any order it likes.
- class dagrt.language.AssignFunctionCall(assignees, function_id, parameters, kw_parameters=None, **kwargs)[source]¶
This statement encodes function calls. It should be noted that function calls can also be encoded as expressions involving calls, however the existence of this separate statement is justified by two facts:
Some backends (such as Fortran) choose to separate out function calls into individual statements. This statement provides a natural way to encode them.
See
dagrt.codegen.transform.isolate_function_calls
for a transform that accomplishes this.Calling functions with multiple return values is not supported as part of dagrt’s language.
- assignees¶
A tuple of variables to be passed assigned results from calling
function_id
.
- function_id¶
- parameters¶
A list of expressions to be passed as positional arguments.
- kw_parameters¶
A dictionary mapping names to expressions to be passed as keyword arguments.
Control Statements¶
These statements affect the execution of a phase, or cause a phase to interact with user code.
- class dagrt.language.Raise(error_condition, error_message=None, **kwargs)[source]¶
- error_condition¶
A (Python) exception type to be raised.
- error_message¶
The error message to go along with that exception type.
Miscellaneous Statements¶
Code Container¶
- class dagrt.language.ExecutionPhase(name, next_phase, statements)[source]¶
- name¶
name of this phase
- depends_on¶
a list of statement IDs that need to be executed to complete a successful execution of one round of this phase, excluding their dependencies.
- next_phase¶
name of the next state after this one, if no other state is specified by the user.
- statements¶
is a list of statement instances in no particular order.
- class dagrt.language.DAGCode(phases, initial_phase)[source]¶
- phases¶
is a map from time integrator phase names to
ExecutionPhase
instances
- initial_phase¶
the name of the starting phase
Visualization¶
- dagrt.language.get_dot_dependency_graph(code, use_stmt_ids=False)[source]¶
Return a string in the dot language depicting dependencies among kernel statements.
- dagrt.language.show_dependency_graph(*args, **kwargs)[source]¶
Show the dependency graph generated by
get_dot_dependency_graph()
in a browser. Accepts the same arguments as that function.
Code Creation¶
- class dagrt.language.CodeBuilder(name)[source]¶
- name¶
The name of the phase being generated
- statements¶
The set of statements generated for the phase
Language support:
- assign(assignees, expression, loops=None)[source]¶
Generate code for an assignment.
assignees may be a variable, a subscript (if referring to an array), or a tuple of variables. There must be exactly one assignee unless expression is a function call.
loops is a list of tuples of the form (identifier, start_index, stop_index).
Control flow:
Context manager:
Graph generation:
- as_execution_phase(next_phase)[source]¶
Return the generated graph as an
ExecutionPhase
.- Parameters:
next_phase – The name of the default next phase
Convenience functions:
- __call__()[source]¶
Alias for
CodeBuilder.assign()
.
- assign_implicit_1(assignee, solve_component, expression, guess, solver_id=None)[source]¶
Special case of AssignImplicit when there is 1 component to solve for.
Function registry¶
The function registry is used by targets to resolve external functions and invoke user-specified code, including but not limited to ODE right-hand sides.
- class dagrt.function_registry.Function(language_to_codegen=None, **kwargs)[source]¶
- result_names¶
A list of names of the return values of the function. Note that these names serve as documentation and as identifiers to be used for variables receiving function results inside generated code implementing the call to the function (e.g. in the Fortran backend). They have no relationship to the names to which the results ultimately get assigned.
- identifier¶
The name of the function.
- arg_names¶
The names of the arguments to the function.
- default_dict¶
A dictionary mapping argument names to default values.
- get_result_kinds(arg_kinds, check)[source]¶
Return a tuple of the
dagrt.data.SymbolKind
instances for the values this function returns if arguments of the kinds arg_kinds are supplied.The length of the returned tuple must match the lenght of
result_names
.- Parameters:
arg_kinds – a dictionary mapping numbers (for positional arguments) or identifiers (for keyword arguments) to
dagrt.data.SymbolKind
instances indicating the types of the arguments being passed to the function. Some elements of arg_kinds may be None if their kinds have yet not been determined.check – A
bool
. If True, none of arg_kinds will be None, and argument kind checking should be performed.
- register_codegen(language, codegen_function)[source]¶
Return a copy of self with codegen_function registered as a code generator for language.
The interface for codegen_function depends on the code generator being used.
- resolve_args(arg_dict)[source]¶
Resolve positional and keyword arguments to an argument list.
See also
dagrt.utils.resolve_args()
.- Parameters:
arg_dict – a dictionary mapping numbers (for positional arguments) or identifiers (for keyword arguments) to values
- class dagrt.function_registry.FunctionRegistry(id_to_function=None)[source]¶
-
- __getitem__(function_id)[source]¶
Return the
Function
with identifier function_id.- Raises:
FunctionNotFound – when function_id was not found
- register_codegen(function_id, language, codegen)[source]¶
Register a code generation helper object for target language for the function with identifier function_id.
- Parameters:
codegen – an object obeying an interface suitable for code generation for language. This interface depends on the code generator being used.
- dagrt.function_registry.base_function_registry¶
The default function registry, containing all the built-in functions (see Built-ins).
Registering new functions¶
- dagrt.function_registry.register_ode_rhs(function_registry, output_type_id, identifier=None, input_type_ids=None, input_names=None)[source]¶
Register a function as an ODE right-hand side.
Functions registered through this call have the following characteristics. First, there is a single return value of the user type whose type identifier is output_type_id. Second, the function has as its first argument a scalar named t. Last, the remaining argument list to the function consists of user type values.
For example, considering the ODE \(y' = f(t, y)\), the following call registers a right-hand side function with name f and user type y:
freg = register_ode_rhs(freg, "y", identifier="f")
- Parameters:
function_registry – the base function registry
output_type_id – a string, the user type ID returned by the call.
identifier – the full name of the function. If not provided, defaults to <func> + output_type_id.
input_type_ids – a tuple of strings, the identifiers of the user types which are the arguments to the right-hand side function. An automatically added t argument occurs before these arguments. If not provided, defaults to (output_type_id,).
input_names – a tuple of strings, the names of the inputs. If not provided, defaults to input_type_ids.
- Returns:
a new
FunctionRegistry
- dagrt.function_registry.register_function(function_registry, identifier, arg_names, default_dict=None, result_names=(), result_kinds=())[source]¶
Register a function returning output(s) of fixed kind.
- Parameters:
function_registry – the base
FunctionRegistry
identifier – a string, the function identifier
arg_names – a list of strings, the names of the arguments
default_dict – a dictionary mapping argument names to default values
result_names – a list of strings, the names of the output(s)
result_kinds – a list of
dagrt.data.SymbolKind
s, the kinds of the output(s)
- Returns:
a new
FunctionRegistry
Built-ins¶
The built-in functions are listed below. This also serves as their language documentation.
- class dagrt.function_registry.Norm1(language_to_codegen=None, **kwargs)[source]¶
norm_1(x)
returns the 1-norm of x. x is a user type or array.
- class dagrt.function_registry.Norm2(language_to_codegen=None, **kwargs)[source]¶
norm_2(x)
returns the 2-norm of x. x is a user type or array.
- class dagrt.function_registry.NormInf(language_to_codegen=None, **kwargs)[source]¶
norm_inf(x)
returns the infinity-norm of x. x is a user type or array.
- class dagrt.function_registry.ElementwiseAbs(language_to_codegen=None, **kwargs)[source]¶
elementwise_abs(x)
takes the elementwise absolute value of x. x is a user type, array, or scalar.
- class dagrt.function_registry.DotProduct(language_to_codegen=None, **kwargs)[source]¶
dot_product(x, y)
return the dot product of x and y. The complex conjugate of x is taken first, if applicable. x and y are either arrays (that must be of the same length) or the same user type.
- class dagrt.function_registry.Len(language_to_codegen=None, **kwargs)[source]¶
len(x)
returns the number of degrees of freedom in x. x is a user type or array.
- class dagrt.function_registry.IsNaN(language_to_codegen=None, **kwargs)[source]¶
isnan(x)
returns True if and only if there are any NaNs in x. x is a user type, scalar, or array.
- class dagrt.function_registry.Array_(language_to_codegen=None, **kwargs)[source]¶
array(n)
returns an empty array with n entries in it. n must be an integer.
- class dagrt.function_registry.MatMul(language_to_codegen=None, **kwargs)[source]¶
matmul(a, b, a_cols, b_cols)
returns a 1D array containing the matrix resulting from multiplying the arrays a and b (both interpreted as matrices, with a number of columns a_cols and b_cols respectively).
- class dagrt.function_registry.Transpose(language_to_codegen=None, **kwargs)[source]¶
transpose(a, a_cols)
returns a 1D array containing the matrix resulting from transposing the array a (interpreted as a matrix with a_cols columns).
- class dagrt.function_registry.LinearSolve(language_to_codegen=None, **kwargs)[source]¶
linear_solve(a, b, a_cols, b_cols)
returns a 1D array containing the matrix resulting from multiplying the matrix inverse of a by b, both interpreted as matrices, with a number of columns a_cols and b_cols respectively.