About

About#

In this document we will try to explain the process that is happening behind the scenes when an .ode file is parsed and code is generated.

To do this exercise we will consider the following ODE file called lorentz.ode

ode_string = """
# This is the Lorentz system
# And it is part of this tutorial

parameters(
sigma=12.0,
rho=21.0,
beta=2.4
)

states(x=ScalarParam(1.0, unit="m", description="x variable"), y=2.0,z=3.05)

dx_dt = sigma * (y - x)  # The derivative of x
dy_dt = x * (rho - z) - y  # m/s
dz_dt = x * y - beta * z
"""

from gotranx.load import ode_from_string
ode = ode_from_string(ode_string, name="Lorentz")
print(ode)

2024-11-05 20:05:02 [info     ] Num states 3

2024-11-05 20:05:02 [info     ] Num parameters 3

ODE(Lorentz, num_states=3, num_parameters=3)

To see what output is generated from this ODE you can check out Your first ODE file.

Atoms#

This ODE has 3 parameters (sigma, rho and beta), 3 states (x, y and z) and 3 assignments (dx_dt, dy_dt and dz_dt). Parameters, states and assignments are subclasses of Atom which is the most primitive building block in gotranx

        classDiagram
    Atom <|-- Parameter
    Atom <|-- State
    Atom <|-- Assignment
    class Atom{
        name: str
        symbol: sympy.Symbol
        components: tuple[str, ...]
        description: str
        unit_str: str
        unit: pint.Unit

    }
    class Parameter{
        value: sympy.Number
    }
    class State{
        value: sympy.Number
    }
    class Assignment{
        value: Expression
        expr: sympy.Expression
        comment: Comment
    }
    Assignment <|-- StateDerivative
    Assignment <|-- Intermediate
    class Expression{
        tree: lark.Tree
        dependencies: set[str]
    }
    class StateDerivative{
        state: State
    }

An Atom contains a number of different fields

name is the name of the variable represented as a string. For example of the name of the parameter rho is the string "rho"
symbol is similar to name this this is a sympy object and this is used within the expressions in the assignments.
components is just a list of components that a given atom belongs to. In this simple ODE we don’t have any components (or practically speaking we have one component). However in lager ODE systems it might be useful to group parameters, states and assignments into different components. In these cases it is possible for an atom to be part of several components.
description is just a string with some information. In our example, the state x has the description "x variable" and dx_dt has the description "The derivative of x".
unit_str is a string representation of a unit, for example x has the unit string "m" while dy_dt has the unit string m/s. If no using is provided this is set to None
unit is a pint unit and this can be used e.g to convert to and from different units.

We note that the 3 assignments are a special type of assignment called a StateDerivative. There is also another type of assignment called and Intermediate. The StateDerivative is special because it is associated with a given State and represents the temporal derivative of the state variable. For example dx_dt is associated with the state x.

Whenever you have a state variable, there has to be a corresponding state derivative. We can try to create an ODE with a missing derivative

from gotranx.load import ode_from_string

ode_from_string("states(x=1, y=2)\ndx_dt = x + y")

---------------------------------------------------------------------------
ComponentNotCompleteError                 Traceback (most recent call last)
Cell In[2], line 3
      1 from gotranx.load import ode_from_string
----> 3 ode_from_string("states(x=1, y=2)\ndx_dt = x + y")

File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/gotranx/load.py:35, in ode_from_string(text, name)
     32 if not isinstance(result, LarkODE):
     33     raise exceptions.InvalidODEException(text=text, atoms=result)
---> 35 ode = make_ode(
     36     components=result.components,
     37     name=name,
     38     comments=result.comments,
     39 )
     40 logger.info(f"Num states {ode.num_states}")
     41 logger.info(f"Num parameters {ode.num_parameters}")

File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/gotranx/ode.py:229, in make_ode(components, comments, name)
    203 def make_ode(
    204     components: Sequence[Component],
    205     comments: Sequence[atoms.Comment] | None = None,
    206     name: str = "ODE",
    207 ) -> ODE:
    208     """Create an ODE from a list of components
    209 
    210     Parameters
   (...)
    227         If a symbol is duplicated
    228     """
--> 229     check_components(components=components)
    230     t = sp.Symbol("t")
    231     # components = add_temporal_state(components, t)

File /opt/hostedtoolcache/Python/3.10.15/x64/lib/python3.10/site-packages/gotranx/ode.py:39, in check_components(components)
     37 for comp in components:
     38     if not comp.is_complete():
---> 39         raise exceptions.ComponentNotCompleteError(
     40             component_name=comp.name,
     41             missing_state_derivatives=[state.name for state in comp.states_without_derivatives],
     42         )

ComponentNotCompleteError: Component '' is not complete. Missing state derivatives for ['y']

Parsing an ODE file#

When a file is parsed it is first opened, turned into a string and then sent to the lark parser

Lark then tries to parse the text using the grammar and turns each object into a tree which is in turn assembled into components using the transformer class.

        flowchart LR
    FILE[.ode file] --> PARSER[Lark Parser]
    PARSER --> TRANS[Transformer]
    TRANS --> DESC[Description]
    TRANS --> TREE[Syntax Tree]
    ATOMS --> COMP[Components] --> ODE
    TRANS --> COMP
    TRANS --> ODE
    TREE --> ATOMS[Atom]

    DESC --> ODE

Code generation#

To generate code we pass the ODE to a code generator object. A code generator object inherits from the gotranx.codegen.CodeGenerator class. For example we could create a PythonCodeGenerator by passing in the ode, i.e

from gotranx.codegen.python import PythonCodeGenerator

codegen = PythonCodeGenerator(ode)

We can now generate code for the different methods. For example we can generate code for the initial_state_values

print(codegen.initial_state_values())

def init_state_values(**values):
    """Initialize state values"""
    # x=1.0, y=2.0, z=3.05

    states = numpy.array([1.0, 2.0, 3.05], dtype=numpy.float64)

    for key, value in values.items():
        states[state_index(key)] = value

    return states

Each code generator is associated with a template that follows the gotranx.templates.Template protocol.

        flowchart TD
    subgraph gen [Code generators]
    PYTHON_CODEGEN[python]
    C_CODEGEN[C]
    end
    ODE[ODE file] --> gen
    subgraph tem [Templates]
    PY_TEMP[Python template] --> PYTHON_CODEGEN
    C_TEMP[C template] --> C_CODEGEN
    end
    subgraph code [Code]
    PYTHON_CODEGEN -. Specific methods .-> PY_CODE[Python Code]
    C_CODEGEN -. Specific methods .-> C_CODE[C Code]
    end

You can checkout Adding a new language to see how to add support for a new language.

About

Contents

About#

Atoms#

Parsing an ODE file#

Code generation#