Commons

In this section, the components commonly used over the program are described.

odatse.Info

This class treats the input parameters. It contains the following four instance variables.

• base : dict[str, Any]

  • Parameters for whole program such as the directory where the output will be written.

• solver : dict[str, Any]

  • Parameters for Solver

• algorithm : dict[str, Any]

  • Parameters for Algorithm

• runner : dict[str, Any]

  • Parameters for Runner

An instance of Info is initialized by passing a dict which has the following four sub dictionaries, base, solver, algorithm, and runner. (Some of them can be omitted.) Each sub dictionary is set to the corresponding field of Info. Alternatively, it can be created by passing to the class method from_file a path to input file in TOML format.

base items

As items of base field, root_dir indicating the root dirctory of the calculation, and output_dir for output results will be set automatically as follows.

• Root directory root_dir

  • The default value is "." (the current directory).

  • The value of root_dir will be converted to an absolute path.

  • The leading ~ will be expanded to the user’s home directory.

  • Specifically, the following code is executed:

    p = pathlib.Path(base.get("root_dir", "."))
    base["root_dir"] = p.expanduser().absolute()
    

• Output directory output_dir

  • The leading ~ will be expanded to the user’s home directory.

  • If an absolute path is given, it is set as-is.

  • If a relative path is given, it is regarded to be relative to root_dir.

  • The default value is ".", that is, the same to root_dir

  • Specifically, the following code is executed:

    p = pathlib.Path(base.get("work_dir", "."))
    p = p.expanduser()
    base["work_dir"] = base["root_dir"] / p
    

odatse.Runner

Runner is a class that connects Algorithm and Solver. The constructor of Runner takes instances of Solver, Info, Mapping, and Limitation. If the instance of Mapping is omitted, TrivialMapping is assumed that does no transformation. If the instance of Limitation is omitted, Unlimited is assumed that do not impose constraints.

submit(self, x: np.ndarray, args: Tuple[int,int]) -> float method invokes the solver and returns the value of objective function f(x). submit internally uses the instance of Limitation to check whether the search parameter x satisfies the constraints. Then, it applies the instance of Mapping to obtain from x the input y = mapping(x) that is actually used by the solver.

See Input file for details how/which components of info Runner uses.

odatse.Mapping

Mapping is a class that describes mappings from the search parameters of the inverse problem analysis algorithms to the variables of the direct problem solvers. It is defined as a function object class that has __call__(self, x: np.ndarray) -> np.ndarray method. In the current version, a trivial transformation TrivialMapping and an affine mapping Affine are defined.

TrivialMapping

TrivialMapping provides a trivial transformation \(x\to x\), that is, no transformation. It is taken as a default to the argument of Runner class.

Affine

Affine provides an affine mapping \(x \to y = A x + b\). The coefficients A and b should be given as constructor arguments, or passed as dictionary elements through the from_dict class method. In case when they are specified in the input file of ODAT-SE, the format of the parameter may be referred to the input file section of the manual.

odatse.Limitation

Limitation is a class that describes constraints on the \(N\) dimensional parameter space \(x\) searched by the inverse problem analysis algorithms. It is defined as a class that have the method judge(self, x: np.ndarray) -> bool. In the current version, Unlimited class that imposes no constraint, and Inequality class that represents the linear inequality constraint.

Unlimited

Unlimited represents that no constraint is imposed. judge method always returns True. It is taken as a default to the argument of Runner class.

Inequality

Inequality is a class that expresses \(M\) constraints imposed on \(N\) dimensional search parameters \(x\) in the form \(A x + b > 0\) where \(A\) is a \(M \times N\) matrix and \(b\) is a \(M\) dimensional vector.

The coefficients A and b should be given as constructor arguments, or passed as dictionary elements through the from_dict class method. In case when they are specified in the input file of ODAT-SE, the format of the parameter may be referred to the input file section of the manual.