Solver

Solver

The Solver class provides a generic interface for solving linear systems of equations using different iterative solvers such as GMRES, BiCGSTAB, and LGMRES, and the GMResCounter class is used to count the number of iterations and display the residual or current iterate during the GMRES solver.

Initializes a solver object with specified parameters and creates a logger object.

Parameters:

Name	Type	Description	Default
solver_type	str	The type of solver to be used. Defaults to "gmres".	'gmres'
tolerance	float	The desired accuracy of the solver.	0.0001
max_iter	int	The maximum number of iterations that the solver will perform.	10000.0
restart	int	The number of iterations after which the solver will restart.	100.0

Source code in yasfpy/solver.py

def __init__(
    self,
    solver_type: str = "gmres",
    tolerance: float = 1e-4,
    max_iter: int = 1e4,
    restart: int = 1e2,
):
    """Initializes a solver object with specified parameters and creates a logger object.

    Args:
        solver_type (str, optional): The type of solver to be used. Defaults to "gmres".
        tolerance (float): The desired accuracy of the solver.
        max_iter (int): The maximum number of iterations that the solver will perform.
        restart (int): The number of iterations after which the solver will restart.
    """
    self.type = solver_type.lower()
    self.tolerance = tolerance
    self.max_iter = int(max_iter)
    self.restart = int(restart)

    self.log = log.scattering_logger(__name__)

type = solver_type.lower() instance-attribute

tolerance = tolerance instance-attribute

max_iter = int(max_iter) instance-attribute

restart = int(restart) instance-attribute

log = log.scattering_logger(__name__) instance-attribute

run

Runs the solver on the given linear system of equations.

Parameters:

Name	Type	Description	Default
a	LinearOperator	The linear operator representing the system matrix.	required
b	ndarray	The right-hand side vector.	required
x0	ndarray	The initial guess for the solution. If not provided, a copy of b will be used.	None

Returns:

Name	Type	Description
value	ndarray	The solution to the linear system of equations.
err_code	int	The error code indicating the convergence status of the solver.

Source code in yasfpy/solver.py

def run(self, a: LinearOperator, b: np.ndarray, x0: np.ndarray = None):
    """
    Runs the solver on the given linear system of equations.

    Args:
        a (LinearOperator): The linear operator representing the system matrix.
        b (np.ndarray): The right-hand side vector.
        x0 (np.ndarray, optional): The initial guess for the solution. If not provided, a copy of b will be used.

    Returns:
        value (np.ndarray): The solution to the linear system of equations.
        err_code (int): The error code indicating the convergence status of the solver.

    """
    if x0 is None:
        x0 = np.copy(b)

    if np.any(np.isnan(b)):
        print(b)

    if self.type == "bicgstab":
        # Add your code here for the bicgstab solver
        pass
        counter = GMResCounter(callback_type="x")
        value, err_code = bicgstab(
            a,
            b,
            x0,
            tol=self.tolerance,
            atol=0,
            maxiter=self.max_iter,
            callback=counter,
        )
    elif self.type == "gmres":
        counter = GMResCounter(callback_type="pr_norm")
        value, err_code = gmres(
            a,
            b,
            x0,
            restart=self.restart,
            tol=self.tolerance,
            atol=self.tolerance**2,
            maxiter=self.max_iter,
            callback=counter,
            callback_type="pr_norm",
        )
    elif self.type == "lgmres":
        counter = GMResCounter(callback_type="x")
        value, err_code = lgmres(
            a,
            b,
            x0,
            tol=self.tolerance,
            atol=self.tolerance**2,
            maxiter=self.max_iter,
            callback=counter,
        )
    else:
        self.log.error("Please specify a valid solver type")
        exit(1)

    return value, err_code

GMResCounter

Bases: object

The GMResCounter class is a helper class that counts the number of iterations and displays the residual or current iterate during the GMRES solver.

Initializes an object with optional display and callback type parameters.

Parameters:

Name	Type	Description	Default
disp	bool	A boolean flag that determines whether or not to display the progress of the algorithm. If disp is set to True, the algorithm will display the progress. If disp is set to False, the algorithm will not display the progress.	False
callback_type	str	The type of callback to be used. It can have two possible values.	'pr_norm'

Source code in yasfpy/solver.py

def __init__(self, disp: bool = False, callback_type: str = "pr_norm"):
    """Initializes an object with optional display and callback type parameters.

    Args:
        disp (bool, optional): A boolean flag that determines whether or not to display the progress
            of the algorithm. If `disp` is set to `True`, the algorithm will display the progress.
            If `disp` is set to `False`, the algorithm will not display the progress.
        callback_type (str, optional): The type of callback to be used. It can have two possible values.

    """
    self.log = log.scattering_logger(__name__)
    self._disp = disp
    self.niter = 0
    if callback_type == "pr_norm":
        # self.header = "% 10s \t % 15s" % ("Iteration", "Residual")
        self.header = " Iteration \t        Residual"
    elif callback_type == "x":
        # self.header = "% 10s \t %s" % ("Iteration", "Current Iterate")
        self.header = " Iteration \t Current Iterate"

log = log.scattering_logger(__name__) instance-attribute

niter = 0 instance-attribute

header = ' Iteration \t Residual' instance-attribute

__call__

The function increments a counter, formats a message based on the input, logs the header and message, and prints the header and message if the _disp flag is True.

Parameters:

Name	Type	Description	Default
rk	Union[ndarray, float]	The parameter rk can be either a float or a numpy array.	None

Source code in yasfpy/solver.py

def __call__(self, rk=None):
    """The function increments a counter, formats a message based on the input, logs the header and
    message, and prints the header and message if the `_disp` flag is True.

    Args:
        rk (Union[np.ndarray, float]): The parameter `rk` can be either a float or a numpy array.

    """
    self.niter += 1
    if isinstance(rk, float):
        # msg = "% 10i \t % 15.5f" % (self.niter, rk)
        msg = f"{self.niter:10} \t {rk:15.5f}"
    elif isinstance(rk, np.ndarray):
        # msg = "% 10i \t " % self.niter + np.array2string(rk)
        msg = f"{self.niter:10} \t {np.array2string(rk)}"

    self.log.numerics(self.header)
    self.log.numerics(msg)
    if self._disp:
        print(self.header)
        print(msg)

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