pymrm.solve

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Nonlinear-solver utilities used by pymrm.

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Public API¶

clip_approach(values, dummy, lower_bounds = 0, upper_bounds = None, factor = 0)¶

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Project values onto bounds, optionally with a relaxed approach rule.

Parameters¶

• values (numpy.ndarray) Values to modify in place.

• dummy (Any) Placeholder argument kept for API compatibility.

• lower_bounds, upper_bounds (float or numpy.ndarray, optional) Lower and upper bounds. Scalars and broadcastable arrays are supported.

• factor (float, optional) Relaxation factor for out-of-bound entries. 0 applies strict clipping. Non-zero values apply a linear approach update toward the violated bound.

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newton(function, initial_guess, args = (), tol = 1.49012e-08, maxfev = 100, solver = None, lin_solver_kwargs = None, callback = None, rtol = 0.0)¶

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Solve function(x) = 0 with Newton iterations.

Parameters¶

• function (callable) Callable with signature function(x, *args) -> (residual, jacobian).

• initial_guess (numpy.ndarray) Starting point of the iterations.

• args (tuple, optional) Extra positional arguments passed to function.

• tol (float or numpy.ndarray, optional) Absolute stopping tolerance on the Newton update. With the default rtol=0 and a scalar tol the iteration stops when the infinity norm of the update is below tol. This is an ABSOLUTE criterion: for unknowns much smaller than tol (trace concentrations, for example) it can stop after one step with a wrong answer. Scale the unknowns to order one, or use tol=0 with rtol. An array must broadcast to the unknowns.

• maxfev (int, optional) Maximum number of Newton iterations.

• solver ({‘spsolve’, ‘cg’, ‘bicgstab’, ‘splu’} or callable, optional) Linear solver used for each Newton step. If None, the routine picks 'spsolve' for smaller systems and 'bicgstab' for larger systems. When 'splu' is selected, the Jacobian returned by function is expected to be an already-decomposed SuperLU object (as returned by scipy.sparse.linalg.splu), and the solve step calls its .solve() method directly. A callable solver must accept (jac_matrix, rhs, **kwargs) and return the solution vector.

• lin_solver_kwargs (dict, optional) Keyword arguments forwarded to the selected linear solver.

• callback (callable, optional) Optional hook called as callback(x, residual) after each iteration.

• rtol (float, optional) Relative stopping tolerance. When rtol > 0 or tol is an array, the iteration stops when every component satisfies abs(update) <= tol + rtol * abs(x). tol=0, rtol=1e-8 gives a purely relative criterion.

Returns¶

• scipy.optimize.OptimizeResult Result object with fields x, success, nit, fun, message and step_norm (infinity norm of the last update). fun is the residual evaluated at the iterate BEFORE the last update, not at x; evaluate function(x) to check the final residual.

Raises¶

• ValueError If solver is not one of the supported names and is not callable.

• RuntimeError If an iterative linear solver fails to converge.

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