schrodinger.application.jaguar.discretized_1d_function module

Module that implements useful tasks involving handling a discretely sampled continous, one-dimensional function. The continuous function is approximated by cubic splines.

schrodinger.application.jaguar.discretized_1d_function.bracket_zeros(nsegments: int, xa: float, xb: float, function: Callable, args: Tuple, zero_thresh: float = 1e-10) → List[List[float]]

helper function for discretized function. Brackets zeros in the function between xa xb by breaking the line into npts segments. Function is called by apply(function,((x),args)) Returns list of lists holding (xa,xb) that brackets the root

Parameters

  • nsegments – number of segments

  • xa – beginning of range

  • xb – end of range

  • function – function to be minimized

  • args – additional parameters need to call function

  • zero_thresh – threshold for considering a number zero

Returns

list of endpoints of all segments which bracket a root (function changes sign)

class schrodinger.application.jaguar.discretized_1d_function.DiscretelySampledFunction(x: Iterable[float], f: Iterable[float])

Bases: object

class to handle a discretely sampled function uses cubic splines to provide continuous values

__init__(x: Iterable[float], f: Iterable[float])

Initialize the function :param x: points at which the function is sampled :param f: funciton values at the points

evaluate(x: Union[Iterable[float], float], der: int = 0, boundary: str = 'none') → Union[Iterable[float], float]

evaluate the function(der=0) derivative(der=1) or second derivative(der=2) at the point x optionally an ‘up’ or ‘down’ boundary can be applied of the form +/- 0.5 * (x-xmin/xmax)**2 if boundary is ‘none’ x must be in a valid range

Parameters

  • x – point to evaluate function (f(x))

  • der – order of derivative (default=0)

  • boundary – type of boundary to apply

Returns

value of function (or derivative) if x is an iterable a list of values will be returned

critical_points(nsegments: int = 29) → Dict[str, numpy.ndarray[Any, numpy.dtype[numpy.float64]]]

find and return all critical points of the function

Parameters

nsegments – number of segments used to initially bracket zeros 29 seemed reasonable for most applications.

Returns

dictionary holding the locations of ‘minima’ and ‘maxima’ critical points