Module Archimedes.Sampler

Adaptative sampling of functions.

High level functions

type strategy = float -> float -> float

A strategy is a function f t1 t2 that returns an internal point tm between t1 and t2 which will be used to decide if we need to increment precision or not. The given t1 and t2 will always be finite.

type cost = Matrix.rectangle -> float -> float -> float -> float -> float -> float -> float

A cost f bb x0 y0 xm ym x1 y1 which returns the cost measuring how much the three points (x0, y0), (xm, ym), and (x1, y1) differ from a straight line. bb is a rough bounding box of the set of points that can be used to determine whether two points are close (in relative measure). A cost <= 0. means one is satisfied with drawing straight lines connecting the three points.

val xy : ?tlog:bool -> ?fn0:float -> ?n:int -> ?strategy:strategy -> ?cost:cost -> (float -> float * float) -> float -> float -> float array * float array

xy f t1 t2 samples the parametric function f on the interval going from t1 to t2. Returns a list of the points in the sample.

  • parameter tlog

    do we need to step in a logarithmic way ?

  • parameter fn0

    fraction of n defining the number of steps for the initial sampling of the function (that will later be refined). Must be 0 < fn0 <= 1. Default: 0.1.

  • parameter min_step

    don't increment precision more than this threshold

  • parameter n

    is a maximum number of evaluations of f that are allowed. Default: 100.

  • parameter strategy

    a customized strategy.

  • parameter cost

    a customized cost.

val x : ?tlog:bool -> ?fn0:float -> ?n:int -> ?strategy:strategy -> ?cost:cost -> (float -> float) -> float -> float -> float array * float array

x f x1 x2 same as Sampler.xy but for the scalar function f on the interval going from x1 to x2.

val strategy_midpoint : strategy

The default strategy: choose the middle point

val strategy_random : strategy

A strategy that avoids aliasing sampling, but not efficient: chooses randomly a point between t1 and t2

val strategy_center_random : strategy

A more efficient strategy that avoids aliasing sampling: chooses randomly a points between t1 and t2 in its 10% center interval

val cost_angle : cost

Measures the angle at the middle point (xm, ym), the flatter the angle, the lower the cost.

val cost_angle_dist : cost

Measures the angle at the middle point (xm, ym), the flatter the angle, the better and combines it with the distance of the points (x0, y0) and (x1, y1) to the middle point, the smaller the distance, the better.

val cost_angle_log : bool -> bool -> cost

Same criterion as cost_angle suitable for logarithmic cordinates.