pytriqs.utility.dichotomy

pytriqs.utility.dichotomy.dichotomy(function, x_init, y_value, precision_on_y, delta_x, max_loops=1000, x_name='', y_name='', verbosity=1)[source]

Finds \(x\) that solves \(y = f(x)\).

Starting at x_init, which is used as the lower upper/bound, dichotomy finds first the upper/lower bound by adding/subtracting delta_x. Then bisection is used to refine \(x\) until abs(f(x) - y_value) < precision_on_y or max_loops is reached.

Parameters:
  • function (function, real valued) – Function \(f(x)\). It must take only one real parameter.
  • x_init (double) – Initial guess for x. On success, returns the new value of x.
  • y_value (double) – Target value for y.
  • precision_on_y (double) – Stops if abs(f(x) - y_value) < precision_on_y.
  • delta_x (double) – \(\Delta x\) added/subtracted from x_init until the second bound is found.
  • max_loops (integer, optional) – Maximum number of loops (default is 1000).
  • x_name (string, optional) – Name of variable x used for printing.
  • y_name (string, optional) – Name of variable y used for printing.
  • verbosity (integer, optional) – Verbosity level.
Returns:

(x,y) – \(x\) and \(y=f(x)\). Returns (None, None) if dichotomy failed.
Return type:

(double, double)