krotov.shapes module

Functions that may be used for the update_shape value in the options-dict for each control (pulse_options parameter in optimize_pulses()), or for generating guess pulses

Summary

Functions:

blackman	Blackman window shape
box	Box-shape (Theta-function)
flattop	Flat shape (one) with a switch-on/switch-off from zero
one_shape	Shape function 1 for all values of t
qutip_callback	Convert func into the correct form of a QuTiP time-dependent control
zero_shape	Shape function 0 for all values of t

__all__: blackman, box, flattop, one_shape, qutip_callback, zero_shape

Reference

krotov.shapes.qutip_callback(func, **kwargs)

Convert func into the correct form of a QuTiP time-dependent control

QuTiP requires that “callback” functions that are used to express time-dependent controls take a parameter t and args. This function takes a function func that takes t as its first parameter and an arbitrary number of other parameters. The given kwargs set values for these other parameters. Parameters not contained in kwargs are set at runtime from the args dict.

krotov.shapes.zero_shape(t)

Shape function 0 for all values of t

krotov.shapes.one_shape(t)

Shape function 1 for all values of t

krotov.shapes.flattop(t, t_start, t_stop, t_rise, t_fall=None, func='blackman')

Flat shape (one) with a switch-on/switch-off from zero

The flattop function starts at 0, and ramps to to 1 during the t_rise interval. For func='blackman', the switch-on shape is half of a Blackman window (see blackman()). For func='sinsq, it is a sine-squared curve. The function then remains at value 1, before ramping down to 0 again during t_fall.

Parameters

• t (float) – Time point or time grid

• t_start (float) – Start of flattop window

• t_stop (float) – Stop of flattop window

• t_rise (float) – Duration of ramp-up, starting at t_start

• t_fall (float) – Duration of ramp-down, ending at t_stop. If not given, t_fall=t_rise.

• func (str) – One of ‘blackman’, ‘sinsq’

Note

You may use numpy.vectorize to transform this into a shape function for arrays, functools.partial() to fix the function arguments other than t, creating a function suitable for the update_shape value of pulse_options, and qutip_callback() to create a function suitable as a time-dependent control in QuTiP.

krotov.shapes.box(t, t_start, t_stop)

Box-shape (Theta-function)

The shape is 0 before t_start and after t_stop and 1 elsewhere.

Parameters

• t (float) – Time point or time grid

• t_start (float) – First value of t for which the box has value 1

• t_stop (float) – Last value of t for which the box has value 1

Note

You may use numpy.vectorize, functools.partial(), or qutip_callback(), cf. flattop().

krotov.shapes.blackman(t, t_start, t_stop, a=0.16)

Blackman window shape

\[B(t; t_0, t_1) = \frac{1}{2}\left( 1 - a - \cos\left(2\pi \frac{t - t_0}{t_1 - t_0}\right) + a \cos\left(4\pi \frac{t - t_0}{t_1 - t_0}\right) \right)\,,\]

with \(a = 0.16\).

See http://en.wikipedia.org/wiki/Window_function#Blackman_windows

A Blackman shape looks nearly identical to a Gaussian with a 6-sigma interval between t_start and t_stop. Unlike the Gaussian, however, it will go exactly to zero at the edges. Thus, Blackman pulses are often preferable to Gaussians.

Parameters

• t (float or numpy.ndarray) – Time point or time grid

• t_start (float) – Starting point \(t_0\) of Blackman shape

• t_stop (float) – End point \(t_1\) of Blackman shape

• a (float) – Blackman coefficient.

Returns

If t is a float, return the value of the Blackman shape at t. If t is an array, return an array of same size as t, containing the values for the Blackman shape (zero before t_start and after t_stop)

Return type

float or numpy.ndarray