rydiqule.stack_solvers.cyrk_solver.cyrk_solve

rydiqule.stack_solvers.cyrk_solver.cyrk_solve(eoms_base: ndarray, const_base: ndarray, eom_time_r: ndarray, const_r: ndarray, eom_time_i: ndarray, const_i: ndarray, time_inputs: Sequence[Callable[[float], complex]], t_eval: ndarray, init_cond: ndarray, eqns: Literal['orig', 'flat'] = 'orig', **kwargs) → ndarray

Solve a set of Optical Bloch Equations (OBEs) with rydiqule’s time solving convention using CyRK’s pysolve_ivp.

Uses matrix components of the equations of motion provided by the methods of a Sensor(). Designed to be used as a wrapped function within solve_time(). Builds and solves equations of motion according rydiqule’s time solving conventions. Sets up and solves dx/dt = A(t)x + b(t)

For larger solve systems, max_ram_MB kwarg for pysolve_ivp will likely need to be increased from its default of 2000.

Parameters:

• eoms_base (numpy.ndarray) – The matrix of shape (*l,n,n) representing the non time-varying portion of the matrix A in the equations of motion.

• const_base (numpy.ndarray) – The array of shape (*l, n) representing the non time-varying portion of the vector b in the equations of motion.

• eoms_time_r (numpy.ndarraynumpy) – The matrix of shape (n_t, *l, n, n) representing the real time-varying portion of the matrix A, where n_t is the length of time_inputs. The ith slice along the first axis should be multiplied by the real part of the ith entry in time_inputs.

• const_r (numpy.nd_array) – The matrix of shape (n_t, *l, n) representing the real time-varying portion of the vector b, where n_t is the length of time_inputs. The ith slice along the first axis should be multiplied by the real part of the ith entry in time_inputs.

• eoms_time_i (numpy.ndarray) – The matrix of shape (n_t, *l, n, n) representing the imaginary time-varying portion of the matrix A, where n_t is the length of time_inputs. The ith slice along the first axis should be multiplied by the imaginary part of the ith entry in time_inputs.

• const_i (numpy.nd_array) – The matrix of shape (n_t, *l, n) representing the imaginary time-varying portion of the vector b, where n_t is the length of time_inputs. The ith slice along the first axis should be multiplied by the imaginary part of the ith entry in time_inputs.

• time_inputs (list(callable)) – List of callable functions of length n_t. The functions should take a single floating point as an input representing the time in microseconds, and return a real or complex floating point value represent an electric field in V/m at that time. Return type of each function must be the same for all inputs t.

• t_eval (numpy.ndarray) – Array of times to sample the integration at. This array must have dtype of float64.

• init_cond (numpy.ndarray) – Matrix of shape (*l, n) representing the initial state of the system.

• eqns ({"orig", "flat"}) – Method used to generate the derivative equations. Options are orig (which uses a numpy reshaping approach) and flat (which uses flat array indexing).

• **kwargs (dict:) – Additional keyword arguments passed to pysolve_ivp.

Returns:

The matrix solution of shape (*l,n,n_t) representing the density matrix of the system at each time t.

Return type:

numpy.ndarray

Raises:

RydiquleError – If system size exceeds cyrk backend limit of 65535 equations. If we see this error a lot, consider getting CyRK project to increase it by changing type of y_size from unisgned short.