SDE

class pydaddy.sde.SDE(**kwargs)

Bases: object

A class to form a basic SDE from data

Parameters

• X (array_like) – time series data

• t_int (float) – time step in time series

• Dt (int) – analysis time step

• inc (float) – max increment for binning thae data

Returns

• diff (array_like) – diffusion in time series

• drift (array_like) – drift in time series

• avgdiff (array_like) – avarage diffusion

• avgdrift (array_like) – average drift

• meta private:

_diffusion(X, t_int, dt=1)

Get Diffusion coefficient vector of data

Parameters

• X (array_like) – time series data

• t_int (float) – time step in time series

• dt (int) – diffusion calculation timescale

Returns

diff – Diffusion

Return type

array.

_diffusion_from_residual(X, F, t_int, dt=1)

Get diffusion using residuals about drift function.

Parameters

• (np.array) (X) –

• (float) (t_int) –

• (Callable) (F) –

_diffusion_x_from_residual(x, y, A1, t_int, dt)

_diffusion_xy(x, y, t_int, dt)

Get cross-correlation coefficients between x and y arrays.

Parameters

• x (numpy.array) – x data

• y (numpy.array) – y data

• t_int (float) – time difference betwen consecutive observations

• dt (diffusion calculation timescale) –

Returns

diffusion_xy – cross-correlation coefficients between x and y data

Return type

numpy.array

_diffusion_xy_from_residual(x, y, A1, A2, t_int, dt)

_diffusion_y_from_residual(x, y, A2, t_int, dt)

_diffusion_yx(x, y, t_int, dt)

Get cross-correlation coefficients between x and y arrays.

Parameters

• x (numpy.array) – x data

• y (numpy.array) – y data

• t_int (float) – time difference betwen consecutive observations

• dt (diffusion calculation timescale) –

Returns

diffusion_xy – cross-correlation coefficients between y and x data

Return type

numpy.array

_drift(X, t_int, Dt)

Get Drift coeffecient vector of data.

Parameters

• X (array_like) – Time Series data

• t_int (float) – time difference betwen consecutive observations

• Dt (float) – drift calculation timescale

Returns

diff – Diffusion in time series

Return type

array_like

Notes

Drift is calculated as follows

\[drift = \frac{x(i+Dt)-x(i)}{tint * Dt}\]

_drift_and_diffusion(X, t_int, Dt, dt, inc, drift_threshold, drift_degree, drift_alpha, diff_threshold, diff_degree, diff_alpha, fast_mode)

Get drift and diffusion coefficients for a given timeseries data

Parameters

• X (numpy.array) – time series data

• t_int (float) – time difference betwen consecutive observations

• Dt (int) – timescale to calculate drift

• dt (int) – timescale to claculate diffusion

• inc (float) – step increments in order parameter

• drift_threshold (float or None) – threshold to use for fitting drift function. If None, automatic model selection will be used.

• diff_threshold (float or None) – threshold to use for fitting diffusion function. If None, automatic model selection will be used.

Returns

• —

• diff (array) – diffusion of the data

• drift (array.) – drift, of the data

• avgdiff (array) – average diffusion

• avgdrift (array) – average drift

• op (array) – order parameter

_isValidRange(r)

Checks if the specified range of order parameter is valid range

Parameters

r (tuple, list) – range of order parameter

Returns

True if valid, False if not.

Return type

bool

_km_coefficient(order, X, t_int)

_order_parameter(X, inc, r)

Get order parameter array for a given range and increments

If range is None or not valid, order parameter array will be generated considering maxmium and mimimum limits of the data as the range

Parameters

• X (numpy.array) – data

• inc (float) – step increments in order parameter

• r (tuple, list) – range of the order parameter

Returns

first element will be the order parameter array second element is the rangen used

Return type

tuple

_residual(X, t_int, Dt, dt=1)

Get the residual.

_vector_drift_diff(x, y, inc_x, inc_y, t_int, Dt, dt, drift_threshold, drift_degree, drift_alpha, diff_threshold, diff_degree, diff_alpha, fast_mode)

Get average binned drift and diffusion coefficients for given x and y data

Parameters

• x (array_like) – timeseries x data

• y (array_like) – timesereis y data

• inc_x (float) – step increment of order parameter for x

• inc_y (float) – step increment of order parameter for y

• Dt (int) – timescale to calculate drift

• dt (int) – timescale to calculate diffusion

Returns

[avgdriftX, avgdriftY, avgdiffX, avgdiffY, avgdiffXY, op_x, op_y]

Return type

list