System data

class deepSI.system_data.System_data(u=None, y=None, x=None, cheat_n=0, normed=False, dt=None)

System Data to be used

u

The u input signal, first dimension is time.

Type:

array

y

The y output signal, first dimension is time. It can be not present.

Type:

array or None

x

The x internal state signal, first dimension is time. (often unused)

Type:

array or None

nu

Number of input dimensions. None -> self.u.shape == (N) Number -> self.u.shape == (N,nu) Tuple -> self.u.shape == (N,…)

Type:

None, Number, Tuple

ny

Number of input dimensions. None -> self.u.shape == (N) Tuple -> self.y.shape == (N,…)

Type:

None, Number, Tuple

cheat_n

Number of samples copied when simulation was applied. This number of samples will not be used to calculate RMS and such.

Type:

int

multi_u

Check for multi dimensional u, used to check SISO.

Type:

bool

multi_y

Check for multi dimensional y, used to check SISO.

Type:

bool

normed

Check if this data set is normed (i.e. was used as norm.transform(sys_data)) mostly used for debugging.

Type:

bool

__init__(u=None, y=None, x=None, cheat_n=0, normed=False, dt=None)

Create System data to be used in fitting, plotted and

Parameters:

• u (array or list or None) – Input signal with an array where the first dimension is time

• y (array or list or None) – output signal with an array where the first dimension is time

• x (array or list or None) – internal state signal with an array where the first dimension is time

• cheat_n (int) – Number of samples copied when simulation was applied. This number of samples will not be used to calculate RMS and such.

• normed (bool) – Check if this data set is normed (i.e. was used as norm.transform(sys_data)) mostly used for debugging.

property N_samples

property ny

Number of output dimensions. None or number or tuple

property nu

Number of input dimensions. None or number or tuple

property nx

Number of internal states. None or number or tuple

flatten()

Flatten both u and y to (N,nu) and (N,ny) returns a new System_data

reshape_as(other)

Inverse of .flatten and will reshape both u and y to (N,) + other.u.shape[1:] and (N,) + other.y.shape[1:]

to_IO_data(na=10, nb=10, stride=1, online_construct=False, feedthrough=False)

Transforms the system data to Input-Output structure (hist,Y) with y length of na, and u length of nb

Parameters:

• na (int) – y history considered

• nb (int) – u history considered

Returns:

• hist (ndarray of (Samples, na*ny + nb*nu)) – array of combination of historical inputs and output as [u[k-nb:k].flat,y[k-na:k].flat] for many k

• Y (ndarray (Samples, features) or (Samples)) – array of single step ahead [y]

to_hist_future_data(na=10, nb=10, nf=5, na_right=0, nb_right=0, stride=1, force_multi_u=False, force_multi_y=False, online_construct=False)

Transforms the system data to encoder structure as structure (uhist,yhist,ufuture,yfuture) of

Made for simulation error and multi step error methods

Parameters:

• na (int) – y history considered

• nb (int) – u history considered

• nf (int) – future inputs considered

Returns:

• uhist (ndarray (samples, nb, nu) or (sample, nb) if nu=None) – array of [u[k-nb],….,u[k - 1 + nb_right]]

• yhist (ndarray (samples, na, ny) or (sample, na) if ny=None) – array of [y[k-na],….,y[k - 1 + na_right]]

• ufuture (ndarray (samples, nf, nu) or (sample, nf) if nu=None) – array of [u[k],….,u[k+nf-1]]

• yfuture (ndarray (samples, nf, ny) or (sample, nf) if ny=None) – array of [y[k],….,y[k+nf-1]]

to_ss_data(nf=20, stride=1, force_multi_u=False, force_multi_y=False, online_construct=False)

to_encoder_data(na=10, nb=10, nf=5, stride=1, force_multi_u=False, force_multi_y=False, online_construct=False)

Transforms the system data to encoder structure as structure (hist,ufuture,yfuture) of

Parameters:

• na (int) – y history considered

• nb (int) – u history considered

• nf (int) – future inputs considered

• stride (int) – skipping data for smaller data set.

• force_multi_u (bool) – converts to ufuture to #(samples, time_seq, nu) always

• force_multi_y (bool) – converts to yfuture to #(samples, time_seq, ny) always

Returns:

• hist (ndarray (samples, ny*na + nu*nb)) – array of concat of u[k-nb-nf:k-nf].flat and y[k-na-nf:k-nf].flat

• ufuture (ndarray (samples, nf, nu) or (sample, nf) if nu=None) – array of [u[k],….,u[k+nf-1]]

• yfuture (ndarray (samples, nf, ny) or (sample, nf) if ny=None) – array of [y[k],….,y[k+nf-1]]

to_video(file_name='video.mp4', scale_factor=10, vmin=0, vmax=1, fps=60)

Used cv2 to create a video from y of shape y.shape = (frames, ny1, ny2)

plot_state_space_3d(nmax=2000, kernal=None, interpol_n=10)

save(file)

Saves data with savez, see also load_system_data

plot(show=False)

Very simple plotting function

BFR(real, multi_average=True)

Best Fit Rate in percent i.e. 100*(1 - np.sum((y-yhat)**2)**0.5/np.std(y)) (100 = best possible fit)

NRMS(real, multi_average=True, per_channel=True)

Normalized root mean square i.e. np.sum((y-yhat)**2)**0.5/np.std(y) (0 = best fit possible)

NRMS_per_channel(real, multi_average=True)

Normalized root mean square i.e. np.sum((y-yhat)**2)**0.5/np.std(y) (0 = best fit possible)

NRMS_mean_channels(real, multi_average=True)

Normalized root mean square i.e. np.sum((y-yhat)**2)**0.5/np.std(y) (0 = best fit possible)

RMS(real, multi_average=True)

Root mean square error

MSE(real, multi_average=True)

mean square error

MAE(real, multi_average=True)

mean absolute error

VAF(real, multi_average=True)

Variance accounted also known as R^2

calculated as 100*(1 - np.mean((y-yhat)**2)/np.std(y)**2) (100 = best possible fit)

__sub__(other)

Calculate the difference between y two System_data a number or array

train_test_split(split_fraction=0.25)

returns 2 data sets of length n*(1-split_fraction) and n*split_fraction respectively (left, right) split

__getitem__(arg)

Slice the System_data in time index

__len__()

Number of samples len(system_data) = self.N_samples

down_sample_by_average(factor)

Down sample method

Parameters:

factor (int) – length will be (original length)/factor

down_sample_by_decimate(factor)

Down sample method :param factor: length will be (original length)/factor :type factor: int

down_sample_by_MIMO(factor)

Down sample method

Parameters:

factor (int) – length will be (original length)/factor

__annotations__ = {}

__module__ = 'deepSI.system_data.system_data'

class deepSI.system_data.System_data_list(sys_data_list=None)

A list of System_data, has most methods of System_data in a list form with only some exceptions listed below

sdl

Type:

list of System_data

y

concatenated y of system_data contained in sdl

Type:

array

u

concatenated u of system_data contained in sdl

Type:

array

append(System_data) adds element to sdl

extend(list) adds elements to sdl

__getitem__(number) get (ith system data, time slice)

__init__(sys_data_list=None)

sanity_check()

property normed

property N_samples

property ny

property nu

property y

property u

property n_cheat

property dt

flatten()

reshape_as(other)

Inverse of .flatten and will reshape both u and y to (N,) + other.u.shape[1:] and (N,) + other.y.shape[1:]

to_IO_data(na=10, nb=10, stride=1, online_construct=False, feedthrough=False)

to_hist_future_data(na=10, nb=10, na_right=0, nb_right=0, nf=5, stride=1, force_multi_u=False, force_multi_y=False, online_construct=False)

to_ss_data(nf=20, stride=1, force_multi_u=False, force_multi_y=False, online_construct=False)

to_encoder_data(na=10, nb=10, nf=5, stride=1, force_multi_u=False, force_multi_y=False, online_construct=False)

save(file)

Saves data

plot(show=False)

Very simple plotting function

weighted_mean(vals)

RMS(real, multi_average=True)

MSE(real, multi_average=True)

MAE(real, multi_average=True)

__sub__(other)

train_test_split(split_fraction=0.25)

return 2 data sets of length n*(1-split_fraction) and n*split_fraction respectively (left, right) split

__getitem__(arg)

get (ith system data, time slice)

__len__()

append(other)

extend(other)

down_sample_by_average(factor)

Down sample method

Parameters:

factor (int) – length will be (original length)/factor

down_sample_by_decimate(factor)

Down sample method

Parameters:

factor (int) – length will be (original length)/factor

down_sample_by_MIMO(factor)

Down sample method

Parameters:

factor (int) – length will be (original length)/factor

__annotations__ = {}

__module__ = 'deepSI.system_data.system_data'

class deepSI.system_data.System_data_norm(u0=0, ustd=1, y0=0, ystd=1)

A utility to normalize system_data before fitting or usage

u0

average u to be subtracted

Type:

float or array

ustd

standard divination of u to be divided by

Type:

float or array

y0

average y to be subtracted

Type:

float or array

ystd

standard divination of y to be divided by

Type:

float or array

__init__(u0=0, ustd=1, y0=0, ystd=1)

property is_id

make_training_data(sys_data)

fit(sys_data)

set the values of u0, ustd, y0 and ystd using sys_data (can be a list) given

transform(sys_data)

Transform the data by

u <- (sys_data.u-self.u0)/self.ustd y <- (sys_data.y-self.y0)/self.ystd

Parameters:

sys_data (System_data) – sys_data to be transformed

Return type:

System_data or System_data_list if a list was given

inverse_transform(sys_data)

Inverse Transform the data by

u <- sys_data.u*self.ustd+self.u0 y <- sys_data.y*self.ystd+self.y0

Parameters:

sys_data (System_data) –

Return type:

System_data or System_data_list if a list was given

__module__ = 'deepSI.system_data.system_data'

deepSI.system_data.load_system_data(file)

Load System_data from .npz file