optim_tools

Collection of tools that can be used in optimization schemes. Only put tools here that are so general that they can be used by several optimization schemes. If some method is only applicable to the update scheme you are implementing, leave it in that class.

aug_optim_state(state, list_state)

Augment the state variables to get one augmented array.

Parameters:

Name	Type	Description	Default
state	dict	Dictionary of state variables for optimization. OBS: 1D arrays!	required
list_state	list	Fixed list of keys in the state dictionary.	required

Returns:

Name	Type	Description
aug_state	ndarray	Augmented 1D array of state variables.

clip_state(x, bounds)

Clip a state vector according to the bounds

Parameters:

Name	Type	Description	Default
x	array_like	The input state	required
bounds	array_like	(min, max) pairs for each element in x. None is used to specify no bound.	required

Returns:

Name	Type	Description
x	ndarray	The state after truncation

corr2BlockDiagonal(state, corr)

Makes the correlation matrix block diagonal. The blocks are the state varible types.

Parameters:

Name	Type	Description	Default
state		Current control state, including state names	required
corr	array_like	Correlation matrix, of shape (d, d)	required

Returns:

Name	Type	Description
corr_blocks	list	block matrices, one for each variable type

corr2cov(corr, std)

Transfroms a correlation matrix to a covaraince matrix

Parameters:

Name	Type	Description	Default
corr	array_like	The correlation matrix, of shape (d,d).	required
std	array_like	Array of the standard deviations, of shape (d, ).	required

Returns:

Name	Type	Description
out	ndarray	The covaraince matrix, of shape (d,d)

cov2corr(cov)

Transfroms a covaraince matrix to a correlation matrix

Parameters:

Name	Type	Description	Default
cov	array_like	The covaraince matrix, of shape (d,d).	required

Returns:

Name	Type	Description
out	ndarray	The correlation matrix, of shape (d,d)

get_optimize_result(obj)

Collect optimize results based on requested

Parameters:

Name	Type	Description	Default
obj	Optimize	An instance of an optimization class	required

Returns:

Name	Type	Description
save_dict	OptimizeResult	The requested optimization results

get_sym_pos_semidef(a)

Force matrix to positive semidefinite

Parameters:

Name	Type	Description	Default
a	array_like	The input matrix, of shape (d,d)	required

Returns:

Name	Type	Description
a	ndarray	The positive semidefinite matrix, of shape (d,d)

save_optimize_results(intermediate_result)

Save optimize results

Parameters:

Name	Type	Description	Default
intermediate_result	OptimizeResult	An instance of an OptimizeResult class	required

time_correlation(a, state, n_timesteps, dt=1.0)

Constructs correlation matrix with time correlation using an autoregressive model.

\[ Corr(t_1, t_2) = a^{|t_1 - t_2|} \]

Assumes that each varaible in state is time-order such that x = [x1, x2,..., xi,..., xn], where i is the time index, and xi is d-dimensional.

Parameters:

Name	Type	Description	Default
a	float	Correlation coef, in range (0, 1).	required
state	dict	Control state (represented in a dict).	required
n_timesteps	int	Number of time-steps to correlate for each component.	required
dt	float or int	Duration between each time-step. Default is 1.	1.0

Returns:

Name	Type	Description
out	ndarray	Correlation matrix with time correlation

update_optim_state(aug_state, state, list_state)

Extract the separate state variables from an augmented state array.

It is assumed that the augmented state array is made in the aug_optim_state method, hence this is the reverse method.

Parameters:

Name	Type	Description	Default
aug_state	ndarray	Augmented state array. OBS: 1D array.	required
state	dict	Dictionary of state variables for optimization.	required
list_state	list	Fixed list of keys in the state dictionary.	required

Returns:

Name	Type	Description
state	dict	State dictionary updated with aug_state.