Utilities Functions

pysimrel.utilities.get_cov(rel_pos, rsq, kappa, lmd, random_seed=None)

Compute Covariances

Compute covariances at the position specified in rel_pos recursively using the function sample_cov satisfying the rsq and the eigen values in kappa and lmd.

Parameters:

• rel_pos (list) – position of relevant components
• rsq (list) – A list of coefficient of determination
• kappa (list) – A list of eigenvalues related to response variables
• lmd (list) – A list of eigenvalues related to predictor variables
• random_seed (int) – An integer for random state

Returns:

A matrix of dimension equals to the length of kappa by length of lmd with computed covariances at the position specified in rel_pos.

Return type:

np.array

pysimrel.utilities.get_eigen(rate, nvar, min_value=0.0001)

Compute eigen values using exponential decay function.

\[\lambda_i = \text{exp}^{-\gamma(i-1)}\]

Parameters:

• rate – rate of exponential decay factor
• nvar – Number of variables (number of eigenvalues to compute)
• min_value – Lower limit for smallest eigenvalue

Returns:

A list of eigenvalues

pysimrel.utilities.get_relpred(n_pred, n_relpred, pos_relcomp, random_state=None)

Identify relevant predictors through sampling

Get relevant and irrelevant position of predictor variables. The irrelevant components index are the one which are not in pos_relcomp. The number of extra components are defined in n_relpred.

Parameters:

• n_pred (int) – Number of predictor variables
• n_relpred (list) – List of number of predictors relevant for each response
• pos_relcomp (list) – List of List containing the position index of relevant components
• random_state (int) – An integer for random state

Returns:

A dictionary with relevant and irrelevant position index of predictors

Return type:

dict

pysimrel.utilities.get_rotate(mat, pred_pos, random_state=None)

Fill up a block of matrix mat based on position index in pred_pos. The block will be an orthogonal rotation matrix.

Parameters:

• mat (np.array) – A matrix possibly a square matrix as covariance
• pred_pos (list) – A list of position index for the block rotation
• random_state (int) – An integer for random state to control randomness

Returns:

A matrix of same size as mat but filled with an orthogonal block

Return type:

np.array

pysimrel.utilities.get_rotation(rel_irrel_pred)

Create orthogonal rotation matrix

Creates an orthogonal rotation matrix from dictionary of relevant and irrelevant positions using get_rotate function.

Parameters:rel_irrel_pred (dict) – A dictionary of relevant and irrelevant position (possibly obtained from the function get_relpred. Returns:An orthogonal rotation matrix Return type:np.array

pysimrel.utilities.parse_param(parm: Union[str, int, None])

Parse the parameters from string to a nested list

Parameters:parm (str, int) – Either integer, float (in some cases) or mostly string Returns:A nested list of parsed parameters Return type:list

pysimrel.utilities.sample_cov(lmd, rsq, pos, kappa, alpha_)

Compute covariance satisfying given parameters

Compute covariance from a sample of uniform distribution satisfying rsq, a set of lmd and kappa

Parameters:

• lmd (set or list) – A set of eigenvalue of predictors at position specified by pos.
• rsq (float) – Coefficient of determination
• pos (list) – Position index of in which covariance need to be non-zero
• kappa (list) – Eigenvalue corresponding to response (univariate) or response component (multivariate)
• alpha – A sample from univariate distribution between -1 and 1

Returns:

An array of computed covariances of length equals to lmd.

Return type:

np.array

pysimrel.utilities.sample_extra_pos(rs, n_extra_pos, extra_pos, irrel_pos)

Sample Extra Position Required

Sample position index of extra relevant predictors from irrelevant predictors in irrel_pos.

Parameters:

• rs (int) – A numpy RandomSeed object
• n_extra_pos (int) – An integer for number of extra position index to sample
• extra_pos (list) – A list container for collecting extra relevant components
• irrel_pos (list) – A list or set of irrelevant position indices

Returns:

a list of relevant and irrelevant position indices

Return type:

list