Misc¶
Miscellaneous utilities.
-
class
active_subspaces.utils.misc.
BoundedNormalizer
(lb, ub)¶ A class for normalizing bounded inputs.
-
lb
¶ ndarray
a matrix of size m-by-1 that contains lower bounds on the simulation inputs
-
ub
¶ ndarray
a matrix of size m-by-1 that contains upper bounds on the simulation inputs
See also
utils.misc.UnboundedNormalizer
-
normalize
(X)¶ Return corresponding points shifted and scaled to [-1,1]^m.
Parameters: X (ndarray) – contains all input points one wishes to normalize. The shape of X is M-by-m. The components of each row of X should be between lb and ub. Returns: X_norm – contains the normalized inputs corresponding to X. The components of each row of X_norm should be between -1 and 1. Return type: ndarray
-
unnormalize
(X)¶ Return corresponding points shifted and scaled to [lb, ub].
Parameters: X (ndarray) – contains all input points one wishes to unnormalize. The shape of X is M-by-m. The components of each row of X should be between -1 and 1. Returns: X_unnorm – contains the unnormalized inputs corresponding to X. The components of each row of X_unnorm should be between lb and ub. Return type: ndarray
-
-
class
active_subspaces.utils.misc.
Normalizer
¶ An abstract class for normalizing inputs.
-
normalize
(X)¶ Return corresponding points in normalized domain.
Parameters: X (ndarray) – contains all input points one wishes to normalize Returns: X_norm – contains the normalized inputs corresponding to X Return type: ndarray Notes
Points in X should be oriented as an m-by-n ndarray, where each row corresponds to an m-dimensional point in the problem domain.
-
unnormalize
(X)¶ Return corresponding points shifted and scaled to [-1,1]^m.
Parameters: X (ndarray) – contains all input points one wishes to unnormalize Returns: X_unnorm – contains the unnormalized inputs corresponding to X Return type: ndarray Notes
Points in X should be oriented as an m-by-n ndarray, where each row corresponds to an m-dimensional point in the normalized domain.
-
-
class
active_subspaces.utils.misc.
UnboundedNormalizer
(mu, C)¶ A class for normalizing unbounded, Gaussian inputs to standard normals.
-
mu
¶ ndarray
a matrix of size m-by-1 that contains the mean of the Gaussian simulation inputs
-
L
¶ ndarray
a matrix size m-by-m that contains the Cholesky factor of the covariance matrix of the Gaussian simulation inputs.
See also
utils.misc.BoundedNormalizer
Notes
A simulation with unbounded inputs is assumed to have a Gaussian weight function associated with the inputs. The covariance of the Gaussian weight function should be full rank.
-
normalize
(X)¶ Return points transformed to a standard normal distribution.
Parameters: X (ndarray) – contains all input points one wishes to normalize. The shape of X is M-by-m. The components of each row of X should be a draw from a Gaussian with mean mu and covariance C. Returns: X_norm – contains the normalized inputs corresponding to X. The components of each row of X_norm should be draws from a standard multivariate normal distribution. Return type: ndarray
-
unnormalize
(X)¶ Transform points to original Gaussian.
Return corresponding points transformed to draws from a Gaussian distribution with mean mu and covariance C.
Parameters: X (ndarray) – contains all input points one wishes to unnormalize. The shape of X is M-by-m. The components of each row of X should be draws from a standard multivariate normal. Returns: X_unnorm – contains the unnormalized inputs corresponding to X. The components of each row of X_unnorm should represent draws from a multivariate normal with mean mu and covariance C. Return type: ndarray
-
-
active_subspaces.utils.misc.
atleast_2d
(A, oned_as='row')¶ Ensures the array A is at least two dimensions.
Parameters: - A (ndarray) – matrix
- oned_as (str, optional) – should be either ‘row’ or ‘col’. It determines whether the array A should be expanded as a 2d row or 2d column (default ‘row’)
-
active_subspaces.utils.misc.
atleast_2d_col
(A)¶ Wrapper for atleast_2d(A, ‘col’)
Notes
Thanks to Trent Lukaczyk for these functions!
-
active_subspaces.utils.misc.
atleast_2d_row
(A)¶ Wrapper for atleast_2d(A, ‘row’)
Notes
Thanks to Trent Lukaczyk for these functions!
-
active_subspaces.utils.misc.
conditional_expectations
(f, ind)¶ Compute conditional expectations and variances for given function values.
Parameters: - f (ndarray) – an ndarry of function evaluations
- ind (ndarray[int]) – index array that tells which values of f correspond to the same value for the active variable.
Returns: - Ef (ndarray) – an ndarray containing the conditional expectations
- Vf (ndarray) – an ndarray containing the conditional variances
Notes
This function computes the mean and variance for all values in the ndarray f that have the same index in ind. The indices in ind correspond to values of the active variables.
-
active_subspaces.utils.misc.
process_inputs
(X)¶ Check a matrix of input values for the right shape.
Parameters: X (ndarray) – contains input points. The shape of X should be M-by-m. Returns: - X (ndarray) – the same as the input
- M (int) – number of rows in X
- m (int) – number of columns in X
-
active_subspaces.utils.misc.
process_inputs_outputs
(X, f)¶ Check matrix of input values and a vector of outputs for correct shapes.
Parameters: - X (ndarray) – contains input points. The shape of X should be M-by-m.
- f (ndarray) – M-by-1 matrix
Returns: - X (ndarray) – the same as the input
- f (ndarray) – the same as the output
- M (int) – number of rows in X
- m (int) – number of columns in X