core module¶
Constraints aggregation core functions.
Functions:

Aggregate IKS Constraints for inequality constraints. 

Jacobian of the IKS Constraints aggregation method for inequality constraints. 

Aggregate inequality constraints. 

Transform a vector of equalities into a Kreisselmeier–Steinhauser function. 

Transform a vector of equalities into a scalar equivalent constraint. 

Aggregate inequality constraints. 

Transform a vector of equalities into a max of all values. 

Transform a vector of equalities into the max of all the values. 

Transform a vector of equalities into a sum of squared constraints. 

Transform a vector of equalities into a sum of squared constraints. 

Transform a vector of equalities into a sum of squared constraints. 
 gemseo.algos.aggregation.core.iks_agg(orig_val, indices=None, rho=100.0, scale=1.0)[source]¶
Aggregate IKS Constraints for inequality constraints.
See [KH15].
 Parameters
orig_val (numpy.ndarray) – The original constraint values.
indices (Optional[Sequence[int]]) –
The indices to generate a subset of the outputs to aggregate. If
None
, aggregate all the outputs.By default it is set to None.
rho (float) –
The multiplicative parameter in the exponential.
By default it is set to 100.0.
scale (Union[float, numpy.ndarray]) –
The scaling factor for multiplying the constraints.
By default it is set to 1.0.
 Returns
The aggregated value.
 Return type
float
 gemseo.algos.aggregation.core.iks_agg_jac(orig_val, indices=None, rho=100.0, scale=1.0)[source]¶
Jacobian of the IKS Constraints aggregation method for inequality constraints.
Kennedy, Graeme J., and Jason E. Hicken. “Improved constraintaggregation methods.” Computer Methods in Applied Mechanics and Engineering 289 (2015): 332354.
 Parameters
orig_val (numpy.ndarray) – The original constraint values.
indices (Optional[Sequence[int]]) –
The indices to generate a subset of the outputs to aggregate. If
None
, aggregate all the outputs.By default it is set to None.
rho (float) –
The multiplicative parameter in the exponential.
By default it is set to 100.0.
scale (Union[float, numpy.ndarray]) –
The scaling factor for multiplying the constraints.
By default it is set to 1.0.
 Returns
The aggregated function Jacobian.
 Return type
numpy.ndarray
 gemseo.algos.aggregation.core.iks_agg_jac_v(orig_val, orig_jac, indices=None, rho=100.0, scale=1.0)[source]¶
Aggregate inequality constraints.
Jacobian vector product of the IKS Constraints aggregation method for inequality constraints.
See [KH15].
 Parameters
orig_val (numpy.ndarray) – The original constraint values.
orig_jac (numpy.ndarray) – The original constraint jacobian.
indices (Optional[Sequence[int]]) –
The indices to generate a subset of the outputs to aggregate. If
None
, aggregate all the outputs.By default it is set to None.
rho (float) –
The multiplicative parameter in the exponential.
By default it is set to 100.0.
scale (Union[float, numpy.ndarray]) –
The scaling factor for multiplying the constraints.
By default it is set to 1.0.
 Returns
The aggregated function Jacobian vector product.
 Return type
numpy.ndarray
 gemseo.algos.aggregation.core.ks_agg(orig_val, indices=None, rho=100.0, scale=1.0)[source]¶
Transform a vector of equalities into a Kreisselmeier–Steinhauser function.
Kreisselmeier G, Steinhauser R (1983) Application of Vector Performance Optimization to a Robust Control Loop Design for a Fighter Aircraft. International Journal of Control 37(2):251–284, doi:10.1080/00207179.1983.9753066
Graeme J. Kennedy, Jason E. Hicken, Improved constraintaggregation methods, Computer Methods in Applied Mechanics and Engineering, Volume 289, 2015, Pages 332354, ISSN 00457825, https://doi.org/10.1016/j.cma.2015.02.017. (http://www.sciencedirect.com/science/article/pii/S0045782515000663)
 Parameters
orig_val (numpy.ndarray) – The original constraint values.
indices (Optional[Sequence[int]]) –
The indices to generate a subset of the outputs to aggregate. If
None
, aggregate all the outputs.By default it is set to None.
rho (float) –
The multiplicative parameter in the exponential.
By default it is set to 100.0.
scale (Union[float, numpy.ndarray]) –
The scaling factor for multiplying the constraints.
By default it is set to 1.0.
 Returns
The aggregated function value.
 Return type
float
 gemseo.algos.aggregation.core.ks_agg_jac(orig_val, indices=None, rho=100.0, scale=1.0)[source]¶
Transform a vector of equalities into a scalar equivalent constraint.
Jacobian of the Constraints aggregation method for inequality constraints.
 Parameters
orig_val (numpy.ndarray) – The original constraint values.
indices (Optional[Sequence[int]]) –
The indices to generate a subset of the outputs to aggregate. If
None
, aggregate all the outputs.By default it is set to None.
rho (float) –
The multiplicative parameter in the exponential.
By default it is set to 100.0.
scale (Union[float, numpy.ndarray]) –
The scaling factor for multiplying the constraints.
By default it is set to 1.0.
 Returns
The aggregated function Jacobian.
 Return type
numpy.ndarray
 gemseo.algos.aggregation.core.ks_agg_jac_v(orig_val, orig_jac, indices=None, rho=100.0, scale=1.0)[source]¶
Aggregate inequality constraints.
Jacobian vector product of the constraints aggregation method for inequality constraints.
 Parameters
orig_val (numpy.ndarray) – The original constraint values.
orig_jac (numpy.ndarray) – The original constraint jacobian.
indices (Optional[Sequence[int]]) –
The indices to generate a subset of the outputs to aggregate. If
None
, aggregate all the outputs.By default it is set to None.
rho (float) –
The multiplicative parameter in the exponential.
By default it is set to 100.0.
scale (Union[float, numpy.ndarray]) –
The scaling factor for multiplying the constraints.
By default it is set to 1.0.
 Returns
The aggregated function Jacobian vector product.
 Return type
numpy.ndarray
 gemseo.algos.aggregation.core.max_agg(orig_val, indices=None, scale=1.0)[source]¶
Transform a vector of equalities into a max of all values.
Constraints aggregation method for inequality constraints.
 Parameters
orig_val (numpy.ndarray) – The original constraint values.
indices (Optional[Sequence[int]]) –
The indices to generate a subset of the outputs to aggregate. If
None
, aggregate all the outputs.By default it is set to None.
scale (Union[float, numpy.ndarray]) –
The scaling factor for multiplying the constraints.
By default it is set to 1.0.
 Returns
The aggregated function.
 Return type
float
 gemseo.algos.aggregation.core.max_agg_jac_v(orig_val, orig_jac, indices=None, scale=1.0)[source]¶
Transform a vector of equalities into the max of all the values.
Jacobian vector product of the max constraints aggregation method for inequality constraints.
 Parameters
orig_val (numpy.ndarray) – The original constraint values.
orig_jac (numpy.ndarray) – The original constraint jacobian.
indices (Optional[Sequence[int]]) –
The indices to generate a subset of the outputs to aggregate. If
None
, aggregate all the outputs.By default it is set to None.
scale (Union[float, numpy.ndarray]) –
The scaling factor for multiplying the constraints.
By default it is set to 1.0.
 Returns
The aggregated function.
 Return type
numpy.ndarray
 gemseo.algos.aggregation.core.sum_square_agg(orig_val, indices=None, scale=1.0)[source]¶
Transform a vector of equalities into a sum of squared constraints.
 Parameters
orig_val (numpy.ndarray) – The original constraint values.
indices (Optional[Sequence[int]]) –
The indices to generate a subset of the outputs to aggregate. If
None
, scale all the constraint values.By default it is set to None.
scale (Union[float, numpy.ndarray]) –
The scaling factor for multiplying the constraints.
By default it is set to 1.0.
 Returns
The aggregated function.
 Return type
numpy.ndarray
 gemseo.algos.aggregation.core.sum_square_agg_jac(orig_val, indices=None, scale=1.0)[source]¶
Transform a vector of equalities into a sum of squared constraints.
Jacobian of the constraints aggregation method for equality constraints.
 Parameters
orig_val (numpy.ndarray) – The original constraint values.
indices (Optional[Sequence[int]]) –
The indices to generate a subset of the outputs to aggregate. If
None
, aggregate all the outputs.By default it is set to None.
scale (Union[float, numpy.ndarray]) –
The scaling factor for multiplying the constraints.
By default it is set to 1.0.
 Returns
The aggregated function Jacobian.
 Return type
numpy.ndarray
 gemseo.algos.aggregation.core.sum_square_agg_jac_v(orig_val, orig_jac, indices=None, scale=1.0)[source]¶
Transform a vector of equalities into a sum of squared constraints.
Jacobian vector product of the constraints aggregation method for equality constraints.
 Parameters
orig_val (numpy.ndarray) – The original constraint values.
orig_jac (numpy.ndarray) – The original constraint jacobian.
indices (Optional[Sequence[int]]) –
The indices to generate a subset of the outputs to aggregate. If
None
, aggregate all the outputs.By default it is set to None.
scale (Union[float, numpy.ndarray]) –
The scaling factor for multiplying the constraints.
By default it is set to 1.0.
 Returns
The aggregated function Jacobian vector product.
 Return type
numpy.ndarray