get_dfds_dcds

(function from pyomo.contrib.sensitivity_toolbox.sens)

pyomo.contrib.sensitivity_toolbox.sens.get_dfds_dcds(model, theta_names, tee=False, solver_options=None)[source]

This function calculates gradient vector of the objective function and constraints with respect to the variables and parameters.

For example, given:

\[\begin{split}\min f:\ & p1*x1 + p2*(x2^2) + p1*p2 \\ s.t.\ & c1: x1 + x2 = p1 \\ & c2: x2 + x3 = p2 \\ & 0 <= x1, x2, x3 <= 10 \\ & p1 = 10 \\ & p2 = 5\end{split}\]

  • Variables = (x1, x2, x3, p1, p2)

  • Fix p1 and p2 with estimated values

The following terms are used to define the output dimensions: - Ncon = number of constraints - Nvar = number of variables (Nx + Ntheta) - Nx = number of decision (primal) variables - Ntheta = number of uncertain parameters.

Parameters:

  • model (Pyomo ConcreteModel) – model should include an objective function

  • theta_names (list of strings) – List of Var names

  • tee (bool, optional) – Indicates that ef solver output should be teed

  • solver_options (dict, optional) – Provides options to the solver (also the name of an attribute)

Returns:

  • gradient_f (numpy.ndarray) – Length Nvar array. A gradient vector of the objective function with respect to the (decision variables, parameters) at the optimal solution

  • gradient_c (scipy.sparse.csr.csr_matrix) – Ncon by Nvar size sparse matrix. A Jacobian matrix of the constraints with respect to the (decision variables, parameters) at the optimal solution. Each row contains [row number, column number, and value], column order follows variable order in col and index starts from 0. Note that it follows k_aug. If no constraint exists, return []

  • col (list) – Size Nvar list of variable names

  • row (list) – Size Ncon+1 list of constraints and objective function names. The final element is the objective function name.

  • line_dic (dict) – column numbers of the theta_names in the model. Index starts from 1

Raises: