Solving

calculate_fisher_criterion(fsmp: ~eDPM.model.fisher_model.FisherModelParametrized, criterion=<function fisher_determinant>, relative_sensitivities=False, verbose=False)

Calculate the Fisher information optimality criterion for a chosen Fisher model.

Parameters:

• fsmp (FisherModelParametrized) – The parametrized FisherModel with a chosen values for the sampled variables.

• criterion (callable) –

  Choose the optimality criterion to determine the objective function and quantify the Experimental Design. The default is “fisher_determinant”.

  • fisher_determinant

    Use the D-optimality criterion that maximizes the determinant of the Fisher Information matrix.

  • fisher_mineigenval

    Use the E-optimality criterion that maximizes the minimal eigenvalue of the Fisher Information matrix.

  • fisher_sumeigenval

    Use the A-optimality criterion that maximizes the sum of all eigenvalues of the Fisher Information matrix.

  • fisher_ratioeigenval

    Use the modified E-optimality criterion that maximizes the ratio of the minimal and maximal eigenvalues of the Fisher Information matrix.

• relative_sensitivities (bool, optional) – Use relative local sensitivities \(s_{ij} = \dfrac{\partial y_i}{\partial p_j} \dfrac{p_j}{y_i}\) instead of absolute. Defaults to False.

Returns:

The result of the Fisher information optimality criterion represented as a FisherResults object.

Return type:

FisherResults

get_S_matrix(fsmp: FisherModelParametrized, relative_sensitivities=False, **kwargs)

Calculate the sensitivity matrix for a Fisher Model.

Parameters:

• fsmp (FisherModelParametrized) – The parametrized FisherModel with a chosen values for the sampled variables.

• relative_sensitivities (bool, optional) – Use relative local sensitivities \(s_{ij} = \frac{\partial y_i}{\partial p_j} \frac{p_j}{y_i}\) instead of absolute. Defaults to False.

Returns:

The sensitivity matrix S, the cobvariance matrix C, the object of type FisherResultSingle with ODEs solutions.

Return type:

np.ndarray, np.ndarray, FisherResultSingle

ode_rhs(t, x, ode_fun, ode_dfdx, ode_dfdp, ode_dfdx0, inputs, parameters, ode_args, n_x, n_p)

Calculate the right-hand side of the ODEs system, containing the model definition with state variables \(\dot x = f(x, t, u, u, c)\) and the equations for the local sensitivities \(\dot s = \frac{\partial f}{\partial x} s + \frac{\partial f}{\partial p}\).

Parameters:

• t (np.ndarray) – The measurement times \(t\).

• x (np.ndarray) – The array containing the state variables \(x\) and sensitivities \(s\).

• ode_fun (callable) – The ODEs right-hand side function \(f\) for the state variables \(x\).

• ode_dfdx (callable) – The derivative of the ODEs function with respect to state variables \(x\).

• ode_dfdp (callable) – The derivative of the ODEs function with respect to parameters \(p\).

• inputs (list) – The inputs of the system.

• parameters – The estimated parameters of the system \(p\).

• ode_args (tuple) – The ode_args of the system \(c\).

• n_x (int) – The number of the state variables of the system.

• n_p (int) – The number of the estimated parameters of the system.

Returns:

The right-hand side of the ODEs system for sensitivities calculation.

Return type:

np.ndarray

fisher_determinant(fsmp: FisherModelParametrized, S, C)

Calculate the determinant of the Fisher information matrix (the D-optimality criterion) using the sensitivity matrix.

Parameters:

• fsmp (FisherModelParametrized) – The parametrized FisherModel with a chosen values for the sampled variables.

• S (np.ndarray) – The sensitivity matrix.

• C (np.ndarray) – The covariance matrix of the measurement errors.

Returns:

The determinant of the Fisher information matrix.

Return type:

float

fisher_mineigenval(fsmp: FisherModelParametrized, S, C)

Calculate the minimal eigenvalue of the Fisher information matrix (the E-optimality criterion) using the sensitivity matrix.

Parameters:

• fsmp (FisherModelParametrized) – The parametrized FisherModel with a chosen values for the sampled variables.

• S (np.ndarray) – The sensitivity matrix.

• C (np.ndarray) – The covariance matrix of the measurement errors.

Returns:

The minimal eigenvalue of the Fisher information matrix.

Return type:

float

fisher_ratioeigenval(fsmp: FisherModelParametrized, S, C)

Calculate the ratio of the minimal and maximal eigenvalues of the Fisher information matrix (the modified E-optimality criterion) using the sensitivity matrix.

Parameters:

• fsmp (FisherModelParametrized) – The parametrized FisherModel with a chosen values for the sampled variables.

• S (np.ndarray) – The sensitivity matrix.

• C (np.ndarray) – The covariance matrix of the measurement errors.

Returns:

The ratio of the minimal and maximal eigenvalues of the Fisher information matrix.

Return type:

float

fisher_sumeigenval(fsmp: FisherModelParametrized, S, C)

Calculate the sum of the all eigenvalues of the Fisher information matrix (the A-optimality criterion) using the sensitivity matrix.

Parameters:

• fsmp (FisherModelParametrized) – The parametrized FisherModel with a chosen values for the sampled variables.

• S (np.ndarray) – The sensitivity matrix.

• C (np.ndarray) – The covariance matrix of the measurement errors.

Returns:

The sum of the eigenvalues of the Fisher information matrix.

Return type:

float

display_entries(table, terminal_size, caption=None)

display_fsmp_details(fsmp: ~eDPM.model.fisher_model.FisherModelParametrized, pp=<pprint.PrettyPrinter object>, terminal_size=(80, 20))

display_fsr_details(fsr: ~eDPM.model.fisher_model.FisherResults, pp=<pprint.PrettyPrinter object>, terminal_size=(80, 20))

display_heading(string, terminal_size=(80, 20))

generate_matrix_cols(M, name, terminal_size=(80, 20))