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Ipopt Documentation
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Ipopt Documentation
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Base class for all NLP's that use standard triplet matrix form and dense vectors. More...
#include <IpTNLP.hpp>
Inheritance diagram for Ipopt::TNLP:Public Types | |
| enum | LinearityType { LINEAR , NON_LINEAR } |
| Linearity-types of variables and constraints. More... | |
| enum | IndexStyleEnum { C_STYLE = 0 , FORTRAN_STYLE = 1 } |
| typedef std::map< std::string, std::vector< std::string > > | StringMetaDataMapType |
| typedef std::map< std::string, std::vector< Index > > | IntegerMetaDataMapType |
| typedef std::map< std::string, std::vector< Number > > | NumericMetaDataMapType |
Private Member Functions | |
Default Compiler Generated Methods | |
(Hidden to avoid implicit creation/calling). These methods are not implemented and we do not want the compiler to implement them for us, so we declare them private and do not define them. This ensures that they will not be implicitly created/called. | |
| TNLP (const TNLP &) | |
| Copy Constructor. | |
| void | operator= (const TNLP &) |
| Default Assignment Operator. | |
Base class for all NLP's that use standard triplet matrix form and dense vectors.
This is the standard base class for all NLP's that use the standard triplet matrix form and dense vectors. The class TNLPAdapter then converts this interface to an interface that can be used directly by Ipopt.
This interface presents the problem form:
\begin{eqnarray*} \mathrm{min} && f(x) \\ \mathrm{s.t.} && g_L \leq g(x) \leq g_U \\ && x_L \leq x \leq x_U \end{eqnarray*}
In order to specify an equality constraint, set \(g_{L,i} = g_{U,i}\). The value that indicates "infinity" for the bounds (i.e. the variable or constraint has no lower bound (-infinity) or upper bound (+infinity)) is set through the option nlp_lower_bound_inf and nlp_upper_bound_inf, respectively. To indicate that a variable has no upper or lower bound, set the bound to -ipopt_inf or +ipopt_inf, respectively.
Definition at line 47 of file IpTNLP.hpp.
| typedef std::map<std::string, std::vector<std::string> > Ipopt::TNLP::StringMetaDataMapType |
Definition at line 70 of file IpTNLP.hpp.
| typedef std::map<std::string, std::vector<Index> > Ipopt::TNLP::IntegerMetaDataMapType |
Definition at line 71 of file IpTNLP.hpp.
| typedef std::map<std::string, std::vector<Number> > Ipopt::TNLP::NumericMetaDataMapType |
Definition at line 72 of file IpTNLP.hpp.
Linearity-types of variables and constraints.
| Enumerator | |
|---|---|
| LINEAR | Constraint/Variable is linear. |
| NON_LINEAR | Constraint/Variable is non-linear. |
Definition at line 52 of file IpTNLP.hpp.
| Enumerator | |
|---|---|
| C_STYLE | |
| FORTRAN_STYLE | |
Definition at line 74 of file IpTNLP.hpp.
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inline |
Definition at line 60 of file IpTNLP.hpp.
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inlinevirtual |
Default destructor.
Definition at line 64 of file IpTNLP.hpp.
| Ipopt::TNLP::DECLARE_STD_EXCEPTION | ( | INVALID_TNLP | ) |
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pure virtual |
Method to request the initial information about the problem.
Ipopt uses this information when allocating the arrays that it will later ask you to fill with values. Be careful in this method since incorrect values will cause memory bugs which may be very difficult to find.
| n | (out) Storage for the number of variables \(x\) |
| m | (out) Storage for the number of constraints \(g(x)\) |
| nnz_jac_g | (out) Storage for the number of nonzero entries in the Jacobian |
| nnz_h_lag | (out) Storage for the number of nonzero entries in the Hessian |
| index_style | (out) Storage for the index style, the numbering style used for row/col entries in the sparse matrix format (TNLP::C_STYLE: 0-based, TNLP::FORTRAN_STYLE: 1-based; see also Triplet Format for Sparse Matrices) |
Implemented in Ipopt::AmplTNLP, Ipopt::StdInterfaceTNLP, and Ipopt::TNLPReducer.
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inlinevirtual |
Method to request meta data for the variables and the constraints.
This method is used to pass meta data about variables or constraints to Ipopt. The data can be either of integer, numeric, or string type. Ipopt passes this data on to its internal problem representation. The meta data type is a std::map with std::string as key type and a std::vector as value type. So far, Ipopt itself makes only use of string meta data under the key idx_names. With this key, variable and constraint names can be passed to Ipopt, which are shown when printing internal vector or matrix data structures if Ipopt is run with a high value for the option. This allows a user to identify the original variables and constraints corresponding to Ipopt's internal problem representation.
If this method is not overloaded, the default implementation does not set any meta data and returns false.
Reimplemented in Ipopt::SensAmplTNLP, and Ipopt::AmplTNLP.
Definition at line 126 of file IpTNLP.hpp.
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pure virtual |
Method to request bounds on the variables and constraints.
| n | (in) the number of variables \(x\) in the problem |
| x_l | (out) the lower bounds \(x^L\) for the variables \(x\) |
| x_u | (out) the upper bounds \(x^U\) for the variables \(x\) |
| m | (in) the number of constraints \(g(x)\) in the problem |
| g_l | (out) the lower bounds \(g^L\) for the constraints \(g(x)\) |
| g_u | (out) the upper bounds \(g^U\) for the constraints \(g(x)\) |
The values of n and m that were specified in TNLP::get_nlp_info are passed here for debug checking. Setting a lower bound to a value less than or equal to the value of the option nlp_lower_bound_inf will cause Ipopt to assume no lower bound. Likewise, specifying the upper bound above or equal to the value of the option nlp_upper_bound_inf will cause Ipopt to assume no upper bound. These options are set to -1019 and 1019, respectively, by default, but may be modified by changing these options.
Implemented in Ipopt::SensAmplTNLP, Ipopt::AmplTNLP, Ipopt::StdInterfaceTNLP, and Ipopt::TNLPReducer.
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inlinevirtual |
Method to request scaling parameters.
This is only called if the options are set to retrieve user scaling, that is, if nlp_scaling_method is chosen as "user-scaling". The method should provide scaling factors for the objective function as well as for the optimization variables and/or constraints. The return value should be true, unless an error occurred, and the program is to be aborted.
The value returned in obj_scaling determines, how Ipopt should internally scale the objective function. For example, if this number is chosen to be 10, then Ipopt solves internally an optimization problem that has 10 times the value of the original objective function provided by the TNLP. In particular, if this value is negative, then Ipopt will maximize the objective function instead of minimizing it.
The scaling factors for the variables can be returned in x_scaling, which has the same length as x in the other TNLP methods, and the factors are ordered like x. use_x_scaling needs to be set to true, if Ipopt should scale the variables. If it is false, no internal scaling of the variables is done. Similarly, the scaling factors for the constraints can be returned in g_scaling, and this scaling is activated by setting use_g_scaling to true.
As a guideline, we suggest to scale the optimization problem (either directly in the original formulation, or after using scaling factors) so that all sensitivities, i.e., all non-zero first partial derivatives, are typically of the order 0.1-10.
Reimplemented in Ipopt::AmplTNLP, Ipopt::StdInterfaceTNLP, and Ipopt::TNLPReducer.
Definition at line 211 of file IpTNLP.hpp.
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inlinevirtual |
Method to request the variables linearity.
This method is never called by Ipopt, but is used by Bonmin to get information about which variables occur only in linear terms. Ipopt passes the array var_types of length at least n, which should be filled with the appropriate linearity type of the variables (TNLP::LINEAR or TNLP::NON_LINEAR).
The default implementation just returns false and does not fill the array.
Reimplemented in Ipopt::TNLPReducer.
Definition at line 243 of file IpTNLP.hpp.
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inlinevirtual |
Method to request the constraints linearity.
This method is never called by Ipopt, but is used by Bonmin to get information about which constraints are linear. Ipopt passes the array const_types of size m, which should be filled with the appropriate linearity type of the constraints (TNLP::LINEAR or TNLP::NON_LINEAR).
The default implementation just returns false and does not fill the array.
Reimplemented in Ipopt::AmplTNLP, and Ipopt::TNLPReducer.
Definition at line 265 of file IpTNLP.hpp.
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pure virtual |
Method to request the starting point before iterating.
| n | (in) the number of variables \(x\) in the problem; it will have the same value that was specified in TNLP::get_nlp_info |
| init_x | (in) if true, this method must provide an initial value for \(x\) |
| x | (out) the initial values for the primal variables \(x\) |
| init_z | (in) if true, this method must provide an initial value for the bound multipliers \(z^L\) and \(z^U\) |
| z_L | (out) the initial values for the bound multipliers \(z^L\) |
| z_U | (out) the initial values for the bound multipliers \(z^U\) |
| m | (in) the number of constraints \(g(x)\) in the problem; it will have the same value that was specified in TNLP::get_nlp_info |
| init_lambda | (in) if true, this method must provide an initial value for the constraint multipliers \(\lambda\) |
| lambda | (out) the initial values for the constraint multipliers, \(\lambda\) |
The boolean variables indicate whether the algorithm requires to have x, z_L/z_u, and lambda initialized, respectively. If, for some reason, the algorithm requires initializations that cannot be provided, false should be returned and Ipopt will stop. The default options only require initial values for the primal variables \(x\).
Note, that the initial values for bound multiplier components for absent bounds ( \(x^L_i=-\infty\) or \(x^U_i=\infty\)) are ignored.
Implemented in Ipopt::AmplTNLP, Ipopt::StdInterfaceTNLP, and Ipopt::TNLPReducer.
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inlinevirtual |
Method to provide an Ipopt warm start iterate which is already in the form Ipopt requires it internally for warm starts.
This method is only for expert users. The default implementation does not provide a warm start iterate and returns false.
| warm_start_iterate | storage for warm start iterate in the form Ipopt requires it internally |
Reimplemented in Ipopt::TNLPReducer.
Definition at line 322 of file IpTNLP.hpp.
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pure virtual |
Method to request the value of the objective function.
| n | (in) the number of variables \(x\) in the problem; it will have the same value that was specified in TNLP::get_nlp_info |
| x | (in) the values for the primal variables \(x\) at which the objective function \(f(x)\) is to be evaluated |
| new_x | (in) false if any evaluation method (eval_*) was previously called with the same values in x, true otherwise. This can be helpful when users have efficient implementations that calculate multiple outputs at once. Ipopt internally caches results from the TNLP and generally, this flag can be ignored. |
| obj_value | (out) storage for the value of the objective function \(f(x)\) |
Implemented in Ipopt::AmplTNLP, Ipopt::StdInterfaceTNLP, and Ipopt::TNLPReducer.
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pure virtual |
Method to request the gradient of the objective function.
| n | (in) the number of variables \(x\) in the problem; it will have the same value that was specified in TNLP::get_nlp_info |
| x | (in) the values for the primal variables \(x\) at which the gradient \(\nabla f(x)\) is to be evaluated |
| new_x | (in) false if any evaluation method (eval_*) was previously called with the same values in x, true otherwise; see also TNLP::eval_f |
| grad_f | (out) array to store values of the gradient of the objective function \(\nabla f(x)\). The gradient array is in the same order as the \(x\) variables (i.e., the gradient of the objective with respect to x[2] should be put in grad_f[2]). |
Implemented in Ipopt::AmplTNLP, Ipopt::StdInterfaceTNLP, and Ipopt::TNLPReducer.
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pure virtual |
Method to request the constraint values.
| n | (in) the number of variables \(x\) in the problem; it will have the same value that was specified in TNLP::get_nlp_info |
| x | (in) the values for the primal variables \(x\) at which the constraint functions \(g(x)\) are to be evaluated |
| new_x | (in) false if any evaluation method (eval_*) was previously called with the same values in x, true otherwise; see also TNLP::eval_f |
| m | (in) the number of constraints \(g(x)\) in the problem; it will have the same value that was specified in TNLP::get_nlp_info |
| g | (out) array to store constraint function values \(g(x)\), do not add or subtract the bound values \(g^L\) or \(g^U\). |
Implemented in Ipopt::AmplTNLP, Ipopt::StdInterfaceTNLP, and Ipopt::TNLPReducer.
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pure virtual |
Method to request either the sparsity structure or the values of the Jacobian of the constraints.
The Jacobian is the matrix of derivatives where the derivative of constraint function \(g_i\) with respect to variable \(x_j\) is placed in row \(i\) and column \(j\). See Triplet Format for Sparse Matrices for a discussion of the sparse matrix format used in this method.
| n | (in) the number of variables \(x\) in the problem; it will have the same value that was specified in TNLP::get_nlp_info |
| x | (in) first call: NULL; later calls: the values for the primal variables \(x\) at which the constraint Jacobian \(\nabla g(x)^T\) is to be evaluated |
| new_x | (in) false if any evaluation method (eval_*) was previously called with the same values in x, true otherwise; see also TNLP::eval_f |
| m | (in) the number of constraints \(g(x)\) in the problem; it will have the same value that was specified in TNLP::get_nlp_info |
| nele_jac | (in) the number of nonzero elements in the Jacobian; it will have the same value that was specified in TNLP::get_nlp_info |
| iRow | (out) first call: array of length nele_jac to store the row indices of entries in the Jacobian of the constraints; later calls: NULL |
| jCol | (out) first call: array of length nele_jac to store the column indices of entries in the Jacobian of the constraints; later calls: NULL |
| values | (out) first call: NULL; later calls: array of length nele_jac to store the values of the entries in the Jacobian of the constraints |
x and values will be NULL. If the arguments x and values are not NULL, then Ipopt expects that the value of the Jacobian as calculated from array x is stored in array values (using the same order as used when specifying the sparsity structure). At this call, the arguments iRow and jCol will be NULL. Implemented in Ipopt::AmplTNLP, Ipopt::StdInterfaceTNLP, and Ipopt::TNLPReducer.
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inlinevirtual |
Method to request either the sparsity structure or the values of the Hessian of the Lagrangian.
The Hessian matrix that Ipopt uses is
\[ \sigma_f \nabla^2 f(x_k) + \sum_{i=1}^m\lambda_i\nabla^2 g_i(x_k) \]
for the given values for \(x\), \(\sigma_f\), and \(\lambda\). See Triplet Format for Sparse Matrices for a discussion of the sparse matrix format used in this method.
| n | (in) the number of variables \(x\) in the problem; it will have the same value that was specified in TNLP::get_nlp_info |
| x | (in) first call: NULL; later calls: the values for the primal variables \(x\) at which the Hessian is to be evaluated |
| new_x | (in) false if any evaluation method (eval_*) was previously called with the same values in x, true otherwise; see also TNLP::eval_f |
| obj_factor | (in) factor \(\sigma_f\) in front of the objective term in the Hessian |
| m | (in) the number of constraints \(g(x)\) in the problem; it will have the same value that was specified in TNLP::get_nlp_info |
| lambda | (in) the values for the constraint multipliers \(\lambda\) at which the Hessian is to be evaluated |
| new_lambda | (in) false if any evaluation method was previously called with the same values in lambda, true otherwise |
| nele_hess | (in) the number of nonzero elements in the Hessian; it will have the same value that was specified in TNLP::get_nlp_info |
| iRow | (out) first call: array of length nele_hess to store the row indices of entries in the Hessian; later calls: NULL |
| jCol | (out) first call: array of length nele_hess to store the column indices of entries in the Hessian; later calls: NULL |
| values | (out) first call: NULL; later calls: array of length nele_hess to store the values of the entries in the Hessian |
x, lambda, and values will be NULL. If the arguments x, lambda, and values are not NULL, then Ipopt expects that the value of the Hessian as calculated from arrays x and lambda are stored in array values (using the same order as used when specifying the sparsity structure). At this call, the arguments iRow and jCol will be NULL.A default implementation is provided, in case the user wants to set quasi-Newton approximations to estimate the second derivatives and doesn't not need to implement this method.
Reimplemented in Ipopt::AmplTNLP, Ipopt::StdInterfaceTNLP, and Ipopt::TNLPReducer.
Definition at line 472 of file IpTNLP.hpp.
Return the number of variables that appear nonlinearly in the objective function or in at least one constraint function.
If -1 is returned as number of nonlinear variables, Ipopt assumes that all variables are nonlinear. Otherwise, it calls get_list_of_nonlinear_variables with an array into which the indices of the nonlinear variables should be written - the array has the length num_nonlin_vars, which is identical with the return value of get_number_of_nonlinear_variables(). It is assumed that the indices are counted starting with 1 in the FORTRAN_STYLE, and 0 for the C_STYLE.
The default implementation returns -1, i.e., all variables are assumed to be nonlinear.
Reimplemented in Ipopt::AmplTNLP, and Ipopt::TNLPReducer.
Definition at line 526 of file IpTNLP.hpp.
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inlinevirtual |
Return the indices of all nonlinear variables.
This method is called only if limited-memory quasi-Newton option is used and get_number_of_nonlinear_variables() returned a positive number. This number is provided in parameter num_nonlin_var.
The method must store the indices of all nonlinear variables in pos_nonlin_vars, where the numbering starts with 0 order 1, depending on the numbering style determined in get_nlp_info.
Reimplemented in Ipopt::AmplTNLP, and Ipopt::TNLPReducer.
Definition at line 543 of file IpTNLP.hpp.
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pure virtual |
This method is called when the algorithm has finished (successfully or not) so the TNLP can digest the outcome, e.g., store/write the solution, if any.
| status | (in) gives the status of the algorithm
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| n | (in) the number of variables \(x\) in the problem; it will have the same value that was specified in TNLP::get_nlp_info |
| x | (in) the final values for the primal variables |
| z_L | (in) the final values for the lower bound multipliers |
| z_U | (in) the final values for the upper bound multipliers |
| m | (in) the number of constraints \(g(x)\) in the problem; it will have the same value that was specified in TNLP::get_nlp_info |
| g | (in) the final values of the constraint functions |
| lambda | (in) the final values of the constraint multipliers |
| obj_value | (in) the final value of the objective function |
| ip_data | (in) provided for expert users |
| ip_cq | (in) provided for expert users |
Implemented in Ipopt::SensAmplTNLP, Ipopt::AmplTNLP, Ipopt::StdInterfaceTNLP, and Ipopt::TNLPReducer.
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inlinevirtual |
This method returns any metadata collected during the run of the algorithm.
This method is called just before finalize_solution is called. The returned data includes the metadata provided by TNLP::get_var_con_metadata. Each metadata can be of type string, integer, or numeric. It can be associated to either the variables or the constraints. The metadata that was associated with the primal variable vector is stored in var_..._md. The metadata associated with the constraint multipliers is stored in con_..._md. The metadata associated with the bound multipliers is stored in var_..._md, with the suffixes "_z_L", and "_z_U", denoting lower and upper bounds.
If the user doesn't overload this method in her implementation of the class derived from TNLP, the default implementation does nothing.
Reimplemented in Ipopt::SensAmplTNLP.
Definition at line 619 of file IpTNLP.hpp.
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inlinevirtual |
Intermediate Callback method for the user.
This method is called once per iteration (during the convergence check), and can be used to obtain information about the optimization status while Ipopt solves the problem, and also to request a premature termination.
The information provided by the entities in the argument list correspond to what Ipopt prints in the iteration summary (see also Ipopt Output), except for inf_pr, which by default corresponds to the original problem in the log but to the scaled internal problem in this callback. Further information can be obtained from the ip_data and ip_cq objects. The current iterate and violations of feasibility and optimality can be accessed via the methods Ipopt::TNLP::get_curr_iterate() and Ipopt::TNLP::get_curr_violations(). These methods translate values for the internal representation of the problem from ip_data and ip_cq objects into the TNLP representation.
It is not required to implement (overload) this method. The default implementation always returns true.
Reimplemented in Ipopt::StdInterfaceTNLP, and Ipopt::TNLPReducer.
Definition at line 665 of file IpTNLP.hpp.
| bool Ipopt::TNLP::get_curr_iterate | ( | const IpoptData * | ip_data, |
| IpoptCalculatedQuantities * | ip_cq, | ||
| bool | scaled, | ||
| Index | n, | ||
| Number * | x, | ||
| Number * | z_L, | ||
| Number * | z_U, | ||
| Index | m, | ||
| Number * | g, | ||
| Number * | lambda | ||
| ) | const |
Get primal and dual variable values of the current iterate.
This method can be used to get the values of the current iterate, e.g., during intermediate_callback(). The method expects the number of variables (dimension of x), number of constraints (dimension of g(x)), and allocated arrays of appropriate lengths as input.
The method translates the x(), c(), d(), y_c(), y_d(), z_L(), and z_U() vectors from IpoptData::curr() of the internal NLP representation into the form used by the TNLP. For the correspondence between scaled and unscaled solutions, see the detailed description of OrigIpoptNLP. If Ipopt is in restoration mode, it maps the current iterate of restoration NLP (see RestoIpoptNLP) back to the original TNLP.
If there are fixed variables and fixed_variable_treatment=make_parameter, then requesting z_L and z_U can trigger a reevaluation of the Gradient of the objective function and the Jacobian of the constraint functions.
| ip_data | (in) Ipopt Data |
| ip_cq | (in) Ipopt Calculated Quantities |
| scaled | (in) whether to retrieve scaled or unscaled iterate |
| n | (in) the number of variables \(x\) in the problem; can be arbitrary if skipping x, z_L, and z_U |
| x | (out) buffer to store value of primal variables \(x\), must have length at least n; pass NULL to skip retrieving x |
| z_L | (out) buffer to store the lower bound multipliers \(z_L\), must have length at least n; pass NULL to skip retrieving z_L and z_U |
| z_U | (out) buffer to store the upper bound multipliers \(z_U\), must have length at least n; pass NULL to skip retrieving z_U and z_U |
| m | (in) the number of constraints \(g(x)\); can be arbitrary if skipping g and lambda |
| g | (out) buffer to store the constraint values \(g(x)\), must have length at least m; pass NULL to skip retrieving g |
| lambda | (out) buffer to store the constraint multipliers \(\lambda\), must have length at least m; pass NULL to skip retrieving lambda |
| bool Ipopt::TNLP::get_curr_violations | ( | const IpoptData * | ip_data, |
| IpoptCalculatedQuantities * | ip_cq, | ||
| bool | scaled, | ||
| Index | n, | ||
| Number * | x_L_violation, | ||
| Number * | x_U_violation, | ||
| Number * | compl_x_L, | ||
| Number * | compl_x_U, | ||
| Number * | grad_lag_x, | ||
| Index | m, | ||
| Number * | nlp_constraint_violation, | ||
| Number * | compl_g | ||
| ) | const |
Get primal and dual infeasibility of the current iterate.
This method can be used to get the violations of constraints and optimality conditions at the current iterate, e.g., during intermediate_callback(). The method expects the number of variables (dimension of x), number of constraints (dimension of g(x)), and allocated arrays of appropriate lengths as input.
The method makes the vectors behind (unscaled_)curr_orig_bounds_violation(), (unscaled_)curr_nlp_constraint_violation(), (unscaled_)curr_dual_infeasibility(), (unscaled_)curr_complementarity() from IpoptCalculatedQuantities of the internal NLP representation available into the form used by the TNLP. If Ipopt is in restoration mode, it maps the current iterate of restoration NLP (see RestoIpoptNLP) back to the original TNLP.
| ip_data | (in) Ipopt Data |
| ip_cq | (in) Ipopt Calculated Quantities |
| scaled | (in) whether to retrieve scaled or unscaled violations |
| n | (in) the number of variables \(x\) in the problem; can be arbitrary if skipping compl_x_L, compl_x_U, and grad_lag_x |
| x_L_violation | (out) buffer to store violation of original lower bounds on variables (max(orig_x_L-x,0)), must have length at least n; pass NULL to skip retrieving orig_x_L |
| x_U_violation | (out) buffer to store violation of original upper bounds on variables (max(x-orig_x_U,0)), must have length at least n; pass NULL to skip retrieving orig_x_U |
| compl_x_L | (out) buffer to store violation of complementarity for lower bounds on variables ( \((x-x_L)z_L\)), must have length at least n; pass NULL to skip retrieving compl_x_L |
| compl_x_U | (out) buffer to store violation of complementarity for upper bounds on variables ( \((x_U-x)z_U\)), must have length at least n; pass NULL to skip retrieving compl_x_U |
| grad_lag_x | (out) buffer to store gradient of Lagrangian w.r.t. variables \(x\), must have length at least n; pass NULL to skip retrieving grad_lag_x |
| m | (in) the number of constraints \(g(x)\); can be arbitrary if skipping lambda |
| nlp_constraint_violation | (out) buffer to store violation of constraints \(max(g_l-g(x),g(x)-g_u,0)\), must have length at least m; pass NULL to skip retrieving constraint_violation |
| compl_g | (out) buffer to store violation of complementarity of constraint ( \((g(x)-g_l)*\lambda^+ + (g_l-g(x))*\lambda^-\), where \(\lambda^+=max(0,\lambda)\) and \(\lambda^-=max(0,-\lambda)\) (componentwise)), must have length at least m; pass NULL to skip retrieving compl_g |