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L_237
[INTERNAL]::
rootfinder(str name, str solver, dict:SX rfp, dict opts) -> Function rootfinder(str name, str solver, dict:MX rfp, dict opts) -> Function rootfinder(str name, str solver, Function f, dict opts) -> Function.......
::
rootfinder(str name, str solver, dict:SX rfp, dict opts)[INTERNAL]
Create a solver for rootfinding problems Takes a function where one of the inputs is unknown and one of the outputs is a residual function that is always zero, defines a new function where the the unknown input has been replaced by a guess for the unknown and the residual output has been replaced by the calculated value for the input.
For a function [y0, y1, ...,yi, .., yn] = F(x0, x1, ..., xj, ..., xm),
where xj is unknown and yi=0, defines a new function [y0, y1, ...,xj, .., yn] = G(x0, x1, ..., xj_guess, ..., xm),
xj and yi must have the same dimension and d(yi)/d(xj) must be invertable.
By default, the first input is unknown and the first output is the
residual. General information
List of available options
+------------------+-----------------+------------------+------------------+ | Id | Type | Description | Used in | +==================+=================+==================+==================+ | ad_weight | OT_DOUBLE | Weighting factor | casadi::Function | | | | for derivative | Internal | | | | calculation.When | | | | | there is an | | | | | option of either | | | | | using forward or | | | | | reverse mode | | | | | directional | | | | | derivatives, the | | | | | condition ad_wei | | | | | ght*nf<=(1- | | | | | ad_weight)*na is | | | | | used where nf | | | | | and na are | | | | | estimates of the | | | | | number of | | | | | forward/reverse | | | | | mode directional | | | | | derivatives | | | | | needed. By | | | | | default, | | | | | ad_weight is | | | | | calculated | | | | | automatically, | | | | | but this can be | | | | | overridden by | | | | | setting this | | | | | option. In | | | | | particular, 0 | | | | | means forcing | | | | | forward mode and | | | | | 1 forcing | | | | | reverse mode. | | | | | Leave unset for | | | | | (class specific) | | | | | heuristics. | | +------------------+-----------------+------------------+------------------+ | ad_weight_sp | OT_DOUBLE | Weighting factor | casadi::Function | | | | for sparsity | Internal | | | | pattern | | | | | calculation calc | | | | | ulation.Override | | | | | s default | | | | | behavior. Set to | | | | | 0 and 1 to force | | | | | forward and | | | | | reverse mode | | | | | respectively. | | | | | Cf. option | | | | | "ad_weight". | | | | | When set to -1, | | | | | sparsity is | | | | | completely | | | | | ignored and | | | | | dense matrices | | | | | are used. | | +------------------+-----------------+------------------+------------------+ | always_inline | OT_BOOL | Force inlining. | casadi::Function | | | | | Internal | +------------------+-----------------+------------------+------------------+ | cache | OT_DICT | Prepopulate the | casadi::Function | | | | function cache. | Internal | | | | Default: empty | | +------------------+-----------------+------------------+------------------+ | common_options | OT_DICT | Options for | casadi::OracleFu | | | | auto-generated | nction | | | | functions | | +------------------+-----------------+------------------+------------------+ | compiler | OT_STRING | Just-in-time | casadi::Function | | | | compiler plugin | Internal | | | | to be used. | | +------------------+-----------------+------------------+------------------+ | constraints | OT_INTVECTOR | Constrain the | casadi::Rootfind | | | | unknowns. 0 | er | | | | (default): no | | | | | constraint on | | | | | ui, 1: ui >= | | | | | 0.0, -1: ui <= | | | | | 0.0, 2: ui > | | | | | 0.0, -2: ui < | | | | | 0.0. | | +------------------+-----------------+------------------+------------------+ | custom_jacobian | OT_FUNCTION | Override | casadi::Function | | | | CasADi's AD. Use | Internal | | | | together with | | | | | 'jac_penalty': | | | | | 0. Note: Highly | | | | | experimental. | | | | | Syntax may break | | | | | often. | | +------------------+-----------------+------------------+------------------+ | der_options | OT_DICT | Default options | casadi::Function | | | | to be used to | Internal | | | | populate | | | | | forward_options, | | | | | reverse_options, | | | | | and | | | | | jacobian_options | | | | | before those | | | | | options are | | | | | merged in. | | +------------------+-----------------+------------------+------------------+ | derivative_of | OT_FUNCTION | The function is | casadi::Function | | | | a derivative of | Internal | | | | another | | | | | function. The | | | | | type of | | | | | derivative | | | | | (directional | | | | | derivative, | | | | | Jacobian) is | | | | | inferred from | | | | | the function | | | | | name. | | +------------------+-----------------+------------------+------------------+ | dump | OT_BOOL | Dump function to | casadi::Function | | | | file upon first | Internal | | | | evaluation. | | | | | [false] | | +------------------+-----------------+------------------+------------------+ | dump_dir | OT_STRING | Directory to | casadi::Function | | | | dump | Internal | | | | inputs/outputs | | | | | to. Make sure | | | | | the directory | | | | | exists [.] | | +------------------+-----------------+------------------+------------------+ | dump_format | OT_STRING | Choose file | casadi::Function | | | | format to dump | Internal | | | | matrices. See | | | | | DM.from_file | | | | | [mtx] | | +------------------+-----------------+------------------+------------------+ | dump_in | OT_BOOL | Dump numerical | casadi::Function | | | | values of inputs | Internal | | | | to file | | | | | (readable with | | | | | DM.from_file ) | | | | | [default: false] | | +------------------+-----------------+------------------+------------------+ | dump_out | OT_BOOL | Dump numerical | casadi::Function | | | | values of | Internal | | | | outputs to file | | | | | (readable with | | | | | DM.from_file ) | | | | | [default: false] | | +------------------+-----------------+------------------+------------------+ | enable_fd | OT_BOOL | Enable | casadi::Function | | | | derivative | Internal | | | | calculation by | | | | | finite | | | | | differencing. | | | | | [default: | | | | | false]] | | +------------------+-----------------+------------------+------------------+ | enable_forward | OT_BOOL | Enable | casadi::Function | | | | derivative | Internal | | | | calculation | | | | | using generated | | | | | functions for | | | | | Jacobian-times- | | | | | vector products | | | | | - typically | | | | | using forward | | | | | mode AD - if | | | | | available. | | | | | [default: true] | | +------------------+-----------------+------------------+------------------+ | enable_jacobian | OT_BOOL | Enable | casadi::Function | | | | derivative | Internal | | | | calculation | | | | | using generated | | | | | functions for | | | | | Jacobians of all | | | | | differentiable | | | | | outputs with | | | | | respect to all | | | | | differentiable | | | | | inputs - if | | | | | available. | | | | | [default: true] | | +------------------+-----------------+------------------+------------------+ | enable_reverse | OT_BOOL | Enable | casadi::Function | | | | derivative | Internal | | | | calculation | | | | | using generated | | | | | functions for | | | | | transposed | | | | | Jacobian-times- | | | | | vector products | | | | | - typically | | | | | using reverse | | | | | mode AD - if | | | | | available. | | | | | [default: true] | | +------------------+-----------------+------------------+------------------+ | error_on_fail | OT_BOOL | Throw exceptions | casadi::ProtoFun | | | | when function | ction | | | | evaluation fails | | | | | (default true). | | +------------------+-----------------+------------------+------------------+ | expand | OT_BOOL | Replace MX with | casadi::OracleFu | | | | SX expressions | nction | | | | in problem | | | | | formulation | | | | | [false] | | +------------------+-----------------+------------------+------------------+ | fd_method | OT_STRING | Method for | casadi::Function | | | | finite | Internal | | | | differencing | | | | | [default | | | | | 'central'] | | +------------------+-----------------+------------------+------------------+ | fd_options | OT_DICT | Options to be | casadi::Function | | | | passed to the | Internal | | | | finite | | | | | difference | | | | | instance | | +------------------+-----------------+------------------+------------------+ | forward_options | OT_DICT | Options to be | casadi::Function | | | | passed to a | Internal | | | | forward mode | | | | | constructor | | +------------------+-----------------+------------------+------------------+ | gather_stats | OT_BOOL | Deprecated | casadi::Function | | | | option | Internal | | | | (ignored): | | | | | Statistics are | | | | | now always | | | | | collected. | | +------------------+-----------------+------------------+------------------+ | implicit_input | OT_INT | Index of the | casadi::Rootfind | | | | input that | er | | | | corresponds to | | | | | the actual root- | | | | | finding | | +------------------+-----------------+------------------+------------------+ | implicit_output | OT_INT | Index of the | casadi::Rootfind | | | | output that | er | | | | corresponds to | | | | | the actual root- | | | | | finding | | +------------------+-----------------+------------------+------------------+ | input_scheme | OT_STRINGVECTOR | Deprecated | casadi::Function | | | | option (ignored) | Internal | +------------------+-----------------+------------------+------------------+ | inputs_check | OT_BOOL | Throw exceptions | casadi::Function | | | | when the | Internal | | | | numerical values | | | | | of the inputs | | | | | don't make sense | | +------------------+-----------------+------------------+------------------+ | is_diff_in | OT_BOOLVECTOR | Indicate for | casadi::Function | | | | each input if it | Internal | | | | should be | | | | | differentiable. | | +------------------+-----------------+------------------+------------------+ | is_diff_out | OT_BOOLVECTOR | Indicate for | casadi::Function | | | | each output if | Internal | | | | it should be | | | | | differentiable. | | +------------------+-----------------+------------------+------------------+ | jac_penalty | OT_DOUBLE | When requested | casadi::Function | | | | for a number of | Internal | | | | forward/reverse | | | | | directions, it | | | | | may be cheaper | | | | | to compute first | | | | | the full | | | | | jacobian and | | | | | then multiply | | | | | with seeds, | | | | | rather than | | | | | obtain the | | | | | requested | | | | | directions in a | | | | | straightforward | | | | | manner. Casadi | | | | | uses a heuristic | | | | | to decide which | | | | | is cheaper. A | | | | | high value of | | | | | 'jac_penalty' | | | | | makes it less | | | | | likely for the | | | | | heurstic to | | | | | chose the full | | | | | Jacobian | | | | | strategy. The | | | | | special value -1 | | | | | indicates never | | | | | to use the full | | | | | Jacobian | | | | | strategy | | +------------------+-----------------+------------------+------------------+ | jacobian_functio | OT_FUNCTION | Function object | casadi::Rootfind | | n | | for calculating | er | | | | the Jacobian | | | | | (autogenerated | | | | | by default) | | +------------------+-----------------+------------------+------------------+ | jacobian_options | OT_DICT | Options to be | casadi::Function | | | | passed to a | Internal | | | | Jacobian | | | | | constructor | | +------------------+-----------------+------------------+------------------+ | jit | OT_BOOL | Use just-in-time | casadi::Function | | | | compiler to | Internal | | | | speed up the | | | | | evaluation | | +------------------+-----------------+------------------+------------------+ | jit_cleanup | OT_BOOL | Cleanup up the | casadi::Function | | | | temporary source | Internal | | | | file that jit | | | | | creates. | | | | | Default: true | | +------------------+-----------------+------------------+------------------+ | jit_name | OT_STRING | The file name | casadi::Function | | | | used to write | Internal | | | | out code. The | | | | | actual file | | | | | names used | | | | | depend on 'jit_t | | | | | emp_suffix' and | | | | | include | | | | | extensions. | | | | | Default: | | | | | 'jit_tmp' | | +------------------+-----------------+------------------+------------------+ | jit_options | OT_DICT | Options to be | casadi::Function | | | | passed to the | Internal | | | | jit compiler. | | +------------------+-----------------+------------------+------------------+ | jit_serialize | OT_STRING | Specify | casadi::Function | | | | behaviour when | Internal | | | | serializing a | | | | | jitted function: | | | | | SOURCE|link|embe | | | | | d. | | +------------------+-----------------+------------------+------------------+ | jit_temp_suffix | OT_BOOL | Use a temporary | casadi::Function | | | | (seemingly | Internal | | | | random) filename | | | | | suffix for | | | | | generated code | | | | | and libraries. | | | | | This is desired | | | | | for thread- | | | | | safety. This | | | | | behaviour may | | | | | defeat caching | | | | | compiler | | | | | wrappers. | | | | | Default: true | | +------------------+-----------------+------------------+------------------+ | linear_solver | OT_STRING | User-defined | casadi::Rootfind | | | | linear solver | er | | | | class. Needed | | | | | for | | | | | sensitivities. | | +------------------+-----------------+------------------+------------------+ | linear_solver_op | OT_DICT | Options to be | casadi::Rootfind | | tions | | passed to the | er | | | | linear solver. | | +------------------+-----------------+------------------+------------------+ | max_io | OT_INT | Acceptable | casadi::Function | | | | number of inputs | Internal | | | | and outputs. | | | | | Warn if | | | | | exceeded. | | +------------------+-----------------+------------------+------------------+ | max_num_dir | OT_INT | Specify the | casadi::Function | | | | maximum number | Internal | | | | of directions | | | | | for derivative | | | | | functions. | | | | | Overrules the | | | | | builtin optimize | | | | | d_num_dir. | | +------------------+-----------------+------------------+------------------+ | monitor | OT_STRINGVECTOR | Set of user | casadi::OracleFu | | | | problem | nction | | | | functions to be | | | | | monitored | | +------------------+-----------------+------------------+------------------+ | never_inline | OT_BOOL | Forbid inlining. | casadi::Function | | | | | Internal | +------------------+-----------------+------------------+------------------+ | output_scheme | OT_STRINGVECTOR | Deprecated | casadi::Function | | | | option (ignored) | Internal | +------------------+-----------------+------------------+------------------+ | post_expand | OT_BOOL | After | casadi::Function | | | | construction, | Internal | | | | expand this | | | | | Function . | | | | | Default: False | | +------------------+-----------------+------------------+------------------+ | post_expand_opti | OT_DICT | Options to be | casadi::Function | | ons | | passed to post- | Internal | | | | construction | | | | | expansion. | | | | | Default: empty | | +------------------+-----------------+------------------+------------------+ | print_in | OT_BOOL | Print numerical | casadi::Function | | | | values of inputs | Internal | | | | [default: false] | | +------------------+-----------------+------------------+------------------+ | print_out | OT_BOOL | Print numerical | casadi::Function | | | | values of | Internal | | | | outputs | | | | | [default: false] | | +------------------+-----------------+------------------+------------------+ | print_time | OT_BOOL | print | casadi::ProtoFun | | | | information | ction | | | | about execution | | | | | time. Implies | | | | | record_time. | | +------------------+-----------------+------------------+------------------+ | record_time | OT_BOOL | record | casadi::ProtoFun | | | | information | ction | | | | about execution | | | | | time, for | | | | | retrieval with | | | | | stats(). | | +------------------+-----------------+------------------+------------------+ | regularity_check | OT_BOOL | Throw exceptions | casadi::ProtoFun | | | | when NaN or Inf | ction | | | | appears during | | | | | evaluation | | +------------------+-----------------+------------------+------------------+ | reverse_options | OT_DICT | Options to be | casadi::Function | | | | passed to a | Internal | | | | reverse mode | | | | | constructor | | +------------------+-----------------+------------------+------------------+ | show_eval_warnin | OT_BOOL | Show warnings | casadi::OracleFu | | gs | | generated from | nction | | | | function | | | | | evaluations | | | | | [true] | | +------------------+-----------------+------------------+------------------+ | specific_options | OT_DICT | Options for | casadi::OracleFu | | | | specific auto- | nction | | | | generated | | | | | functions, | | | | | overwriting the | | | | | defaults from | | | | | common_options. | | | | | Nested | | | | | dictionary. | | +------------------+-----------------+------------------+------------------+ | user_data | OT_VOIDPTR | A user-defined | casadi::Function | | | | field that can | Internal | | | | be used to | | | | | identify the | | | | | function or pass | | | | | additional | | | | | information | | +------------------+-----------------+------------------+------------------+ | verbose | OT_BOOL | Verbose | casadi::ProtoFun | | | | evaluation for | ction | | | | debugging | | +------------------+-----------------+------------------+------------------+
Input scheme: casadi::RootfinderInput (ROOTFINDER_NUM_IN = 2)
+---------------+-------+---------------------------------+ | Full name | Short | Description | +===============+=======+=================================+ | ROOTFINDER_X0 | x0 | Initial guess for the solution. | +---------------+-------+---------------------------------+ | ROOTFINDER_P | p | Parameters. | +---------------+-------+---------------------------------+
Output scheme: casadi::RootfinderOutput (ROOTFINDER_NUM_OUT = 1)
+--------------+-------+--------------------------------------+ | Full name | Short | Description | +==============+=======+======================================+ | ROOTFINDER_X | x | Solution to the system of equations. | +--------------+-------+--------------------------------------+
List of plugins
kinsol
fast_newton
nlpsol
newton
Note: some of the plugins in this list might not be available on your
system. Also, there might be extra plugins available to you that are not listed here. You can obtain their documentation with
Rootfinder.doc("myextraplugin")
KINSOL interface from the Sundials suite
Extra doc: https://github.com/casadi/casadi/wiki/L_226
List of available options
+---------------------------+-----------------+----------------------------+ | Id | Type | Description | +===========================+=================+============================+ | abstol | OT_DOUBLE | Stopping criterion | | | | tolerance | +---------------------------+-----------------+----------------------------+ | disable_internal_warnings | OT_BOOL | Disable KINSOL internal | | | | warning messages | +---------------------------+-----------------+----------------------------+ | exact_jacobian | OT_BOOL | Use exact Jacobian | | | | information | +---------------------------+-----------------+----------------------------+ | f_scale | OT_DOUBLEVECTOR | Equation scaling factors | +---------------------------+-----------------+----------------------------+ | iterative_solver | OT_STRING | gmres|bcgstab|tfqmr | +---------------------------+-----------------+----------------------------+ | linear_solver_type | OT_STRING | dense|banded|iterative|use | | | | r_defined | +---------------------------+-----------------+----------------------------+ | lower_bandwidth | OT_INT | Lower bandwidth for banded | | | | linear solvers | +---------------------------+-----------------+----------------------------+ | max_iter | OT_INT | Maximum number of Newton | | | | iterations. Putting 0 sets | | | | the default value of | | | | KinSol. | +---------------------------+-----------------+----------------------------+ | max_krylov | OT_INT | Maximum Krylov space | | | | dimension | +---------------------------+-----------------+----------------------------+ | pretype | OT_STRING | Type of preconditioner | +---------------------------+-----------------+----------------------------+ | print_level | OT_INT | Verbosity level | +---------------------------+-----------------+----------------------------+ | strategy | OT_STRING | Globalization strategy | +---------------------------+-----------------+----------------------------+ | u_scale | OT_DOUBLEVECTOR | Variable scaling factors | +---------------------------+-----------------+----------------------------+ | upper_bandwidth | OT_INT | Upper bandwidth for banded | | | | linear solvers | +---------------------------+-----------------+----------------------------+ | use_preconditioner | OT_BOOL | Precondition an iterative | | | | solver | +---------------------------+-----------------+----------------------------+
Implements simple newton iterations to solve an implicit function.
Extra doc: https://github.com/casadi/casadi/wiki/L_237
List of available options
+------------+-----------+-------------------------------------------------+ | Id | Type | Description | +============+===========+=================================================+ | abstol | OT_DOUBLE | Stopping criterion tolerance on ||g||__inf) | +------------+-----------+-------------------------------------------------+ | abstolStep | OT_DOUBLE | Stopping criterion tolerance on step size | +------------+-----------+-------------------------------------------------+ | max_iter | OT_INT | Maximum number of Newton iterations to perform | | | | before returning. | +------------+-----------+-------------------------------------------------+
Implements simple newton iterations to solve an implicit function.
Extra doc: https://github.com/casadi/casadi/wiki/L_236
List of available options
+-----------------+-----------+--------------------------------------------+ | Id | Type | Description | +=================+===========+============================================+ | abstol | OT_DOUBLE | Stopping criterion tolerance on max(|F|) | +-----------------+-----------+--------------------------------------------+ | abstolStep | OT_DOUBLE | Stopping criterion tolerance on step size | +-----------------+-----------+--------------------------------------------+ | line_search | OT_BOOL | Enable line-search (default: true) | +-----------------+-----------+--------------------------------------------+ | max_iter | OT_INT | Maximum number of Newton iterations to | | | | perform before returning. | +-----------------+-----------+--------------------------------------------+ | print_iteration | OT_BOOL | Print information about each iteration | +-----------------+-----------+--------------------------------------------+
Joel Andersson
Extra doc: https://github.com/casadi/casadi/wiki/L_21r
Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/rootfinder.hpp#L96
Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/rootfinder.cpp#L96-L99
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::
rootfinder(str name, str solver, dict:MX rfp, dict opts) rootfinder(str name, str solver, Function f, dict opts)[INTERNAL]
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