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Joris Gillis edited this page Apr 4, 2023 · 3 revisions

Standard documentation for interpolant:

 [INTERNAL]

::

 interpolant(str name, str solver, [[float]] grid, int m, dict opts) -> Function
 interpolant(str name, str solver, [int] grid_dims, int m, dict opts) -> Function
 interpolant(str name, str solver, [[float]] grid, [float] values, dict opts) -> Function
 interpolant(str name, str solver, [int] grid_dims, [float] values, dict opts) -> Function

Parametric variant of interpolant.

The resulting function will have an additional argument for the grid

By default, derivatives wrt the coefficients are not supported (zero). Some interpolant plugins may support the inline=true which enables correct derivatives

Extra doc: https://github.com/casadi/casadi/wiki/L_1p5

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/interpolant.hpp#L171

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/interpolant.cpp#L171-L187

.......

::

 interpolant(str name, str solver, [[float]] grid, [float] values, dict opts)

[INTERNAL]

An interpolant function for lookup table data

Parameters:

name: label for the resulting Function

solver: name of the plugin

grid: collection of 1D grids whose outer product defines the full N-D

rectangular grid

values: flattened vector of all values for all gridpoints

Syntax 1D

::

 * # Python
 * xgrid = np.linspace(1,6,6)
 * V = [-1,-1,-2,-3,0,2]
 * LUT = casadi.interpolant("LUT","bspline",[xgrid],V)
 * print(LUT(2.5))
 *

::

 * % Matlab
 * xgrid = 1:6;
 * V = [-1 -1 -2 -3 0 2];
 * LUT = casadi.interpolant('LUT','bspline',{xgrid},V);
 * LUT(2.5)
 *

Syntax 2D

::

 * # Python
 * xgrid = np.linspace(-5,5,11)
 * ygrid = np.linspace(-4,4,9)
 * X,Y = np.meshgrid(xgrid,ygrid,indexing='ij')
 * R = np.sqrt(5*X**2 + Y**2)+ 1
 * data = np.sin(R)/R
 * data_flat = data.ravel(order='F')
 * LUT = casadi.interpolant('name','bspline',[xgrid,ygrid],data_flat)
 * print(LUT([0.5,1]))
 * \enverbatim
 * \verbatim
 * % Matlab
 * xgrid = -5:1:5;
 * ygrid = -4:1:4;
 * R = sqrt(5*X.^2 + Y.^2)+ 1;
 * V = sin(R)./(R);
 * LUT = interpolant('LUT','bspline',{xgrid, ygrid},V(:));
 * LUT([0.5 1])
 *

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 | +------------------+-----------------+------------------+------------------+ | batch_x | OT_INT | Evaluate a batch | casadi::Interpol | | | | of different | ant | | | | inputs at once | | | | | (default 1). | | +------------------+-----------------+------------------+------------------+ | cache | OT_DICT | Prepopulate the | casadi::Function | | | | function cache. | Internal | | | | Default: empty | | +------------------+-----------------+------------------+------------------+ | compiler | OT_STRING | Just-in-time | casadi::Function | | | | compiler plugin | Internal | | | | to be used. | | +------------------+-----------------+------------------+------------------+ | 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). | | +------------------+-----------------+------------------+------------------+ | 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. | | +------------------+-----------------+------------------+------------------+ | inline | OT_BOOL | Implement the | casadi::Interpol | | | | lookup table in | ant | | | | MX primitives. | | | | | Useful when you | | | | | need derivatives | | | | | with respect to | | | | | grid and/or | | | | | coefficients. | | | | | Such derivatives | | | | | are | | | | | fundamentally | | | | | dense, so use | | | | | with caution. | | +------------------+-----------------+------------------+------------------+ | 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_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 | | +------------------+-----------------+------------------+------------------+ | lookup_mode | OT_STRINGVECTOR | Specifies, for | casadi::Interpol | | | | each grid | ant | | | | dimension, the | | | | | lookup algorithm | | | | | used to find the | | | | | correct index. | | | | | 'linear' uses a | | | | | for-loop + | | | | | break; (default | | | | | when | | | | | #knots<=100), | | | | | 'exact' uses | | | | | floored division | | | | | (only for | | | | | uniform grids), | | | | | 'binary' uses a | | | | | binary search. | | | | | (default when | | | | | #knots>100). | | +------------------+-----------------+------------------+------------------+ | 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. | | +------------------+-----------------+------------------+------------------+ | 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 | | +------------------+-----------------+------------------+------------------+ | 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 | | +------------------+-----------------+------------------+------------------+

List of plugins

  • bspline

  • linear

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
Interpolant.doc("myextraplugin")

bspline

Extra doc: https://github.com/casadi/casadi/wiki/L_239

List of available options

+-----------------------+--------------+-----------------------------------+ | Id | Type | Description | +=======================+==============+===================================+ | algorithm | OT_STRING | Algorithm used for fitting the | | | | data: 'not_a_knot' (default, same | | | | as Matlab), 'smooth_linear'. | +-----------------------+--------------+-----------------------------------+ | degree | OT_INTVECTOR | Sets, for each grid dimension, | | | | the degree of the spline. | +-----------------------+--------------+-----------------------------------+ | linear_solver | OT_STRING | Solver used for constructing the | | | | coefficient tensor. | +-----------------------+--------------+-----------------------------------+ | linear_solver_options | OT_DICT | Options to be passed to the | | | | linear solver. | +-----------------------+--------------+-----------------------------------+ | smooth_linear_frac | OT_DOUBLE | When 'smooth_linear' algorithm is | | | | active, determines sharpness | | | | between 0 (sharp, as linear | | | | interpolation) and 0.5 | | | | (smooth).Default value is 0.1. | +-----------------------+--------------+-----------------------------------+

linear

Extra doc: https://github.com/casadi/casadi/wiki/L_23b

List of available options

+-------------+-----------------+------------------------------------------+ | Id | Type | Description | +=============+=================+==========================================+ | lookup_mode | OT_STRINGVECTOR | Sets, for each grid dimenion, the lookup | | | | algorithm used to find the correct | | | | index. 'linear' uses a for-loop + break; | | | | 'exact' uses floored division (only for | | | | uniform grids). | +-------------+-----------------+------------------------------------------+

Joel Andersson

Extra doc: https://github.com/casadi/casadi/wiki/L_21p

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/interpolant.hpp#L125

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/interpolant.cpp#L125-L147

.............

.......

::

 interpolant(str name, str solver, [[float]] grid, int m, dict opts)

[INTERNAL] Parametric variant of interpolant.

The resulting function will have an additional argument for the

coefficients

By default, derivatives wrt the coefficients are not supported (zero). Some interpolant plugins may support the inline=true which enables correct derivatives

Extra doc: https://github.com/casadi/casadi/wiki/L_1p3

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/interpolant.hpp#L189

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/interpolant.cpp#L189-L203

.............

.......

::

 interpolant(str name, str solver, [int] grid_dims, int m, dict opts)

[INTERNAL] Parametric variant of interpolant.

The resulting function will have additional arguments for the grid and

coefficients

By default, derivatives wrt the coefficients are not supported (zero). Some interpolant plugins may support the inline=true which enables correct derivatives

Extra doc: https://github.com/casadi/casadi/wiki/L_1p4

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/interpolant.hpp#L205

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/interpolant.cpp#L205-L213

.............

.......

::

 interpolant(str name, str solver, [int] grid_dims, [float] values, dict opts)

[INTERNAL] Parametric variant of interpolant.

The resulting function will have an additional argument for the grid

By default, derivatives wrt the coefficients are not supported (zero). Some interpolant plugins may support the inline=true which enables correct derivatives

Extra doc: https://github.com/casadi/casadi/wiki/L_1p5

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/interpolant.hpp#L171

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/interpolant.cpp#L171-L187

.............

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