CasADi Python API¶

1. Expression tools¶

acos(*args)¶

acos(float x) -> float
acos(DM x) -> DM
acos(SX x) -> SX
acos(MX x) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_p8

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L374

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L374-L376

acosh(*args)¶

acosh(float x) -> float
acosh(DM x) -> DM
acosh(SX x) -> SX
acosh(MX x) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L446

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L446-L448

adj(*args)¶

adj(DM A) -> DM
adj(SX A) -> SX

Extra doc: https://github.com/casadi/casadi/wiki/L_18p

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L504

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L504-L506

asin(*args)¶

asin(float x) -> float
asin(DM x) -> DM
asin(SX x) -> SX
asin(MX x) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_p7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L362

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L362-L364

asinh(*args)¶

asinh(float x) -> float
asinh(DM x) -> DM
asinh(SX x) -> SX
asinh(MX x) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L434

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L434-L436

atan(*args)¶

atan(float x) -> float
atan(DM x) -> DM
atan(SX x) -> SX
atan(MX x) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_p6

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L350

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L350-L352

atan2(*args)¶

atan2(float x, float y) -> float
atan2(DM x, DM y) -> DM
atan2(SX x, SX y) -> SX
atan2(MX x, MX y) -> MX

theta = atan2(y,x) corresponds to x = r cos(theta), y = r sin(theta)

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L648

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L648-L650

atanh(*args)¶

atanh(float x) -> float
atanh(DM x) -> DM
atanh(SX x) -> SX
atanh(MX x) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L422

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L422-L424

bilin(*args)¶

bilin(DM A, DM x) -> DM
bilin(SX A, SX x) -> SX
bilin(MX A, MX x) -> MX
bilin(DM A, DM x, DM y) -> DM
bilin(SX A, SX x, SX y) -> SX
bilin(MX A, MX x, MX y) -> MX

1. Parameters:¶

y: can be omitted, in which case x^T A x is calculated

Extra doc: https://github.com/casadi/casadi/wiki/L_1bo

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L409

blockcat(*args)¶

blockcat([[DM]] v) -> DM
blockcat([[SX]] v) -> SX
blockcat([[MX]] v) -> MX
blockcat(Sparsity A, Sparsity B, Sparsity C, Sparsity D) -> Sparsity
blockcat(DM A, DM B, DM C, DM D) -> DM
blockcat(SX A, SX B, SX C, SX D) -> SX
blockcat(MX A, MX B, MX C, MX D) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_3m

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L234

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L234-L236

bspline(*args)¶

bspline(MX x, DM coeffs, [[float]] knots, [int] degree, int m, dict opts) -> MX
bspline(MX x, MX coeffs, [[float]] knots, [int] degree, int m, dict opts) -> MX

ceil(*args)¶

ceil(float x) -> float
ceil(DM x) -> DM
ceil(SX x) -> SX
ceil(MX x) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L530

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L530-L532

chol(*args)¶

chol(DM A) -> DM
chol(SX A) -> SX

Performs and LDL transformation [L,D] = ldl(A) and returns diag(sqrt(D))*L’

Extra doc: https://github.com/casadi/casadi/wiki/L_18v

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L562

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L562-L564

cofactor(*args)¶

cofactor(DM x, int i, int j) -> DM
cofactor(SX x, int i, int j) -> SX

Extra doc: https://github.com/casadi/casadi/wiki/L_18r

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L518

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L518-L520

collocation_coeff(*args)¶

collocation_coeff([float] tau) -> (DM OUTPUT, DM OUTPUT, DM OUTPUT)

Obtain collocation interpolating matrices.

A collocation method poses a polynomial Pi that interpolates exactly

through an initial state (0,X_0) and helper states at collocation points (tau_j,Xc_j) with j=1..degree.

This function computes the linear mapping between dPi/dt and coefficients Z=[X_0 Xc].

1. Parameters:¶

tau: location of collocation points (length: degree), as obtained from

collocation_points

C: interpolating coefficients to obtain derivatives. Size: (degree+1)-by-

degree

You may find the slopes of Pi at the collocation points as

dPi/dt @ Xc = (1/h) Z*C,

with h the length of the integration interval.

1. Parameters:¶

D: interpolating coefficients to obtain end state. Size: (degree+1)-by-1

You may find the end point of Pi as

Pi @X_f = Z*D

1. Parameters:¶

B: quadrature coefficients Size: degree-by-1

Given quadrature righ-hand-sides ‘quad’ evaluated at the collocation

points, you may find the integrated quadratures as

q = quad*B*h

Extra doc: https://github.com/casadi/casadi/wiki/L_1sq

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.hpp#L233

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.cpp#L233-L287

collocation_points(*args)¶

collocation_points(int order, str scheme) -> [float]

Obtain collocation points of specific order and scheme.

1. Parameters:¶

order: Which order (1 to 9 supported)

scheme: ‘radau’ or ‘legendre’

Extra doc: https://github.com/casadi/casadi/wiki/L_1so

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.hpp#L120

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.cpp#L120-L122

conditional(*args)¶

conditional(DM ind, [DM] x, DM x_default, bool short_circuit) -> DM
conditional(SX ind, [SX] x, SX x_default, bool short_circuit) -> SX
conditional(MX ind, [MX] x, MX x_default, bool short_circuit) -> MX

If the condition

1. Parameters:¶

ind: evaluates to the integer k, where 0<=k<f.size(), then x[k] will be

returned, otherwise

x_default: will be returned.

Extra doc: https://github.com/casadi/casadi/wiki/L_1cj

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L647

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L647-L650

constpow(*args)¶

constpow(float x, float y) -> float
constpow(DM x, DM y) -> DM
constpow(SX x, SX y) -> SX
constpow(MX x, MX y) -> MX

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L720

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L720-L722

convexify(*args)¶

convexify(MX H, dict opts) -> MX

copysign(*args)¶

copysign(float x, float y) -> float
copysign(DM x, DM y) -> DM
copysign(SX x, SX y) -> SX
copysign(MX x, MX y) -> MX

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L710

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L710-L712

cos(*args)¶

cos(float x) -> float
cos(DM x) -> DM
cos(SX x) -> SX
cos(MX x) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_p4

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L326

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L326-L328

cosh(*args)¶

cosh(float x) -> float
cosh(DM x) -> DM
cosh(SX x) -> SX
cosh(MX x) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L410

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L410-L412

cross(*args)¶

cross(DM a, DM b, int dim) -> DM
cross(SX a, SX b, int dim) -> SX
cross(MX a, MX b, int dim) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1bu

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L467

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L467-L469

cse(*args)¶

cse(DM e) -> DM
cse([DM] e) -> [DM]
cse([SX] e) -> [SX]
cse(SX e) -> SX
cse(MX e) -> MX
cse([MX] e) -> [MX]

Extra doc: https://github.com/casadi/casadi/wiki/L_1cp

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L702

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L702-L704

cumsum(*args)¶

cumsum(DM A, int axis) -> DM
cumsum(SX A, int axis) -> SX
cumsum(MX A, int axis) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1lm

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/casadi_misc.hpp#L916

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/casadi_misc.hpp#L916-L924

dae_init_gen(*args)¶

dae_init_gen(dict:SX dae, dict:SX dae_red, str init_solver, dict:DM init_strength, dict init_solver_options) -> Function
dae_init_gen(dict:MX dae, dict:MX dae_red, str init_solver, dict:DM init_strength, dict init_solver_options) -> Function

Obtain a generator Function for producing consistent initial guesses of a reduced DAE.

1. Parameters:¶

dae: Original (unreduced) DAE structure

dae_red: Reduced DAE (see dae_reduce_index)

init_solver: NLP solver plugin name for nlpsol used to construct an initial

init_strength: Influence the nature of the NLP Structure with keys x_impl, dx_impl, z

should: match the variable size corresponding to that key. For each variable

the meaning of the corresponding DM value is as follows: When >=0,

indicates that the provided initial guess is used in a quadratic penalty (value used as weight) When -1, indicates that the provided initial guess must be observed (simple bound on variable)

init_solver_options: NLP solver options to be passed to nlpsol

init_gen A function to generate a consistent initial guess that can be: used to pass to an integrator constructed from a semi explict reduced DAE

Inputs: x_impl, dx_impl, z: initial guesses in the original DAE space

p: parameters

t: time Outputs:

x0, z0: (semi explicit) integrator states and algebraic variables;

typically used as input for integrators

See:: dae_reduce_index

Extra doc: https://github.com/casadi/casadi/wiki/L_1sv

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.hpp#L1215

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.cpp#L1215-L1218

dae_init_gen(dict:SX dae, dict:SX dae_red, str init_solver, dict:DM init_strength, dict init_solver_options)

[INTERNAL] Obtain a generator Function for producing consistent initial guesses of a reduced DAE.

1. Parameters:¶

dae: Original (unreduced) DAE structure

dae_red: Reduced DAE (see dae_reduce_index)

init_solver: NLP solver plugin name for nlpsol used to construct an initial

init_strength: Influence the nature of the NLP Structure with keys x_impl, dx_impl, z

should: match the variable size corresponding to that key. For each variable

the meaning of the corresponding DM value is as follows: When >=0,

indicates that the provided initial guess is used in a quadratic penalty (value used as weight) When -1, indicates that the provided initial guess must be observed (simple bound on variable)

init_solver_options: NLP solver options to be passed to nlpsol

init_gen A function to generate a consistent initial guess that can be: used to pass to an integrator constructed from a semi explict reduced DAE

Inputs: x_impl, dx_impl, z: initial guesses in the original DAE space

p: parameters

t: time Outputs:

x0, z0: (semi explicit) integrator states and algebraic variables;

typically used as input for integrators

See:: dae_reduce_index

Extra doc: https://github.com/casadi/casadi/wiki/L_1sv

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.hpp#L1215

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.cpp#L1215-L1218

dae_init_gen(dict:MX dae, dict:MX dae_red, str init_solver, dict:DM init_strength, dict init_solver_options)

[INTERNAL] Obtain a generator Function for producing consistent initial guesses of a reduced DAE.

1. Parameters:¶

dae: Original (unreduced) DAE structure

dae_red: Reduced DAE (see dae_reduce_index)

init_solver: NLP solver plugin name for nlpsol used to construct an initial

init_strength: Influence the nature of the NLP Structure with keys x_impl, dx_impl, z

should: match the variable size corresponding to that key. For each variable

the meaning of the corresponding DM value is as follows: When >=0,

indicates that the provided initial guess is used in a quadratic penalty (value used as weight) When -1, indicates that the provided initial guess must be observed (simple bound on variable)

init_solver_options: NLP solver options to be passed to nlpsol

init_gen A function to generate a consistent initial guess that can be: used to pass to an integrator constructed from a semi explict reduced DAE

Inputs: x_impl, dx_impl, z: initial guesses in the original DAE space

p: parameters

t: time Outputs:

x0, z0: (semi explicit) integrator states and algebraic variables;

typically used as input for integrators

See:: dae_reduce_index

Extra doc: https://github.com/casadi/casadi/wiki/L_1sv

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.hpp#L1210

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.cpp#L1210-L1213

dae_map_semi_expl(*args)¶

dae_map_semi_expl(dict:SX dae, dict:SX dae_red) -> (dict:SX , Function OUTPUT, Function OUTPUT)
dae_map_semi_expl(dict:MX dae, dict:MX dae_red) -> (dict:MX , Function OUTPUT, Function OUTPUT)

Turn a reduced DAE into a semi explicit form suitable for CasADi

integrator.

1. Parameters:¶

dae: Original (unreduced) DAE structure

dae_red: Reduced DAE (see dae_reduce_index)

state_to_orig: A mapping of integrator (semi explicit) states to states of the original DAE

phi: A function to compute the invariants of the reduced DAE Inputs: x and z: (semi explicit) integrator states; typically integrator outputs xf and zf

p: parameters

t: time

Semi explicit DAE dictionary, suitable to pass to a CasADi integrator

See:: dae_reduce_index

Extra doc: https://github.com/casadi/casadi/wiki/L_1su

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.hpp#L1205

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.cpp#L1205-L1208

dae_map_semi_expl(dict:SX dae, dict:SX dae_red)

[INTERNAL] Turn a reduced DAE into a semi explicit form suitable for CasADi

integrator.

1. Parameters:¶

dae: Original (unreduced) DAE structure

dae_red: Reduced DAE (see dae_reduce_index)

state_to_orig: A mapping of integrator (semi explicit) states to states of the original DAE

phi: A function to compute the invariants of the reduced DAE Inputs: x and z: (semi explicit) integrator states; typically integrator outputs xf and zf

p: parameters

t: time

Semi explicit DAE dictionary, suitable to pass to a CasADi integrator

See:: dae_reduce_index

Extra doc: https://github.com/casadi/casadi/wiki/L_1su

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.hpp#L1205

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.cpp#L1205-L1208

dae_map_semi_expl(dict:MX dae, dict:MX dae_red)

[INTERNAL] Turn a reduced DAE into a semi explicit form suitable for CasADi

integrator.

1. Parameters:¶

dae: Original (unreduced) DAE structure

dae_red: Reduced DAE (see dae_reduce_index)

state_to_orig: A mapping of integrator (semi explicit) states to states of the original DAE

phi: A function to compute the invariants of the reduced DAE Inputs: x and z: (semi explicit) integrator states; typically integrator outputs xf and zf

p: parameters

t: time

Semi explicit DAE dictionary, suitable to pass to a CasADi integrator

See:: dae_reduce_index

Extra doc: https://github.com/casadi/casadi/wiki/L_1su

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.hpp#L1200

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.cpp#L1200-L1203

dae_reduce_index(*args)¶

dae_reduce_index(dict:SX dae, dict opts) -> (dict:SX , dict OUTPUT)
dae_reduce_index(dict:MX dae, dict opts) -> (dict:MX , dict OUTPUT)

Reduce index.

Index reduction leads to a new set of variables and equations.

In the process, a set of constraints (algebraic equations or derivatives) a.k.a invariants is constructed that are invariant to the

boundary-value-problem outcome will keep satisfying those constraints automatically, even though they are not part of the reduced DAE.

For any practical numerical integration method, there will be numerical drift away from satisfaction of those constraints. In other words, you will

original zero.

A classic mitigation technique is Baumgarte stabilization: you add these invariants to the reduced DAE as a correction term that acts in a way to make small (numerical) perturbations to the invariants decay to the origin as a dampened linear system.

in which a certain set of constraints (algebraic equations or derivatives) has been dropped in favour of

1. Parameters:¶

dae: Expression dictionary describing the DAE

Each value must be a dense column vector.

keys: x_impl: symbol for implicit differential states

dx_impl: symbol for implicit differential state derivatives

z: symbol for algebraic variables

alg: expression for algebraic equations

t: symbol for time

p: symbol for parameters

1. Parameters:¶

opts: Option dictionary

‘baumgarte_pole’: double Poles (inverse time constants) of the Baumgarte invariant correction term. Must be <0 to dampen out perturbations 0 (default) amounts to no correction. Corresponds to -gamma of equation (1.5)

Sebastian Reich. “Stabilization of: DAEs and invariant manifolds.”

Numerische Mathematik 67.2 (1994): 131-149.

1. Parameters:¶

stats: Statistics

Expression dictionary describing the reduced DAE

In addition the fields allowed in the input DAE, the following keys occur:

x: symbol for explicit differential states

ode: expression for right-hand-side of explicit differential states

I: expression for invariants

Extra doc: https://github.com/casadi/casadi/wiki/L_23h

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.hpp#L1060

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.cpp#L1060-L1062

dae_reduce_index(dict:SX dae, dict opts)

[INTERNAL] Reduce index.

Index reduction leads to a new set of variables and equations.

In the process, a set of constraints (algebraic equations or derivatives) a.k.a invariants is constructed that are invariant to the

boundary-value-problem outcome will keep satisfying those constraints automatically, even though they are not part of the reduced DAE.

For any practical numerical integration method, there will be numerical drift away from satisfaction of those constraints. In other words, you will

original zero.

in which a certain set of constraints (algebraic equations or derivatives) has been dropped in favour of

1. Parameters:¶

dae: Expression dictionary describing the DAE

Each value must be a dense column vector.

keys: x_impl: symbol for implicit differential states

dx_impl: symbol for implicit differential state derivatives

z: symbol for algebraic variables

alg: expression for algebraic equations

t: symbol for time

p: symbol for parameters

1. Parameters:¶

opts: Option dictionary

Sebastian Reich. “Stabilization of: DAEs and invariant manifolds.”

Numerische Mathematik 67.2 (1994): 131-149.

1. Parameters:¶

stats: Statistics

Expression dictionary describing the reduced DAE

In addition the fields allowed in the input DAE, the following keys occur:

x: symbol for explicit differential states

ode: expression for right-hand-side of explicit differential states

I: expression for invariants

Extra doc: https://github.com/casadi/casadi/wiki/L_23h

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.hpp#L1060

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.cpp#L1060-L1062

dae_reduce_index(dict:MX dae, dict opts)

[INTERNAL] Reduce index.

Index reduction leads to a new set of variables and equations.

In the process, a set of constraints (algebraic equations or derivatives) a.k.a invariants is constructed that are invariant to the

boundary-value-problem outcome will keep satisfying those constraints automatically, even though they are not part of the reduced DAE.

For any practical numerical integration method, there will be numerical drift away from satisfaction of those constraints. In other words, you will

original zero.

in which a certain set of constraints (algebraic equations or derivatives) has been dropped in favour of

1. Parameters:¶

dae: Expression dictionary describing the DAE

Each value must be a dense column vector.

keys: x_impl: symbol for implicit differential states

dx_impl: symbol for implicit differential state derivatives

z: symbol for algebraic variables

alg: expression for algebraic equations

t: symbol for time

p: symbol for parameters

1. Parameters:¶

opts: Option dictionary

Sebastian Reich. “Stabilization of: DAEs and invariant manifolds.”

Numerische Mathematik 67.2 (1994): 131-149.

1. Parameters:¶

stats: Statistics

Expression dictionary describing the reduced DAE

In addition the fields allowed in the input DAE, the following keys occur:

x: symbol for explicit differential states

ode: expression for right-hand-side of explicit differential states

I: expression for invariants

Extra doc: https://github.com/casadi/casadi/wiki/L_23h

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.hpp#L1056

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/integration_tools.cpp#L1056-L1058

densify(*args)¶

densify(DM x) -> DM
densify(SX x) -> SX
densify(MX x) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1cg

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L617

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L617-L619

depends_on(*args)¶

depends_on(DM f, DM arg) -> bool
depends_on(SX f, SX arg) -> bool
depends_on(MX f, MX arg) -> bool

The argument must be symbolic

Extra doc: https://github.com/casadi/casadi/wiki/L_1ck

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L657

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L657-L659

det(*args)¶

det(DM A) -> DM
det(SX A) -> SX
det(MX A) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1bx

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L488

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L488-L488

detect_simple_bounds(*args)¶

detect_simple_bounds(SX xX, SX p, SX g, SX lbg, SX ubg) -> ([int] OUTPUT, SX OUTPUT, SX OUTPUT, Function OUTPUT, Function OUTPUT)
detect_simple_bounds(MX xX, MX p, MX g, MX lbg, MX ubg) -> ([int] OUTPUT, MX OUTPUT, MX OUTPUT, Function OUTPUT, Function OUTPUT)

detect_simple_bounds(SX xX, SX p, SX g, SX lbg, SX ubg)

[INTERNAL] Detect simple bounds from general constraints.

Given parametric constraints:

*   subject to lbg(p) <= g(x,p) <= ubg(p)
*

Returns an equivalent set

*   subject to  lbg(p)(gi) <= g(x,p)(gi) <= ubg(p)(gi)
*               lbx(p) <= x                 <= ubx(p)
*

1. Parameters:¶

lam_forward: (lam_g,p)->(lam_sg,lam_x)

lam_backward: (lam_sg,lam_x,p)->(lam_g)

Extra doc: https://github.com/casadi/casadi/wiki/L_1sw

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/nlp_tools.hpp#L217

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/nlp_tools.cpp#L217-L225

detect_simple_bounds(MX xX, MX p, MX g, MX lbg, MX ubg)

[INTERNAL]

diag(*args)¶

diag(DM A) -> DM
diag(SX A) -> SX
diag(MX A) -> MX

When the input is square, the diagonal elements are returned. If the input is vector-like, a diagonal matrix is constructed with it.

Extra doc: https://github.com/casadi/casadi/wiki/L_1cd

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L596

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L596-L598

diagsplit(*args)¶

diagsplit(Sparsity x, int incr) -> [Sparsity]
diagsplit(DM x, int incr) -> [DM]
diagsplit(SX x, int incr) -> [SX]
diagsplit(MX x, int incr) -> [MX]
diagsplit(Sparsity x, [int] output_offset) -> [Sparsity]
diagsplit(DM x, [int] output_offset) -> [DM]
diagsplit(SX x, [int] output_offset) -> [SX]
diagsplit(MX x, [int] output_offset) -> [MX]
diagsplit(Sparsity x, int incr1, int incr2) -> [Sparsity]
diagsplit(Sparsity x, [int] output_offset1, [int] output_offset2) -> [Sparsity]
diagsplit(DM x, int incr1, int incr2) -> [DM]
diagsplit(DM x, [int] output_offset1, [int] output_offset2) -> [DM]
diagsplit(SX x, int incr1, int incr2) -> [SX]
diagsplit(SX x, [int] output_offset1, [int] output_offset2) -> [SX]
diagsplit(MX x, int incr1, int incr2) -> [MX]
diagsplit(MX x, [int] output_offset1, [int] output_offset2) -> [MX]

1. Parameters:¶

incr1: Row dimension of each matrix

incr2: Column dimension of each matrix

diagsplit(diagsplit(x, …)) = x

Extra doc: https://github.com/casadi/casadi/wiki/L_3t

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L324

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L324-L326

diff(*args)¶

diff(DM A, int n, int axis) -> DM
diff(SX A, int n, int axis) -> SX
diff(MX A, int n, int axis) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1ln

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/casadi_misc.hpp#L938

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/casadi_misc.hpp#L938-L945

difference(*args)¶

difference([MX] a, [MX] b) -> [MX]

order

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L854

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L854-L856

dot(*args)¶

dot(DM x, DM y) -> DM
dot(SX x, SX y) -> SX
dot(MX x, MX y) -> MX

with x and y matrices of the same dimension

Extra doc: https://github.com/casadi/casadi/wiki/L_1ca

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L565

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L565-L567

eig_symbolic(*args)¶

eig_symbolic(DM m) -> DM
eig_symbolic(SX m) -> SX

This will only work for up to 3x3 matrices

Extra doc: https://github.com/casadi/casadi/wiki/L_199

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L833

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L833-L835

einstein(*args)¶

einstein(DM A, DM B, [int] dim_a, [int] dim_b, [int] dim_c, [int] a, [int] b, [int] c) -> DM
einstein(SX A, SX B, [int] dim_a, [int] dim_b, [int] dim_c, [int] a, [int] b, [int] c) -> SX
einstein(MX A, MX B, [int] dim_a, [int] dim_b, [int] dim_c, [int] a, [int] b, [int] c) -> MX
einstein(DM A, DM B, DM C, [int] dim_a, [int] dim_b, [int] dim_c, [int] a, [int] b, [int] c) -> DM
einstein(SX A, SX B, SX C, [int] dim_a, [int] dim_b, [int] dim_c, [int] a, [int] b, [int] c) -> SX
einstein(MX A, MX B, MX C, [int] dim_a, [int] dim_b, [int] dim_c, [int] a, [int] b, [int] c) -> MX

Computes the product: C_c = A_a + B_b where a b c are index/einstein

notation in an encoded form

For example, an matrix-matrix product may be written as: C_ij = A_ik B_kj

The encoded form uses strictly negative numbers to indicate labels. For the

Extra doc: https://github.com/casadi/casadi/wiki/L_r5

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L533

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L646-L652

eq(*args)¶

eq(float x, float y) -> float
eq(DM x, DM y) -> DM
eq(SX x, SX y) -> SX
eq(MX x, MX y) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L191

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L191-L193

erf(*args)¶

erf(float x) -> float
erf(DM x) -> DM
erf(SX x) -> SX
erf(MX x) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L542

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L542-L544

erfinv(*args)¶

erfinv(float x) -> float
erfinv(DM x) -> DM
erfinv(SX x) -> SX
erfinv(MX x) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L554

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L554-L556

evalf(*args)¶

evalf(DM x) -> DM
evalf(SX x) -> DM
evalf(MX x) -> DM

An error is raised when the expression contains symbols

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L816

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L816-L818

exp(*args)¶

exp(float x) -> float
exp(DM x) -> DM
exp(SX x) -> SX
exp(MX x) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L458

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L458-L460

expand(*args)¶

expand(DM ex) -> (DM OUTPUT1, DM OUTPUT2)
expand(SX ex) -> (SX OUTPUT1, SX OUTPUT2)

Extra doc: https://github.com/casadi/casadi/wiki/L_192

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L620

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L620-L623

expm(*args)¶

expm(DM A) -> DM
expm(SX A) -> SX
expm(MX A) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_23w

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L790

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L790-L792

expm1(*args)¶

expm1(float x) -> float
expm1(DM x) -> DM
expm1(SX x) -> SX
expm1(MX x) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L506

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L506-L508

expm_const(*args)¶

expm_const(DM A, DM t) -> DM
expm_const(SX A, SX t) -> SX
expm_const(MX A, MX t) -> MX

Computes expm(A*t) with A constant

1. Parameters:¶

A[in]: Square matrix

t[in]: Scalar

Extra doc: https://github.com/casadi/casadi/wiki/L_23v

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L782

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L782-L784

extract(*args)¶

extract([DM] ex, dict opts) -> ([DM] OUTPUT1, [DM] OUTPUT2, [DM] OUTPUT3)
extract([SX] ex, dict opts) -> ([SX] OUTPUT1, [SX] OUTPUT2, [SX] OUTPUT3)
extract([MX] ex, dict opts) -> ([MX] OUTPUT1, [MX] OUTPUT2, [MX] OUTPUT3)

Extra doc: https://github.com/casadi/casadi/wiki/L_1d5

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L959

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L959-L964

find(*args)¶

find(MX x) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1le

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/casadi_misc.hpp#L611

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/casadi_misc.hpp#L611-L617

floor(*args)¶

floor(float x) -> float
floor(DM x) -> DM
floor(SX x) -> SX
floor(MX x) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L518

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L518-L520

fmax(*args)¶

fmax(float x, float y) -> float
fmax(DM x, DM y) -> DM
fmax(SX x, SX y) -> SX
fmax(MX x, MX y) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L684

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L684-L686

fmin(*args)¶

fmin(float x, float y) -> float
fmin(DM x, DM y) -> DM
fmin(SX x, SX y) -> SX
fmin(MX x, MX y) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L672

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L672-L674

fmod(*args)¶

fmod(float x, float y) -> float
fmod(DM x, DM y) -> DM
fmod(SX x, SX y) -> SX
fmod(MX x, MX y) -> MX

This Function follows the convention of https://en.cppreference.com/w/c/numeric/math/fmod

Notably: fmod(5,3) -> 2

fmod(5,-3) -> 2

fmod(-5,3) -> -2

fmod(-5,-3) -> -2

This is equivalent to Python’s numpy.fmod and Matlab’s rem.

seealso remainder

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L613

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L613-L615

gauss_quadrature(*args)¶

gauss_quadrature(DM f, DM x, DM a, DM b, int order) -> DM
gauss_quadrature(SX f, SX x, SX a, SX b, int order) -> SX
gauss_quadrature(DM f, DM x, DM a, DM b, int order, DM w) -> DM
gauss_quadrature(SX f, SX x, SX a, SX b, int order, SX w) -> SX

Extra doc: https://github.com/casadi/casadi/wiki/L_196

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L732

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L732-L736

ge(*args)¶

ge(float x, float y) -> float
ge(DM x, DM y) -> DM
ge(SX x, SX y) -> SX
ge(MX x, MX y) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L176

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L176-L178

gradient(*args)¶

gradient(DM ex, DM arg) -> DM
gradient(SX ex, SX arg) -> SX
gradient(MX ex, MX arg) -> MX

1. Parameters:¶

ex[in]: Scalar expression to take the gradient of

arg[in]: Vector expression of symbols

opts[in]: Options

Dense column vector

Extra doc: https://github.com/casadi/casadi/wiki/L_23x

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L812

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L812-L814

graph_substitute(*args)¶

graph_substitute(MX ex, [MX] v, [MX] vdef) -> MX
graph_substitute([MX] ex, [MX] v, [MX] vdef) -> [MX]

Substitute variable var with expression expr in multiple expressions,

preserving nodes

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L734

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L734-L738

gt(*args)¶

gt(float x, float y) -> float
gt(DM x, DM y) -> DM
gt(SX x, SX y) -> SX
gt(MX x, MX y) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L161

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L161-L163

heaviside(*args)¶

heaviside(DM x) -> DM
heaviside(SX x) -> SX

[ begin {cases} H(x) = 0 & x<0 \ H(x) = 1/2 & x=0 \ H(x) = 1 & x>0 \ end {cases} ]

Extra doc: https://github.com/casadi/casadi/wiki/L_195

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L668

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L668-L670

hessian(*args)¶

hessian(DM ex, DM arg, dict opts) -> (DM , DM OUTPUT1)
hessian(SX ex, SX arg, dict opts) -> (SX , SX OUTPUT1)
hessian(MX ex, MX arg, dict opts) -> (MX , MX OUTPUT1)

Extra doc: https://github.com/casadi/casadi/wiki/L_23z

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L865

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L865-L868

horzsplit(*args)¶

horzsplit(Sparsity v, int incr) -> [Sparsity]
horzsplit(DM v, int incr) -> [DM]
horzsplit(SX v, int incr) -> [SX]
horzsplit(MX v, int incr) -> [MX]
horzsplit(Sparsity v, [int] offset) -> [Sparsity]
horzsplit(DM v, [int] offset) -> [DM]
horzsplit(SX v, [int] offset) -> [SX]
horzsplit(MX v, [int] offset) -> [MX]

1. Parameters:¶

incr: Size (width) of each group of columns

horzcat(horzsplit(x, …)) = x

seealso horzsplit_n

Extra doc: https://github.com/casadi/casadi/wiki/L_3h

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L134

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L134-L136

horzsplit_n(*args)¶

horzsplit_n(Sparsity v, int n) -> [Sparsity]
horzsplit_n(DM v, int n) -> [DM]
horzsplit_n(SX v, int n) -> [SX]
horzsplit_n(MX v, int n) -> [MX]

1. Parameters:¶

n: Number of groups of columns

Will error when the number of columns is not a multiple of n

horzcat(horzsplit(x, …)) = x

seealso horzsplit

Extra doc: https://github.com/casadi/casadi/wiki/L_277

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L149

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L149-L151

hypot(*args)¶

hypot(float x, float y) -> float
hypot(DM x, DM y) -> DM
hypot(SX x, SX y) -> SX
hypot(MX x, MX y) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L742

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L742-L744

if_else(*args)¶

if_else(DM cond, DM if_true, DM if_false, bool short_circuit) -> DM
if_else(SX cond, SX if_true, SX if_false, bool short_circuit) -> SX
if_else(MX cond, MX if_true, MX if_false, bool short_circuit) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_113

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/sx_elem.hpp#L265

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/sx_elem.hpp#L265-L267

interp1d(*args)¶

interp1d([float] x, DM v, [float] xq, str mode, bool equidistant) -> DM
interp1d([float] x, SX v, [float] xq, str mode, bool equidistant) -> SX
interp1d([float] x, MX v, [float] xq, str mode, bool equidistant) -> MX

The data-points to be interpolated are given as (x[i], v[i]). xq[j] is: used as interplating value

Extra doc: https://github.com/casadi/casadi/wiki/L_1bh

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L311

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L311-L314

inv(*args)¶

inv(DM A) -> DM
inv(SX A) -> SX
inv(MX A) -> MX
inv(DM A, str lsolver, dict opts) -> DM
inv(SX A, str lsolver, dict opts) -> SX
inv(MX A, str lsolver, dict opts) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_10y

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/sx_elem.hpp#L222

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/sx_elem.cpp#L159-L165

inv_minor(*args)¶

inv_minor(DM A) -> DM
inv_minor(SX A) -> SX
inv_minor(MX A) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1by

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L493

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L493-L493

inv_node(*args)¶

inv_node(MX x) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L807

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L807-L809

inv_skew(*args)¶

inv_skew(DM a) -> DM
inv_skew(SX a) -> SX
inv_skew(MX a) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1bw

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L481

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L481-L483

is_equal(*args)¶

is_equal(float x, float y, int depth) -> bool
is_equal(DM x, DM y, int depth) -> bool
is_equal(SX x, SX y, int depth) -> bool
is_equal(MX x, MX y, int depth) -> bool

Depth=0 checks if the expressions are identical, i.e. points to the same node.

a = x*x b = x*x

is_equal(a,b,0) will return false, but a.is_equal(a,b,1) will return true

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L703

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L703-L705

is_linear(*args)¶

is_linear(DM expr, DM var) -> bool
is_linear(SX expr, SX var) -> bool
is_linear(MX expr, MX var) -> bool

False negatives are possible (an expression may not be recognised as linear

Extra doc: https://github.com/casadi/casadi/wiki/L_1d0

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L895

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L895-L897

is_quadratic(*args)¶

is_quadratic(DM expr, DM var) -> bool
is_quadratic(SX expr, SX var) -> bool
is_quadratic(MX expr, MX var) -> bool

False negatives are possible (an expression may not be recognised as

quadratic while it really is), false positives not.

Extra doc: https://github.com/casadi/casadi/wiki/L_1d1

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L906

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L906-L908

jacobian(*args)¶

jacobian(DM ex, DM arg, dict opts) -> DM
jacobian(SX ex, SX arg, dict opts) -> SX
jacobian(MX ex, MX arg, dict opts) -> MX

Sparse matrix

Extra doc: https://github.com/casadi/casadi/wiki/L_1cv

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L799

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L799-L802

jacobian_sparsity(*args)¶

jacobian_sparsity(DM f, DM x) -> Sparsity
jacobian_sparsity(SX f, SX x) -> Sparsity
jacobian_sparsity(MX f, MX x) -> Sparsity

Equivalent to, but cheaper to compute than, jacobian(f,x). sparsity()

Extra doc: https://github.com/casadi/casadi/wiki/L_259

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L884

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L884-L886

jtimes(*args)¶

jtimes(DM ex, DM arg, DM v, bool tr) -> DM
jtimes(SX ex, SX arg, SX v, bool tr) -> SX
jtimes(MX ex, MX arg, MX v, bool tr) -> MX

This is equivalent to mul(jacobian(ex, arg), v) or mul(jacobian(ex, arg).T, v) for tr set to false and true respectively. If contrast to these

expressions, it will use directional derivatives which is typically (but not necessarily) more efficient if the complete Jacobian is not needed and v has few rows.

Extra doc: https://github.com/casadi/casadi/wiki/L_1cw

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L832

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L832-L835

kron(*args)¶

kron(Sparsity a, Sparsity b) -> Sparsity
kron(DM a, DM b) -> DM
kron(SX a, SX b) -> SX
kron(MX a, MX b) -> MX

Creates a block matrix in which each element (i, j) is a_ij*b

Extra doc: https://github.com/casadi/casadi/wiki/L_47

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L451

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L451-L453

ldivide(*args)¶

ldivide(float x, float y) -> float
ldivide(DM x, DM y) -> DM
ldivide(SX x, SX y) -> SX
ldivide(MX x, MX y) -> MX

ldl(*args)¶

ldl(DM A, bool amd) -> (DM OUTPUT1, DM OUTPUT2, [int] OUTPUT3)
ldl(SX A, bool amd) -> (SX OUTPUT1, SX OUTPUT2, [int] OUTPUT3)

Returns D and the strictly upper triangular entries of L^T I.e. ones on the

definite matrices.

Extra doc: https://github.com/casadi/casadi/wiki/L_18w

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L573

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L573-L576

ldl_solve(*args)¶

ldl_solve(DM b, DM D, DM LT, [int] p) -> DM
ldl_solve(SX b, SX D, SX LT, [int] p) -> SX

Extra doc: https://github.com/casadi/casadi/wiki/L_18x

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L582

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L582-L585

le(*args)¶

le(float x, float y) -> float
le(DM x, DM y) -> DM
le(SX x, SX y) -> SX
le(MX x, MX y) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L146

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L146-L148

linear_coeff(*args)¶

linear_coeff(DM ex, DM arg, bool check) -> (DM OUTPUT1, DM OUTPUT2)
linear_coeff(SX ex, SX arg, bool check) -> (SX OUTPUT1, SX OUTPUT2)
linear_coeff(MX ex, MX arg, bool check) -> (MX OUTPUT1, MX OUTPUT2)

A x + b

1. Parameters:¶

check[in]: When true (default)m, A is checked to be independent of x. Provided to

Extra doc: https://github.com/casadi/casadi/wiki/L_1d3

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L933

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L933-L936

linearize(*args)¶

linearize(DM f, DM x, DM x0) -> DM
linearize(SX f, SX x, SX x0) -> SX
linearize(MX f, MX x, MX x0) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1cs

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L740

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L740-L743

linspace(*args)¶

linspace(DM a, DM b, int nsteps) -> DM
linspace(SX a, SX b, int nsteps) -> SX
linspace(MX a, MX b, int nsteps) -> MX

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/casadi_misc.hpp#L836

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/casadi_misc.hpp#L836-L847

log(*args)¶

log(float x) -> float
log(DM x) -> DM
log(SX x) -> SX
log(MX x) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L470

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L470-L472

log10(*args)¶

log10(float x) -> float
log10(DM x) -> DM
log10(SX x) -> SX
log10(MX x) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L482

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L482-L484

log1p(*args)¶

log1p(float x) -> float
log1p(DM x) -> DM
log1p(SX x) -> SX
log1p(MX x) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L494

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L494-L496

logsumexp(*args)¶

logsumexp(DM a) -> DM
logsumexp(SX a) -> SX
logsumexp(MX a) -> MX
logsumexp(DM a, DM margin) -> DM
logsumexp(SX a, SX margin) -> SX
logsumexp(MX a, MX margin) -> MX

Scaled such that max(x) <= logsumexp(x, margin) <= max(x)+margin

Extra doc: https://github.com/casadi/casadi/wiki/L_1bs

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L451

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L451-L454

low(*args)¶

low(MX v, MX p, dict options) -> MX

If failed, returns the number of rows

Extra doc: https://github.com/casadi/casadi/wiki/L_r8

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L713

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L713-L715

lt(*args)¶

lt(float x, float y) -> float
lt(DM x, DM y) -> DM
lt(SX x, SX y) -> SX
lt(MX x, MX y) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L131

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L131-L133

mac(*args)¶

mac(Sparsity X, Sparsity Y, Sparsity Z) -> Sparsity
mac(DM X, DM Y, DM Z) -> DM
mac(SX X, SX Y, SX Z) -> SX
mac(MX X, MX Y, MX Z) -> MX

Matrix product of two matrices (x and y), adding the result to a third

matrix z. The result has the same sparsity pattern as C meaning that other entries of (x*y) are ignored. The operation is equivalent to:

z+mtimes(x,y).project(z.sparsity()).

Extra doc: https://github.com/casadi/casadi/wiki/L_3x

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L358

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L358-L360

matrix_expand(*args)¶

matrix_expand(MX e, [MX] boundary, dict options) -> MX
matrix_expand([MX] e, [MX] boundary, dict options) -> [MX]

Expand the given expression e, optionally supplying expressions contained in it at which expansion should stop.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L759

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L759-L763

minor(*args)¶

minor(DM x, int i, int j) -> DM
minor(SX x, int i, int j) -> SX

Extra doc: https://github.com/casadi/casadi/wiki/L_18q

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L511

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L511-L513

minus(*args)¶

minus(float x, float y) -> float
minus(DM x, DM y) -> DM
minus(SX x, SX y) -> SX
minus(MX x, MX y) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L83

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L83-L85

mldivide(*args)¶

mldivide(DM x, DM y) -> DM
mldivide(SX x, SX y) -> SX
mldivide(MX x, MX y) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1bm

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L383

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L383-L385

mmax(*args)¶

mmax(DM x) -> DM
mmax(SX x) -> SX
mmax(MX x) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1d9

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L997

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L997-L999

mmin(*args)¶

mmin(DM x) -> DM
mmin(SX x) -> SX
mmin(MX x) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1d8

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L988

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L988-L990

mpower(*args)¶

mpower(DM x, DM n) -> DM
mpower(SX x, SX n) -> SX
mpower(MX x, MX n) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1bi

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L319

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L319-L321

mrdivide(*args)¶

mrdivide(DM x, DM y) -> DM
mrdivide(SX x, SX y) -> SX
mrdivide(MX x, MX y) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1bl

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L376

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L376-L378

mtaylor(*args)¶

mtaylor(DM ex, DM x, DM a, int order) -> DM
mtaylor(SX ex, SX x, SX a, int order) -> SX
mtaylor(DM ex, DM x, DM a, int order, [int] order_contributions) -> DM
mtaylor(SX ex, SX x, SX a, int order, [int] order_contributions) -> SX

Do Taylor expansions until the aggregated order of a term is equal to

‘order’. The aggregated order of $x^n y^m$ equals $n+m$.

The argument order_contributions can denote how match each variable

contributes to the aggregated order. If x=[x, y] and

order_contributions=[1, 2], then the aggregated order of $x^n y^m$ equals $1n+2m$.

Example usage

>>> taylor(sin(x+y),[x, y],[a, b], 1)

>>> taylor(sin(x+y),[x, y],[0, 0], 4)

>>> taylor(sin(x+y),[x, y],[0, 0], 4,[1, 2])

Extra doc: https://github.com/casadi/casadi/wiki/L_23s

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L801

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L801-L805

mtimes(*args)¶

mtimes([Sparsity] args) -> Sparsity
mtimes([DM] args) -> DM
mtimes([SX] args) -> SX
mtimes([MX] args) -> MX
mtimes(Sparsity x, Sparsity y) -> Sparsity
mtimes(DM x, DM y) -> DM
mtimes(SX x, SX y) -> SX
mtimes(MX x, MX y) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_3w

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L345

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L345-L347

n_nodes(*args)¶

n_nodes(DM A) -> int
n_nodes(SX A) -> int
n_nodes(MX A) -> int

ne(*args)¶

ne(float x, float y) -> float
ne(DM x, DM y) -> DM
ne(SX x, SX y) -> SX
ne(MX x, MX y) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L206

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L206-L208

no_grad(*args)¶

no_grad(MX expr) -> MX

variables.

seealso stop_diff

Extra doc: https://github.com/casadi/casadi/wiki/L_25m

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L832

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L832-L834

no_hess(*args)¶

no_hess(MX expr) -> MX

variables.

seealso stop_diff

Extra doc: https://github.com/casadi/casadi/wiki/L_25n

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L841

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L841-L843

norm_0_mul(*args)¶

norm_0_mul(Sparsity x, Sparsity y) -> int
norm_0_mul(DM x, DM y) -> int
norm_0_mul(SX x, SX y) -> int
norm_0_mul(MX x, MX y) -> int

norm_1(*args)¶

norm_1(DM x) -> DM
norm_1(SX x) -> SX
norm_1(MX x) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1c6

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L539

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L539-L539

norm_2(*args)¶

norm_2(DM x) -> DM
norm_2(SX x) -> SX
norm_2(MX x) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1c5

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L534

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L534-L534

norm_fro(*args)¶

norm_fro(DM x) -> DM
norm_fro(SX x) -> SX
norm_fro(MX x) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1c4

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L529

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L529-L529

norm_inf(*args)¶

norm_inf(DM x) -> DM
norm_inf(SX x) -> SX
norm_inf(MX x) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1c7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L544

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L544-L544

norm_inf_mul(*args)¶

norm_inf_mul(DM x, DM y) -> DM
norm_inf_mul(SX x, SX y) -> SX

Extra doc: https://github.com/casadi/casadi/wiki/L_190

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L605

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L605-L607

nullspace(*args)¶

nullspace(DM A) -> DM
nullspace(SX A) -> SX
nullspace(MX A) -> MX

Finds Z m-by-(m-n) such that AZ = 0 with A n-by-m with m > n

Assumes A is full rank

Inspired by Numerical Methods in Scientific Computing by Ake Bjorck

Extra doc: https://github.com/casadi/casadi/wiki/L_1cb

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L579

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L579-L581

pinv(*args)¶

pinv(DM A) -> DM
pinv(SX A) -> SX
pinv(MX A) -> MX
pinv(DM A, str lsolver, dict opts) -> DM
pinv(SX A, str lsolver, dict opts) -> SX
pinv(MX A, str lsolver, dict opts) -> MX

If the matrix A is fat (size1>size2), mul(A, pinv(A)) is unity. If the

matrix A is slender (size2<size1), mul(pinv(A), A) is unity.

Extra doc: https://github.com/casadi/casadi/wiki/L_1cu

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L767

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L767-L770

plus(*args)¶

plus(float x, float y) -> float
plus(DM x, DM y) -> DM
plus(SX x, SX y) -> SX
plus(MX x, MX y) -> MX

poly_coeff(*args)¶

poly_coeff(DM ex, DM x) -> DM
poly_coeff(SX ex, SX x) -> SX

1. Parameters:¶

ex: Scalar expression that represents a polynomial

x: Scalar symbol that the polynomial is build up with

Extra doc: https://github.com/casadi/casadi/wiki/L_197

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L813

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L813-L816

poly_roots(*args)¶

poly_roots(DM p) -> DM
poly_roots(SX p) -> SX

This will only work for polynomials up to order 3 It is assumed that the roots are real.

Extra doc: https://github.com/casadi/casadi/wiki/L_198

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L824

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L824-L826

polyval(*args)¶

polyval(DM p, DM x) -> DM
polyval(SX p, SX x) -> SX
polyval(MX p, MX x) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1cc

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L586

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L586-L588

power(*args)¶

power(float x, float n) -> float
power(DM x, DM n) -> DM
power(SX x, SX n) -> SX
power(MX x, MX n) -> MX

print_operator(*args)¶

print_operator(DM xb, [str] args) -> str
print_operator(SX xb, [str] args) -> str
print_operator(MX xb, [str] args) -> str

arguments.

Extra doc: https://github.com/casadi/casadi/wiki/L_1d4

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L952

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L952-L954

project(*args)¶

project(DM A, Sparsity sp, bool intersect) -> DM
project(SX A, Sparsity sp, bool intersect) -> SX
project(MX A, Sparsity sp, bool intersect) -> MX

nonzeros taken from an existing matrix

Extra doc: https://github.com/casadi/casadi/wiki/L_1ch

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L626

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L626-L629

pw_const(*args)¶

pw_const(DM t, DM tval, DM val) -> DM
pw_const(SX t, SX tval, SX val) -> SX

Create a piecewise constant function with n=val.size() intervals

Inputs:

1. Parameters:¶

t: a scalar variable (e.g. time)

tval: vector with the discrete values of t at the interval transitions

(length n-1)

val: vector with the value of the function for each interval (length n)

Extra doc: https://github.com/casadi/casadi/wiki/L_193

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L635

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L635-L639

pw_lin(*args)¶

pw_lin(DM t, DM tval, DM val) -> DM
pw_lin(SX t, SX tval, SX val) -> SX

Create a piecewise linear function

Create a piecewise linear function:

Inputs:

tval vector with the the discrete values of t (monotonically increasing)

val vector with the corresponding function values (same length as tval)

Extra doc: https://github.com/casadi/casadi/wiki/L_194

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L652

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L652-L655

qr(*args)¶

qr(DM A) -> (DM OUTPUT1, DM OUTPUT2)
qr(SX A) -> (SX OUTPUT1, SX OUTPUT2)

More stable than the classical Gram-Schmidt, but may break down if the: rows of A are nearly linearly dependent See J. Demmel: Applied
Numerical Linear: Algebra (algorithm 3.1.). Note that in SWIG, Q and R

are returned by value.

Extra doc: https://github.com/casadi/casadi/wiki/L_18s

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L530

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L530-L532

qr_solve(*args)¶

qr_solve(DM b, DM v, DM r, DM beta, [int] prinv, [int] pc, bool tr) -> DM
qr_solve(SX b, SX v, SX r, SX beta, [int] prinv, [int] pc, bool tr) -> SX

Extra doc: https://github.com/casadi/casadi/wiki/L_18u

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L549

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L549-L554

qr_sparse(*args)¶

qr_sparse(DM A, bool amd) -> (DM OUTPUT1, DM OUTPUT2, DM OUTPUT3, [int] OUTPUT4, [int] OUTPUT5)
qr_sparse(SX A, bool amd) -> (SX OUTPUT1, SX OUTPUT2, SX OUTPUT3, [int] OUTPUT4, [int] OUTPUT5)

See T. Davis: Direct Methods for Sparse Linear Systems

Extra doc: https://github.com/casadi/casadi/wiki/L_18t

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L539

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L539-L543

quadratic_coeff(*args)¶

quadratic_coeff(DM ex, DM arg, bool check) -> (DM OUTPUT1, DM OUTPUT2, DM OUTPUT3)
quadratic_coeff(SX ex, SX arg, bool check) -> (SX OUTPUT1, SX OUTPUT2, SX OUTPUT3)
quadratic_coeff(MX ex, MX arg, bool check) -> (MX OUTPUT1, MX OUTPUT2, MX OUTPUT3)

1/2*x’ A x + b’ x + c

e = 0.5*bilin(A,x,x)+dot(b,x)+c

1. Parameters:¶

check[in]: When true (default), A is checked to be independent of x. Provided to deal with false positive dependency checks.

Extra doc: https://github.com/casadi/casadi/wiki/L_1d2

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L920

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L920-L923

ramp(*args)¶

ramp(DM x) -> DM
ramp(SX x) -> SX

[ begin {cases} R(x) = 0 & x <= 1 \ R(x) = x & x > 1

\ end {cases} ]

Also called: slope function

Extra doc: https://github.com/casadi/casadi/wiki/L_23p

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L717

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L717-L719

rank1(*args)¶

rank1(DM A, DM alpha, DM x, DM y) -> DM
rank1(SX A, SX alpha, SX x, SX y) -> SX
rank1(MX A, MX alpha, MX x, MX y) -> MX

Calculates A + 1/2 * alpha * x*y’

Extra doc: https://github.com/casadi/casadi/wiki/L_1bp

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L422

rdivide(*args)¶

rdivide(float x, float y) -> float
rdivide(DM x, DM y) -> DM
rdivide(SX x, SX y) -> SX
rdivide(MX x, MX y) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L115

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L115-L117

rectangle(*args)¶

rectangle(DM x) -> DM
rectangle(SX x) -> SX

[ begin {cases} Pi(x) = 1 & |x| < 1/2 \ Pi(x) =: 1/2

& |x| = 1/2 \ Pi(x) = 0 & |x| > 1/2 \ end {cases} ]

Also called: gate function, block function, band function, pulse function, window function

Extra doc: https://github.com/casadi/casadi/wiki/L_23n

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L685

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L685-L687

remainder(*args)¶

remainder(float x, float y) -> float
remainder(DM x, DM y) -> DM
remainder(SX x, SX y) -> SX
remainder(MX x, MX y) -> MX

This Function follows the convention of https://en.cppreference.com/w/c/numeric/math/remainder

Notably: remainder(5,3) -> -1

remainder(5,-3) -> -1

remainder(-5,3) -> 1

remainder(-5,-3) -> 1

This is equivalent to Python’s math.remainder. There is no equivalence: in

Matlab.

seealso fmod

Extra doc: https://github.com/casadi/casadi/wiki/L_24x

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L634

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L634-L636

repmat(*args)¶

repmat(Sparsity A, int n, int m) -> Sparsity
repmat(Sparsity A, (int,int) rc) -> Sparsity
repmat(DM A, int n, int m) -> DM
repmat(DM A, (int,int) rc) -> DM
repmat(SX A, int n, int m) -> SX
repmat(SX A, (int,int) rc) -> SX
repmat(MX A, int n, int m) -> MX
repmat(MX A, (int,int) rc) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_49

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L465

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L465-L467

repsum(*args)¶

repsum(DM A, int n, int m) -> DM
repsum(SX A, int n, int m) -> SX
repsum(MX A, int n, int m) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1d7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L980

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L980-L982

reshape(*args)¶

reshape(Sparsity a, (int,int) rc) -> Sparsity
reshape(Sparsity a, Sparsity sp) -> Sparsity
reshape(DM a, (int,int) rc) -> DM
reshape(DM a, Sparsity sp) -> DM
reshape(SX a, (int,int) rc) -> SX
reshape(SX a, Sparsity sp) -> SX
reshape(MX a, (int,int) rc) -> MX
reshape(MX a, Sparsity sp) -> MX
reshape(Sparsity a, int nrow, int ncol) -> Sparsity
reshape(DM a, int nrow, int ncol) -> DM
reshape(SX a, int nrow, int ncol) -> SX
reshape(MX a, int nrow, int ncol) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_42

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L407

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L407-L409

shared(*args)¶

shared([DM] ex, str v_prefix, str v_suffix) -> ([DM] OUTPUT1, [DM] OUTPUT2, [DM] OUTPUT3)
shared([SX] ex, str v_prefix, str v_suffix) -> ([SX] OUTPUT1, [SX] OUTPUT2, [SX] OUTPUT3)
shared([MX] ex, str v_prefix, str v_suffix) -> ([MX] OUTPUT1, [MX] OUTPUT2, [MX] OUTPUT3)

Extra doc: https://github.com/casadi/casadi/wiki/L_b0

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/shared_object.hpp#L198

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/shared_object.cpp#L141-L147

sign(*args)¶

sign(float x) -> float
sign(DM x) -> DM
sign(SX x) -> SX
sign(MX x) -> MX

sign(x) := -1 for x<0 sign(x) := 1 for x>0, sign(0) := 0 sign(NaN) := NaN

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L571

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L571-L573

simplify(*args)¶

simplify(float x) -> float
simplify(DM x) -> DM
simplify(SX x) -> SX
simplify(MX x) -> MX

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L944

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L944-L946

sin(*args)¶

sin(float x) -> float
sin(DM x) -> DM
sin(SX x) -> SX
sin(MX x) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_p3

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L314

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L314-L316

sinh(*args)¶

sinh(float x) -> float
sinh(DM x) -> DM
sinh(SX x) -> SX
sinh(MX x) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L398

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L398-L400

skew(*args)¶

skew(DM a) -> DM
skew(SX a) -> SX
skew(MX a) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1bv

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L474

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L474-L476

soc(*args)¶

soc(DM x, DM y) -> DM
soc(SX x, SX y) -> SX
soc(MX x, MX y) -> MX

1. Parameters:¶

x: vector expression of size n

y: scalar expression

soc(x,y) computes [y*eye(n) x; x’ y]

soc(x,y) positive semi definite <=> || x ||_2 <= y

Extra doc: https://github.com/casadi/casadi/wiki/L_1bj

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L334

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L334-L336

solve(*args)¶

solve(DM A, DM b) -> DM
solve(SX A, SX b) -> SX
solve(MX A, MX b) -> MX
solve(DM A, DM b, str lsolver, dict opts) -> DM
solve(SX A, SX b, str lsolver, dict opts) -> SX
solve(MX A, MX b, str lsolver, dict opts) -> MX

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/optistack.hpp#L221

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/optistack.cpp#L161-L167

sparsify(*args)¶

sparsify(DM A, float tol) -> DM
sparsify(SX A, float tol) -> SX

Extra doc: https://github.com/casadi/casadi/wiki/L_191

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L613

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L613-L615

sparsity_cast(*args)¶

sparsity_cast(Sparsity a, Sparsity sp) -> Sparsity
sparsity_cast(DM a, Sparsity sp) -> DM
sparsity_cast(SX a, Sparsity sp) -> SX
sparsity_cast(MX a, Sparsity sp) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_24z

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L414

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L414-L416

sprank(*args)¶

sprank(Sparsity A) -> int
sprank(DM A) -> int
sprank(SX A) -> int
sprank(MX A) -> int

sqrt(*args)¶

sqrt(float x) -> float
sqrt(DM x) -> DM
sqrt(SX x) -> SX
sqrt(MX x) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_p1

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L290

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L290-L292

stop_diff(*args)¶

stop_diff(MX expr, int order) -> MX
stop_diff(MX expr, MX var, int order) -> MX

variables.

Extra doc: https://github.com/casadi/casadi/wiki/L_25o

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L849

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L849-L851

substitute(*args)¶

substitute(DM ex, DM v, DM vdef) -> DM
substitute([DM] ex, [DM] v, [DM] vdef) -> [DM]
substitute(SX ex, SX v, SX vdef) -> SX
substitute([SX] ex, [SX] v, [SX] vdef) -> [SX]
substitute(MX ex, MX v, MX vdef) -> MX
substitute([MX] ex, [MX] v, [MX] vdef) -> [MX]

Extra doc: https://github.com/casadi/casadi/wiki/L_1cm

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L673

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L673-L676

substitute_inplace(*args)¶

substitute_inplace([DM] v, bool reverse) -> ([DM] INOUT1, [DM] INOUT2)
substitute_inplace([SX] v, bool reverse) -> ([SX] INOUT1, [SX] INOUT2)
substitute_inplace([MX] v, bool reverse) -> ([MX] INOUT1, [MX] INOUT2)

Substitute variables v out of the expressions vdef sequentially, as well as

Extra doc: https://github.com/casadi/casadi/wiki/L_1cn

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L685

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L685-L689

sum1(*args)¶

sum1(Sparsity x) -> Sparsity
sum1(DM x) -> DM
sum1(SX x) -> SX
sum1(MX x) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_4p

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L586

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L586-L586

sum2(*args)¶

sum2(Sparsity x) -> Sparsity
sum2(DM x) -> DM
sum2(SX x) -> SX
sum2(MX x) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_4q

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L591

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L591-L591

sumsqr(*args)¶

sumsqr(DM X) -> DM
sumsqr(SX X) -> SX
sumsqr(MX X) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1bq

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L429

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L429-L431

symvar(*args)¶

symvar(DM x) -> [DM]
symvar(SX x) -> [SX]
symvar(MX x) -> [MX]

Returned vector is ordered according to the order of variable()/parameter(): calls used to create the variables

Extra doc: https://github.com/casadi/casadi/wiki/L_1u

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/optistack.hpp#L548

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/optistack.cpp#L440-L446

tan(*args)¶

tan(float x) -> float
tan(DM x) -> DM
tan(SX x) -> SX
tan(MX x) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_p5

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L338

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L338-L340

tangent(*args)¶

tangent(DM ex, DM arg) -> DM
tangent(SX ex, SX arg) -> SX
tangent(MX ex, MX arg) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_23y

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L819

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L819-L821

tanh(*args)¶

tanh(float x) -> float
tanh(DM x) -> DM
tanh(SX x) -> SX
tanh(MX x) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_p9

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L386

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L386-L388

taylor(*args)¶

taylor(DM ex, DM x, DM a, int order) -> DM
taylor(SX ex, SX x, SX a, int order) -> SX

Calculate the Taylor expansion of expression ‘ex’ up to order ‘order’ with respect to variable ‘x’ around the point ‘a’

$(x)=f(a)+f’(a)(x-a)+f’’(a)frac

{(x-a)^2}{2!}+f’’’(a)frac{(x-a)^3}{3!}+ldots$

Example usage:

>>> taylor(sin(x), x)

>>   x

Extra doc: https://github.com/casadi/casadi/wiki/L_23q

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L758

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L758-L760

times(*args)¶

times(float x, float y) -> float
times(DM x, DM y) -> DM
times(SX x, SX y) -> SX
times(MX x, MX y) -> MX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L99

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_expression.hpp#L99-L101

trace(*args)¶

trace(DM a) -> DM
trace(SX a) -> SX
trace(MX a) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1c1

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L514

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L514-L514

transpose(*args)¶

transpose(Sparsity X) -> Sparsity
transpose(DM X) -> DM
transpose(SX X) -> SX
transpose(MX X) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_3y

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L365

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L365-L367

triangle(*args)¶

triangle(DM x) -> DM
triangle(SX x) -> SX

[ begin {cases} Lambda(x) = 0 & |x| >= 1 \ Lambda(x)

Extra doc: https://github.com/casadi/casadi/wiki/L_23o

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L700

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L700-L702

tril(*args)¶

tril(Sparsity a, bool includeDiagonal) -> Sparsity
tril(DM a, bool includeDiagonal) -> DM
tril(SX a, bool includeDiagonal) -> SX
tril(MX a, bool includeDiagonal) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_46

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L442

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L442-L444

tril2symm(*args)¶

tril2symm(DM a) -> DM
tril2symm(SX a) -> SX
tril2symm(MX a) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1c2

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L519

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L519-L519

triu(*args)¶

triu(Sparsity a, bool includeDiagonal) -> Sparsity
triu(DM a, bool includeDiagonal) -> DM
triu(SX a, bool includeDiagonal) -> SX
triu(MX a, bool includeDiagonal) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_45

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L435

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L435-L437

triu2symm(*args)¶

triu2symm(DM a) -> DM
triu2symm(SX a) -> SX
triu2symm(MX a) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1c3

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L524

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L524-L524

unite(*args)¶

unite(DM A, DM B) -> DM
unite(SX A, SX B) -> SX
unite(MX A, MX B) -> MX

Extra doc: https://github.com/casadi/casadi/wiki/L_1ce

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L603

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L603-L605

vec(*args)¶

vec(Sparsity a) -> Sparsity
vec(DM a) -> DM
vec(SX a) -> SX
vec(MX a) -> MX

Reshapes/vectorizes the matrix such that the shape becomes (expr.numel(), 1). Columns are stacked on top of each other. Same as reshape(expr, expr.numel(), 1)

a c b d

a b c d

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L386

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/sparsity_interface.hpp#L386-L388

which_depends(*args)¶

which_depends(DM expr, DM var, int order, bool tr) -> [bool]
which_depends(SX expr, SX var, int order, bool tr) -> [bool]
which_depends(MX expr, MX var, int order, bool tr) -> [bool]

Extra doc: https://github.com/casadi/casadi/wiki/L_1cz

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L874

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/generic_matrix.hpp#L874-L877

2. Classes¶

2.1. DM¶

class DM(*args)¶

.. py:method:: DM.assign(*args)

static binary(*args)¶

binary(int op, DM x, DM y) -> DM

clear(*args)¶

clear(self)

dep(*args)¶

dep(self, int ch) -> DM

static deserialize(*args)¶

deserialize(std::istream & stream) -> DM
deserialize(casadi::DeserializingStream & s) -> DM
deserialize(str s) -> DM

disp(*args)¶

disp(self, bool more)

Print a representation of the object.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L877

element_hash(*args)¶

element_hash(self) -> int

elements(*args)¶

elements(self) -> [float]

Get all elements.

Extra doc: https://github.com/casadi/casadi/wiki/L_1a3

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1150

enlarge(*args)¶

enlarge(self, int nrow, int ncol, [int] rr, [int] cc, bool ind1)

Enlarge matrix.

Make the matrix larger by inserting empty rows and columns, keeping the existing non-zeros

Extra doc: https://github.com/casadi/casadi/wiki/L_19i

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L952

erase(*args)¶

erase(self, [int] rr, bool ind1)
erase(self, [int] rr, [int] cc, bool ind1)

Erase a submatrix (leaving structural zeros in its place)

Erase elements of a matrix

Extra doc: https://github.com/casadi/casadi/wiki/L_19g

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L937

erase(self, [int] rr, bool ind1)

[INTERNAL] Erase a submatrix (leaving structural zeros in its place)

Erase elements of a matrix

Extra doc: https://github.com/casadi/casadi/wiki/L_19g

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L937

erase(self, [int] rr, [int] cc, bool ind1)

[INTERNAL] Erase a submatrix (leaving structural zeros in its place)

Erase rows and/or columns of a matrix

Extra doc: https://github.com/casadi/casadi/wiki/L_19f

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L929

export_code(*args)¶

export_code(self, str lang, dict options)

static eye(*args)¶

eye(int n) -> DM

static from_file(*args)¶

from_file(str filename, str format_hint) -> DM

full(*args)¶

full(self) -> PyObject *

get(*args)¶

get(self, bool ind1, Sparsity sp) -> DM
get(self, bool ind1, Slice rr) -> DM
get(self, bool ind1, IM rr) -> DM
get(self, bool ind1, Slice rr, Slice cc) -> DM
get(self, bool ind1, Slice rr, IM cc) -> DM
get(self, bool ind1, IM rr, Slice cc) -> DM
get(self, bool ind1, IM rr, IM cc) -> DM

static get_free(*args)¶

get_free(Function f) -> [DM]

static get_input(*args)¶

get_input(Function f) -> [DM]

static get_max_depth(*args)¶

get_max_depth() -> int

get_nz(*args)¶

get_nz(self, bool ind1, Slice k) -> DM
get_nz(self, bool ind1, IM k) -> DM

has_duplicates(*args)¶

has_duplicates(self) -> bool

has_nz(*args)¶

has_nz(self, int rr, int cc) -> bool

Returns true if the matrix has a non-zero at location rr, cc.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L219

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_impl.hpp#L65-L67

has_zeros(*args)¶

has_zeros(self) -> bool

Check if the matrix has any zero entries which are not structural zeros.

Extra doc: https://github.com/casadi/casadi/wiki/L_1a1

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1140

static inf(*args)¶

inf(int nrow, int ncol) -> DM
inf((int,int) rc) -> DM
inf(Sparsity sp) -> DM

create a matrix with all inf

Extra doc: https://github.com/casadi/casadi/wiki/L_19k

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1005

inf(int nrow, int ncol)

[INTERNAL] create a matrix with all inf

Extra doc: https://github.com/casadi/casadi/wiki/L_19k

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1004

inf((int,int) rc)

[INTERNAL] create a matrix with all inf

Extra doc: https://github.com/casadi/casadi/wiki/L_19k

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1005

inf(Sparsity sp)

[INTERNAL] create a matrix with all inf

Extra doc: https://github.com/casadi/casadi/wiki/L_19k

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1003

info(*args)¶

info(self) -> dict

is_commutative(*args)¶

is_commutative(self) -> bool

is_constant(*args)¶

is_constant(self) -> bool

Check if the matrix is constant (note that false negative answers are possible)

Extra doc: https://github.com/casadi/casadi/wiki/L_19v

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1100

is_eye(*args)¶

is_eye(self) -> bool

check if the matrix is an identity matrix (note that false negative answers

are possible)

Extra doc: https://github.com/casadi/casadi/wiki/L_1a0

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1129

is_integer(*args)¶

is_integer(self) -> bool

Check if the matrix is integer-valued.

(note that false negative answers are possible)

Extra doc: https://github.com/casadi/casadi/wiki/L_19w

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1107

is_leaf(*args)¶

is_leaf(self) -> bool

is_minus_one(*args)¶

is_minus_one(self) -> bool

check if the matrix is -1 (note that false negative answers are

possible)

Extra doc: https://github.com/casadi/casadi/wiki/L_19z

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1122

is_one(*args)¶

is_one(self) -> bool

check if the matrix is 1 (note that false negative answers are

possible)

Extra doc: https://github.com/casadi/casadi/wiki/L_19y

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1117

is_op(*args)¶

is_op(self, int op) -> bool

is_regular(*args)¶

is_regular(self) -> bool

is_smooth(*args)¶

is_smooth(self) -> bool

is_symbolic(*args)¶

is_symbolic(self) -> bool

is_valid_input(*args)¶

is_valid_input(self) -> bool

is_zero(*args)¶

is_zero(self) -> bool

check if the matrix is 0 (note that false negative answers are

possible)

Extra doc: https://github.com/casadi/casadi/wiki/L_19x

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1112

static matrix_matrix(*args)¶

matrix_matrix(int op, DM x, DM y) -> DM

static matrix_scalar(*args)¶

matrix_scalar(int op, DM x, DM y) -> DM

n_dep(*args)¶

n_dep(self) -> int

name(*args)¶

name(self) -> str

static nan(*args)¶

nan(int nrow, int ncol) -> DM
nan((int,int) rc) -> DM
nan(Sparsity sp) -> DM

create a matrix with all nan

Extra doc: https://github.com/casadi/casadi/wiki/L_19l

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1014

nan(int nrow, int ncol)

[INTERNAL] create a matrix with all nan

Extra doc: https://github.com/casadi/casadi/wiki/L_19l

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1013

nan((int,int) rc)

[INTERNAL] create a matrix with all nan

Extra doc: https://github.com/casadi/casadi/wiki/L_19l

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1014

nan(Sparsity sp)

[INTERNAL] create a matrix with all nan

Extra doc: https://github.com/casadi/casadi/wiki/L_19l

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1012

nonzeros(*args)¶

nonzeros(self) -> [float]

Get all nonzeros.

Extra doc: https://github.com/casadi/casadi/wiki/L_1a4

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1157

op(*args)¶

op(self) -> int

print_dense(*args)¶

print_dense(self, bool truncate)

Print dense matrix-stype.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L889

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_impl.hpp#L686-L688

print_scalar(*args)¶

print_scalar(self)

Print scalar.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L883

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_impl.hpp#L609-L633

print_sparse(*args)¶

print_sparse(self, bool truncate)

Print sparse matrix style.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L892

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_impl.hpp#L691-L693

print_split(*args)¶

print_split(self) -> ([str] OUTPUT, [str] OUTPUT)

Get strings corresponding to the nonzeros and the interdependencies.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L873

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_impl.hpp#L696-L700

print_vector(*args)¶

print_vector(self, bool truncate)

Print vector-style.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L886

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_impl.hpp#L636-L638

printme(*args)¶

printme(self, DM y) -> DM

static rand(*args)¶

rand(int nrow, int ncol) -> DM
rand((int,int) rc) -> DM
rand(Sparsity sp) -> DM

Create a matrix with uniformly distributed random numbers.

Extra doc: https://github.com/casadi/casadi/wiki/L_1ab

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1216

rand(Sparsity sp)

rand(int nrow, int ncol)

[INTERNAL] Create a matrix with uniformly distributed random numbers.

Extra doc: https://github.com/casadi/casadi/wiki/L_1ab

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1212

rand((int,int) rc)

[INTERNAL] Create a matrix with uniformly distributed random numbers.

Extra doc: https://github.com/casadi/casadi/wiki/L_1ab

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1216

remove(*args)¶

remove(self, [int] rr, [int] cc)

Remove columns and rows.

Remove/delete rows and/or columns of a matrix

Extra doc: https://github.com/casadi/casadi/wiki/L_19h

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L944

reserve(*args)¶

reserve(self, int nnz)
reserve(self, int nnz, int ncol)

reset_input(*args)¶

reset_input(self)

resize(*args)¶

resize(self, int nrow, int ncol)

static rng(*args)¶

rng(int seed)

static scalar_matrix(*args)¶

scalar_matrix(int op, DM x, DM y) -> DM

serialize(*args)¶

serialize(self) -> str
serialize(self, casadi::SerializingStream & s)

Serialize an object.

Extra doc: https://github.com/casadi/casadi/wiki/L_1ah

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1264

serialize(self, casadi::SerializingStream & s)

[INTERNAL] Serialize an object.

Extra doc: https://github.com/casadi/casadi/wiki/L_1ah

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1264

serialize(self)

[INTERNAL] Serialize.

Extra doc: https://github.com/casadi/casadi/wiki/L_1ae

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1249

set(*args)¶

set(self, DM m, bool ind1, Sparsity sp)
set(self, DM m, bool ind1, Slice rr)
set(self, DM m, bool ind1, IM rr)
set(self, DM m, bool ind1, Slice rr, Slice cc)
set(self, DM m, bool ind1, Slice rr, IM cc)
set(self, DM m, bool ind1, IM rr, Slice cc)
set(self, DM m, bool ind1, IM rr, IM cc)

static set_max_depth(*args)¶

set_max_depth(int eq_depth)

set_nz(*args)¶

set_nz(self, DM m, bool ind1, Slice k)
set_nz(self, DM m, bool ind1, IM k)

static set_precision(*args)¶

set_precision(int precision)

static set_scientific(*args)¶

set_scientific(bool scientific)

static set_width(*args)¶

set_width(int width)

sparse(*args)¶

sparse(self) -> PyObject *

sparsity(*args)¶

sparsity(self) -> Sparsity

Get an owning reference to the sparsity pattern.

Extra doc: https://github.com/casadi/casadi/wiki/L_19j

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L979

str(*args)¶

str(self, bool more) -> str

Get string representation.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L880

to_file(*args)¶

to_file(self, str filename, str format)

Export numerical matrix to file

Supported formats:

*   - .mtx   Matrix Market (sparse)
*   - .txt   Ascii full precision representation (sparse)
*            Whitespace separated, aligned.
*            Comments with # % or /
*            Uses C locale
*            Structural zeros represented by 00
*            Does not scale well for large sparse matrices
*

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1284

static triplet(*args)¶

triplet([int] row, [int] col, DM d) -> DM
triplet([int] row, [int] col, DM d, (int,int) rc) -> DM
triplet([int] row, [int] col, DM d, int nrow, int ncol) -> DM

static type_name(*args)¶

type_name() -> str

static unary(*args)¶

unary(int op, DM x) -> DM

2.2. SX¶

class SX(*args)¶

.. py:method:: SX.binary(*args)

clear(*args)¶

clear(self)

dep(*args)¶

dep(self, int ch) -> SX

static deserialize(*args)¶

deserialize(std::istream & stream) -> SX
deserialize(casadi::DeserializingStream & s) -> SX
deserialize(str s) -> SX

disp(*args)¶

disp(self, bool more)

Print a representation of the object.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L877

element_hash(*args)¶

element_hash(self) -> int

elements(*args)¶

elements(self) -> [SXElem]

Get all elements.

Extra doc: https://github.com/casadi/casadi/wiki/L_1a3

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1150

enlarge(*args)¶

enlarge(self, int nrow, int ncol, [int] rr, [int] cc, bool ind1)

Enlarge matrix.

Make the matrix larger by inserting empty rows and columns, keeping the existing non-zeros

Extra doc: https://github.com/casadi/casadi/wiki/L_19i

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L952

erase(*args)¶

erase(self, [int] rr, bool ind1)
erase(self, [int] rr, [int] cc, bool ind1)

Erase a submatrix (leaving structural zeros in its place)

Erase elements of a matrix

Extra doc: https://github.com/casadi/casadi/wiki/L_19g

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L937

erase(self, [int] rr, bool ind1)

[INTERNAL] Erase a submatrix (leaving structural zeros in its place)

Erase elements of a matrix

Extra doc: https://github.com/casadi/casadi/wiki/L_19g

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L937

erase(self, [int] rr, [int] cc, bool ind1)

[INTERNAL] Erase a submatrix (leaving structural zeros in its place)

Erase rows and/or columns of a matrix

Extra doc: https://github.com/casadi/casadi/wiki/L_19f

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L929

export_code(*args)¶

export_code(self, str lang, dict options)

static eye(*args)¶

eye(int n) -> SX

static from_file(*args)¶

from_file(str filename, str format_hint) -> DM

get(*args)¶

get(self, bool ind1, Sparsity sp) -> SX
get(self, bool ind1, Slice rr) -> SX
get(self, bool ind1, IM rr) -> SX
get(self, bool ind1, Slice rr, Slice cc) -> SX
get(self, bool ind1, Slice rr, IM cc) -> SX
get(self, bool ind1, IM rr, Slice cc) -> SX
get(self, bool ind1, IM rr, IM cc) -> SX

static get_free(*args)¶

get_free(Function f) -> [SX]

static get_input(*args)¶

get_input(Function f) -> [SX]

static get_max_depth(*args)¶

get_max_depth() -> int

get_nz(*args)¶

get_nz(self, bool ind1, Slice k) -> SX
get_nz(self, bool ind1, IM k) -> SX

has_duplicates(*args)¶

has_duplicates(self) -> bool

has_nz(*args)¶

has_nz(self, int rr, int cc) -> bool

Returns true if the matrix has a non-zero at location rr, cc.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L219

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_impl.hpp#L65-L67

has_zeros(*args)¶

has_zeros(self) -> bool

Check if the matrix has any zero entries which are not structural zeros.

Extra doc: https://github.com/casadi/casadi/wiki/L_1a1

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1140

static inf(*args)¶

inf(int nrow, int ncol) -> SX
inf((int,int) rc) -> SX
inf(Sparsity sp) -> SX

create a matrix with all inf

Extra doc: https://github.com/casadi/casadi/wiki/L_19k

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1005

inf(int nrow, int ncol)

[INTERNAL] create a matrix with all inf

Extra doc: https://github.com/casadi/casadi/wiki/L_19k

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1004

inf((int,int) rc)

[INTERNAL] create a matrix with all inf

Extra doc: https://github.com/casadi/casadi/wiki/L_19k

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1005

inf(Sparsity sp)

[INTERNAL] create a matrix with all inf

Extra doc: https://github.com/casadi/casadi/wiki/L_19k

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1003

info(*args)¶

info(self) -> dict

is_commutative(*args)¶

is_commutative(self) -> bool

is_constant(*args)¶

is_constant(self) -> bool

Check if the matrix is constant (note that false negative answers are possible)

Extra doc: https://github.com/casadi/casadi/wiki/L_19v

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1100

is_eye(*args)¶

is_eye(self) -> bool

check if the matrix is an identity matrix (note that false negative answers

are possible)

Extra doc: https://github.com/casadi/casadi/wiki/L_1a0

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1129

is_integer(*args)¶

is_integer(self) -> bool

Check if the matrix is integer-valued.

(note that false negative answers are possible)

Extra doc: https://github.com/casadi/casadi/wiki/L_19w

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1107

is_leaf(*args)¶

is_leaf(self) -> bool

is_minus_one(*args)¶

is_minus_one(self) -> bool

check if the matrix is -1 (note that false negative answers are

possible)

Extra doc: https://github.com/casadi/casadi/wiki/L_19z

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1122

is_one(*args)¶

is_one(self) -> bool

check if the matrix is 1 (note that false negative answers are

possible)

Extra doc: https://github.com/casadi/casadi/wiki/L_19y

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1117

is_op(*args)¶

is_op(self, int op) -> bool

is_regular(*args)¶

is_regular(self) -> bool

is_smooth(*args)¶

is_smooth(self) -> bool

is_symbolic(*args)¶

is_symbolic(self) -> bool

is_valid_input(*args)¶

is_valid_input(self) -> bool

is_zero(*args)¶

is_zero(self) -> bool

check if the matrix is 0 (note that false negative answers are

possible)

Extra doc: https://github.com/casadi/casadi/wiki/L_19x

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1112

static matrix_matrix(*args)¶

matrix_matrix(int op, SX x, SX y) -> SX

static matrix_scalar(*args)¶

matrix_scalar(int op, SX x, SX y) -> SX

n_dep(*args)¶

n_dep(self) -> int

name(*args)¶

name(self) -> str

static nan(*args)¶

nan(int nrow, int ncol) -> SX
nan((int,int) rc) -> SX
nan(Sparsity sp) -> SX

create a matrix with all nan

Extra doc: https://github.com/casadi/casadi/wiki/L_19l

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1014

nan(int nrow, int ncol)

[INTERNAL] create a matrix with all nan

Extra doc: https://github.com/casadi/casadi/wiki/L_19l

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1013

nan((int,int) rc)

[INTERNAL] create a matrix with all nan

Extra doc: https://github.com/casadi/casadi/wiki/L_19l

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1014

nan(Sparsity sp)

[INTERNAL] create a matrix with all nan

Extra doc: https://github.com/casadi/casadi/wiki/L_19l

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1012

nonzeros(*args)¶

nonzeros(self) -> [SXElem]

Get all nonzeros.

Extra doc: https://github.com/casadi/casadi/wiki/L_1a4

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1157

op(*args)¶

op(self) -> int

print_dense(*args)¶

print_dense(self, bool truncate)

Print dense matrix-stype.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L889

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_impl.hpp#L686-L688

print_scalar(*args)¶

print_scalar(self)

Print scalar.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L883

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_impl.hpp#L609-L633

print_sparse(*args)¶

print_sparse(self, bool truncate)

Print sparse matrix style.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L892

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_impl.hpp#L691-L693

print_split(*args)¶

print_split(self) -> ([str] OUTPUT, [str] OUTPUT)

Get strings corresponding to the nonzeros and the interdependencies.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L873

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_impl.hpp#L696-L700

print_vector(*args)¶

print_vector(self, bool truncate)

Print vector-style.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L886

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_impl.hpp#L636-L638

printme(*args)¶

printme(self, SX y) -> SX

static rand(*args)¶

rand(int nrow, int ncol) -> SX
rand((int,int) rc) -> SX
rand(Sparsity sp) -> SX

Create a matrix with uniformly distributed random numbers.

Extra doc: https://github.com/casadi/casadi/wiki/L_1ab

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1216

rand(Sparsity sp)

rand(int nrow, int ncol)

[INTERNAL] Create a matrix with uniformly distributed random numbers.

Extra doc: https://github.com/casadi/casadi/wiki/L_1ab

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1212

rand((int,int) rc)

[INTERNAL] Create a matrix with uniformly distributed random numbers.

Extra doc: https://github.com/casadi/casadi/wiki/L_1ab

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1216

remove(*args)¶

remove(self, [int] rr, [int] cc)

Remove columns and rows.

Remove/delete rows and/or columns of a matrix

Extra doc: https://github.com/casadi/casadi/wiki/L_19h

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L944

reserve(*args)¶

reserve(self, int nnz)
reserve(self, int nnz, int ncol)

reset_input(*args)¶

reset_input(self)

resize(*args)¶

resize(self, int nrow, int ncol)

static rng(*args)¶

rng(int seed)

static scalar_matrix(*args)¶

scalar_matrix(int op, SX x, SX y) -> SX

serialize(*args)¶

serialize(self) -> str
serialize(self, casadi::SerializingStream & s)

Serialize an object.

Extra doc: https://github.com/casadi/casadi/wiki/L_1ah

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1264

serialize(self, casadi::SerializingStream & s)

[INTERNAL] Serialize an object.

Extra doc: https://github.com/casadi/casadi/wiki/L_1ah

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1264

serialize(self)

[INTERNAL] Serialize.

Extra doc: https://github.com/casadi/casadi/wiki/L_1ae

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1249

set(*args)¶

set(self, SX m, bool ind1, Sparsity sp)
set(self, SX m, bool ind1, Slice rr)
set(self, SX m, bool ind1, IM rr)
set(self, SX m, bool ind1, Slice rr, Slice cc)
set(self, SX m, bool ind1, Slice rr, IM cc)
set(self, SX m, bool ind1, IM rr, Slice cc)
set(self, SX m, bool ind1, IM rr, IM cc)

static set_max_depth(*args)¶

set_max_depth(int eq_depth)

set_nz(*args)¶

set_nz(self, SX m, bool ind1, Slice k)
set_nz(self, SX m, bool ind1, IM k)

static set_precision(*args)¶

set_precision(int precision)

static set_scientific(*args)¶

set_scientific(bool scientific)

static set_width(*args)¶

set_width(int width)

sparsity(*args)¶

sparsity(self) -> Sparsity

Get an owning reference to the sparsity pattern.

Extra doc: https://github.com/casadi/casadi/wiki/L_19j

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L979

str(*args)¶

str(self, bool more) -> str

Get string representation.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L880

to_file(*args)¶

to_file(self, str filename, str format)

Export numerical matrix to file

Supported formats:

*   - .mtx   Matrix Market (sparse)
*   - .txt   Ascii full precision representation (sparse)
*            Whitespace separated, aligned.
*            Comments with # % or /
*            Uses C locale
*            Structural zeros represented by 00
*            Does not scale well for large sparse matrices
*

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/matrix_decl.hpp#L1284

static triplet(*args)¶

triplet([int] row, [int] col, SX d) -> SX
triplet([int] row, [int] col, SX d, (int,int) rc) -> SX
triplet([int] row, [int] col, SX d, int nrow, int ncol) -> SX

static type_name(*args)¶

type_name() -> str

static unary(*args)¶

unary(int op, SX x) -> SX

2.3. MX¶

class MX(*args)¶

MX -  Matrix expression.

The MX class is used to build up trees made up from MXNodes. It is a more

general graph representation than the scalar expression, SX, and much less efficient for small objects. On the other hand, the class allows much more general operations than does SX, in particular matrix valued

The MX class is designed to have identical syntax with the Matrix<> template

representation of the values at a node. By keeping the syntaxes identical, it is possible to switch from one class to the other, as well as inlining MX functions to SXElem functions.

Note that an operation is always “lazy”, making a matrix multiplication will create a matrix multiplication node, not perform the actual multiplication.

Joel Andersson

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

C++ includes: mx.hpp

attachAssert(*args)¶

attachAssert(self, MX y, str fail_message) -> MX

returns itself, but with an assertion attached

If y does not evaluate to 1, a runtime error is raised

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L866

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L699-L704

static binary(*args)¶

binary(int op, MX x, MX y) -> MX

Create nodes by their ID.

Extra doc: https://github.com/casadi/casadi/wiki/L_r1

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L411

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L507-L532

static bspline_dual(*args)¶

bspline_dual([float] x, [[float]] knots, [int] degree, dict opts) -> DM

dep(*args)¶

dep(self, int ch) -> MX

Get the nth dependency as MX.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L236

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L730-L732

static deserialize(*args)¶

deserialize(casadi::DeserializingStream & s) -> MX

static einstein(*args)¶

einstein(MX A, MX B, [int] dim_a, [int] dim_b, [int] dim_c, [int] a, [int] b, [int] c) -> MX
einstein(MX A, MX B, MX C, [int] dim_a, [int] dim_b, [int] dim_c, [int] a, [int] b, [int] c) -> MX

Computes an einstein dense tensor contraction.

Computes the product: C_c = A_a + B_b where a b c are index/einstein

notation in an encoded form

For example, an matrix-matrix product may be written as: C_ij = A_ik B_kj

The encoded form uses strictly negative numbers to indicate labels. For the

Extra doc: https://github.com/casadi/casadi/wiki/L_r5

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L533

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L646-L652

einstein(MX A, MX B, [int] dim_a, [int] dim_b, [int] dim_c, [int] a, [int] b, [int] c)

[INTERNAL] Computes an einstein dense tensor contraction.

Computes the product: C_c = A_a + B_b where a b c are index/einstein

notation in an encoded form

For example, an matrix-matrix product may be written as: C_ij = A_ik B_kj

The encoded form uses strictly negative numbers to indicate labels. For the

Extra doc: https://github.com/casadi/casadi/wiki/L_r5

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L533

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L646-L652

einstein(MX A, MX B, MX C, [int] dim_a, [int] dim_b, [int] dim_c, [int] a, [int] b, [int] c)

[INTERNAL] Computes an einstein dense tensor contraction.

Computes the product: C_c = A_a + B_b where a b c are index/einstein

notation in an encoded form

For example, an matrix-matrix product may be written as: C_ij = A_ik B_kj

The encoded form uses strictly negative numbers to indicate labels. For the

Extra doc: https://github.com/casadi/casadi/wiki/L_r5

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L527

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L638-L644

enlarge(*args)¶

enlarge(self, int nrow, int ncol, [int] rr, [int] cc, bool ind1)

Enlarge matrix.

Make the matrix larger by inserting empty rows and columns, keeping the existing non-zeros

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L211

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L618-L626

erase(*args)¶

erase(self, [int] rr, bool ind1)
erase(self, [int] rr, [int] cc, bool ind1)

Erase a submatrix (leaving structural zeros in its place)

Erase elements of a matrix

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L204

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L604-L616

erase(self, [int] rr, bool ind1)

[INTERNAL] Erase a submatrix (leaving structural zeros in its place)

Erase elements of a matrix

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L204

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L604-L616

erase(self, [int] rr, [int] cc, bool ind1)

[INTERNAL] Erase a submatrix (leaving structural zeros in its place)

Erase rows and/or columns of a matrix

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L196

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L590-L602

eval_mx(*args)¶

eval_mx(self, [MX] arg) -> [MX]

Evaluate the MX node with new symbolic dependencies.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L912

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L2347-L2353

static eye(*args)¶

eye(int n) -> MX

get(*args)¶

get(self, bool ind1, int rr) -> MX
get(self, bool ind1, Sparsity sp) -> MX
get(self, bool ind1, Slice rr) -> MX
get(self, bool ind1, IM rr) -> MX
get(self, bool ind1, MX rr) -> MX
get(self, bool ind1, int rr, int cc) -> MX
get(self, bool ind1, int rr, Slice cc) -> MX
get(self, bool ind1, Slice rr, int cc) -> MX
get(self, bool ind1, Slice rr, Slice cc) -> MX
get(self, bool ind1, Slice rr, IM cc) -> MX
get(self, bool ind1, Slice rr, MX cc) -> MX
get(self, bool ind1, IM rr, Slice cc) -> MX
get(self, bool ind1, IM rr, IM cc) -> MX
get(self, bool ind1, MX rr, Slice cc) -> MX
get(self, bool ind1, MX rr, MX cc) -> MX

Get a submatrix, two arguments

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L473

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L218-L221

get(self, bool ind1, IM rr)
get(self, bool ind1, Slice rr, IM cc)
get(self, bool ind1, IM rr, Slice cc)
get(self, bool ind1, IM rr, IM cc)

get(self, bool ind1, int rr)

[INTERNAL] Get a submatrix, single argument

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L449

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L449-L451

get(self, bool ind1, Sparsity sp)

[INTERNAL] Get a submatrix, single argument

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L447

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L194-L200

get(self, bool ind1, Slice rr)

[INTERNAL] Get a submatrix, single argument

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L445

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L171-L174

get(self, bool ind1, MX rr)

[INTERNAL] Get a submatrix, single argument

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L448

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L202-L206

get(self, bool ind1, int rr, int cc)

[INTERNAL] Get a submatrix, two arguments

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L467

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L467-L470

get(self, bool ind1, int rr, Slice cc)

[INTERNAL] Get a submatrix, two arguments

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L462

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L462-L464

get(self, bool ind1, Slice rr, int cc)

[INTERNAL] Get a submatrix, two arguments

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L458

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L458-L460

get(self, bool ind1, Slice rr, Slice cc)

[INTERNAL] Get a submatrix, two arguments

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L456

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L141-L144

get(self, bool ind1, Slice rr, MX cc)

[INTERNAL] Get a submatrix, two arguments

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L472

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L208-L211

get(self, bool ind1, MX rr, Slice cc)

[INTERNAL] Get a submatrix, two arguments

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L471

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L213-L216

get(self, bool ind1, MX rr, MX cc)

[INTERNAL] Get a submatrix, two arguments

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L473

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L218-L221

static get_free(*args)¶

get_free(Function f) -> [MX]

static get_input(*args)¶

get_input(Function f) -> [MX]

static get_max_depth(*args)¶

get_max_depth() -> int

get_nz(*args)¶

get_nz(self, bool ind1, int kk) -> MX
get_nz(self, bool ind1, Slice kk) -> MX
get_nz(self, bool ind1, IM kk) -> MX
get_nz(self, bool ind1, MX kk) -> MX
get_nz(self, bool ind1, Slice inner, MX outer) -> MX
get_nz(self, bool ind1, MX inner, Slice outer) -> MX
get_nz(self, bool ind1, MX inner, MX outer) -> MX

Get a set of nonzeros

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L501

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L427-L430

get_nz(self, bool ind1, IM kk)

get_nz(self, bool ind1, int kk)

[INTERNAL] Get a set of nonzeros

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L496

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L496-L498

get_nz(self, bool ind1, Slice kk)

[INTERNAL] Get a set of nonzeros

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L493

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L384-L387

get_nz(self, bool ind1, MX kk)

[INTERNAL] Get a set of nonzeros

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L495

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L422-L425

get_nz(self, bool ind1, Slice inner, MX outer)

[INTERNAL] Get a set of nonzeros

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L500

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L432-L435

get_nz(self, bool ind1, MX inner, Slice outer)

[INTERNAL] Get a set of nonzeros

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L499

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L437-L440

get_nz(self, bool ind1, MX inner, MX outer)

[INTERNAL] Get a set of nonzeros

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L501

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L427-L430

get_output(*args)¶

get_output(self, int oind) -> MX

Get an output.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L246

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L849-L851

get_temp(*args)¶

get_temp(self) -> int

has_duplicates(*args)¶

has_duplicates(self) -> bool

has_output(*args)¶

has_output(self) -> bool

Check if a multiple output node.

Extra doc: https://github.com/casadi/casadi/wiki/L_284

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L280

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L762-L764

static inf(*args)¶

inf(int nrow, int ncol) -> MX
inf((int,int) rc) -> MX
inf(Sparsity sp) -> MX

create a matrix with all inf

Extra doc: https://github.com/casadi/casadi/wiki/L_r2

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L421

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L554-L556

inf(int nrow, int ncol)

[INTERNAL] create a matrix with all inf

Extra doc: https://github.com/casadi/casadi/wiki/L_r2

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L420

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L550-L552

inf((int,int) rc)

[INTERNAL] create a matrix with all inf

Extra doc: https://github.com/casadi/casadi/wiki/L_r2

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L421

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L554-L556

inf(Sparsity sp)

[INTERNAL] create a matrix with all inf

Extra doc: https://github.com/casadi/casadi/wiki/L_r2

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L419

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L558-L560

info(*args)¶

info(self) -> dict

Obtain information about node

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L387

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L802-L804

static interpn_linear(*args)¶

interpn_linear([MX] x, MX v, [MX] xq, dict opts) -> MX

is_binary(*args)¶

is_binary(self) -> bool

Is binary operation.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L378

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L790-L792

is_call(*args)¶

is_call(self) -> bool

Check if evaluation.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L269

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L750-L752

is_commutative(*args)¶

is_commutative(self) -> bool

Check if commutative operation.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L292

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L826-L831

is_constant(*args)¶

is_constant(self) -> bool

Check if constant.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L266

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L746-L748

is_eye(*args)¶

is_eye(self) -> bool

check if identity

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L352

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L973-L975

is_minus_one(*args)¶

is_minus_one(self) -> bool

check if zero (note that false negative answers are possible)

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L367

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L989-L991

is_multiplication(*args)¶

is_multiplication(self) -> bool

Check if multiplication.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L289

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L774-L776

is_norm(*args)¶

is_norm(self) -> bool

Check if norm.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L295

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L778-L780

is_one(*args)¶

is_one(self) -> bool

check if zero (note that false negative answers are possible)

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L362

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L985-L987

is_op(*args)¶

is_op(self, int op) -> bool

Is it a certain operation.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L286

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L770-L772

is_output(*args)¶

is_output(self) -> bool

Check if evaluation output.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L275

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L758-L760

is_regular(*args)¶

is_regular(self) -> bool

Checks if expression does not contain NaN or Inf.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L375

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L997-L1003

is_symbolic(*args)¶

is_symbolic(self) -> bool

Check if symbolic.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L263

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L742-L744

is_transpose(*args)¶

is_transpose(self) -> bool

Is the expression a transpose?

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L372

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L993-L995

is_unary(*args)¶

is_unary(self) -> bool

Is unary operation.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L381

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L794-L796

is_valid_input(*args)¶

is_valid_input(self) -> bool

Check if matrix can be used to define function inputs.

Valid inputs for MXFunctions are combinations of Reshape, concatenations and SymbolicMX

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L302

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L901-L903

is_zero(*args)¶

is_zero(self) -> bool

check if zero (note that false negative answers are possible)

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L357

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L977-L983

join_primitives(*args)¶

join_primitives(self, [DM] v) -> DM
join_primitives(self, [SX] v) -> SX
join_primitives(self, [MX] v) -> MX

Join an expression along symbolic primitives.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L329

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L957-L963

join_primitives(self, [DM] v)

[INTERNAL] Join an expression along symbolic primitives.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L329

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L957-L963

join_primitives(self, [SX] v)

[INTERNAL] Join an expression along symbolic primitives.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L328

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L949-L955

join_primitives(self, [MX] v)

[INTERNAL] Join an expression along symbolic primitives.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L327

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L941-L947

mapping(*args)¶

mapping(self) -> IM

Get an IM representation of a GetNonzeros or SetNonzeros node.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L881

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L833-L835

monitor(*args)¶

monitor(self, str comment) -> MX

Monitor an expression.

Returns itself, but with the side effect of printing the nonzeros along with a comment

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L873

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L706-L708

n_dep(*args)¶

n_dep(self) -> int

Get the number of dependencies of a binary SXElem.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L251

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L734-L736

n_out(*args)¶

n_out(self) -> int

Number of outputs.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L241

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L845-L847

n_primitives(*args)¶

n_primitives(self) -> int

Get the number of primitives for MXFunction inputs/outputs.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L307

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L905-L907

name(*args)¶

name(self) -> str

Get the name.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L254

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L738-L740

static nan(*args)¶

nan(int nrow, int ncol) -> MX
nan((int,int) rc) -> MX
nan(Sparsity sp) -> MX

create a matrix with all nan

Extra doc: https://github.com/casadi/casadi/wiki/L_r3

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L430

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L566-L568

nan(int nrow, int ncol)

[INTERNAL] create a matrix with all nan

Extra doc: https://github.com/casadi/casadi/wiki/L_r3

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L429

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L562-L564

nan((int,int) rc)

[INTERNAL] create a matrix with all nan

Extra doc: https://github.com/casadi/casadi/wiki/L_r3

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L430

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L566-L568

nan(Sparsity sp)

[INTERNAL] create a matrix with all nan

Extra doc: https://github.com/casadi/casadi/wiki/L_r3

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L428

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L570-L572

op(*args)¶

op(self) -> int

Get operation type.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L384

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L798-L800

primitives(*args)¶

primitives(self) -> [MX]

Get primitives.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L312

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L909-L915

printme(*args)¶

printme(self, MX b) -> MX

reset_input(*args)¶

reset_input(self)

serialize(*args)¶

serialize(self, casadi::SerializingStream & s)

Serialize an object.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L392

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L806-L808

set(*args)¶

set(self, MX m, bool ind1, Sparsity sp)
set(self, MX m, bool ind1, Slice rr)
set(self, MX m, bool ind1, IM rr)
set(self, MX m, bool ind1, Slice rr, Slice cc)
set(self, MX m, bool ind1, Slice rr, IM cc)
set(self, MX m, bool ind1, IM rr, Slice cc)
set(self, MX m, bool ind1, IM rr, IM cc)

set(self, MX m, bool ind1, IM rr)
set(self, MX m, bool ind1, Slice rr, IM cc)
set(self, MX m, bool ind1, IM rr, Slice cc)
set(self, MX m, bool ind1, IM rr, IM cc)

set(self, MX m, bool ind1, Sparsity sp)

[INTERNAL] Set a submatrix, single argument

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L480

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L371-L382

set(self, MX m, bool ind1, Slice rr)

[INTERNAL] Set a submatrix, single argument

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L478

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L298-L301

set(self, MX m, bool ind1, Slice rr, Slice cc)

[INTERNAL] Set a submatrix, two arguments

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L485

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L223-L226

static set_max_depth(*args)¶

set_max_depth(int eq_depth)

set_nz(*args)¶

set_nz(self, MX m, bool ind1, int kk)
set_nz(self, MX m, bool ind1, Slice kk)
set_nz(self, MX m, bool ind1, IM kk)
set_nz(self, MX m, bool ind1, MX kk)

Set a set of nonzeros

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L509

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L509-L509

set_nz(self, MX m, bool ind1, IM kk)

set_nz(self, MX m, bool ind1, int kk)

[INTERNAL] Set a set of nonzeros

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L509

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L509-L509

set_nz(self, MX m, bool ind1, Slice kk)

[INTERNAL] Set a set of nonzeros

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L506

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L442-L445

set_nz(self, MX m, bool ind1, MX kk)

[INTERNAL] Set a set of nonzeros

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L508

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L503-L505

set_temp(*args)¶

set_temp(self, int t)

sparsity(*args)¶

sparsity(self) -> Sparsity

Get an owning reference to the sparsity pattern.

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

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

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L189-L189

split_primitives(*args)¶

split_primitives(self, DM x) -> [DM]
split_primitives(self, SX x) -> [SX]
split_primitives(self, MX x) -> [MX]

Split up an expression along symbolic primitives.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L320

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L933-L939

split_primitives(self, DM x)

[INTERNAL] Split up an expression along symbolic primitives.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L320

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L933-L939

split_primitives(self, SX x)

[INTERNAL] Split up an expression along symbolic primitives.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L319

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L925-L931

split_primitives(self, MX x)

[INTERNAL] Split up an expression along symbolic primitives.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L318

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L917-L923

static test_cast(*args)¶

test_cast(casadi::SharedObjectInternal const * ptr) -> bool

to_DM(*args)¶

to_DM(self) -> DM

static type_name(*args)¶

type_name() -> str

static unary(*args)¶

unary(int op, MX x) -> MX

Create nodes by their ID.

Extra doc: https://github.com/casadi/casadi/wiki/L_r1

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L412

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L534-L536

which_function(*args)¶

which_function(self) -> Function

Get function - only valid when is_call() is true.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L272

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L754-L756

which_output(*args)¶

which_output(self) -> int

Get the index of evaluation output - only valid when is_output() is true.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.hpp#L283

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/mx.cpp#L766-L768

2.4. Sparsity¶

class Sparsity(*args)¶

.. py:method:: Sparsity.add_nz(*args)

module:: casadi.casadi

add_nz(self, int rr, int cc) -> int

amd(*args)¶

amd(self) -> [int]

append(*args)¶

append(self, Sparsity sp)

appendColumns(*args)¶

appendColumns(self, Sparsity sp)

static band(*args)¶

band(int n, int p) -> Sparsity

static banded(*args)¶

banded(int n, int p) -> Sparsity

btf(*args)¶

btf(self) -> (int , [int] OUTPUT, [int] OUTPUT, [int] OUTPUT, [int] OUTPUT, [int] OUTPUT, [int] OUTPUT)

bw_lower(*args)¶

bw_lower(self) -> int

bw_upper(*args)¶

bw_upper(self) -> int

colind(*args)¶

colind(self) -> [int]
colind(self, int cc) -> int

columns(*args)¶

columns(self) -> int

combine(*args)¶

combine(self, Sparsity y, bool f0x_is_zero, bool function0_is_zero) -> Sparsity

compress(*args)¶

compress(self) -> [int]

static compressed(*args)¶

compressed([int] v, bool order_rows) -> Sparsity

static dense(*args)¶

dense(int nrow, int ncol) -> Sparsity
dense((int,int) rc) -> Sparsity

density(*args)¶

density(self) -> float

static deserialize(*args)¶

deserialize(std::istream & stream) -> Sparsity
deserialize(casadi::DeserializingStream & s) -> Sparsity
deserialize(str s) -> Sparsity

dfs(*args)¶

dfs(self, int j, int top, [int] pinv) -> (int , [int] INOUT, [int] INOUT, [bool] INOUT)

static diag(*args)¶

diag(int nrow) -> Sparsity
diag((int,int) rc) -> Sparsity
diag(int nrow, int ncol) -> Sparsity

dim(*args)¶

dim(self, bool with_nz) -> str

enlarge(*args)¶

enlarge(self, int nrow, int ncol, [int] rr, [int] cc, bool ind1)

enlargeColumns(*args)¶

enlargeColumns(self, int ncol, [int] cc, bool ind1)

enlargeRows(*args)¶

enlargeRows(self, int nrow, [int] rr, bool ind1)

erase(*args)¶

erase(self, [int] rr, bool ind1) -> [int]
erase(self, [int] rr, [int] cc, bool ind1) -> [int]

etree(*args)¶

etree(self, bool ata) -> [int]

export_code(*args)¶

export_code(self, str lang, dict options)

find(*args)¶

find(self, bool ind1) -> [int]

static from_file(*args)¶

from_file(str filename, str format_hint) -> Sparsity

get_ccs(*args)¶

get_ccs(self) -> ([int] OUTPUT, [int] OUTPUT)

get_col(*args)¶

get_col(self) -> [int]

get_crs(*args)¶

get_crs(self) -> ([int] OUTPUT, [int] OUTPUT)

get_diag(*args)¶

get_diag(self) -> (Sparsity , [int] OUTPUT)

get_lower(*args)¶

get_lower(self) -> [int]

get_nz(*args)¶

get_nz(self) -> [int]
get_nz(self, int rr, int cc) -> int
get_nz(self, [int] rr, [int] cc) -> [int]

get_triplet(*args)¶

get_triplet(self) -> ([int] OUTPUT, [int] OUTPUT)

get_upper(*args)¶

get_upper(self) -> [int]

has_nz(*args)¶

has_nz(self, int rr, int cc) -> bool

hash(*args)¶

hash(self) -> std::size_t

info(*args)¶

info(self) -> dict

intersect(*args)¶

intersect(self, Sparsity y) -> Sparsity

is_column(*args)¶

is_column(self) -> bool

is_dense(*args)¶

is_dense(self) -> bool

is_diag(*args)¶

is_diag(self) -> bool

is_empty(*args)¶

is_empty(self, bool both) -> bool

is_equal(*args)¶

is_equal(self, Sparsity y) -> bool
is_equal(self, int nrow, int ncol, [int] colind, [int] row) -> bool

is_orthonormal(*args)¶

is_orthonormal(self, bool allow_empty) -> bool

is_orthonormal_columns(*args)¶

is_orthonormal_columns(self, bool allow_empty) -> bool

is_orthonormal_rows(*args)¶

is_orthonormal_rows(self, bool allow_empty) -> bool

is_permutation(*args)¶

is_permutation(self) -> bool

is_reshape(*args)¶

is_reshape(self, Sparsity y) -> bool

is_row(*args)¶

is_row(self) -> bool

is_scalar(*args)¶

is_scalar(self, bool scalar_and_dense) -> bool

is_selection(*args)¶

is_selection(self, bool allow_empty) -> bool

is_singular(*args)¶

is_singular(self) -> bool

is_square(*args)¶

is_square(self) -> bool

is_stacked(*args)¶

is_stacked(self, Sparsity y, int n) -> bool

is_subset(*args)¶

is_subset(self, Sparsity rhs) -> bool

is_symmetric(*args)¶

is_symmetric(self) -> bool

is_transpose(*args)¶

is_transpose(self, Sparsity y) -> bool

is_tril(*args)¶

is_tril(self, bool strictly) -> bool

is_triu(*args)¶

is_triu(self, bool strictly) -> bool

is_vector(*args)¶

is_vector(self) -> bool

static kkt(*args)¶

kkt(Sparsity H, Sparsity J, bool with_x_diag, bool with_lam_g_diag) -> Sparsity

largest_first(*args)¶

largest_first(self) -> [int]

ldl(*args)¶

ldl(self, bool amd) -> (Sparsity , [int] OUTPUT)

static lower(*args)¶

lower(int n) -> Sparsity

makeDense(*args)¶

makeDense(self) -> (Sparsity , [int] OUTPUT)

nnz(*args)¶

nnz(self) -> int

nnz_diag(*args)¶

nnz_diag(self) -> int

nnz_lower(*args)¶

nnz_lower(self, bool strictly) -> int

nnz_upper(*args)¶

nnz_upper(self, bool strictly) -> int

static nonzeros(*args)¶

nonzeros(int nrow, int ncol, [int] nz, bool ind1) -> Sparsity

numel(*args)¶

numel(self) -> int

pattern_inverse(*args)¶

pattern_inverse(self) -> Sparsity

static permutation(*args)¶

permutation([int] p, bool invert) -> Sparsity

permutation_vector(*args)¶

permutation_vector(self, bool invert) -> [int]

pmult(*args)¶

pmult(self, [int] p, bool permute_rows, bool permute_columns, bool invert_permutation) -> Sparsity

postfix_dim(*args)¶

postfix_dim(self) -> str

qr_sparse(*args)¶

qr_sparse(self, bool amd) -> (Sparsity OUTPUT, Sparsity OUTPUT, [int] OUTPUT, [int] OUTPUT)

removeDuplicates(*args)¶

removeDuplicates(self) -> [int]

repr_el(*args)¶

repr_el(self, int k) -> str

resize(*args)¶

resize(self, int nrow, int ncol)

row(*args)¶

row(self) -> [int]
row(self, int el) -> int

static rowcol(*args)¶

rowcol([int] row, [int] col, int nrow, int ncol) -> Sparsity

rows(*args)¶

rows(self) -> int

rowsSequential(*args)¶

rowsSequential(self, bool strictly) -> bool

static scalar(*args)¶

scalar(bool dense_scalar) -> Sparsity

scc(*args)¶

scc(self) -> (int , [int] OUTPUT, [int] OUTPUT)

serialize(*args)¶

serialize(self) -> str
serialize(self, casadi::SerializingStream & s)

size(*args)¶

size(self) -> (int,int)
size(self, int axis) -> int

size1(*args)¶

size1(self) -> int

size2(*args)¶

size2(self) -> int

sparsity_cast_mod(*args)¶

sparsity_cast_mod(self, Sparsity X, Sparsity Y) -> Sparsity

spy(*args)¶

spy(self)

spy_matlab(*args)¶

spy_matlab(self, str mfile)

star_coloring(*args)¶

star_coloring(self, int ordering, int cutoff) -> Sparsity

star_coloring2(*args)¶

star_coloring2(self, int ordering, int cutoff) -> Sparsity

sub(*args)¶

sub(self, [int] rr, Sparsity sp, bool ind1) -> (Sparsity , [int] OUTPUT)
sub(self, [int] rr, [int] cc, bool ind1) -> (Sparsity , [int] OUTPUT)

static test_cast(*args)¶

test_cast(casadi::SharedObjectInternal const * ptr) -> bool

to_file(*args)¶

to_file(self, str filename, str format_hint)

transpose(*args)¶

transpose(self, bool invert_mapping) -> (Sparsity , [int] OUTPUT)

static triplet(*args)¶

triplet(int nrow, int ncol, [int] row, [int] col) -> Sparsity
triplet(int nrow, int ncol, [int] row, [int] col, bool invert_mapping) -> (Sparsity , [int] OUTPUT)

static type_name(*args)¶

type_name() -> str

uni_coloring(*args)¶

uni_coloring(self, Sparsity AT, int cutoff) -> Sparsity

static unit(*args)¶

unit(int n, int el) -> Sparsity

unite(*args)¶

unite(self, Sparsity y) -> Sparsity

static upper(*args)¶

upper(int n) -> Sparsity

2.5. Function¶

class Function(*args)¶

Function object.

A Function instance is a general multiple-input, multiple-output function where each input and output can be a sparse matrix.

immutable class; copying a class instance is very cheap and its behavior (with some exceptions) is not affected by calling its member functions.

Joel Andersson

Extra doc: https://github.com/casadi/casadi/wiki/L_1uw

>List of available options

Id	Type	Description	Used in
ad_weight	OT_DOUBLE	Weighting factor for derivative calculation.When there is an option of either using forward or reverse mode directional derivatives, the condition ad_wei ghtnf<=(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.	casadi::Function Internal
ad_weight_sp	OT_DOUBLE	Weighting factor for sparsity 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.	casadi::Function Internal
always_inline	OT_BOOL	Force inlining.	casadi::Function Internal
cache	OT_DICT	Prepopulate the function cache. Default: empty	casadi::Function Internal
compiler	OT_STRING	Just-in-time compiler plugin to be used.	casadi::Function Internal
custom_jacobian	OT_FUNCTION	Override CasADi’s AD. Use together with ‘jac_penalty’: 0. Note: Highly experimental. Syntax may break often.	casadi::Function Internal
der_options	OT_DICT	Default options to be used to populate forward_options, reverse_options, and jacobian_options before those options are merged in.	casadi::Function Internal
derivative_of	OT_FUNCTION	The function is a derivative of another function. The type of derivative (directional derivative, Jacobian) is inferred from the function name.	casadi::Function Internal
dump	OT_BOOL	Dump function to file upon first evaluation. [false]	casadi::Function Internal
dump_dir	OT_STRING	Directory to dump inputs/outputs to. Make sure the directory exists [.]	casadi::Function Internal
dump_format	OT_STRING	Choose file format to dump matrices. See DM.from_file [mtx]	casadi::Function Internal
dump_in	OT_BOOL	Dump numerical values of inputs to file (readable with DM.from_file ) [default: false]	casadi::Function Internal
dump_out	OT_BOOL	Dump numerical values of outputs to file (readable with DM.from_file ) [default: false]	casadi::Function Internal
enable_fd	OT_BOOL	Enable derivative calculation by finite differencing. [default: false]]	casadi::Function Internal
enable_forward	OT_BOOL	Enable derivative calculation using generated functions for Jacobian-times- vector products - typically using forward mode AD - if available. [default: true]	casadi::Function Internal
enable_jacobian	OT_BOOL	Enable derivative calculation using generated functions for Jacobians of all differentiable outputs with respect to all differentiable inputs - if available. [default: true]	casadi::Function Internal
enable_reverse	OT_BOOL	Enable derivative calculation using generated functions for transposed Jacobian-times- vector products - typically using reverse mode AD - if available. [default: true]	casadi::Function Internal
error_on_fail	OT_BOOL	Throw exceptions when function evaluation fails (default true).	casadi::ProtoFun ction
external_transfo rm	OT_VECTORVECTOR	List of external _transform instruction arguments. Default: empty	casadi::Function Internal
fd_method	OT_STRING	Method for finite differencing [default ‘central’]	casadi::Function Internal
fd_options	OT_DICT	Options to be passed to the finite difference instance	casadi::Function Internal
forward_options	OT_DICT	Options to be passed to a forward mode constructor	casadi::Function Internal
gather_stats	OT_BOOL	Deprecated option (ignored): Statistics are now always collected.	casadi::Function Internal
input_scheme	OT_STRINGVECTOR	Deprecated option (ignored)	casadi::Function Internal
inputs_check	OT_BOOL	Throw exceptions when the numerical values of the inputs don’t make sense	casadi::Function Internal
is_diff_in	OT_BOOLVECTOR	Indicate for each input if it should be differentiable.	casadi::Function Internal
is_diff_out	OT_BOOLVECTOR	Indicate for each output if it should be differentiable.	casadi::Function Internal
jac_penalty	OT_DOUBLE	When requested for a number of 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	casadi::Function Internal
jacobian_options	OT_DICT	Options to be passed to a Jacobian constructor	casadi::Function Internal
jit	OT_BOOL	Use just-in-time compiler to speed up the evaluation	casadi::Function Internal
jit_cleanup	OT_BOOL	Cleanup up the temporary source file that jit creates. Default: true	casadi::Function Internal
jit_name	OT_STRING	The file name used to write out code. The actual file names used depend on ‘jit_t emp_suffix’ and include extensions. Default: ‘jit_tmp’	casadi::Function Internal
jit_options	OT_DICT	Options to be passed to the jit compiler.	casadi::Function Internal
jit_serialize	OT_STRING	Specify behaviour when serializing a jitted function: SOURCE\|link\|embe d.	casadi::Function Internal
jit_temp_suffix	OT_BOOL	Use a temporary (seemingly random) filename suffix for generated code and libraries. This is desired for thread- safety. This behaviour may defeat caching compiler wrappers. Default: true	casadi::Function Internal
max_io	OT_INT	Acceptable number of inputs and outputs. Warn if exceeded.	casadi::Function Internal
max_num_dir	OT_INT	Specify the maximum number of directions for derivative functions. Overrules the builtin optimize d_num_dir.	casadi::Function Internal
never_inline	OT_BOOL	Forbid inlining.	casadi::Function Internal
output_scheme	OT_STRINGVECTOR	Deprecated option (ignored)	casadi::Function Internal
post_expand	OT_BOOL	After construction, expand this Function . Default: False	casadi::Function Internal
post_expand_opti ons	OT_DICT	Options to be passed to post- construction expansion. Default: empty	casadi::Function Internal
print_in	OT_BOOL	Print numerical values of inputs [default: false]	casadi::Function Internal
print_out	OT_BOOL	Print numerical values of outputs [default: false]	casadi::Function Internal
print_time	OT_BOOL	print information about execution time. Implies record_time.	casadi::ProtoFun ction
record_time	OT_BOOL	record information about execution time, for retrieval with stats() .	casadi::ProtoFun ction
regularity_check	OT_BOOL	Throw exceptions when NaN or Inf appears during evaluation	casadi::ProtoFun ction
reverse_options	OT_DICT	Options to be passed to a reverse mode constructor	casadi::Function Internal
user_data	OT_VOIDPTR	A user-defined field that can be used to identify the function or pass additional information	casadi::Function Internal
verbose	OT_BOOL	Verbose evaluation for debugging	casadi::ProtoFun ction

C++ includes: function.hpp

assert_size_in(*args)¶

assert_size_in(self, int i, int nrow, int ncol)

Assert that an input dimension is equal so some given value.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1189

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1754-L1760

assert_size_out(*args)¶

assert_size_out(self, int i, int nrow, int ncol)

Assert that an output dimension is equal so some given value.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1192

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1762-L1767

assert_sparsity_out(*args)¶

assert_sparsity_out(self, int i, Sparsity sp, int n, bool allow_all_zero_sparse)

Assert that an output sparsity is a multiple of some given sparsity.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1195

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1769-L1778

static bspline(*args)¶

bspline(str name, [[float]] knots, [float] coeffs, [int] degree, int m, dict opts) -> Function

buffer()¶: Create a FunctionBuffer object for evaluating with minimal overhead

cache(*args)¶

cache(self) -> dict

Get all functions in the cache.

Extra doc: https://github.com/casadi/casadi/wiki/L_26i

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1212

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1804-L1811

call(*args)¶

call(self, dict:DM arg, bool always_inline, bool never_inline) -> dict:DM
call(self, [DM] arg, bool always_inline, bool never_inline) -> [DM]
call(self, [SX] arg, bool always_inline, bool never_inline) -> [SX]
call(self, dict:SX arg, bool always_inline, bool never_inline) -> dict:SX
call(self, dict:MX arg, bool always_inline, bool never_inline) -> dict:MX
call(self, [MX] arg, bool always_inline, bool never_inline) -> [MX]

Evaluate the function symbolically or numerically.

Extra doc: https://github.com/casadi/casadi/wiki/L_1w7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L524

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1445-L1452

call(self, dict:DM arg, bool always_inline, bool never_inline)

[INTERNAL] Evaluate the function symbolically or numerically.

Extra doc: https://github.com/casadi/casadi/wiki/L_1w7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L520

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1427-L1434

call(self, [DM] arg, bool always_inline, bool never_inline)

[INTERNAL] Evaluate the function symbolically or numerically.

Extra doc: https://github.com/casadi/casadi/wiki/L_1w7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L514

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L356-L363

call(self, [SX] arg, bool always_inline, bool never_inline)

[INTERNAL] Evaluate the function symbolically or numerically.

Extra doc: https://github.com/casadi/casadi/wiki/L_1w7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L516

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L365-L372

call(self, dict:SX arg, bool always_inline, bool never_inline)

[INTERNAL] Evaluate the function symbolically or numerically.

Extra doc: https://github.com/casadi/casadi/wiki/L_1w7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L522

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1436-L1443

call(self, dict:MX arg, bool always_inline, bool never_inline)

[INTERNAL] Evaluate the function symbolically or numerically.

Extra doc: https://github.com/casadi/casadi/wiki/L_1w7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L524

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1445-L1452

call(self, [MX] arg, bool always_inline, bool never_inline)

[INTERNAL] Evaluate the function symbolically or numerically.

Extra doc: https://github.com/casadi/casadi/wiki/L_1w7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L518

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L374-L381

change_option(*args)¶

change_option(self, str option_name, GenericType option_value)

Change option after object creation for debugging.

This is only possible for a selected number of options that do not change the numerical results of the computation, e.g. to enable a more

output or saving to file.

Extra doc: https://github.com/casadi/casadi/wiki/L_1w2

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L455

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1147-L1157

static check_name(*args)¶

check_name(str name) -> bool

checkout(*args)¶

checkout(self) -> int

Checkout a memory object.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1199

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1742-L1744

static conditional(*args)¶

conditional(str name, Function f, dict opts) -> Function
conditional(str name, [Function] f, Function f_def, dict opts) -> Function

convert_in(*args)¶

convert_in(self, dict:DM arg) -> [DM]
convert_in(self, [DM] arg) -> dict:DM
convert_in(self, [SX] arg) -> dict:SX
convert_in(self, dict:SX arg) -> [SX]
convert_in(self, dict:MX arg) -> [MX]
convert_in(self, [MX] arg) -> dict:MX

Convert from/to input/output lists/map.

Will raise an error when an unknown key is used or a list has incorrect size. Does not perform sparsity checking.

Extra doc: https://github.com/casadi/casadi/wiki/L_1x7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L996

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1626-L1628

convert_in(self, dict:DM arg)

[INTERNAL] Convert from/to input/output lists/map.

Will raise an error when an unknown key is used or a list has incorrect size. Does not perform sparsity checking.

Extra doc: https://github.com/casadi/casadi/wiki/L_1x7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L988

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1594-L1596

convert_in(self, [DM] arg)

[INTERNAL] Convert from/to input/output lists/map.

Will raise an error when an unknown key is used or a list has incorrect size. Does not perform sparsity checking.

Extra doc: https://github.com/casadi/casadi/wiki/L_1x7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L987

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1590-L1592

convert_in(self, [SX] arg)

[INTERNAL] Convert from/to input/output lists/map.

Will raise an error when an unknown key is used or a list has incorrect size. Does not perform sparsity checking.

Extra doc: https://github.com/casadi/casadi/wiki/L_1x7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L991

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1606-L1608

convert_in(self, dict:SX arg)

[INTERNAL] Convert from/to input/output lists/map.

Will raise an error when an unknown key is used or a list has incorrect size. Does not perform sparsity checking.

Extra doc: https://github.com/casadi/casadi/wiki/L_1x7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L992

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1610-L1612

convert_in(self, dict:MX arg)

[INTERNAL] Convert from/to input/output lists/map.

Will raise an error when an unknown key is used or a list has incorrect size. Does not perform sparsity checking.

Extra doc: https://github.com/casadi/casadi/wiki/L_1x7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L996

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1626-L1628

convert_in(self, [MX] arg)

[INTERNAL] Convert from/to input/output lists/map.

Will raise an error when an unknown key is used or a list has incorrect size. Does not perform sparsity checking.

Extra doc: https://github.com/casadi/casadi/wiki/L_1x7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L995

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1622-L1624

convert_out(*args)¶

convert_out(self, dict:DM arg) -> [DM]
convert_out(self, [DM] arg) -> dict:DM
convert_out(self, [SX] arg) -> dict:SX
convert_out(self, dict:SX arg) -> [SX]
convert_out(self, dict:MX arg) -> [MX]
convert_out(self, [MX] arg) -> dict:MX

Convert from/to input/output lists/map.

Will raise an error when an unknown key is used or a list has incorrect size. Does not perform sparsity checking.

Extra doc: https://github.com/casadi/casadi/wiki/L_1x7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L998

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1634-L1636

convert_out(self, dict:DM arg)

[INTERNAL] Convert from/to input/output lists/map.

Will raise an error when an unknown key is used or a list has incorrect size. Does not perform sparsity checking.

Extra doc: https://github.com/casadi/casadi/wiki/L_1x7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L990

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1602-L1604

convert_out(self, [DM] arg)

[INTERNAL] Convert from/to input/output lists/map.

Will raise an error when an unknown key is used or a list has incorrect size. Does not perform sparsity checking.

Extra doc: https://github.com/casadi/casadi/wiki/L_1x7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L989

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1598-L1600

convert_out(self, [SX] arg)

[INTERNAL] Convert from/to input/output lists/map.

Will raise an error when an unknown key is used or a list has incorrect size. Does not perform sparsity checking.

Extra doc: https://github.com/casadi/casadi/wiki/L_1x7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L993

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1614-L1616

convert_out(self, dict:SX arg)

[INTERNAL] Convert from/to input/output lists/map.

Will raise an error when an unknown key is used or a list has incorrect size. Does not perform sparsity checking.

Extra doc: https://github.com/casadi/casadi/wiki/L_1x7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L994

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1618-L1620

convert_out(self, dict:MX arg)

[INTERNAL] Convert from/to input/output lists/map.

Will raise an error when an unknown key is used or a list has incorrect size. Does not perform sparsity checking.

Extra doc: https://github.com/casadi/casadi/wiki/L_1x7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L998

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1634-L1636

convert_out(self, [MX] arg)

[INTERNAL] Convert from/to input/output lists/map.

Will raise an error when an unknown key is used or a list has incorrect size. Does not perform sparsity checking.

Extra doc: https://github.com/casadi/casadi/wiki/L_1x7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L997

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1630-L1632

default_in(*args)¶

default_in(self, int ind) -> float

Get default input value.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vm

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L346

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1454-L1456

static deserialize(*args)¶

deserialize(std::istream & stream) -> Function
deserialize(casadi::DeserializingStream & s) -> Function
deserialize(str s) -> Function

expand(*args)¶

expand(self) -> Function
expand(self, str name, dict opts) -> Function

Expand a function to SX.

Extra doc: https://github.com/casadi/casadi/wiki/L_1v5

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L207

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L317-L333

expand(self)

[INTERNAL] Expand a function to SX.

Extra doc: https://github.com/casadi/casadi/wiki/L_1v5

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L206

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L307-L315

expand(self, str name, dict opts)

[INTERNAL] Expand a function to SX.

Extra doc: https://github.com/casadi/casadi/wiki/L_1v5

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L207

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L317-L333

export_code(*args)¶

export_code(self, str lang, dict options) -> str
export_code(self, str lang, str fname, dict options)

Export function in specific language.

Only allowed for (a subset of) SX/MX Functions

Extra doc: https://github.com/casadi/casadi/wiki/L_1wz

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L902

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1275-L1279

export_code(self, str lang, dict options)

[INTERNAL] Export function in specific language.

Only allowed for (a subset of) SX/MX Functions

Extra doc: https://github.com/casadi/casadi/wiki/L_1wz

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L902

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1275-L1279

export_code(self, str lang, str fname, dict options)

[INTERNAL] Export function in specific language.

Only allowed for (a subset of) SX/MX Functions

Extra doc: https://github.com/casadi/casadi/wiki/L_1wz

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L875

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1236-L1240

factory(*args)¶

factory(self, str name, [str] s_in, [str] s_out, dict:[str] aux, dict opts) -> Function

find_function(*args)¶

find_function(self, str name, int max_depth) -> Function

Get a specific function embedded in the expression graphs.

1. Parameters:¶

max_depth: Maximum depth - a negative number indicates no maximum

Extra doc: https://github.com/casadi/casadi/wiki/L_1y7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1242

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1857-L1874

find_functions(*args)¶

find_functions(self, int max_depth) -> [Function]

Get all functions embedded in the expression graphs.

1. Parameters:¶

max_depth: Maximum depth - a negative number indicates no maximum

Extra doc: https://github.com/casadi/casadi/wiki/L_1y6

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1234

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1839-L1855

static fix_name(*args)¶

fix_name(str name) -> str

fold(*args)¶

fold(self, int N, dict opts) -> Function

Create a mapaccumulated version of this function.

Suppose the function has a signature of:

f: (x, u) -> (x_next , y )

The the mapaccumulated version has the signature:

F: (x0, U) -> (X , Y )

 with
     U: horzcat([u0, u1, ..., u_(N-1)])
     X: horzcat([x1, x2, ..., x_N])
     Y: horzcat([y0, y1, ..., y_(N-1)])

 and
     x1, y0 <- f(x0, u0)
     x2, y1 <- f(x1, u1)
     ...
     x_N, y_(N-1) <- f(x_(N-1), u_(N-1))

Mapaccum has the following benefits over writing an equivalent for- loop:

much faster at construction time

potentially much faster compilation times (for codegen)

offers a trade-off between memory and evaluation time

The base (settable through the options dictionary, default 10), is used to create a tower of function calls, containing unrolled for- loops of length maximum base.

This technique is much more scalable in terms of memory-usage, but slightly

similar to that: of a for-loop with a check-pointing instruction after

each chunk of iterations with size base.

Set base to -1 to unroll all the way; no gains in memory efficiency here.

Extra doc: https://github.com/casadi/casadi/wiki/L_1wi

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L698

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L508-L514

forward(*args)¶

forward(self, int nfwd) -> Function

Get a function that calculates nfwd forward derivatives.

 Returns a function with <tt>n_in + n_out + n_in</tt> inputs
 and <tt>nfwd</tt> outputs.
 The first <tt>n_in</tt> inputs correspond to nondifferentiated inputs.
 The next <tt>n_out</tt> inputs correspond to nondifferentiated outputs.
 and the last <tt>n_in</tt> inputs correspond to forward seeds,
 stacked horizontally
 The  <tt>n_out</tt> outputs correspond to forward sensitivities,
 stacked horizontally.     *
 <tt>(n_in = n_in(), n_out = n_out())</tt>

The functions returned are cached, meaning that if called multiple timed
with the same value, then multiple references to the same function will be returned.

Extra doc: https://github.com/casadi/casadi/wiki/L_1wq

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L800

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1110-L1116

free_mx(*args)¶

free_mx(self) -> [MX]

Get all the free variables of the function.

Extra doc: https://github.com/casadi/casadi/wiki/L_1xb

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1019

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1650-L1656

free_sx(*args)¶

free_sx(self) -> [SX]

Get all the free variables of the function.

Extra doc: https://github.com/casadi/casadi/wiki/L_1xa

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1014

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1642-L1648

generate(*args)¶

generate(self, dict opts) -> str
generate(self, str fname, dict opts) -> str

Export / Generate C code for the function.

Extra doc: https://github.com/casadi/casadi/wiki/L_1wv

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L840

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1163-L1165

generate(self, dict opts)

[INTERNAL] Export / Generate C code for the function.

Extra doc: https://github.com/casadi/casadi/wiki/L_1wv

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L840

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1163-L1165

generate(self, str fname, dict opts)

[INTERNAL] Export / Generate C code for the function.

Extra doc: https://github.com/casadi/casadi/wiki/L_1wu

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L835

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1167-L1171

generate_dependencies(*args)¶

generate_dependencies(self, str fname, dict opts) -> str

Export / Generate C code for the dependency function.

Extra doc: https://github.com/casadi/casadi/wiki/L_1ww

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L845

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1173-L1175

generate_in(*args)¶

generate_in(self, str fname) -> [DM]
generate_in(self, str fname, [DM] arg)

Export an input file that can be passed to generate C code with a main.

See:: generate_out
See:: convert_in to convert between dict/map and vector

Extra doc: https://github.com/casadi/casadi/wiki/L_1wx

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L855

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1207-L1217

generate_in(self, str fname)

[INTERNAL] Export an input file that can be passed to generate C code with a main.

See:: generate_out
See:: convert_in to convert between dict/map and vector

Extra doc: https://github.com/casadi/casadi/wiki/L_1wx

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L855

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1207-L1217

generate_in(self, str fname, [DM] arg)

[INTERNAL] Export an input file that can be passed to generate C code with a main.

See:: generate_out
See:: convert_in to convert between dict/map and vector

Extra doc: https://github.com/casadi/casadi/wiki/L_1wx

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L854

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1177-L1190

generate_lifted(*args)¶

generate_lifted(self) -> (Function OUTPUT, Function OUTPUT)

Extract the functions needed for the Lifted Newton method.

Extra doc: https://github.com/casadi/casadi/wiki/L_1xc

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1024

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1670-L1676

generate_out(*args)¶

generate_out(self, str fname) -> [DM]
generate_out(self, str fname, [DM] arg)

Export an output file that can be checked with generated C code

output.

See:: generate_in
See:: convert_out to convert between dict/map and vector

Extra doc: https://github.com/casadi/casadi/wiki/L_1wy

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L866

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1219-L1229

generate_out(self, str fname)

[INTERNAL] Export an output file that can be checked with generated C code

output.

See:: generate_in
See:: convert_out to convert between dict/map and vector

Extra doc: https://github.com/casadi/casadi/wiki/L_1wy

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L866

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1219-L1229

generate_out(self, str fname, [DM] arg)

[INTERNAL] Export an output file that can be checked with generated C code

output.

See:: generate_in
See:: convert_out to convert between dict/map and vector

Extra doc: https://github.com/casadi/casadi/wiki/L_1wy

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L865

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1192-L1205

get_free(*args)¶

get_free(self) -> [str]

Get free variables as a string.

Extra doc: https://github.com/casadi/casadi/wiki/L_1x9

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1009

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1159-L1161

get_function(*args)¶

get_function(self) -> [str]
get_function(self, str name) -> Function

Get a dependency function.

Extra doc: https://github.com/casadi/casadi/wiki/L_1y4

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1222

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1822-L1828

get_function(self, str name)

[INTERNAL] Get a dependency function.

Extra doc: https://github.com/casadi/casadi/wiki/L_1y4

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1222

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1822-L1828

get_function(self)

[INTERNAL] Get a list of all functions.

Extra doc: https://github.com/casadi/casadi/wiki/L_1y3

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1217

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1813-L1820

has_free(*args)¶

has_free(self) -> bool

Does the function have free variables.

Extra doc: https://github.com/casadi/casadi/wiki/L_1x8

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1004

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1666-L1668

has_function(*args)¶

has_function(self, str fname) -> bool

Check if a particular dependency exists.

Extra doc: https://github.com/casadi/casadi/wiki/L_1y5

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1227

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1830-L1837

has_option(*args)¶

has_option(self, str option_name) -> bool

Does a particular option exist.

Extra doc: https://github.com/casadi/casadi/wiki/L_1w1

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L447

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1138-L1145

has_spfwd(*args)¶

has_spfwd(self) -> bool

Is the class able to propagate seeds through the algorithm?

Extra doc: https://github.com/casadi/casadi/wiki/L_1xl

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1078

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1658-L1660

has_sprev(*args)¶

has_sprev(self) -> bool

Is the class able to propagate seeds through the algorithm?

Extra doc: https://github.com/casadi/casadi/wiki/L_1xl

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1079

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1662-L1664

hessian_old(*args)¶

hessian_old(self, int iind, int oind) -> Function

Extra doc: https://github.com/casadi/casadi/wiki/L_1w5

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L471

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L895-L903

static if_else(*args)¶

if_else(str name, Function f_true, Function f_false, dict opts) -> Function

index_in(*args)¶

index_in(self, str name) -> int

Find the index for a string describing a particular entry of an input scheme.

example: schemeEntry(“x_opt”) -> returns NLPSOL_X if FunctionInternal adheres to SCHEME_NLPINput

Extra doc: https://github.com/casadi/casadi/wiki/L_1vk

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L333

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L958-L964

index_out(*args)¶

index_out(self, str name) -> int

Find the index for a string describing a particular entry of an output

example: schemeEntry(“x_opt”) -> returns NLPSOL_X if FunctionInternal adheres to SCHEME_NLPINput

Extra doc: https://github.com/casadi/casadi/wiki/L_1vl

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L341

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L966-L972

info(*args)¶

info(self) -> dict

Obtain information about function

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1245

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1903-L1905

instruction_MX(*args)¶

instruction_MX(self, int k) -> MX

Get the MX node corresponding to an instruction (MXFunction)

Extra doc: https://github.com/casadi/casadi/wiki/L_1xj

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1064

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1686-L1692

instruction_constant(*args)¶

instruction_constant(self, int k) -> float

Get the floating point output argument of an instruction (SXFunction)

Extra doc: https://github.com/casadi/casadi/wiki/L_1xh

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1052

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1718-L1724

instruction_id(*args)¶

instruction_id(self, int k) -> int

Identifier index of the instruction (SXFunction/MXFunction)

Extra doc: https://github.com/casadi/casadi/wiki/L_1xf

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1040

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1702-L1708

instruction_input(*args)¶

instruction_input(self, int k) -> [int]

Locations in the work vector for the inputs of the instruction.

(SXFunction/MXFunction)

Extra doc: https://github.com/casadi/casadi/wiki/L_1xg

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1047

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1710-L1716

instruction_output(*args)¶

instruction_output(self, int k) -> [int]

Location in the work vector for the output of the instruction.

(SXFunction/MXFunction)

Extra doc: https://github.com/casadi/casadi/wiki/L_1xi

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1059

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1726-L1732

instructions_sx(*args)¶

instructions_sx(self) -> SX

Get the SX node corresponding to all instructions (SXFunction)

Note: input and output instructions have no SX representation. This method returns nan for those instructions.

Extra doc: https://github.com/casadi/casadi/wiki/L_1xk

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1072

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1694-L1700

is_a(*args)¶

is_a(self, str type, bool recursive) -> bool

Check if the function is of a particular type.

Optionally check if name matches one of the base classes (default true)

Extra doc: https://github.com/casadi/casadi/wiki/L_1xw

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1144

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1638-L1640

is_diff_in(*args)¶

is_diff_in(self) -> [bool]
is_diff_in(self, int ind) -> bool

Get differentiability of inputs/output.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vt

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L390

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1038-L1044

is_diff_in(self)

[INTERNAL] Get differentiability of inputs/output.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vt

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L390

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1038-L1044

is_diff_in(self, int ind)

[INTERNAL] Get differentiability of inputs/output.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vt

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L388

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1022-L1028

is_diff_out(*args)¶

is_diff_out(self) -> [bool]
is_diff_out(self, int ind) -> bool

Get differentiability of inputs/output.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vt

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L391

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1046-L1052

is_diff_out(self)

[INTERNAL] Get differentiability of inputs/output.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vt

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L391

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1046-L1052

is_diff_out(self, int ind)

[INTERNAL] Get differentiability of inputs/output.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vt

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L389

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1030-L1036

jac_sparsity(*args)¶

jac_sparsity(self, bool compact) -> [Sparsity]
jac_sparsity(self, int oind, int iind, bool compact) -> Sparsity

Get, if necessary generate, the sparsity of a single Jacobian block.

Extra doc: https://github.com/casadi/casadi/wiki/L_1wt

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L830

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L942-L948

jac_sparsity(self, bool compact)

[INTERNAL] Get, if necessary generate, the sparsity of all Jacobian blocks.

Extra doc: https://github.com/casadi/casadi/wiki/L_1ws

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L825

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L931-L940

jac_sparsity(self, int oind, int iind, bool compact)

[INTERNAL] Get, if necessary generate, the sparsity of a single Jacobian block.

Extra doc: https://github.com/casadi/casadi/wiki/L_1wt

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L830

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L942-L948

jacobian(*args)¶

jacobian(self) -> Function

Calculate all Jacobian blocks.

Generates a function that takes all non-differentiated inputs and outputs and calculates all Jacobian blocks. Inputs that are not needed

routine are all-zero sparse matrices with the correct dimensions. Output blocks that are not calculated, e.g. if the corresponding input or output is marked non-differentiated are also all-zero sparse. The Jacobian blocks are sorted starting by all the blocks for the first output, then all the blocks for the second output and so on. E.g. f : (x, y) -> (r, s) results in the function jac_f : (x, y, out_r, out_s) -> (jac_r_x, jac_r_y, jac_s_x,

This function is cached.

Extra doc: https://github.com/casadi/casadi/wiki/L_1w6

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L508

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L915-L921

jacobian_old(*args)¶

jacobian_old(self, int iind, int oind) -> Function

Extra doc: https://github.com/casadi/casadi/wiki/L_1w4

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L466

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L887-L893

static jit(*args)¶

jit(str name, str body, [str] name_in, [str] name_out, dict opts) -> Function
jit(str name, str body, [str] name_in, [str] name_out, [Sparsity] sparsity_in, [Sparsity] sparsity_out, dict opts) -> Function

Create a just-in-time compiled function from a C language string.

The names and sparsity patterns of all the inputs and outputs must be

provided. If sparsities are not provided, all inputs and outputs are

assumed to be scalar. Only specify the function body, assuming that input and output nonzeros are stored in arrays with the specified naming convension. The data type used is ‘casadi_real’, which is typically equal to ‘double or another data type with the same API as ‘double.

Inputs may be null pointers. This means that the all entries are zero.

Outputs may be null points. This means that the corresponding result can be

If an error occurs in the evaluation, issue “return 1;”;

The final generated function will have a structure similar to:

casadi_int fname(const casadi_real** arg, casadi_real** res, casadi_int* iw, casadi_real* w, void* mem) { const casadi_real *x1, *x2; casadi_real *r1, *r2; x1 = *arg++; x2 = *arg++; r1 = *res++; r2 =

<FUNCTION_BODY> return 0; }

Extra doc: https://github.com/casadi/casadi/wiki/L_1v3

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

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L293-L305

jit(str name, str body, [str] name_in, [str] name_out, dict opts)

[INTERNAL] Create a just-in-time compiled function from a C language string.

The names and sparsity patterns of all the inputs and outputs must be

provided. If sparsities are not provided, all inputs and outputs are

Inputs may be null pointers. This means that the all entries are zero.

Outputs may be null points. This means that the corresponding result can be

If an error occurs in the evaluation, issue “return 1;”;

The final generated function will have a structure similar to:

casadi_int fname(const casadi_real** arg, casadi_real** res, casadi_int* iw, casadi_real* w, void* mem) { const casadi_real *x1, *x2; casadi_real *r1, *r2; x1 = *arg++; x2 = *arg++; r1 = *res++; r2 =

<FUNCTION_BODY> return 0; }

Extra doc: https://github.com/casadi/casadi/wiki/L_1v3

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L185

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L284-L291

jit(str name, str body, [str] name_in, [str] name_out, [Sparsity] sparsity_in, [Sparsity] sparsity_out, dict opts)

[INTERNAL] Create a just-in-time compiled function from a C language string.

The names and sparsity patterns of all the inputs and outputs must be

provided. If sparsities are not provided, all inputs and outputs are

Inputs may be null pointers. This means that the all entries are zero.

Outputs may be null points. This means that the corresponding result can be

If an error occurs in the evaluation, issue “return 1;”;

The final generated function will have a structure similar to:

casadi_int fname(const casadi_real** arg, casadi_real** res, casadi_int* iw, casadi_real* w, void* mem) { const casadi_real *x1, *x2; casadi_real *r1, *r2; x1 = *arg++; x2 = *arg++; r1 = *res++; r2 =

<FUNCTION_BODY> return 0; }

Extra doc: https://github.com/casadi/casadi/wiki/L_1v3

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

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L293-L305

static load(*args)¶

load(str filename) -> Function

map(*args)¶

map(self, int n, str parallelization) -> Function
map(self, int n, [bool] reduce_in, [bool] reduce_out, dict opts) -> Function
map(self, int n, str parallelization, int max_num_threads) -> Function
map(self, str name, str parallelization, int n, [str] reduce_in, [str] reduce_out, dict opts) -> Function
map(self, str name, str parallelization, int n, [int] reduce_in, [int] reduce_out, dict opts) -> Function

Map with reduction.

A subset of the inputs are non-repeated and a subset of the outputs summed up.

Extra doc: https://github.com/casadi/casadi/wiki/L_1wk

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L745

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L636-L642

map(self, int n, [bool] reduce_in, [bool] reduce_out, dict opts)

[INTERNAL] Map with reduction.

A subset of the inputs are non-repeated and a subset of the outputs summed up.

Extra doc: https://github.com/casadi/casadi/wiki/L_1wk

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L745

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L636-L642

map(self, str name, str parallelization, int n, [str] reduce_in, [str] reduce_out, dict opts)

[INTERNAL] Map with reduction.

A subset of the inputs are non-repeated and a subset of the outputs summed up.

Extra doc: https://github.com/casadi/casadi/wiki/L_1wk

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L741

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L667-L674

map(self, str name, str parallelization, int n, [int] reduce_in, [int] reduce_out, dict opts)

[INTERNAL] Map with reduction.

A subset of the inputs are non-repeated and a subset of the outputs summed up.

Extra doc: https://github.com/casadi/casadi/wiki/L_1wk

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L737

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L644-L665

map(self, int n, str parallelization, int max_num_threads)

[INTERNAL]

map(self, int n, str parallelization)

[INTERNAL] Create a mapped version of this function.

Suppose the function has a signature of:

f: (a, p) -> ( s )

The the mapped version has the signature:

F: (A, P) -> (S )

 with
     A: horzcat([a0, a1, ..., a_(N-1)])
     P: horzcat([p0, p1, ..., p_(N-1)])
     S: horzcat([s0, s1, ..., s_(N-1)])
 and
     s0 <- f(a0, p0)
     s1 <- f(a1, p1)
     ...
     s_(N-1) <- f(a_(N-1), p_(N-1))

1. Parameters:¶

parallelization: Type of parallelization used: unroll|serial|openmp

Extra doc: https://github.com/casadi/casadi/wiki/L_1wj

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L726

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L708-L743

mapaccum(*args)¶

mapaccum(self, int N, dict opts) -> Function
mapaccum(self, str name, int N, dict opts) -> Function
mapaccum(self, str name, int N, int n_accum, dict opts) -> Function
mapaccum(self, str name, int n, [str] accum_in, [str] accum_out, dict opts) -> Function
mapaccum(self, str name, int n, [int] accum_in, [int] accum_out, dict opts) -> Function

Create a mapaccumulated version of this function.

Suppose the function has a signature of:

f: (x, u) -> (x_next , y )

The the mapaccumulated version has the signature:

F: (x0, U) -> (X , Y )

 with
     U: horzcat([u0, u1, ..., u_(N-1)])
     X: horzcat([x1, x2, ..., x_N])
     Y: horzcat([y0, y1, ..., y_(N-1)])

 and
     x1, y0 <- f(x0, u0)
     x2, y1 <- f(x1, u1)
     ...
     x_N, y_(N-1) <- f(x_(N-1), u_(N-1))

Mapaccum has the following benefits over writing an equivalent for- loop:

much faster at construction time

potentially much faster compilation times (for codegen)

offers a trade-off between memory and evaluation time

The base (settable through the options dictionary, default 10), is used to create a tower of function calls, containing unrolled for- loops of length maximum base.

This technique is much more scalable in terms of memory-usage, but slightly

similar to that: of a for-loop with a check-pointing instruction after

each chunk of iterations with size base.

Set base to -1 to unroll all the way; no gains in memory efficiency here.

Extra doc: https://github.com/casadi/casadi/wiki/L_1wi

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L697

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L515-L517

mapaccum(self, int N, dict opts)

[INTERNAL] Create a mapaccumulated version of this function.

Suppose the function has a signature of:

f: (x, u) -> (x_next , y )

The the mapaccumulated version has the signature:

F: (x0, U) -> (X , Y )

 with
     U: horzcat([u0, u1, ..., u_(N-1)])
     X: horzcat([x1, x2, ..., x_N])
     Y: horzcat([y0, y1, ..., y_(N-1)])

 and
     x1, y0 <- f(x0, u0)
     x2, y1 <- f(x1, u1)
     ...
     x_N, y_(N-1) <- f(x_(N-1), u_(N-1))

Mapaccum has the following benefits over writing an equivalent for- loop:

much faster at construction time

potentially much faster compilation times (for codegen)

offers a trade-off between memory and evaluation time

The base (settable through the options dictionary, default 10), is used to create a tower of function calls, containing unrolled for- loops of length maximum base.

This technique is much more scalable in terms of memory-usage, but slightly

similar to that: of a for-loop with a check-pointing instruction after

each chunk of iterations with size base.

Set base to -1 to unroll all the way; no gains in memory efficiency here.

Extra doc: https://github.com/casadi/casadi/wiki/L_1wi

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L697

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L515-L517

mapaccum(self, str name, int N, dict opts)

[INTERNAL] Create a mapaccumulated version of this function.

Suppose the function has a signature of:

f: (x, u) -> (x_next , y )

The the mapaccumulated version has the signature:

F: (x0, U) -> (X , Y )

 with
     U: horzcat([u0, u1, ..., u_(N-1)])
     X: horzcat([x1, x2, ..., x_N])
     Y: horzcat([y0, y1, ..., y_(N-1)])

 and
     x1, y0 <- f(x0, u0)
     x2, y1 <- f(x1, u1)
     ...
     x_N, y_(N-1) <- f(x_(N-1), u_(N-1))

Mapaccum has the following benefits over writing an equivalent for- loop:

much faster at construction time

potentially much faster compilation times (for codegen)

offers a trade-off between memory and evaluation time

The base (settable through the options dictionary, default 10), is used to create a tower of function calls, containing unrolled for- loops of length maximum base.

This technique is much more scalable in terms of memory-usage, but slightly

similar to that: of a for-loop with a check-pointing instruction after

each chunk of iterations with size base.

Set base to -1 to unroll all the way; no gains in memory efficiency here.

Extra doc: https://github.com/casadi/casadi/wiki/L_1wi

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L686

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L518-L520

mapaccum(self, str name, int N, int n_accum, dict opts)

[INTERNAL] Create a mapaccumulated version of this function.

Suppose the function has a signature of:

f: (x, u) -> (x_next , y )

The the mapaccumulated version has the signature:

F: (x0, U) -> (X , Y )

 with
     U: horzcat([u0, u1, ..., u_(N-1)])
     X: horzcat([x1, x2, ..., x_N])
     Y: horzcat([y0, y1, ..., y_(N-1)])

 and
     x1, y0 <- f(x0, u0)
     x2, y1 <- f(x1, u1)
     ...
     x_N, y_(N-1) <- f(x_(N-1), u_(N-1))

Mapaccum has the following benefits over writing an equivalent for- loop:

much faster at construction time

potentially much faster compilation times (for codegen)

offers a trade-off between memory and evaluation time

The base (settable through the options dictionary, default 10), is used to create a tower of function calls, containing unrolled for- loops of length maximum base.

This technique is much more scalable in terms of memory-usage, but slightly

similar to that: of a for-loop with a check-pointing instruction after

each chunk of iterations with size base.

Set base to -1 to unroll all the way; no gains in memory efficiency here.

Extra doc: https://github.com/casadi/casadi/wiki/L_1wi

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L687

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L521-L549

mapaccum(self, str name, int n, [str] accum_in, [str] accum_out, dict opts)

[INTERNAL] Create a mapaccumulated version of this function.

Suppose the function has a signature of:

f: (x, u) -> (x_next , y )

The the mapaccumulated version has the signature:

F: (x0, U) -> (X , Y )

 with
     U: horzcat([u0, u1, ..., u_(N-1)])
     X: horzcat([x1, x2, ..., x_N])
     Y: horzcat([y0, y1, ..., y_(N-1)])

 and
     x1, y0 <- f(x0, u0)
     x2, y1 <- f(x1, u1)
     ...
     x_N, y_(N-1) <- f(x_(N-1), u_(N-1))

Mapaccum has the following benefits over writing an equivalent for- loop:

much faster at construction time

potentially much faster compilation times (for codegen)

offers a trade-off between memory and evaluation time

The base (settable through the options dictionary, default 10), is used to create a tower of function calls, containing unrolled for- loops of length maximum base.

This technique is much more scalable in terms of memory-usage, but slightly

similar to that: of a for-loop with a check-pointing instruction after

each chunk of iterations with size base.

Set base to -1 to unroll all the way; no gains in memory efficiency here.

Extra doc: https://github.com/casadi/casadi/wiki/L_1wi

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L693

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L626-L634

mapaccum(self, str name, int n, [int] accum_in, [int] accum_out, dict opts)

[INTERNAL] Create a mapaccumulated version of this function.

Suppose the function has a signature of:

f: (x, u) -> (x_next , y )

The the mapaccumulated version has the signature:

F: (x0, U) -> (X , Y )

 with
     U: horzcat([u0, u1, ..., u_(N-1)])
     X: horzcat([x1, x2, ..., x_N])
     Y: horzcat([y0, y1, ..., y_(N-1)])

 and
     x1, y0 <- f(x0, u0)
     x2, y1 <- f(x1, u1)
     ...
     x_N, y_(N-1) <- f(x_(N-1), u_(N-1))

Mapaccum has the following benefits over writing an equivalent for- loop:

much faster at construction time

potentially much faster compilation times (for codegen)

offers a trade-off between memory and evaluation time

The base (settable through the options dictionary, default 10), is used to create a tower of function calls, containing unrolled for- loops of length maximum base.

This technique is much more scalable in terms of memory-usage, but slightly

similar to that: of a for-loop with a check-pointing instruction after

each chunk of iterations with size base.

Set base to -1 to unroll all the way; no gains in memory efficiency here.

Extra doc: https://github.com/casadi/casadi/wiki/L_1wi

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L689

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L596-L624

mapsum(*args)¶

mapsum(self, [MX] x, str parallelization) -> [MX]

Evaluate symbolically in parallel and sum (matrix graph)

1. Parameters:¶

parallelization: Type of parallelization used: unroll|serial|openmp

Extra doc: https://github.com/casadi/casadi/wiki/L_1wh

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L642

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L755-L762

max_in(*args)¶

max_in(self, int ind) -> float

Get largest input value.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vn

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L351

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1458-L1460

min_in(*args)¶

min_in(self, int ind) -> float

Get smallest input value.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vo

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L356

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1462-L1464

mx_in(*args)¶

mx_in(self) -> [MX]
mx_in(self, int ind) -> MX
mx_in(self, str iname) -> MX

Get symbolic primitives equivalent to the input expressions.

There is no guarantee that subsequent calls return unique answers

Extra doc: https://github.com/casadi/casadi/wiki/L_1x4

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L949

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1566-L1568

mx_in(self)

[INTERNAL] Get symbolic primitives equivalent to the input expressions.

There is no guarantee that subsequent calls return unique answers

Extra doc: https://github.com/casadi/casadi/wiki/L_1x4

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L949

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1566-L1568

mx_in(self, int ind)

[INTERNAL] Get symbolic primitives equivalent to the input expressions.

There is no guarantee that subsequent calls return unique answers

Extra doc: https://github.com/casadi/casadi/wiki/L_1x4

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L945

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1558-L1560

mx_in(self, str iname)

[INTERNAL] Get symbolic primitives equivalent to the input expressions.

There is no guarantee that subsequent calls return unique answers

Extra doc: https://github.com/casadi/casadi/wiki/L_1x4

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L946

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L946-L948

mx_out(*args)¶

mx_out(self) -> [MX]
mx_out(self, int ind) -> MX
mx_out(self, str oname) -> MX

Get symbolic primitives equivalent to the output expressions.

There is no guarantee that subsequent calls return unique answers

Extra doc: https://github.com/casadi/casadi/wiki/L_1x5

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L967

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1570-L1572

mx_out(self)

[INTERNAL] Get symbolic primitives equivalent to the output expressions.

There is no guarantee that subsequent calls return unique answers

Extra doc: https://github.com/casadi/casadi/wiki/L_1x5

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L967

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1570-L1572

mx_out(self, int ind)

[INTERNAL] Get symbolic primitives equivalent to the output expressions.

There is no guarantee that subsequent calls return unique answers

Extra doc: https://github.com/casadi/casadi/wiki/L_1x5

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L963

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1562-L1564

mx_out(self, str oname)

[INTERNAL] Get symbolic primitives equivalent to the output expressions.

There is no guarantee that subsequent calls return unique answers

Extra doc: https://github.com/casadi/casadi/wiki/L_1x5

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L964

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L964-L966

n_in(*args)¶

n_in(self) -> int

Get the number of function inputs.

Extra doc: https://github.com/casadi/casadi/wiki/L_1v8

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L228

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L818-L820

n_instructions(*args)¶

n_instructions(self) -> int

Number of instruction in the algorithm (SXFunction/MXFunction)

Extra doc: https://github.com/casadi/casadi/wiki/L_1xe

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1035

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1678-L1684

n_nodes(*args)¶

n_nodes(self) -> int

Number of nodes in the algorithm.

Extra doc: https://github.com/casadi/casadi/wiki/L_1xd

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1030

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1734-L1740

n_out(*args)¶

n_out(self) -> int

Get the number of function outputs.

Extra doc: https://github.com/casadi/casadi/wiki/L_1v9

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L233

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L822-L824

name(*args)¶

name(self) -> str

Name of the function.

Extra doc: https://github.com/casadi/casadi/wiki/L_1xv

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1137

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1281-L1288

name_in(*args)¶

name_in(self) -> [str]
name_in(self, int ind) -> str

Get input scheme name by index.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vi

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L320

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L974-L980

name_in(self, int ind)

[INTERNAL] Get input scheme name by index.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vi

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L320

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L974-L980

name_in(self)

[INTERNAL] Get input scheme.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vg

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L310

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L950-L952

name_out(*args)¶

name_out(self) -> [str]
name_out(self, int ind) -> str

Get output scheme name by index.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vj

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L325

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L982-L988

name_out(self, int ind)

[INTERNAL] Get output scheme name by index.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vj

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L325

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L982-L988

name_out(self)

[INTERNAL] Get output scheme.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vh

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L315

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L954-L956

nnz_in(*args)¶

nnz_in(self) -> int
nnz_in(self, int ind) -> int
nnz_in(self, str iname) -> int

Get number of input nonzeros.

For a particular input or for all of the inputs

Extra doc: https://github.com/casadi/casadi/wiki/L_1vc

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L271

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L271-L271

nnz_in(self)

[INTERNAL] Get number of input nonzeros.

For a particular input or for all of the inputs

Extra doc: https://github.com/casadi/casadi/wiki/L_1vc

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L269

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L850-L852

nnz_in(self, int ind)

[INTERNAL] Get number of input nonzeros.

For a particular input or for all of the inputs

Extra doc: https://github.com/casadi/casadi/wiki/L_1vc

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L270

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L866-L868

nnz_in(self, str iname)

[INTERNAL] Get number of input nonzeros.

For a particular input or for all of the inputs

Extra doc: https://github.com/casadi/casadi/wiki/L_1vc

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L271

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L271-L271

nnz_out(*args)¶

nnz_out(self) -> int
nnz_out(self, int ind) -> int
nnz_out(self, str oname) -> int

Get number of output nonzeros.

For a particular output or for all of the outputs

Extra doc: https://github.com/casadi/casadi/wiki/L_1vd

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L282

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L282-L282

nnz_out(self)

[INTERNAL] Get number of output nonzeros.

For a particular output or for all of the outputs

Extra doc: https://github.com/casadi/casadi/wiki/L_1vd

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L280

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L854-L856

nnz_out(self, int ind)

[INTERNAL] Get number of output nonzeros.

For a particular output or for all of the outputs

Extra doc: https://github.com/casadi/casadi/wiki/L_1vd

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L281

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L870-L872

nnz_out(self, str oname)

[INTERNAL] Get number of output nonzeros.

For a particular output or for all of the outputs

Extra doc: https://github.com/casadi/casadi/wiki/L_1vd

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L282

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L282-L282

nominal_in(*args)¶

nominal_in(self, int ind) -> [float]

Get nominal input value.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vp

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L361

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1466-L1468

nominal_out(*args)¶

nominal_out(self, int ind) -> [float]

Get nominal output value.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vq

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L366

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1470-L1472

numel_in(*args)¶

numel_in(self) -> int
numel_in(self, int ind) -> int
numel_in(self, str iname) -> int

Get number of input elements.

For a particular input or for all of the inputs

Extra doc: https://github.com/casadi/casadi/wiki/L_1ve

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L293

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L293-L293

numel_in(self)

[INTERNAL] Get number of input elements.

For a particular input or for all of the inputs

Extra doc: https://github.com/casadi/casadi/wiki/L_1ve

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L291

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L858-L860

numel_in(self, int ind)

[INTERNAL] Get number of input elements.

For a particular input or for all of the inputs

Extra doc: https://github.com/casadi/casadi/wiki/L_1ve

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L292

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L874-L876

numel_in(self, str iname)

[INTERNAL] Get number of input elements.

For a particular input or for all of the inputs

Extra doc: https://github.com/casadi/casadi/wiki/L_1ve

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L293

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L293-L293

numel_out(*args)¶

numel_out(self) -> int
numel_out(self, int ind) -> int
numel_out(self, str oname) -> int

Get number of output elements.

For a particular output or for all of the outputs

Extra doc: https://github.com/casadi/casadi/wiki/L_1vf

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L304

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L304-L304

numel_out(self)

[INTERNAL] Get number of output elements.

For a particular output or for all of the outputs

Extra doc: https://github.com/casadi/casadi/wiki/L_1vf

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L302

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L862-L864

numel_out(self, int ind)

[INTERNAL] Get number of output elements.

For a particular output or for all of the outputs

Extra doc: https://github.com/casadi/casadi/wiki/L_1vf

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L303

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L878-L880

numel_out(self, str oname)

[INTERNAL] Get number of output elements.

For a particular output or for all of the outputs

Extra doc: https://github.com/casadi/casadi/wiki/L_1vf

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L304

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L304-L304

nz_from_in(*args)¶

nz_from_in(self, [DM] arg) -> [float]

Convert from/to flat vector of input/output nonzeros.

Extra doc: https://github.com/casadi/casadi/wiki/L_1x6

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L974

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1574-L1576

nz_from_out(*args)¶

nz_from_out(self, [DM] arg) -> [float]

Convert from/to flat vector of input/output nonzeros.

Extra doc: https://github.com/casadi/casadi/wiki/L_1x6

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L975

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1578-L1580

nz_to_in(*args)¶

nz_to_in(self, [float] arg) -> [DM]

Convert from/to flat vector of input/output nonzeros.

Extra doc: https://github.com/casadi/casadi/wiki/L_1x6

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L976

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1582-L1584

nz_to_out(*args)¶

nz_to_out(self, [float] arg) -> [DM]

Convert from/to flat vector of input/output nonzeros.

Extra doc: https://github.com/casadi/casadi/wiki/L_1x6

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L977

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1586-L1588

oracle(*args)¶

oracle(self) -> Function

Get oracle.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vu

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L407

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1877-L1883

print_dimensions(*args)¶

print_dimensions(self)

Print dimensions of inputs and outputs.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vy

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L432

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1126-L1128

print_option(*args)¶

print_option(self, str name)

Print all information there is to know about a certain option.

Extra doc: https://github.com/casadi/casadi/wiki/L_1w0

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L442

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1134-L1136

print_options(*args)¶

print_options(self)

Print options to a stream.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vz

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L437

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1130-L1132

release(*args)¶

release(self, int mem)

Release a memory object.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1202

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1746-L1748

reverse(*args)¶

reverse(self, int nadj) -> Function

Get a function that calculates nadj adjoint derivatives.

 Returns a function with <tt>n_in + n_out + n_out</tt> inputs
 and <tt>n_in</tt> outputs.
 The first <tt>n_in</tt> inputs correspond to nondifferentiated inputs.
 The next <tt>n_out</tt> inputs correspond to nondifferentiated outputs.
 and the last <tt>n_out</tt> inputs correspond to adjoint seeds,
 stacked horizontally
 The  <tt>n_in</tt> outputs correspond to adjoint sensitivities,
 stacked horizontally.     *
 <tt>(n_in = n_in(), n_out = n_out())</tt>

 <tt>(n_in = n_in(), n_out = n_out())</tt>

The functions returned are cached, meaning that if called multiple timed
with the same value, then multiple references to the same function will be returned.

Extra doc: https://github.com/casadi/casadi/wiki/L_1wr

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L820

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1118-L1124

save(*args)¶

save(self, str fname, dict opts)

Save Function to a file.

See:: load

Extra doc: https://github.com/casadi/casadi/wiki/L_240

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L900

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1243-L1246

serialize(*args)¶

serialize(self, dict opts) -> str

Serialize.

Extra doc: https://github.com/casadi/casadi/wiki/L_1x2

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L893

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1248-L1252

size1_in(*args)¶

size1_in(self, int ind) -> int
size1_in(self, str iname) -> int

Get input dimension.

Extra doc: https://github.com/casadi/casadi/wiki/L_1va

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L240

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L240-L240

size1_in(self, int ind)

[INTERNAL] Get input dimension.

Extra doc: https://github.com/casadi/casadi/wiki/L_1va

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L239

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L826-L828

size1_in(self, str iname)

[INTERNAL] Get input dimension.

Extra doc: https://github.com/casadi/casadi/wiki/L_1va

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L240

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L240-L240

size1_out(*args)¶

size1_out(self, int ind) -> int
size1_out(self, str oname) -> int

Get output dimension.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vb

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L254

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L254-L254

size1_out(self, int ind)

[INTERNAL] Get output dimension.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vb

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L253

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L834-L836

size1_out(self, str oname)

[INTERNAL] Get output dimension.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vb

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L254

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L254-L254

size2_in(*args)¶

size2_in(self, int ind) -> int
size2_in(self, str iname) -> int

Get input dimension.

Extra doc: https://github.com/casadi/casadi/wiki/L_1va

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L242

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L242-L242

size2_in(self, int ind)

[INTERNAL] Get input dimension.

Extra doc: https://github.com/casadi/casadi/wiki/L_1va

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L241

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L830-L832

size2_in(self, str iname)

[INTERNAL] Get input dimension.

Extra doc: https://github.com/casadi/casadi/wiki/L_1va

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L242

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L242-L242

size2_out(*args)¶

size2_out(self, int ind) -> int
size2_out(self, str oname) -> int

Get output dimension.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vb

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L256

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L256-L256

size2_out(self, int ind)

[INTERNAL] Get output dimension.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vb

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L255

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L838-L840

size2_out(self, str oname)

[INTERNAL] Get output dimension.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vb

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L256

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L256-L256

size_in(*args)¶

size_in(self, int ind) -> (int,int)
size_in(self, str iname) -> (int,int)

Get input dimension.

Extra doc: https://github.com/casadi/casadi/wiki/L_1va

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L244

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L244-L246

size_in(self, int ind)

[INTERNAL] Get input dimension.

Extra doc: https://github.com/casadi/casadi/wiki/L_1va

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L243

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L842-L844

size_in(self, str iname)

[INTERNAL] Get input dimension.

Extra doc: https://github.com/casadi/casadi/wiki/L_1va

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L244

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L244-L246

size_out(*args)¶

size_out(self, int ind) -> (int,int)
size_out(self, str oname) -> (int,int)

Get output dimension.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vb

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L258

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L258-L260

size_out(self, int ind)

[INTERNAL] Get output dimension.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vb

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L257

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L846-L848

size_out(self, str oname)

[INTERNAL] Get output dimension.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vb

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L258

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L258-L260

slice(*args)¶

slice(self, str name, [int] order_in, [int] order_out, dict opts) -> Function

returns a new function with a selection of inputs/outputs of the

original

Extra doc: https://github.com/casadi/casadi/wiki/L_1wl

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L754

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L746-L753

sparsity_in(*args)¶

sparsity_in(self, int ind) -> Sparsity
sparsity_in(self, str iname) -> Sparsity

Get sparsity of a given input.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vr

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L373

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L998-L1004

sparsity_in(self, int ind)

[INTERNAL] Get sparsity of a given input.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vr

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L372

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L990-L996

sparsity_in(self, str iname)

[INTERNAL] Get sparsity of a given input.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vr

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L373

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L998-L1004

sparsity_jac(*args)¶

sparsity_jac(self, str iind, int oind, bool compact, bool symmetric) -> Sparsity
sparsity_jac(self, int iind, int oind, bool compact, bool symmetric) -> Sparsity
sparsity_jac(self, int iind, str oind, bool compact, bool symmetric) -> Sparsity
sparsity_jac(self, str iind, str oind, bool compact, bool symmetric) -> Sparsity

block

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L485

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L485-L488

sparsity_jac(self, str iind, int oind, bool compact, bool symmetric)

[DEPRECATED] Get, if necessary generate, the sparsity of a Jacobian block

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L477

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L477-L480

sparsity_jac(self, int iind, int oind, bool compact, bool symmetric)

[DEPRECATED] Get, if necessary generate, the sparsity of a Jacobian block

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L475

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L906-L912

sparsity_jac(self, int iind, str oind, bool compact, bool symmetric)

[DEPRECATED] Get, if necessary generate, the sparsity of a Jacobian block

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L481

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L481-L484

sparsity_jac(self, str iind, str oind, bool compact, bool symmetric)

[DEPRECATED] Get, if necessary generate, the sparsity of a Jacobian block

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L485

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L485-L488

sparsity_out(*args)¶

sparsity_out(self, int ind) -> Sparsity
sparsity_out(self, str iname) -> Sparsity

Get sparsity of a given output.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vs

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L381

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1014-L1020

sparsity_out(self, int ind)

[INTERNAL] Get sparsity of a given output.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vs

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L380

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1006-L1012

sparsity_out(self, str iname)

[INTERNAL] Get sparsity of a given output.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vs

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L381

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1014-L1020

stats(*args)¶

stats(self, int mem) -> dict

Get all statistics obtained at the end of the last evaluate call.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L932

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L927-L929

sx_in(*args)¶

sx_in(self) -> [SX]
sx_in(self, int iind) -> SX
sx_in(self, str iname) -> SX

Get symbolic primitives equivalent to the input expressions.

There is no guarantee that subsequent calls return unique answers

Extra doc: https://github.com/casadi/casadi/wiki/L_1x4

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L944

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1542-L1548

sx_in(self)

[INTERNAL] Get symbolic primitives equivalent to the input expressions.

There is no guarantee that subsequent calls return unique answers

Extra doc: https://github.com/casadi/casadi/wiki/L_1x4

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L944

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1542-L1548

sx_in(self, int iind)

[INTERNAL] Get symbolic primitives equivalent to the input expressions.

There is no guarantee that subsequent calls return unique answers

Extra doc: https://github.com/casadi/casadi/wiki/L_1x4

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L940

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1526-L1532

sx_in(self, str iname)

[INTERNAL] Get symbolic primitives equivalent to the input expressions.

There is no guarantee that subsequent calls return unique answers

Extra doc: https://github.com/casadi/casadi/wiki/L_1x4

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L941

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L941-L943

sx_out(*args)¶

sx_out(self) -> [SX]
sx_out(self, int oind) -> SX
sx_out(self, str oname) -> SX

Get symbolic primitives equivalent to the output expressions.

There is no guarantee that subsequent calls return unique answers

Extra doc: https://github.com/casadi/casadi/wiki/L_1x5

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L962

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1550-L1556

sx_out(self)

[INTERNAL] Get symbolic primitives equivalent to the output expressions.

There is no guarantee that subsequent calls return unique answers

Extra doc: https://github.com/casadi/casadi/wiki/L_1x5

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L962

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1550-L1556

sx_out(self, int oind)

[INTERNAL] Get symbolic primitives equivalent to the output expressions.

There is no guarantee that subsequent calls return unique answers

Extra doc: https://github.com/casadi/casadi/wiki/L_1x5

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L958

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1534-L1540

sx_out(self, str oname)

[INTERNAL] Get symbolic primitives equivalent to the output expressions.

There is no guarantee that subsequent calls return unique answers

Extra doc: https://github.com/casadi/casadi/wiki/L_1x5

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L959

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L959-L961

sz_arg(*args)¶

sz_arg(self) -> size_t

Get required length of arg field.

Extra doc: https://github.com/casadi/casadi/wiki/L_1xm

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1085

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1058-L1058

sz_iw(*args)¶

sz_iw(self) -> size_t

Get required length of iw field.

Extra doc: https://github.com/casadi/casadi/wiki/L_1xo

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1095

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1062-L1062

sz_res(*args)¶

sz_res(self) -> size_t

Get required length of res field.

Extra doc: https://github.com/casadi/casadi/wiki/L_1xn

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1090

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1060-L1060

sz_w(*args)¶

sz_w(self) -> size_t

Get required length of w field.

Extra doc: https://github.com/casadi/casadi/wiki/L_1xp

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L1100

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1064-L1064

static type_name(*args)¶

type_name() -> str

uses_output(*args)¶

uses_output(self) -> bool

Do the derivative functions need nondifferentiated outputs?

Extra doc: https://github.com/casadi/casadi/wiki/L_1w3

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L460

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L882-L884

which_depends(*args)¶

which_depends(self, str s_in, [str] s_out, int order, bool tr) -> [bool]

Which variables enter with some order.

1. Parameters:¶

order: Only 1 (linear) and 2 (nonlinear) allowed

tr: Flip the relationship. Return which expressions contain the variables

Extra doc: https://github.com/casadi/casadi/wiki/L_1vx

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L425

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1795-L1802

wrap(*args)¶

wrap(self) -> Function

Wrap in an Function instance consisting of only one MX call.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vv

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L412

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1885-L1887

wrap_as_needed(*args)¶

wrap_as_needed(self, dict opts) -> Function

Wrap in a Function with options.

Extra doc: https://github.com/casadi/casadi/wiki/L_1vw

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/function.hpp#L417

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/function.cpp#L1889-L1891

3. Solvers¶

3.1. NLP¶

nlpsol(*args)¶

nlpsol(str name, str solver, Importer compiler, dict opts) -> Function
nlpsol(str name, str solver, NlpBuilder nl, dict opts) -> Function
nlpsol(str name, str solver, dict:SX nlp, dict opts) -> Function
nlpsol(str name, str solver, dict:MX nlp, dict opts) -> Function
nlpsol(str name, str solver, str fname, dict opts) -> Function
nlpsol(str name, str solver, Function nlp, dict opts) -> Function

nlpsol(str name, str solver, dict:SX nlp, dict opts)

[INTERNAL]

Create an NLP solver Creates a solver for the following parametric

nonlinear program (NLP):

min          F(x, p)
x

subject to
LBX <=   x    <= UBX
LBG <= G(x, p) <= UBG
p  == P

nx: number of decision variables
ng: number of constraints
np: number of parameters

General information

>List of available options

Id	Type	Description	Used in
ad_weight	OT_DOUBLE	Weighting factor for derivative calculation.When there is an option of either using forward or reverse mode directional derivatives, the condition ad_wei ghtnf<=(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.	casadi::Function Internal
ad_weight_sp	OT_DOUBLE	Weighting factor for sparsity 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.	casadi::Function Internal
always_inline	OT_BOOL	Force inlining.	casadi::Function Internal
bound_consistenc y	OT_BOOL	Ensure that primal-dual solution is consistent with the bounds	casadi::Nlpsol
cache	OT_DICT	Prepopulate the function cache. Default: empty	casadi::Function Internal
calc_f	OT_BOOL	Calculate ‘f’ in the Nlpsol base class	casadi::Nlpsol
calc_g	OT_BOOL	Calculate ‘g’ in the Nlpsol base class	casadi::Nlpsol
calc_lam_p	OT_BOOL	Calculate ‘lam_p’ in the Nlpsol base class	casadi::Nlpsol
calc_lam_x	OT_BOOL	Calculate ‘lam_x’ in the Nlpsol base class	casadi::Nlpsol
calc_multipliers	OT_BOOL	Calculate Lagrange multipliers in the Nlpsol base class	casadi::Nlpsol
common_options	OT_DICT	Options for auto-generated functions	casadi::OracleFu nction
compiler	OT_STRING	Just-in-time compiler plugin to be used.	casadi::Function Internal
custom_jacobian	OT_FUNCTION	Override CasADi’s AD. Use together with ‘jac_penalty’: 0. Note: Highly experimental. Syntax may break often.	casadi::Function Internal
der_options	OT_DICT	Default options to be used to populate forward_options, reverse_options, and jacobian_options before those options are merged in.	casadi::Function Internal
derivative_of	OT_FUNCTION	The function is a derivative of another function. The type of derivative (directional derivative, Jacobian) is inferred from the function name.	casadi::Function Internal
detect_simple_bo unds	OT_BOOL	Automatically detect simple bounds (lbx/ubx) (default false). This is hopefully beneficial to speed and robustness but may also have adverse affects: 1) Subtleties in heuristics and stopping criteria may change the solution, 2) IPOPT may lie about multipliers of simple equality bounds unless ‘f ixed_variable_tr eatment’ is set to ‘relax_bounds’.	casadi::Nlpsol
detect_simple_bo unds_is_simple	OT_BOOLVECTOR	For internal use only.	casadi::Nlpsol
detect_simple_bo unds_parts	OT_FUNCTION	For internal use only.	casadi::Nlpsol
detect_simple_bo unds_target_x	OT_INTVECTOR	For internal use only.	casadi::Nlpsol
discrete	OT_BOOLVECTOR	Indicates which of the variables are discrete, i.e. integer- valued	casadi::Nlpsol
dump	OT_BOOL	Dump function to file upon first evaluation. [false]	casadi::Function Internal
dump_dir	OT_STRING	Directory to dump inputs/outputs to. Make sure the directory exists [.]	casadi::Function Internal
dump_format	OT_STRING	Choose file format to dump matrices. See DM.from_file [mtx]	casadi::Function Internal
dump_in	OT_BOOL	Dump numerical values of inputs to file (readable with DM.from_file ) [default: false]	casadi::Function Internal
dump_out	OT_BOOL	Dump numerical values of outputs to file (readable with DM.from_file ) [default: false]	casadi::Function Internal
enable_fd	OT_BOOL	Enable derivative calculation by finite differencing. [default: false]]	casadi::Function Internal
enable_forward	OT_BOOL	Enable derivative calculation using generated functions for Jacobian-times- vector products - typically using forward mode AD - if available. [default: true]	casadi::Function Internal
enable_jacobian	OT_BOOL	Enable derivative calculation using generated functions for Jacobians of all differentiable outputs with respect to all differentiable inputs - if available. [default: true]	casadi::Function Internal
enable_reverse	OT_BOOL	Enable derivative calculation using generated functions for transposed Jacobian-times- vector products - typically using reverse mode AD - if available. [default: true]	casadi::Function Internal
equality	OT_BOOLVECTOR	Indicate an upfront hint which of the constraints are equalities. Some solvers may be able to exploit this knowledge. When true, the corresponding lower and upper bounds are assumed equal. When false, the corresponding bounds may be equal or different.	casadi::Nlpsol
error_on_fail	OT_BOOL	Throw exceptions when function evaluation fails (default true).	casadi::ProtoFun ction
eval_errors_fata l	OT_BOOL	When errors occur during evaluation of f,g,…,stop the iterations	casadi::Nlpsol
expand	OT_BOOL	Replace MX with SX expressions in problem formulation [false]	casadi::OracleFu nction
external_transfo rm	OT_VECTORVECTOR	List of external _transform instruction arguments. Default: empty	casadi::Function Internal
fd_method	OT_STRING	Method for finite differencing [default ‘central’]	casadi::Function Internal
fd_options	OT_DICT	Options to be passed to the finite difference instance	casadi::Function Internal
forward_options	OT_DICT	Options to be passed to a forward mode constructor	casadi::Function Internal
gather_stats	OT_BOOL	Deprecated option (ignored): Statistics are now always collected.	casadi::Function Internal
ignore_check_vec	OT_BOOL	If set to true, the input shape of F will not be checked.	casadi::Nlpsol
input_scheme	OT_STRINGVECTOR	Deprecated option (ignored)	casadi::Function Internal
inputs_check	OT_BOOL	Throw exceptions when the numerical values of the inputs don’t make sense	casadi::Function Internal
is_diff_in	OT_BOOLVECTOR	Indicate for each input if it should be differentiable.	casadi::Function Internal
is_diff_out	OT_BOOLVECTOR	Indicate for each output if it should be differentiable.	casadi::Function Internal
iteration_callba ck	OT_FUNCTION	A function that will be called at each iteration with the solver as input. Check documentation of Callback .	casadi::Nlpsol
iteration_callba ck_ignore_errors	OT_BOOL	If set to true, errors thrown by iteration_callba ck will be ignored.	casadi::Nlpsol
iteration_callba ck_step	OT_INT	Only call the callback function every few iterations.	casadi::Nlpsol
jac_penalty	OT_DOUBLE	When requested for a number of 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	casadi::Function Internal
jacobian_options	OT_DICT	Options to be passed to a Jacobian constructor	casadi::Function Internal
jit	OT_BOOL	Use just-in-time compiler to speed up the evaluation	casadi::Function Internal
jit_cleanup	OT_BOOL	Cleanup up the temporary source file that jit creates. Default: true	casadi::Function Internal
jit_name	OT_STRING	The file name used to write out code. The actual file names used depend on ‘jit_t emp_suffix’ and include extensions. Default: ‘jit_tmp’	casadi::Function Internal
jit_options	OT_DICT	Options to be passed to the jit compiler.	casadi::Function Internal
jit_serialize	OT_STRING	Specify behaviour when serializing a jitted function: SOURCE\|link\|embe d.	casadi::Function Internal
jit_temp_suffix	OT_BOOL	Use a temporary (seemingly random) filename suffix for generated code and libraries. This is desired for thread- safety. This behaviour may defeat caching compiler wrappers. Default: true	casadi::Function Internal
max_io	OT_INT	Acceptable number of inputs and outputs. Warn if exceeded.	casadi::Function Internal
max_num_dir	OT_INT	Specify the maximum number of directions for derivative functions. Overrules the builtin optimize d_num_dir.	casadi::Function Internal
min_lam	OT_DOUBLE	Minimum allowed multiplier value	casadi::Nlpsol
monitor	OT_STRINGVECTOR	Set of user problem functions to be monitored	casadi::OracleFu nction
never_inline	OT_BOOL	Forbid inlining.	casadi::Function Internal
no_nlp_grad	OT_BOOL	Prevent the creation of the ‘nlp_grad’ function	casadi::Nlpsol
oracle_options	OT_DICT	Options to be passed to the oracle function	casadi::Nlpsol
output_scheme	OT_STRINGVECTOR	Deprecated option (ignored)	casadi::Function Internal
post_expand	OT_BOOL	After construction, expand this Function . Default: False	casadi::Function Internal
post_expand_opti ons	OT_DICT	Options to be passed to post- construction expansion. Default: empty	casadi::Function Internal
print_in	OT_BOOL	Print numerical values of inputs [default: false]	casadi::Function Internal
print_out	OT_BOOL	Print numerical values of outputs [default: false]	casadi::Function Internal
print_time	OT_BOOL	print information about execution time. Implies record_time.	casadi::ProtoFun ction
record_time	OT_BOOL	record information about execution time, for retrieval with stats().	casadi::ProtoFun ction
regularity_check	OT_BOOL	Throw exceptions when NaN or Inf appears during evaluation	casadi::ProtoFun ction
reverse_options	OT_DICT	Options to be passed to a reverse mode constructor	casadi::Function Internal
sens_linsol	OT_STRING	Linear solver used for parametric sensitivities (default ‘qr’).	casadi::Nlpsol
sens_linsol_opti ons	OT_DICT	Linear solver options used for parametric sensitivities.	casadi::Nlpsol
show_eval_warnin gs	OT_BOOL	Show warnings generated from function evaluations [true]	casadi::OracleFu nction
specific_options	OT_DICT	Options for specific auto- generated functions, overwriting the defaults from common_options. Nested dictionary.	casadi::OracleFu nction
user_data	OT_VOIDPTR	A user-defined field that can be used to identify the function or pass additional information	casadi::Function Internal
verbose	OT_BOOL	Verbose evaluation for debugging	casadi::ProtoFun ction
verbose_init	OT_BOOL	Print out timing information about the different stages of initialization	casadi::Nlpsol
warn_initial_bou nds	OT_BOOL	Warn if the initial guess does not satisfy LBX and UBX	casadi::Nlpsol

>Input scheme: casadi::NlpsolInput (NLPSOL_NUM_IN = 8)

Full name	Short	Description
NLPSOL_X0	x0	Decision variables, initial guess (nx x 1)
NLPSOL_P	p	Value of fixed parameters (np x 1)
NLPSOL_LBX	lbx	Decision variables lower bound (nx x 1), default -inf.
NLPSOL_UBX	ubx	Decision variables upper bound (nx x 1), default +inf.
NLPSOL_LBG	lbg	Constraints lower bound (ng x 1), default -inf.
NLPSOL_UBG	ubg	Constraints upper bound (ng x 1), default +inf.
NLPSOL_LAM_X0	lam_x0	Lagrange multipliers for bounds on X, initial guess (nx x 1)
NLPSOL_LAM_G0	lam_g0	Lagrange multipliers for bounds on G, initial guess (ng x 1)

>Output scheme: casadi::NlpsolOutput (NLPSOL_NUM_OUT = 6)

Full name	Short	Description
NLPSOL_X	x	Decision variables at the optimal solution (nx x 1)
NLPSOL_F	f	Cost function value at the optimal solution (1 x 1)
NLPSOL_G	g	Constraints function at the optimal solution (ng x 1)
NLPSOL_LAM_X	lam_x	Lagrange multipliers for bounds on X at the solution (nx x 1)
NLPSOL_LAM_G	lam_g	Lagrange multipliers for bounds on G at the solution (ng x 1)
NLPSOL_LAM_P	lam_p	Lagrange multipliers for bounds on P at the solution (np x 1)

List of plugins - AmplInterface

blocksqp
bonmin
fatrop
ipopt
knitro
madnlp
snopt
worhp
feasiblesqpmethod
qrsqp
scpgen
sqpmethod

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 Nlpsol.doc(“myextraplugin”)

1. AmplInterface¶

>List of available options

Id	Type	Description
solver	OT_STRING	AMPL solver binary

1. blocksqp¶

This is a modified version of blockSQP by Janka et al.

Dennis Janka, Joel Andersson

Extra doc: https://github.com/casadi/casadi/wiki/L_224

>List of available options

Id	Type	Description
block_hess	OT_INT	Blockwise Hessian approximation?
col_eps	OT_DOUBLE	Epsilon for COL scaling strategy
col_tau1	OT_DOUBLE	tau1 for COL scaling strategy
col_tau2	OT_DOUBLE	tau2 for COL scaling strategy
conv_strategy	OT_INT	Convexification strategy
delta	OT_DOUBLE	Filter line search parameter, cf. IPOPT paper
delta_h0	OT_DOUBLE	Filter line search parameter, cf. IPOPT paper
eps	OT_DOUBLE	Values smaller than this are regarded as numerically zero
eta	OT_DOUBLE	Filter line search parameter, cf. IPOPT paper
fallback_scaling	OT_INT	If indefinite update is used, the type of fallback strategy
fallback_update	OT_INT	If indefinite update is used, the type of fallback strategy
gamma_f	OT_DOUBLE	Filter line search parameter, cf. IPOPT paper
gamma_theta	OT_DOUBLE	Filter line search parameter, cf. IPOPT paper
globalization	OT_BOOL	Enable globalization
hess_damp	OT_INT	Activate Powell damping for BFGS
hess_damp_fac	OT_DOUBLE	Damping factor for BFGS Powell modification
hess_lim_mem	OT_INT	Full or limited memory
hess_memsize	OT_INT	Memory size for L-BFGS updates
hess_scaling	OT_INT	Scaling strategy for Hessian approximation
hess_update	OT_INT	Type of Hessian approximation
ini_hess_diag	OT_DOUBLE	Initial Hessian guess: diagonal matrix diag(iniHessDiag)
kappa_f	OT_DOUBLE	Filter line search parameter, cf. IPOPT paper
kappa_minus	OT_DOUBLE	Filter line search parameter, cf. IPOPT paper
kappa_plus	OT_DOUBLE	Filter line search parameter, cf. IPOPT paper
kappa_plus_max	OT_DOUBLE	Filter line search parameter, cf. IPOPT paper
kappa_soc	OT_DOUBLE	Filter line search parameter, cf. IPOPT paper
linsol	OT_STRING	The linear solver to be used by the QP method
max_consec_reduced_steps	OT_INT	Maximum number of consecutive reduced steps
max_consec_skipped_updates	OT_INT	Maximum number of consecutive skipped updates
max_conv_qp	OT_INT	How many additional QPs may be solved for convexification per iteration?
max_it_qp	OT_INT	Maximum number of QP iterations per SQP iteration
max_iter	OT_INT	Maximum number of SQP iterations
max_line_search	OT_INT	Maximum number of steps in line search
max_soc_iter	OT_INT	Maximum number of SOC line search iterations
max_time_qp	OT_DOUBLE	Maximum number of time in seconds per QP solve per SQP iteration
nlinfeastol	OT_DOUBLE	Nonlinear feasibility tolerance
obj_lo	OT_DOUBLE	Lower bound on objective function [-inf]
obj_up	OT_DOUBLE	Upper bound on objective function [inf]
opttol	OT_DOUBLE	Optimality tolerance
print_header	OT_BOOL	Print solver header at startup
print_iteration	OT_BOOL	Print SQP iterations
print_maxit_reached	OT_BOOL	Print error when maximum number of SQP iterations reached
qp_init	OT_BOOL	Use warmstarting
qpsol	OT_STRING	The QP solver to be used by the SQP method
qpsol_options	OT_DICT	Options to be passed to the QP solver
restore_feas	OT_BOOL	Use feasibility restoration phase
rho	OT_DOUBLE	Feasibility restoration phase parameter
s_f	OT_DOUBLE	Filter line search parameter, cf. IPOPT paper
s_theta	OT_DOUBLE	Filter line search parameter, cf. IPOPT paper
schur	OT_BOOL	Use qpOASES Schur compliment approach
skip_first_globalization	OT_BOOL	No globalization strategy in first iteration
theta_max	OT_DOUBLE	Filter line search parameter, cf. IPOPT paper
theta_min	OT_DOUBLE	Filter line search parameter, cf. IPOPT paper
warmstart	OT_BOOL	Use warmstarting
which_second_derv	OT_INT	For which block should second derivatives be provided by the user
zeta	OT_DOUBLE	Feasibility restoration phase parameter

1. bonmin¶

When in warmstart mode, output NLPSOL_LAM_X may be used as input

NOTE: Even when max_iter == 0, it is not guaranteed that input(NLPSOL_X0) == output(NLPSOL_X). Indeed if bounds on X or constraints are unmet, they will differ.

For a good tutorial on BONMIN, see http://drops.dagstuhl.de/volltexte/2009/2089/pdf/09061.WaechterAndreas.Paper.2089.pdf

A good resource about the algorithms in BONMIN is: Wachter and L. T.

Biegler, On the Implementation of an Interior-Point Filter Line-Search

Algorithm for Large-Scale Nonlinear Programming, Mathematical Programming 106(1), pp. 25-57, 2006 (As Research Report RC 23149, IBM T. J. Watson Research Center, Yorktown, USA

Caveats: with default options, multipliers for the decision variables are wrong

‘make_constraint’ or ‘relax_bounds’ to obtain correct results.

Extra doc: https://github.com/casadi/casadi/wiki/L_223

>List of available options

Id	Type	Description
bonmin	OT_DICT	Options to be passed to BONMIN
con_integer_md	OT_DICT	Integer metadata (a dictionary with lists of integers) about constraints to be passed to BONMIN
con_numeric_md	OT_DICT	Numeric metadata (a dictionary with lists of reals) about constraints to be passed to BONMIN
con_string_md	OT_DICT	String metadata (a dictionary with lists of strings) about constraints to be passed to BONMIN
grad_f	OT_FUNCTION	Function for calculating the gradient of the objective (column, autogenerated by default)
grad_f_options	OT_DICT	Options for the autogenerated gradient of the objective.
hess_lag	OT_FUNCTION	Function for calculating the Hessian of the Lagrangian (autogenerated by default)
hess_lag_options	OT_DICT	Options for the autogenerated Hessian of the Lagrangian.
jac_g	OT_FUNCTION	Function for calculating the Jacobian of the constraints (autogenerated by default)
jac_g_options	OT_DICT	Options for the autogenerated Jacobian of the constraints.
pass_nonlinear_constrai nts	OT_BOOL	Pass list of constraints entering nonlinearly to BONMIN
pass_nonlinear_variable s	OT_BOOL	Pass list of variables entering nonlinearly to BONMIN
sos1_groups	OT_INTVECTORVECTOR	Options for the autogenerated gradient of the objective.
sos1_priorities	OT_INTVECTOR	Options for the autogenerated gradient of the objective.
sos1_weights	OT_DOUBLEVECTORVECTOR	Options for the autogenerated gradient of the objective.
var_integer_md	OT_DICT	Integer metadata (a dictionary with lists of integers) about variables to be passed to BONMIN
var_numeric_md	OT_DICT	Numeric metadata (a dictionary with lists of reals) about variables to be passed to BONMIN
var_string_md	OT_DICT	String metadata (a dictionary with lists of strings) about variables to be passed to BONMIN

1. fatrop¶

>List of available options

Id	Type	Description
N	OT_INT	OCP horizon
convexify_margin	OT_DOUBLE	When using a convexification strategy, make sure that the smallest eigenvalue is at least this (default: 1e-7).
convexify_strategy	OT_STRING	NONE\|regularize\|eigen- reflect\|eigen-clip. Strategy to convexify the Lagrange Hessian before passing it to the solver.
debug	OT_BOOL	Produce debug information (default: false)
fatrop	OT_DICT	Options to be passed to fatrop
ng	OT_INTVECTOR	Number of non-dynamic constraints, length N+1
nu	OT_INTVECTOR	Number of controls, length N+1
nx	OT_INTVECTOR	Number of states, length N+1
structure_detection	OT_STRING	NONE \| auto \| manual

Fatrop is a solver developed at KU Leuven by Lander Vanroye and Wilm Decre.

efficient.

With structure_detection = ‘none’ (default), it will behave as a general- purpose dense nonlinear program solver.

With structure_detection = ‘manual’, you can specify a block structure.

Let’s say you perform multiply shooting with a system

x_k+1 = A_k x_k + B_k u_k

Suppose your constraint Jacobian looks like:

nx0  nu0  nx1  nu1  nx2  nu2
-----------------------------

nx1 |A0 B0 I0: ng1 |C0 D0 nx2 | A1 B1 I1 ng2 | C1 D1 ng3 | C2 D2

with n* capturing the number of states, inputs, and constraints in each block.

You can then specify this structure with:

N = 2 nx = [nx0 ,nx1, nx2] nu = [nu0, nu1, nu2] ng = [ng1, ng2, ng3]

With structure_detection = ‘auto’, the block-defining parameters nx, nu, ng, and N are automatically detected from the sparsity pattern.

1. ipopt¶

When in warmstart mode, output NLPSOL_LAM_X may be used as input

NOTE: Even when max_iter == 0, it is not guaranteed that input(NLPSOL_X0) == output(NLPSOL_X). Indeed if bounds on X or constraints are unmet, they will differ.

For a good tutorial on IPOPT, see http://drops.dagstuhl.de/volltexte/2009/2089/pdf/09061.WaechterAndreas.Paper.2089.pdf

A good resource about the algorithms in IPOPT is: Wachter and L. T.

Biegler, On the Implementation of an Interior-Point Filter Line-Search

Algorithm for Large-Scale Nonlinear Programming, Mathematical Programming 106(1), pp. 25-57, 2006 (As Research Report RC 23149, IBM T. J. Watson Research Center, Yorktown, USA

Caveats: with default options, multipliers for the decision variables are wrong

‘make_constraint’ or ‘relax_bounds’ to obtain correct results.

Extra doc: https://github.com/casadi/casadi/wiki/L_21y

>List of available options

Id	Type	Description
clip_inactive_lam	OT_BOOL	Explicitly set Lagrange multipliers to 0 when bound is deemed inactive (default: false).
con_integer_md	OT_DICT	Integer metadata (a dictionary with lists of integers) about constraints to be passed to IPOPT
con_numeric_md	OT_DICT	Numeric metadata (a dictionary with lists of reals) about constraints to be passed to IPOPT
con_string_md	OT_DICT	String metadata (a dictionary with lists of strings) about constraints to be passed to IPOPT
convexify_margin	OT_DOUBLE	When using a convexification strategy, make sure that the smallest eigenvalue is at least this (default: 1e-7).
convexify_strategy	OT_STRING	NONE\|regularize\|eigen- reflect\|eigen-clip. Strategy to convexify the Lagrange Hessian before passing it to the solver.
grad_f	OT_FUNCTION	Function for calculating the gradient of the objective (column, autogenerated by default)
hess_lag	OT_FUNCTION	Function for calculating the Hessian of the Lagrangian (autogenerated by default)
inactive_lam_strategy	OT_STRING	Strategy to detect if a bound is inactive. RELTOL: use solver-defined constraint tolerance * inactive_lam_value\|abstol: use inactive_lam_value
inactive_lam_value	OT_DOUBLE	Value used in inactive_lam_strategy (default: 10).
ipopt	OT_DICT	Options to be passed to IPOPT
jac_g	OT_FUNCTION	Function for calculating the Jacobian of the constraints (autogenerated by default)
max_iter_eig	OT_DOUBLE	Maximum number of iterations to compute an eigenvalue decomposition (default: 50).
pass_nonlinear_variables	OT_BOOL	Pass list of variables entering nonlinearly to IPOPT
var_integer_md	OT_DICT	Integer metadata (a dictionary with lists of integers) about variables to be passed to IPOPT
var_numeric_md	OT_DICT	Numeric metadata (a dictionary with lists of reals) about variables to be passed to IPOPT
var_string_md	OT_DICT	String metadata (a dictionary with lists of strings) about variables to be passed to IPOPT

1. knitro¶

KNITRO interface

Extra doc: https://github.com/casadi/casadi/wiki/L_22c

>List of available options

Id	Type	Description
complem_variables	OT_INTVECTORVECTOR	List of complementary constraints on simple bounds. Pair (i, j) encodes complementarity between the bounds on variable i and variable j.
contype	OT_INTVECTOR	Type of constraint
detect_linear_constraint s	OT_BOOL	Detect type of constraints
knitro	OT_DICT	Options to be passed to KNITRO
options_file	OT_STRING	Read options from file (solver specific)

1. madnlp¶

>List of available options

Id	Type	Description
convexify_margin	OT_DOUBLE	When using a convexification strategy, make sure that the smallest eigenvalue is at least this (default: 1e-7).
convexify_strategy	OT_STRING	NONE\|regularize\|eigen-reflect\|eigen- clip. Strategy to convexify the Lagrange Hessian before passing it to the solver.
madnlp	OT_DICT	Options to be passed to madnlp
ng	OT_INTVECTOR	Number of constraints
nw	OT_INTVECTOR	Number of variables

1. snopt¶

SNOPT interface

Extra doc: https://github.com/casadi/casadi/wiki/L_22m

>List of available options

Id	Type	Description
snopt	OT_DICT	Options to be passed to SNOPT
start	OT_STRING	Warm-start options for Worhp: cold\|warm\|hot

1. worhp¶

WORHP interface

Designed for Worhp 1.12

>List of available options

Id	Type	Description
worhp	OT_DICT	Options to be passed to WORHP

1. feasiblesqpmethod¶

A textbook FeasibleSQPMethod

Extra doc: https://github.com/casadi/casadi/wiki/L_241

>List of available options

Id	Type	Description
anderson_memory	OT_INT	Anderson memory. If Anderson is used default is 1, else default is 0.
contraction_acceptance_val ue	OT_DOUBLE	If the empirical contraction rate in the feasibility iterations is above this value in the heuristics the iterations are aborted.
convexify_margin	OT_DOUBLE	When using a convexification strategy, make sure that the smallest eigenvalue4 is at least this (default: 1e-7).
convexify_strategy	OT_STRING	NONE\|regularize\|eigen- reflect\|eigen-clip. Strategy to convexify the Lagrange Hessian before passing it to the solver.
f	OT_FUNCTION	Function for calculating the objective function (autogenerated by default)
feas_tol	OT_DOUBLE	Feasibility tolerance. Below this tolerance an iterate is considered to be feasible.
g	OT_FUNCTION	Function for calculating the constraints (autogenerated by default)
grad_f	OT_FUNCTION	Function for calculating the gradient of the objective (autogenerated by default)
hess_lag	OT_FUNCTION	Function for calculating the Hessian of the Lagrangian (autogenerated by default)
hessian_approximation	OT_STRING	limited-memory\|exact
init_feasible	OT_BOOL	Initialize the QP subproblems with a feasible initial value (default: false).
jac_g	OT_FUNCTION	Function for calculating the Jacobian of the constraints (autogenerated by default)
lbfgs_memory	OT_INT	Size of L-BFGS memory.
max_inner_iter	OT_DOUBLE	Maximum number of inner iterations.
max_iter	OT_INT	Maximum number of SQP iterations
max_iter_eig	OT_DOUBLE	Maximum number of iterations to compute an eigenvalue decomposition (default: 50).
merit_memory	OT_INT	Size of memory to store history of merit function values
min_iter	OT_INT	Minimum number of SQP iterations
optim_tol	OT_DOUBLE	Optimality tolerance. Below this value an iterate is considered to be optimal.
print_header	OT_BOOL	Print the header with problem statistics
print_iteration	OT_BOOL	Print the iterations
print_status	OT_BOOL	Print a status message after solving
qpsol	OT_STRING	The QP solver to be used by the SQP method [qpoases]
qpsol_options	OT_DICT	Options to be passed to the QP solver
solve_type	OT_STRING	The solver type: Either SQP or SLP. Defaults to SQP
tol_du	OT_DOUBLE	Stopping criterion for dual infeasability
tol_pr	OT_DOUBLE	Stopping criterion for primal infeasibility
tr_acceptance	OT_DOUBLE	Is the trust-region ratio above this value, the step is accepted.
tr_alpha1	OT_DOUBLE	Lower alpha in trust- region size criterion.
tr_alpha2	OT_DOUBLE	Upper alpha in trust- region size criterion.
tr_eta1	OT_DOUBLE	Lower eta in trust-region acceptance criterion.
tr_eta2	OT_DOUBLE	Upper eta in trust-region acceptance criterion.
tr_rad0	OT_DOUBLE	Initial trust-region radius.
tr_rad_max	OT_DOUBLE	Maximum trust-region radius.
tr_rad_min	OT_DOUBLE	Minimum trust-region radius.
tr_scale_vector	OT_DOUBLEVECTOR	Vector that tells where trust-region is applied.
tr_tol	OT_DOUBLE	Trust-region tolerance. Below this value another scalar is equal to the trust region radius.
use_anderson	OT_BOOL	Use Anderson Acceleration. (default false)
watchdog	OT_INT	Number of watchdog iterations in feasibility iterations. After this amount of iterations, it is checked with the contraction acceptance value, if iterations are converging.

1. qrsqp¶

A textbook SQPMethod

Extra doc: https://github.com/casadi/casadi/wiki/L_22u

1. scpgen¶

A structure-exploiting sequential quadratic programming (to be come

sequential convex programming) method for nonlinear programming.

Extra doc: https://github.com/casadi/casadi/wiki/L_232

>List of available options

Id	Type	Description
beta	OT_DOUBLE	Line-search parameter, restoration factor of stepsize
c1	OT_DOUBLE	Armijo condition, coefficient of decrease in merit
codegen	OT_BOOL	C-code generation
hessian_approximation	OT_STRING	gauss-newton\|exact
lbfgs_memory	OT_INT	Size of L-BFGS memory.
max_iter	OT_INT	Maximum number of SQP iterations
max_iter_ls	OT_INT	Maximum number of linesearch iterations
merit_memsize	OT_INT	Size of memory to store history of merit function values
merit_start	OT_DOUBLE	Lower bound for the merit function parameter
name_x	OT_STRINGVECTOR	Names of the variables.
print_header	OT_BOOL	Print the header with problem statistics
print_x	OT_INTVECTOR	Which variables to print.
qpsol	OT_STRING	The QP solver to be used by the SQP method
qpsol_options	OT_DICT	Options to be passed to the QP solver
reg_threshold	OT_DOUBLE	Threshold for the regularization.
regularize	OT_BOOL	Automatic regularization of Lagrange Hessian.
tol_du	OT_DOUBLE	Stopping criterion for dual infeasability
tol_pr	OT_DOUBLE	Stopping criterion for primal infeasibility
tol_pr_step	OT_DOUBLE	Stopping criterion for the step size
tol_reg	OT_DOUBLE	Stopping criterion for regularization

1. sqpmethod¶

A textbook SQPMethod

Extra doc: https://github.com/casadi/casadi/wiki/L_22x

>List of available options

Id	Type	Description
beta	OT_DOUBLE	Line-search parameter, restoration factor of stepsize
c1	OT_DOUBLE	Armijo condition, coefficient of decrease in merit
convexify_margin	OT_DOUBLE	When using a convexification strategy, make sure that the smallest eigenvalue is at least this (default: 1e-7).
convexify_strategy	OT_STRING	NONE\|regularize\|eigen- reflect\|eigen-clip. Strategy to convexify the Lagrange Hessian before passing it to the solver.
elastic_mode	OT_BOOL	Enable the elastic mode which is used when the QP is infeasible (default: false).
gamma_0	OT_DOUBLE	Starting value for the penalty parameter of elastic mode (default: 1).
gamma_1_min	OT_DOUBLE	Minimum value for gamma_1 (default: 1e-5).
gamma_max	OT_DOUBLE	Maximum value for the penalty parameter of elastic mode (default: 1e20).
hess_lag	OT_FUNCTION	Function for calculating the Hessian of the Lagrangian (autogenerated by default)
hessian_approximation	OT_STRING	limited-memory\|exact
init_feasible	OT_BOOL	Initialize the QP subproblems with a feasible initial value (default: false).
jac_fg	OT_FUNCTION	Function for calculating the gradient of the objective and Jacobian of the constraints (autogenerated by default)
lbfgs_memory	OT_INT	Size of L-BFGS memory.
max_iter	OT_INT	Maximum number of SQP iterations
max_iter_eig	OT_DOUBLE	Maximum number of iterations to compute an eigenvalue decomposition (default: 50).
max_iter_ls	OT_INT	Maximum number of linesearch iterations
merit_memory	OT_INT	Size of memory to store history of merit function values
min_iter	OT_INT	Minimum number of SQP iterations
min_step_size	OT_DOUBLE	The size (inf-norm) of the step size should not become smaller than this.
print_header	OT_BOOL	Print the header with problem statistics
print_iteration	OT_BOOL	Print the iterations
print_status	OT_BOOL	Print a status message after solving
qpsol	OT_STRING	The QP solver to be used by the SQP method [qpoases]
qpsol_options	OT_DICT	Options to be passed to the QP solver
second_order_corrections	OT_BOOL	Enable second order corrections. These are used when a step is considered bad by the merit function and constraint norm (default: false).
tol_du	OT_DOUBLE	Stopping criterion for dual infeasability
tol_pr	OT_DOUBLE	Stopping criterion for primal infeasibility

Joel Andersson

Extra doc: https://github.com/casadi/casadi/wiki/L_21q

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/nlpsol.hpp#L120

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/nlpsol.cpp#L120-L123

nlpsol(str name, str solver, Importer compiler, dict opts)
nlpsol(str name, str solver, NlpBuilder nl, dict opts)
nlpsol(str name, str solver, dict:MX nlp, dict opts)
nlpsol(str name, str solver, str fname, dict opts)
nlpsol(str name, str solver, Function nlp, dict opts)

[INTERNAL]

3.2. QP¶

3.2.1. High-level¶

qpsol(*args)¶

qpsol(str name, str solver, dict:SX qp, dict opts) -> Function
qpsol(str name, str solver, dict:MX qp, dict opts) -> Function

3.2.2. Low-level¶

conic(*args)¶

conic(str name, str solver, dict:Sparsity qp, dict opts) -> Function

Create a QP solver Solves the following strictly convex problem:

min          1/2 x' H x + g' x
x

subject to
LBA <= A x <= UBA
LBX <= x   <= UBX

resize(Q x, np, np) + P >= 0 (psd)

with :
H sparse (n x n) positive definite
g dense  (n x 1)
A sparse (nc x n)
Q sparse symmetric (np^2 x n)
P sparse symmetric (np x nq)

n: number of decision variables (x)
nc: number of constraints (A)
nq: shape of psd constraint matrix

If H is not positive-definite, the solver should throw an error.

Second-order cone constraints can be added as psd constraints through a helper function ‘soc’:

x in R^n y in R

|| x ||_2 <= y

<=>

soc(x, y) psd

This can be proven with soc(x, y)=[y*I x; x’ y] using the Shur complement.

General information

>List of available options

Id	Type	Description	Used in
ad_weight	OT_DOUBLE	Weighting factor for derivative calculation.When there is an option of either using forward or reverse mode directional derivatives, the condition ad_wei ghtnf<=(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.	casadi::Function Internal
ad_weight_sp	OT_DOUBLE	Weighting factor for sparsity 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.	casadi::Function Internal
always_inline	OT_BOOL	Force inlining.	casadi::Function Internal
cache	OT_DICT	Prepopulate the function cache. Default: empty	casadi::Function Internal
compiler	OT_STRING	Just-in-time compiler plugin to be used.	casadi::Function Internal
custom_jacobian	OT_FUNCTION	Override CasADi’s AD. Use together with ‘jac_penalty’: 0. Note: Highly experimental. Syntax may break often.	casadi::Function Internal
der_options	OT_DICT	Default options to be used to populate forward_options, reverse_options, and jacobian_options before those options are merged in.	casadi::Function Internal
derivative_of	OT_FUNCTION	The function is a derivative of another function. The type of derivative (directional derivative, Jacobian) is inferred from the function name.	casadi::Function Internal
discrete	OT_BOOLVECTOR	Indicates which of the variables are discrete, i.e. integer- valued	casadi::Conic
dump	OT_BOOL	Dump function to file upon first evaluation. [false]	casadi::Function Internal
dump_dir	OT_STRING	Directory to dump inputs/outputs to. Make sure the directory exists [.]	casadi::Function Internal
dump_format	OT_STRING	Choose file format to dump matrices. See DM.from_file [mtx]	casadi::Function Internal
dump_in	OT_BOOL	Dump numerical values of inputs to file (readable with DM.from_file ) [default: false]	casadi::Function Internal
dump_out	OT_BOOL	Dump numerical values of outputs to file (readable with DM.from_file ) [default: false]	casadi::Function Internal
enable_fd	OT_BOOL	Enable derivative calculation by finite differencing. [default: false]]	casadi::Function Internal
enable_forward	OT_BOOL	Enable derivative calculation using generated functions for Jacobian-times- vector products - typically using forward mode AD - if available. [default: true]	casadi::Function Internal
enable_jacobian	OT_BOOL	Enable derivative calculation using generated functions for Jacobians of all differentiable outputs with respect to all differentiable inputs - if available. [default: true]	casadi::Function Internal
enable_reverse	OT_BOOL	Enable derivative calculation using generated functions for transposed Jacobian-times- vector products - typically using reverse mode AD - if available. [default: true]	casadi::Function Internal
equality	OT_BOOLVECTOR	Indicate an upfront hint which of the constraints are equalities. Some solvers may be able to exploit this knowledge. When true, the corresponding lower and upper bounds are assumed equal. When false, the corresponding bounds may be equal or different.	casadi::Conic
error_on_fail	OT_BOOL	Throw exceptions when function evaluation fails (default true).	casadi::ProtoFun ction
external_transfo rm	OT_VECTORVECTOR	List of external _transform instruction arguments. Default: empty	casadi::Function Internal
fd_method	OT_STRING	Method for finite differencing [default ‘central’]	casadi::Function Internal
fd_options	OT_DICT	Options to be passed to the finite difference instance	casadi::Function Internal
forward_options	OT_DICT	Options to be passed to a forward mode constructor	casadi::Function Internal
gather_stats	OT_BOOL	Deprecated option (ignored): Statistics are now always collected.	casadi::Function Internal
input_scheme	OT_STRINGVECTOR	Deprecated option (ignored)	casadi::Function Internal
inputs_check	OT_BOOL	Throw exceptions when the numerical values of the inputs don’t make sense	casadi::Function Internal
is_diff_in	OT_BOOLVECTOR	Indicate for each input if it should be differentiable.	casadi::Function Internal
is_diff_out	OT_BOOLVECTOR	Indicate for each output if it should be differentiable.	casadi::Function Internal
jac_penalty	OT_DOUBLE	When requested for a number of 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	casadi::Function Internal
jacobian_options	OT_DICT	Options to be passed to a Jacobian constructor	casadi::Function Internal
jit	OT_BOOL	Use just-in-time compiler to speed up the evaluation	casadi::Function Internal
jit_cleanup	OT_BOOL	Cleanup up the temporary source file that jit creates. Default: true	casadi::Function Internal
jit_name	OT_STRING	The file name used to write out code. The actual file names used depend on ‘jit_t emp_suffix’ and include extensions. Default: ‘jit_tmp’	casadi::Function Internal
jit_options	OT_DICT	Options to be passed to the jit compiler.	casadi::Function Internal
jit_serialize	OT_STRING	Specify behaviour when serializing a jitted function: SOURCE\|link\|embe d.	casadi::Function Internal
jit_temp_suffix	OT_BOOL	Use a temporary (seemingly random) filename suffix for generated code and libraries. This is desired for thread- safety. This behaviour may defeat caching compiler wrappers. Default: true	casadi::Function Internal
max_io	OT_INT	Acceptable number of inputs and outputs. Warn if exceeded.	casadi::Function Internal
max_num_dir	OT_INT	Specify the maximum number of directions for derivative functions. Overrules the builtin optimize d_num_dir.	casadi::Function Internal
never_inline	OT_BOOL	Forbid inlining.	casadi::Function Internal
output_scheme	OT_STRINGVECTOR	Deprecated option (ignored)	casadi::Function Internal
post_expand	OT_BOOL	After construction, expand this Function . Default: False	casadi::Function Internal
post_expand_opti ons	OT_DICT	Options to be passed to post- construction expansion. Default: empty	casadi::Function Internal
print_in	OT_BOOL	Print numerical values of inputs [default: false]	casadi::Function Internal
print_out	OT_BOOL	Print numerical values of outputs [default: false]	casadi::Function Internal
print_problem	OT_BOOL	Print a numeric description of the problem	casadi::Conic
print_time	OT_BOOL	print information about execution time. Implies record_time.	casadi::ProtoFun ction
record_time	OT_BOOL	record information about execution time, for retrieval with stats().	casadi::ProtoFun ction
regularity_check	OT_BOOL	Throw exceptions when NaN or Inf appears during evaluation	casadi::ProtoFun ction
reverse_options	OT_DICT	Options to be passed to a reverse mode constructor	casadi::Function Internal
user_data	OT_VOIDPTR	A user-defined field that can be used to identify the function or pass additional information	casadi::Function Internal
verbose	OT_BOOL	Verbose evaluation for debugging	casadi::ProtoFun ction

>Input scheme: casadi::ConicInput (CONIC_NUM_IN = 12)

Full name	Short	Description
CONIC_H	h	The square matrix H: sparse, (n x n). Only the lower triangular part is actually used. The matrix is assumed to be symmetrical.
CONIC_G	g	The vector g: dense, (n x 1)
CONIC_A	a	The matrix A: sparse, (nc x n) - product with x must be dense.
CONIC_LBA	lba	dense, (nc x 1)
CONIC_UBA	uba	dense, (nc x 1)
CONIC_LBX	lbx	dense, (n x 1)
CONIC_UBX	ubx	dense, (n x 1)
CONIC_X0	x0	dense, (n x 1)
CONIC_LAM_X0	lam_x0	dense
CONIC_LAM_A0	lam_a0	dense
CONIC_Q	q	The matrix Q: sparse symmetric, (np^2 x n)
CONIC_P	p	The matrix P: sparse symmetric, (np x np)

>Output scheme: casadi::ConicOutput (CONIC_NUM_OUT = 4)

Full name	Short	Description
CONIC_X	x	The primal solution.
CONIC_COST	cost	The optimal cost.
CONIC_LAM_A	lam_a	The dual solution corresponding to linear bounds.
CONIC_LAM_X	lam_x	The dual solution corresponding to simple bounds.

List of plugins - cbc

clp
cplex
daqp
fatrop
gurobi
highs
hpipm
hpmpc
ooqp
osqp
proxqp
qpoases
sqic
superscs
ipqp
nlpsol
qrqp

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 Conic.doc(“myextraplugin”)

1. cbc¶

Interface to Cbc solver for sparse Quadratic Programs

Extra doc: https://github.com/casadi/casadi/wiki/L_221

>List of available options

Id	Type	Description
cbc	OT_DICT	Options to be passed to CBC.Three sets of options are supported. The first can be found in OsiSolverParameters.hpp. The second can be found in CbcModel.hpp. The third are options that can be passed to CbcMain1.
hot_start	OT_BOOL	Hot start with x0 [Default false].
sos_groups	OT_INTVECTORVECTOR	Definition of SOS groups by indices.
sos_types	OT_INTVECTOR	Specify 1 or 2 for each SOS group.
sos_weights	OT_DOUBLEVECTORVECTOR	Weights corresponding to SOS entries.

1. clp¶

Interface to Clp solver for sparse Quadratic Programs

Extra doc: https://github.com/casadi/casadi/wiki/L_22d

>List of available options

Id	Type	Description
clp	OT_DICT	Options to be passed to CLP. A first set of options can be found in ClpParameters.hpp. eg. ‘PrimalTolerance’. There are other options in additions. ‘AutomaticScaling’ (bool) is recognised. ‘initial_solve’ (default off) activates the use of Clp’s initialSolve. ‘initial_solve_options’ takes a dictionary with following keys (see ClpSolve.hpp): SolveType (string), PresolveType (string), NumberPasses, SpecialOptions (intvectorvector), IndependentOptions (intvectorvector).

1. cplex¶

Interface to Cplex solver for sparse Quadratic Programs

Extra doc: https://github.com/casadi/casadi/wiki/L_22a

>List of available options

Id	Type	Description
cplex	OT_DICT	Options to be passed to CPLEX
dep_check	OT_INT	Detect redundant constraints.
dump_filename	OT_STRING	The filename to dump to.
dump_to_file	OT_BOOL	Dumps QP to file in CPLEX format.
mip_start	OT_BOOL	Hot start integers with x0 [Default false].
qp_method	OT_INT	Determines which CPLEX algorithm to use.
sos_groups	OT_INTVECTORVECTOR	Definition of SOS groups by indices.
sos_types	OT_INTVECTOR	Specify 1 or 2 for each SOS group.
sos_weights	OT_DOUBLEVECTORVECTOR	Weights corresponding to SOS entries.
tol	OT_DOUBLE	Tolerance of solver
version_suffix	OT_STRING	Specify version of cplex to load. We will attempt to load l ibcplex<version_suffix>.[so\|dll \|dylib]. Default value is taken from CPLEX_VERSION env variable.
warm_start	OT_BOOL	Use warm start with simplex methods (affects only the simplex methods).

1. daqp¶

Interface to Daqp solver for sparse Quadratic Programs, see daqp.dev for more information and https://www.maths.ed.ac.uk/hall/Daqp/DaqpOptions.html for a list of options.

Extra doc: https://github.com/casadi/casadi/wiki/L_27p

>List of available options

Id	Type	Description
daqp	OT_DICT	Options to be passed to Daqp.

1. fatrop¶

Interface to Fatrop Solver

In order to use this interface, you must:

Decision variables must only by state and control, and the variable

ordering must be [x0 u0 x1 u1 …]

The constraints must be in order: [ gap0 lincon0 gap1 lincon1 ]

gap: Ak+1 = Ak xk + Bk uk lincon: yk= Ck xk + Dk uk

A0 B0 -I
C0 D0
       A1 B1 -I
       C1 D1

where I must be a diagonal sparse matrix Either supply all of N, nx, ng, nu options or rely on automatic detection

Extra doc: https://github.com/casadi/casadi/wiki/L_27g

>List of available options

Id	Type	Description
N	OT_INT	OCP horizon
fatrop	OT_DICT	Options to be passed to fatrop
ng	OT_INTVECTOR	Number of non-dynamic constraints, length N+1
nu	OT_INTVECTOR	Number of controls, length N
nx	OT_INTVECTOR	Number of states, length N+1
structure_detection	OT_STRING	NONE \| auto \| manual

1. gurobi¶

Interface to the GUROBI Solver for quadratic programming

Extra doc: https://github.com/casadi/casadi/wiki/L_22q

>List of available options

Id	Type	Description
gurobi	OT_DICT	Options to be passed to gurobi.
sos_groups	OT_INTVECTORVECTOR	Definition of SOS groups by indices.
sos_types	OT_INTVECTOR	Specify 1 or 2 for each SOS group.
sos_weights	OT_DOUBLEVECTORVECTOR	Weights corresponding to SOS entries.
vtype	OT_STRINGVECTOR	Type of variables: [CONTINUOUS\|bin ary\|integer\|semicont\|semiint]

1. highs¶

Interface to HiGHS solver for sparse Quadratic Programs, see highs.dev for more information and https://www.maths.ed.ac.uk/hall/HiGHS/HighsOptions.html

Extra doc: https://github.com/casadi/casadi/wiki/L_22f

>List of available options

Id	Type	Description
highs	OT_DICT	Options to be passed to HiGHS.

1. hpipm¶

Interface to HPIPM Solver

In order to use this interface, you must:

Decision variables must only by state and control, and the variable

ordering must be [x0 u0 x1 u1 …]

The constraints must be in order: [ gap0 lincon0 gap1 lincon1 ]

gap: Ak+1 = Ak xk + Bk uk lincon: yk= Ck xk + Dk uk

A0 B0 -I
C0 D0
       A1 B1 -I
       C1 D1

where I must be a diagonal sparse matrix Either supply all of N, nx, ng, nu options or rely on automatic detection

Extra doc: https://github.com/casadi/casadi/wiki/L_242

>List of available options

Id	Type	Description
N	OT_INT	OCP horizon
hpipm	OT_DICT	Options to be passed to hpipm
inf	OT_DOUBLE	Replace infinities by this amount [default: 1e8]
ng	OT_INTVECTOR	Number of non-dynamic constraints, length N+1
nu	OT_INTVECTOR	Number of controls, length N
nx	OT_INTVECTOR	Number of states, length N+1

1. hpmpc¶

Interface to HMPC Solver

In order to use this interface, you must:

Decision variables must only by state and control, and the variable

ordering must be [x0 u0 x1 u1 …]

The constraints must be in order: [ gap0 lincon0 gap1 lincon1 ]

gap: Ak+1 = Ak xk + Bk uk lincon: yk= Ck xk + Dk uk

A0 B0 -I
C0 D0
       A1 B1 -I
       C1 D1

where I must be a diagonal sparse matrix Either supply all of N, nx, ng, nu options or rely on automatic detection

Extra doc: https://github.com/casadi/casadi/wiki/L_22p

>List of available options

Id	Type	Description
N	OT_INT	OCP horizon
blasfeo_target	OT_STRING	hpmpc target
inf	OT_DOUBLE	HPMPC cannot handle infinities. Infinities will be replaced by this option’s value.
max_iter	OT_INT	Max number of iterations
mu0	OT_DOUBLE	Max element in cost function as estimate of max multiplier
ng	OT_INTVECTOR	Number of non-dynamic constraints, length N+1
nu	OT_INTVECTOR	Number of controls, length N
nx	OT_INTVECTOR	Number of states, length N+1
print_level	OT_INT	Amount of diagnostic printing [Default: 1].
target	OT_STRING	hpmpc target
tol	OT_DOUBLE	Tolerance in the duality measure
warm_start	OT_BOOL	Use warm-starting

1. ooqp¶

Interface to the OOQP Solver for quadratic programming The current

implementation assumes that OOQP is configured with the MA27 sparse linear solver.

NOTE: when doing multiple calls to evaluate(), check if you need to

reInit();

Extra doc: https://github.com/casadi/casadi/wiki/L_222

>List of available options

Id	Type	Description
artol	OT_DOUBLE	tolerance as provided with setArTol to OOQP
mutol	OT_DOUBLE	tolerance as provided with setMuTol to OOQP
print_level	OT_INT	Print level. OOQP listens to print_level 0, 10 and 100

1. osqp¶

Interface to the OSQP Solver for quadratic programming

Extra doc: https://github.com/casadi/casadi/wiki/L_220

Interface to the PROXQP Solver for quadratic programming

Extra doc: https://github.com/casadi/casadi/wiki/L_243

>List of available options

Id	Type	Description
osqp	OT_DICT	const Options to be passed to osqp.
warm_start_dual	OT_BOOL	Use lam_a0 and lam_x0 input to warmstart [Default: truw].
warm_start_primal	OT_BOOL	Use x0 input to warmstart [Default: true].

1. proxqp¶

>List of available options

Id	Type	Description
proxqp	OT_DICT	const proxqp options.
warm_start_dual	OT_BOOL	Use y and z input to warmstart [Default: true].
warm_start_primal	OT_BOOL	Use x input to warmstart [Default: true].

1. qpoases¶

Interface to QPOases Solver for quadratic programming

Extra doc: https://github.com/casadi/casadi/wiki/L_22o

>List of available options

Id	Type	Description
CPUtime	OT_DOUBLE	The maximum allowed CPU time in seconds for the whole initialisation (and the actually required one on output). Disabled if unset.
boundRelaxation	OT_DOUBLE	Initial relaxation of bounds to start homotopy and initial value for far bounds.
boundTolerance	OT_DOUBLE	If upper and lower bounds differ less than this tolerance, they are regarded equal, i.e. as equality constraint.
enableCholeskyRefactorisation	OT_INT	Specifies the frequency of a full re-factorisation of projected Hessian matrix: 0: turns them off, 1: uses them at each iteration etc.
enableDriftCorrection	OT_INT	Specifies the frequency of drift corrections: 0: turns them off.
enableEqualities	OT_BOOL	Specifies whether equalities should be treated as always active (True) or not (False)
enableFarBounds	OT_BOOL	Enables the use of far bounds.
enableFlippingBounds	OT_BOOL	Enables the use of flipping bounds.
enableFullLITests	OT_BOOL	Enables condition-hardened (but more expensive) LI test.
enableInertiaCorrection	OT_BOOL	Should working set be repaired when negative curvature is discovered during hotstart.
enableNZCTests	OT_BOOL	Enables nonzero curvature tests.
enableRamping	OT_BOOL	Enables ramping.
enableRegularisation	OT_BOOL	Enables automatic Hessian regularisation.
epsDen	OT_DOUBLE	Denominator tolerance for ratio tests.
epsFlipping	OT_DOUBLE	Tolerance of squared Cholesky diagonal factor which triggers flipping bound.
epsIterRef	OT_DOUBLE	Early termination tolerance for iterative refinement.
epsLITests	OT_DOUBLE	Tolerance for linear independence tests.
epsNZCTests	OT_DOUBLE	Tolerance for nonzero curvature tests.
epsNum	OT_DOUBLE	Numerator tolerance for ratio tests.
epsRegularisation	OT_DOUBLE	Scaling factor of identity matrix used for Hessian regularisation.
finalRamping	OT_DOUBLE	Final value for ramping strategy.
growFarBounds	OT_DOUBLE	Factor to grow far bounds.
hessian_type	OT_STRING	Type of Hessian - see qpOASES documentation [UNKNO WN\|posdef\|semidef\|indef\|zero \|identity]]
initialFarBounds	OT_DOUBLE	Initial size for far bounds.
initialRamping	OT_DOUBLE	Start value for ramping strategy.
initialStatusBounds	OT_STRING	Initial status of bounds at first iteration.
linsol_plugin	OT_STRING	Linear solver plugin
maxDualJump	OT_DOUBLE	Maximum allowed jump in dual variables in linear independence tests.
maxPrimalJump	OT_DOUBLE	Maximum allowed jump in primal variables in nonzero curvature tests.
max_schur	OT_INT	Maximal number of Schur updates [75]
nWSR	OT_INT	The maximum number of working set recalculations to be performed during the initial homotopy. Default is 5(nx + nc)
numRefinementSteps	OT_INT	Maximum number of iterative refinement steps.
numRegularisationSteps	OT_INT	Maximum number of successive regularisation steps.
printLevel	OT_STRING	Defines the amount of text output during QP solution, see Section 5.7
schur	OT_BOOL	Use Schur Complement Approach [false]
sparse	OT_BOOL	Formulate the QP using sparse matrices. [false]
terminationTolerance	OT_DOUBLE	Relative termination tolerance to stop homotopy.

1. sqic¶

Interface to the SQIC solver for quadratic programming

Extra doc: https://github.com/casadi/casadi/wiki/L_21s

1. superscs¶

Interface to the SuperSCS solver for conic programming

Joris Gillis, 2019

Extra doc: https://github.com/casadi/casadi/wiki/L_21z

>List of available options

Id	Type	Description
superscs	OT_DICT	Options to be passed to superscs.

1. ipqp¶

Solves QPs using a Mehrotra predictor-corrector interior point method

Extra doc: https://github.com/casadi/casadi/wiki/L_23c

>List of available options

Id	Type	Description
constr_viol_tol	OT_DOUBLE	Constraint violation tolerance [1e-8].
dual_inf_tol	OT_DOUBLE	Dual feasibility violation tolerance [1e-8]
linear_solver	OT_STRING	A custom linear solver creator function [default: ldl]
linear_solver_options	OT_DICT	Options to be passed to the linear solver
max_iter	OT_INT	Maximum number of iterations [1000].
min_lam	OT_DOUBLE	Smallest multiplier treated as inactive for the initial active set [0].
print_header	OT_BOOL	Print header [true].
print_info	OT_BOOL	Print info [true].
print_iter	OT_BOOL	Print iterations [true].

1. nlpsol¶

Solve QPs using an Nlpsol Use the ‘nlpsol’ option to specify the NLP solver: to use.

Extra doc: https://github.com/casadi/casadi/wiki/L_235

>List of available options

Id	Type	Description
nlpsol	OT_STRING	Name of solver.
nlpsol_options	OT_DICT	Options to be passed to solver.

1. qrqp¶

Solve QPs using an active-set method

Extra doc: https://github.com/casadi/casadi/wiki/L_22y

>List of available options

Id	Type	Description
constr_viol_tol	OT_DOUBLE	Constraint violation tolerance [1e-8].
dual_inf_tol	OT_DOUBLE	Dual feasibility violation tolerance [1e-8]
max_iter	OT_INT	Maximum number of iterations [1000].
min_lam	OT_DOUBLE	Smallest multiplier treated as inactive for the initial active set [0].
print_header	OT_BOOL	Print header [true].
print_info	OT_BOOL	Print info [true].
print_iter	OT_BOOL	Print iterations [true].
print_lincomb	OT_BOOL	Print dependant linear combinations of constraints [false]. Printed numbers are 0-based indices into the vector of [simple bounds;linear bounds]

Joel Andersson

Extra doc: https://github.com/casadi/casadi/wiki/L_21n

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/conic.hpp#L43

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/conic.cpp#L43-L46

3.3. Integrator¶

integrator(*args)¶

integrator(str name, str solver, dict:SX dae, dict opts) -> Function
integrator(str name, str solver, dict:MX dae, dict opts) -> Function
integrator(str name, str solver, Function dae, dict opts) -> Function
integrator(str name, str solver, dict:SX dae, float t0, [float] tout, dict opts) -> Function
integrator(str name, str solver, dict:SX dae, float t0, float tf, dict opts) -> Function
integrator(str name, str solver, dict:MX dae, float t0, [float] tout, dict opts) -> Function
integrator(str name, str solver, dict:MX dae, float t0, float tf, dict opts) -> Function
integrator(str name, str solver, Function dae, float t0, [float] tout, dict opts) -> Function
integrator(str name, str solver, Function dae, float t0, float tf, dict opts) -> Function

integrator(str name, str solver, dict:SX dae, dict opts)

Create an ODE/DAE integrator Solves an initial value problem (IVP) coupled to a terminal value problem with differential equation given as an implicit

quadratures:

Initial conditions at t=t0
x(t0)  = x0
q(t0)  = 0

Forward integration from t=t0 to t=tf
der(x) = function(x, z, p, t)                  Forward ODE
0 = fz(x, z, p, t)                  Forward algebraic equations
der(q) = fq(x, z, p, t)                  Forward quadratures

Terminal conditions at t=tf
rx(tf)  = rx0
rq(tf)  = 0

Backward integration from t=tf to t=t0
der(rx) = gx(rx, rz, rp, x, z, p, t)        Backward ODE
0 = gz(rx, rz, rp, x, z, p, t)        Backward algebraic equations
der(rq) = gq(rx, rz, rp, x, z, p, t)        Backward quadratures

where we assume that both the forward and backwards integrations are index-1
(i.e. dfz/dz, dgz/drz are invertible) and furthermore that
gx, gz and gq have a linear dependency on rx, rz and rp.

General information

>List of available options

Id	Type	Description	Used in
ad_weight	OT_DOUBLE	Weighting factor for derivative calculation.When there is an option of either using forward or reverse mode directional derivatives, the condition ad_wei ghtnf<=(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.	casadi::Function Internal
ad_weight_sp	OT_DOUBLE	Weighting factor for sparsity 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.	casadi::Function Internal
always_inline	OT_BOOL	Force inlining.	casadi::Function Internal
augmented_option s	OT_DICT	Options to be passed down to the augmented integrator, if one is constructed.	casadi::Integrat or
cache	OT_DICT	Prepopulate the function cache. Default: empty	casadi::Function Internal
common_options	OT_DICT	Options for auto-generated functions	casadi::OracleFu nction
compiler	OT_STRING	Just-in-time compiler plugin to be used.	casadi::Function Internal
custom_jacobian	OT_FUNCTION	Override CasADi’s AD. Use together with ‘jac_penalty’: 0. Note: Highly experimental. Syntax may break often.	casadi::Function Internal
der_options	OT_DICT	Default options to be used to populate forward_options, reverse_options, and jacobian_options before those options are merged in.	casadi::Function Internal
derivative_of	OT_FUNCTION	The function is a derivative of another function. The type of derivative (directional derivative, Jacobian) is inferred from the function name.	casadi::Function Internal
dump	OT_BOOL	Dump function to file upon first evaluation. [false]	casadi::Function Internal
dump_dir	OT_STRING	Directory to dump inputs/outputs to. Make sure the directory exists [.]	casadi::Function Internal
dump_format	OT_STRING	Choose file format to dump matrices. See DM.from_file [mtx]	casadi::Function Internal
dump_in	OT_BOOL	Dump numerical values of inputs to file (readable with DM.from_file ) [default: false]	casadi::Function Internal
dump_out	OT_BOOL	Dump numerical values of outputs to file (readable with DM.from_file ) [default: false]	casadi::Function Internal
enable_fd	OT_BOOL	Enable derivative calculation by finite differencing. [default: false]]	casadi::Function Internal
enable_forward	OT_BOOL	Enable derivative calculation using generated functions for Jacobian-times- vector products - typically using forward mode AD - if available. [default: true]	casadi::Function Internal
enable_jacobian	OT_BOOL	Enable derivative calculation using generated functions for Jacobians of all differentiable outputs with respect to all differentiable inputs - if available. [default: true]	casadi::Function Internal
enable_reverse	OT_BOOL	Enable derivative calculation using generated functions for transposed Jacobian-times- vector products - typically using reverse mode AD - if available. [default: true]	casadi::Function Internal
error_on_fail	OT_BOOL	Throw exceptions when function evaluation fails (default true).	casadi::ProtoFun ction
expand	OT_BOOL	Replace MX with SX expressions in problem formulation [false]	casadi::Integrat or
external_transfo rm	OT_VECTORVECTOR	List of external _transform instruction arguments. Default: empty	casadi::Function Internal
fd_method	OT_STRING	Method for finite differencing [default ‘central’]	casadi::Function Internal
fd_options	OT_DICT	Options to be passed to the finite difference instance	casadi::Function Internal
forward_options	OT_DICT	Options to be passed to a forward mode constructor	casadi::Function Internal
gather_stats	OT_BOOL	Deprecated option (ignored): Statistics are now always collected.	casadi::Function Internal
grid	OT_DOUBLEVECTOR	[DEPRECATED] Time grid	casadi::Integrat or
input_scheme	OT_STRINGVECTOR	Deprecated option (ignored)	casadi::Function Internal
inputs_check	OT_BOOL	Throw exceptions when the numerical values of the inputs don’t make sense	casadi::Function Internal
is_diff_in	OT_BOOLVECTOR	Indicate for each input if it should be differentiable.	casadi::Function Internal
is_diff_out	OT_BOOLVECTOR	Indicate for each output if it should be differentiable.	casadi::Function Internal
jac_penalty	OT_DOUBLE	When requested for a number of 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	casadi::Function Internal
jacobian_options	OT_DICT	Options to be passed to a Jacobian constructor	casadi::Function Internal
jit	OT_BOOL	Use just-in-time compiler to speed up the evaluation	casadi::Function Internal
jit_cleanup	OT_BOOL	Cleanup up the temporary source file that jit creates. Default: true	casadi::Function Internal
jit_name	OT_STRING	The file name used to write out code. The actual file names used depend on ‘jit_t emp_suffix’ and include extensions. Default: ‘jit_tmp’	casadi::Function Internal
jit_options	OT_DICT	Options to be passed to the jit compiler.	casadi::Function Internal
jit_serialize	OT_STRING	Specify behaviour when serializing a jitted function: SOURCE\|link\|embe d.	casadi::Function Internal
jit_temp_suffix	OT_BOOL	Use a temporary (seemingly random) filename suffix for generated code and libraries. This is desired for thread- safety. This behaviour may defeat caching compiler wrappers. Default: true	casadi::Function Internal
max_io	OT_INT	Acceptable number of inputs and outputs. Warn if exceeded.	casadi::Function Internal
max_num_dir	OT_INT	Specify the maximum number of directions for derivative functions. Overrules the builtin optimize d_num_dir.	casadi::Function Internal
monitor	OT_STRINGVECTOR	Set of user problem functions to be monitored	casadi::OracleFu nction
nadj	OT_INT	Number of adjoint sensitivities to be calculated [0]	casadi::Integrat or
never_inline	OT_BOOL	Forbid inlining.	casadi::Function Internal
nfwd	OT_INT	Number of forward sensitivities to be calculated [0]	casadi::Integrat or
number_of_finite _elements	OT_INT	Target number of finite elements. The actual number may be higher to accommodate all output times	casadi::Integrat or
output_scheme	OT_STRINGVECTOR	Deprecated option (ignored)	casadi::Function Internal
output_t0	OT_BOOL	[DEPRECATED] Output the state at the initial time	casadi::Integrat or
post_expand	OT_BOOL	After construction, expand this Function . Default: False	casadi::Function Internal
post_expand_opti ons	OT_DICT	Options to be passed to post- construction expansion. Default: empty	casadi::Function Internal
print_in	OT_BOOL	Print numerical values of inputs [default: false]	casadi::Function Internal
print_out	OT_BOOL	Print numerical values of outputs [default: false]	casadi::Function Internal
print_stats	OT_BOOL	Print out statistics after integration	casadi::Integrat or
print_time	OT_BOOL	print information about execution time. Implies record_time.	casadi::ProtoFun ction
record_time	OT_BOOL	record information about execution time, for retrieval with stats().	casadi::ProtoFun ction
regularity_check	OT_BOOL	Throw exceptions when NaN or Inf appears during evaluation	casadi::ProtoFun ction
reverse_options	OT_DICT	Options to be passed to a reverse mode constructor	casadi::Function Internal
rootfinder	OT_STRING	An implicit function solver	casadi::Integrat or
rootfinder_optio ns	OT_DICT	Options to be passed to the NLP Solver	casadi::Integrat or
show_eval_warnin gs	OT_BOOL	Show warnings generated from function evaluations [true]	casadi::OracleFu nction
simplify	OT_BOOL	Implement as MX Function (codege neratable/serial izable) default: false	casadi::Integrat or
simplify_options	OT_DICT	Any options to pass to simplified form Function constructor	casadi::Integrat or
specific_options	OT_DICT	Options for specific auto- generated functions, overwriting the defaults from common_options. Nested dictionary.	casadi::OracleFu nction
t0	OT_DOUBLE	[DEPRECATED] Beginning of the time horizon	casadi::Integrat or
tf	OT_DOUBLE	[DEPRECATED] End of the time horizon	casadi::Integrat or
user_data	OT_VOIDPTR	A user-defined field that can be used to identify the function or pass additional information	casadi::Function Internal
verbose	OT_BOOL	Verbose evaluation for debugging	casadi::ProtoFun ction

>Input scheme: casadi::IntegratorInput (INTEGRATOR_NUM_IN = 7)

Full name	Short	Description
INTEGRATOR_X0	x0	Differential state at the initial time.
INTEGRATOR_Z0	z0	Initial guess for the algebraic variable at the initial time.
INTEGRATOR_P	p	Parameters.
INTEGRATOR_U	u	Piecewise constant control, a new control interval starts at each output time.
INTEGRATOR_ADJ_XF	adj_xf	Adjoint seeds corresponding to the states at the output times.
INTEGRATOR_ADJ_ZF	adj_zf	Adjoint seeds corresponding to the algebraic variables at the output times.
INTEGRATOR_ADJ_QF	adj_qf	Adjoint seeds corresponding to the quadratures at the output times.

>Output scheme: casadi::IntegratorOutput (INTEGRATOR_NUM_OUT = 7)

Full name	Short	Description
INTEGRATOR_XF	xf	Differential state at all output times.
INTEGRATOR_ZF	zf	Algebraic variable at all output times.
INTEGRATOR_QF	qf	Quadrature state at all output times.
INTEGRATOR_ADJ_X0	adj_x0	Adjoint sensitivities corresponding to the initial state.
INTEGRATOR_ADJ_Z0	adj_z0	Adjoint sensitivities corresponding to the algebraic variable guess.
INTEGRATOR_ADJ_P	adj_p	Adjoint sensitivities corresponding to the parameter vector.
INTEGRATOR_ADJ_U	adj_u	Adjoint sensitivities corresponding to the control vector.

List of plugins - cvodes

idas
collocation
rk

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 Integrator.doc(“myextraplugin”)

1. cvodes¶

Interface to CVodes from the Sundials suite.

A call to evaluate will integrate to the end.

You can retrieve the entire state trajectory as follows, after the evaluate

times t_i.

Extra doc: https://github.com/casadi/casadi/wiki/L_228

>List of available options

Id	Type	Description
abstol	OT_DOUBLE	Absolute tolerence for the IVP solution
always_recalculate_jacobian	OT_BOOL	Recalculate Jacobian before factorizations, even if Jacobian is current [default: true]
disable_internal_warnings	OT_BOOL	Disable SUNDIALS internal warning messages
fsens_all_at_once	OT_BOOL	Calculate all right hand sides of the sensitivity equations at once
fsens_err_con	OT_BOOL	include the forward sensitivities in all error controls
interpolation_type	OT_STRING	Type of interpolation for the adjoint sensitivities
linear_multistep_method	OT_STRING	Integrator scheme: BDF\|adams
linear_solver	OT_STRING	A custom linear solver creator function [default: qr]
linear_solver_options	OT_DICT	Options to be passed to the linear solver
max_krylov	OT_INT	Maximum Krylov subspace size
max_multistep_order	OT_INT	Maximum order for the (variable-order) multistep method
max_num_steps	OT_INT	Maximum number of integrator steps
max_order	OT_DOUBLE	Maximum order
max_step_size	OT_DOUBLE	Max step size [default: 0/inf]
min_step_size	OT_DOUBLE	Min step size [default: 0/0.0]
newton_scheme	OT_STRING	Linear solver scheme in the Newton method: DIRECT\|gmres\|bcgstab\|tfqmr
nonlin_conv_coeff	OT_DOUBLE	Coefficient in the nonlinear convergence test
nonlinear_solver_iteration	OT_STRING	Nonlinear solver type: NEWTON\|functional
quad_err_con	OT_BOOL	Should the quadratures affect the step size control
reltol	OT_DOUBLE	Relative tolerence for the IVP solution
scale_abstol	OT_BOOL	Scale absolute tolerance by nominal value
second_order_correction	OT_BOOL	Second order correction in the augmented system Jacobian [true]
sensitivity_method	OT_STRING	Sensitivity method: SIMULTANEOUS\|staggered
step0	OT_DOUBLE	initial step size [default: 0/estimated]
steps_per_checkpoint	OT_INT	Number of steps between two consecutive checkpoints
stop_at_end	OT_BOOL	[DEPRECATED] Stop the integrator at the end of the interval
use_preconditioner	OT_BOOL	Precondition the iterative solver [default: true]

1. idas¶

Interface to IDAS from the Sundials suite.

Extra doc: https://github.com/casadi/casadi/wiki/L_225

>List of available options

Id	Type	Description
abstol	OT_DOUBLE	Absolute tolerence for the IVP solution
abstolv	OT_DOUBLEVECTOR	Absolute tolerarance for each component
calc_ic	OT_BOOL	Use IDACalcIC to get consistent initial conditions.
calc_icB	OT_BOOL	Use IDACalcIC to get consistent initial conditions for backwards system [default: equal to calc_ic].
cj_scaling	OT_BOOL	IDAS scaling on cj for the user-defined linear solver module
constraints	OT_INTVECTOR	Constrain the solution y=[x,z]. 0 (default): no constraint on yi, 1: yi >= 0.0, -1: yi <= 0.0, 2: yi > 0.0, -2: yi < 0.0.
disable_internal_warnings	OT_BOOL	Disable SUNDIALS internal warning messages
first_time	OT_DOUBLE	First requested time as a fraction of the time interval
fsens_err_con	OT_BOOL	include the forward sensitivities in all error controls
init_xdot	OT_DOUBLEVECTOR	Initial values for the state derivatives
interpolation_type	OT_STRING	Type of interpolation for the adjoint sensitivities
linear_solver	OT_STRING	A custom linear solver creator function [default: qr]
linear_solver_options	OT_DICT	Options to be passed to the linear solver
max_krylov	OT_INT	Maximum Krylov subspace size
max_multistep_order	OT_INT	Maximum order for the (variable-order) multistep method
max_num_steps	OT_INT	Maximum number of integrator steps
max_order	OT_DOUBLE	Maximum order
max_step_size	OT_DOUBLE	Maximim step size
newton_scheme	OT_STRING	Linear solver scheme in the Newton method: DIRECT\|gmres\|bcgstab\|tfqmr
nonlin_conv_coeff	OT_DOUBLE	Coefficient in the nonlinear convergence test
quad_err_con	OT_BOOL	Should the quadratures affect the step size control
reltol	OT_DOUBLE	Relative tolerence for the IVP solution
scale_abstol	OT_BOOL	Scale absolute tolerance by nominal value
second_order_correction	OT_BOOL	Second order correction in the augmented system Jacobian [true]
sensitivity_method	OT_STRING	Sensitivity method: SIMULTANEOUS\|staggered
step0	OT_DOUBLE	initial step size [default: 0/estimated]
steps_per_checkpoint	OT_INT	Number of steps between two consecutive checkpoints
stop_at_end	OT_BOOL	[DEPRECATED] Stop the integrator at the end of the interval
suppress_algebraic	OT_BOOL	Suppress algebraic variables in the error testing
use_preconditioner	OT_BOOL	Precondition the iterative solver [default: true]

1. collocation¶

Fixed-step implicit Runge-Kutta integrator ODE/DAE integrator based on collocation schemes

The method is still under development

Extra doc: https://github.com/casadi/casadi/wiki/L_234

>List of available options

Id	Type	Description
collocation_scheme	OT_STRING	Collocation scheme: radau\|legendre
interpolation_order	OT_INT	Order of the interpolating polynomials
number_of_finite_elements	OT_INT	Target number of finite elements. The actual number may be higher to accommodate all output times
rootfinder	OT_STRING	An implicit function solver
rootfinder_options	OT_DICT	Options to be passed to the NLP Solver
simplify	OT_BOOL	Implement as MX Function (codegeneratable/serializable) default: false
simplify_options	OT_DICT	Any options to pass to simplified form Function constructor

1. rk¶

Fixed-step explicit Runge-Kutta integrator for ODEs Currently implements RK4.

The method is still under development

Extra doc: https://github.com/casadi/casadi/wiki/L_23a

Joel Andersson

Extra doc: https://github.com/casadi/casadi/wiki/L_21k

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/integrator.hpp#L109

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/integrator.cpp#L109-L112

integrator(str name, str solver, dict:MX dae, dict opts)
integrator(str name, str solver, Function dae, dict opts)
integrator(str name, str solver, dict:SX dae, float t0, [float] tout, dict opts)
integrator(str name, str solver, dict:SX dae, float t0, float tf, dict opts)
integrator(str name, str solver, dict:MX dae, float t0, [float] tout, dict opts)
integrator(str name, str solver, dict:MX dae, float t0, float tf, dict opts)
integrator(str name, str solver, Function dae, float t0, [float] tout, dict opts)
integrator(str name, str solver, Function dae, float t0, float tf, dict opts)

[INTERNAL]

3.4. Rootfinding¶

rootfinder(*args)¶

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

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 for derivative calculation.When there is an option of either using forward or reverse mode directional derivatives, the condition ad_wei ghtnf<=(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.	casadi::Function Internal
ad_weight_sp	OT_DOUBLE	Weighting factor for sparsity 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.	casadi::Function Internal
always_inline	OT_BOOL	Force inlining.	casadi::Function Internal
cache	OT_DICT	Prepopulate the function cache. Default: empty	casadi::Function Internal
common_options	OT_DICT	Options for auto-generated functions	casadi::OracleFu nction
compiler	OT_STRING	Just-in-time compiler plugin to be used.	casadi::Function Internal
constraints	OT_INTVECTOR	Constrain the unknowns. 0 (default): no constraint on ui, 1: ui >= 0.0, -1: ui <= 0.0, 2: ui > 0.0, -2: ui < 0.0.	casadi::Rootfind er
custom_jacobian	OT_FUNCTION	Override CasADi’s AD. Use together with ‘jac_penalty’: 0. Note: Highly experimental. Syntax may break often.	casadi::Function Internal
der_options	OT_DICT	Default options to be used to populate forward_options, reverse_options, and jacobian_options before those options are merged in.	casadi::Function Internal
derivative_of	OT_FUNCTION	The function is a derivative of another function. The type of derivative (directional derivative, Jacobian) is inferred from the function name.	casadi::Function Internal
dump	OT_BOOL	Dump function to file upon first evaluation. [false]	casadi::Function Internal
dump_dir	OT_STRING	Directory to dump inputs/outputs to. Make sure the directory exists [.]	casadi::Function Internal
dump_format	OT_STRING	Choose file format to dump matrices. See DM.from_file [mtx]	casadi::Function Internal
dump_in	OT_BOOL	Dump numerical values of inputs to file (readable with DM.from_file ) [default: false]	casadi::Function Internal
dump_out	OT_BOOL	Dump numerical values of outputs to file (readable with DM.from_file ) [default: false]	casadi::Function Internal
enable_fd	OT_BOOL	Enable derivative calculation by finite differencing. [default: false]]	casadi::Function Internal
enable_forward	OT_BOOL	Enable derivative calculation using generated functions for Jacobian-times- vector products - typically using forward mode AD - if available. [default: true]	casadi::Function Internal
enable_jacobian	OT_BOOL	Enable derivative calculation using generated functions for Jacobians of all differentiable outputs with respect to all differentiable inputs - if available. [default: true]	casadi::Function Internal
enable_reverse	OT_BOOL	Enable derivative calculation using generated functions for transposed Jacobian-times- vector products - typically using reverse mode AD - if available. [default: true]	casadi::Function Internal
error_on_fail	OT_BOOL	Throw exceptions when function evaluation fails (default true).	casadi::ProtoFun ction
expand	OT_BOOL	Replace MX with SX expressions in problem formulation [false]	casadi::OracleFu nction
external_transfo rm	OT_VECTORVECTOR	List of external _transform instruction arguments. Default: empty	casadi::Function Internal
fd_method	OT_STRING	Method for finite differencing [default ‘central’]	casadi::Function Internal
fd_options	OT_DICT	Options to be passed to the finite difference instance	casadi::Function Internal
forward_options	OT_DICT	Options to be passed to a forward mode constructor	casadi::Function Internal
gather_stats	OT_BOOL	Deprecated option (ignored): Statistics are now always collected.	casadi::Function Internal
implicit_input	OT_INT	Index of the input that corresponds to the actual root- finding	casadi::Rootfind er
implicit_output	OT_INT	Index of the output that corresponds to the actual root- finding	casadi::Rootfind er
input_scheme	OT_STRINGVECTOR	Deprecated option (ignored)	casadi::Function Internal
inputs_check	OT_BOOL	Throw exceptions when the numerical values of the inputs don’t make sense	casadi::Function Internal
is_diff_in	OT_BOOLVECTOR	Indicate for each input if it should be differentiable.	casadi::Function Internal
is_diff_out	OT_BOOLVECTOR	Indicate for each output if it should be differentiable.	casadi::Function Internal
jac_penalty	OT_DOUBLE	When requested for a number of 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	casadi::Function Internal
jacobian_functio n	OT_FUNCTION	Function object for calculating the Jacobian (autogenerated by default)	casadi::Rootfind er
jacobian_options	OT_DICT	Options to be passed to a Jacobian constructor	casadi::Function Internal
jit	OT_BOOL	Use just-in-time compiler to speed up the evaluation	casadi::Function Internal
jit_cleanup	OT_BOOL	Cleanup up the temporary source file that jit creates. Default: true	casadi::Function Internal
jit_name	OT_STRING	The file name used to write out code. The actual file names used depend on ‘jit_t emp_suffix’ and include extensions. Default: ‘jit_tmp’	casadi::Function Internal
jit_options	OT_DICT	Options to be passed to the jit compiler.	casadi::Function Internal
jit_serialize	OT_STRING	Specify behaviour when serializing a jitted function: SOURCE\|link\|embe d.	casadi::Function Internal
jit_temp_suffix	OT_BOOL	Use a temporary (seemingly random) filename suffix for generated code and libraries. This is desired for thread- safety. This behaviour may defeat caching compiler wrappers. Default: true	casadi::Function Internal
linear_solver	OT_STRING	User-defined linear solver class. Needed for sensitivities.	casadi::Rootfind er
linear_solver_op tions	OT_DICT	Options to be passed to the linear solver.	casadi::Rootfind er
max_io	OT_INT	Acceptable number of inputs and outputs. Warn if exceeded.	casadi::Function Internal
max_num_dir	OT_INT	Specify the maximum number of directions for derivative functions. Overrules the builtin optimize d_num_dir.	casadi::Function Internal
monitor	OT_STRINGVECTOR	Set of user problem functions to be monitored	casadi::OracleFu nction
never_inline	OT_BOOL	Forbid inlining.	casadi::Function Internal
output_scheme	OT_STRINGVECTOR	Deprecated option (ignored)	casadi::Function Internal
post_expand	OT_BOOL	After construction, expand this Function . Default: False	casadi::Function Internal
post_expand_opti ons	OT_DICT	Options to be passed to post- construction expansion. Default: empty	casadi::Function Internal
print_in	OT_BOOL	Print numerical values of inputs [default: false]	casadi::Function Internal
print_out	OT_BOOL	Print numerical values of outputs [default: false]	casadi::Function Internal
print_time	OT_BOOL	print information about execution time. Implies record_time.	casadi::ProtoFun ction
record_time	OT_BOOL	record information about execution time, for retrieval with stats().	casadi::ProtoFun ction
regularity_check	OT_BOOL	Throw exceptions when NaN or Inf appears during evaluation	casadi::ProtoFun ction
reverse_options	OT_DICT	Options to be passed to a reverse mode constructor	casadi::Function Internal
show_eval_warnin gs	OT_BOOL	Show warnings generated from function evaluations [true]	casadi::OracleFu nction
specific_options	OT_DICT	Options for specific auto- generated functions, overwriting the defaults from common_options. Nested dictionary.	casadi::OracleFu nction
user_data	OT_VOIDPTR	A user-defined field that can be used to identify the function or pass additional information	casadi::Function Internal
verbose	OT_BOOL	Verbose evaluation for debugging	casadi::ProtoFun ction

>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”)

1. kinsol¶

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

1. fast_newton¶

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.

1. nlpsol¶

1. newton¶

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

rootfinder(str name, str solver, dict:MX rfp, dict opts)
rootfinder(str name, str solver, Function f, dict opts)

[INTERNAL]

3.5. Linear systems¶

class Linsol(*args)¶

Linear solver.

Create a solver for linear systems of equations Solves the linear system A*X = B or A^T*X = B for X with A square and non-singular

If A is structurally singular, an error will be thrown during init. If: A is numerically singular, the prepare step will fail.

General informationList of plugins - csparsecholesky

csparse
ma27
lapacklu
lapackqr
mumps
ldl
qr
tridiag
symbolicqr

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 Linsol.doc(“myextraplugin”)

1. csparsecholesky¶

Linsol with CSparseCholesky Interface

Extra doc: https://github.com/casadi/casadi/wiki/L_21u

1. csparse¶

Linsol with CSparse Interface

Extra doc: https://github.com/casadi/casadi/wiki/L_21t

1. ma27¶

Interface to the sparse direct linear solver MA27 Works for symmetric

indefinite systems Partly adopted from qpOASES 3.2 Joel Andersson

Extra doc: https://github.com/casadi/casadi/wiki/L_229

1. lapacklu¶

This class solves the linear system A.x=b by making an LU factorization of A: A = L.U, with L lower and U upper triangular

Extra doc: https://github.com/casadi/casadi/wiki/L_22h

>List of available options

Id	Type	Description
allow_equilibration_failure	OT_BOOL	Non-fatal error when equilibration fails
equilibration	OT_BOOL	Equilibrate the matrix

1. lapackqr¶

This class solves the linear system A.x=b by making an QR factorization of A: A = Q.R, with Q orthogonal and R upper triangular

Extra doc: https://github.com/casadi/casadi/wiki/L_22g

>List of available options

Id	Type	Description
max_nrhs	OT_INT	Maximum number of right-hand-sides that get processed in a single pass [default:10].

1. mumps¶

Interface to the sparse direct linear solver MUMPS Works for symmetric indefinite systems Joel Andersson

Extra doc: https://github.com/casadi/casadi/wiki/L_22t

>List of available options

Id	Type	Description
posdef	OT_BOOL	Positive definite
symmetric	OT_BOOL	Symmetric matrix

1. ldl¶

Linear solver using sparse direct LDL factorization

Extra doc: https://github.com/casadi/casadi/wiki/L_233

1. qr¶

Linear solver using sparse direct QR factorization

Extra doc: https://github.com/casadi/casadi/wiki/L_22z

1. tridiag¶

Linear solver for tridiagonal matrices

Extra doc: https://github.com/casadi/casadi/wiki/L_22v

1. symbolicqr¶

Linear solver for sparse least-squares problems Inspired from https://github.com/scipy/scipy/blob/v0.14.0/scipy/sparse/linalg/isolve/lsqr.py#L96

Extra doc: https://github.com/casadi/casadi/wiki/L_230

Linsol based on QR factorization with sparsity pattern based reordering without partial pivoting

Extra doc: https://github.com/casadi/casadi/wiki/L_231

>List of available options

Id	Type	Description
fopts	OT_DICT	Options to be passed to generated function objects

Joel Andersson

Extra doc: https://github.com/casadi/casadi/wiki/L_1kh

C++ includes: linsol.hpp

static doc(*args)¶

doc(str name) -> str

static has_plugin(*args)¶

has_plugin(str name) -> bool

static load_plugin(*args)¶

load_plugin(str name)

neig(*args)¶

neig(self, DM A) -> int

Number of negative eigenvalues.

Not available for all solvers

Extra doc: https://github.com/casadi/casadi/wiki/L_1kk

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/linsol.hpp#L119

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/linsol.cpp#L165-L170

nfact(*args)¶

nfact(self, DM A)

Numeric factorization of the linear system.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/linsol.hpp#L106

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/linsol.cpp#L126-L129

plugin_name(*args)¶

plugin_name(self) -> str

Query plugin name.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/linsol.hpp#L97

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/linsol.cpp#L64-L66

rank(*args)¶

 rank(self, DM A) -> int

Matrix rank.

Not available for all solvers

Extra doc: https://github.com/casadi/casadi/wiki/L_1kl

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/linsol.hpp#L126

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/linsol.cpp#L176-L181

sfact(*args)¶

sfact(self, DM A)

Symbolic factorization of the linear system, e.g. selecting pivots.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/linsol.hpp#L103

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/linsol.cpp#L104-L107

solve(*args)¶

 solve(self, DM A, DM B, bool tr) -> DM
 solve(self, MX A, MX B, bool tr) -> MX

Solve linear system of equations

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/linsol.hpp#L111

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/linsol.cpp#L100-L102

solve(self, DM A, DM B, bool tr)

[INTERNAL]: Solve linear system of equations

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/linsol.hpp#L110

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/linsol.cpp#L72-L98

solve(self, MX A, MX B, bool tr)

[INTERNAL]: Solve linear system of equations

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/linsol.hpp#L111

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/linsol.cpp#L100-L102

sparsity(*args)¶

sparsity(self) -> Sparsity

Get linear system sparsity.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/linsol.hpp#L100

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/linsol.cpp#L68-L70

stats(*args)¶

stats(self, int mem) -> dict

Get all statistics obtained at the end of the last evaluate call.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/linsol.hpp#L129

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/linsol.cpp#L217-L219

static type_name(*args)¶

type_name() -> str

4. Advanced¶

4.1. DaeBuilder¶

class DaeBuilder(*args)¶

A symbolic representation of a differential-algebraic equations model.

1. Variables:¶

t:      independent variable (usually time)
c:      constants
p:      parameters
d:      dependent parameters (time independent)
u:      controls
w:      dependent variables  (time dependent)
x:      differential states
z:      algebraic variables
q:      quadrature states
y:      outputs

1. Equations:¶

differential equations: \dot{x} ==  ode(...)
algebraic equations:          0 ==  alg(...)
quadrature equations:   \dot{q} == quad(...)
dependent parameters:         d == ddef(d_prev,p)
dependent variables:          w == wdef(w_prev,x,z,u,p,t)
output equations:             y == ydef(...)
initial equations:     init_lhs == init_rhs(...)
events:      when when_cond < 0: when_lhs := when_rhs

Joel Andersson

Extra doc: https://github.com/casadi/casadi/wiki/L_5c

C++ includes: dae_builder.hpp

add_aux(*args)¶

add_aux(self, str name, int n) -> MX

Add an auxiliary variable.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L320

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L518-L522

add_c(*args)¶

add_c(self, str name, MX new_cdef) -> MX

Add a new constant.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L302

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L482-L489

add_d(*args)¶

add_d(self, str name, MX new_ddef) -> MX

Add a new dependent parameter.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L305

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L491-L498

add_fun(*args)¶

add_fun(self, Function f) -> Function
add_fun(self, str name, Importer compiler, dict opts) -> Function
add_fun(self, str name, [str] arg, [str] res, dict opts) -> Function

Add an external function.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L413

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L770-L773

add_fun(self, Function f)

[INTERNAL] Add an already existing function.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L410

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L751-L758

add_fun(self, str name, [str] arg, [str] res, dict opts)

[INTERNAL] Add a function from loaded expressions.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L405

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L760-L768

add_fun(self, str name, Importer compiler, dict opts)

[INTERNAL] Add an external function.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L413

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L770-L773

add_init(*args)¶

add_init(self, MX lhs, MX rhs)

Add an initial equation.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L323

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L524-L527

add_lc(*args)¶

add_lc(self, str name, [str] f_out)

Add a named linear combination of output expressions.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L445

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L711-L718

add_p(*args)¶

add_p(self, str name) -> MX

Add a new parameter.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L287

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L437-L444

add_q(*args)¶

add_q(self, str name) -> MX

Add a new quadrature state.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L299

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L473-L480

add_t(*args)¶

add_t(self, str name) -> MX

Add an independent variable (time)

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L284

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L430-L435

add_u(*args)¶

add_u(self, str name) -> MX

Add a new control.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L290

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L446-L453

add_variable(*args)¶

add_variable(self, MX new_v)
add_variable(self, str name, int n) -> MX
add_variable(self, str name, Sparsity sp) -> MX

Add a new variable from symbolic expressions.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L645

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L332-L335

add_variable(self, MX new_v)

[INTERNAL] Add a new variable from symbolic expressions.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L645

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L332-L335

add_variable(self, str name, int n)

[INTERNAL] Add a new variable: returns corresponding symbolic expression.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L639

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L322-L324

add_variable(self, str name, Sparsity sp)

[INTERNAL] Add a new variable: returns corresponding symbolic expression.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L642

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L326-L330

add_variable_new(*args)¶

add_variable_new(self, MX new_v) -> size_t
add_variable_new(self, str name, int n) -> size_t
add_variable_new(self, str name, Sparsity sp) -> size_t

Add a new variable from symbolic expressions.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L654

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L347-L351

add_variable_new(self, MX new_v)

[INTERNAL] Add a new variable from symbolic expressions.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L654

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L347-L351

add_variable_new(self, str name, int n)

[INTERNAL] Add a new variable: returns corresponding symbolic expression.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L648

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L337-L339

add_variable_new(self, str name, Sparsity sp)

[INTERNAL] Add a new variable: returns corresponding symbolic expression.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L651

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L341-L345

add_w(*args)¶

add_w(self, str name, MX new_wdef) -> MX

Add a new dependent variable.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L308

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L500-L507

add_when(*args)¶

add_when(self, MX cond, MX lhs, MX rhs)

Add a when statement.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L326

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L529-L533

add_x(*args)¶

add_x(self, str name) -> MX

Add a new differential state.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L293

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L455-L462

add_y(*args)¶

add_y(self, str name, MX new_ydef) -> MX

Add a new output.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L311

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L509-L516

add_z(*args)¶

add_z(self, str name) -> MX

Add a new algebraic variable.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L296

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L464-L471

alg(*args)¶

alg(self) -> [MX]

Algebraic equations.

Extra doc: https://github.com/casadi/casadi/wiki/L_5i

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L113

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L79-L81

all_variables(*args)¶

all_variables(self) -> [str]

Get a list of all variables.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L660

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L305-L312

attribute(*args)¶

attribute(self, str a, [str] name) -> [float]
attribute(self, str a, str name) -> float

Get an attribute.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L599

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L949-L957

attribute(self, str a, str name)

[INTERNAL] Get an attribute, single variable.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L555

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L940-L947

attribute(self, str a, [str] name)

[INTERNAL] Get an attribute.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L599

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L949-L957

aux(*args)¶

aux(self) -> [MX]

Auxiliary variables: Used e.g. to define functions.

Extra doc: https://github.com/casadi/casadi/wiki/L_5v

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L182

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L131-L133

beq(*args)¶

beq(self, str name) -> MX

Get/set the binding equation for a variable

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L490

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L594-L601

c(*args)¶

c(self) -> [str]

Named constants.

Extra doc: https://github.com/casadi/casadi/wiki/L_5p

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L148

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L107-L109

causality(*args)¶

causality(self, str name) -> str

Get/set the causality

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L514

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L663-L665

cdef(*args)¶

cdef(self) -> [MX]

Definitions of named constants.

Extra doc: https://github.com/casadi/casadi/wiki/L_5q

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L153

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L111-L113

clear_all(*args)¶

clear_all(self, str v)

Clear all variables of a type.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L333

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L414-L420

clear_in(*args)¶

clear_in(self, str v)

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L371

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L371-L371

create(*args)¶

create(self, str name, dict opts) -> Function
create(self, str name, [str] name_in, [str] name_out, dict opts) -> Function
create(self, str fname, [str] name_in, [str] name_out, bool sx, bool lifted_calls) -> Function

Load a function from an FMU DLL, standard IO conforming with

simulator.

1. Parameters:¶

opts: Optional settings

Extra doc: https://github.com/casadi/casadi/wiki/L_6f

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L472

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L742-L749

create(self, str name, dict opts)

[INTERNAL] Load a function from an FMU DLL, standard IO conforming with

simulator.

1. Parameters:¶

opts: Optional settings

Extra doc: https://github.com/casadi/casadi/wiki/L_6f

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L472

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L742-L749

create(self, str name, [str] name_in, [str] name_out, dict opts)

[INTERNAL] Construct a function object, names provided.

1. Parameters:¶

name_in: Names of all the inputs

name_out: Names of all the outputs

opts: Optional settings

Extra doc: https://github.com/casadi/casadi/wiki/L_6e

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L460

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L731-L740

create(self, str fname, [str] name_in, [str] name_out, bool sx, bool lifted_calls)

[INTERNAL] Construct a function object, legacy syntax.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L448

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L720-L729

d(*args)¶

d(self) -> [str]

Dependent parameters.

Extra doc: https://github.com/casadi/casadi/wiki/L_5r

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L158

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L115-L117

ddef(*args)¶

ddef(self) -> [MX]

Definitions of dependent parameters.

Interdependencies are allowed but must be non-cyclic.

Extra doc: https://github.com/casadi/casadi/wiki/L_5s

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L165

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L119-L121

dependent_fun(*args)¶

dependent_fun(self, str fname, [str] s_in, [str] s_out) -> Function

Construct a function for evaluating dependent parameters.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L475

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L827-L836

der(*args)¶

der(self, [str] name) -> [str]
der(self, str name) -> str

Get the time derivative of an expression, single variable.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L552

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L568-L581

der(self, [str] name)

[INTERNAL] Get the time derivative of an expression.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L486

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L583-L592

der(self, str name)

[INTERNAL] Get the time derivative of an expression, single variable.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L552

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L568-L581

derivatives(*args)¶

derivatives(self) -> [str]

Model structure: derivatives.

Extra doc: https://github.com/casadi/casadi/wiki/L_62

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L218

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L164-L171

description(*args)¶

description(self, str name) -> str

Get/set description

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L502

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L635-L637

dimension(*args)¶

dimension(self, str name) -> [int]

Get the dimensions of a variable.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L546

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L707-L709

display_unit(*args)¶

display_unit(self, str name) -> str

Get/set the display unit

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L538

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L695-L697

eliminate_quad(*args)¶

eliminate_quad(self)

Eliminate quadrature states and turn them into ODE states.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L381

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L248-L254

eliminate_w(*args)¶

eliminate_w(self)

Eliminate all dependent variables.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L375

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L611-L617

export_fmu(*args)¶

export_fmu(self, dict opts) -> [str]

Export instance into an FMU.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L442

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L240-L246

fun(*args)¶

fun(self) -> [Function]
fun(self, str name) -> Function

Get all functions.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L423

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L814-L816

fun(self, str name)

[INTERNAL] Get function by name.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L420

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L784-L791

fun(self)

[INTERNAL] Get all functions.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L423

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L814-L816

gather_fun(*args)¶

gather_fun(self, int max_depth)

Collect embedded functions from the expression graph.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L426

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L793-L812

get(*args)¶

get(self, [str] name) -> [GenericType]
get(self, str name) -> GenericType

Evaluate the values for a set of variables at the initial time.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L636

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1158-L1173

get(self, [str] name)

[INTERNAL] Evaluate the values for a set of variables at the initial time.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L636

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1158-L1173

get(self, str name)

[INTERNAL] Evaluate the values for a set of variables at the initial time, single

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L594

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1154-L1156

has_fun(*args)¶

has_fun(self, str name) -> bool

Does a particular function already exist?

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L417

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L775-L782

has_t(*args)¶

has_t(self) -> bool

Is there a time variable?

Extra doc: https://github.com/casadi/casadi/wiki/L_64

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L231

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L182-L184

has_variable(*args)¶

has_variable(self, str name) -> bool

Check if a particular variable exists.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L657

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L296-L303

init_lhs(*args)¶

init_lhs(self) -> [MX]

Initial conditions, left-hand-side.

Extra doc: https://github.com/casadi/casadi/wiki/L_5w

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L187

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L135-L137

init_rhs(*args)¶

init_rhs(self) -> [MX]

Initial conditions, right-hand-side.

Extra doc: https://github.com/casadi/casadi/wiki/L_5x

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L192

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L139-L141

initial(*args)¶

initial(self, str name) -> str

Get/set the initial property

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L526

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L679-L681

initial_unknowns(*args)¶

initial_unknowns(self) -> [str]

Model structure: initial unknowns.

Extra doc: https://github.com/casadi/casadi/wiki/L_63

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L223

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L173-L180

jac_sparsity(*args)¶

jac_sparsity(self, [str] onames, [str] inames) -> Sparsity

Get Jacobian sparsity.

Extra doc: https://github.com/casadi/casadi/wiki/L_6g

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L668

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1175-L1183

lift(*args)¶

lift(self, bool lift_shared, bool lift_calls)

Lift problem formulation by extracting shared subexpressions.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L378

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L619-L625

load_fmi_description(*args)¶

load_fmi_description(self, str filename)

Import problem description from FMI or XML.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L439

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L222-L228

max(*args)¶

max(self, [str] name) -> [float]
max(self, str name) -> float

Get the upper bound.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L612

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1019-L1026

max(self, str name)

[INTERNAL] Get the upper bound, single variable.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L567

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1010-L1017

max(self, [str] name)

[INTERNAL] Get the upper bound.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L612

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1019-L1026

min(*args)¶

min(self, [str] name) -> [float]
min(self, str name) -> float

Get the lower bound.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L606

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L985-L992

min(self, str name)

[INTERNAL] Get the lower bound, single variable.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L561

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L976-L983

min(self, [str] name)

[INTERNAL] Get the lower bound.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L606

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L985-L992

name(*args)¶

name(self) -> str

Name of instance.

Extra doc: https://github.com/casadi/casadi/wiki/L_5d

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L86

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L59-L61

nc(*args)¶

nc(self) -> int

Named constants.

Extra doc: https://github.com/casadi/casadi/wiki/L_6b

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L266

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L210-L212

nd(*args)¶

nd(self) -> int

Dependent parameters.

Extra doc: https://github.com/casadi/casadi/wiki/L_6c

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L271

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L214-L216

nominal(*args)¶

nominal(self, [str] name) -> [float]
nominal(self, str name) -> float

Get the nominal value.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L618

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1053-L1060

nominal(self, str name)

[INTERNAL] Get the nominal value, single variable.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L573

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1044-L1051

nominal(self, [str] name)

[INTERNAL] Get the nominal value.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L618

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1053-L1060

np(*args)¶

np(self) -> int

Parameters.

Extra doc: https://github.com/casadi/casadi/wiki/L_6a

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L261

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L206-L208

nq(*args)¶

nq(self) -> int

Quadrature states.

Extra doc: https://github.com/casadi/casadi/wiki/L_67

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L246

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L194-L196

nu(*args)¶

nu(self) -> int

Free controls.

Extra doc: https://github.com/casadi/casadi/wiki/L_69

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L256

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L202-L204

numel(*args)¶

numel(self, str name) -> int

Get the number of elements of a variable.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L543

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L703-L705

nw(*args)¶

nw(self) -> int

Dependent variables.

Extra doc: https://github.com/casadi/casadi/wiki/L_6d

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L276

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L218-L220

nx(*args)¶

nx(self) -> int

Differential states.

Extra doc: https://github.com/casadi/casadi/wiki/L_65

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L236

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L186-L188

ny(*args)¶

 ny(self) -> int

Output variables.

Extra doc: https://github.com/casadi/casadi/wiki/L_68

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L251

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L198-L200

nz(*args)¶

nz(self) -> int

Algebraic variables.

Extra doc: https://github.com/casadi/casadi/wiki/L_66

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L241

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L190-L192

ode(*args)¶

ode(self) -> [MX]

Ordinary differential equations (ODE)

Extra doc: https://github.com/casadi/casadi/wiki/L_5g

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L103

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L71-L73

oracle(*args)¶

oracle(self, bool sx, bool elim_w, bool lifted_calls) -> Function

Get the (cached) oracle, SX or MX.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L663

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L818-L825

outputs(*args)¶

outputs(self) -> [str]

Model structure: outputs.

Extra doc: https://github.com/casadi/casadi/wiki/L_61

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L213

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L155-L162

p(*args)¶

p(self) -> [str]

Parameters.

Extra doc: https://github.com/casadi/casadi/wiki/L_5o

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L143

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L103-L105

parse_fmi(*args)¶

parse_fmi(self, str filename)

Import existing problem from FMI/XML

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L433

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L433-L433

provides_directional_derivative(*args)¶

provides_directional_derivative(self) -> bool

Does the FMU provide support for analytic derivatives.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L436

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L230-L238

prune(*args)¶

prune(self, bool prune_p, bool prune_u)

Prune unused controls.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L393

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L280-L286

q(*args)¶

q(self) -> [str]

Quadrature states.

Extra doc: https://github.com/casadi/casadi/wiki/L_5j

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L118

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L83-L85

quad(*args)¶

quad(self) -> [MX]

Quadrature equations.

Extra doc: https://github.com/casadi/casadi/wiki/L_5k

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L123

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L87-L89

register_c(*args)¶

register_c(self, str name)

register_d(*args)¶

register_d(self, str name)

register_p(*args)¶

register_p(self, str name)

register_q(*args)¶

register_q(self, str name)

register_t(*args)¶

register_t(self, str name)

register_u(*args)¶

register_u(self, str name)

register_w(*args)¶

register_w(self, str name)

register_x(*args)¶

register_x(self, str name)

register_y(*args)¶

register_y(self, str name)

register_z(*args)¶

register_z(self, str name)

reset(*args)¶

reset(self)

sanity_check(*args)¶

sanity_check(self)

Check if dimensions match.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L329

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L551-L557

set(*args)¶

set(self, [str] name, [float] val)
set(self, [str] name, [str] val)
set(self, str name, float val)
set(self, str name, str val)

Set the current value (string)

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L633

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1145-L1152

set(self, [str] name, [str] val)

[INTERNAL] Set the current value (string)

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L633

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1145-L1152

set(self, str name, float val)
set(self, str name, str val)

[INTERNAL]

set(self, [str] name, [float] val)

[INTERNAL] Set the current value.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L630

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1137-L1143

set_alg(*args)¶

set_alg(self, str name, MX alg_rhs)

Specificy the residual equation for an algebraic variable.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L317

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L543-L549

set_all(*args)¶

set_all(self, str v, [str] name)

Set all variables of a type.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L336

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L422-L428

set_attribute(*args)¶

set_attribute(self, str a, [str] name, [float] val)
set_attribute(self, str a, str name, float val)

Set an attribute.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L602

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L967-L974

set_attribute(self, str a, str name, float val)

[INTERNAL] Set an attribute, single variable.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L558

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L959-L965

set_attribute(self, str a, [str] name, [float] val)

[INTERNAL] Set an attribute.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L602

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L967-L974

set_beq(*args)¶

set_beq(self, str name, MX val)

Get/set the binding equation for a variable

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L491

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L603-L609

set_causality(*args)¶

set_causality(self, str name, str val)

Get/set the causality

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L515

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L667-L669

set_description(*args)¶

set_description(self, str name, str val)

Get/set description

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L503

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L639-L641

set_display_unit(*args)¶

set_display_unit(self, str name, str val)

Get/set the display unit

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L539

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L699-L701

set_initial(*args)¶

set_initial(self, str name, str val)

Get/set the initial property

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L527

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L683-L685

set_max(*args)¶

set_max(self, [str] name, [float] val)
set_max(self, str name, float val)

Set the upper bound.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L615

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1036-L1042

set_max(self, str name, float val)

[INTERNAL] Set the upper bound, single variable.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L570

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1028-L1034

set_max(self, [str] name, [float] val)

[INTERNAL] Set the upper bound.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L615

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1036-L1042

set_min(*args)¶

set_min(self, [str] name, [float] val)
set_min(self, str name, float val)

Set the lower bound.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L609

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1002-L1008

set_min(self, str name, float val)

[INTERNAL] Set the lower bound, single variable.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L564

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L994-L1000

set_min(self, [str] name, [float] val)

[INTERNAL] Set the lower bound.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L609

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1002-L1008

set_nominal(*args)¶

set_nominal(self, [str] name, [float] val)
set_nominal(self, str name, float val)

Set the nominal value.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L621

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1070-L1076

set_nominal(self, str name, float val)

[INTERNAL] Set the nominal value, single variable.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L576

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1062-L1068

set_nominal(self, [str] name, [float] val)

[INTERNAL] Set the nominal value.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L621

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1070-L1076

set_ode(*args)¶

set_ode(self, str name, MX ode_rhs)

Specify the ordinary differential equation for a state.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L314

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L535-L541

set_q(*args)¶

set_q(self, [str] name)

set_start(*args)¶

set_start(self, [str] name, [float] val)
set_start(self, str name, float val)

Set the start attribute.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L627

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1105-L1111

set_start(self, [str] name, [float] val)

[INTERNAL] Set the start attribute.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L627

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1105-L1111

set_start(self, str name, float val)

[INTERNAL] Set the start attribute, single variable.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L582

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1097-L1103

set_type(*args)¶

set_type(self, str name, str val)

Get/set the type

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L509

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L654-L661

set_u(*args)¶

set_u(self, [str] name)

set_unit(*args)¶

set_unit(self, str name, str val)

Get/set the unit

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L533

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L691-L693

set_value_reference(*args)¶

set_value_reference(self, str name, int val)

Get/set value reference

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L497

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L631-L633

set_variability(*args)¶

set_variability(self, str name, str val)

Get/set the variability

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L521

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L675-L677

set_x(*args)¶

set_x(self, [str] name)

set_y(*args)¶

set_y(self, [str] name)

set_z(*args)¶

set_z(self, [str] name, [str] alg)

sort_d(*args)¶

sort_d(self)

Sort dependent parameters.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L384

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L256-L262

sort_w(*args)¶

sort_w(self)

Sort dependent variables.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L387

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L264-L270

sort_z(*args)¶

sort_z(self, [str] z_order)

Sort algebraic variables.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L390

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L272-L278

start(*args)¶

start(self, [str] name) -> [float]
start(self, str name) -> float

Get the start attribute.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L624

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1088-L1095

start(self, [str] name)

[INTERNAL] Get the start attribute.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L624

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1088-L1095

start(self, str name)

[INTERNAL] Get the start attribute, single variable.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L579

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L1078-L1086

t(*args)¶

t(self) -> MX

Independent variable (usually time)

Extra doc: https://github.com/casadi/casadi/wiki/L_5e

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L93

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L63-L65

tear(*args)¶

tear(self)

Identify iteration variables and residual equations using naming

convention.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L396

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L288-L294

type(*args)¶

type(self, str name, int fmi_version) -> str

Get/set the type

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L508

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L643-L652

type_name(*args)¶

type_name(self) -> str

Readable name of the class.

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L74

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L74-L74

u(*args)¶

u(self) -> [str]

Free controls.

Extra doc: https://github.com/casadi/casadi/wiki/L_5n

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L138

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L99-L101

unit(*args)¶

unit(self, str name) -> str

Get/set the unit

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L532

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L687-L689

value_reference(*args)¶

value_reference(self, str name) -> int

Get/set value reference

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L496

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L627-L629

var(*args)¶

var(self, str name) -> MX

Get variable expression by name

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L481

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L559-L566

variability(*args)¶

variability(self, str name) -> str

Get/set the variability

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L520

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L671-L673

w(*args)¶

w(self) -> [str]

Dependent variables.

Extra doc: https://github.com/casadi/casadi/wiki/L_5t

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L170

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L123-L125

wdef(*args)¶

wdef(self) -> [MX]

Dependent variables and corresponding definitions.

Interdependencies are allowed but must be non-cyclic.

Extra doc: https://github.com/casadi/casadi/wiki/L_5u

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L177

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L127-L129

when_cond(*args)¶

when_cond(self) -> [MX]

When statement: triggering condition.

Extra doc: https://github.com/casadi/casadi/wiki/L_5y

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L197

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L143-L145

when_lhs(*args)¶

when_lhs(self) -> [MX]

When statement: left-hand-side.

Extra doc: https://github.com/casadi/casadi/wiki/L_5z

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L202

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L147-L149

when_rhs(*args)¶

when_rhs(self) -> [MX]

When statement: right-hand-side.

Extra doc: https://github.com/casadi/casadi/wiki/L_60

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L207

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L151-L153

x(*args)¶

x(self) -> [str]

Differential states.

Extra doc: https://github.com/casadi/casadi/wiki/L_5f

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L98

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L67-L69

y(*args)¶

 y(self) -> [str]

Output variables.

Extra doc: https://github.com/casadi/casadi/wiki/L_5l

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L128

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L91-L93

ydef(*args)¶

ydef(self) -> [MX]

Definitions of output variables.

Extra doc: https://github.com/casadi/casadi/wiki/L_5m

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L133

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L95-L97

z(*args)¶

z(self) -> [str]

Algebraic variables.

Extra doc: https://github.com/casadi/casadi/wiki/L_5h

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.hpp#L108

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/dae_builder.cpp#L75-L77

4.2. Callback¶

class Callback(*args)¶

Callback function functionality.

This class provides a public API to the FunctionInternal class that can be subclassed by the user, who is then able to implement the different virtual

FunctionInternal, but only allows: calling, not being called.

The user is responsible for not deleting this class for the lifetime of the

Joris Gillis, Joel Andersson

Extra doc: https://github.com/casadi/casadi/wiki/L_o0

C++ includes: callback.hpp

construct(*args)¶

construct(self, str name, dict opts)

Construct internal object.

This is the step that actually construct the internal object, as the class constructor only creates a null pointer. It should be called from the user constructor.

Extra doc: https://github.com/casadi/casadi/wiki/L_o5

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L78

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.cpp#L36-L42

eval(*args)¶

eval(self, [DM] arg) -> [DM]

Evaluate numerically, using temporary matrices and work vectors.

This signature is not thread-safe. For guaranteed thread-safety, use eval_buffer

Extra doc: https://github.com/casadi/casadi/wiki/L_o8

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L106

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.cpp#L60-L62

eval_buffer(*args)¶

eval_buffer(self, double const ** arg, [int] sizes_arg, double ** res, [int] sizes_res) -> int

A copy-free low level interface.

In Python, you will be passed two tuples of memoryview objects Note that only the structural nonzeros are present in the memoryview objects/buffers.

Make sure to override has_eval_buffer() to indicate support for this method.

Extra doc: https://github.com/casadi/casadi/wiki/L_o9

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L116

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.cpp#L53-L56

finalize(*args)¶

finalize(self)

Finalize the object.

This function is called after the construction and init steps are

completed, but before user functions are called. It is called recursively for the whole class hierarchy, starting with the highest level.

Extra doc: https://github.com/casadi/casadi/wiki/L_o7

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L98

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L98-L98

get_forward(*args)¶

get_forward(self, int nfwd, str name, [str] inames, [str] onames, dict opts) -> Function

Return function that calculates forward derivatives.

forward(nfwd) returns a cached instance if available, and calls Function get_forward(casadi_int nfwd) if no cached version is available.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L191

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.cpp#L105-L110

get_jac_sparsity(*args)¶

get_jac_sparsity(self, int oind, int iind, bool symmetric) -> Sparsity

Return sparsity of Jacobian of all input elements.

with respect to all output elements

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L219

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L219-L220

get_jacobian(*args)¶

get_jacobian(self, str name, [str] inames, [str] onames, dict opts) -> Function

Return Jacobian of all input elements with respect to all output

elements.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L176

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.cpp#L97-L102

get_n_in(*args)¶

get_n_in(self) -> int

Get the number of inputs.

This function is called during construction.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L129

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.cpp#L64-L66

get_n_out(*args)¶

get_n_out(self) -> int

Get the number of outputs.

This function is called during construction.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L136

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.cpp#L68-L70

get_name_in(*args)¶

get_name_in(self, int i) -> str

Get the name of an input.

This function is called during construction.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L157

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.cpp#L80-L82

get_name_out(*args)¶

get_name_out(self, int i) -> str

Get the name of an output.

This function is called during construction.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L164

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.cpp#L84-L86

get_reverse(*args)¶

get_reverse(self, int nadj, str name, [str] inames, [str] onames, dict opts) -> Function

Return function that calculates adjoint derivatives.

reverse(nadj) returns a cached instance if available, and calls Function get_reverse(casadi_int nadj) if no cached version is available.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L206

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.cpp#L117-L122

get_sparsity_in(*args)¶

get_sparsity_in(self, int i) -> Sparsity

Get the sparsity of an input.

This function is called during construction.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L143

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.cpp#L72-L74

get_sparsity_out(*args)¶

get_sparsity_out(self, int i) -> Sparsity

Get the sparsity of an output.

This function is called during construction.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L150

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.cpp#L76-L78

has_eval_buffer(*args)¶

has_eval_buffer(self) -> bool

Does the Callback class support a copy-free low level interface: ?

Extra doc: https://github.com/casadi/casadi/wiki/L_265

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L122

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.cpp#L57-L59

has_forward(*args)¶

has_forward(self, int nfwd) -> bool

Return function that calculates forward derivatives.

forward(nfwd) returns a cached instance if available, and calls Function get_forward(casadi_int nfwd) if no cached version is available.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L190

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.cpp#L112-L114

has_jac_sparsity(*args)¶

has_jac_sparsity(self, int oind, int iind) -> bool

Return sparsity of Jacobian of all input elements.

with respect to all output elements

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L218

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L218-L218

has_jacobian(*args)¶

has_jacobian(self) -> bool

Return Jacobian of all input elements with respect to all output

elements.

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L175

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.cpp#L92-L94

has_reverse(*args)¶

has_reverse(self, int nadj) -> bool

Return function that calculates adjoint derivatives.

reverse(nadj) returns a cached instance if available, and calls Function get_reverse(casadi_int nadj) if no cached version is available.

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

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

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.cpp#L124-L126

init(*args)¶

init(self)

Initialize the object.

This function is called after the object construction (for the whole class hierarchy) is complete, but before the finalization step. It is called recursively for the whole class hierarchy, starting with the lowest level.

Extra doc: https://github.com/casadi/casadi/wiki/L_o6

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L88

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L88-L88

static type_name(*args)¶

type_name() -> str

uses_output(*args)¶

uses_output(self) -> bool

Do the derivative functions need nondifferentiated outputs?

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

Doc source: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.hpp#L169

Implementation: https://github.com/casadi/casadi/blob/develop/casadi/core/callback.cpp#L88-L90

4.3. GlobalOptions¶

class GlobalOptions(*args)¶

Collects global CasADi options.

Note to developers: use sparingly. Global options are - in general - a rather bad idea

this class must never be instantiated. Access its static members directly

Joris Gillis

Extra doc: https://github.com/casadi/casadi/wiki/L_23m

C++ includes: global_options.hpp

static getCasadiIncludePath(*args)¶

getCasadiIncludePath() -> str

static getCasadiPath(*args)¶

getCasadiPath() -> str

static getHierarchicalSparsity(*args)¶

getHierarchicalSparsity() -> bool

static getMaxNumDir(*args)¶

getMaxNumDir() -> int

static getSimplificationOnTheFly(*args)¶

getSimplificationOnTheFly() -> bool

static setCasadiIncludePath(*args)¶

setCasadiIncludePath(str path)

static setCasadiPath(*args)¶

setCasadiPath(str path)

static setHierarchicalSparsity(*args)¶

setHierarchicalSparsity(bool flag)

static setMaxNumDir(*args)¶

setMaxNumDir(int ndir)

static setSimplificationOnTheFly(*args)¶

setSimplificationOnTheFly(bool flag)

4.4. CasadiMeta¶

class CasadiMeta(*args)¶

Collects global CasADi meta information.

Joris Gillis

Extra doc: https://github.com/casadi/casadi/wiki/L_23k

C++ includes: casadi_meta.hpp

static build_type(*args)¶

build_type() -> char const *

static compiler(*args)¶

compiler() -> char const *

static compiler_flags(*args)¶

compiler_flags() -> char const *

static compiler_id(*args)¶

compiler_id() -> char const *

static feature_list(*args)¶

feature_list() -> char const *

static git_describe(*args)¶

git_describe() -> char const *

static git_revision(*args)¶

git_revision() -> char const *

static install_prefix(*args)¶

install_prefix() -> char const *

static modules(*args)¶

modules() -> char const *

static plugins(*args)¶

plugins() -> char const *

static version(*args)¶

version() -> char const *