latest released May 17, 2023

Grab a binary from the table:

WindowsLinuxMac classic (High Sierra or above)Mac M1
Matlab R2018b or later R2018b or later R2018b or later R2020b or later (normal Matlab)
R2018b or later (Open Beta)
Octave 6.2.0 or later 6.2.0 or later 6.2.0 or later 6.2.0 or later
Python pip install casadi (needs pip -V>=8.1)





Matlab/OctavePython

x = MX.sym('x')
disp(jacobian(sin(x),x))



x = MX.sym("x")
print(jacobian(sin(x),x))



Get started with the example pack. Onboarding pointers have been gathered by the community at our wiki.

## Symbolic expressions

• hypot(x,y) = sqrt(x*x+y*y)
• log1p(x) = log(1+x)
• expm1(x) = exp(x-1)
• Added operation remainder with the semantics of the C operation
• breaking AD rule of fmin/fmax is now symmetric: jacobian(fmin(x,y),vertcat(x,y)) used to be [1 0] for x==y. Now yields [0.5 0.5].
• Added AD rules for mmin/mmax
• Added logsumexp which behaves like log(sum(exp(x))) but is numerically more accurate (and no overflow issues).
• breaking vertcat/vcat,horzcat/hcat, etc now return a DM type instead of a Sparsity type #2549
• breaking CasADi-Matlab mod has been renamed to rem, because its numerical behaviour is like the builtin-Matlab rem. The builtin-Matlab mod has no CasADi counterpart. CasADi-Python mod has been removed, because its numerical behaviour is not like numpy.mod. #2767. numpy.mod has no counterpart in CasADi; only fmod is equivalent.
• Fixed flaw in codegen with MX if_else

### Common subexpression elimination

• Added Common Subexpression Elimination #1540 for MX and SX. CasADi can now efficiently eliminate redundant computation by inspecting an expression graph and removing redundant nodes.

Before, CasADi internals would avoid introducing redundant nodes during operations on a given expression, but the user was responsible to avoid duplication when constructing that expression.

There is a function cse() that you may apply to expressions:

x = MX.sym('x')

# User responsibility
sx = sin(x)
y = sqrt(sx)+sx # MX(@1=sin(x), (sqrt(@1)+@1))

# cse
y = sqrt(sin(x))+sin(x) # MX((sqrt(sin(x))+sin(x)))
y = cse(y) # MX(@1=sin(x), (sqrt(@1)+@1))


There is a boolean option cse that may be used when constructing a Function:

x = MX.sym('x')

f = Function('f',[x],[sqrt(sin(x))+sin(x)],{"cse":True})
f.disp(True)

f:(i0)->(o0) MXFunction
Algorithm:
@0 = input
@0 = sin(@0)
@1 = sqrt(@0)
@1 = (@1+@0)
output = @1


The technique scales favorably for large graphs.

### Triangular solve triangular solve nodes in MX

MX how has atomic support for solving upper and lower triangular linear systems without allocating any linear solver instance. The operation handles the case with unity diagonal separately for efficiency and supports C code generation. To use the feature, call casadi.solve(A, b) (Python or MATLAB/Octave)

# Python

// C++
casadi::MX x = solve(A, b);  // for argument-dependent lookup, alternatively casadi::MX::solve(A, b) for static function


Cf. #2688.

## Function

• breaking SX/MX Function construction with free variables (i.e. symbols used in the output expressions that are not declared as inputs) now fails immediately unless the allow_free option is used.
• breaking SX/MX Function construction now fails if there are duplicates in input names or output names, unless the allow_duplicate_io_names option is used #2604.
• breaking Serialization: files saved with CasADi 3.5.5 will load in CasADi 3.6.0 (unittested), except for Functions that include a ‘mumps’ linear solver since serialization of this solver was deficient, and except for Functions that include an Integrator.
• breaking custom_jacobian semantics changed. The Function must now return individual blocks (Jacobian of an output w.r.t. to an input)
• breaking Changed API part for Jacobian sparsity (relevant for advanced use through external or Callback)
bool has_jac_sparsity(casadi_int oind, casadi_int iind) const override;

• Function.find_function Can be used to retrieve Functions in a hierarchy.
• Avoid truncation in printing #2452
• breaking: Function outputs that are not used (passed a null pointer internally) will be logged (dump_in option ) as nan instead of earlier 0. E.g. Ipopt nlp_grad_f has two outputs, f and grad_f_x. The f output is not used internally, so will be logged as nan.

## Code-generation

• Function objects with an external call can now be codegenerated.
• mmin/mmax now support codegeneration

## Solvers/plugins

• nlpsol/Opti.solver can now take an option ‘detect_simple_bounds’ (default False) that will promote general constraints to simple bounds (lbx/ubx).
• Added SPRAL linear solver for Ipopt
• Added QP solvers HPIPM, Proxqp, Highs
• CPLEX interface will dynamically load libcplex<CPLEX_VERSION>, where CPLEX_VERSION is read from environmental variables. Same strategy for Gurobi.
• SqpMethod Eigen-reflect/eigen-clip incorrect #2896

### Generalized integrator support

The Integrator class, which solves initial-value problems in ODEs and DAEs has been thoroughly refactored. Changes include:

• The integrator class now has a much more mature support for returning the IVP solution at multiple time points. It can now be obtained by providing a time grid to the integrator constructor. Unlike before, this support should now work in combination with forward/adjoint sensitivity analysis (to any order) and sparsity pattern calculations. Cf. #2823.
• The integrator class now includes support for a piecewise constant control (u). The interface will keep track of changes to u and avoid integrating past such changes; for the Sundials (CVODES/IDAS) interfaces by setting a “stop time”, for fixed step integrators by aligning the integration points with the grid points. Cf. #3025. Development versions of CasADi included support for this in a dedicated class, called Simulator, but this class has now been removed (breaking) and the functionality has been ported to the Integrator class. If you had code looking like cs.integrator('sim_function', 'cvodes', dae, tgrid, opts), you may replace it by cs.integrator('sim_function', 'cvodes', dae, 0, tgrid[1:], opts).
• The Integrator class now much better exploits the problem structure in the sensitivity calculations, especially adjoint (and forward-over-adjoint, adjoint-over-adjoint) sensitivity calculations. Cf. #2823, #3047. The sensitivity analysis relies to a much less extent on symbolic reformulations and instead uses calls to the Function class for derivative calculations - this makes the class now more efficient for use with non-symbolic DAEs, including FMUs or other external models.
• breaking The options t0, tf, output_t0 and grid have been deprecated and will result in a warning if used. Instead, the user can provide equivalent information via the integrator constructor, cf. previous point.
• The backward states are no longer part of the DAE formulation. They are now derived from a user specified number of sensitivity equations (nadj). This is a slight restriction in the possible problem formulations, but on the other hand allows for a much better exploitation of adjoint sensitivity structure. The the backward states remain in the integrator class function inputs and outputs, but have now been renamed to align with their meaning; adj_xf means the adjoint seeds corresponding to xf (before they were called rx0), adj_p are the adjoint sensitivities corresponding to p (before called rqf and so on.
• An option scale_abstol has been added to the Sundials integrators. If this is set to true, nominal values for the differential state and algebraic variables will be passed on to the solver. Cf. #3046

See “multipoint_simulation” in the example pack for a good starting point.

## Function factory

• breaking* Hessian blocks are now symmetric by default instead of returning only the upper triangular part. Prefix with triu: to get the old behavior.
• breaking Multiple Jacobian and/or Hessian blocks can now be calculated more efficiently. Rather than calculating the blocks separately, calculation is done for multiple blocks at once, whenever possible. Cf. #2696.

## DaeBuilder / FMI interoperability

• The dependent parameters d and local dependent variables w have been replaced by the single dependent variables v.
• The DaeBuilder::create function has been reimplemented and now uses the updated Function::factory support (above).
• New proof-of-concept support for export of models in FMI 3.0 format, cf. #3009
• New binary interface to standard FMI, including analytic validated first derivatives and validated hybrid second derivatives, cf. #2779
• The Integrator class has been refactored to efficiently support non-symbolic DAEs, including from FMI - see below.

## Binaries

• Adding Python interfaces for versions 3.10 and 3.11
• Adding builds for Mac silicon
• Octave interface will now dynamically couple with the correct versioned octaveinterp version, such that the new binaries work with future releases of Octave that increment the octaveinterp ABI version number.

## CLI

• There is now a CasADi command line interface, casadi-cli. At the moment, functionality is very limited, just eval_dump, to evaluate Function that have been dumped to the disk (options dump,dump_in)

## Building

• Source builds are no longer dependent on SWIG since Python and Matlab interface files generated by SWIG are now shipped in source archives.
• Source builds can now build and integrate a range third-party open-source solver automatically. E.g. -DWITH_IPOPT=ON -DWITH_BUILD_REQUIRED=ON
• Source builds can now use mockups for a range of third-party commercial solvers. E.g. -DWITH_CPLEX=ON -DWITH_MOCKUP_CPLEX=ON
• Source packages for python pip are now available

## Plugin versions used in binaries

### 3.6.0

• sundials-interface, Interface to the ODE/DAE integrator suite SUNDIALS.
• csparse-interface, Interface to the sparse direct linear solver CSparse.
• superscs-interface, Interface to QP solver SUPERSCS.
• osqp-interface, Interface to QP solver OSQP.
• tinyxml-interface, Interface to the XML parser TinyXML.
• qpoases-interface, Interface to the active-set QP solver qpOASES.
• blocksqp-interface, Interface to the NLP solver blockSQP.
• cplex-interface, Interface to the QP solver CPLEX.
• gurobi-interface, Interface to the (mixed-integer) QP solver GUROBI
• knitro-interface, Interface to the NLP solver KNITRO.
• snopt-interface, Interface to the NLP solver SNOPT.
• worhp-interface, Interface to the NLP solver Worhp (requires gfortran, gomp).
• lapack-interface, Interface to LAPACK.
• mumps-interface, Interface to MUMPS.
• spral-interface, Interface to SPRAL.
• clp-interface, Interface to the LP solver CLP.
• cbc-interface, Interface to the LP solver CBC.
• ipopt-interface, Interface to the NLP solver Ipopt.
• bonmin-interface, Interface to the MINLP framework Bonmin.
• highs-interface, Interface to the MILP / QP solver HiGHS.
• proxqp-interface, Interface to QP solver PROXQP.
• ampl-interface, Interface to the AMPL solver library.

## Changes in 3.6.1

• breaking serialization of integrator is not compatible with 3.6.0 due to bugfixes
• git: master branch has been renamed to main, and has different semantics: it will be the branch where new features are added regularly before they become an official release. Latest official release is available as latest branch.

## Changes in 3.6.3

• KNITRO on linux crashes with a segmentation fault without LD_PRELOAD=<knitro_lin_path>/libiomp5.so.
• Callbacks with one argument are broken in Matlab CasADi

Grab a binary from the table (for MATLAB, use the newest compatible version below):

WindowsLinuxMac (High Sierra or above)
Matlab R2016a or later,
R2014b,
R2014a,
R2013a or R2013b
R2014b or later,
R2014a
R2015a or later,
R2014b,
R2014a
Octave 4.4.1 (32bit / 64bit),
4.4.0 (32bit / 64bit),
5.1.0 (32bit / 64bit),
5.2.0 (32bit / 64bit),
6.1.0 (32bit / 64bit)
4.4.1,
5.1.0,
5.2.0,
6.1.0
5.2.0,
6.1.0(Mojave or higher)
Python Py27 (32bit* / 64bit*),
Py35 (32bit* / 64bit*),
Py36 (32bit* / 64bit*),
Py37 (32bit* / 64bit*),
Py38 (32bit* / 64bit*)
Py39 (32bit* / 64bit*)
Py27,
Py35,
Py36,
Py37,
Py38,
Py39
Py27,
Py35,
Py36,
Py37,
Py38,
Py39
or just pip install casadi (needs pip -V>=8.1)

(*) Check your Python console if you need 32bit or 64bit - bitness should be printed at startup.

Matlab/OctavePython

x = MX.sym('x')
disp(jacobian(sin(x),x))



from sys import path
x = MX.sym("x")
print(jacobian(sin(x),x))



Get started with the example pack.

• CasADi Functions can be serialized now (#308).
f.save('f.casadi')            % Dump any CasADi Function to a file


This enables easy sharing of models/solver isntances beteen Matlab/Python/C++ cross-platform, and enables a form of parallelization.

• You can now evaluate CasADi Functions from C without requiring code-generation. This makes it possible to embed CasADi computations in Fortran, Julia, FMI, …
• All CasADi Functions support timing information now (print_time, default true for QP and NLP solvers). Use record_time to make timings available through f.stats() without printing them.
• map with reduce arguments now has an efficient implementation (no copying/repmat)
• Low-overhead Callback eval support was changed to eval_buffer
• FunctionInternal::finalize no longer takes options dict.
• Options always_inline and never_inline were added
• Options is_diff_in and is_diff_out were added
• (3.5.2) Ctrl-C interrupts are now disabled in multi-threaded Maps since they could result in crashes
• (3.5.2) Sparsity of Callbacks can be set with has_jacobian_sparsity/get_jacobian_sparsity
• (3.5.2) Jitted functions can now be serialized
• (3.5.2) BSpline constructor takes an inline option yielding a fully differentiable (but not very scalable) BSpline operation for MX
• (3.5.5) Fixed performance deficiency in inline BSline derivatives

• breaking: IM type is removed from public API (was used to represent integer sparse matrices). Use DM instead.
• breaking: linspace(0,1,3) and linspace(0.0,1,3) now both return [0 0.5 1] instead of [0 0 1] for the former
• MX supports slicing with MX now (symbolic indexing).
• Issue #2364:
• breaking: veccat of an empty list now returns 0-by-1 instead of 0-by-0.
• jtimes output dimensions have changed when any of the arguments is empty.
• NLP function object’s ’lam_p’ is now 0-by-1 in case of missing parameters.
• (3.5.2) Fixed long-standing bug in cosh derivative
• (3.5.2) An MX operation convexify was added
• (3.5.2) An inefficiency in MX multiplication sparsity was detected and fixed by Mirko Hahn

## Interpolation functionality

• Support for parametric (=changeable only, but not differentiable) grid and/or coefficients for linear/spline interpolation
• for interpolant, new constructors where added that takes dimensions instead of concrete vectors
• Support for symbolic (differentiable) grid and coefficients for linear interpolation (set inline option to true).

## Python specific

• Similar functionality in Callbacks
• (3.5.2) fix numpy compatibility (numpy 1.19)
• (3.5.3) fix the numpy fix

## Matlab/Octave specific

• breaking: a(:)=b now behaves like Matlab builtin matrices when a is a CasADi matrix. Before, only the first column of a would be touched by this statement. (#2363)
• breaking: Fixed bug where MX constructor treated a numeric row vector as column vector. Now size(MX(ones(1,4))) returns (1,4) as expected. (#2366)
• Can now use spy directly on DM,MX,SX
• (3.5.2) Printing from a multi-threaded map context is disabled beause it could result in crashes. In linux, you may still see the output from a terminal used to start Matlab

## Opti

• Opti supports conic problems now: Opti('conic')
• One can now easily obtain a parametric solution as a CasADi Function from an Opti instance:
opti = Opti()
x = opti.variable()
y = opti.variable()
p = opti.parameter()

opti.minimize(y**2+sin(x-y-p)**2)
opti.subject_to(x+y>=1)

opti.solver(nlpsolver,nlpsolver_options)

F = opti.to_function("F",[x,p,opti.lam_g],[x,y])

r = F(0,0.1,0)


(3.5.1) Improved support for vertcatted inputs to to_function

• Using Opti together with max_iter is more natural now: use solve_limited() to avoid exceptions to be raised when iterations or time runs out. No need to try/catch.

## Code-generation

• breaking: external now looks for a .dylib file, not .so for mac
• breaking: Codegen API has changes related to thread-local memory:
• void* mem changed to int mem
• alloc_mem, init_mem, free_mem have been purged. checkout and release replace them.
  int mem = checkout();
eval(arg, res, iw, w, mem);
release(mem);

• Codegen ‘CODEGEN_PREFIX’ has been renamed to ‘CASADI_CODEGEN_PREFIX’
• QP solvers (QRQP, OSQP) and SqpMethod codegenerate now. This means that embedded MPC with CasADi is now more practical.
• Runge-Kutta and Collocation Integrator objects can be inlined into code-generatable MX Function with the ‘simplify’ option.
• (3.5.1) an important flaw was corrected that caused incorrect code for expression graphs with logical ‘and’ and ‘or’.
• (3.5.1) fixed regression for expression graphs containing inf/nan
• (3.5.2) fixed bug of a division looking like a comment
• (3.5.2) fixed mem.h regression
• (3.5.2) Made main and mex-related functions c89-compliant

## Solvers

• breaking: NLP solvers - bound_consistency, an option to post-process the primal and dual solution by projecting it on the bounds, introduced in 3.4, was changed to default off

• Sundials was patched to support multi-threading

• WORHP was bumped to v1.13

• SNOPT was bumped to v7.7

• SuperSCS (conic solver) was added

• OSQP (QP solver) was added

• CBC (LP solver) was added

• (3.5.3) AMPL was fixed to allow other solvers than IPOPT

• breaking: SQP Method

• regularize_margin option was added
• regularize (bool) option was removed. To get the effect of regularize=true, specify convexify_strategy='regularize'. Other strategies include clipping eigenvalues.
• line search was reverted from a custom designed thing, to standard textbook L1
• CPLEX and Gurobi got support for sos constraints

• Conic/qpsol interface extended for semidefinite programming and SOCP

• Solvers supporting SOCP: Gurobi, SuperSCS, CPLEX
• breaking: Newton Rootfinder now supports a line_search option (default true)

• Rootfinder now throws an exception by default (’error_on_fail’ option true) when failing to converge

• (3.5.5) Implemented constraints in IDAS and step size limits in CVODES/IDAS integrators

## Convenience tools

• Debugging facilities:
• Function options print_in/print_in print inputs/outputs when numerically evaluating a function
• Function option dump_in/dump_out dumps to the file system
• Function option dump dumps the function itself (loadable with Function.load)
• DM.from_file and DM.to_file with a MatrixMarket and txt support
• Helping interaction with codegen with main=true: Function.generate_in/Function.nz_from_in/Function.nz_to_in to help creating input text files.
• Function.convert_in/Function.convert_out to switch between list and dictionary arguments/results

## Binaries

• (3.5.1) Mac binaries for Matlab was switched to a different build environment. The binaries now require High Sierra or above, and work on Catalina.
• (3.5.4) Mac binaries for Python and octave have been switched just like Matlab
• (3.5.4) Linux binaries for Matlab and Octave have been switched to the manylinux environment, with gfortran dependency now grafted in (included, with a unique alias to avoid name collision)

## Third-party solver interfaces in binaries

Versions used in binaries ( see FAQ ):

softwareversion library license env build env
IPOPT 3.12.3 shipped / /
KNITRO 10.3 libknitro1030.so/knitro1032.dll / KNITRO
CPLEX windows/mac: 12.8.0, linux:12.6.3 libcplex1263.so / libcplex1280.dll ILOG_LICENSE_FILE CPLEX

Grab a binary from the table (for MATLAB, use the newest compatible version below):

WindowsLinuxMac
Matlab R2016a or later,
R2014b,
R2014a,
R2013a or R2013b
R2014b or later,
R2014a
R2015a or later,
R2014b,
R2014a
Octave 4.4.1 (32bit / 64bit),
4.4.0 (32bit / 64bit)
4.4.1,
4.2.2
4.4.0
Python Py27 (32bit* / 64bit*),
Py35 (32bit* / 64bit*),
Py36 (32bit* / 64bit*),
Py37 (32bit* / 64bit*)
Py27,
Py35,
Py36,
Py37
Py27,
Py35,
Py36,
Py37
or just pip install casadi (needs pip -V>=8.1)

(*) Check your Python console if you need 32bit or 64bit - bitness should be printed at startup.

Matlab/OctavePython

x = MX.sym('x')
disp(jacobian(sin(x),x))



from sys import path
x = MX.sym("x")
print(jacobian(sin(x),x))



Get started with the example pack.

## Credit where credit is due: Proper attribution of linear solver routines, reimplementation of code generation for linear solvers #2158, #2134

CasADi 3.3 introduced support for two sparse direct linear solvers relying based on sparse direct QR factorization and sparse direct LDL factorization, respectively. In the release notes and in the code, it was not made clear enough that part of these routines could be considered derivative works of CSparse and LDL, respectively, both under copyright of Tim Davis. In the current release, routines derived from CSparse and LDL are clearly marked as such and to be considered derivative work under LGPL. All these routines reside inside the casadi::Sparsity class. Since CasADi, CSparse and LDL all have the same open-source license (LGPL), this will not introduce any additional restrictions for users.

Since C code generated from CasADi is not LGPL (allowing CasADi users to use the generated code freely), all CSparse and LDL derived routines have been removed or replaced in CasADi’s C runtime. This means that code generation for CasADi’s ‘qr’ and ’ldl’ is now possible without any additional license restrictions. A number of bugs have also been resolved.

## Parametric sensitivity for NLP solvers #724

CasADi 3.4 introduces differentiability for NLP solver instances in CasADi. Derivatives can be calculated efficiently with either forward or reverse mode algorithmic differentiation. We will detail this functionality in future publications, but in the meantime, feel free to reach out to Joel if you have questions about the functionality. The implementation is based on using derivative propagation rules to the implicit function theorem, applied to the nonlinear KKT system. It is part of the NLP solver base class and should in principle work with any NLP solver, although the factorization and solution of the KKT system (based on the sparse QR above) is likely to be a speed bottle neck in applications. The derivative calculations also depend on accurate Lagrange multipliers to be available, in particular with the correct signs for all multipliers. Functions for calculating parametric sensitivities for a particular system can be C code generated.

## A primal-dual active set method for quadratic programming

The parametric sensitivity analysis for NLP solvers, detailed above, is only as good as the multipliers you provide to it. Multipliers from an interior point method such as IPOPT are usually not accurate enough to be used for the parametric sensitivity analysis, which in particular relies on knowledge of the active set. For this reason, we have started work on a primal-dual active set method for quadratic programming. The method relies on the same factorization of the linearized KKT system as the parametric sensitivity analysis and will support C code generation. The solver is available as the “activeset” plugin in CasADi. The method is still work-in-progress and in particular performs poorly if the Hessian matrix is not strictly positive definite.

## Changes in Opti

• describe methods in Matlab now follows index-1 based convention.
• Added show_infeasibilities to help debugging infeasible problems.
• Added opti.lbg,opti.ubg

## Changes in existing functionality

• Some CasADi operations failed when the product of rows and columns of a matrix was larger then 2^31-1. This limit has been raised to 2^63-1 by changing CasADi integer types to casadi_int (long long). The change is hidden for Python/Octave/Matlab users, but C++ users may be affected.
• Fixed various bottlenecks in large scale MX Function initialization
• Non-zero location reports for NaN/Inf now follow index-1 based convention in Matlab interface.

• SX Functions can be serialized/pickled/saved now.
• Added for-loop equivalents to the users guide
• New backend for parallel maps: “thread” target, shipped in the binaries.
• Uniform ‘success’ flag in solver.stats() for nlpsol/conic
• Added evalf function to numerically evaluate an SX/MX matrix that does not depend on any symbols
• Added diff and cumsum (follows the Matlab convention)
• Added a rootfinder plugin (‘fast_newton’) that can code-generate
• Added binary search for Linear/BSpline Interpolant. Used by default for grid dimensions (>=100)

## Binaries

• Binaries now come with a large set of plugins enabled
• Binaries ship with “thread” parallelization
• Binaries are hosted on Github instead of Sourceforge

## Misc

• Default build mode is Release mode once again (as was always intended)
• CasADi passes with -Werror for gcc-6 and gcc-7

Getting error “CasADi is not running from its package context.” in Python? Check that you have casadi-py27-v3.4.5/casadi/casadi.py. If you have casadi-py27-v3.4.5/casadi.py instead, that’s not good; add an extra casadi folder.

Got stuck while installing? You may also try out CasADi without installing, right in your browser (pick Python or Octave/Matlab).

Grab a binary from the table (for MATLAB, use the newest compatible version below):

Windows Linux Mac
Matlab R2014b or later,
R2014a,
R2013a or R2013b
R2014b or later,
R2014a
R2015a or later,
R2014b,
R2014a
Octave 4.2.1 (32bit / 64bit) 4.2.1 4.2.1
Python Py27 (32bit1,2 / 64bit2),
Py35 (32bit2 / 64bit2),
Py36 (32bit2 / 64bit2)
Py27,
Py35,
Py36
Py27,
Py35,
Py36

1 Use this when you have Python(x,y). 2 Check your Python console if you need 32bit or 64bit - bitness should be printed at startup.

Matlab/OctavePython
addpath('.../casadi-matlabR2014a-v3.3.0')
x = MX.sym('x')
disp(jacobian(sin(x),x))

from sys import path
x = MX.sym("x")
print(jacobian(sin(x),x))


New: install with pip install casadi

Get started with the example pack.

## New and improved features

### Support for finite differences

CasADi is now able to calculate derivatives using finite differences approximations. To enable this feature, set the “enable_fd” option to true for a function object. If the function object has built-in derivative support, you can disable it by setting the options enable_forward, enable_reverse and enable_jacobian to false.

The default algorithm is a central difference scheme with automatic step-size selection based on estimates of truncation errors and roundoff errors. You can change this to a (cheaper, but less accurate) one-sided scheme by setting fd_method to forward or backward. There is also an experimental discontinuity avoiding scheme (suitable if the function is differentiated near nonsmooth points that can be enable by setting fd_method to smoothing.

### New linear solvers with support for C code generation

Two sparse direct linear solvers have been added to CasADi’s runtime core: One based on an up-looking QR factorization, calculated using Householder reflections, and one sparse direct LDL method (square-root free variant of Cholesky). These solvers are available for both SX and MX, for MX as the linear solver plugins “qr” and “ldl”, for MX as the methods “SX::qr_sparse” and “SX::ldl”. They also support for C code generation (with the exception of LDL in MX).

### Faster symbolic processing of MX graphs

A speed bottleneck, related to the topological sorting of large MX graphs has been identified and resolved. The complexity of the sorting algorithms is now linear in all cases.

### Other improvements

• A\y and y'/A now work in Matlab/Octave
• Matrix power works
• First major release with Opti
• shell compiler now works on Windows, allowing to do jit using Visual Studio
• Added introspection methods instruction_* that work for SX/MX Functions. See accessing_mx_algorithm example to see how you can walk an MX graph.
• Experimental feature to export SX/MX functions to pure-Matlab code.
• DM::rand creates a matrix with random numbers. DM::rng controls the seeding of the random number generator.

## Distribution/build system

• Python interface no longer searches for/links to Python libraries (on Linux, OSX)
• Python interface no longer depends on Numpy at compile-time; CasADi works for any numpy version now
• Python binaries and wheels have come a step closer to true manylinux. CasADi should now run on CentOS 5.

## API changes

### Refactored printing of function objects

The default printout of Function instances is now shorter and consistent across different Function derived classes (SX/MX functions, NLP solvers, integrators, etc.). The new syntax is:

from casadi import *
x = SX.sym('x')
y = SX.sym('x',2)
f = Function('f', [x,y],[sin(x)+y], ['x', 'y'], ['r'])
print(f) # f:(x,y)->(r) SXFunction
f.disp() # Equivalent syntax (MATLAB style)
f.disp(True) # Print algorithm


I.e. you get a list of inputs, with dimension if non-scalar, and a name of the internal class (here SXFunction). You can also get the name as a string: str(f) or f.str(). If you want to print the algorithm, pass an optional argument “True”, i.e. f.str(True) or f.disp(True).

### Changes to the codegen C API

The C API has seen continued improvements, in particular regarding the handling of external functions with memory allocation. See the user guide for the latest API.

### Other changes

• inv() is now more efficient for large SX/DM matrices, and is evaluatable for MX (cparse by default). The old variant is still available for SX/MX as inv_minor, and for MX as inv_node.
• Linear solver-related defaults are now set to csparse as opposed to symbolicqr
• In Matlab, when the CasADi result is a vector<bool>, this gets mapped to a logical matrix. E.g. which_depends is affected by this change.
• The sum-of-squares operator is now called sumsqr instead of sum_square.
• The API of the Linsol class has changed.
Getting error “CasADi is not running from its package context.” in Python? Check that you have casadi-py27-v3.3.0/casadi/casadi.py. If you have casadi-py27-v3.3.0/casadi.py instead, that’s not good; add an extra casadi folder.

Grab a binary from the table (for MATLAB, use the newest compatible version below):

Windows 64 bit Linux (14.04+) Mac
Matlab R2014b or later R2014b or later R2015a or later
R2014a R2014a R2014b
R2013a or R2013b R2014a
Octave 4.2.1 32bit or 64bit 4.2.1 4.2.1
Python Py27 (py 32bit or py 64bit ) Py27 Py27
Py35 (py 32bit or py 64bit ) Py35 Py35
Py36 (py 32bit or py 64bit ) Py36 Py36

Matlab/OctavePython
addpath('.../casadi-matlabR2014a-v3.2.3')
x = MX.sym('x')
disp(jacobian(sin(x),x))

from sys import path
x = MX.sym("x")
print(jacobian(sin(x),x))


New: install with pip install casadi (you must have pip --version >= 8.1!)

## New features

• Introduced differentiable exponential matrix node expm (requires slicot)
• Introduced differentiable N-dimensional lookup tables: interpolant with ‘bspline’ solver.

## Bugs in the SUNDIALS interface fixed

CasADi 3.1 included a refactored support for ODE/DAE sensitivity analysis. While more efficient, this also exposed some bugs that have now been fixed in the CasADi 3.2 release, including:

• A bug affecting second order sensitivity analysis using CVODES was fixed. Cf. #1924.
• Segfault in IDAS Cf. #1911.

## API changes

• The if_else and conditional operations are now non-short-circuiting by default for both SX and MX. This means that if_else(c,x,y) is now equivalent to if_else(c,x,y,False) and not if_else(c,x,y,True) as before. Also note that if_else(c,x,y,True) is only supported for MX. Cf. #1968.
• The functions Function::jacobian, Function::derivative and Function::hessian, which have had an internal character since CasADi 3.0, have been deprecated and will be removed in their current forms in the next release. The user is encouraged to work with expressions (e.g. J = jacobian(f,x) or Jv = jtimes(f,x,v) or [H,g] = hessian(f,x)) or use Function::factory (*). To allow a smooth transition, Function::jacobian and Function::hessian will be available as Function::jacobian_old and Function::hessian_old in this and next release. Cf. #1777.

(*) example in Matlab:

x = MX.sym('x')
y = x^2;
f = Function('f',{x},{y})
%J = f.jacobian(0,0) replacement:
J = Function('J',{x},{jacobian(y,x), y}) % alternative 1
J = f.factory('J',{'i0'},{'jac:o0:i0','o0'}) % alternative 2
%H = f.hessian(0,0) replacement:
[H,g] = hessian(y,x);
H = Function('H',{x},{H,g}) % alternative 1
H = f.factory('H',{'i0'},{'hess:o0:i0:i0','grad:o0:i0'}) % alternative 2


## Improvements to C code generation

• The generated code now follows stricter coding standards. It should now be possible to compile the code with the GCC flags -Wall -Werror. Cf. #1741.

## Changes to the build system

• The build system has been refactored and CasADi/C++ can be conveniently compiled with Visual Studio C++ on Windows. The installation now also includes CMake configure files, which makes it convenient to locate and use a CasADi installation in C++ code. Cf. #1982.
• The logic for source builds have changed. Before, the build system would try to locate third-party packages on the system and compile and install the third-party interfaces if this was successful. Now, the logic is that third-party packages are not installed unless the user specifically indicates this e.g. -DWITH_IPOPT=ON. Cf. #1989, #1988.
• The default installation directories for the SWIG interfaces (for Python, Octave and MATLAB) has changed. It is now installed as subdirectories of the CMAKE_INSTALL_PREFIX location by default, but this can be changed by explicitly setting the CMake variables BIN_PREFIX, CMAKE_PREFIX, INCLUDE_PREFIX, LIB_PREFIX, MATLAB_PREFIX and PYTHON_PREFIX. A flat installation directory (without subdirectories) can be obtained by setting the WITH_SELFCONTAINED option. This is the default behavior on Windows. Cf. #1991, #1990

## Changes to precompiled binaries

Python 2.6 (#1976), Python 3.6 (#1987) and Octave 4.2 (#2002, #2000) are now supported.

Get started with the example pack.

Getting error “CasADi is not running from its package context.” in Python? Check that you have casadi-py27-np1.9.1-v3.2.3/casadi/casadi.py. If you have casadi-py27-np1.9.1-v3.2.3/casadi.py instead, that’s not good; add an extra casadi folder.

Extra links for the adventurous: more versions, nightly builds, source build instructions