SUNDIALS: SUite of Nonlinear and DIfferential/ALgebraic Equation Solvers

IDA is a package for the solution of differential-algebraic equation (DAE) systems in the form F(t,y,y’)=0. It is written in C, but derived from the package DASPK which is written in Fortran.

The integration method in IDA is variable-order, variable-coefficient BDF in fixed-leading-coefficient form. The method order varies between 1 and 5. The solution of the resulting nonlinear system is accomplished with some form of Newton iteration. In the cases of a direct linear solver (dense, banded, or sparse), the nonlinear iteration is a Modified Newton iteration, in that the Jacobian is fixed (and usually out of date). When using any of the Krylov methods as the linear solver, the iteration is an Inexact Newton iteration, using the current Jacobian (through matrix-free products), in which the linear residual is nonzero but controlled.

The implicit nonlinear systems within implicit integrators are solved approximately at each integration step using a modified Newton method, an Inexact Newton method, or a fixed-point solver (functional iteration). For the Newton-based methods and the serial or threaded NVECTOR modules in SUNDIALS, IDA provides both direct (dense, band, or sparse) and preconditioned Krylov iterative (GMRES, BiCGStab, TFQMR) linear solvers. When used with one of the distributed parallel NVECTOR modules, including PETSc and hypre vectors, or a user-provided vector data structure, only the Krylov solvers are available, although a user may supply their own linear solver for any data structures if desired.  In addition to the basic Krylov method modules, the IDA package also contains a preconditioner module called IDABBDPRE, which provides a band-block-diagonal preconditioner for use with the distributed memory parallel vector.

For use with Fortran applications, a set of Fortran/C interface routines, called FIDA, is also supplied. These are written in C, but assume that the user calling program and all user-supplied routines are in Fortran.

See Software page for download and documentation.


ida release history

What’s New in v.4.0.0-dev.1

Version 4.0.0-dev.1 is a second step toward the full 4.0.0 release which should be complete by end of 2018.  The 4.0.0 release will include a full redesign of our nonlinear solver interfaces allowing for encapsulation of the nonlinear solvers and ease in interfacing outside nonlinear solver packages as well as a restructuring of the ARKode package to allow for more time stepping options.

  • New features and/or enhancements

An API for encapsulating the nonlinear solvers used in SUNDIALS implicit
integrators has been introduced and are utilized by the CVODE and IDA packages.
The other SUNDIALS packages will be updated to use generic nonlinear solver in a
later release. The goal of this API is to ease the introduction of new nonlinear
solver options in SUNDIALS integrators and allow for external or user-supplied
nonlinear solvers. The SUNNONLINSOL API and provided SUNNONLINSOL modules are
described in a new user guide chapter and follow the same object oriented design
and implementation used by the NVECTOR, SUNMATRIX, and SUNLINSOL modules.

SUNNONLINSOL modules are intended to solve nonlinear systems formulated as
either a rootfinding problem F(y)=0 or a fixed-point problem y=G(Y).
Currently two SUNNONLINSOL implementations are provided,
previous integrator specific implementations of a Newton iteration and a
fixed-point iteration (previously referred to as functional iteration),
respectively. Additionally, the fixed-point iteration can use Anderson’s method
to accelerate convergence. Example programs using each of these nonlinear solver
modules in a standalone manner have been added and all CVODE AND IDA example programs
have been updated to use generic SUNNONLINSOL modules.

In IDA the SUNNONLINSOL_NEWTON module is also the default nonlinear solver
(and it is the only nonlinear solver enabled for IDA at this time)
Since IDA previously only used an internal implementation
of a Newton iteration for nonlinear solves, no changes are required to user
programs and functions for setting the nonlinear solver options (e.g.,
IDASetMaxNonlinIters) or getting nonlinear solver statistics (e.g.,
IDAGetNumNonlinSolvIters) remain unchanged and internally call generic

What’s New in v.3.1.2

  • Updated the minimum required version of CMake to 2.8.12 and enabled using rpath by default to locate shared libraries on OSX.
  • Fixed Windows specific problem where ‘sunindextype’ was not correctly defined when using 64-bit integers for the SUNDIALS index type. On Windows ‘sunindextype’ is now defined as the MSVC basic type ‘__int64’

  • Added sparse SUNMatrix “Reallocate” routine to allow specification of the nonzero storage.

  • Updated the KLU SUNLinearSolver module to set constants for the two reinitialization types, and fixed a bug in the full reinitialization approach where the sparse SUNMatrix pointer would go out of scope on some architectures.

  • Updated the “ScaleAdd” and “ScaleAddI” implementations in the sparse SUNMatrix module to more optimally handle the case where the target matrix contained sufficient storage for the sum, but had the wrong sparsity pattern.  The sum now occurs in-place, by performing the sum backwards in the existing storage.  However, it is still more efficient if the user-supplied Jacobian routine allocates storage for the sum ‘I+ gamma J’ manually (with zero entries if needed).

  • Changed the LICENSE install path to ‘instdir/include/sundials’.

What’s new in v.4.0.0-dev

Version 4.0.0-dev is a first step toward the full 4.0.0 release which should be complete by end of 2018.  The 4.0.0 release will inlude a full redesign of our nonlinear solver interfaces allowing for encapsulation of the nonlinear solvers and ease in interfacing outside nonlinear solver packages.

  • New features and/or enhancements
    • Three fused vector operations and seven vector array operations have been added to the NVECTOR API. These optional operations are intended to increase data reuse in vector operations, reduce parallel communication on distributed memory systems, and lower the number of kernel launches on systems with accelerators. The new operations are N_VLinearCombination, N_VScaleAddMulti, N_VDotProdMulti, N_VLinearCombinationVectorArray, N_VScaleVectorArray, N_VConstVectorArray, N_VWrmsNormVectorArray, N_VWrmsNormMaskVectorArray, N_VScaleAddMultiVectorArray, and N_VLinearCombinationVectorArray. If any of these operations are defined as NULL in an NVECTOR implementation the NVECTOR interface will automatically call standard NVECTOR operations as necessary.   Details on the new operations can be found in the user guide Chapter on the NVECTOR API.
    • Several changes were made to the build system.
      • If MPI is enabled and MPI compiler wrappers are not set, the build system will check if  CMAKE_<language>_COMPILER can compile MPI programs before trying to locate and use an MPI installation. The native CMake FindMPI module is now used to locate an MPI installation.
      • The options for setting MPI compiler wrappers and the executable for running MPI programs have been updated to align with those in the native CMake FindMPI module. This included changing MPI_MPICC to MPI_C_COMPILER, MPI_MPICXX to MPI_CXX_COMPILER, combining MPI_MPIF77 and MPI_MPIF90 to MPI_Fortran_COMPILER, and changing MPI_RUN_COMMAND to MPIEXEC.
      • When a Fortran name-mangling scheme is needed (e.g., LAPACK_ENABLE is ON) the build system will infer the scheme from the Fortran compiler. If a Fortran compiler is not available or the inferred or default scheme needs to be overridden, the advanced options SUNDIALS_F77_FUNC_CASE and SUNDIALS_F77_FUNC_UNDERSCORES can be used to manually set the name-mangling scheme and bypass trying to infer the scheme.
      • Parts of the main CMakeLists.txt file were moved to new files in the src and example directories to make the CMake configuration file structure more modular.

What’s new in v.3.1.1

  • Fixed a potential memory leak in the SPGMR and SPFGMR linear solvers: if “Initialize” was called multiple times then the solver memory was reallocated (without being freed).
  • Fixed C++11 compiler errors/warnings about incompatible use of string literals.

  • Updated KLU SUNLinearSolver module to use a typedef for the precision-specific solve function to be used (to avoid compiler warnings).

  • Added missing typecasts for some (void*) pointers (again, to avoid compiler warnings).

  • Bugfix in sunmatrix_sparse.c where we had used ‘int’ instead of ‘sunindextype’ in one location.

  • Added missing #include <stdio.h> in NVECTOR and SUNMATRIX header files.

  • Fixed an indexing bug in the CUDA NVECTOR implementation of N_VWrmsNormMask and revised the RAJA NVECTOR implementation of N_VWrmsNormMask to work with mask arrays using values other than zero or one. Replaced doubles with realtypes in the RAJA vector test functions.

  • Fixed compilation issue with GCC 7.3.0 and Fortran programs that do not require a SUNMatrix or SUNLinearSolver module (e.g. iterative linear solvers, explicit methods in ARKode, functional iteration in CVODE, etc.).

  • In IDA and IDAS

    • Added missing prototypes for IDASpilsGetNumJTSetupEvals in IDA and IDAS.

What’s new in v.3.1.0?

  • New features and/or enhancements
    • Added NVECTOR print functions that write vector data to a specified file (e.g., N_VPrintFile_Serial).
    • Added ‘make test’ and ‘make test_install’ options to the build system for testing SUNDIALS after building with ‘make’ and installing with ‘make install’ respectively.
    • Added “Changes in …” (latest version) to Intro. in all User Guides.

What’s new in v3.0.0?

  • New features and/or enhancements
    • New linear solver API and interfaces for all SUNDIALS packages and linear solvers.  The goal of the redesign of these interfaces was to provide more encapsulation and ease in interfacing custom linear solvers and interoperability with linear solver libraries.
      • Added generic SUNMATRIX module with three provided implementations: dense, banded, and sparse.  These implementations replicate previous SUNDIALS Dls and Sls matrix structures in a single object-oriented API.
      • Added example problems demonstrating use of generic SUNMATRIX modules.
      • Added generic SUNLINEARSOLVER module with eleven provided implementations: dense, banded, LAPACK dense, LAPACK band, KLU, SuperLU_MT, SPGMR, SPBCGS, SPTFQMR, SPFGMR, and PCG.  These implementations replicate previous SUNDIALS generic linear solvers in a single object-oriented API.
      • Added example problems demonstrating use of generic SUNLINEARSOLVER modules.
      • Expanded package-provided direct linear solver (Dls) interfaces and scaled, preconditioned, iterative linear solver (Spils) interfaces to utilize generic SUNMATRIX and SUNLINEARSOLVER objects.
      • Removed package-specific, linear solver-specific, solver modules (e.g. CVDENSE, KINBAND, IDAKLU, ARKSPGMR) since their functionality is entirely replicated by the generic Dls/Spils interfaces and SUNLINEARSOLVER/SUNMATRIX modules.  The exception is CVDIAG, a diagonal approximate Jacobian solver available to CVODE and CVODES.
      • Converted all SUNDIALS example problems to utilize new generic SUNMATRIX and SUNLINEARSOLVER objects, along with updated Dls and Spils linear solver interfaces.
      • Added Spils interface routines to ARKode, CVODE, CVODES, IDA and IDAS to allow specification of a user-provided “JTSetup” routine. This change supports users who wish to set up data structures for the user-provided Jacobian-times-vector (“JTimes”) routine, and where the cost of one JTSetup setup per Newton iteration can be amortized between multiple JTimes calls.
    • Two new NVECTOR modules added: for CUDA and RAJA support for GPU systems.  These vectors are supplied to provide very basic support for running on GPU architectures.  Users are advised that these vectors both move all data to the GPU device upon construction, and speedup will only be realized if the user also conducts the right-hand-side function evaluation on the device. In addition, these vectors assume the problem fits on one GPU. For further information about RAJA, users are referred to the web site,
    • Addition of sunindextype option for 32- or 64-bit integer data index types within all SUNDIALS structures.
      • Sunindextype can be int64_t or int32_t or long long int and int depending on machine support for portable types.
      • The Fortran interfaces continue to use long_int for indices, except for their sparse matrix interface that now uses the new sunindextype.
      • Includes interfaces to PETSc, hypre, SuperLU_MT, and KLU with either 64-bit or 32-bit capabilities depending how the user configures SUNDIALS.
    • Temporary vectors were removed from preconditioner setup and solve routines for all packages.  It is assumed that all necessary data for user-provided preconditioner operations will be allocated and stored in user-provided data structures.
    • The file include/sundials_fconfig.h was added.  This file contains SUNDIALS type information for use in Fortran programs. 
    • Added support for many xSDK-compliant build system keys.
      • The xSDK is a movement in scientific software to provide a foundation for the rapid and efficient production of high-quality, sustainable extreme-scale scientific applications. 
      • More information can be found at
    • Added functions SUNDIALSGetVersion and SUNDIALSGetVersionNumber to
      get SUNDIALS release version information at runtime.

    • To avoid potential namespace conflicts, the macros defining booleantype values TRUE and FALSE have been changed to SUNTRUE and SUNFALSE respectively.

    • In build system:
      • Added separate BLAS_ENABLE and BLAS_LIBRARIES CMake variables.
      • Additional error checking during CMake configuration.
      • Fixed minor CMake bugs.
      • Renamed CMake options to enable/disable examples for greater clarity and added option to enable/disable Fortran 77 examples:
        • Changed F90_ENABLE to EXAMPLES_ENABLE_F90.
        • Added EXAMPLES_ENABLE_F77 option.
    • Corrections and additions to all User Guides.


  • Bug fixes
    • Added missing prototype for IDASetMaxBacksIC in ida.h.

What’s new in v2.9.0?

  • New features and/or enhancements
    • Two new NVECTOR modules added: for Hypre ParVector and PETSc.
    • In vector API, added new required function, N_VGetVectorID.
    • Upgrades to sparse solver interfaces; now support CSR matrix type with KLU solver.
    • Example codes were changed from using NV_DATA macro to using N_VGetArrayPointer_* when using the native vectors shipped with SUNDIALS.
    • Updated to return integers from linear solver and preconditioner ‘free’ functions.
    • In FIDA, added missing Fortran interface routines so that users can supply the sparse Jacobian routine.
    • Minor corrections and additions to User Guide, including removal of references to specific NVECTOR names in usage skeletons.
    • Added idaFoodWeb_kry.c, idaFoodWeb_bnd_omp.c, and idaFoodWeb_kry_omp.c examples using OpenMP.
    • Added optional input function IDASetMaxBacksIC to limit number of linesearch backtrack operations in IDACalcIC.  User guides amended accordingly.
  • Bug fixes
    • Fixed memory leak in banded preconditioner interface.
    • Fixed some examples w.r.t. switch to new macro/function names SUNRexp etc.
    • Various minor fixes to installation-related files.
    • Corrected name N_VCloneEmptyVectorArray to N_VCloneVectorArrayEmpty in all documentation files.
    • Corrected example idaFoodWeb_bnd.c in PrintOutput (wrong component printed).

What’s new in v2.8.0?

  • New features
    • Added interface to the sparse direct solver KLU.
    • Added interface to SuperLU_MT.
  • Bug fixes
    • Fixed minor bug in IDARootfind involving rootdir input.
    • Fixed line setting smu in IDALapackBand.
  • Changes to the FIDA module
    • In optional input routines FIDASETIIN, FIDASETRIN, and FIDASETVIN, removed the optional fourth argument key_length.
    • Revised integer declarations in all examples so that those which must match a C type long int are declared INTEGER*8.
  • Changes related to the build system
    • Dropped support and documentation of the Autotools mode of installation.

What’s new in v2.7.0?

  • Bug fixes
    • linear solver memory set to zero after being created.
    • linear solver memory is freed on an error return.
    • memory leak fixed in two IDASp***Free functions.
  • Changes to user interface
    • Problem size and related integers (bandwidth parameters etc.) all have type long int, except for those in user calls specifying BLAS/LAPACK routines.
    • added IDAGetDky for optional output retrieval.

What’s new in v2.6.0?

  • New features
    • new linear solver module, based on Blas and Lapack for both dense and banded matrices.
    • option to specify which direction of zero-crossing is to be monitored while performing rootfinding.
  • Changes to user interface
    • reorganization of all linear solver modules into two families (besides the existing family of scaled preconditioned iterative linear solvers, the direct solvers, including the new Lapack-based ones, were also organized into a direct family).
    • maintaining a single pointer to user data, optionally specified through a Set-type function.
    • general streamlining of the preconditioner modules distributed with the solver.

What’s new in v2.5.0?

  • Bug fixes
    • fixed bug in final stopping times to resolve potential conflicts when tout is close to tstop.
    • fixed bug in he internal difference-quotient dense and banded Jacobian approximations, related to the estimation of the perturbation (which could have lead to a failure of the linear solver when zero components with sufficiently small absolute tolerances were present).
  • Changes to user interface
    • the user interface to the consistent initial conditions calculations has been modified. The IDACalcIC arguments t0, yy0, and yp0 were removed and a new function, IDAGetconsistentIC is now provided.
  • Changes related to the build system
    • rearranged the entire SUNDIALS source tree.
    • all exported header files are now installed in separate subdirectories of the installtion include directory.
    • header files are included now by specifying the relative path (e.g. #include <cvode/cvode.h>).

What’s new in v2.4.0?

  • New features
    • added IDASPBCG interface module to allow IDA to interface with the shared SPBCG (scaled preconditioned Bi-CGSTAB) linear solver module.
    • added IDASPTFQMR interface module to allow IDA to interface with the shared SPTFQMR (scaled preconditioned TFQMR) linear solver module.
    • added FIDA (Fortran interface to IDA).
    • added support for SPBCG and SPTFQMR to the IDABBDPRE preconditioner module.
    • added rootfinding feature in IDA.
    • added support for interpreting failures in user-supplied functions.
  • Changes to user interface
    • changed argument of IDAFree and IDABBDPrecFree to be the address of the respective memory block pointer, so that its NULL value is propagated back to the calling function.
    • added IDASPBCG module which defines appropriate IDSpbcg* functions to allow IDA to interface with the shared SPBCG linear solver module.
    • added IDABBDSpbcg function to IDABBDPRE module to support SPBCG linear solver module.
    • changed function type names to accomodate all the Scaled Preconditioned Iterative Linear Solvers now available:
      IDASpgmrJactimesVecFn -> IDASpilsJacTimesVecFn
      IDASpgmrPrecSetupFn -> IDASpilsPrecSetupFn
      IDASpgmrPrecSolveFn -> IDASpilsPrecSolveFn
    • changed some names for IDABBDPRE function outputs.
    • added option for user-supplied error handler function.
    • added IDAGetEstLocalErrors() to return estimated local errors.
    • renamed all exported header files (except for ida.h, all header files have the prefix ida_).
    • changed naming scheme for IDA examples.
  • Changes related to the build system
    • the main IDA header file (ida.h) is still exported to the install include directory. However, all other IDA header files are exported into an ida subdirectory of the install include directory.
    • the IDA library now contains all shared object files (there is no separate libsundials_shared library any more).

What’s new in v2.3.0?

  • New features
    • added option for user-provided error weight computation function (of type IDAEwtFn specified through IDASetEwtFn).
  • Changes to user interface
    • IDA now stores tolerances through values rather than references (to resolve potential scoping issues).
    • IDA now stores the constraints and id vectors (if defined) through values ratherthan references.
    • IDA now passes information back to the user through values rather than references (error weights).
    • IDAMalloc, IDAReInit, IDASetTolerances: added option itol=IDA_WF to indicate user-supplied function for computing the error weights; reltol is now declared as realtype. Note that it is now illegal to call IDASetTolerances before IDAMalloc. It is now legal to deallocate the absolute tolerance N_Vector right after its use.
    • IDAGetErrorWeights: the user is now responsible for allocating space for the N_Vector in which error weights will be copied.
    • IDACalcIC takes as additional arguments (t0,y0,yp0). As a consequence, it can be called at any time to correct a pair (y,y’).
    • Passing a value of 0 for the maximum step size or for maxsteps results in the solver using the corresponding default value (infinity, and 500, respectively).
    • Several optional input functions were combined into a single one (IDADenseSetJacFn and IDADenseSetJacData, IDABandSetJacFn and IDABandSetJacData, IDASpgmrSetPrecSolveFn and IDASpgmrSetPrecSetFn and IDASpgmrSetPrecData, IDASpgmrSetJacTimesVecFn and IDASpgmrSetJacData).

What’s new in v2.2.2?

  • Changes to documentation
    • added section with numerical values of all input and output solver constants.
    • added more detailed notes on the type of absolute tolerances.
    • fixed several typos and removed reference to inexistent function IDASetMinStep.
  • Changes related to the build system
    • fixed autoconf-related bug to allow configuration with the PGI Fortran compiler.
    • modified to use customized detection of the Fortran name mangling scheme (autoconf’s AC_F77_WRAPPERS routine is problematic on some platforms).
    • added –with-mpi-flags as a configure option to allow user to specify MPI-specific flags.

What’s new in v2.2.1?

  • Changes related to the build system
    • changed order of compiler directives in header files to avoid compilation errors when using a C++ compiler.
    • changed method of generating sundials_config.h to avoid potential warnings of redefinition of preprocessor symbols.
  • Changes to documentation
    • fixed various mistakes and typos in the user guide and example programs documents.

What’s new in v2.2.0?

  • New feature
    • added option to disable all error messages.
  • Bug fixes
    • in the solution of the nonlinear system, the correction for small constraint violation is to ee, not y.
    • besides delaying the order increase until the 2nd step, we now also delay doubling the step size, to avoid using information from times before t0.
  • Changes related to the NVECTOR module
    • removed machEnv, redefined table of vector operations (now contained in the N_Vector structure itself).
    • all IDA functions create new N_Vector variables through cloning, using an N_Vector passed by the user as a template.
  • Changes to type names and IDA constants
    • removed type ‘integertype’; instead use int or long int, as appropriate.
    • restructured the list of return values from the various IDA functions.
    • changed all IDA constants (inputs and return values) to have the prefix ‘IDA_’ (e.g. IDA_SUCCESS).
    • renamed various function types to have the prefix ‘IDA’ (e.g. IDAResFn).
  • Changes to optional input/ouput
    • added IDASet* and IDAGet* functions for optional inputs/outputs, replacing the arrays iopt and ropt.
    • added new optional inputs (e.g. maximum number of Newton iterations, maximum number of convergence failures, etc).
    • added new function IDAGetSolution for dense output.
    • the value of the last return flag from any function within a linear solver module can be obtained as an optional output (e.g. IDADenseGetLastFlag).
  • Changes to user-callable functions
    • added new function IDACreate which initializes the IDA solver object and returns a pointer to the IDA memory block.
    • removed N (problem size) from all functions except the initialization functions for the direct linear solvers (IDADense and IDABand).
    • shortened argument lists of most IDA functions (the arguments that were dropped can now be specified through IDASet* functions).
    • removed reinitialization functions for band/dense/SPGMR linear solvers (same functionality can be obtained using IDA*Set* functions).
    • in IDABBDPRE, added a new function, IDABBDSpgmr to initialize the SPGMR linear solver with the BBD preconditioner.
    • function names changed in IDABBDPRE for uniformity.
  • Changes to user-supplied functions
    • removed N (probem dimension) from argument lists.
    • shortened argument lists for user dense/band/SPGMR Jacobian routines.
    • in IDASPGMR, shortened argument lists for user preconditioner functions.
    • in IDABBDPRE, added Nlocal, the local vector size, as an argument to IDABBDLocalFn and IDABBDCommFn.