SUNDIALS: SUite of Nonlinear and DIfferential/ALgebraic Equation Solvers

KINSOL is a solver for nonlinear algebraic systems. It includes a Newton-Krylov solver as well as Picard and fixed point solvers, both of which can be accelerated with Anderson acceleration. KINSOL is based on the previous Fortran package NKSOL of Brown and Saad.

KINSOL’s Newton solver employs the Inexact Newton method. As this solver is intended mainly for large systems, four iterative methods are provided to solve the resulting linear systems–GMRES, Bi-CGStab, TFQMR, and FGMRES. These are Krylov methods, implemented with scaling and preconditioning, and can be used with all versions of the NVECTOR module.

For the sake of convenience to users with smaller systems, KINSOL (used with the serial NVECTOR module) also includes direct (dense, banded, and sparse) linear solvers for the linear systems. In this case the nonlinear iteration is a Modified Newton method.

In addition, KINSOL (used with the serial NVECTOR module) also includes interfaces to the sparse direct solvers, KLU, and the the multi-threaded sparse solver, SuperLU_MT.

In addition to the basic Krylov method modules, the KINSOL package includes a module called KINBBDPRE, which provides a band-block-diagonal preconditioner for the native MPI parallel vector.

For use with Fortran applications, a set of Fortran/C interface routines, called FKINSOL, 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.


kinsol release history

What’s New in v.4.0.0-dev.1

No changes were made in this package for this development release.

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 KINSOL:
    • Fixed a minor bug in KINPrintInfo where a case was missing for KIN_REPTD_SYSFUNC_ERR leading to an undefined info message.

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
    • Corrected KINSOL fcmix name translation for FKIN_SPFGMR.

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.
    • Added FKINCREATE and FKININIT routines to split FKINMALLOC routine into two pieces.  FKINMALLOC remains for backward compatibility, but documentation for it has been removed.
    • Added kinFoodWeb_kry_omp.c OpenMP example.
  • 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.
    • In FKINSOL, 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.
    • Minor bug fix in Picard iteration so that newest iterate is returned.
    • Minor bug fix in line search to prevent infinite loop when beta condition fails and lambda is below minimum size.

What’s new in v2.8.0?

  • New features
    • Added fixed-point iteration and Picard iteration as globalization strategy options, both with Anderson acceleration.
    • Added interface to the sparse direct solver KLU.
    • Added interface to SuperLU_MT.
    • Added interface to FGMRES.
  • Bug fixes
    • Corrected two return values in function KINStop.
    • Fixed line setting smu in KINLapackBand.
    • Fixed bug involving initialization of mxnewtstep.
    • Fixed bug in difference quotient increments in kinDlsBandDQJac.
    • Fixed an incorrect return value ier in FKINSOL function FKINfunc.
  • Changes to the FKINSOL module
    • In optional input routines FKINSETIIN, FKINSETRIN, and FKINSETVIN, 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
    • Three major logic bugs were fixed – involving updating the solution vector, updating the linesearch parameter, and a missing error return.
    • Three minor errors were fixed – involving setting etachoice in the Matlab/KINSOL interface, a missing error case in KINPrintInfo, and avoiding an exponential overflow in the evaluation of omega.
    • linear solver memory set to zero after being created.
    • linear solver memory is freed on an error return.
  • 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.

What’s new in v2.6.0?

  • New features
    • new linear solver module, based on Blas and Lapack for both dense and banded matrices.
  • 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 band-block-diagonal preconditioner module distributed with the solver.

What’s new in v2.5.0?

  • 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 <kinsol/kinsol.h>).

What’s new in v2.4.0?

  • New features
    • added direct linear solvers (dense and band, provided through the KINDENSE and KINBAND modules, respectively) thus adding modified (and exact) Newton methods to KINSOL.
    • added KINSPBCG interface module to allow KINSOL to interface with the shared SPBCG (scaled preconditioned Bi-CGSTAB) linear solver module.
    • added KINSPTFQMR interface module to allow KINSOL to interface with the shared SPTFQMR (scaled preconditioned TFQMR) linear solver module.
    • added support for SPBCG and SPTFQMR to the KINBBDPRE preconditioner module.
    • added option to KINBBDPRE preconditioner module to allow specification of different half-bandwidths for difference quotient approximation and retained matrix.
    • added support for interpreting failures in user-supplied functions.
  • Bug fixes
    • corrected a bug in the preconditioner logic that caused the initial call to the preconditioner setup routine (controlled by KINSetNoInitSetup) to be skipped during subsequent calls to KINSol.
  • Changes to underlying algorithm
    • modified the KINBBDPRE preconditioner module to allow the use of different half-bandwidths for the difference quotient approximation and the retained matrix.
    • added nonlinear residual monitoring scheme to control Jacobian updating when a direct linear solver is used (modified Newton iteration).
  • Changes to user interface
    • changed argument of KINFree and KINBBDPrecFree to be the address of the respective memory block pointer, so that its NULL value is propagated back to the calling function.
    • modified the argument list of KINBBDPrecAlloc to allow specification of the upper and lower half-bandwidths to be used in the computation of the local Jacobian blocks (mudq, mldq), and the half-bandwidths of the retained banded approximation to the local Jacobian block (mukeep, mlkeep).
    • added KINSPBCG module which defines appropriate KINSpbcg* functions to allow KINSOL to interface with the shared SPBCG linear solver module.
    • added KINBBDSpbcg function to KINBBDPRE module to support SPBCG linear solver module.
    • changed function type names to accomodate all the Scaled Preconditioned Iterative Linear Solvers now available:
      KINSpgmrJactimesVecFn -> KINSpilsJacTimesVecFn
      KINSpgmrPrecSetupFn -> KINSpilsPrecSetupFn
      KINSpgmrPrecSolveFn -> KINSpilsPrecSolveFn
    • changed function types so that all user-supplied functions return an integer flag.
    • changed some names for KINBBDPRE function outputs.
    • added option for user-supplied error handler function.
    • added option for user-supplied info handler function.
    • renamed all exported header files (except for kinsol.h, all header files have the prefix kinsol_).
    • changed naming scheme for KINSOL examples.
  • Changes to FKINSOL module:
    • modified argument list of FKINBBDINIT to accomadate changes made to KINBBDPRE module, so now user must specify the upper and lower half-bandwidths for the difference quotient approximation (mudq, mldq) and the retained matrix (mukeep, mlkeep).
    • added support for KINSPBCG/SPBCG (added FKIN*SPBCG* functions).
    • added support for KINSPTFQMR/SPTFQMR (added FKIN*SPTFQMR* functions).
    • added support for KINDENSE/DENSE (added FKIN*DENSE* functions).
    • added support for KINBAND/BAND (added FKIN*DENSE* functions).
    • Optional inputs are now set using routines FKINSETIIN (integer inputs), FKINSETRIN (real inputs), and FKINSETVIN (vector inputs) through pairs key-value. Optional outputs are still obtained from two arrays (IOUT and ROUT), owned by the user and passed as arguments to FKINMALLOC.
  • Changes related to the build system
    • updated configure script and Makefiles for Fortran examples to avoid C++ compiler errors (now use CC and MPICC to link only if necessary).
    • the main KINSOL header file (kinsol.h) is still exported to the install include directory. However, all other KINSOL header files are exported into a kinsol subdirectory of the install include directory.
    • the KINSOL library now contains all shared object files (there is no separate libsundials_shared library any more).

What’s new in v2.3.0?

  • Changes to user interface
    • KINSOL now stores an actual copy of the constraints vector rather than just a pointer in order to resolve potential scoping issues.
    • several optional input functions were combined into a single function:
      - KINSpgmrSetPrecSetupFn, KINSpgmrSetPrecSolveFn and KINSpgmrSetPrecData were combined into KINSpgmrSetPreconditioner
      - KINSpgmrSetJacTimesVecFn and KINSpgmrSetJacData were combined into KINSpgmrSetJacTimesVecFn
  • Changes to FKINSOL module:
    • due to changes to the main solver, if FKPSOL is provided, then FKPSET must also be defined, even if it is empty.

What’s new in v2.2.2?

  • Bug fixes
    • fixed bug in computation of the scaled step length.
    • fixed bug in logic for disabling the call to the preconditioner setup function at the first iteration.
  • Changes to documentation
    • added section with numerical values of all input and output solver constants.
  • 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.
    • updated Makefiles for Fortran examples to avoid C++ compiler errors (now use CC and MPICC to link).

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.

What’s new in v2.2.0?

  • New feature
    • added option to disable all error messages.
  • Bug fixes
    • fixed constraints-related bug.
    • fixed bug in implementation of line-search method related to beta-condition.
    • corrected value of ealpha variable (related to forcing term).
  • Changes related to NVECTOR module
    • removed machEnv, redefined table of vector operations (now contained in the N_Vector structure itself).
    • all KINSOL functions create new N_Vector variables through cloning, using an N_Vector passed by the user as a template.
  • Changes to type names and KINSOL constants
    • removed type ‘integertype’; instead use ‘int’ or ‘long int’, as appropriate.
    • restructured the list of return values from the various KINSOL functions.
    • changed all KINSOL constants (inputs and return values) to have the prefix ‘KIN_’ (e.g. KIN_SUCCESS).
    • renamed function type ‘SysFn’ to ‘KINSysFn’.
  • Changes to underlying algorithms
    • modified line-search backtracking scheme to use cubic interpolation after the first backtrack, if possible.
    • changed implementation of constraints:
      constraints[i] = 0 then u[i] NOT constrained
      constraints[i] = +1 then u[i] >= 0
      constraints[i] = -1 then u[i] <= 0
      constraints[i] = +2 then u[i] > 0
      constraints[i] = -2 then u[i] < 0
      where u is the solution vector (see the KINSOL User Guide [1] for additional details).
  • Changes to optional input/output
    • added KINSet* and KINGet* functions for optional inputs/outputs, replacing the arrays iopt and ropt.
    • added new optional inputs (e.g. maximum number of nonlinear iterations between calls to preconditioner setup routine, etc.).
    • the value of the last return flag from any function within the SPGMR linear solver module can be obtained as an optional output using KINSpgmrGetLastFlag.
  • Changes to user-callable functions
    • added new function KINCreate which initializes the KINSOL solver object and returns a pointer to the KINSOL memory block.
    • removed N (problem size) from all functions.
    • shortened argument lists of most KINSOL functions (the arguments that were dropped can now be specified through KINSet* functions).
    • removed reinitialization functions for SPGMR linear solver (same functionality can be obtained using KINSpgmrSet* functions).
  • Changes to user-supplied functions
    • removed N (problem dimension) from argument lists.
    • in KINSPGMR, shortened argument lists for user preconditioner functions.