                           CVODES 
                 Release 2.8.1, March 30, 2015
               Alan C. Hindmarsh and Radu Serban
          Center for Applied Scientific Computing, LLNL

CVODES is a solver for stiff and nonstiff ODE systems (initial value 
problem) given in explicit form y' = f(t,y,p) with sensitivity analysis 
capabilities (both forward and adjoint modes). 
It is written in ANSI standard C.

CVODES can be used both on serial and parallel computers.  The 
main difference is in the NVECTOR module of vector kernels.  The desired 
version is obtained when compiling the example files by linking the 
appropriate library of NVECTOR kernels.  In the parallel versions,
communication between processors is done with MPI, with OpenMP, or with Pthreads.

When used with the serial NVECTOR module, CVODES provides both direct (dense 
and band) and preconditioned Krylov (iterative) linear solvers. Three different
iterative solvers are available: scaled preconditioned GMRES (SPGMR), scaled 
preconditioned BiCGStab (SPBCG), and scaled preconditioned TFQMR (SPTFQMR). 
When CVODES is used with the parallel NVECTOR module, only the Krylov linear solvers 
are available. (An approximate diagonal Jacobian option is available with both 
versions.)  For the serial version, there is a banded preconditioner module 
called CVBANDPRE available for use with the Krylov solvers, while for the parallel 
version there is a preconditioner module called CVBBDPRE which provides a
band-block-diagonal preconditioner.

CVODES is part of a software family called SUNDIALS: SUite of Nonlinear and 
DIfferential/ALgebraic equation Solvers [4].  This suite consists of CVODE, 
CVODES, ARKode, IDA, IDAS, and KINSOL.  The directory structure of the 
package supplied reflects this family relationship.

The notes below provide the location of documentation, directions for the 
installation of the CVODES package, and relevant references. Following that 
is a brief history of revisions to the package.


A. Documentation
----------------

/sundials/doc/cvodes/ contains PDF files for the CVODES User Guide [1] (cvs_guide.pdf)
and the CVODES Examples [2] (cvs_examples.pdf) documents.


B. Installation
---------------

For basic installation instructions see the file /sundials/INSTALL_GUIDE.pdf. 
For complete installation instructions see the "Installation Procedure"
chapter in the CVODES User Guide.


C. References
-------------

[1] A. C. Hindmarsh and R. Serban, "User Documentation for CVODES v2.8.0," 
    LLNL technical report UCRL-SM-208111, ??? 2014.

[2] A. C. Hindmarsh and R. Serban, "Example Programs for CVODES v2.8.0," 
    LLNL technical report UCRL-SM-208115, ??? 2014.

[3] R. Serban and A. C. Hindmarsh, "CVODES: the Sensitivity-Enabled ODE 
    solver in SUNDIALS," Proceedings of IDETC/CIE 2005, Sept. 2005, 
    Long Beach, CA.

[4] A. C. Hindmarsh, P. N. Brown, K. E. Grant, S. L. Lee, R. Serban, 
    D. E. Shumaker, and C. S. Woodward, "SUNDIALS, Suite of Nonlinear and 
    Differential/Algebraic Equation Solvers," ACM Trans. Math. Softw., 
    31(3), pp. 363-396, 2005.


D. Releases
-----------

v. 2.8.1   - Mar. 2015
v. 2.8.0   - Mar. 2015
v. 2.7.0   - Mar. 2012
v. 2.6.0   - May  2009
v. 2.5.0   - Nov. 2006
v. 2.4.0   - Mar. 2006
v. 2.3.0   - May. 2005
v. 2.2.0   - Apr. 2005
v. 2.1.2   - Mar. 2005
v. 2.1.1   - Jan. 2005
v. 2.1.0   - Dec. 2004
v. 1.0     - Jul. 2002 (first SUNDIALS release)


E. Revision History
-------------------


v. 2.8.0 (Mar. 2015) ---> v. 2.8.1 (Mar. 2015)
---------------------------------------------
- Bug fixes
  - Fixed loop limit bug in SlsAddMat function.
  - In interfaces to KLU and SuperLUMT, added #include lines, 
    and removed redundant KLU structure allocations.
  - Minor documentation updates

v. 2.7.0 (Mar. 2012) ---> v. 2.8.0 (Mar. 2015)
---------------------------------------------

- New features
   - Two major additions were made to the linear system solvers that are
     availble for use with the CVODE solver.  If using the supplied serial
     NVECTOR module, interfaces to the KLU sparse direct solver and to the
     SuperLU_MT solver (the multi-threaded version of SuperLU) were added.
     As part of these additions, a sparse matrix (CSC format) structure 
     was added to CVODES.
   - Two new NVECTOR modules have been added for parallel computing
     environments --- one for openMP, denoted NVECTOR_OPENMP,
     and one for Pthreads, denoted NVECTOR_PTHREADS.
   - An option was added in the case of Adjoint Sensitivity Analysis with
     dense or banded Jacobian:  With a call to CVDlsSetDenseJacFnBS or
     CVDlsSetBandJacFnBS, the user can specify a user-supplied Jacobian
     function of type CVDls***JacFnBS, for the case where the backward
     problem depends on the forward sensitivities.
   - For the Adjoint Sensitivity Analysis case in which the backward problem
     depends on the forward sensitivities, options have been added to allow
     for user-supplied pset, psolve, and jtimes functions.

- Bug fixes
   - In cvRootfind, a minor bug was corrected, where the input
     array rootdir was ignored, and a line was added to break out of
     root-search loop if the initial interval size is below the tolerance
     ttol.
   - In CVLapackBand, the line smu = MIN(N-1,mu+ml) was changed to
     smu = mu + ml to correct an illegal input error for DGBTRF/DGBTRS.
   - In CVodeQuadSensInit, the line cv_mem->cv_fQS_data = ...
     was corrected (missing Q).
   - Two minor bugs were fixed regarding the testing of input on the first
     call to CVode -- one involving tstop and one involving the
     initialization of *tret.
   - The initialization nefQS = 0 was added.

- Changes to user interface
   - In the User Guide, a paragraph was added in Section 6.2.1 on
     CVodeAdjReInit, and a paragraph was added in Section 6.2.9 on
     CVodeGetAdjY.

- Other
   - In order to avoid possible name conflicts, the mathematical macro and
     function names MIN, MAX, SQR, RAbs, RSqrt, RExp, RPowerI, and RPowerR
     were changed to SUNMIN, SUNMAX, SUNSQR, SUNRabs, SUNRsqrt, SUNRexp,
     SRpowerI, and SUNRpowerR, respectively.  These names occur in both the
     solver and in various example programs.

v. 2.6.0 (May 2009) ---> v. 2.7.0 (Mar. 2012)
---------------------------------------------

- Bug fixes
   - errors in the logic for the integration of backward problems were
     identified and fixed.
   - in CVSetTqBDF, the logic was changed to avoid a divide by zero.
   - after the solver memory is created, it is set to zero before being filled.
   - in each linear solver interface function, the linear solver memory is
     freed on an error return, and the **Free function now includes a
     line setting to NULL the main memory pointer to the linear solver memory.
   - in rootfinding functions cvRcheck1/cvRcheck2, when an exact zero is found,
     the array glo at the left endpoint is adjusted instead of shifting tlo.

- Changes to user interface
   - One significant design change was made with this release: The problem
     size and its relatives, bandwidth parameters, related internal indices,
     pivot arrays, and the optional output lsflag have all been
     changed from type int to type long int, except for the
     problem size and bandwidths in user calls to routines specifying
     BLAS/LAPACK routines for the dense/band linear solvers.  The function
     NewIntArray is replaced by a pair NewIntArray/NewLintArray,
     for int and long int arrays, respectively.
   - in a minor change to the user interface, the type of the index
     which in CVODES was changed from long int to int.
   - in the installation files, we modified the treatment of the macro
     SUNDIALS_USE_GENERIC_MATH, so that the parameter GENERIC_MATH_LIB is
     either defined (with no value) or not defined.

v. 2.5.0 (Nov. 2006) ---> v. 2.6.0 (May 2009)
---------------------------------------------

- New features
   - added a new linear solver module based on Blas + Lapack for
     both dense and banded matrices.
   - added optional input to specify which direction of zero-crossing
     is to be monitored while performing root-finding. The root information
     array iroots (returned by CVodeGetRootInfo) also encodes the 
     direction of zero-crossing.
   - added support for performing FSA of quadrature variables (see functions
     CVode**QuadSens**).
   - in the adjoint module, added support for integrating forward sensitivities
     of states and quadrature variables during the forward integration
     phase (e.g. for computing 2nd order sensitivity information using
     the "forward over adjoint" method).
   - in the adjoint module, added support for propagating backwards in time
     multiple adjoint systems, each initialized at posibly different times.
   - added option for reinitializing the adjoint module in order to
     solve a new adjoint problem (with same number of steps between
     check points and the same interpolation type).

- Bug fixes
   - in the rootfinding algorithm, fixed a bug resulting in unnecessary
     evaluations of the root functions after reinitialization of the
     solver right after a return at a root.
   - in the initial step size calculation, restrict h based on tstop.
   - modified the setting and use of the tq[] array.  Now tq[i] (i = 1,2,3)
     are defined to be the reciprocals of what they were before.  This
     eliminates a rare crash that can occur with xistar_inv = 0.

- Changes to user interface
   - renamed all **Malloc functions to **Init
   - tolerances are now specified through separate functions instead of
     the initialization functions CVodeInit (former CVodeMalloc) and 
     CVodeReInit. Depending on the tolerance type, one of 3 functions
     must be called before the first call to CVode.
   - tolerances for quadratures, sensitivities, and quadrature sensitivities
     are specified in a manner similar to that for state variables, with the
     exception that toelrances for quadratures and quadrature sensitivities
     are required only if the corresponding variables are included in the
     error test.
   - removed function inputs from argument lists of all re-initialization
     functions.
   - all user-supplied functions now receive the same pointer to user data
     (instead of having different ones for the system evaluation, Jacobian
     information functions, etc.)
   - removed CV_NORMAL_TSTOP and CV_ONE_STEP_TSTOP named constants for the
     itask argument to CVode/CVodeF. A tstop value is now both set and activated
     through CVodeSetStopTime. Once tstop is reached it is also deactivated.
     A new value can be then specified by calling again CVodeSetStopTime.
   - common functionality for all direct linear solvers (dense, band, and
     the new Lapack solver) has been collected into the DLS (Direct Linear
     Solver) module, similar to the SPILS module for the iterative linear 
     solvers. All optional input and output functions for these linear 
     solver now have the prefix 'CVDls'. In addition, in order to include
     the new Lapack-based linear solver, all dimensions for these linear
     solvers (problem sizes, bandwidths, etc) are now of type 'int' 
     (instead of 'long int').
   - the initialization functions for the two preconditioner modules,
     CVBANDPRE and CVBBDPRE were renamed ***Init (from ***Alloc) and they
     do not return a pointer to preconditioner memory anymore. Instead,
     all preconditioner module-related functions are now called with
     the main solver memory pointer as their first argument. When using
     one of these two modules, there is no need to use special functions
     to attach one of the SPILS linear solvers (instead use one of
     CVSpgmr, CVSpbcg, or CVSptfqmr). Moreover, there is no need to call
     a memory deallocation function for the preconditioner module.
   - CVodeSensMalloc was replaced by CVodeSensInit and CvodeSensInit1. 
     The sensitivity RHS function is now passed as an argument to these
     initialization functions. The former takes as argument fS a function
     of type CVSensRhsFn, while the latter takes as argument fS1 of type
     CVSensRhs1Fn. Removed the functions CVodeSetSensRhsFn and CVodeSetSensRhs1Fn.
   - changed the API for all functions in the adjoint module related to 
     initialization, set-up, and solution of backward problems. A backward problem
     is always identified by its index (of type int) returned by the CvodeCreateB
     function.
   - the extraction functions CVodeGetQuad, CVodeGetSens, and CVodeGetSens1
     now return the values of quadrature and sensitivity variables, respectively,
     at the same time as that at which CVode returned the solution (for dense
     output of quadrature or sensitivity variables, the user can only use
     CVodeGetQuadDky, CVodeGetSensDky, or CVodeGetSensDky1). Similar functions are
     available for the new quadrature sensitivity feature.
   - changed names CVSpilsSetDelt and delt to CVSpilsSetEpsLin and eplifac.
   - added the error return CV_RTFUNC_FAIL.

v. 2.4.0 (Mar. 2006) ---> v. 2.5.0 (Nov. 2006)
----------------------------------------------

- Bug fixes
   - fixed wrong logic in final stopping tests: now we check if
     tout was reached before checking if tstop was reached.
   - added a roundoff factor when testing whether tn was just returned
     (in root finding) to prevent an unnecessary return.
  - fixed bug in CVodeB in searching for the current check point
     (i.e. the check point for which interpolation data is available)
   - fixed bug in CVodeF to ensure that in NORMAL mode no extra
     step is taken (which sometimes resulted in an error from the 
     interpolated output function).
   - changed address variable type in CVadjCheckPointRec structure from
     'unsigned int' to 'void *' to avoid address truncation/mangling on
     64-bit platforms (see CVS_P1).

- Changes related to the build system
   - reorganized source tree: header files in ${srcdir}/include/cvodes,
     source files in ${srcdir}/src/cvodes,examples in ${srcdir}/examples/cvodes
   - exported header files are installed unde ${includedir}/cvodes

- Changes to user interface
   - all included header files use relative paths from ${includedir}
   - changed the API for specifying the DQ method used to approximate 
     the sensitivity equations: renamed CVodeSetSensRho to CVodeSetSensDQMethod.
     The user passes two values: DQtype (CV_CENTERED or CV_FORWARD) and
     DQrhomax (the cut-off value for switching between simultaneous and
     separate approximations of the two terms in the sensi. eqs.)

v. 2.3.0 (May. 2005) ---> v. 2.4.0 (Mar. 2006)
----------------------------------------------

- New features
   - added CVSPBCG interface module to allow CVODES to interface with the
     shared SPBCG (scaled preconditioned Bi-CGSTAB) linear solver module.
   - added CVSPTFQMR interface module to allow CVODES to interface with
     the shared SPTFQMR (scaled preconditioned TFQMR) linear solver module.
   - added support for SPBCG and SPTFQMR to the CVBBDPRE and CVBANDPRE 
     preconditioner modules.
   - added support for interpreting failures in user-supplied functions.
   - added a new variable-degree polynomial interpolation method as an
     an alternative to the current cubic Hermite interpolation for the
     adjoint module.

- Changes to user interface
   - changed argument of CVodeFree, CVBandPrecFree, CVBBDPrecFree, and 
     CVadjFree to be the address of the respective memory block pointer, 
     so that its NULL value is propagated back to the calling function.
   - added CVSPBCG module which defines appropriate CVSpbcg* functions to
     allow CVODES to interface with the shared SPBCG linear solver module.
   - added CVBBDSpbcg function to CVBBDPRE module and CVBPSpbcg function to
     CVBANDPRE module to support SPBCG linear solver module.
   - added CVBBDSptfqmr function to CVBBDPRE module and CVBPSptfqmr function to
     CVBANDPRE module to support SPTFQMR linear solver module.
   - changed function type names (not the actual definition) to accomodate
     all the Scaled Preconditioned Iterative Linear Solvers now available:
       CVSpgmrJactimesVecFn -> CVSpilsJacTimesVecFn
       CVSpgmrPrecSetupFn   -> CVSpilsPrecSetupFn
       CVSpgmrPrecSolveFn   -> CVSpilsPrecSolveFn 
   - changed function types so that all user-supplied functions return
     an integer flag (not all of them currently used).
   - changed some names for CVBBDPRE and CVBANDPRE function outputs
   - added option for user-supplied error handler function.
   - added a argument to CVadjMalloc to specify the type of interpolation 
     (possible values are CV_HERMITE for cubic Hermite and CV_POLYNOMIAL
     for variable-order polynomial interpolation)
   - renamed all exported header files (except for cvodes.h and cvodea.h all 
     header files have the prefix 'cvodes_')
   - changed naming scheme for CVODES examples

- Changes related to the build system
   - the main CVODES header files (cvodes.h and cvodea.h) are still exported to 
     the install include directory. However, all other CVODES header files are 
     exported into a 'cvodes' subdirectory of the install include directory.
   - the CVODES library now contains all shared object files (there is no separate
     libsundials_shared library anymore)

v. 2.2.0 (Apr. 2005) ---> v. 2.3.0 (May. 2005)
----------------------------------------------

- Bug fixes
   - in the adjoint module, fixed bug in storing interpolation data at
     a point corresponding to a check point (improperly scaled y').

- Changes to user interface
   - removed CVadjGetcheckPointsList from the list of user-callable functions.

v. 2.1.2 (Mar. 2005) ---> v. 2.2.0 (Apr. 2005)
----------------------------------------------

- New features
   - added option for user-provided error weight computation function for
     the solution vector (of type CVEwtFn specified through CVodeSetEwtFn).

- Changes to user interface
   - CVODES now stores tolerances through values rather than references 
     (to resolve potential scoping issues). 
   - CVODES now passes information back to the user through values rather
     than references (error weights, estimated local errors, root info,
     STAGGERED1 statistics, etc.)
   - CVodeMalloc, CVodeReInit, CVodeSetTolerances: added option itol=CV_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
     CVodeSetTolerances before CVodeMalloc. It is now legal to deallocate
     the absolute tolerance N_Vector right after its use.
   - Several optional input functions were combined into a single one
     (CVodeRootInit and CvodeSetGdata, CVDenseSetJacFn and CVDenseSetJacData,
     CVBandSetJacFn and CVBandSetJacData, CVSpgmrSetPrecSolveFn and 
     CVSpgmrSetPrecSetFn and CVSpgmrSetPrecData, CVSpgmrSetJacTimesVecFn and
     CVSpgmrSetJacData).
   - Removed CVodeSetQuadtolerances. CVodeSetQuadErrCon now sets both the
     error control flag and the tolerances for quadratures.
   - CVodeSetQuadErrCon, CVodeSetSensTolerances: the relative tolerance
     must now be passed as a realtype. It is now illegal to call 
     CVodeSetQuadErrCon before CVodeQuadMalloc or to call CVodeSetSensTolerances
     before CVodeSensMalloc.
   - CvodeSensMalloc: removed p and plist from argument list.
   - CVodeSensParams replaces CVodeSensPbar and sets p, pbar, and plist. NULL
     can be passed for any of them if it will not be needed given the current
     set of options. The array pbar must now contain Ns non-zero realtype
     values giving order of magnitude for the parameters with respect to which
     sensitivities will be computed. The array plist can now only have positive 
     entries. 
   - CVodeGetErrorWeights, CVodeGetQuadErrorWeights: the user is now responsible 
     for allocating space for the N_Vector in which error weights will be copied.
   - CVodeGetEstLocalErrors: the user is now responsible for allocating space
     for the N_Vector in which estimated local errors will be copied.
   - CVodeGetRootInfo: the user is now responsible for allocating space
     for the int array in which root information will be copied.
   - CVodeGetNumStgrSensNonlinSolvIters, CVodeGetNumStgrSensNonlinSolvConvFails:
     the user is now responsible for allocating space for the long int arrays 
     in which STAGGERED1 statistics will be copied.
   - CVodeMallocB, CVodeReInitB, CVodeSetQuadErrConB: the relative tolerance
     for the backward integration must now be passed as a realtype. It is now
     illegal to call CVodeSetQuadErrConB before CVQuadMallocB.
   - Passing a value of 0 for the maximum step size, the minimum step
     size, or for maxsteps results in the solver using the corresponding
     default value (infinity, 0, 500, respectively)
   - User-callable functions in the adjoint module were modified similarly
     to their corresponding counterparts for forward simulation.


v. 2.1.1 (Jan. 2005) ---> v. 2.1.2 (Mar. 2005)
----------------------------------------------

- Bug fixes
   - fixed bug in CVode function:  Initial setting of tretlast = *tret = tn removed
     (correcting erroneous behavior at first call to CVRcheck3).
   - removed redundant setting of tretlast = *tret = tn at CLOSE_ROOTS return from CVode.
   - fixed bug in CVCompleteStep related to quadrature and sensitivity variables
     (leading to wrong values at a BDF order increase)
   - in CVUpperBoundH0, fixed a potential, although not harmful, use of 
     uninitialized memory
   - changed implicit type conversion to explicit in check_flag() routine in
     examples to avoid C++ compiler errors

- 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
   - added more details on ownership of memory for the array returned by CVodeGetRootInfo 
   - corrected/added descriptions of error returns.
   - added description of --with-mpi-flags option

- 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)


v. 2.1.0 (Dec. 2004) ---> v. 2.1.1 (Jan. 2005)
----------------------------------------------

- New features
   - added function CVodeSensToggle to allow activation/deactivation of
     sensitivity calculations without memory allocation/deallocation.

- Bug fixes
   - fixed bug in CVCompleteStep related to quadrature and sensitivity variables
     (leading to wrong values at a BDF order increase).
   - in CVUpperBoundH0, fixed a potential, although not harmful, use of 
     uninitialized memory.
   - fixed logic in testing for negative values of user-supplied absolute tolerances
     for sensitivity variables.
  
- Changes related to the build system
   - changed order of compiler directives in header files to avoid compilation
     errors when using a C++ compiler.

v. 1.0 (Jul. 2002) ---> v. 2.1.0 (Dec. 2004)
--------------------------------------------

- New features
   - added quadrature integration capabilities.
   - added root finding capabilities.
   - added option for different user data structures for ODE r.h.s.
     and sensitivity r.h.s.
   - in adjoint module, added interface to CVBBDPRE for the backward 
     phase.
   - in adjoint module, added option for using CVDIAG during backward 
     phase.
   - in adjoint module, added option for ONE_STEP integration during 
     backward phase.
   - in adjoint module, added option to reinitialize the backward 
     integration phase (and perform a new backward integration using
     the same check points).
   - in adjoint module, relaxed assumption that t_final > t_0 (now
     accepts t_final < t_0).

- Bug fixes
   - fixed bug in adjustment of sensitivity Nordsieck history array on an
     order decrease (when using BDF).
   - in adjoint module, fixed a potential use of memory before being set.
   - in adjoint module, fixed a bug related to data saved at check points.
     This addresses the case in which an order increase is deemed necessary
     at the very first step after a check-point.

- Changes related to the NVECTOR module 
  (see also the file sundials/shared/README)
   - removed machEnv, redefined table of vector operations (now contained
     in the N_Vector structure itself).
   - all CVODES functions create new N_Vector variables through cloning, using
     an N_Vector passed by the user as a template.

- Changes to type names and CVODES constants
   - removed type 'integertype'; instead use int or long int, as appropriate.
   - restructured the list of return values from the various CVODES functions.
   - changed all CVODES constants (inputs and return values) to have the
     prefix 'CV_' (e.g. CV_SUCCESS).
   - renamed various function types to have the prefix 'CV' (e.g. CVRhsFn).

- Changes to optional input/ouput
   - added CVodeSet* and CVodeGet* 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).
   - the value of the last return flag from any function within a linear
     solver module can be obtained as an optional output (e.g. CVDenseGetLastFlag).
  
- Changes to user-callable functions
   - renamed header files to have prefix 'cv' instead of 'cvs' (e.g. cvdense.h
     replaces cvsdense.h).
   - added new function CVodeCreate which initializes the CVODES solver
     object and returns a pointer to the CVODES memory block.
   - removed N (problem size) from all functions except the initialization
     functions for the direct linear solvers (CVDense and CVBand).
   - shortened argument lists of most CVODES functions (the arguments that
     were dropped can now be specified through CVodeSet* functions).
   - removed reinitialization functions for band/dense/SPGMR linear
     solvers (same functionality can be obtained using CV*Set* functions).
   - in CVBBDPRE, added a new function, CVBBDSpgmr to initialize the
     SPGMR linear solver with the BBD preconditioner.
   - function names changed in CVBANDPRE and CVBBDPRE 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 CVSPGMR, shortened argument lists for user preconditioner functions.
