3.4. Using CVODE for IVP Solution
This chapter is concerned with the use of CVODE for the solution of initial value problems (IVPs). The following sections treat the header files and the layout of the user’s main program, and provide descriptions of the CVODE usercallable functions and usersupplied functions.
The sample programs described in the companion document [72] may also be helpful. Those codes may be used as templates (with the removal of some lines used in testing) and are included in the CVODE package.
Users with applications written in Fortran should see §1.9, which describes interfacing with CVODE from Fortran.
The user should be aware that not all SUNLinearSolver
and SUNMatrix
modules are compatible with all N_Vector
implementations. Details on
compatibility are given in the documentation for each SUNMatrix
module
(§9) and each SUNLinearSolver
module (§10).
For example, NVECTOR_PARALLEL
is not compatible with the dense, banded, or
sparse SUNMatrix
types, or with the corresponding dense, banded, or sparse
SUNLinearSolver
modules. Please check §9 and
§10 to verify compatibility between these modules. In addition
to that documentation, we note that the CVBANDPRE preconditioning module is only
compatible with the NVECTOR_SERIAL
, NVECTOR_OPENMP
, and
NVECTOR_PTHREADS
vector implementations, and the preconditioner module
CVBBDPRE can only be used with NVECTOR_PARALLEL
. It is not recommended to
use a threaded vector module with SuperLU_MT unless it is the NVECTOR_OPENMP
module, and SuperLU_MT is also compiled with OpenMP.
CVODE uses various constants for both input and output. These are defined as needed in this chapter, but for convenience are also listed separately in §3.5.
3.4.1. Access to library and header files
At this point, it is assumed that the installation of CVODE, following the
procedure described in §1.1, has been completed successfully.
In the proceeding text, the directories libdir
and incdir
are the
installation library and include directories, respectively. For a default
installation, these are instdir/lib
and instdir/include
, respectively,
where instdir
is the directory where SUNDIALS was installed.
Regardless of where the user’s application program resides, its
associated compilation and load commands must make reference to the
appropriate locations for the library and header files required by
CVODE. CVODE symbols are found in libdir/libsundials_cvode.lib
.
Thus, in addition to linking to libdir/libsundials_core.lib
, CVODE
users need to link to the CVODE library. Symbols for additional SUNDIALS
modules, vectors and algebraic solvers, are found in
<libdir>/libsundials_nvec*.lib
<libdir>/libsundials_sunmat*.lib
<libdir>/libsundials_sunlinsol*.lib
<libdir>/libsundials_sunnonlinsol*.lib
<libdir>/libsundials_sunmem*.lib
The file extension .lib
is typically .so
for shared libraries
and .a
for static libraries.
The relevant header files for CVODE are located in the subdirectories
incdir/include/cvode
. To use CVODE the application needs to include
the header file for CVODE in addition to the SUNDIALS core header file:
#include <sundials/sundials_core.h> // Provides core SUNDIALS types
#include <cvode/cvode.h> // CVODE provides linear multistep methods
The calling program must also include an N_Vector
implementation header file, of the form
nvector/nvector_*.h
. See §8 for the appropriate name.
If using a nondefault nonlinear solver module, or when interacting with a
SUNNonlinearSolver
module directly, the calling program must
also include a SUNNonlinearSolver
implementation header file,
of the form sunnonlinsol/sunnonlinsol_*.h
where *
is the name of
the nonlinear solver module (see §11 for more
information).
If using a nonlinear solver that requires the solution of a linear system of the form
(3.7) (e.g., the default Newton iteration), then a linear solver module header file
will be required. In this case it will be necessary to include the header file for a
SUNLinearSolver
solver, which is of the form sunlinsol/sunlinsol_***.h
(see §10 for more information).
If the linear solver is matrixbased, the linear solver header will also include a
header file of the from sunmatrix/sunmatrix_*.h
where *
is the name of the
matrix implementation compatible with the linear solver (see §9 for
more information).
Other headers may be needed, according to the choice of preconditioner, etc. For example, in the
example (see [72]), preconditioning is done with a blockdiagonal matrix. For this,
even though the SUNLINSOL_SPGMR
linear solver is used, the header
sundials_dense.h
is included for access to the underlying generic dense matrix
arithmetic routines.
3.4.2. A skeleton of the user’s main program
The following is a skeleton of the user’s main program (or calling
program) for the integration of an ODE IVP. Most of the steps are
independent of the N_Vector
, SUNMatrix
, SUNLinearSolver
, and
SUNNonlinearSolver
implementations used. For the steps that are not, refer
to §8, §9, §10, and
§11 for the specific name of the
function to be called or macro to be referenced.
Initialize parallel or multithreaded environment, if appropriate For example, call
MPI_Init
to initialize MPI if used, or set the number of threads to use within the threaded vector functions if used.
 Create the SUNDIALS context object
Call
SUNContext_Create()
to allocate theSUNContext
object.Set problem dimensions etc. This generally includes the problem size
N
, and may include the local vector lengthNlocal
.Note: The variables
N
andNlocal
should be of typesunindextype
.Set vector of initial values To set the vector of initial values, use the appropriate functions defined by the particular
N_Vector
implementation.For native SUNDIALS vector implementations, use a call of the form
y0 = N_VMake_***(..., ydata)
if the array containing the initial values of \(y\) already exists. Otherwise, create a new vector by making a call of the formN_VNew_***(...)
, and then set its elements by accessing the underlying data with a call of the formydata = N_VGetArrayPointer(y0)
.For HYPRE and PETSC vector wrappers, first create and initialize the underlying vector, and then create an
N_Vector
wrapper with a call of the formy0 = N_VMake_***(yvec)
, whereyvec
is a HYPRE or PETSC vector. Note that calls likeN_VNew_***(...)
andN_VGetArrayPointer(...)
are not available for these vector wrappers.See §8 for details.
Create CVODE object Call
CVodeCreate()
to create the CVODE memory block and to specify the linear multistep method.CVodeCreate()
returns a pointer to the CVODE memory structure.See §3.4.3.1 for details.
Initialize CVODE solver Call
CVodeInit()
to provide required problem specifications, allocate internal memory for CVODE, and initialize CVODE.CVodeInit()
returns a flag, the value of which indicates either success or an illegal argument value.See §3.4.3.1 for details.
Specify integration tolerances Call
CVodeSStolerances()
orCVodeSVtolerances()
to specify either a scalar relative tolerance and scalar absolute tolerance, or a scalar relative tolerance and a vector of absolute tolerances, respectively. Alternatively, callCVodeWFtolerances()
to specify a function which sets directly the weights used in evaluating WRMS vector norms.See §3.4.3.2 for details.
Create matrix object If a nonlinear solver requiring a linear solve will be used (e.g., the default Newton iteration) and the linear solver will be a matrixbased linear solver, then a template Jacobian matrix must be created by calling the appropriate constructor function defined by the particular
SUNMatrix
implementation.For the native SUNDIALS
SUNMatrix
implementations, the matrix object may be created using a call of the formSUN***Matrix(...)
where***
is the name of the matrix (see §9 for details).Create linear solver object If a nonlinear solver requiring a linear solver is chosen (e.g., the default Newton iteration), then the desired linear solver object must be created by calling the appropriate constructor function defined by the particular
SUNLinearSolver
implementation.For any of the SUNDIALSsupplied
SUNLinearSolver
implementations, the linear solver object may be created using a call of the formSUNLinearSolver LS = SUNLinSol_*(...);
where*
can be replaced with “Dense”, “SPGMR”, or other options, as discussed in §3.4.3.5 and §10.Set linear solver optional inputs Call functions from the selected linear solver module to change optional inputs specific to that linear solver. See the documentation for each
SUNLinearSolver
module in §10 for details.Attach linear solver module If a nonlinear solver requiring a linear solver is chosen (e.g., the default Newton iteration), then initialize the CVLS linear solver interface by attaching the linear solver object (and matrix object, if applicable) with a call
ier = CVodeSetLinearSolver(cvode_mem, NLS)
(for details see §3.4.3.5):Alternately, if the CVODEspecific diagonal linear solver module, CVDIAG, is desired, initialize the linear solver module and attach it to CVODE with the call to
CVodeSetLinearSolver()
.Set optional inputs Call
`CVodeSet***
functions to change any optional inputs that control the behavior of CVODE from their default values. See §3.4.3.10 for details.Create nonlinear solver object (optional) If using a nondefault nonlinear solver (see §3.4.3.6), then create the desired nonlinear solver object by calling the appropriate constructor function defined by the particular
SUNNonlinearSolver
implementation (e.g.,NLS = SUNNonlinSol_***(...);
where***
is the name of the nonlinear solver (see §11 for details).Attach nonlinear solver module (optional) If using a nondefault nonlinear solver, then initialize the nonlinear solver interface by attaching the nonlinear solver object by calling
ier = CVodeSetNonlinearSolver
(see §3.4.3.6 for details).Set nonlinear solver optional inputs (optional) Call the appropriate set functions for the selected nonlinear solver module to change optional inputs specific to that nonlinear solver. These must be called after
CVodeInit()
if using the default nonlinear solver or after attaching a new nonlinear solver to CVODE, otherwise the optional inputs will be overridden by CVODE defaults. See §11 for more information on optional inputs.Specify rootfinding problem (optional) Call
CVodeRootInit()
to initialize a rootfinding problem to be solved during the integration of the ODE system. See §3.4.3.7, and see §3.4.3.10.5 for relevant optional input calls.Advance solution in time For each point at which output is desired, call
ier = CVode(cvode_mem, tout, yout, tret itask)
. Hereitask
specifies the return mode. The vectoryout
(which can be the same as the vectory0
above) will contain \(y(t)\). SeeCVode()
for details.Get optional outputs Call
CV*Get*
functions to obtain optional output. See §3.4.3.12 for details.Deallocate memory for solution vector Upon completion of the integration, deallocate memory for the vector
y
(oryout
) by calling the appropriate destructor function defined by theN_Vector
implementation.Free solver memory Call
CVodeFree()
to free the memory allocated by CVODE.Free nonlinear solver memory (optional) If a nondefault nonlinear solver was used, then call
SUNNonlinSolFree()
to free any memory allocated for theSUNNonlinearSolver
object.Free linear solver and matrix memory Call
SUNLinSolFree()
andSUNMatDestroy()
to free any memory allocated for the linear solver and matrix objects created above.Free the SUNContext object Call
SUNContext_Free()
to free the memory allocated for theSUNContext
object.Finalize MPI, if used Call
MPI_Finalize
to terminate MPI.
3.4.3. Usercallable functions
This section describes the CVODE functions that are called by the user to setup and then solve an IVP. Some of these are required. However, starting with §3.4.3.10, the functions listed involve optional inputs/outputs or restarting, and those paragraphs may be skipped for a casual use of CVODE. In any case, refer to §3.4.2 for the correct order of these calls.
On an error, each usercallable function returns a negative value and
sends an error message to the error handler routine, which prints the
message on stderr
by default. However, the user can set a file as error output
or can provide his own error handler function (see §3.4.3.10.1).
3.4.3.1. CVODE initialization and deallocation functions
The following three functions must be called in the order listed. The last one is to be called only after the IVP solution is complete, as it frees the CVODE memory block created and allocated by the first two calls.

void *CVodeCreate(int lmm, SUNContext sunctx)
The function
CVodeCreate()
instantiates a CVODE solver object and specifies the solution method. Arguments:
lmm
– specifies the linear multistep method and must be one of two possible values:CV_ADAMS
orCV_BDF
.sunctx
– theSUNContext
object (see §1.4)
 Return Value:
If successful,
CVodeCreate()
returns a pointer to the newly created CVODE memory block (of typevoid *
). Otherwise, it returnsNULL
.
Notes: The recommended choices for
lmm
areCV_ADAMS
for nonstiff problems andCV_BDF
for stiff problems. The default Newton iteration is recommended for stiff problems, and the fixedpoint solver (previously referred to as the functional iteration in this guide) is recommended for nonstiff problems. For details on how to attach a different nonlinear solver module to CVODE see the description ofCVodeSetNonlinearSolver()
.

int CVodeInit(void *cvode_mem, CVRhsFn f, sunrealtype t0, N_Vector y0)
The function
CVodeInit
provides required problem and solution specifications, allocates internal memory, and initializes CVODE. Arguments:
cvode_mem
– pointer to the CVODE memory block returned byCVodeCreate()
.f
– is the C function which computes the righthand side function f in the ODE. This function has the formf(t, y, ydot, user_data)
(for full details seeCVRhsFn
).t0
– is the initial value of t.y0
– is the initial value of y.
 Return Value:
CV_SUCCESS
– The call was successful.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.CV_MEM_FAIL
– A memory allocation request has failed.CV_ILL_INPUT
– An input argument toCVodeInit
has an illegal value.
 Notes:
If an error occurred,
CVodeInit
also sends an error message to the error handler function.

void CVodeFree(void **cvode_mem);
The function
CVodeFree
frees the memory allocated by a previous call toCVodeCreate()
. Arguments:
Pointer to the CVODE memory block.
 Return Value:
The function
CVodeFree
has no return value.
3.4.3.2. CVODE tolerance specification functions
One of the following three functions must be called to specify the
integration tolerances (or directly specify the weights used in
evaluating WRMS vector norms). Note that this call must be made after
the call to CVodeInit()

int CVodeSStolerances(void *cvode_mem, sunrealtype reltol, sunrealtype abstol)
The function
CVodeSStolerances
specifies scalar relative and absolute tolerances. Arguments:
cvode_mem
– pointer to the CVODE memory block returned byCVodeCreate()
reltol
– is the scalar relative error tolerance.abstol
– is the scalar absolute error tolerance.
 Return value:
CV_SUCCESS
– The call was successfulCV_MEM_NULL
– The CVODE memory block was not initializedCV_NO_MALLOC
– The allocation function returnedNULL
CV_ILL_INPUT
– One of the input tolerances was negative.

int CVodeSVtolerances(void *cvode_mem, sunrealtype reltol, N_Vector abstol)
The function
CVodeSVtolerances
specifies scalar relative tolerance and vector absolute tolerances. Arguments:
cvode_mem
– pointer to the CVODE memory block returned byCVodeCreate()
reltol
– is the scalar relative error tolerance.abstol
– is the vector of absolute error tolerances.
 Return value:
CV_SUCCESS
– The call was successfulCV_MEM_NULL
– The CVODE memory block was not initializedCV_NO_MALLOC
– The allocation function returnedNULL
CV_ILL_INPUT
– The relative error tolerance was negative or the absolute tolerance had a negative component.
 Notes:
This choice of tolerances is important when the absolute error tolerance needs to be different for each component of the state vector y.

int CVodeWFtolerances(void *cvode_mem, CVEwtFn efun)
The function
CVodeWFtolerances
specifies a usersupplied functionefun
that sets the multiplicative error weights W_i for use in the weighted RMS norm, which are normally defined by (3.6). Arguments:
cvode_mem
– pointer to the CVODE memory block returned byCVodeCreate()
efun
– is the C function which defines theewt
vector (seeCVEwtFn
).
 Return value:
CV_SUCCESS
– The call was successfulCV_MEM_NULL
– The CVODE memory block was not initializedCV_NO_MALLOC
– The allocation function returnedNULL
3.4.3.3. General advice on choice of tolerances
For many users, the appropriate choices for tolerance values in reltol
and abstol
are a
concern. The following pieces of advice are relevant.
(1) The scalar relative tolerance reltol
is to be set to control relative errors. So
\(\texttt{reltol} = 10^{4}\) means that errors are controlled to .01%. We do not recommend
using reltol
larger than \(10^{3}\). On the other hand, reltol
should not be so small
that it is comparable to the unit roundoff of the machine arithmetic (generally
around \(10^{15}\)).
(2) The absolute tolerances abstol
(whether scalar or vector) need to be set to control
absolute errors when any components of the solution vector y
may be so small that
pure relative error control is meaningless. For example, if y[i]
starts at some
nonzero value, but in time decays to zero, then pure relative error control on y[i]
makes no sense (and is overly costly) after y[i]
is below some noise level. Then
abstol
(if scalar) or abstol[i]
(if a vector) needs to be set to that noise level. If the different
components have different noise levels, then abstol
should be a vector. See the example cvsRoberts_dns
in the CVODE package, and the discussion of it in the CVODE Examples document
[113]. In that problem, the three components vary betwen 0 and 1,
and have different noise levels; hence the abstol
vector. It is impossible to give any
general advice on abstol
values, because the appropriate noise levels are completely
problemdependent. The user or modeler hopefully has some idea as to what those
noise levels are.
(3) Finally, it is important to pick all the tolerance values conservatively, because they control the error committed on each individual time step. The final (global) errors are some sort of accumulation of those perstep errors. A good rule of thumb is to reduce the tolerances by a factor of .01 from the actual desired limits on errors. So if you want .01% accuracy (globally), a good choice is \(\texttt{reltol} = 10^{6}\). But in any case, it is a good idea to do a few experiments with the tolerances to see how the computed solution values vary as tolerances are reduced.
3.4.3.4. Advice on controlling unphysical negative values
In many applications, some components in the true solution are always positive or nonnegative, though at times very small. In the numerical solution, however, small negative (hence unphysical) values can then occur. In most cases, these values are harmless, and simply need to be controlled, not eliminated. The following pieces of advice are relevant.
(1) The way to control the size of unwanted negative computed values is with tighter absolute tolerances. Again this requires some knowledge of the noise level of these components, which may or may not be different for different components. Some experimentation may be needed.
(2) If output plots or tables are being generated, and it is important to avoid
having negative numbers appear there (for the sake of avoiding a long
explanation of them, if nothing else), then eliminate them, but only in the
context of the output medium. Then the internal values carried by the solver are
unaffected. Remember that a small negative value in y
returned by CVODE, with
magnitude comparable to abstol
or less, is equivalent to zero as far as the computation
is concerned.
(3) The user’s righthand side routine f
should never change a negative value in
the solution vector y
to a nonnegative value, as a “solution” to this problem.
This can cause instability. If the f
routine cannot tolerate a zero or negative
value (e.g. because there is a square root or log of it), then the offending
value should be changed to zero or a tiny positive number in a temporary
variable (not in the input y
vector) for the purposes of computing \(f(t,y)\).
(4) Positivity and nonnegativity constraints on components can be enforced by use of the recoverable error return feature in the usersupplied righthand side function. However, because this option involves some extra overhead cost, it should only be exercised if the use of absolute tolerances to control the computed values is unsuccessful.
3.4.3.5. Linear solver interface functions
As previously explained, if the nonlinear solver requires the solution of linear systems of the form (3.7) (e.g., the default Newton iteration), there are two CVODE linear solver interfaces currently available for this task: CVLS and CVDIAG.
The first corresponds to the main linear solver interface in CVODE,
that supports all valid SUNLinearSolver
modules. Here, matrixbased
SUNLinearSolver
modules utilize SUNMatrix
objects to store the
approximate Jacobian matrix \(J = \partial{f}/\partial{y}\), the
Newton matrix \(M = I\gamma J\), and factorizations used throughout
the solution process. Conversely, matrixfree SUNLinearSolver
modules
instead use iterative methods to solve the Newton systems of equations,
and only require the action of the matrix on a vector, \(Mv\).
With most of these methods, preconditioning can be done on the left
only, the right only, on both the left and right, or not at all. The
exceptions to this rule are SPFGMR that supports right
preconditioning only and PCG that performs symmetric
preconditioning. For the specification of a preconditioner, see the
iterative linear solver sections in §3.4.3.10
and §3.4.4.
If preconditioning is done, usersupplied functions define linear operators corresponding to left and right preconditioner matrices \(P_1\) and \(P_2\) (either of which could be the identity matrix), such that the product \(P_1 P_2\) approximates the matrix \(M = I  \gamma J\) of (3.8).
The CVDIAG linear solver interface supports a direct linear solver, that uses only a diagonal approximation to \(J\).
To specify a generic linear solver to CVODE, after the call to CVodeCreate()
but
before any calls to CVode()
, the user’s program must create the appropriate
SUNLinearSolver
object and call the function CVodeSetLinearSolver()
, as documented below. To create the
SUNLinearSolver
object, the user may call one of the SUNDIALSpackaged SUNLinearSolver
module constructor routines via a call of the form SUNLinearSolver LS = SUNLinSol_*(...);
Alternately, a usersupplied SUNLinearSolver
module may be created and used instead. The
use of each of the generic linear solvers involves certain constants,
functions and possibly some macros, that are likely to be needed in the
user code. These are available in the corresponding header file
associated with the specific SUNMatrix
or SUNLinearSolver
module in
question, as described in §9 and
§10.
Once this solver object has been constructed, the user should attach it
to CVODE via a call to CVodeSetLinearSolver()
. The first argument passed to this function
is the CVODE memory pointer returned by CVodeCreate()
; the second argument is the
desired SUNLinearSolver
object to use for solving linear systems. The
third argument is an optional SUNMatrix
object to accompany
matrixbased SUNLinearSolver
inputs (for matrixfree linear solvers, the
third argument should be NULL
). A call to this function initializes the
CVLS linear solver interface, linking it to the main CVODE
integrator, and allows the user to specify additional parameters and
routines pertinent to their choice of linear solver.
To instead specify the CVODEspecific diagonal linear solver
interface, the user’s program must call CVDiag()
, as documented below. The first
argument passed to this function is the CVODE memory pointer
returned by CVodeCreate()
.

int CVodeSetLinearSolver(void *cvode_mem, SUNLinearSolver LS, SUNMatrix J)
The function
CVodeSetLinearSolver
attaches a genericSUNLinearSolver
objectLS
and corresponding template JacobianSUNMatrix
objectJ
(if applicable) to CVODE, initializing the CVLS linear solver interface. Arguments:
cvode_mem
– pointer to the CVODE memory block.LS
–SUNLinearSolver
object to use for solving linear systems of the form (3.7)J
–SUNMatrix
object for used as a template for the Jacobian (orNULL
if not applicable).
 Return value:
CVLS_SUCCESS
– The CVLS initialization was successful.CVLS_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVLS_ILL_INPUT
– The CVLS interface is not compatible with theLS
orJ
input objects or is incompatible with the currentN_Vector
module.CVLS_SUNLS_FAIL
– A call to theLS
object failed.CVLS_MEM_FAIL
– A memory allocation request failed.
 Notes:
If
LS
is a matrixbased linear solver, then the template Jacobian matrixJ
will be used in the solve process, so if additional storage is required within theSUNMatrix
object (e.g. for factorization of a banded matrix), ensure that the input object is allocated with sufficient size (see §9 for further information).When using sparse linear solvers, it is typically much more efficient to supply
J
so that it includes the full sparsity pattern of the Newton system matrices \(M=I\gamma J\), even ifJ
itself has zeros in nonzero locations of I. The reasoning for this is that M is constructed inplace, on top of the userspecified values ofJ
, so if the sparsity pattern inJ
is insufficient to store M then it will need to be resized internally by CVODE.
Added in version 4.0.0: Replaces the deprecated functions
CVDlsSetLinearSolver
andCVSpilsSetLinearSolver
.

int CVDiag(void *cvode_mem)
The function
CVDiag
selects the CVDIAG linear solver. The user’s main program must include thecvode_diag.h
header file. Arguments:
cvode_mem
– pointer to the CVODE memory block.
 Return value:
CVDIAG_SUCCESS
– The CVDIAG initialization was successful.CVDIAG_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVDIAG_ILL_INPUT
– The CVDIAG solver is not compatible with the currentN_Vector
module.CVDIAG_MEM_FAIL
– A memory allocation request failed.
 Notes:
The CVDIAG solver is the simplest of all of the available CVODE linear solvers. The CVDIAG solver uses an approximate diagonal Jacobian formed by way of a difference quotient. The user does not have the option of supplying a function to compute an approximate diagonal Jacobian.
3.4.3.6. Nonlinear solver interface function
By default CVODE uses the SUNNonlinearSolver
implementation of Newton’s
method defined by the SUNNONLINSOL_NEWTON module.
To specify a different nonlinear solver in CVODE, the user’s program must create
a SUNNonlinearSolver
object by calling the appropriate constructor routine.
The user must then attach the SUNNonlinearSolver
object by calling
CVodeSetNonlinearSolver()
, as documented below.
When changing the nonlinear solver in CVODE, CVodeSetNonlinearSolver()
must be called after CVodeInit()
. If any calls to CVode()
have been made,
then CVODE will need to be reinitialized by calling CVodeReInit()
to ensure
that the nonlinear solver is initialized correctly before any subsequent calls
to CVode()
.
The first argument passed to the routine CVodeSetNonlinearSolver()
is
the CVODE memory pointer returned by CVodeCreate()
and the second
argument is the SUNNonlinearSolver
object to use for solving the nonlinear
system (3.7) or (3.5). A call to this function
attaches the nonlinear solver to the main CVODE integrator.

int CVodeSetNonlinearSolver(void *cvode_mem, SUNNonlinearSolver NLS)
The function
CVodeSetNonlinearSolver
attaches aSUNNonlinearSolver
object (NLS
) to CVODE. Arguments:
 Return value:
CV_SUCCESS
– The nonlinear solver was successfully attached.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
CV_ILL_INPUT
– TheSUNNonlinearSolver
object isNULL
, does not implement the required nonlinear solver operations, is not of the correct type, or the residual function, convergence test function, or maximum number of nonlinear iterations could not be set.
3.4.3.7. Rootfinding initialization function
While solving the IVP, CVODE has the capability to find the roots of
a set of userdefined functions. To activate the root finding algorithm,
call the following function. This is normally called only once, prior to
the first call to CVode()
, but if the rootfinding problem is to be changed
during the solution, CVodeRootInit()
can also be called prior to a continuation call to CVode()

int CVodeRootInit(void *cvode_mem, int nrtfn, CVRootFn g)
The function
CVodeRootInit
specifies that the roots of a set of functions \(g_i(t,y)\) are to be found while the IVP is being solved. Arguments:
cvode_mem
– pointer to the CVODE memory block returned byCVodeCreate()
.nrtfn
– is the number of root functions \(g_i\).g
– is the C function which defines thenrtfn
functions \(g_i(t,y)\) whose roots are sought. SeeCVRootFn
for details.
 Return value:
CV_SUCCESS
– The call was successful.CV_MEM_NULL
– Thecvode_mem
argument wasNULL
.CV_MEM_FAIL
– A memory allocation failed.CV_ILL_INPUT
– The functiong
isNULL
, butnrtfn
\(> 0\).
 Notes:
If a new IVP is to be solved with a call to
CVodeReInit
, where the new IVP has no rootfinding problem but the prior one did, then callCVodeRootInit
withnrtfn=0
.
3.4.3.8. Projection initialization function
When solving an IVP with a constraint equation, CVODE has the capability to project the solution onto the constraint manifold after each time step. To activate the projection capability with a userdefined projection function, call the following set function:

int CVodeSetProjFn(void *cvode_mem, CVProjFn proj)
The function
CVodeSetProjFn
enables or disables projection with a userdefined projection function. Arguments:
cvode_mem
– is a pointer to the CVODE memory block returned byCVodeCreate()
.proj
– is the C function which defines the projection. SeeCVProjFn
for details.
 Return value:
CV_SUCCESS
– The call was successful.CV_MEM_NULL
– Thecvode_mem
argument wasNULL
.CV_MEM_FAIL
– A memory allocation failed.CV_ILL_INPUT
– The projection function isNULL
or the method type is notCV_BDF
.
 Notes:
At this time projection is only supported with BDF methods. If a new IVP is to be solved with a call to
CVodeReInit
, where the new IVP does not have a constraint equation but the prior one did, then callCVodeSetProjFrequency
with an input of0
to disable projection.
Added in version 5.3.0.
3.4.3.9. CVODE solver function
This is the central step in the solution process — the call to perform
the integration of the IVP. One of the input arguments (itask
) specifies one
of two modes as to where CVODE is to return a solution. But these
modes are modified if the user has set a stop time (with CVodeSetStopTime()
) or requested
rootfinding.

int CVode(void *cvode_mem, sunrealtype tout, N_Vector yout, sunrealtype *tret, int itask)
The function
CVode
integrates the ODE over an interval in t. Arguments:
cvode_mem
– pointer to the CVODE memory block.tout
– the next time at which a computed solution is desired.yout
– the computed solution vector.tret
– the time reached by the solver (output).itask
– a flag indicating the job of the solver for the next user step. TheCV_NORMAL
option causes the solver to take internal steps until it has reached or just passed the userspecifiedtout
parameter. The solver then interpolates in order to return an approximate value of \(y({tout})\). TheCV_ONE_STEP
option tells the solver to take just one internal step and then return the solution at the point reached by that step.
 Return value:
CV_SUCCESS
–CVode
succeeded and no roots were found.CV_TSTOP_RETURN
–CVode
succeeded by reaching the stopping point specified through the optional input functionCVodeSetStopTime()
.CV_ROOT_RETURN
–CVode
succeeded and found one or more roots. In this case,tret
is the location of the root. Ifnrtfn
\(>1\), callCVodeGetRootInfo()
to see which \(g_i\) were found to have a root.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.CV_NO_MALLOC
– The CVODE memory was not allocated by a call toCVodeInit()
.CV_ILL_INPUT
– One of the inputs toCVode
was illegal, or some other input to the solver was illegal or missing. The latter category includes the following situations:The tolerances have not been set.
A component of the error weight vector became zero during internal timestepping.
The linear solver initialization function (called by the user after calling
CVodeCreate()
) failed to set the linear solverspecificlsolve
field incvode_mem
.A root of one of the root functions was found both at a point \(t\) and also very near \(t\).
CV_TOO_CLOSE
– The initial time \(t_0\) and the output time \(t_{out}\) are too close to each other and the user did not specify an initial step size.CV_TOO_MUCH_WORK
– The solver tookmxstep
internal steps but still could not reachtout
. The default value formxstep
isMXSTEP_DEFAULT = 500
.CV_TOO_MUCH_ACC
– The solver could not satisfy the accuracy demanded by the user for some internal step.CV_ERR_FAILURE
– Either error test failures occurred too many times (MXNEF = 7
) during one internal time step, or with \(h = h_{min}\).CV_CONV_FAILURE
– Either convergence test failures occurred too many times (MXNCF = 10
) during one internal time step, or with \(h = h_{min}\).CV_LINIT_FAIL
– The linear solver interface’s initialization function failed.CV_LSETUP_FAIL
– The linear solver interface’s setup function failed in an unrecoverable manner.CV_LSOLVE_FAIL
– The linear solver interface’s solve function failed in an unrecoverable manner.CV_CONSTR_FAIL
– The inequality constraints were violated and the solver was unable to recover.CV_RHSFUNC_FAIL
– The righthand side function failed in an unrecoverable manner.CV_FIRST_RHSFUNC_FAIL
– The righthand side function had a recoverable error at the first call.CV_REPTD_RHSFUNC_ERR
– Convergence test failures occurred too many times due to repeated recoverable errors in the righthand side function. This flag will also be returned if the righthand side function had repeated recoverable errors during the estimation of an initial step size.CV_UNREC_RHSFUNC_ERR
– The righthand function had a recoverable error, but no recovery was possible. This failure mode is rare, as it can occur only if the righthand side function fails recoverably after an error test failed while at order one.CV_RTFUNC_FAIL
– The rootfinding function failed.
 Notes:
The vector
yout
can occupy the same space as the vectory0
of initial conditions that was passed toCVodeInit
.In the
CV_ONE_STEP
mode,tout
is used only on the first call, and only to get the direction and a rough scale of the independent variable.If a stop time is enabled (through a call to
CVodeSetStopTime
), thenCVode
returns the solution attstop
. Once the integrator returns at a stop time, any future testing fortstop
is disabled (and can be reenabled only though a new call toCVodeSetStopTime
).All failure return values are negative and so the test
flag < 0
will trap allCVode
failures.On any error return in which one or more internal steps were taken by
CVode
, the returned values oftret
andyout
correspond to the farthest point reached in the integration. On all other error returns,tret
andyout
are left unchanged from the previousCVode
return.
3.4.3.10. Optional input functions
There are numerous optional input parameters that control the behavior of the CVODE solver. CVODE provides functions that can be used to change these optional input parameters from their default values. The main inputs are divided into the following categories:
Table 3.1 lists the main CVODE optional input functions,
Table 3.2 lists the CVLS linear solver interface optional input functions,
Table 3.3 lists the CVNLS nonlinear solver interface optional input functions,
Table 3.4 lists the CVODE step size adaptivity optional input functions,
Table 3.5 lists the rootfinding optional input functions, and
Table 3.6 lists the projection optional input functions.
These optional inputs are described in detail in the remainder of this section. Note that the diagonal linear solver module has no optional inputs. For the most casual use of CVODE, the reader can skip to §3.4.4.
We note that, on an error return, all of the optional input functions send an
error message to the error handler function. All error return values are
negative, so the test flag < 0
will catch all errors.
The optional input calls can, unless otherwise noted, be executed in any order.
A call to an CVodeSet***
function can, unless otherwise noted, be made
at any time from the user’s calling program and, if successful, takes effect
immediately.
3.4.3.10.1. Main solver optional input functions
Optional input 
Function name 
Default 

User data 


Maximum order for BDF method 
5 

Maximum order for Adams method 
12 

Maximum no. of internal steps before \(t_{out}\) 
500 

Maximum no. of warnings for \(t_n+h=t_n\) 
10 

Flag to activate stability limit detection 


Initial step size 
estimated 

Minimum absolute step size 
0.0 

Maximum absolute step size 
\(\infty\) 

Value of \(t_{stop}\) 
undefined 

Interpolate at \(t_{stop}\) 


Disable the stop time 
N/A 

Maximum no. of error test failures 
7 

Inequality constraints on solution 

Flag to activate specialized fused kernels 


int CVodeSetUserData(void *cvode_mem, void *user_data)
The function
CVodeSetUserData
specifies the user data blockuser_data
and attaches it to the main CVODE memory block. Arguments:
cvode_mem
– pointer to the CVODE memory block.user_data
– pointer to the user data.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
 Notes:
If specified, the pointer to
user_data
is passed to all usersupplied functions that have it as an argument. Otherwise, aNULL
pointer is passed.Warning
If
user_data
is needed in user linear solver or preconditioner functions, the call toCVodeSetUserData
must be made before the call to specify the linear solver.

int CVodeSetMonitorFn(void *cvode_mem, CVMonitorFn monitorfn)
The function
CVodeSetMonitorFn
specifies a user function,monitorfn
, to be called at some interval of successfully completed CVODE time steps. Arguments:
cvode_mem
– pointer to the CVODE memory block.monitorfn
– usersupplied monitor function (NULL
by default); aNULL
input will turn off monitoring
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
 Notes:
The frequency with which the monitor function is called can be set with the function
CVodeSetMonitorFrequency
.Warning
Modifying the solution in this function will result in undefined behavior. This function is only intended to be used for monitoring the integrator. SUNDIALS must be built with the CMake option
SUNDIALS_BUILD_WITH_MONITORING
, to utilize this function. See §1.1 for more information.

int CVodeSetMonitorFrequency(void *cvode_mem, long int nst)
The function
CVodeSetMonitorFrequency
specifies the interval, measured in successfully completed CVODE timesteps, at which the monitor function should be called. Arguments:
cvode_mem
– pointer to the CVODE memory block.nst
– number of successful steps inbetween calls to the monitor function 0 by default; a 0 input will turn off monitoring.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initializedCVodeCreate()
.
 Notes:
The monitor function that will be called can be set with
CVodeSetMonitorFn
.Warning
Modifying the solution in this function will result in undefined behavior. This function is only intended to be used for monitoring the integrator. SUNDIALS must be built with the CMake option
SUNDIALS_BUILD_WITH_MONITORING
, to utilize this function. See §1.1 for more information.

int CVodeSetMaxOrd(void *cvode_mem, int maxord)
The function
CVodeSetMaxOrd
specifies the maximum order of the linear multistep method. Arguments:
cvode_mem
– pointer to the CVODE memory block.maxord
– value of the maximum method order. This must be positive.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.CV_ILL_INPUT
– The specified valuemaxord
is \(\leq 0\), or larger than its previous value.
 Notes:
The default value is
ADAMS_Q_MAX = 12
for the AdamsMoulton method andBDF_Q_MAX = 5
for the BDF method. Sincemaxord
affects the memory requirements for the internal CVODE memory block, its value cannot be increased past its previous value.An input value greater than the default will result in the default value.

int CVodeSetMaxNumSteps(void *cvode_mem, long int mxsteps)
The function
CVodeSetMaxNumSteps
specifies the maximum number of steps to be taken by the solver in its attempt to reach the next output time. Arguments:
cvode_mem
– pointer to the CVODE memory block.mxsteps
– maximum allowed number of steps.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
 Notes:
Passing
mxsteps
= 0 results in CVODE using the default value (500).Passing
mxsteps
< 0 disables the test (not recommended).

int CVodeSetMaxHnilWarns(void *cvode_mem, int mxhnil)
The function
CVodeSetMaxHnilWarns
specifies the maximum number of messages issued by the solver warning that \(t+h=t\) on the next internal step. Arguments:
cvode_mem
– pointer to the CVODE memory block.mxhnil
– maximum number of warning messages \((> 0)\).
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
 Notes:
The default value is 10. A negative value for
mxhnil
indicates that no warning messages should be issued.

int CVodeSetStabLimDet(void *cvode_mem, sunbooleantype stldet)
The function
CVodeSetStabLimDet
indicates if the BDF stability limit detection algorithm should be used. See §3.2.4 for further details. Arguments:
cvode_mem
– pointer to the CVODE memory block.stldet
– flag controlling stability limit detection (SUNTRUE
= on;SUNFALSE
= off)
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.CV_ILL_INPUT
– The linear multistep method is not set toCV_BDF
.
 Notes:
The default value is
SUNFALSE
. Ifstldet = SUNTRUE
when BDF is used and the method order is greater than or equal to 3, then an internal function,CVsldet
, is called to detect a possible stability limit. If such a limit is detected, then the order is reduced.

int CVodeSetInitStep(void *cvode_mem, sunrealtype hin)
The function
CVodeSetInitStep
specifies the initial step size. Arguments:
cvode_mem
– pointer to the CVODE memory block.hin
– value of the initial step size to be attempted. Pass 0.0 to use the default value.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
 Notes:
By default, CVODE estimates the initial step size to be the solution \(h\) of the equation \(0.5 h^2 \ddot{y} = 1\), where \(\ddot{y}\) is an estimated second derivative of the solution at \(t_0\).

int CVodeSetMinStep(void *cvode_mem, sunrealtype hmin)
The function
CVodeSetMinStep
specifies a lower bound on the magnitude of the step size. Arguments:
cvode_mem
– pointer to the CVODE memory block.hmin
– minimum absolute value of the step size \((\geq 0.0)\).
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.CV_ILL_INPUT
– Eitherhmin
is nonpositive or it exceeds the maximum allowable step size.
 Notes:
The default value is 0.0.

int CVodeSetMaxStep(void *cvode_mem, sunrealtype hmax)
The function
CVodeSetMaxStep
specifies an upper bound on the magnitude of the step size. Arguments:
cvode_mem
– pointer to the CVODE memory block.hmax
– maximum absolute value of the step size \(( \geq 0.0 )\).
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.CV_ILL_INPUT
– Eitherhmax
is nonpositive or it is smaller than the minimum allowable step size.
 Notes:
Pass
hmax
= 0.0 to obtain the default value \(\infty\).

int CVodeSetStopTime(void *cvode_mem, sunrealtype tstop)
The function
CVodeSetStopTime
specifies the value of the independent variable \(t\) past which the solution is not to proceed. Arguments:
cvode_mem
– pointer to the CVODE memory block.tstop
– value of the independent variable past which the solution should not proceed.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.CV_ILL_INPUT
– The value oftstop
is not beyond the current \(t\) value, \(t_n\).
 Notes:
The default, if this routine is not called, is that no stop time is imposed.
Once the integrator returns at a stop time, any future testing for
tstop
is disabled (and can be reenabled only though a new call toCVodeSetStopTime
).A stop time not reached before a call to
CVodeReInit()
will remain active but can be disabled by callingCVodeClearStopTime()
.

int CVodeSetInterpolateStopTime(void *cvode_mem, sunbooleantype interp)
The function
CVodeSetInterpolateStopTime
specifies that the output solution should be interpolated when the current \(t\) equals the specifiedtstop
(instead of merely copying the internal solution \(y_n\)). Arguments:
cvode_mem
– pointer to the CVODES memory block.interp
– flag indicating to use interpolation (1) or copy (0).
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODES memory block was not initialized through a previous call toCVodeCreate()
.
Added in version 6.6.0.

int CVodeClearStopTime(void *cvode_mem)
Disables the stop time set with
CVodeSetStopTime()
. Arguments:
cvode_mem
– pointer to the CVODE memory block.
 Return value:
CV_SUCCESS
if successfulCV_MEM_NULL
if the CVODE memory isNULL
 Notes:
The stop time can be reenabled though a new call to
CVodeSetStopTime()
.
Added in version 6.5.1.

int CVodeSetMaxErrTestFails(void *cvode_mem, int maxnef)
The function
CVodeSetMaxErrTestFails
specifies the maximum number of error test failures permitted in attempting one step. Arguments:
cvode_mem
– pointer to the CVODE memory block.maxnef
– maximum number of error test failures allowed on one step \((> 0)\).
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
 Notes:
The default value is 7.

int CVodeSetConstraints(void *cvode_mem, N_Vector constraints)
The function
CVodeSetConstraints
specifies a vector defining inequality constraints for each component of the solution vector y. Arguments:
cvode_mem
– pointer to the CVODE memory block.constraints
– vector of constraint flags. Ifconstraints[i]
is0.0 then no constraint is imposed on \(y_i\).
1.0 then \(y_i\) will be constrained to be \(y_i \ge 0.0\).
1.0 then \(y_i\) will be constrained to be \(y_i \le 0.0\).
2.0 then \(y_i\) will be constrained to be \(y_i > 0.0\).
2.0 then \(y_i\) will be constrained to be \(y_i < 0.0\).
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
CV_ILL_INPUT
– The constraints vector contains illegal values.
 Notes:
The presence of a non
NULL
constraints vector that is not 0.0 in all components will cause constraint checking to be performed. However, a call with 0.0 in all components ofconstraints
will result in an illegal input return. ANULL
constraints vector will disable constraint checking.

int CVodeSetUseIntegratorFusedKernels(void *cvode_mem, sunbooleantype onoff)
The function
CVodeSetUseIntegratorFusedKernels
informs CVODE that it should use specialized fused kernels internally, if available. The specialized kernels may offer performance improvements for small problem sizes. Users should beware that these kernels can cause changes in the behavior of the integrator. By default, these kernels are not used. Must be called afterCVodeInit()
. Arguments:
cvode_mem
– pointer to the CVODE memory block.onoff
– boolean flag to turn on the specialized kernels (SUNTRUE
), or to turn them off (SUNFALSE
).
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
 Notes:
SUNDIALS must be compiled appropriately for specialized kernels to be available. The CMake option
SUNDIALS_BUILD_PACKAGE_FUSED_KERNELS
must be set toON
when SUNDIALS is compiled. See the entry for this option in §1.2.2 for more information. Currently, the fused kernels are only supported when using CVODE with the NVECTOR_CUDA and NVECTOR_HIP implementations of theN_Vector
.
3.4.3.10.2. Linear solver interface optional input functions
Optional input 
Function name 
Default 

Max allowed \(\gamma\) change without a linear solver setup 
0.3 

Max allowed \(\gamma\) change to update the Jacobian / preconditioner after a NLS failure 
0.2 

Linear solver setup frequency 
20 

Jacobian / preconditioner update frequency 
51 

Jacobian function 
DQ 

Linear System function 
internal 

Enable or disable linear solution scaling 
on 

Jacobiantimesvector functions 
NULL, DQ 

Jacobiantimesvector DQ RHS function 
NULL 

Preconditioner functions 
NULL, NULL 

Ratio between linear and nonlinear tolerances 
0.05 

Newton linear solve tolerance conversion factor 
vector length 
The mathematical explanation of the linear solver methods available to CVODE is provided in §3.2.1. We group the usercallable routines into four categories: general routines concerning the overall CVLS linear solver interface, optional inputs for matrixbased linear solvers, optional inputs for matrixfree linear solvers, and optional inputs for iterative linear solvers. We note that the matrixbased and matrixfree groups are mutually exclusive, whereas the “iterative” tag can apply to either case.
As discussed in §3.2.1, CVODE strives to reuse matrix and preconditioner data for as many solves as possible to amortize the high costs of matrix construction and factorization. To that end, CVODE provides usercallable routines to modify this behavior. Recall that the Newton system matrices are \(M(t,y) = I  \gamma J(t,y)\), where the righthand side function has Jacobian matrix \(J(t,y) = \dfrac{\partial f(t,y)}{\partial y}\).
The matrix or preconditioner for \(M\) can only be updated within a
call to the linear solver ‘setup’ routine. In general, the frequency
with which this setup routine is called may be controlled with the msbp
argument to CVodeSetLSetupFrequency()
. When this occurs, the validity of \(M\) for successive
time steps intimately depends on whether the corresponding
\(\gamma\) and \(J\) inputs remain valid.
At each call to the linear solver setup routine the decision to update \(M\) with a new value of \(\gamma\), and to reuse or reevaluate Jacobian information, depends on several factors including:
the success or failure of previous solve attempts,
the success or failure of the previous time step attempts,
the change in \(\gamma\) from the value used when constructing \(M\), and
the number of steps since Jacobian information was last evaluated.
Jacobian information is considered outofdate when \(msbj\) or more steps
have been completed since the last update, in which case it will be recomputed during the next
linear solver setup call. The value of \(msbj\) is controlled with the
msbj
argument to CVodeSetJacEvalFrequency()
.
For linearsolvers with usersupplied
preconditioning the above factors are used to determine whether to recommend
updating the Jacobian information in the preconditioner (i.e., whether to set
jok
to SUNFALSE
in calling the usersupplied preconditioner setup
function. For matrixbased linear solvers
these factors determine whether the matrix
\(J(t,y) = \dfrac{\partial f(t,y)}{\partial y}\)
should be updated (either with an internal finite
difference approximation or a call to the usersupplied Jacobian function; if not then the previous value is reused and the system matrix
\(M(t,y) \approx I  \gamma J(t,y)\) is recomputed using the current
\(\gamma\) value.

int CVodeSetDeltaGammaMaxLSetup(void *cvode_mem, sunrealtype dgmax_lsetup)
The function
CVodeSetDeltaGammaMaxLSetup
specifies the maximum allowed \(\gamma\) change that does not require a linear solver setup call. Ifgamma_current / gamma_previous  1 > dgmax_lsetup
, the linear solver setup function is called.If
dgmax_lsetup
is \(< 0\), the default value (0.3) will be used. Arguments:
cvode_mem
– pointer to the CVODE memory block.dgmax_lsetup
– the \(\gamma\) change threshold.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
Added in version 6.2.0.

int CVodeSetDeltaGammaMaxBadJac(void *cvode_mem, sunrealtype dgmax_jbad)
The function
CVodeSetDeltaGammaMaxBadJac
specifies the maximum allowed \(\gamma\) change after a NLS failure that requires updating the Jacobian / preconditioner. Ifgamma_current < dgmax_jbad
, the Jacobian evaluation and/or preconditioner setup functions will be called.Positive values of
dgmax_jbad
specify the threshold, all other values will result in using the default value (0.2). Arguments:
cvode_mem
– pointer to the CVODE memory block.dgmax_jbad
– the \(\gamma\) change threshold.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
Added in version 6.2.0.

int CVodeSetLSetupFrequency(void *cvode_mem, long int msbp)
The function
CVodeSetLSetupFrequency
specifies the frequency of calls to the linear solver setup function. Arguments:
cvode_mem
– pointer to the CVODE memory block.msbp
– the linear solver setup frequency.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.CV_ILL_INPUT
– The frequencymsbp
is negative.
 Notes:
Positive values of
msbp
specify the linear solver setup frequency. For example, an input of1
means the setup function will be called every time step while an input of2
means it will be called called every other time step. Ifmsbp = 0
, the default value of 20 will be used. Otherwise an error is returned.

int CVodeSetJacEvalFrequency(void *cvode_mem, long int msbj)
The function
CVodeSetJacEvalFrequency
Specifies the number of steps after which the Jacobian information is considered outofdate, \(msbj\) from §3.2.1.1. Arguments:
cvode_mem
– pointer to the CVODE memory block.msbj
– the Jacobian recomputation or preconditioner update frequency.
 Return value:
CVLS_SUCCESS
– The optional value has been successfully set.CVLS_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVLS_LMEM_NULL
– The CVLS linear solver interface has not been initialized.CVLS_ILL_INPUT
– The frequencymsbj
is negative.
 Notes:
If
nstlj
is the step number at which the Jacobian information was lasted updated andnst
is the current step number,nst  nstlj >= msbj
indicates the Jacobian information will be updated during the next linear solver setup call.As the Jacobian update frequency is only checked within calls to the linear solver setup routine, Jacobian information may be more than
msbj
steps old when updated depending on when a linear solver setup call occurs. See §3.2.1.1 for more information on when linear solver setups are performed.If
msbj = 0
, the default value of 51 will be used. Otherwise an error is returned.This function must be called after the CVLS linear solver interface has been initialized through a call to
CVodeSetLinearSolver()
.
When using matrixbased linear solver modules, the CVLS solver interface
needs a function to compute an approximation to the Jacobian matrix \(J(t,y)\) or
the linear system \(M = I  \gamma J\). The function to evaluate \(J(t,y)\) must
be of type CVLsJacFn
. The user can supply a Jacobian function, or if using
a SUNMATRIX_DENSE or SUNMATRIX_BAND
matrix \(J\), can use the default internal difference quotient
approximation that comes with the CVLS solver. To specify a usersupplied Jacobian function
jac
, CVLS provides the function CVodeSetJacFn()
. The CVLS
interface passes the pointer user_data
to the Jacobian function. This
allows the user to create an arbitrary structure with relevant problem data and
access it during the execution of the usersupplied Jacobian function, without
using global data in the program. The pointer user_data
may be specified
through CVodeSetUserData()
.

int CVodeSetJacFn(void *cvode_mem, CVLsJacFn jac)
The function
CVodeSetJacFn
specifies the Jacobian approximation function to be used for a matrixbased solver within the CVLS interface. Arguments:
cvode_mem
– pointer to the CVODE memory block.jac
– userdefined Jacobian approximation function.
 Return value:
CVLS_SUCCESS
– The optional value has been successfully set.CVLS_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVLS_LMEM_NULL
– The CVLS linear solver interface has not been initialized.
 Notes:
This function must be called after the CVLS linear solver interface has been initialized through a call to
CVodeSetLinearSolver()
.By default, CVLS uses an internal difference quotient function for the SUNMATRIX_DENSE and SUNMATRIX_BAND modules. If
NULL
is passed tojac
, this default function is used. An error will occur if nojac
is supplied when using other matrix types.
Added in version 4.0.0: Replaces the deprecated function
CVDlsSetJacFn
.
To specify a usersupplied linear system function linsys
, CVLS provides
the function CVodeSetLinSysFn()
. The CVLS interface passes the pointer
user_data
to the linear system function. This allows the user to create an
arbitrary structure with relevant problem data and access it during the
execution of the usersupplied linear system function, without using global data
in the program. The pointer user_data
may be specified through
CVodeSetUserData()
.

int CVodeSetLinSysFn(void *cvode_mem, CVLsLinSysFn linsys)
The function
CVodeSetLinSysFn
specifies the linear system approximation function to be used for a matrixbased solver within the CVLS interface. Arguments:
cvode_mem
– pointer to the CVODE memory block.linsys
– userdefined linear system approximation function.
 Return value:
CVLS_SUCCESS
– The optional value has been successfully set.CVLS_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVLS_LMEM_NULL
– The CVLS linear solver interface has not been initialized.
 Notes:
This function must be called after the CVLS linear solver interface has been initialized through a call to
CVodeSetLinearSolver()
.By default, CVLS uses an internal linear system function leveraging the
SUNMatrix
API to form the system \(M = I  \gamma J\) using either an internal finite difference approximation or usersupplied function to compute the Jacobian. Iflinsys
isNULL
, this default function is used.The function type
CVLsLinSysFn
is described in §3.4.4.6.
When using a matrixbased linear solver the matrix information will be updated
infrequently to reduce matrix construction and, with direct solvers,
factorization costs. As a result the value of \(\gamma\) may not be current and,
with BDF methods, a scaling factor is applied to the solution of the linear
system to account for the lagged value of \(\gamma\). See
§10.3.1 for more details. The function
CVodeSetLinearSolutionScaling()
can be used to disable this scaling when
necessary, e.g., when providing a custom linear solver that updates the matrix
using the current \(\gamma\) as part of the solve.

int CVodeSetLinearSolutionScaling(void *cvode_mem, sunbooleantype onoff)
The function
CVodeSetLinearSolutionScaling()
enables or disables scaling the linear system solution to account for a change in \(\gamma\) in the linear system. For more details see §10.3.1. Arguments:
cvode_mem
– pointer to the CVODE memory block.onoff
– flag to enable (SUNTRUE
) or disable (SUNFALSE
) scaling.
 Return value:
CVLS_SUCCESS
– The flag value has been successfully set.CVLS_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVLS_LMEM_NULL
– The CVLS linear solver interface has not been initialized.CVLS_ILL_INPUT
– The attached linear solver is not matrixbased or the linear multistep method type is not BDF.
 Notes:
This function must be called after the CVLS linear solver interface has been initialized through a call to
CVodeSetLinearSolver
.By default scaling is enabled with matrixbased linear solvers when using BDF methods.
When using matrixfree linear solver modules, the CVLS solver interface requires a function to compute an approximation to the product between the Jacobian matrix \(J(t,y)\) and a vector \(v\). The user can supply a Jacobiantimesvector approximation function or use the default internal difference quotient function that comes with the CVLS interface.
A userdefined Jacobianvector product
function must be of type CVLsJacTimesVecFn
and
can be specified through a call to CVodeSetJacTimes()
(see
§3.4.4.8 for specification details).
The evaluation and processing of any Jacobianrelated data needed by
the user’s Jacobiantimesvector function may be done in the optional
usersupplied function jtsetup
(see §3.4.4.9 for
specification details).
The pointer user_data
received through CVodeSetUserData()
(or
a pointer to NULL
if user_data
was not specified)
is passed to the Jacobiantimesvector setup and product functions, jtsetup
and
jtimes
, each time they are called. This allows the user to
create an arbitrary structure with relevant problem data and access it
during the execution of the usersupplied functions
without using global data in the program.

int CVodeSetJacTimes(void *cvode_mem, CVLsJacTimesSetupFn jtsetup, CVLsJacTimesVecFn jtimes)
The function
CVodeSetJacTimes
specifies the Jacobianvector setup and product functions. Arguments:
cvode_mem
– pointer to the CVODE memory block.jtsetup
– userdefined Jacobianvector setup function of typeCVLsJacTimesSetupFn
.jtimes
– userdefined Jacobianvector product function of typeCVLsJacTimesVecFn
.
 Return value:
CVLS_SUCCESS
– The optional value has been successfully set.CVLS_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVLS_LMEM_NULL
– The CVLS linear solver has not been initialized.CVLS_SUNLS_FAIL
– An error occurred when setting up the system matrixtimesvector routines in theSUNLinearSolver
object used by the CVLS interface.
 Notes:
The default is to use an internal finite difference quotient for
jtimes
and to omitjtsetup
. IfNULL
is passed tojtimes
, these defaults are used. A user may specify nonNULL
jtimes
andNULL
jtsetup
inputs.This function must be called after the CVLS linear solver interface has been initialized through a call to
CVodeSetLinearSolver()
.
Added in version 4.0.0: Replaces the deprecated function
CVSpilsSetJacTimes
.
When using the internal difference quotient the user may optionally supply an
alternative righthand side function for use in the Jacobianvector product
approximation by calling CVodeSetJacTimesRhsFn()
. The alternative righthand
side function should compute a suitable (and differentiable) approximation to
the righthand side function provided to CVodeInit()
. For example, as done in
[46], the alternative function may use lagged values when
evaluating a nonlinearity in the righthand side to avoid differencing a
potentially nondifferentiable factor.

int CVodeSetJacTimesRhsFn(void *cvode_mem, CVRhsFn jtimesRhsFn)
The function
CVodeSetJacTimesRhsFn
specifies an alternative ODE righthand side function for use in the internal Jacobianvector product difference quotient approximation. Arguments:
cvode_mem
– pointer to the CVODE memory block.jtimesRhsFn
– is the C function which computes the alternative ODE righthand side function to use in Jacobianvector product difference quotient approximations. This function has the formf(t, y, ydot, user\_data)
(for full details seeCVRhsFn
).
 Return value:
CVLS_SUCCESS
– The optional value has been successfully set.CVLS_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVLS_LMEM_NULL
– The CVLS linear solver has not been initialized.CVLS_ILL_INPUT
– The internal difference quotient approximation is disabled.
 Notes:
The default is to use the righthand side function provided to
CVodeInit()
in the internal difference quotient. If the input righthand side function isNULL
, the default is used.This function must be called after the CVLS linear solver interface has been initialized through a call to
CVodeSetLinearSolver()
.
When using an iterative linear solver, the user may supply a
preconditioning operator to aid in solution of the system. This
operator consists of two usersupplied functions, psetup
and
psolve
, that are supplied to CVODE using the function
CVodeSetPreconditioner()
. The psetup
function supplied to
this routine should handle evaluation and preprocessing of any
Jacobian data needed by the user’s preconditioner solve function,
psolve
. The user data pointer received through
CVodeSetUserData()
(or a pointer to NULL
if user data was not
specified) is passed to the psetup
and psolve
functions.
This allows the user to create an arbitrary structure with relevant
problem data and access it during the execution of the usersupplied
preconditioner functions without using global data in the program.
Also, as described in §3.2.1, the CVLS interface requires that iterative linear solvers stop when the norm of the preconditioned residual satisfies
where \(\epsilon\) is the nonlinear solver tolerance, and the default
\(\epsilon_L = 0.05\); this value may be modified by the user through
the CVodeSetEpsLin()
function.

int CVodeSetPreconditioner(void *cvode_mem, CVLsPrecSetupFn psetup, CVLsPrecSolveFn psolve)
The function
CVodeSetPreconditioner
specifies the preconditioner setup and solve functions. Arguments:
cvode_mem
– pointer to the CVODE memory block.psetup
– userdefined preconditioner setup function. PassNULL
if no setup is necessary.psolve
– userdefined preconditioner solve function.
 Return value:
CVLS_SUCCESS
– The optional values have been successfully set.CVLS_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVLS_LMEM_NULL
– The CVLS linear solver has not been initialized.CVLS_SUNLS_FAIL
– An error occurred when setting up preconditioning in theSUNLinearSolver
object used by the CVLS interface.
 Notes:
The default is
NULL
for both arguments (i.e., no preconditioning).This function must be called after the CVLS linear solver interface has been initialized through a call to
CVodeSetLinearSolver()
.The function type
CVLsPrecSolveFn
is described in §3.4.4.10.The function type
CVLsPrecSetupFn
is described in §3.4.4.11
Added in version 4.0.0: Replaces the deprecated function
CVSpilsSetPreconditioner
.

int CVodeSetEpsLin(void *cvode_mem, sunrealtype eplifac)
The function
CVodeSetEpsLin
specifies the factor by which the Krylov linear solver’s convergence test constant is reduced from the nonlinear solver test constant. Arguments:
cvode_mem
– pointer to the CVODE memory block.eplifac
– linear convergence safety factor \((\ge 0)\).
 Return value:
CVLS_SUCCESS
– The optional value has been successfully set.CVLS_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVLS_LMEM_NULL
– The CVLS linear solver has not been initialized.CVLS_ILL_INPUT
– The factoreplifac
is negative.
 Notes:
The default value is 0.05.
This function must be called after the CVLS linear solver interface has been initialized through a call to
CVodeSetLinearSolver()
.If
eplifac
= 0.0 is passed, the default value is used.
Added in version 4.0.0: Replaces the deprecated function
CVSpilsSetEpsLin
.

int CVodeSetLSNormFactor(void *cvode_mem, sunrealtype nrmfac)
The function
CVodeSetLSNormFactor
specifies the factor to use when converting from the integrator tolerance (WRMS norm) to the linear solver tolerance (L2 norm) for Newton linear system solves e.g.,tol_L2 = fac * tol_WRMS
. Arguments:
cvode_mem
– pointer to the CVODE memory block.nrmfac
– the norm conversion factor. Ifnrmfac
is:\(> 0\) then the provided value is used.
\(= 0\) then the conversion factor is computed using the vector length, i.e.,
nrmfac = N_VGetLength(y)
(default).\(< 0\) then the conversion factor is computed using the vector dot product, i.e.,
nrmfac = N_VDotProd(v,v)
where all the entries ofv
are one.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
 Notes:
This function must be called after the CVLS linear solver interface has been initialized through a call to
CVodeSetLinearSolver()
.Prior to the introduction of
N_VGetLength
in SUNDIALS v5.0.0 (CVODE v5.0.0) the value ofnrmfac
was computed using the vector dot product i.e., thenrmfac < 0
case.
3.4.3.10.3. Nonlinear solver interface optional input functions
Optional input 
Function name 
Default 

Maximum no. of nonlinear iterations 
3 

Maximum no. of convergence failures 
10 

Coefficient in the nonlinear convergence test 
0.1 

ODE RHS function for nonlinear system evaluations 

The following functions can be called to set optional inputs controlling the nonlinear solver.

int CVodeSetMaxNonlinIters(void *cvode_mem, int maxcor)
The function
CVodeSetMaxNonlinIters
specifies the maximum number of nonlinear solver iterations permitted per step. Arguments:
cvode_mem
– pointer to the CVODE memory block.maxcor
– maximum number of nonlinear solver iterations allowed per step \((> 0)\).
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.CV_MEM_FAIL
– TheSUNNonlinearSolver
module isNULL
.
 Notes:
The default value is 3.

int CVodeSetMaxConvFails(void *cvode_mem, int maxncf)
The function
CVodeSetMaxConvFails
specifies the maximum number of nonlinear solver convergence failures permitted during one step. Arguments:
cvode_mem
– pointer to the CVODE memory block.maxncf
– maximum number of allowable nonlinear solver convergence failures per step \((> 0)\).
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
 Notes:
The default value is 10.

int CVodeSetNonlinConvCoef(void *cvode_mem, sunrealtype nlscoef)
The function
CVodeSetNonlinConvCoef
specifies the safety factor used in the nonlinear convergence test (see §3.2.1). Arguments:
cvode_mem
– pointer to the CVODE memory block.nlscoef
– coefficient in nonlinear convergence test \((> 0)\).
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
 Notes:
The default value is 0.1.

int CVodeSetNlsRhsFn(void *cvode_mem, CVRhsFn f)
The function
CVodeSetNlsRhsFn
specifies an alternative righthand side function for use in nonlinear system function evaluations. Arguments:
cvode_mem
– pointer to the CVODE memory block.f
– is the alternative C function which computes the righthand side function \(f\) in the ODE (for full details seeCVRhsFn
).
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
 Notes:
The default is to use the implicit righthand side function provided to
CVodeInit()
in nonlinear system function evaluations. If the input righthand side function isNULL
, the default is used.When using a nondefault nonlinear solver, this function must be called after
CVodeSetNonlinearSolver()
.
3.4.3.10.4. Time step adaptivity optional input functions
Optional input 
Function name 
Default 

Fixed step size factor bounds \(\eta_{\mathrm{min\_fx}}\) and \(\eta_{\mathrm{max\_fx}}\) 
0 and 1.5 

Largest allowed step size change factor in the first step \(\eta_{\mathrm{max\_fs}}\) 
\(10^4\) 

Largest allowed step size change factor for early steps \(\eta_{\mathrm{max\_es}}\) 
10 

Number of time steps to use the early step size change factor 
10 

Largest allowed step size change factor after a successful step \(\eta_{\mathrm{max\_gs}}\) 
10 

Smallest allowed step size change factor after a successful step \(\eta_{\mathrm{min}}\) 
1.0 

Smallest allowed step size change factor after an error test fail \(\eta_{\mathrm{min\_ef}}\) 
0.1 

Largest allowed step size change factor after multiple error test fails \(\eta_{\mathrm{max\_ef}}\) 
0.2 

Number of error failures necessary for \(\eta_{\mathrm{max\_ef}}\) 
2 

Step size change factor after a nonlinear solver convergence failure \(\eta_{\mathrm{cf}}\) 
0.25 
The following functions can be called to set optional inputs to control the step size adaptivity.
Note
The default values for the step size adaptivity tuning parameters have a long history of success and changing the values is generally discouraged. However, users that wish to experiment with alternative values should be careful to make changes gradually and with testing to determine their effectiveness.

int CVodeSetEtaFixedStepBounds(void *cvode_mem, sunrealtype eta_min_fx, sunrealtype eta_max_fx)
The function
CVodeSetEtaFixedStepBounds
specifies the interval lower (\(\eta_{\mathrm{min\_fx}}\)) and upper (\(\eta_{\mathrm{max\_fx}}\)) bounds in which the step size will remain unchanged i.e., if \(\eta_{\mathrm{min\_fx}} < \eta < \eta_{\mathrm{max\_fx}}\), then \(\eta = 1\).The default values are \(\eta_{\mathrm{min\_fx}} = 0\) and \(\eta_{\mathrm{max\_fx}} = 1.5\)
 Arguments:
cvode_mem
– pointer to the CVODE memory block.eta_min_fx
– value of the lower bound of the fixed step interval. Ifeta_min_fx
is \(< 0\) or \(\geq 1\), the default value is used.eta_max_fx
– value of the upper bound of the fixed step interval. Ifeta_max_fx
is \(< 1\), the default value is used.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
Added in version 6.2.0.

int CVodeSetEtaMaxFirstStep(void *cvode_mem, sunrealtype eta_max_fs)
The function
CVodeSetEtaMaxFirstStep
specifies the maximum step size factor after the first time step, \(\eta_{\mathrm{max\_fs}}\).The default value is \(\eta_{\mathrm{max\_fs}} = 10^4\).
 Arguments:
cvode_mem
– pointer to the CVODE memory block.eta_max_fs
– value of the maximum step size factor after the first time step. Ifeta_max_fs
is \(\leq 1\), the default value is used.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
Added in version 6.2.0.

int CVodeSetEtaMaxEarlyStep(void *cvode_mem, sunrealtype eta_max_es)
The function
CVodeSetEtaMaxEarlyStepEtaMax
specifies the maximum step size factor for steps early in the integration, \(\eta_{\mathrm{max\_es}}\).The default value is \(\eta_{\mathrm{max\_es}} = 10\).
 Arguments:
cvode_mem
– pointer to the CVODE memory block.eta_max_es
– value of the maximum step size factor for early in the integration. Ifeta_max_es
is \(\leq 1\), the default value is used.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
Note
The factor for the first time step is set by
CVodeSetEtaMaxFirstStep()
.The number of time steps that use the early integration maximum step size factor \(\eta_{\mathrm{max\_es}}\) can be set with
CVodeSetNumStepsEtaMaxEarlyStep()
.Added in version 6.2.0.

int CVodeSetNumStepsEtaMaxEarlyStep(void *cvode_mem, long int small_nst)
The function
CVodeSetNumStepsEtaMaxEarlyStep
specifies the number of steps to use the early integration maximum step size factor, \(\eta_{\mathrm{max\_es}}\).The default value is 10.
 Arguments:
cvode_mem
– pointer to the CVODE memory block.small_nst
– value of the maximum step size factor for early in the integration. Ifsmall_nst
is \(< 0\), the default value is used. If thesmall_nst
is 0, then the value set byCVodeSetEtaMax()
is used.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
Note
The factor \(\eta_{\mathrm{max\_es}}\) can be set with
CVodeSetEtaMaxEarlyStep()
.Added in version 6.2.0.

int CVodeSetEtaMax(void *cvode_mem, sunrealtype eta_max_gs)
The function
CVodeSetEtaMax
specifies the maximum step size factor, \(\eta_{\mathrm{max\_gs}}\).The default value is \(\eta_{\mathrm{max\_gs}} = 10\).
 Arguments:
cvode_mem
– pointer to the CVODE memory block.eta_max_gs
– value of the maximum step size factor. Ifeta_max_gs
is \(\leq 1\), the default value is used.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
Note
The factor for the first time step is set by
CVodeSetEtaMaxFirstStep()
.The factor for steps early in the integration is set by
CVodeSetEtaMaxEarlyStep()
.Added in version 6.2.0.

int CVodeSetEtaMin(void *cvode_mem, sunrealtype eta_min)
The function
CVodeSetEtaMin
specifies the minimum step size factor, \(\eta_{\mathrm{min}}\).The default value is \(\eta_{\mathrm{min}} = 1.0\).
 Arguments:
cvode_mem
– pointer to the CVODE memory block.eta_min
– value of the minimum step size factor. Ifeta_min
is \(\leq 0\) or \(\geq 1\), the default value is used.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
Added in version 6.2.0.

int CVodeSetEtaMinErrFail(void *cvode_mem, sunrealtype eta_min_ef)
The function
CVodeSetEtaMinErrFail
specifies the minimum step size factor after an error test failure, \(\eta_{\mathrm{min\_ef}}\).The default value is \(\eta_{\mathrm{min\_ef}} = 0.1\).
 Arguments:
cvode_mem
– pointer to the CVODE memory block.eta_min_ef
– value of the minimum step size factor after an error test failure. Ifeta_min_ef
is \(\leq 0\) or \(\geq 1\), the default value is used.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
Added in version 6.2.0.

int CVodeSetEtaMaxErrFail(void *cvode_mem, sunrealtype eta_max_ef)
The function
CVodeSetEtaMaxErrFail
specifies the maximum step size factor after multiple error test failures, \(\eta_{\mathrm{max\_ef}}\).The default value is \(\eta_{\mathrm{min\_ef}} = 0.2\).
 Arguments:
cvode_mem
– pointer to the CVODE memory block.eta_max_ef
– value of the maximum step size factor after an multiple error test failures. Ifeta_min_ef
is \(\leq 0\) or \(\geq 1\), the default value is used.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
Note
The number of error test failures necessary to enforce the maximum step size factor \(\eta_{\mathrm{min\_ef}}\) can be set with
CVodeSetNumFailsEtaMaxErrFail()
.Added in version 6.2.0.

int CVodeSetNumFailsEtaMaxErrFail(void *cvode_mem, int small_nef)
The function
CVodeSetNumFailsEtaMaxErrFail
specifies the number of error test failures necessary to enforce the maximum step size factor \(\eta_{\mathrm{max\_ef}}\).The default value is 2.
 Arguments:
cvode_mem
– pointer to the CVODE memory block.small_nst
– value of the maximum step size factor for early in the integration. Ifsmall_nst
is \(< 0\), the default value is used. If thesmall_nst
is 0, then the value set byCVodeSetEtaMax()
is used.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
Note
The factor \(\eta_{\mathrm{max\_ef}}\) can be set with
CVodeSetEtaMaxErrFail()
.Added in version 6.2.0.

int CVodeSetEtaConvFail(void *cvode_mem, sunrealtype eta_cf)
The function
CVodeSetEtaConvFail
specifies the step size factor after a nonlinear solver failure \(\eta_{\mathrm{cf}}\).The default value is \(\eta_{\mathrm{cf}} = 0.25\).
 Arguments:
cvode_mem
– pointer to the CVODE memory block.eta_cf
– value of the maximum step size factor after a nonlinear solver failure. Ifeta_cf
is \(\leq 0\) or \(\geq 1\), the default value is used.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
Added in version 6.2.0.
3.4.3.10.5. Rootfinding optional input functions
Optional input 
Function name 
Default 

Direction of zerocrossing 
both 

Disable rootfinding warnings 
none 
The following functions can be called to set optional inputs to control the rootfinding algorithm.

int CVodeSetRootDirection(void *cvode_mem, int *rootdir)
The function
CVodeSetRootDirection
specifies the direction of zerocrossings to be located and returned. Arguments:
cvode_mem
– pointer to the CVODE memory block.rootdir
– state array of lengthnrtfn
, the number of root functions \(g_i\), as specified in the call to the functionCVodeRootInit()
. A value of \(0\) forrootdir[i]
indicates that crossing in either direction for \(g_i\) should be reported. A value of \(+1\) or \(1\) indicates that the solver should report only zerocrossings where \(g_i\) is increasing or decreasing, respectively.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.CV_ILL_INPUT
– rootfinding has not been activated through a call toCVodeRootInit()
.
 Notes:
The default behavior is to monitor for both zerocrossing directions.

int CVodeSetNoInactiveRootWarn(void *cvode_mem)
The function
CVodeSetNoInactiveRootWarn
disables issuing a warning if some root function appears to be identically zero at the beginning of the integration. Arguments:
cvode_mem
– pointer to the CVODE memory block.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
 Notes:
CVODE will not report the initial conditions as a possible zerocrossing (assuming that one or more components \(g_i\) are zero at the initial time). However, if it appears that some \(g_i\) is identically zero at the initial time (i.e., \(g_i\) is zero at the initial time and after the first step), CVODE will issue a warning which can be disabled with this optional input function.
3.4.3.10.6. Projection optional input functions
Optional input 
Function name 
Default 

Enable or disable error estimate projection 


Projection frequency 
1 

Maximum number of projection failures 
10 

Projection solve tolerance 
0.1 

Step size reduction factor after a failed projection 
0.25 
The following functions can be called to set optional inputs to control the projection when solving an IVP with constraints.

int CVodeSetProjErrEst(void *cvode_mem, sunbooleantype onoff)
The function
CVodeSetProjErrEst
enables or disables projection of the error estimate by the projection function. Arguments:
cvode_mem
– is a pointer to the CVODE memory block.onoff
– is a flag indicating if error projection should be enabled (SUNTRUE
) or disabled (SUNFALSE
).
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.CV_PROJ_MEM_NULL
– The projection memory isNULL
i.e., the projection functionality has not been enabled.
Added in version 5.3.0.

int CVodeSetProjFrequency(void *cvode_mem, long int freq)
The function
CVodeSetProjFrequency
specifies the frequency with which the projection is performed. Arguments:
cvode_mem
– is a pointer to the CVODE memory block.freq
– is the frequency with which to perform the projection. The default is 1 (project every step), a value of 0 will disable projection, and a value \(< 0\) will restore the default.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.CV_PROJ_MEM_NULL
– The projection memory isNULL
i.e., the projection functionality has not been enabled.
Added in version 5.3.0.

int CVodeSetMaxNumProjFails(void *cvode_mem, int max_fails)
The function
CVodeSetMaxNumProjFails
specifies the maximum number of projection failures in a step attempt before an unrecoverable error is returned. Arguments:
cvode_mem
– is a pointer to the CVODE memory block.max_fails
– is the maximum number of projection failures. The default is 10 and an input value \(< 1\) will restore the default.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.CV_PROJ_MEM_NULL
– The projection memory isNULL
i.e., the projection functionality has not been enabled.
Added in version 5.3.0.

int CVodeSetEpsProj(void *cvode_mem, sunrealtype eps)
The function
CVodeSetEpsProj
specifies the tolerance for the nonlinear constrained least squares problem solved by the projection function. Arguments:
cvode_mem
– is a pointer to the CVODE memory block.eps
– is the tolerance (default 0.1) for the the nonlinear constrained least squares problem solved by the projection function. A value \(\leq 0\) will restore the default.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.CV_PROJ_MEM_NULL
– The projection memory isNULL
i.e., the projection functionality has not been enabled.
Added in version 5.3.0.

int CVodeSetProjFailEta(void *cvode_mem, sunrealtype eta)
The function
CVodeSetProjFailEta
specifies the time step reduction factor to apply on a projection function failure. Arguments:
cvode_mem
– is a pointer to the CVODE memory block.eps
– is the time step reduction factor to apply on a projection function failure (default 0.25). A value \(\leq 0\) or \(> 1\) will restore the default.
 Return value:
CV_SUCCESS
– The optional value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.CV_PROJ_MEM_NULL
– The projection memory isNULL
i.e., the projection functionality has not been enabled.
Added in version 5.3.0.
3.4.3.11. Interpolated output function
An optional function CVodeGetDky
is available to obtain additional output values.
This function should only be called after a successful return from CVode
as it
provides interpolated values either of \(y\) or of its derivatives
(up to the current order of the integration method) interpolated to any
value of \(t\) in the last internal step taken by CVODE.
The call to the function has the following form:

int CVodeGetDky(void *cvode_mem, sunrealtype t, int k, N_Vector dky)
The function
CVodeGetDky
computes thek
th derivative of the functiony
at timet
, i.e. \(\dfrac{\mathrm d^{k}y}{\mathrm dt^{k}}(t)\), where \(t_n  h_u \leq t \leq t_n\), \(t_n\) denotes the current internal time reached, and \(h_u\) is the last internal step size successfully used by the solver. The user may requestk
= \(0, 1, \ldots, q_u\), where \(q_u\) is the current order (optional outputqlast
). Arguments:
cvode_mem
– pointer to the CVODE memory block.t
– the value of the independent variable at which the derivative is to be evaluated.k
– the derivative order requested.dky
– vector containing the derivative. This vector must be allocated by the user.
 Return value:
CV_SUCCESS
–CVodeGetDky
succeeded.CV_BAD_K
–k
is not in the range \(0, 1, \ldots, q_u\).CV_BAD_T
–t
is not in the interval \([t_n  h_u , t_n]\).CV_BAD_DKY
– Thedky
argument wasNULL
.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
 Notes:
It is only legal to call the function
CVodeGetDky
after a successful return fromCVode()
. SeeCVodeGetCurrentTime()
,CVodeGetLastOrder()
, andCVodeGetLastStep()
in the next section for access to \(t_n\), \(q_u\), and \(h_u\), respectively.
3.4.3.12. Optional output functions
CVODE provides an extensive set of functions that can be used to obtain solver performance information. Table 3.7 lists all optional output functions in CVODE, which are then described in detail in the remainder of this section.
Some of the optional outputs, especially the various counters, can be
very useful in determining how successful the CVODE solver is in
doing its job. For example, the counters nsteps
and nfevals
provide a rough measure of
the overall cost of a given run, and can be compared among runs with
differing input options to suggest which set of options is most
efficient. The ratio nniters/nsteps
measures the performance of the nonlinear solver in
solving the nonlinear systems at each time step; typical values for this
range from 1.1 to 1.8. The ratio njevals/nniters
(in the case of a matrixbased linear
solver), and the ratio npevals/nniters
(in the case of an iterative linear solver)
measure the overall degree of nonlinearity in these systems, and also
the quality of the approximate Jacobian or preconditioner being used.
Thus, for example, njevals/nniters
can indicate if a usersupplied Jacobian is
inaccurate, if this ratio is larger than for the case of the
corresponding internal Jacobian. The ratio nliters/nniters
measures the performance of
the Krylov iterative linear solver, and thus (indirectly) the quality of
the preconditioner.
Optional output 
Function name 

CVODE main solver 

Size of CVODE real and integer workspaces 

Cumulative number of internal steps 

No. of calls to r.h.s. function 

No. of calls to linear solver setup function 

No. of local error test failures that have occurred 

No. of failed steps due to a nonlinear solver failure 

Order used during the last step 

Order to be attempted on the next step 

No. of order reductions due to stability limit detection 

Actual initial step size used 

Step size used for the last step 

Step size to be attempted on the next step 

Current internal time reached by the solver 

Suggested factor for tolerance scaling 

Error weight vector for state variables 

Estimated local error vector 

No. of nonlinear solver iterations 

No. of nonlinear convergence failures 

All CVODE integrator statistics 

CVODE nonlinear solver statistics 

User data pointer 

Array showing roots found 

No. of calls to user root function 

Print all statistics 

Name of constant associated with a return flag 

CVLS linear solver interface 

Stored Jacobian of the ODE RHS function 

Time at which the Jacobian was evaluated 

Step number at which the Jacobian was evaluated 

Size of real and integer workspaces 

No. of Jacobian evaluations 

No. of r.h.s. calls for finite diff. Jacobian[vector] evals. 

No. of linear iterations 

No. of linear convergence failures 

No. of preconditioner evaluations 

No. of preconditioner solves 

No. of Jacobianvector setup evaluations 

No. of Jacobianvector product evaluations 

Get all linear solver statistics in one function call 

Last return from a linear solver function 

Name of constant associated with a return flag 

CVDIAG linear solver interface 

Size of CVDIAG real and integer workspaces 

No. of r.h.s. calls for finite diff. Jacobian evals. 

Last return from a CVDIAG function 

Name of constant associated with a return flag 
3.4.3.12.1. Main solver optional output functions
CVODE provides several usercallable functions that can be used to obtain different quantities that may be of interest to the user, such as solver workspace requirements, solver performance statistics, as well as additional data from the CVODE memory block (a suggested tolerance scaling factor, the error weight vector, and the vector of estimated local errors). Functions are also provided to extract statistics related to the performance of the CVODE nonlinear solver used. As a convenience, additional information extraction functions provide the optional outputs in groups. These optional output functions are described next.

int CVodeGetWorkSpace(void *cvode_mem, long int *lenrw, long int *leniw)
The function
CVodeGetWorkSpace
returns the CVODE real and integer workspace sizes. Arguments:
cvode_mem
– pointer to the CVODE memory block.lenrw
– the number ofsunrealtype
values in the CVODE workspace.leniw
– the number of integer values in the CVODE workspace.
 Return value:
CV_SUCCESS
– The optional output values have been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
 Notes:
In terms of the problem size \(N\), the maximum method order \(\texttt{maxord}\), and the number \(\texttt{nrtfn}\) of root functions (see §3.4.3.7) the actual size of the real workspace, in
sunrealtype
words, is given by the following:base value: \(\texttt{lenrw} = 96 + ( \texttt{maxord} + 5) N_r + 3\texttt{nrtfn}\);
using
CVodeSVtolerances()
: \(\texttt{lenrw} = \texttt{lenrw} + N_r\);with constraint checking (see
CVodeSetConstraints()
): \(\texttt{lenrw} = \texttt{lenrw} + N_r\);
where \(N_r\) is the number of real words in one
N_Vector
(\(\approx N\)).The size of the integer workspace (without distinction between
int
andlong int
words) is given by:base value: \(\texttt{leniw} = 40 + ( \texttt{maxord} + 5)N_i + \texttt{nrtfn}\);
using
CVodeSVtolerances()
: \(\texttt{leniw} = \texttt{leniw} + N_i\);with constraint checking: \(\texttt{lenrw} = \texttt{lenrw} + N_i\);
where \(N_i\) is the number of integer words in one
N_Vector
(= 1 forNVECTOR_SERIAL
and2*npes
forNVECTOR_PARALLEL
andnpes
processors).For the default value of \(\texttt{maxord}\), no rootfinding, no constraints, and without using
CVodeSVtolerances()
, these lengths are given roughly by:For the Adams method: \(\texttt{lenrw} = 96 + 17N\) and \(\texttt{leniw} = 57\)
For the BDF method: \(\texttt{lenrw} = 96 + 10N\) and \(\texttt{leniw} = 50\)

int CVodeGetNumSteps(void *cvode_mem, long int *nsteps)
The function
CVodeGetNumSteps
returns the cumulative number of internal steps taken by the solver (total so far). Arguments:
cvode_mem
– pointer to the CVODE memory block.nsteps
– number of steps taken by CVODE.
 Return value:
CV_SUCCESS
– The optional output value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.

int CVodeGetNumRhsEvals(void *cvode_mem, long int *nfevals)
The function
CVodeGetNumRhsEvals
returns the number of calls to the user’s righthand side function. Arguments:
cvode_mem
– pointer to the CVODE memory block.nfevals
– number of calls to the user’sf
function.
 Return value:
CV_SUCCESS
– The optional output value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
 Notes:
The
nfevals
value returned byCVodeGetNumRhsEvals
does not account for calls made tof
by a linear solver or preconditioner module.

int CVodeGetNumLinSolvSetups(void *cvode_mem, long int *nlinsetups)
The function
CVodeGetNumLinSolvSetups
returns the number of calls made to the linear solver’s setup function. Arguments:
cvode_mem
– pointer to the CVODE memory block.nlinsetups
– number of calls made to the linear solver setup function.
 Return value:
CV_SUCCESS
– The optional output value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.

int CVodeGetNumErrTestFails(void *cvode_mem, long int *netfails)
The function
CVodeGetNumErrTestFails
returns the number of local error test failures that have occurred. Arguments:
cvode_mem
– pointer to the CVODE memory block.netfails
– number of error test failures.
 Return value:
CV_SUCCESS
– The optional output value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.

int CVodeGetNumStepSolveFails(void *cvode_mem, long int *ncnf)
Returns the number of failed steps due to a nonlinear solver failure.
 Arguments:
cvode_mem
– pointer to the CVODE memory block.ncnf
– number of step failures.
 Return value:
CV_SUCCESS
– The optional output value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.

int CVodeGetLastOrder(void *cvode_mem, int *qlast)
The function
CVodeGetLastOrder
returns the integration method order used during the last internal step. Arguments:
cvode_mem
– pointer to the CVODE memory block.qlast
– method order used on the last internal step.
 Return value:
CV_SUCCESS
– The optional output value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.

int CVodeGetCurrentOrder(void *cvode_mem, int *qcur)
The function
CVodeGetCurrentOrder
returns the integration method order to be used on the next internal step. Arguments:
cvode_mem
– pointer to the CVODE memory block.qcur
– method order to be used on the next internal step.
 Return value:
CV_SUCCESS
– The optional output value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.

int CVodeGetLastStep(void *cvode_mem, sunrealtype *hlast)
The function
CVodeGetLastStep
returns the integration step size taken on the last internal step. Arguments:
cvode_mem
– pointer to the CVODE memory block.hlast
– step size taken on the last internal step.
 Return value:
CV_SUCCESS
– The optional output value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.

int CVodeGetCurrentStep(void *cvode_mem, sunrealtype *hcur)
The function
CVodeGetCurrentStep
returns the integration step size to be attempted on the next internal step. Arguments:
cvode_mem
– pointer to the CVODE memory block.hcur
– step size to be attempted on the next internal step.
 Return value:
CV_SUCCESS
– The optional output value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.

int CVodeGetActualInitStep(void *cvode_mem, sunrealtype *hinused)
The function
CVodeGetActualInitStep
returns the value of the integration step size used on the first step. Arguments:
cvode_mem
– pointer to the CVODE memory block.hinused
– actual value of initial step size.
 Return value:
CV_SUCCESS
– The optional output value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
 Notes:
Even if the value of the initial integration step size was specified by the user through a call to
CVodeSetInitStep
, this value might have been changed by CVODE to ensure that the step size is within the prescribed bounds (\(h_min \leq h_0 \leq h_max\)), or to satisfy the local error test condition.

int CVodeGetCurrentTime(void *cvode_mem, sunrealtype *tcur)
The function
CVodeGetCurrentTime
returns the current internal time reached by the solver. Arguments:
cvode_mem
– pointer to the CVODE memory block.tcur
– current internal time reached.
 Return value:
CV_SUCCESS
– The optional output value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.

int CVodeGetNumStabLimOrderReds(void *cvode_mem, long int *nslred)
The function
CVodeGetNumStabLimOrderReds
returns the number of order reductions dictated by the BDF stability limit sdetection algorithm (see §3.2.4). Arguments:
cvode_mem
– pointer to the CVODE memory block.nslred
– number of order reductions due to stability limit detection.
 Return value:
CV_SUCCESS
– The optional output value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
 Notes:
If the stability limit detection algorithm was not initialized (
CVodeSetStabLimDet()
was not called), thennslred
= 0.

int CVodeGetTolScaleFactor(void *cvode_mem, sunrealtype *tolsfac)
The function
CVodeGetTolScaleFactor
returns a suggested factor by which the user’s tolerances should be scaled when too much accuracy has been requested for some internal step. Arguments:
cvode_mem
– pointer to the CVODE memory block.tolsfac
– suggested scaling factor for usersupplied tolerances.
 Return value:
CV_SUCCESS
– The optional output value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.

int CVodeGetErrWeights(void *cvode_mem, N_Vector eweight)
The function
CVodeGetErrWeights
returns the solution error weights at the current time. These are the reciprocals of the \(W_i\) given by (3.6). Arguments:
cvode_mem
– pointer to the CVODE memory block.eweight
– solution error weights at the current time.
 Return value:
CV_SUCCESS
– The optional output value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
Warning
The user must allocate memory for
eweight
.

int CVodeGetEstLocalErrors(void *cvode_mem, N_Vector ele)
The function
CVodeGetEstLocalErrors
returns the vector of estimated local errors. Arguments:
cvode_mem
– pointer to the CVODE memory block.ele
– estimated local errors.
 Return value:
CV_SUCCESS
– The optional output value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
Warning
The user must allocate memory for
ele
.The values returned in
ele
are valid only ifCVode()
returned a nonnegative value.The
ele
vector, togther with theeweight
vector fromCVodeGetErrWeights()
, can be used to determine how the various components of the system contributed to the estimated local error test. Specifically, that error test uses the RMS norm of a vector whose components are the products of the components of these two vectors. Thus, for example, if there were recent error test failures, the components causing the failures are those with largest values for the products, denoted loosely aseweight[i]*ele[i]
.

int CVodeGetIntegratorStats(void *cvode_mem, long int *nsteps, long int *nfevals, long int *nlinsetups, long int *netfails, int *qlast, int *qcur, sunrealtype *hinused, sunrealtype *hlast, sunrealtype *hcur, sunrealtype *tcur)
The function
CVodeGetIntegratorStats
returns the CVODE integrator statistics as a group. Arguments:
cvode_mem
– pointer to the CVODE memory block.nsteps
– number of steps taken by CVODE.nfevals
– number of calls to the user’sf
function.nlinsetups
– number of calls made to the linear solver setup function.netfails
– number of error test failures.qlast
– method order used on the last internal step.qcur
– method order to be used on the next internal step.hinused
– actual value of initial step size.hlast
– step size taken on the last internal step.hcur
– step size to be attempted on the next internal step.tcur
– current internal time reached.
 Return value:
CV_SUCCESS
– The optional output values have been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.

int CVodeGetNumNonlinSolvIters(void *cvode_mem, long int *nniters)
The function
CVodeGetNumNonlinSolvIters
returns the number of nonlinear iterations performed. Arguments:
cvode_mem
– pointer to the CVODE memory block.nniters
– number of nonlinear iterations performed.
 Return value:
CV_SUCCESS
– The optional output values have been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.CV_MEM_FAIL
– TheSUNNonlinearSolver
module isNULL

int CVodeGetNumNonlinSolvConvFails(void *cvode_mem, long int *nncfails)
The function
CVodeGetNumNonlinSolvConvFails
returns the number of nonlinear convergence failures that have occurred. Arguments:
cvode_mem
– pointer to the CVODE memory block.nncfails
– number of nonlinear convergence failures.
 Return value:
CV_SUCCESS
– The optional output value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.

int CVodeGetNonlinSolvStats(void *cvode_mem, long int *nniters, long int *nncfails)
The function
CVodeGetNonlinSolvStats
returns the CVODE nonlinear solver statistics as a group. Arguments:
cvode_mem
– pointer to the CVODE memory block.nniters
– number of nonlinear iterations performed.nncfails
– number of nonlinear convergence failures.
 Return value:
CV_SUCCESS
– The optional output value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.CV_MEM_FAIL
– TheSUNNonlinearSolver
module isNULL

int CVodeGetUserData(void *cvode_mem, void **user_data)
The function
CVodeGetUserData
returns the user data pointer provided toCVodeSetUserData()
. Arguments:
cvode_mem
– pointer to the CVODE memory block.user_data
– memory reference to a user data pointer.
 Return value:
CV_SUCCESS
– The optional output value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
Added in version 6.3.0.

int CVodePrintAllStats(void *cvode_mem, FILE *outfile, SUNOutputFormat fmt)
The function
CVodePrintAllStats
outputs all of the integrator, nonlinear solver, linear solver, and other statistics. Arguments:
cvode_mem
– pointer to the CVODE memory block.outfile
– pointer to output file.fmt
– the output format:SUN_OUTPUTFORMAT_TABLE
– prints a table of valuesSUN_OUTPUTFORMAT_CSV
– prints a commaseparated list of key and value pairs e.g.,key1,value1,key2,value2,...
 Return value:
CV_SUCCESS
– The output was successfully.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.CV_ILL_INPUT
– An invalid formatting option was provided.
Note
The file
scripts/sundials_csv.py
provides python utility functions to read and output the data from a SUNDIALS CSV output file using the key and value pair format.Added in version 6.2.0.

char *CVodeGetReturnFlagName(int flag)
The function
CVodeGetReturnFlagName
returns the name of the CVODE constant corresponding toflag
. Arguments:
flag
– return flag from a CVODE function.
 Return value:
A string containing the name of the corresponding constant
3.4.3.12.2. Rootfinding optional output functions
There are two optional output functions associated with rootfinding.

int CVodeGetRootInfo(void *cvode_mem, int *rootsfound)
The function
CVodeGetRootInfo
returns an array showing which functions were found to have a root. Arguments:
cvode_mem
– pointer to the CVODE memory block.rootsfound
– array of lengthnrtfn
with the indices of the user functions \(g_i\) found to have a root. For \(i=0,\ldots,\texttt{nrtfn}1\),rootsfound[i]
\(\ne 0\) if \(g_i\) has a root, androotsfound[i]
\(= 0\) if not.
 Return value:
CV_SUCCESS
– The optional output values have been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
 Notes:
Note that, for the components \(g_i\) for which a root was found, the sign of
rootsfound[i]
indicates the direction of zerocrossing. A value of +1 indicates that \(g_i\) is increasing, while a value of 1 indicates a decreasing \(g_i\). A value of 0 indicates that either no root was found for \(g_i\), or that \(g_i\) varies in the direction opposite to that indicated byrootdir[i]
in the case thatCVodeSetRootDirection()
was used to only track zerocrossings in one direction.
Warning
The user must allocate memory for the vector
rootsfound
.

int CVodeGetNumGEvals(void *cvode_mem, long int *ngevals)
The function
CVodeGetNumGEvals
returns the cumulative number of calls made to the usersupplied root function \(g\). Arguments:
cvode_mem
– pointer to the CVODE memory block.ngevals
– number of calls made to the user’s function \(g\) thus far.
 Return value:
CV_SUCCESS
– The optional output value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.
3.4.3.12.3. Projection optional output functions
The following optional output functions are available for retrieving information and statistics related the projection when solving an IVP with constraints.

int CVodeGetNumProjEvals(void *cvode_mem, long int *nproj)
The function
CVodeGetNumProjEvals
returns the current total number of projection evaluations. Arguments:
cvode_mem
– pointer to the CVODE memory block.nproj
– the number of calls to the projection function.
 Return value:
CV_SUCCESS
– The optional output value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.CV_PROJ_MEM_NULL
– The projection memory isNULL
i.e., the projection functionality has not been enabled.
Added in version 5.3.0.

int CVodeGetNumProjFails(void *cvode_mem, long int *npfails)
The function
CVodeGetNumProjFails
returns the current total number of projection evaluation failures. Arguments:
cvode_mem
– pointer to the CVODE memory block.npfails
– the number of projection failures.
 Return value:
CV_SUCCESS
– The optional output value has been successfully set.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.CV_PROJ_MEM_NULL
– The projection memory isNULL
, i.e., the projection functionality has not been enabled.
Added in version 5.3.0.
3.4.3.12.4. CVLS linear solver interface optional output functions
The following optional outputs are available from the CVLS modules:
workspace requirements, number of calls to the Jacobian routine, number
of calls to the righthand side routine for finitedifference Jacobian
or Jacobianvector product approximation, number of linear iterations,
number of linear convergence failures, number of calls to the
preconditioner setup and solve routines, number of calls to the
Jacobianvector setup and product routines, and last return value from a
linear solver function. Note that, where the name of an output would
otherwise conflict with the name of an optional output from the main
solver, a suffix (for Linear Solver) has been added (e.g. lenrwLS
).

int CVodeGetJac(void *cvode_mem, SUNMatrix *J)
Returns the internally stored copy of the Jacobian matrix of the ODE righthand side function.
 Parameters:
cvode_mem – the CVODE memory structure
J – the Jacobian matrix
 Return values:
CVLS_SUCCESS – the output value has been successfully set
CVLS_MEM_NULL –
cvode_mem
wasNULL
CVLS_LMEM_NULL – the linear solver interface has not been initialized
Warning
This function is provided for debugging purposes and the values in the returned matrix should not be altered.

int CVodeGetJacTime(void *cvode_mem, sunrealtype *t_J)
Returns the time at which the internally stored copy of the Jacobian matrix of the ODE righthand side function was evaluated.
 Parameters:
cvode_mem – the CVODE memory structure
t_J – the time at which the Jacobian was evaluated
 Return values:
CVLS_SUCCESS – the output value has been successfully set
CVLS_MEM_NULL –
cvode_mem
wasNULL
CVLS_LMEM_NULL – the linear solver interface has not been initialized

int CVodeGetJacNumSteps(void *cvode_mem, long int *nst_J)
Returns the value of the internal step counter at which the internally stored copy of the Jacobian matrix of the ODE righthand side function was evaluated.
 Parameters:
cvode_mem – the CVODE memory structure
nst_J – the value of the internal step counter at which the Jacobian was evaluated
 Return values:
CVLS_SUCCESS – the output value has been successfully set
CVLS_MEM_NULL –
cvode_mem
wasNULL
CVLS_LMEM_NULL – the linear solver interface has not been initialized

int CVodeGetLinWorkSpace(void *cvode_mem, long int *lenrwLS, long int *leniwLS)
The function
CVodeGetLinWorkSpace
returns the sizes of the real and integer workspaces used by the CVLS linear solver interface. Arguments:
cvode_mem
– pointer to the CVODE memory block.lenrwLS
– the number ofsunrealtype
values in the CVLS workspace.leniwLS
– the number of integer values in the CVLS workspace.
 Return value:
CVLS_SUCCESS
– The optional output values have been successfully set.CVLS_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVLS_LMEM_NULL
– The CVLS linear solver has not been initialized.
 Notes:
The workspace requirements reported by this routine correspond only to memory allocated within this interface and to memory allocated by the
SUNLinearSolver
object attached to it. The template Jacobian matrix allocated by the user outside of CVLS is not included in this report.
Added in version 4.0.0: Replaces the deprecated functions
CVDlsGetWorkspace
andCVSpilsGetWorkspace
.

int CVodeGetNumJacEvals(void *cvode_mem, long int *njevals)
The function
CVodeGetNumJacEvals
returns the number of calls made to the CVLS Jacobian approximation function. Arguments:
cvode_mem
– pointer to the CVODE memory block.njevals
– the number of calls to the Jacobian function.
 Return value:
CVLS_SUCCESS
– The optional output value has been successfully set.CVLS_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVLS_LMEM_NULL
– The CVLS linear solver has not been initialized.
Added in version 4.0.0: Replaces the deprecated function
CVDlsGetNumJacEvals
.

int CVodeGetNumLinRhsEvals(void *cvode_mem, long int *nfevalsLS)
The function
CVodeGetNumLinRhsEvals
returns the number of calls made to the usersupplied righthand side function due to the finite difference Jacobian approximation or finite difference Jacobianvector product approximation. Arguments:
cvode_mem
– pointer to the CVODE memory block.nfevalsLS
– the number of calls made to the usersupplied righthand side function.
 Return value:
CVLS_SUCCESS
– The optional output value has been successfully set.CVLS_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVLS_LMEM_NULL
– The CVLS linear solver has not been initialized.
 Notes:
The value
nfevalsLS
is incremented only if one of the default internal difference quotient functions is used.
Added in version 4.0.0: Replaces the deprecated functions
CVDlsGetNumRhsEvals
andCVSpilsGetNumRhsEvals
.

int CVodeGetNumLinIters(void *cvode_mem, long int *nliters)
The function
CVodeGetNumLinIters
returns the cumulative number of linear iterations. Arguments:
cvode_mem
– pointer to the CVODE memory block.nliters
– the current number of linear iterations.
 Return value:
CVLS_SUCCESS
– The optional output value has been successfully set.CVLS_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVLS_LMEM_NULL
– The CVLS linear solver has not been initialized.
Added in version 4.0.0: Replaces the deprecated function
CVSpilsGetNumLinIters
.

int CVodeGetNumLinConvFails(void *cvode_mem, long int *nlcfails)
The function
CVodeGetNumLinConvFails
returns the cumulative number of linear convergence failures. Arguments:
cvode_mem
– pointer to the CVODE memory block.nlcfails
– the current number of linear convergence failures.
 Return value:
CVLS_SUCCESS
– The optional output value has been successfully set.CVLS_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVLS_LMEM_NULL
– The CVLS linear solver has not been initialized.
Added in version 4.0.0: Replaces the deprecated function
CVSpilsGetNumConvFails
.

int CVodeGetNumPrecEvals(void *cvode_mem, long int *npevals)
The function
CVodeGetNumPrecEvals
returns the number of preconditioner evaluations, i.e., the number of calls made topsetup
withjok = SUNFALSE
. Arguments:
cvode_mem
– pointer to the CVODE memory block.npevals
– the current number of calls topsetup
.
 Return value:
CVLS_SUCCESS
– The optional output value has been successfully set.CVLS_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVLS_LMEM_NULL
– The CVLS linear solver has not been initialized.
Added in version 4.0.0: Replaces the deprecated function
CVSpilsGetNumPrecEvals
.

int CVodeGetNumPrecSolves(void *cvode_mem, long int *npsolves)
The function
CVodeGetNumPrecSolves
returns the cumulative number of calls made to the preconditioner solve function,psolve
. Arguments:
cvode_mem
– pointer to the CVODE memory block.npsolves
– the current number of calls topsolve
.
 Return value:
CVLS_SUCCESS
– The optional output value has been successfully set.CVLS_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVLS_LMEM_NULL
– The CVLS linear solver has not been initialized.

int CVodeGetNumJTSetupEvals(void *cvode_mem, long int *njtsetup)
The function
CVodeGetNumJTSetupEvals
returns the cumulative number of calls made to the Jacobianvector setup functionjtsetup
. Arguments:
cvode_mem
– pointer to the CVODE memory block.njtsetup
– the current number of calls tojtsetup
.
 Return value:
CVLS_SUCCESS
– The optional output value has been successfully set.CVLS_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVLS_LMEM_NULL
– The CVLS linear solver has not been initialized.

int CVodeGetNumJtimesEvals(void *cvode_mem, long int *njvevals)
The function
CVodeGetNumJtimesEvals
returns the cumulative number of calls made to the Jacobianvector functionjtimes
. Arguments:
cvode_mem
– pointer to the CVODE memory block.njvevals
– the current number of calls tojtimes
.
 Return value:
CVLS_SUCCESS
– The optional output value has been successfully set.CVLS_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVLS_LMEM_NULL
– The CVLS linear solver has not been initialized.

int CVodeGetLinSolveStats(void *cvode_mem, long int *njevals, long int *nfevalsLS, long int *nliters, long int *nlcfails, long int *npevals, long int *npsolves, long int *njtsetups, long int *njtimes)
The function
CVodeGetLinSolveStats
returns CVODE linear solver statistics. Arguments:
cvode_mem
– pointer to the CVODE memory block.njevals
– the current number of calls to the Jacobian function.nfevalsLS
– the current number of calls made to the usersupplied righthand side function by the linear solver.nliters
– the current number of linear iterations.nlcfails
– the current number of linear convergence failures.npevals
– the current number of calls topsetup
.npsolves
– the current number of calls topsolve
.njtsetup
– the current number of calls tojtsetup
.njtimes
– the current number of calls tojtimes
.
 Return value:
CVLS_SUCCESS
– The optional output value has been successfully set.CVLS_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVLS_LMEM_NULL
– The CVLS linear solver has not been initialized.

int CVodeGetLastLinFlag(void *cvode_mem, long int *lsflag)
The function
CVodeGetLastLinFlag
returns the last return value from a CVLS routine. Arguments:
cvode_mem
– pointer to the CVODE memory block.lsflag
– the value of the last return flag from a CVLS function.
 Return value:
CVLS_SUCCESS
– The optional output value has been successfully set.CVLS_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVLS_LMEM_NULL
– The CVLS linear solver has not been initialized.
 Notes:
If the CVLS setup function failed (i.e.,
CVode()
returnedCV_LSETUP_FAIL
) when using theSUNLINSOL_DENSE
orSUNLINSOL_BAND
modules, then the value oflsflag
is equal to the column index (numbered from one) at which a zero diagonal element was encountered during the LU factorization of the (dense or banded) Jacobian matrix.If the CVLS setup function failed when using another
SUNLinearSolver
module, thenlsflag
will beSUNLS_PSET_FAIL_UNREC
,SUNLS_ASET_FAIL_UNREC
, orSUN_ERR_EXT_FAIL
.If the CVLS solve function failed (i.e.,
CVode()
returnedCV_LSOLVE_FAIL
), thenlsflag
contains the error return flag from theSUNLinearSolver
object, which will be one of:SUN_ERR_ARG_CORRUPTRRUPT
, indicating that theSUNLinearSolver
memory isNULL
;SUNLS_ATIMES_FAIL_UNREC
, indicating an unrecoverable failure in the Jv function;SUNLS_PSOLVE_FAIL_UNREC
, indicating that the preconditioner solve functionpsolve
failed unrecoverably;SUNLS_GS_FAIL
, indicating a failure in the GramSchmidt procedure (SPGMR and SPFGMR only);SUNLS_QRSOL_FAIL
, indicating that the matrix R was found to be singular during the QR solve phase (SPGMR and SPFGMR only); orSUN_ERR_EXT_FAIL
, indicating an unrecoverable failure in an external iterative linear solver package.
Added in version 4.0.0: Replaces the deprecated functions
CVDlsGetLastFlag
andCVSpilsGetLastFlag
.

int CVodeGetLinReturnFlagName(long int lsflag)
The function
CVodeGetLinReturnFlagName
returns the name of the CVLS constant corresponding tolsflag
. Arguments:
lsflag
– a return flag from aCVLS
function.
 Return value:
The return value is a string containing the name of the corresponding constant. If \(1 \leq \text{lsflag} \leq N\) (LU factorization failed), this routine returns “NONE”.
Added in version 4.0.0: Replaces the deprecated functions
CVDlsGetReturnFlagName
andCVSpilsGetReturnFlagName
.
3.4.3.12.5. Diagonal linear solver interface optional output functions
The following optional outputs are available from the CVDIAG module:
workspace requirements, number of calls to the righthand side routine
for finitedifference Jacobian approximation, and last return value from
a CVDIAG function. Note that, where the name of an output would
otherwise conflict with the name of an optional output from the main
solver, a suffix (for Linear Solver) has been added here (e.g. lenrwLS
).

int CVDiagGetWorkSpace(void *cvode_mem, long int *lenrwLS, long int *leniwLS)
The function
CVDiagGetWorkSpace
returns the CVDIAG real and integer workspace sizes. Arguments:
cvode_mem
– pointer to the CVODE memory block.lenrwLS
– the number ofsunrealtype
values in the CVDIAG workspace.leniwLS
– the number of integer values in the CVDIAG workspace.
 Return value:
CVDIAG_SUCCESS
– The optional output valus have been successfully set.CVDIAG_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVDIAG_LMEM_NULL
– The CVDIAG linear solver has not been initialized.
 Notes:
In terms of the problem size \(N\), the actual size of the real workspace is roughly \(3 N\)
sunrealtype
words.

int CVDiagGetNumRhsEvals(void *cvode_mem, long int *nfevalsLS)
The function
CVDiagGetNumRhsEvals
returns the number of calls made to the usersupplied righthand side function due to the finite difference Jacobian approximation. Arguments:
cvode_mem
– pointer to the CVODE memory block.nfevalsLS
– the number of calls made to the usersupplied righthand side function.
 Return value:
CVDIAG_SUCCESS
– The optional output value has been successfully set.CVDIAG_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVDIAG_LMEM_NULL
– The CVDIAG linear solver has not been initialized.
 Notes:
The number of diagonal approximate Jacobians formed is equal to the number of calls made to the linear solver setup function (see
CVodeGetNumLinSolvSetups()
).

int CVDiagGetLastFlag(void *cvode_mem, long int *lsflag)
The function
CVDiagGetLastFlag
returns the last return value from a CVDIAG routine. Arguments:
cvode_mem
– pointer to the CVODE memory block.lsflag
– the value of the last return flag from a CVDIAG function.
 Return value:
CVDIAG_SUCCESS
– The optional output value has been successfully set.CVDIAG_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVDIAG_LMEM_NULL
– The CVDIAG linear solver has not been initialized.
 Notes:
If the CVDIAG setup function failed (
CVode()
returnedCV_LSETUP_FAIL
), the value oflsflag
is equal toCVDIAG_INV_FAIL
, indicating that a diagonal element with value zero was encountered. The same value is also returned if the CVDIAG solve function failed (CVode()
returnedCV_LSOLVE_FAIL
).

char *CVDiagGetReturnFlagName(long int lsflag)
The function
CVDiagGetReturnFlagName
returns the name of the CVDIAG constant corresponding tolsflag
. Arguments:
lsflag
– a return flag from aCVDIAG
function.
 Return value:
A string containing the name of the corresponding constant.
3.4.3.13. CVODE reinitialization function
The function CVodeReInit()
reinitializes the main CVODE solver for the solution of
a new problem, where a prior call to CVodeInit()
has been made. The new problem must
have the same size as the previous one. CVodeReInit()
performs the same input checking
and initializations that does, but does no memory allocation, as it
assumes that the existing internal memory is sufficient for the new
problem. A call to CVodeReInit()
deletes the solution history that was stored
internally during the previous integration. Following a successful call
to CVodeReInit()
, call CVode()
again for the solution of the new problem.
The use of CVodeReInit()
requires that the maximum method order, denoted by maxord
, be no
larger for the new problem than for the previous problem. This condition
is automatically fulfilled if the multistep method parameter lmm
is
unchanged (or changed from CV_ADAMS
to CV_BDF
) and the default value for maxord
is specified.
If there are changes to the linear solver specifications, make the appropriate calls to either the linear solver objects themselves, or to the CVLS interface routines, as described in §3.4.3.5. Otherwise, all solver inputs set previously remain in effect.
One important use of the CVodeReInit()
function is in the treating of jump
discontinuities in the RHS function. Except in cases of fairly small
jumps, it is usually more efficient to stop at each point of
discontinuity and restart the integrator with a readjusted ODE model,
using a call to CVodeReInit()
. To stop when the location of the discontinuity is
known, simply make that location a value of tout. To stop when the
location of the discontinuity is determined by the solution, use the
rootfinding feature. In either case, it is critical that the RHS
function not incorporate the discontinuity, but rather have a smooth
extention over the discontinuity, so that the step across it (and
subsequent rootfinding, if used) can be done efficiently. Then use a
switch within the RHS function (communicated through user_data
) that can be
flipped between the stopping of the integration and the restart, so that
the restarted problem uses the new values (which have jumped). Similar
comments apply if there is to be a jump in the dependent variable
vector.

int CVodeReInit(void *cvode_mem, sunrealtype t0, N_Vector y0)
The function
CVodeReInit
provides required problem specifications and reinitializes CVODE. Arguments:
cvode_mem
– pointer to the CVODE memory block.t0
– is the initial value of \(t\).y0
– is the initial value of \(y\).
 Return value:
CV_SUCCESS
– The call was successful.CV_MEM_NULL
– The CVODE memory block was not initialized through a previous call toCVodeCreate()
.CV_NO_MALLOC
– Memory space for the CVODE memory block was not allocated through a previous call toCVodeInit()
.CV_ILL_INPUT
– An input argument was an illegal value.
 Notes:
All previously set options are retained but may be updated by calling the appropriate “Set” functions.
If an error occurred,
CVodeReInit
also sends an error message to the error handler function.
3.4.4. Usersupplied functions
The usersupplied functions consist of one function defining the ODE, (optionally) a function that handles error and warning messages, (optionally) a function that provides the error weight vector, (optionally) one or two functions that provide Jacobianrelated information for the linear solver, and (optionally) one or two functions that define the preconditioner for use in any of the Krylov iterative algorithms.
3.4.4.1. ODE righthand side
The user must provide a function of type defined as follows:

typedef int (*CVRhsFn)(sunrealtype t, N_Vector y, N_Vector ydot, void *user_data);
This function computes the ODE righthand side for a given value of the independent variable \(t\) and state vector \(y\).
 Arguments:
t
– is the current value of the independent variable.y
– is the current value of the dependent variable vector, \(y(t)\).ydot
– is the output vector \(f(t,y)\).user_data
– is theuser_data
pointer passed toCVodeSetUserData()
.
 Return value:
A
CVRhsFn
should return 0 if successful, a positive value if a recoverable error occurred (in which case CVODE will attempt to correct), or a negative value if it failed unrecoverably (in which case the integration is halted andCV_RHSFUNC_FAIL
is returned). Notes:
Allocation of memory for
ydot
is handled within CVODE.A recoverable failure error return from the
CVRhsFn
is typically used to flag a value of the dependent variable \(y\) that is “illegal” in some way (e.g., negative where only a nonnegative value is physically meaningful). If such a return is made, CVODE will attempt to recover (possibly repeating the nonlinear solve, or reducing the step size) in order to avoid this recoverable error return.For efficiency reasons, the righthand side function is not evaluated at the converged solution of the nonlinear solver. Therefore, in general, a recoverable error in that converged value cannot be corrected. (It may be detected when the righthand side function is called the first time during the following integration step, but a successful step cannot be undone.)
There are two other situations in which recovery is not possible even if the righthand side function returns a recoverable error flag. One is when this occurs at the very first call to the
CVRhsFn
(in which case CVODE returnsCV_FIRST_RHSFUNC_ERR
). The other is when a recoverable error is reported byCVRhsFn
after an error test failure, while the linear multistep method order is equal to 1 (in which case CVODE returnsCV_UNREC_RHSFUNC_ERR
).
3.4.4.2. Monitor function
A user may provide a function of type CVMonitorFn
to monitor the integrator progress
throughout a simulation. For example, a user may want to check
integrator statistics as a simulation progresses.

typedef void (*CVMonitorFn)(void *cvode_mem, void *user_data);
This function is used to monitor the CVODE integrator throughout a simulation.
 Arguments:
cvode_mem
– the CVODE memory pointer.user_data
– a pointer to user data, the same as theuser_data
parameter passed toCVodeSetUserData()
.
 Return value:
Should return 0 if successful, or a negative value if unsuccessful.
Warning
This function should only be utilized for monitoring the integrator progress (i.e., for debugging).
3.4.4.3. Error weight function
As an alternative to providing the relative and absolute tolerances, the
user may provide a function of type CVEwtFn
to compute a vector containing the
weights in the WRMS norm
These weights will be used in place of those defined by Eq. (3.6). The function type is defined as follows:

typedef int (*CVEwtFn)(N_Vector y, N_Vector ewt, void *user_data);
This function computes the WRMS error weights for the vector \(y\).
 Arguments:
y
– the value of the dependent variable vector at which the weight vector is to be computed.ewt
– the output vector containing the error weights.user_data
a pointer to user data, the same as theuser_data
parameter passed toCVodeSetUserData()
.
 Return value:
Should return 0 if successful, or 1 if unsuccessful.
 Notes:
Allocation of memory for
ewt
is handled within CVODE.
Warning
The error weight vector must have all components positive. It is the user’s responsiblity to perform this test and return 1 if it is not satisfied.
3.4.4.4. Rootfinding function
If a rootfinding problem is to be solved during the integration of the
ODE system, the user must supply a C function of type CVRootFn
, defined as
follows:

typedef int (*CVRootFn)(sunrealtype t, N_Vector y, sunrealtype *gout, void *user_data);
This function implements a vectorvalued function \(g(t,y)\) such that the roots of the
nrtfn
components \(g_i(t,y)\) are sought. Arguments:
t
– the current value of the independent variable.y
– the current value of the dependent variable vector, \(y(t)\).gout
– the output array of lengthnrtfn
with components \(g_i(t,y)\).user_data
a pointer to user data, the same as theuser_data
parameter passed toCVodeSetUserData()
.
 Return value:
A
CVRootFn
should return 0 if successful or a nonzero value if an error occured (in which case the integration is haled andCVode
returnsCV_RTFUNC_FAIL
. Notes:
Allocation of memory for
gout
is automatically handled within CVODE.
3.4.4.5. Projection function
When solving an IVP with a constraint equation and providing a
userdefined projection operation the projection function must have type
CVProjFn
, defined as follows:

typedef int (*CVProjFn)(sunrealtype t, N_Vector ycur, N_Vector corr, sunrealtype epsProj, N_Vector err, void *user_data);
This function computes the projection of the solution and, if enabled, the error on to the constraint manifold.
 Arguments:
t
– the current value of the independent variable.ycur
– the current value of the dependent variable vector \(y(t)\).corr
– the correction, \(c\), to the dependent variable vector so that \(y(t) + c\) satisfies the constraint equation.epsProj
– the tolerance to use in the nonlinear solver stopping test when solving the nonlinear constrainted least squares problem.err
– is on input the current error estimate, if error projection is enabled (the default) then this should be overwritten with the projected error on output. If error projection is disabled thenerr
isNULL
.user_data
a pointer to user data, the same as theuser_data
parameter passed toCVodeSetUserData()
.
 Return value:
Should return 0 if successful, a negative value if an unrecoverable error occurred (the integration is halted), or a positive value if a recoverable error occurred (the integrator will, in most cases, try to correct and reattempt the step).
 Notes:
The tolerance passed to the projection function (
epsProj
) is the tolerance on the iteration update in the WRMS norm, i.e., the solve should stop when the WRMS norm of the current iterate update is less thanepsProj
.If needed by the user’s projection routine, the error weight vector can be accessed by calling
CVodeGetErrWeights()
, and the unit roundoff is available asSUN_UNIT_ROUNDOFF
defined insundials_types.h
.
Added in version 5.3.0.
3.4.4.6. Jacobian construction (matrixbased linear solvers)
If a matrixbased linear solver module is used (i.e., a nonNULL
SUNMatrix
object was supplied to CVodeSetLinearSolver()
), the user may optionally provide
a function of type CVLsJacFn
for evaluating the Jacobian of the ODE righthand
side function (or an approximation of it). CVLsJacFn
is defined as follows:

typedef int (*CVLsJacFn)(sunrealtype t, N_Vector y, N_Vector fy, SUNMatrix Jac, void *user_data, N_Vector tmp1, N_Vector tmp2, N_Vector tmp3);
This function computes the Jacobian matrix \(J = \dfrac{\partial f}{\partial y}\) (or an approximation to it).
 Arguments:
t
– the current value of the independent variable.y
– the current value of the dependent variable vector, namely the predicted value of \(y(t)\).fy
– the current value of the vector \(f(t,y)\).Jac
– the output Jacobian matrix.user_data
a pointer to user data, the same as theuser_data
parameter passed toCVodeSetUserData()
.tmp1, tmp2, tmp3
– are pointers to memory allocated for variables of typeN_Vector
which can be used by aCVLsJacFn
function as temporary storage or work space.
 Return value:
Should return 0 if successful, a positive value if a recoverable error occurred (in which case CVODE will attempt to correct, while CVLS sets
last_flag
toCVLS_JACFUNC_RECVR
), or a negative value if it failed unrecoverably (in which case the integration is halted,CVode()
returnsCV_LSETUP_FAIL
and CVLS setslast_flag
toCVLS_JACFUNC_UNRECVR
). Notes:
Information regarding the structure of the specific
SUNMatrix
structure (e.g. number of rows, upper/lower bandwidth, sparsity type) may be obtained through using the implementationspecificSUNMatrix
interface functions (see §9 for details).With direct linear solvers (i.e., linear solvers with type
SUNLINEARSOLVER_DIRECT
), the Jacobian matrix \(J(t,y)\) is zeroed out prior to calling the usersupplied Jacobian function so only nonzero elements need to be loaded intoJac
.With the default nonlinear solver (the native SUNDIALS Newton method), each call to the user’s
CVLsJacFn
function is preceded by a call to theCVRhsFn
user function with the same(t,y)
arguments. Thus, the Jacobian function can use any auxiliary data that is computed and saved during the evaluation of the ODE righthand side. In the case of a usersupplied or external nonlinear solver, this is also true if the nonlinear system function is evaluated prior to calling the linear solver setup function.If the user’s
CVLsJacFn
function uses difference quotient approximations, then it may need to access quantities not in the argument list. These include the current step size, the error weights, etc. To obtain these, the user will need to add a pointer tocv_mem
inuser_data
and then use theCVodeGet*
functions described in §3.4.3.12. The unit roundoff can be accessed asSUN_UNIT_ROUNDOFF
defined insundials_types.h
.Dense: A usersupplied dense Jacobian function must load the \(N\) by \(N\) dense matrix
Jac
with an approximation to the Jacobian matrix \(J(t,y)\) at the point \((t, y)\). The accessor macrosSM_ELEMENT_D
andSM_COLUMN_D
allow the user to read and write dense matrix elements without making explicit references to the underlying representation of the SUNMATRIX_DENSE type.SM_ELEMENT_D(J, i, j)
references the \((i, j\text{th})\) element of the dense matrixJac
(with \(i, j = 0\ldots N1\)). This macro is meant for small problems for which efficiency of access is not a major concern. Thus, in terms of the indices \(m\) and \(n\) ranging from 1 to \(N\), the Jacobian element \(J_{m,n}\) can be set using the statementSM_ELEMENT_D(J, m1, n1) =
\(J_{m,n}\). Alternatively,SM_COLUMN_D(J, j)
returns a pointer to the first element of the \(j\)th column ofJac
(with \(j = 0\ldots N1\)), and the elements of the \(j\)th column can then be accessed using ordinary array indexing. Consequently, \(J(m,n)\) can be loaded using the statementscol_n = SM_COLUMN_D(J, n1); col_n[m1] =
\(J(m,n)\). For large problems, it is more efficient to useSM_COLUMN_D
than to useSM_ELEMENT_D
. Note that both of these macros number rows and columns starting from 0. The SUNMATRIX_DENSE type and accessor macros are documented in §9.9.Banded: A usersupplied banded Jacobian function must load the \(N\) by \(N\) banded matrix
Jac
with the elements of the Jacobian \(J(t,y)\) at the point \((t,y)\). The accessor macrosSM_ELEMENT_B
,SM_COLUMN_B
, andSM_COLUMN_ELEMENT_B
allow the user to read and write band matrix elements without making specific references to the underlying representation of the SUNMATRIX_BAND type.SM_ELEMENT_B(J, i, j)
references the \((i,j)\), element of the band matrixJac
, counting from 0. This macro is meant for use in small problems for which efficiency of access is not a major concern. Thus, in terms of the indices \(m\) and \(n\) ranging from 1 to \(N\) with \((m,n)\) within the band defined bymupper
andmlower
, the Jacobian element \(J(m,n)\) can be loaded using the statementSM_ELEMENT_B(J, m1, n1) =
\(J(m,n)\). The elements within the band are those withmupper
\(\le mn \le\)mlower
. Alternatively,SM_COLUMN_B(J, j)
returns a pointer to the diagonal element of the \(j\)th column ofJac
, and if we assign this address tosunrealtype *col_j
, then the \(i\)th element of the \(j\)th column is given bySM_COLUMN_ELEMENT_B(col_j, i, j)
, counting from 0. Thus, for \((m,n)\) within the band, \(J(m,n)\) can be loaded by settingcol_n = SM_COLUMN_B(J, n1); SM_COLUMN_ELEMENT_B(col_n, m1, n1) =
\(J(m,n)\). The elements of the \(j\)th column can also be accessed via ordinary array indexing, but this approach requires knowledge of the underlying storage for a band matrix of type SUNMATRIX_BAND. The arraycol_n
can be indexed frommupper
tomlower
. For large problems, it is more efficient to useSM_COLUMN_B
andSM_COLUMN_ELEMENT_B
than to use theSM_ELEMENT_B
macro. As in the dense case, these macros all number rows and columns starting from 0. The SUNMATRIX_BAND type and accessor macros are documented in §9.12.Sparse: A usersupplied sparse Jacobian function must load the \(N\) by \(N\) compressedsparsecolumn or compressedsparserow matrix
Jac
with an approximation to the Jacobian matrix \(J(t,y)\) at the point \((t,y)\). Storage forJac
already exists on entry to this function, although the user should ensure that sufficient space is allocated inJac
to hold the nonzero values to be set; if the existing space is insufficient the user may reallocate the data and index arrays as needed. The amount of allocated space in a SUNMATRIX_SPARSE object may be accessed using the macroSM_NNZ_S
or the routineSUNSparseMatrix_NNZ
. The SUNMATRIX_SPARSE type and accessor macros are documented in §9.14.
Added in version 4.0.0: Replaces the deprecated type
CVDlsJacFn
.
3.4.4.7. Linear system construction (matrixbased linear solvers)
With matrixbased linear solver modules, as an alternative to optionally
supplying a function for evaluating the Jacobian of the ODE righthand
side function, the user may optionally supply a function of type CVLsLinSysFn
for evaluating the linear system, \(M = I  \gamma J\) (or an
approximation of it). CVLsLinSysFn
is defined as follows:

typedef int (*CVLsLinSysFn)(sunrealtype t, N_Vector y, N_Vector fy, SUNMatrix M, sunbooleantype jok, sunbooleantype *jcur, sunrealtype gamma, void *user_data, N_Vector tmp1, N_Vector tmp2, N_Vector tmp3);
This function computes the linear system matrix \(M = I  \gamma J\) (or an approximation to it).
 Arguments:
t
– the current value of the independent variable.y
– the current value of the dependent variable vector, namely the predicted value of \(y(t)\).fy
– the current value of the vector \(f(t,y)\).M
– the output linear system matrix.jok
– an input flag indicating whether the Jacobianrelated data needs to be updated. Thejok
flag enables reusing of Jacobian data across linear solves however, the user is responsible for storing Jacobian data for reuse.jok = SUNFALSE
means that the Jacobianrelated data must be recomputed from scratch.jok = SUNTRUE
means that the Jacobian data, if saved from the previous call to this function, can be reused (with the current value of \(\gamma\)). A call withjok = SUNTRUE
can only occur after a call withjok = SUNFALSE
.jcur
– a pointer to a flag which should be set toSUNTRUE
if Jacobian data was recomputed, or set toSUNFALSE
if Jacobian data was not recomputed, but saved data was still reused.gamma
– the scalar \(\gamma\) appearing in the matrix \(M = I  \gamma J\).user_data
– a pointer to user data, the same as theuser_data
parameter passed toCVodeSetUserData()
.tmp1, tmp2, tmp3
– are pointers to memory allocated for variables of typeN_Vector
which can be used by aCVLsLinSysFn
function as temporary storage or work space.
 Return value:
Should return 0 if successful, a positive value if a recoverable error occurred (in which case CVODE will attempt to correct, while CVLS sets
last_flag
toCVLS_JACFUNC_RECVR
), or a negative value if it failed unrecoverably (in which case the integration is halted,CVode()
returnsCV_LSETUP_FAIL
and CVLS setslast_flag
toCVLS_JACFUNC_UNRECVR
).
3.4.4.8. Jacobianvector product (matrixfree linear solvers)
If a matrixfree linear solver is to be used (i.e., a NULL
valued
SUNMATRIX was supplied to CVodeSetLinearSolver()
, the user may
provide a function of type CVLsJacTimesVecFn
in the following form,
to compute matrixvector products \(Jv\). If such a function is not supplied,
the default is a difference quotient approximation to these products.

typedef int (*CVLsJacTimesVecFn)(N_Vector v, N_Vector Jv, sunrealtype t, N_Vector y, N_Vector fy, void *user_data, N_Vector tmp);
This function computes the product \(Jv = \dfrac{\partial f(t,y)}{\partial y} v\) (or an approximation to it).
 Arguments:
v
– the vector by which the Jacobian must be multiplied.Jv
– the output vector computed.t
– the current value of the independent variable.y
– the current value of the dependent variable vector.fy
– the current value of the vector \(f(t,y)\).user_data
– a pointer to user data, the same as theuser_data
parameter passed toCVodeSetUserData()
.tmp
– a pointer to memory allocated for a variable of typeN_Vector
which can be used for work space.
 Return value:
The value returned by the Jacobianvector product function should be 0 if successful. Any other return value will result in an unrecoverable error of the generic Krylov solver, in which case the integration is halted.
 Notes:
This function must return a value of \(Jv\) that uses the current value of \(J\), i.e. as evaluated at the current \((t,y)\).
If the user’s
CVLsJacTimesVecFn
function uses difference quotient approximations, it may need to access quantities not in the argument list. These include the current step size, the error weights, etc. To obtain these, the user will need to add a pointer tocvode_mem
touser_data
and then use theCVodeGet*
functions described in §3.4.3.12.1. The unit roundoff can be accessed asSUN_UNIT_ROUNDOFF
defined insundials_types.h
.
Added in version 4.0.0: Replaces the deprecated type
CVSpilsJacTimesVecFn
.
3.4.4.9. Jacobianvector product setup (matrixfree linear solvers)
If the user’s Jacobiantimesvector routine requires that any
Jacobianrelated data be preprocessed or evaluated, then this needs to
be done in a usersupplied function of type CVLsJacTimesSetupFn
, defined as follows:

typedef int (*CVLsJacTimesSetupFn)(sunrealtype t, N_Vector y, N_Vector fy, void *user_data);
This function preprocesses and/or evaluates Jacobianrelated data needed by the Jacobiantimesvector routine.
 Arguments:
t
– the current value of the independent variable.y
– the current value of the dependent variable vector.fy
– the current value of the vector \(f(t,y)\).user_data
– a pointer to user data, the same as theuser_data
parameter passed toCVodeSetUserData()
.
 Return value:
The value returned by the Jacobianvector setup function should be 0 if successful, positive for a recoverable error (in which case the step will be retried), or negative for an unrecoverable error (in which case the integration is halted).
 Notes:
Each call to the Jacobianvector setup function is preceded by a call to the
CVRhsFn
user function with the same \((t,y)\) arguments. Thus, the setup function can use any auxiliary data that is computed and saved during the evaluation of the ODE righthand side.If the user’s
CVLsJacTimesSetupFn
function uses difference quotient approximations, it may need to access quantities not in the argument list. These include the current step size, the error weights, etc. To obtain these, the user will need to add a pointer tocvode_mem
touser_data
and then use theCVodeGet*
functions described in §3.4.3.12.1. The unit roundoff can be accessed asSUN_UNIT_ROUNDOFF
defined insundials_types.h
.
Added in version 4.0.0: Replaces the deprecated type
CVSpilsJacTimesSetupFn
.
3.4.4.10. Preconditioner solve (iterative linear solvers)
If a usersupplied preconditioner is to be used with a SUNLinearSolver
module, then the user must provide a function to solve the linear
system \(Pz = r\), where \(P\) may be either a left or right
preconditioner matrix. Here \(P\) should approximate (at least
crudely) the matrix \(M = I  \gamma J\), where
\(J = \dfrac{\partial f}{\partial y}\). If preconditioning is done on both
sides, the product of the two preconditioner matrices should approximate
\(M\). This function must be of type CVLsPrecSolveFn
, defined as follows:

typedef int (*CVLsPrecSolveFn)(sunrealtype t, N_Vector y, N_Vector fy, N_Vector r, N_Vector z, sunrealtype gamma, sunrealtype delta, int lr, void *user_data);
This function solves the preconditioned system \(Pz = r\).
 Arguments:
t
– the current value of the independent variable.y
– the current value of the dependent variable vector.fy
– the current value of the vector \(f(t,y)\).r
– the righthand side vector of the linear system.z
– the computed output vector.gamma
– the scalar \(gamma\) in the matrix given by \(M=I\gamma J\).delta
– an input tolerance to be used if an iterative method is employed in the solution. In that case, the residual vector \(Res = r  Pz\) of the system should be made less thandelta
in the weighted \(l_2\) norm, i.e., \(\sqrt{\sum_i (Res_i \cdot ewt_i)^2 } <\)delta
. To obtain theN_Vector
ewt
, callCVodeGetErrWeights()
.lr
– an input flag indicating whether the preconditioner solve function is to use the left preconditioner (lr = 1
) or the right preconditioner (lr = 2
).user_data
– a pointer to user data, the same as theuser_data
parameter passed toCVodeSetUserData()
.
 Return value:
The value returned by the preconditioner solve function is a flag indicating whether it was successful. This value should be 0 if successful, positive for a recoverable error (in which case the step will be retried), or negative for an unrecoverable error (in which case the integration is halted).
Added in version 4.0.0: Replaces the deprecated type
CVSpilsPrecSolveFn
.
3.4.4.11. Preconditioner setup (iterative linear solvers)
If the user’s preconditioner requires that any Jacobianrelated data be preprocessed or evaluated, then this needs to be done in a usersupplied function of type , defined as follows:

typedef int (*CVLsPrecSetupFn)(sunrealtype t, N_Vector y, N_Vector fy, sunbooleantype jok, sunbooleantype *jcurPtr, sunrealtype gamma, void *user_data);
This function preprocesses and/or evaluates Jacobianrelated data needed by the preconditioner.
 Arguments:
t
– the current value of the independent variable.y
– the current value of the dependent variable vector, namely the predicted value of \(y(t)\).fy
– the current value of the vector \(f(t,y)\).jok
– an input flag indicating whether the Jacobianrelated data needs to be updated. Thejok
argument provides for the reuse of Jacobian data in the preconditioner solve function.jok = SUNFALSE
means that the Jacobianrelated data must be recomputed from scratch.jok = SUNTRUE
means that the Jacobian data, if saved from the previous call to this function, can be reused (with the current value of \(\gamma\)). A call withjok = SUNTRUE
can only occur after a call withjok = SUNFALSE
.jcur
– a pointer to a flag which should be set toSUNTRUE
if Jacobian data was recomputed, or set toSUNFALSE
if Jacobian data was not recomputed, but saved data was still reused.gamma
– the scalar \(\gamma\) appearing in the matrix \(M = I  \gamma J\).user_data
– a pointer to user data, the same as theuser_data
parameter passed toCVodeSetUserData()
.
 Return value:
The value returned by the preconditioner setup function is a flag indicating whether it was successful. This value should be 0 if successful, positive for a recoverable error (in which case the step will be retried), or negative for an unrecoverable error (in which case the integration is halted).
 Notes:
The operations performed by this function might include forming a crude approximate Jacobian and performing an LU factorization of the resulting approximation to \(M=I  \gamma J\).
With the default nonlinear solver (the native SUNDIALS Newton method), each call to the preconditioner setup function is preceded by a call to the
CVRhsFn
user function with the same \((t,y)\) arguments. Thus, the preconditioner setup function can use any auxiliary data that is computed and saved during the evaluation of the ODE righthand side. In the case of a usersupplied or external nonlinear solver, this is also true if the nonlinear system function is evaluated prior to calling the linear solver setup function (see §11.1.4 for more information).This function is not called in advance of every call to the preconditioner solve function, but rather is called only as often as needed to achieve convergence in the nonlinear solver.
If the user’s
CVLsPrecSetupFn
function uses difference quotient approximations, it may need to access quantities not in the call list. These include the current step size, the error weights, etc. To obtain these, the user will need to add a pointer tocvode_mem
touser_data
and then use theCVodeGet*
functions described in §3.4.3.12. The unit roundoff can be accessed asSUN_UNIT_ROUNDOFF
defined insundials_types.h
.
Added in version 4.0.0: Replaces the deprecated type
CVSpilsPrecSetupFn
.
3.4.5. Preconditioner modules
The efficiency of Krylov iterative methods for the solution of linear systems can be greatly enhanced through preconditioning. For problems in which the user cannot define a more effective, problemspecific preconditioner, CVODE provides a banded preconditioner in the module CVBANDPRE and a bandblockdiagonal preconditioner module CVBBDPRE.
3.4.5.1. A serial banded preconditioner module
This preconditioner provides a band matrix preconditioner for use with
iterative SUNLinearSolver
modules through the CVLS linear solver
interface, in a serial setting. It uses difference quotients of the ODE
righthand side function \(f\) to generate a band matrix of bandwidth
\(m_l + m_u + 1\), where the number of superdiagonals (\(m_u\),
the upper halfbandwidth) and subdiagonals (\(m_l\), the lower
halfbandwidth) are specified by the user, and uses this to form a
preconditioner for use with the Krylov linear solver. Although this
matrix is intended to approximate the Jacobian
\(\dfrac{\partial f}{\partial y}\), it may be a very crude approximation.
The true Jacobian need not be banded, or its true bandwidth may be
larger than \(m_l + m_u + 1\), as long as the banded approximation
generated here is sufficiently accurate to speed convergence as a
preconditioner.
In order to use the CVBANDPRE module, the user need not define any
additional functions. Aside from the header files required for the
integration of the ODE problem (see §3.4.1), to use
the CVBANDPRE module, the main program must include the header file
cvode_bandpre.h
which declares the needed function prototypes.
The following is a summary of the usage of this module. Steps that are
changed from the skeleton program presented in
§3.4.2 are shown in bold.
Initialize multithreaded environment, if appropriate
Create the
SUNContext
object.Set problem dimensions etc.
Set vector of initial values
Create CVODE object
Initialize CVODE solver
Specify integration tolerances
Create linear solver object
When creating the iterative linear solver object, specify the type of preconditioning (
SUN_PREC_LEFT
orSUN_PREC_RIGHT
) to use.Set linear solver optional inputs
Attach linear solver module
Initialize the CVBANDPRE preconditioner module
Specify the upper and lower halfbandwidths (
mu
andml
, respectively) and callflag = CVBandPrecInit(cvode_mem, N, mu, ml);to allocate memory and initialize the internal preconditioner data.
Set optional inputs.
Note that the user should not overwrite the preconditioner setup function or solve function through calls to the
CVodeSetPreconditioner()
optional input function.Create nonlinear solver object
Attach nonlinear solver module
Set nonlinear solver optional inputs
Specify rootfinding problem
Advance solution in time
Get optional outputs
Additional optional outputs associated with CVBANDPRE are available by way of two routines described below,
CVBandPrecGetWorkSpace()
andCVBandPrecGetNumRhsEvals()
.Deallocate memory for solution vector
Free solver memory
Free nonlinear solver memory
Free linear solver memory
Free the SUNContext object
The CVBANDPRE preconditioner module is initialized and attached by calling the following function:

int CVBandPrecInit(void *cvode_mem, sunindextype N, sunindextype mu, sunindextype ml)
The function
CVBandPrecInit
initializes the CVBANDPRE preconditioner and allocates required (internal) memory for it. Arguments:
cvode_mem
– pointer to the CVODE memory block.N
– problem dimension.mu
– upper halfbandwidth of the Jacobian approximation.ml
– lower halfbandwidth of the Jacobian approximation.
 Return value:
CVLS_SUCCESS
– The call toCVBandPrecInit
was successful.CVLS_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVLS_MEM_FAIL
– A memory allocation request has failed.CVLS_LMEM_NULL
– A CVLS linear solver memory was not attached.CVLS_ILL_INPUT
– The supplied vector implementation was not compatible with block band preconditioner.
 Notes:
The banded approximate Jacobian will have nonzero elements only in locations \((i,j)\) with \(\text{ml} \leq ji \leq \text{mu}\).
The following two optional output functions are available for use with the CVBANDPRE module:

int CVBandPrecGetWorkSpace(void *cvode_mem, long int *lenrwBP, long int *leniwBP)
The function
CVBandPrecGetWorkSpace
returns the sizes of the CVBANDPRE real and integer workspaces. Arguments:
cvode_mem
– pointer to the CVODE memory block.lenrwBP
– the number ofsunrealtype
values in teh CVBANDPRE workspace.leniwBP
– the number of integer values in the CVBANDPRE workspace.
 Return value:
CVLS_SUCCESS
– The optional output values have been successfully set.CVLS_PMEM_NULL
– The CVBANDPRE preconditioner has not been initialized.
 Notes:
The workspace requirements reported by this routine correspond only to memory allocated within the CVBANDPRE module (the banded matrix approximation, banded
SUNLinearSolver
object, and temporary vectors).The workspaces referred to here exist in addition to those given by the corresponding function
CVodeGetLinWorkSpace
.

int CVBandPrecGetNumRhsEvals(void *cvode_mem, long int *nfevalsBP)
The function
CVBandPrecGetNumRhsEvals
returns the number of calls made to the usersupplied righthand side function for the finite difference banded Jacobian approximation used within the preconditioner setup function. Arguments:
cvode_mem
– pointer to the CVODE memory block.nfevalsBP
– the number of calls to the user righthand side function.
 Return value:
CVLS_SUCCESS
– The optional output value has been successfully set.CVLS_PMEM_NULL
– The CVBANDPRE preconditioner has not been initialized.
 Notes:
The counter
nfevalsBP
is distinct from the counternfevalsLS
returned by the corresponding functionCVodeGetNumLinRhsEvals()
andnfevals
returned byCVodeGetNumRhsEvals()
.The total number of righthand side function evaluations is the sum of all three of these counters.
3.4.5.2. A parallel bandblockdiagonal preconditioner module
A principal reason for using a parallel ODE solver such as CVODE lies in the solution of partial differential equations (PDEs). Moreover, the use of a Krylov iterative method for the solution of many such problems is motivated by the nature of the underlying linear system of equations (3.7) that must be solved at each time step. The linear algebraic system is large, sparse, and structured. However, if a Krylov iterative method is to be effective in this setting, then a nontrivial preconditioner needs to be used. Otherwise, the rate of convergence of the Krylov iterative method is usually unacceptably slow. Unfortunately, an effective preconditioner tends to be problemspecific.
However, we have developed one type of preconditioner that treats a rather broad class of PDEbased problems. It has been successfully used for several realistic, largescale problems [71] and is included in a software module within the CVODE package. This module works with the parallel vector module NVECTOR_PARALLEL and is usable with any of the Krylov iterative linear solvers through the CVLS interface. It generates a preconditioner that is a blockdiagonal matrix with each block being a band matrix. The blocks need not have the same number of super and subdiagonals and these numbers may vary from block to block. This BandBlockDiagonal Preconditioner module is called CVBBDPRE.
One way to envision these preconditioners is to think of the domain of the computational PDE problem as being subdivided into \(M\) nonoverlapping subdomains. Each of these subdomains is then assigned to one of the \(M\) processes to be used to solve the ODE system. The basic idea is to isolate the preconditioning so that it is local to each process, and also to use a (possibly cheaper) approximate righthand side function. This requires the definition of a new function \(g(t,y)\) which approximates the function \(f(t, y)\) in the definition of the ODE system (3.1). However, the user may set \(g = f\). Corresponding to the domain decomposition, there is a decomposition of the solution vector \(y\) into \(M\) disjoint blocks \(y_m\), and a decomposition of \(g\) into blocks \(g_m\). The block \(g_m\) depends both on \(y_m\) and on components of blocks \(y_{m'}\) associated with neighboring subdomains (socalled ghostcell data). Let \(\bar{y}_m\) denote \(y_m\) augmented with those other components on which \(g_m\) depends. Then we have
and each of the blocks \(g_m(t, \bar{y}_m)\) is uncoupled from the others.
The preconditioner associated with this decomposition has the form
where
and \(J_m\) is a difference quotient approximation to
\(\partial g_m/\partial y_m\). This matrix is taken to be banded, with
upper and lower halfbandwidths mudq
and mldq
defined as
the number of nonzero diagonals above and below the main diagonal,
respectively. The difference quotient approximation is computed using
\(\texttt{mudq} + \texttt{mldq} + 2\) evaluations of \(g_m\), but only a matrix
of bandwidth \(\texttt{mukeep} + \texttt{mlkeep} + 1\) is retained.
Neither pair of parameters need be the true halfbandwidths of the Jacobian of the
local block of \(g\), if smaller values provide a more efficient
preconditioner. The solution of the complete linear system
reduces to solving each of the equations
and this is done by banded LU factorization of \(P_m\) followed by a banded backsolve.
Similar blockdiagonal preconditioners could be considered with different treatments of the blocks \(P_m\). For example, incomplete LU factorization or an iterative method could be used instead of banded LU factorization.
The CVBBDPRE module calls two userprovided functions to construct \(P\):
a required function gloc
(of type CVLocalFn
) which approximates
the righthand side function \(g(t,y) \approx f(t,y)\) and which is computed locally,
and an optional function cfn
(of type CVCommFn
) which performs
all interprocess communication necessary to evaluate the approximate righthand
side \(g\). These are in addition to the usersupplied righthand side function
\(f\). Both functions take as input the same pointer user_data
that is passed
by the user to CVodeSetUserData()
and that was passed to the user’s function \(f\).
The user is responsible for providing space (presumably within user_data
)
for components of \(y\) that are communicated between processes by cfn
, and
that are then used by gloc
, which should not do any communication.

typedef int (*CVLocalFn)(sunindextype Nlocal, sunrealtype t, N_Vector y, N_Vector glocal, void *user_data);
This
gloc
function computes \(g(t,y)\). It loads the vectorglocal
as a function oft
andy
. Arguments:
Nlocal
– the local vector length.t
– the value of the independent variable.y
– the dependent variable.glocal
– the output vector.user_data
– a pointer to user data, the same as theuser_data
parameter passed toCVodeSetUserData()
.
 Return value:
A
CVLocalFn
should return 0 if successful, a positive value if a recoverable error occurred (in which case CVODE will attempt to correct), or a negative value if it failed unrecoverably (in which case the integration is halted andCVode()
returnsCV_LSETUP_FAIL
). Notes:
This function must assume that all interprocess communication of data needed to calculate
glocal
has already been done, and that this data is accessible withinuser_data
.The case where \(g\) is mathematically identical to \(f\) is allowed.

typedef int (*CVCommFn)(sunindextype Nlocal, sunrealtype t, N_Vector y, void *user_data);
This
cfn
function performs all interprocess communication necessary for the execution of thegloc
function above, using the input vectory
. Arguments:
Nlocal
– the local vector length.t
– the value of the independent variable.y
– the dependent variable.user_data
– a pointer to user data, the same as theuser_data
parameter passed toCVodeSetUserData()
.
 Return value:
A
CVCommFn
should return 0 if successful, a positive value if a recoverable error occurred (in which case CVODE will attempt to correct), or a negative value if it failed unrecoverably (in which case the integration is halted andCVode()
returnsCV_LSETUP_FAIL
). Notes:
The
cfn
function is expected to save communicated data in space defined within the data structureuser_data
.Each call to the
cfn
function is preceded by a call to the righthand side function \(f\) with the same \((t,y)\) arguments. Thus,cfn
can omit any communication done by \(f\) if relevant to the evaluation ofglocal
. If all necessary communication was done in \(f\), thencfn = NULL
can be passed in the call toCVBBDPrecInit()
(see below).
Besides the header files required for the integration of the ODE problem
(see §3.4.1), to use the CVBBDPRE module, the main program
must include the header file cvode_bbdpre.h
which declares the needed
function prototypes.
The following is a summary of the usage of this module. Steps that are changed from the skeleton program presented in §3.4.2 are shown in bold.
Initialize MPI environment
Create the
SUNContext
objectSet problem dimensions etc.
Set vector of initial values
Create CVODE object
Initialize CVODE solver
Specify integration tolerances
Create linear solver object
When creating the iterative linear solver object, specify the type of preconditioning (
SUN_PREC_LEFT
orSUN_PREC_RIGHT
) to use.Set linear solver optional inputs
Attach linear solver module
Initialize the CVBBDPRE preconditioner module
Specify the upper and lower halfbandwidths
mudq
andmldq
, andmukeep
andmlkeep
, and callflag = CVBBDPrecInit(&cvode_mem, local_N, mudq, mldq, &mukeep, mlkeep, dqrely, gloc, cfn);to allocate memory and initialize the internal preconditioner data. The last two arguments of
CVBBDPrecInit()
are the two usersupplied functions described above.Set optional inputs
Note that the user should not overwrite the preconditioner setup function or solve function through calls to the
CVodeSetPreconditioner()
optional input function.Create nonlinear solver object
Attach nonlinear solver module
Set nonlinear solver optional inputs
Specify rootfinding problem
Advance solution in time
Get optional outputs
Additional optional outputs associated with CVBBDPRE are available by way of two routines described below,
CVBBDPrecGetWorkSpace()
andCVBBDPrecGetNumGfnEvals()
.Deallocate memory for solution vector
Free solver memory
Free nonlinear solver memory
Free linear solver memory
Free the
SUNContext
objectFinalize MPI
The usercallable functions that initialize or reinitialize the CVBBDPRE preconditioner module are described next.

int CVBBDPrecInit(void *cvode_mem, sunindextype local_N, sunindextype mudq, sunindextype mldq, sunindextype mukeep, sunindextype mlkeep, sunrealtype dqrely, CVLocalFn gloc, CVCommFn cfn)
The function
CVBBDPrecInit
initializes and allocates (internal) memory for the CVBBDPRE preconditioner. Arguments:
cvode_mem
– pointer to the CVODE memory block.local_N
– local vector length.mudq
– upper halfbandwidth to be used in the difference quotient Jacobian approximation.mldq
– lower halfbandwidth to be used in the difference quotient Jacobian approximation.mukeep
– upper halfbandwidth of the retained banded approximate Jacobian block.mlkeep
– lower halfbandwidth of the retained banded approximate Jacobian block.dqrely
– the relative increment in components of \(y\) used in the difference quotient approximations. The default is \(\texttt{dqrely} = \sqrt{\text{unit roundoff}}\), which can be specified by passingdqrely = 0.0
.gloc
– theCVLocalFn
function which computes the approximation \(g(t,y) \approx f(t,y)\).cfn
– theCVCommFn
which performs all interprocess communication required for the computation of \(g(t,y)\).
 Return value:
CVLS_SUCCESS
– The function was successfulCVLS_MEM_NULL
– Thecvode_mem
pointer isNULL
.CVLS_MEM_FAIL
– A memory allocation request has failed.CVLS_LMEM_NULL
– A CVLS linear solver memory was not attached.CVLS_ILL_INPUT
– The supplied vector implementation was not compatible with block band preconditioner.
 Notes:
If one of the halfbandwidths
mudq
ormldq
to be used in the difference quotient calculation of the approximate Jacobian is negative or exceeds the valuelocal_N  1 ``, it is replaced by ``0
orlocal_N  1
accordingly.The halfbandwidths
mudq
andmldq
need not be the true halfbandwidths of the Jacobian of the local block of \(g\) when smaller values may provide a greater efficiency.Also, the halfbandwidths
mukeep
andmlkeep
of the retained banded approximate Jacobian block may be even smaller, to reduce storage and computational costs further.For all four halfbandwidths, the values need not be the same on every processor.
The CVBBDPRE module also provides a reinitialization function to allow
solving a sequence of problems of the same size, with the same linear solver
choice, provided there is no change in local_N
, mukeep
, or mlkeep
.
After solving one problem, and after calling CVodeReInit()
to
reinitialize CVODE for a subsequent problem, a call to CVBBDPrecReInit()
can be made to change any of the following: the halfbandwidths mudq
and
mldq
used in the differencequotient Jacobian approximations, the relative
increment dqrely
, or one of the usersupplied functions gloc
and cfn
.
If there is a change in any of the linear solver inputs, an additional call
to the “set” routines provided by the SUNLinearSolver module, and/or
one or more of the corresponding CVLS “set” functions, must
also be made (in the proper order).

int CVBBDPrecReInit(void *cvode_mem, sunindextype mudq, sunindextype mldq, sunrealtype dqrely)
The function
CVBBDPrecReInit
reinitializes the CVBBDPRE preconditioner. Arguments:
cvode_mem
– pointer to the CVODE memory block.mudq
– upper halfbandwidth to be used in the difference quotient Jacobian approximation.mldq
– lower halfbandwidth to be used in the difference quotient Jacobian approximation.dqrely
– the relative increment in components of
 Return value:
CVLS_SUCCESS
– The function was successfulCVLS_MEM_NULL
– Thecvode_mem
pointer isNULL
.cvode_mem
pointer wasNULL
.CVLS_LMEM_NULL
– A CVLS linear solver memory was not attached.CVLS_PMEM_NULL
– The functionCVBBDPrecInit()
was not previously called
 Notes:
If one of the halfbandwidths
mudq
ormldq
is negative or exceeds the valuelocal_N1
, it is replaced by0
orlocal_N1
accordingly.
The following two optional output functions are available for use with the CVBBDPRE module:

int CVBBDPrecGetWorkSpace(void *cvode_mem, long int *lenrwBBDP, long int *leniwBBDP)
The function
CVBBDPrecGetWorkSpace
returns the local CVBBDPRE real and integer workspace sizes. Arguments:
cvode_mem
– pointer to the CVODE memory block.lenrwBBDP
– local number ofsunrealtype
values in the CVBBDPRE workspace.leniwBBDP
– local number of integer values in the CVBBDPRE workspace.
 Return value:
CVLS_SUCCESS
– The optional output value has been successfully set.CVLS_MEM_NULL
– Thecvode_mem
pointer wasNULL
.CVLS_PMEM_NULL
– The CVBBDPRE preconditioner has not been initialized.
 Notes:
The workspace requirements reported by this routine correspond only to memory allocated within the CVBBDPRE module (the banded matrix approximation, banded
SUNLinearSolver
object, temporary vectors). These values are local to each process. The workspaces referred to here exist in addition to those given by the corresponding functionCVodeGetLinWorkSpace
.

int CVBBDPrecGetNumGfnEvals(void *cvode_mem, long int *ngevalsBBDP)
The function
CVBBDPrecGetNumGfnEvals
returns the number of calls made to the usersuppliedgloc
function due to the finite difference approximation of the Jacobian blocks used within the preconditioner setup function. Arguments:
cvode_mem
– pointer to the CVODE memory block.ngevalsBBDP
– the number of calls made to the usersuppliedgloc
function due to the finite difference approximation of the Jacobian blocks used within the preconditioner setup function.
 Return value:
CVLS_SUCCESS
– The optional output value has been successfully set.CVLS_MEM_NULL
– Thecvode_mem
pointer wasNULL
.CVLS_PMEM_NULL
– The CVBBDPRE preconditioner has not been initialized.
In addition to the ngevalsBBDP
gloc
evaluations,
the costs associated with CVBBDPRE also include nlinsetups
LU
factorizations, nlinsetups
calls to cfn
, npsolves
banded
backsolve calls, and nfevalsLS
righthand side function evaluations,
where nlinsetups
is an optional CVODE output and npsolves
and
nfevalsLS
are linear solver optional outputs (see §3.4.3.12).