acor · active · atol · atolscale · cache_efficient · condition_order · current_method · dae_init_dteps · debug_event · dstates · error_weights · event · event_queue_info · f · fixed_step · jacobian · maxorder · maxstep · minstep · netconlist · order · print_event_queue · queue_mode · re_init · record · record_remove · rtol · simgraph_remove · solve · spike_stat · state_magnitudes · statename · states · statistics · stiff · store_events · use_daspk · use_fast_imem · use_local_dt · use_long_double · use_mxb · ygather · yscatter


class CVode

objref cvode

cvode = new CVode()


Multi order variable time step integration method which may be used in place of the default staggered fixed time step method. The performance benefits can be substantial (factor of more than 10) for problems in which all states vary slowly for long periods of time between fast spikes.

Although for historical reasons, this class is called CVode at the hoc level, in fact it is an interface to a family of methods which are implemented on top of the CVODES and IDA integrators of the SUNDIALS package,

  SUite of Nonlinear and DIfferential/ALgebraic equation Solvers
                   Release 2.0.1, January 2005
     Peter Brown, Aaron Collier, Keith Grant, Alan Hindmarsh,
      Steve Lee, Radu Serban, Dan Shumaker, Carol Woodward
          Center for Applied Scientific Computing, LLNL

(see CVode.use_local_dt() and CVode.use_daspk())

When this class is the finitialize/fadvance calls use the CVode integrator. In the default variable step context, the integrator chooses the time step and fadvance returns after one step. Local accuracy is determined by CVode.atol() and CVode.rtol().

The two major energy barriers to using the method are the requirement that hh type models be expressed in a DERIVATIVE block (instead of the explicit exponential integration step commonly implemented in a PROCEDURE) and that the solver be explicitly notified of the exact time of any discontinuity such as step changes, pulses, and synaptic conductance onset's. These issues are discussed in Channels and Events.

After your mod files are generalized it will probably be convenient to compare the default method with CVode by toggling the Use variable dt checkbox in the Variable Step Control panel NEURON Main Menu ‣ Tools ‣ VariableStepControl.


The consequences of solving continuous equations can be sometimes surprising when one is used to discrete fixed time step simulations. For example if one records an action potential (with either fixed or variable time steps) and plays it back into a voltage clamp; the clamp potential is not a discrete function but an exact step function.

Only the SEClamp works with CVode. VClamp cannot be used with this method.

Also .mod authors must take measures to handle step changes in parameters (Events)


Alternative variable step methods such as CVode.use_local_dt() and CVode.use_daspk() have been folded into this class and it has become a catchall class for invoking any of the numerical methods. For example, CVode.use_mxb() is used to switch between the tree structured matrix solver and the general sparse matrix solver. Not all components work together, see CVode.current_method() for acceptable mixing.





With no argument integrates for one step. All states and assigned variables are consistent at time t. dt is set to the size of the step. With the tout argument, cvode integrates til its step passes tout. Internally cvode returns the interpolated values of the states (at exactly tout) and the CVode class calls the functions necessary to update the assigned variables. Note that cvode.solve(tout) may be called for any value of tout greater than t-dt where dt is the size of its last single step.

For backward compatibility with finitialize/fadvance it is better to use the method instead of calling solve directly.

Prints information about the number of integration steps, function evaluations, newton iterations, etc.


Similar to CVode.statistics() but returns statistics information in the passed Vector argument. The vector will be resized to length 11 and the elements are:

  0  total number of equations (0 unless cvode has been active).
  1  number of NetCon objects.
  2  total number of events delivered.
  3  number of NetCon events delivered.
  4  number of PreSyn events put onto queue.
  5  number of SelfEvents delivered.
  6  number of SelfEvents put onto queue (net_send from mod files).
  7  number of SelfEvents moved (net_move from mod files).
  8  number of items inserted into event queue.
  9  number of items moved to a new time in the event queue.
 10  number of items removed from event queue.





With no arg, prints information on the event queue. It should only be called after an finitialize and before changing any aspect of the model structure. Many types of structure changes invalidate pointers used in the event queue.

With a vector argument, the delivery times are copied to the Vector in proper monotonically increasing order.


cvode.event_queue_info(2, tvec, list)

cvode.event_queue_info(3, tvec, flagvec, list)


Returns NetCon (2) or SelfEvent (3) information currently on the event queue. If the type is 2, NetCon information currently on the event queue is returned: delivery times are returned in tvec and the corresponding NetCon objects are returned in the List arg. If the type is 3, SelfEvent information is returned: delivery times are returned in tvec, the flags are returned in flagvec, and the SelfEvent targets (ArtificialCells are PointProcesses) returned in the List arg.

It should only be called after an finitialize and before changing any aspect of the model structure. Many types of structure changes invalidate pointers used in the event queue.

The delivery times are copied to the Vector in proper monotonically increasing order.


x = cvode.rtol()

x = cvode.rtol(relative)


Returns the local relative error tolerance. With arg, set the relative tolerance. The default relative tolerance is 0.

The solver attempts to use a step size so that the local error for each state is less than

    rtol*|state| + atol*atolscale_for_state

The error test passes if the error in each state, e[i], is such that e[i]/state[i] < rtol OR e[i] < atol*atolscale_for_state (the default atolscale_for_state is 1, see CVode.atolscale() )


x = cvode.atol()

x = cvode.atol(absolute)


Returns the default local absolute error tolerance. With args, set the default absolute tolerance. The default absolute tolerance is 1e-2. A multiplier for specific states may be set with the CVode.atolscale() function and also may be specified in model descriptions.

The solver attempts to use a step size so that the local error for each state is less than

    rtol*|state| + atol*atolscale_for_state

The error test passes if the error in each state, e[i], is such that e[i]/state[i] < rtol OR e[i] < atol*atolscale_for_state

Therefore states should be scaled (or the absolute tolerance reduced) so that when the value is close to 0, the error is not too large.

(See atolscale() for how to set distinct absolute multiplier tolerances for different states.)

Either rtol or atol may be set to 0 but not both. (pure absolute tolerance or pure relative tolerance respectively).


tol = cvode.atolscale(&var, toleranceMultiplier)

tol = cvode.atolscale(&var)

tol = cvode.atolscale("basename" [, toleranceMultiplier])


Specifies the absolute tolerance scale multiplier (default is 1.0) for all STATE's of which the address of var is an instance. Eg. cvode.atolscale(&soma.v(.5), 1e-8) sets the absolute tolerance multiplier for all membrane potentials everywhere. (The syntax for merely specifying a name is admittedly cumbersome but the function is not often needed and it avoids the necessity of explicitly having to parse strings such as "TrigKSyn.G".) The currently specified multiplier for that state name is returned by the function call.

Specification of a particular STATEs absolute tolerance multiplier is only needed if its scale is extremely small or large and is best indicated within the model description file itself using the STATE declaration syntax:n

    state (units) <tolerance>

See nrn/demo/release/cabpump.mod for an example of a model which needs a specific scaling of absolute tolerances (ie, calcium concentration and pump density).

The "basename" form is simpler than the pointer form and was added to simplify the implementation of the AtolTool. The pointer form required the state to actually exist at the specified location. Base names are "v", "vext", state_suffix such as m_hh, and PointProcessName.state such as ExpSyn.g .

Initializes the integrator. This is done by finitialize() when cvode is active().


x = cvode.stiff()

x = cvode.stiff(0-2)


2 is the default. All states computed implicitly.

1 only membrane potential computed implicitly.

0 Adams-Bashforth integration.

x =

x =

x =

following two not yet implemented

x =, dt)

x =


When CVode is active then finitialize() calls CVode.re_init() and fadvance() calls CVode.solve().

This function allows one to toggle between the normal integration method and the CVode method with no changes to existing interpreter code. The return value is whether CVode is active.

With only a single 1 arg, the fadvance calls CVode to do a single variable time step.

With the dt arg, fadvance returns at t+dt.

With a Vector tvec argument, CVode is made active and a sequence of calls to fadvance returns at the times given by the elements of tvec. After the last tvec element, fadvance returns after each step.


x = cvode.maxorder()

x = cvode.maxorder(0 - 12)

Default maximum order for implicit methods is 5. It is usually best to let cvode determine the order. 12 for Adams.


x = cvode.jacobian()

x = cvode.jacobian(0 - 2)

0 is the default. Linear solvers supplied by NEURON. 1 use dense matrix 2 use diagonal matrix


objref dest_vector

dest_vector = new Vector()


Fill the destination Vector with the values of the states. On return dest_vector.size will be the number of states.

Fill the destination Vector with the values of d(state)/dt.

cvode.f(t, yvec, ypvec)
returns f(yvec, t) in ypvec. f is the existing model. Size of yvec must be equal to the number of states ( ie vector size returned by CVode.states()). ypvec will be resized to the proper size. Note that the order of the states in the vector is indicated by the names returned by CVode.statename()


Works only for global variable time step method. Works only with single thread.

Fills the state variables with the values specified in yvec. Size of yvec must be equal to the number of states ( ie vector size returned by CVode.states()). Note that active CVode requires a subsequent CVode.re_init() if one wishes to integrate from the yvec state point.


Works only for global variable time step method. Works only with single thread.

Fills yvec with the state variables (will be resized to the number of states). This is analogous to CVode.states() after a CVode.re_init().


Works only for global variable time step method. Works only with single thread.


Uses the fixed step method to advance the simulation by dt . The initial condition is whatever state values are present (eg subsequent to a previous integration step or CVode.yscatter() or CVode.f() or explicitly user modified state values). The model state values are those after the fixed step integration (but are NOT the same as the current state defined by CVode and returned by CVode.states() (that would be the case only after a subsequent CVode.re_init())) To get the new current states in CVode vector order, use CVode.ygather().

Valid under all circumstances. This is basically an fadvance() using the fixed step method and avoids the overhead of

in order to allow the use of the CVode functions assigning state and evaluating states and dstates/dt


CVode.dstates() are invalid and should be determined by a call to CVode.f() using the current state from CVode.ygather() .



Fill the destination Vector with the values of the weights used to compute the norm of the local error in cvodes and ida.

Fill the destination Vector with the values of the local errors on the last step.


cvode.statename(i, dest_string)

cvode.statename(i, dest_string, style)

Return the hoc name of the i'th string in dest_string The default style, 0, is to attempt to specify the name in terms of object references such as cell[3].syn[2].g. Style 1 specifies the name in terms of the object id, eg. ExpSyn[25].g or Cell[25].soma.v(.5). Style 2 returns the basename, e.g. v, or ExpSyn.g .


List = cvode.netconlist(precell, postcell, target)

List = cvode.netconlist(precell, postcell, target, list)

Returns a new List (or appends to the list in the 4th argument position and returns a reference to that) of NetCon object references whose precell (or pre), postcell, and target match the pattern specified in the first three arguments. These arguments may each be either an object reference or a string. If an object, then each NetCon appended to the list will match that object exactly. String arguments are regular expressions and the NetCon will match if the name of the object has a substring that is accepted by the regular expression. (Object names are the internal names consisting of the template name followed by an index). An empty string, "", is equivalent to ".*" and matches everything in that field. A template name will match all the objects of that particular class. Note that some of the useful special regular expression characters are ".*+^$<>". The "<>" is used instead of the the standard special characters "[]" to specify a character range and obviates escaping the square bracket characters when attempting to match an array string. ie square brackets are not special and only match themselves.

A compact method of iterating over a set of NetCon objects is to create the list iterator

iterator ltr() {local i, cnt  localobj nil
    for i = 0, $o2.count - 1 {
            $o1 = $o2.object(i)
    $o1 = nil

and then take advantage of the automatic creation and destruction of lists with, for example, to print all the postcells that the given precell connects to:

objref xo
for ltr(xo, cvode.netconlist(precell, "", "")) {
    print xo.postcell


cvode.record(&rangevar, yvec, tvec)

cvode.record(&rangevar, yvec, tvec, 1)


Similar to the Vector record() function but also works correctly with the local variable time step method. Limited to recording only range variables of density mechanisms and point processes.

During a run, record the stream of values in the specified range variable into the yvec Vector along with time values into the tvec Vector. Note that each recorded range variable must have a separate tvec which will be different for different cells. On initialization the yvec and tvec Vectors are resized to 1 and the initial value of the range variable and time is stored in the Vectors.

To stop recording into a particular vector, remove all the references either to tvec or yvec or call record_remove() .

If the fourth argument is present and equal to 1, the yvec is recorded only at the existing t values in tvec. This option may slow integration since it requires calculation of states at those particular times.

Remove yvec (and the corresponding xvec) from the list of recorded vectors. See record().



cvode.event(t, "statement")

cvode.event(t, "statement", pointprocess, re_init)


With no argument, an event without a source or target is inserted into the event queue for "delivery" at time t. This has the side effect of causing a return from fadvance() (or CVode.solve() or ParallelContext.psolve() or batch_run() exactly at time t. This is used by the stdrun.hoc file to make sure a simulation stops at tstop or after the appropriate time on pressing "continuerun" or "continuefor". When CVode.use_local_dt() is active, all cells are interpolated to the event time.

If the hoc statement argument is present, the statement is executed (in the object context of the call to cvode.event) when the event time arrives. This statement is normally a call to a procedure which may send another cvode.event. Note that since the event queue is cleared upon finitialize() the cvode.event must be sent after that.

Multiple threads and/or the local variable time step method, sometimes require a bit of extra thought about the purpose of the statement. Should it be executed only in the context of a single thread, should it be executed only in the context of a single cell, and should only the integrator associated with that cell be initialized due to a state change caused by the statement? When the third arg is absent, then before the statement is executed, all cells of all threads are interpolated to time t, all threads join at time t, and the statement is executed by the main thread. A call to CVode.re_init() is allowed. If the third arg (a POINT_PROCESS object) is present, then, the integrator of the cell (if lvardt) containing the POINT_PROCESS is interpolated to time t, and the statement is executed by the thread containing the POINT_PROCESS. Meanwhile, the other threads keep executing. The statement should only access states and parameters associated with the cell containing the POINT_PROCESS. If any states or parameters are changed, then the fourth arg should be set to 1 to cause a re-initialization of only the integrator managing the cell (CVode.re_init is nonsense in this context).


hmin = cvode.minstep()

hmin = cvode.minstep(hmin)

Gets (and sets in the arg form) the minimum time step allowed for a CVODE step. Default is 0.0 . An error message is printed if a time step less than the minimum step is used.


Not very useful. What we'd really like is a minimum first order implicit step.


hmax = cvode.maxstep()

hmax = cvode.maxstep(hmax)

Gets (and sets in the arg form) the maximum value of the step size allowed for a CVODE step. CVODE will not choose a step size larger than this. The default value is 0 and in this case means infinity.


boolean = cvode.use_local_dt()

boolean = cvode.use_local_dt(boolean)

Gets (and sets) the local variable time step method flag. When CVODE is active(), this implies a separate CVODE instance for every cell in the simulation. CVode.record() is the only way at present that variables can be properly obtained when this method is used.


Not well integrated with the existing standard run system graphics because cells are generally at different times and an fadvance only changes the variables for the earliest time cell.

CVode.use_daspk() and use_local_dt cannot both be 1 at present. Toggling one on will toggle the other off.




Prints information whenever an event is generated or delivered. When the argument is true, information is printed at every integration step as well.


boolean = cvode.use_long_double()

booelan = cvode.use_long_double(boolean)

When true, vector methods involving sums over the elements are accumulated in a long double variable. This is useful in debugging when the global variable time step method gives different results for different ParallelContext.nthread() or numbers of processes. It may be the case that the difference is due to differences in round-off error due to the non-associativity of computer addition. I.e when threads are used each thread adds up its own group of numbers and then the group results are added together. When a long double is used as the accumulator for addition, the round off error is much more likely to be the same regardless of the order of addition. Note that this DOES NOT make the simulation more accurate --- just more likely to be identical for different numbers of threads or processes (if the difference without it was due to round off errors during summation).


order = cvode.order()

order = cvode.order(i)

CVODE method order used on the last step. The arg form is for the ith cell instance with the local step method.


boolean = cvode.use_daspk()

boolean = cvode.use_daspk(boolean)


Gets (sets for the arg form) the internal flag with regard to whether to use the IDA method when CVode is active(). If CVode is active and the simulation involves LinearMechanism() or extracellular() mechanisms then the IDA method is automatic and required.

Daspk refers to the Differential Algebraic Solver with the Preconditioned Krylov method. The SUNDIALS package now calls this the IDA (Integrator for Differential-Algebraic problems) integrator but it is really the same thing.


order = cvode.condition_order()

order = cvode.condition_order(1or2)

When condition_order is 1 then NetCon() threshold detection takes place at a time step boundary. This is the default. When condition_order is 2 then NetCon threshold detection times are linearly interpolated within the integration step interval for which the threshold occurred. Second order threshold is limited to variable step methods and is ignored for the fixed step methods. Note that second order threshold detection time may change due to synaptic events within the interval or even be abandoned. It is useful for cells with approach threshold very slowly or with large time steps.


eps = cvode.dae_init_dteps()

eps = cvode.dae_init_dteps(eps)

eps = cvode.dae_init_dteps(eps, style)


The size of the "infinitesimal" fixed fully implicit step used for initialization of the DAE solver, see use_daspk() , in order to meet the the initial condition requirement of f(y',y,t)=0. The default is 1e-9 ms.

The default heuristic for meeting the initial condition requirement based on the pre-initialization value of all the states and an initialization time of t0 is:

t = t0 continuous.

Two dteps voltage solve steps. (does not change t, or membrane mechanism states but changes v,vext). The initial value of y is the present value of the states.

t = t0 + dteps continuous

One dteps step without changing y but it does determine dy/dt of the v, vext portion of states.

t = t0 determine the dy/dt of the membrane mechanism states. (note: membrane mechanism states are all derivative or kinetic scheme states)


A number of things can go wrong with the heuristics used to provide the integrator with a consistent initial condition. When this happens the default behavior is to stop. However one can modify the error handling and/or choose a second initialization heuristic that might work by setting the style method.

The working values of style are 0,1,2, 8,9,10. the latter style group (010 bit set) chooses the alternative heuristic. This alternative is very similar to the default except the third dteps step that determines y' also is allowed to change y. This may be more reliable when the user is not using continuous.

If the 1 or 2 bit is set, a warning is printed instead of an error and the sim continues. If the 2 bit is set, then for the next 1e-6 ms, the integrator solves the equation f(y', y, t)*(1 - exp(-1e-7(t - t0)) where t0 is the initialization time. I call this parasitic since it is supposed to be analogous to every voltage having a small capacitance to ground. It has not been determined if the parasitic heuristic has a reliable mathematical basis and the user should investigate the state change patterns in the neighborhood of the initialization time.

Removes all items from the list of Graph lines recorded during a local variable step simulation. Graph lines would have been added to this list with Graph.



cvode.state_magnitudes(Vector, integer)

maxstate = cvode.state_magnitudes("basename", &maxacor)


cvode.state_magnitudes(1) activates the calculation of the running maximum magnitudes of states and acor. 0 turns it off.

cvode.state_magnitudes(2) creates an internal list of the maximum of the maximum states and acors according to the state basename currently in the model. Statenames not in use have a maximum magnitude state and acor value of -1e9.

maxstate = cvode.state_magnitudes("basename", &maxacor) returns the maxstate and maxacor for the state type, e.g. "v" or "ExpSyn.g", or "m_hh". Note: state type names can be determined from MechanismType and MechanismStandard

cvode.state_magnitudes(Vector, 0) returns all the maximum magnitudes for each state in the Vector. This is analogous to cvode.states(Vector). cvode.state_magnitudes(Vector, 1) returns the maximum magnitudes for each acor in the Vector.

method = cvode.current_method()

A value that indicates

modeltype + 10*use_sparse13 + 100*methodtype + 1000*localtype

where modeltype has the value: 0 if there are no sections or LinearMechanisms (i.e. empty model) 2 if the extracellular mechanism or LinearMechanism is present. (in this case the fully implicit fixed step or daspk methods are required and cvode cannot be used. 1 otherwise

use_sparse13 is 0 if the tree structured matrix solver is used and 1 if the general sparse matrix solver is used. The latter is required for daspk and not allowed for cvode. The fixed step methods can use either. The latter takes about twice as much time as the former.

methodtype = secondorder if CVode is not active. It equals 3 if CVODE is being used and 4 is DASPK is used.

localtype = 1 if the local step method is used. This implies methodtype==3


boolean = cvode.use_mxb()

boolean = cvode.use_mxb(boolean)

Switch between the tree structured matrix solver (0) and the general sparse matrix solver (1). Either is acceptable for fixed step methods. For CVODE only the tree structured solver is allowed. For DASPK only the general sparse solver is allowed.


boolean = cvode.use_fast_imem()

boolean = cvode.use_fast_imem(boolean)

When true, compute i_membrane_ for all segments during a simulation. This is closely related to i_membrane which is computed when the extracellular mechanism is inserted. However, i_membrane_ (note the trailing '_'), has dimensions of nA instead of mA/cm2 (ie. total membrane current out of the segment), is available at 0 area nodes (locations 0 and 1 of every section), does not require that extracellular be inserted (and so is much faster), and works during parallel simuations with variable step methods. (ie. does not require IDA which is currently not available in parallel). i_membrane_ exists as a range variable only when this function has been called with an argument of 1.

Accumulates all the sent events as adjacent pairs in the vector. The pairs are the time at which the event was sent and the time it is to be delivered. The user should do a vec.resize(0) before starting a run. Cvode will stop storing with cvode.store_event(). This is primarily for gathering data to design more efficient priority queues. It may be eliminated when the tq-exper branch is merged back to the main branch. Notice that there is no info about event type or where the event is coming from or going to.

mode = cvode.queue_mode(boolean use_fixed_step_bin_queue, boolean use_self_queue)

Normally, there is one event queue for all pending events. However, for the fixed step method one can obtain marginally better queue performance through the use of a bin queue for NetCon events. This utilizes a queue with bins of size dt which has a very fast insertion time and every time step all the events in a bin are delivered to their targets. Note that the numerics of the simulation will differ compared to the default splay tree queue (which stores double precision delivery times) if NetCon.delay values are not integer multiples of dt. Also, even with the fixed step method and and delays as integer multiples of dt, results can differ at the double precision round off level due to the different order that same time events can be received by the NET_RECEIVE block.

The optional "use_self_queue" (default 0) argument can only be used if the the simulation is run with psolve() method of the ParallelContext and must be selected prior to a call of ParallelContext.set_maxstep() since this special technique requires a computation of the global minimum NetCon.delay() (not just the minimum interprocessor NetCon delay) and that delay must be greater than 0. The technique avoids the use of the normal splay tree queue for self events for ARTIFICIAL_CELLs (events initiated by the net_send call and which may be manipulated by the net_move call in the NET_RECEIVE block). It may thus be considerably faster. However, every minimum NetCon delay interval, all the ARTIFICIAL_CELLS must be iterated to see if there are any outstanding net_send events that need to be handled. Thus it is likely to have a beneficial performance impact only for large numbers of ARTIFICIAL_CELLs which receive many external input events per reasonable minimum delay interval. This method has not receive much testing and the results should be compared with the default queuing method.

Returns 2*use_self_queue + use_fixed_step_bin_queue.

mode = cache_efficient(0or1)

When set, G*v = R matrix and vectors are reallocated in tree order so that all the elements of each type are contiguous in memory. Pointers to these elements used by the GUI, Vector, Pointer, etc. are updated.

Much of the implementation was contributed by Hubert Eichner


ParallelContext.multisplit() automatically sets cache_efficient(1)


The following aspects of model descriptions (.mod files) are relevant to their use with CVode.

KINETIC block - No changes required.

DERIVATIVE block - No changes required. The Jacobian is approximated as a diagonal matrix. If the states are linear in state' = f(state) the diagonal elements are calculated analytically, otherwise the diagonal elements are calculated using the numerical derivative (f(s+.01) - f(s))/.001 .

LINEAR, NONLINEAR blocks - No changes required. However, at this time they can only be SOLVED from a PROCEDURE or FUNCTION, not from the BREAKPOINT block. The nrn/src/nrnoc/vclmp.mod file gives an example of correct usage in which the function icur is called from the BREAKPOINT block and in turn SOLVE's a LINEAR block. If desired, it will be a simple matter to allow these blocks to be solved from the BREAKPOINT block.

SOLVE PROCEDURE within a BREAKPOINT block - Changes probably required. Such a procedure is called once after each return from CVode.solve().


The SOLVE PROCEDURE form was often used to implement the exponential integration method for HH like states and was very efficient in the context of the Crank-Nicholson like staggered time step approach historically used by NEURON. Furthermore the exponential integration often used tables of rates which were calculated under the assumption of a fixed time step, dt. Although it can still be used under some circumstances, the usage to integrate states should be considered obsolete and converted to a DERIVATIVE form. To do this,

  1. replace the PROCEDURE block with a DERIVATIVE block, eg.

    DERIVATIVE states {
    m' = (minf - m)/mtau
  2. replace the SOLVE statement in the BREAKPOINT block with SOLVE states METHOD cnexp

  3. if using tables, store mtau instead of \((1 -\exp(-dt/m_{tau}))\) The nmodl translator will emit c code for both the staggered time step and high order variable time step methods. The only downside is slightly less efficiency with the staggered time step method since the exp(-dt...) is calculated instead of looked up in tables.

In summary, no model should anymore depend on dt.



How does one handle events? This is really the only serious difficulty in writing models that work properly in the context of a variable time step method. All models which involve discontinuous functions of time, eg steps, pulses, synaptic onset, require special provision to notify the integrator that an event has occurred within this time step, ie between t-dt and t. If this is not done, the time step may be so large that it completely misses a pulse or synaptic event. And if it does see the effect of the event, there is a huge inefficiency involved in the variable step method's search for the location of the event and the concomitant tremendous reduction in size of dt.

So, if you change any variable discontinuously in the model at some time tevent, call call


The user may check the return value of this function to decide if something needs changing. Examples of the two styles of usage are:

  1. Just notify and do the logic separately.

            at_time(del + dur)
            if (t >= del && t <= del + dur) {
                    istim = on_value
                    istim = 0
  2. Use the at_time return value to do the logic.

            istim = 0
            if (at_time(del)) {
                    istim = on_value
            if (at_time(del + dur)) {
                    istim = 0

Notice the requirement of initialization or else if the previous run was stopped before del + dur the value of istim would be on_value at the beginning of the next run.

What happens internally when at_time(tevent) is called?

The interesting case (t-dt < tevent <= t) --- First, at_time returns 0. Then CVode changes its step size to (tevent - (t-dt) - epsilon) and redoes the step starting at t-dt. Note that this should be safely prior to the event (so at_time still returns 0), but if not then the above process will repeat until a step size is found for which there is no event. CVode then re-initializes it's internal state and restarts from a new initial condition at tevent+epsilon. Now when at_time is called, it returns 1. Note that in its single step mode, CVode.solve() will return at t = tevent-epsilon, the subsequent call will start the initial condition at t = tevent + epsilon and return after a normal step (usually quite small).

The case (tevent <= t - dt) --- at_time returns 0.

The case (tevent > t) --- at_time returns 0.

Note that an action potential model with axonal delay delivering a "message" to a synaptic model may or may not think it worthwhile to call at_time at the time of threshold (I would just do my own interpolation to set t_threshold) but will certainly call at_time(t_threshold + delay) (and possibly not allow t_threshold to change again until it returns a 1);

I am sorry that the variable time step method requires that the model author take careful account of events but I see no way to have them automatically taken care of.

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