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

`objref cvode`

`cvode = new CVode()`

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,

(see use_local_dt and use_daspk )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

When this class is active 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 atol and 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 VariableStepControl panel (NEURON Main Menu / Tools / VariableStepControl).

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 )

CVode

`cvode.solve()`

`cvode.solve(tout)`

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

CVode

`cvode.statistics()`

CVode

`cvode.spike_stat(vector)`

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.

CVode

`cvode.print_event_queue()`

`cvode.print_event_queue(Vector)`

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

CVode

`cvode.event_queue_info(2, tvec, list)`

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

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.

CVode

`x = cvode.rtol()`

`x = cvode.rtol(relative)`

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

rtol*|state| + atol*atolscale_for_stateThe 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 atolscale )

CVode

`x = cvode.atol()`

`x = cvode.atol(absolute)`

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

rtol*|state| + atol*atolscale_for_stateThe 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).

CVode

`tol = cvode.atolscale(&var, toleranceMultiplier)`

`tol = cvode.atolscale(&var)`

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

`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

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).state (units) <tolerance>

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 .

CVode

`cvode.re_init()`

CVode

`x = cvode.stiff()`

`x = cvode.stiff(0-2)`

1 only membrane potential computed implicitly. 0 Adams-Bashforth integration.

CVode

`x = cvode.active()`

`x = cvode.active(0)`

`x = cvode.active(1)`

`following two not yet implemented`

`x = cvode.active(1, dt)`

`x = cvode.active(tvec)`

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.

CVode

`x = cvode.maxorder()`

`x = cvode.maxorder(0 - 12)`

CVode

`x = cvode.jacobian()`

`x = cvode.jacobian(0 - 2)`

CVode

`objref dest_vector`

`dest_vector = new Vector()`

`cvode.states(dest_vector)`

CVode

`cvode.dstates(dest_vector)`

CVode

`cvode.f(t, yvec, ypvec)`

CVode

`cvode.yscatter(yvec)`

CVode

`cvode.ygather(yvec)`

CVode

`cvode.fixed_step()`

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/dtcvode.active(0) fadvance() cvode.active(1)

CVode

`cvode.error_weights(dest_vector)`

` Fill the destination Vector with the values of the weights used`

`to compute the norm of the local error in cvodes and ida.`

CVode

`cvode.acor(dest_vector)`

` Fill the destination Vector with the values of the local errors`

`on the last step.`

CVode

`cvode.statename(i, dest_string)`

`cvode.statename(i, dest_string, style`

CVode

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

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

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

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

CVode

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

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

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.

CVode

`cvode.record_remove(yvec)`

CVode

`cvode.event(t)`

`cvode.event(t, "statement")`

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

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 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).

CVode

`hmin = cvode.minstep()`

`hmin = cvode.minstep(hmin)`

CVode

`hmax = cvode.maxstep()`

`hmax = cvode.maxstep(hmax)`

CVode

`boolean = cvode.use_local_dt()`

`boolean = cvode.use_local_dt(boolean)`

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

CVode

`cvode.debug_event(1)`

`cvode.debug_event(2)`

CVode

`boolean = cvode.use_long_double()`

`booelan = cvode.use_long_double(boolean)`

CVode

`order = cvode.order()`

`order = cvode.order(i)`

CVode

`boolean = cvode.use_daspk()`

`boolean = cvode.use_daspk(boolean)`

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.

CVode

`order = cvode.condition_order()`

`order = cvode.condition_order(1or2)`

CVode

`eps = cvode.dae_init_dteps()`

`eps = cvode.dae_init_dteps(eps)`

`eps = cvode.dae_init_dteps(eps, style)`

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 Vector.play 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 Vector.play 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)

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 Vector.play 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.

CVode

`cvode.simgraph_remove()`

CVode

`cvode.state_magnitudes(integer)`

`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.

CVode

`method = cvode.current_method()`

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

CVode

`boolean = cvode.use_mxb()`

`boolean = cvode.use_mxb(boolean)`

CVode

`cvode.store_events(vec)`

CVode

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

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 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.

CVode

`mode = cache_efficient(0or1)`

Much of the implementation was contributed by Hubert Eichner

<eichnerh@in.tum.de>

multisplit automatically sets cache_efficient(1)

CVode Channels Concentrations EventsThe 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().

ModelDescriptionIssuesThe 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/mtau)) 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.

ModelDescriptionIssues

ModelDescriptionIssues

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

at_time(tevent)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) at_time(del + dur) if (t >= del && t <= del + dur) { istim = on_value }else{ istim = 0 }

2) Use the at_time return value to do the logic.

INITIAL { 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.