ODEXP(1) - General Commands Manual
odexp - numerical solver for population-based system with gnuplot graphical output
odexp [-a additional odexp options] [-c] [-d] [-i] [-o compiler options] [-p parfile] [-q] [-r] file
odexp is an interactive command line program for numerical simulations and analysis of dynamical systems of particle populations. Particles are defined by a system of ordinary differential equations (ODE), stochastic differential equations (SDE), delay differential equations (DDE), of finite-difference equations (FDE). Particles can die and replicate.
odexp parses and compiles the dynamical system defined in file, and launches a command line tool to explore its dynamics. See EXAMPLES for examples of a dyamical system file. If file is not given, odexp will take the dynamical system from the standard input. When option -o is present, system parameters, initial conditions and options are loaded from file parameterfile
odexp uses the GNU Scientific Library (GSL) for numerical integration of ODEs and DDEs and their linear stability analysis. Solutions are plotted with gnuplot.
-a options
Add options to odexp. options comes as 'option1=value1, option2=value2, ...'
-c
Compile C code only. Generated code must be in place.
-d
Generate code only.
-o options
Add option to the compiler command. Default 'g' for debugging.
-i
Ignore syntax errors try to parse the file anyway.
-p parfile
Optional parameter file. This overrides parameters, timespan and options in the source file.
-q
Quiet mode. Quit after the first run and leave simulation files in place.
-r
Run model. Code must have been compiled.
The odexp file defines an initial value problem (IVP): equations, initial conditions, parameter, auxiliary functions, integration interval, etc. Essential elements are at least one equation, the initial condition and the time span over which integration must take place. Other elements such as options, auxiliary functions and constants can be defined as well. The general structure of the file is
- Description of the dynamical system. Lines start with ##. Comments start with # and run until the end of the line.
- Model parameters. Lines start with PAR
- Parametric expressions. Lines start with EXPR
- Auxiliary functions (AUX)
- Equations (D/DT)
- Mean fields (%M)
- Coupling terms (%C)
- User-defined functions (FUN)
- Timespan (TIMES)
- Options (OPT)
Interactive commands can be entered at the odexp command prompt. Successive commands can be separated with by semi-colons ';'
?
Display this help.
C^y
Repeat last command.
+, =, C^g
Increment current parameter by a multiplicative factor parstep (parstep is an option, see set options).
-, C^h
Decrement current parameter by a multiplicative factor step (step is an option, see set options).
], C^]
Plot next variable of current particle on the y-axis (cyclic).
[, C^[
Plot previous variable of current particle on the y-axis (cyclic).
}, C^}
Plot next particle of current variable on the y-axis (cyclic).
{, C^{
Plot previous particle of current variable on the y-axis (cyclic).
> count
Double count times (default one) the number of output time steps.
< count
Halve count times (default one) the number of output time steps.
# dataset colx coly
Add to plot colx and coly from dataset.
$ id
Print dataset for particle id. If id is missing, print stats dataset in population mode or particle in single mode.
$$,
Print all particles in tall format, using less
*‌ [msg]
Snapshot of current simulation and parameter values with optional msg. and save the current plot to in format given by option printsettings (default postscript eps color). The filenames are made from the first word of msg or the current model filename if msg is absent.
! command
Pass the argument command to the shell.
0, n
Switch to/update normal plot.
9, b
Switch to continuation plot.
7 [timestep | [first | last | previous | next [skip]]]
Switch to particle plot. Optional timestep sets the timestep to plot. Options first and last set timesteps to 0 and the last one. Options previous and next set the timestep to previous or next one. With option skip, previous and next jump skip steps
6
Switch to animate lot.
A
Reset all axes to linear scale.
a us, a su
Set axis u ={x|y|a} to scale s ={l|n}, n for linear (normal) scale and l for log scale, a for all axes.
d
Reload the parameter file (usually to reset model parameters to their default values).
E
Decrease the time span by a factor 2.
e [val]
Multiply the time span by a factor val (default val = 2). Factor val can be less than one.
f
Fit data (not implemented yet).
g cmd
Send the command cmd to gnuplot.
h [d]
Toggle plot hold (on/off). The command hd delays hold to after the next plotting command, making sure that only plotting command issued after the hold command will be displayed.
I
Set initial conditions to their default values.
il
Use the state of the system at t1 (tfinal) as initial conditions.
in
Loop through initial conditions for each variable. Set to I to revert to the default value, press <enter> to keep current initial condition.
is
Set initial condition to steady state. Steady state must have been computed with ms.
l@
List all user-defined functions.
l%
List population birth, replication and death rates.
lc
List all constant arrays.
ld
Print file description (all lines starting with ## in file ).
lf
List all array files (nrows ncols and filenames).
li
List all initial conditions.
ll
List file name and various information.
lo [optiontype]
List options that match optiontype, or all options if optiontype is missing.
lp
List all parameters.
ls
List steady states.
lx [DACME]
List all equations, auxiliary variables, coupling terms, mean fields and parametric expression. Optional subset of DACME to list only those types.
mm
Try to find all steady states.
ms
Find a steady state with starting guess given by initial conditions.
o filename
Load parameters values and options from file filename.
P val
Set current parameter to value val.
p [ind | par] [val]
Make parameter with index ind or name par the current parameter, and set its value to val. When val is missing, the parameter value is unchanged. When ind and par are missing, the current parameter and its value are printed.
Q, q [msg], C^w
Quit and make a snapshot of the parameters. An optional message msg can be added.
R
Rerun the ODE system and update plot. Useful after numerical options have been changed.
r
Repeat the last gnuplot command (this is gnuplot's replot).
set ind | var val
Set the option with index ind or name var to value val.
t [t0] t1
Set time span from t0 to t1. The final time t1 must be larger than t0.
u
Toggle add curves to plot (on/off). This works only when simulations are updated, for instance when parameters are changed. To plot many variables on the same axes, use h (hold) instead. Curves can be labelled with custom keys, by adding a string key to the plot command.
ur
Remove all curves and set curves off.
v { i | x } { j | y } [{ k | z }]
Set 2D/3D view, x-axis to index i (variable x ), y-axis to j (variable y ), and z-axis to k (variable z ). Set variable to T or index -1 for time. 2 takes only the first two arguments, and 3 takes the three arguments
V gnuplot-expression
Plot according to gnuplot-expression. The format @var can be used in place of the corresponding column number. For arrays, the subscripted variable array[i] is named array_i. For example, if x[0],... x[9] are dynamical variables, then V (@x_2):(@x_3/@x_4) would plot the ratio x[3]/x[4] vs x[2]
w
List all particle states
x { ind | var }
Plot variable with index ind or name var on the x-axis
y [ind | var key]
Plot variable with index ind or name var on the y-axis
A dynamical system is specified in a text file with lines starting with keywords for defining equations, parameters, options, etc. Keywords are case-insensitive.
Overview of keywords
PAR
Model parameter. Must be a numerical constant.
EXPR
Parametric expression. Must be an expression, and can depend on model parameters and other parametric expressions.
AUX
Auxiliary function. Must be an expression, and can depend on model parameters, parametric expression and other auxilary functions and dynamical variables.
D/DT
Differential equations for the dynamical variables. Must be an expression, and can depend on model parameters, parametric expressions, auxilary functions and dynamical variables.
INIT
Initial conditions for the dynamical variables.
CONST
Constant arrays.
LET
Prescan macro.
FILE
Array from file
FUN
User-defined function
TIMES
time span
OPT
Numerical and graphical options.
%BIRTH
particle birth rate.
%PROLIF
particle proliferation rate.
%DEATH
particle death rate.
%M
Mean field (average of expression over all particles)
%C
Coupling (for each particle, average of expression over all particles)
PAR
Parameters. Must be numerical scalar (double, int or long). Syntax:
PAR name value [{ attribute, ...} # comment]
Parameters appear in the list of parameters. They can be modified from within odexp and can be ranged over. Parameters are common to all particles.
The variable name must be a valid C variable name.
The value must be a constant number; by default a double, but can be casted to an integer by declaring an attribute int or long.
PAR n 3 {int} # n is declared as an int in the parsed C model file
Shortcuts for parameter declaration Parameters can be declared in name value pairs on a single line, separated by semi-colons ';', or one parameter value pair per line.
These examples are valid
PAR a 0.1; Va b 0.2
PAR a {attribute of a} # comment on a; b {attribute of b} # comment on b
PAR b 0.2 {init} # attribute init for parameters only used
PAR c 0.3 {impl} # attribute impl for parameters used implicitly,
PAR d 0.4 {every} # attribute every for parameters used in expressions,
# initial conditions and auxiliary equations
PAR a 1 {int} # type integer. Warning this comment ends at the semi-colon: b is another parameter!; b 2.3
These examples are not valid
a 0.1; b 0.2 # not ok
Implicit initial condition
If var is a dynamical variable, the declaration
PAR var_0 0.5
declares the parameter var_0, sets it to value 0.5 and implicitly declares the initial condition INIT var var_0.
Optional attributes for auxiliary variables are init[ial] if the parameter occurs in the initial conditions or parametric expression but not in the dynamical equations, impl[icit] if the parameter is only accessed through MU(var) in population rates, or in user-defined functions. Attribute impl can also be used for parameters that are unused, to prevent warning from the C compiler. The attribute ever is used if the parameter occurs in the initial conditions and in the dynamical equations. Attributes int and long are used to cast parameters as integers. They are still stored as doubles.
EXPR
Expressions are functions of parameters. They cannot be modified interactively.
Syntax:
EXPR name expression [{ attribute, ...} # comment]
Expressions are unique to each particle. They are evaluated at the birth of a particle and are constant for the lifetime of the particle. Use ATBIRTH and ATREPLI to specify particle-dependent expressions.
Examples
PAR a 0.1
EXPR c a*a
EXPR rand_array[i=0:5] -1 + 2*rand01[i]
EXPR is_ancestor ATBIRTH*1 + ATREPLI*0
Optional attributes for expression are vect for evaluating the rhs outside a loop. This is useful for arrays that are filled by a function
EXPR arr[i=0:5] myfunc(arr) {vect}
AUX
Auxiliary variables. Auxiliary variables depend on parameters, expressions and dynamical variables.
Syntax:
AUX name expression [{.Va attribute; ...}] [# .Va comment]
]
They are declared as Name Expression pairs, and must be scalars or one-dimensional arrays. Auxiliary variables are useful to monitor quantities that depend on the dynamical variables. They can be plotted, and their values are recorded in the output file current.tab. Auxiliary functions are particle-dependent. They are evaluated at each time step.
AUX d sqrt(x+c)
AUX a[i=0:5] X[i]*X[i]
AUX norm_x sqrt(sum(a,5))
AUX norm_x2 dotprod(X,X,5)
Optional attributes for auxiliary variables are vect for evaluating the rhs outside a loop. This is useful for arrays that are filled by a function
AUX arr[i=0:5] myfunc(arr) {vect}
D/DT
Dynamical variables. Dynamical variables are the dependent variables of the ODE system.
Syntax:
dvar /dt = rhs [{ attribute; ... }] [# comment]
Dynamical variable var is declared as d name /dt followed by = and the rhs of the equation. Example
dx/dt = -a*x
Optional attributes for dynamical variables are hidden to hide the variable from being listed, tag = tag for giving a name to the variable init = value for setting the initial condition.
INIT
Initial conditions.
Syntax:
INIT var expression [{ attribute; ... }] [# comment]
Initial conditions can be numerical, or can be expression that depend on parameters or expressions. For each equation D/DT, there must be an INIT with the corresponding name If initial conditions are expressions, their values can be overruled or reset in odexp.
INIT x 1.0
INIT x b
Optional attributes for dynamical variables are tag = tag for giving a name to the variable
OPT
Options. Options can be preset.
OPT x x1 # set x-axis to plot x1
OPT reltol 1e-3 # set ode solver reltol to 1e-3
TIMES
Timespan. Time span is an array of the form t0 ti ... t1 where t0 and t1 are the initial and final times.
Intermediate values ti are stopping time, where the system is reset to initial condition. This is useful when systems
are discontinuous, and variable need to be reset at known timepoints.
TIMES 0 10
TIMES 0 10 20 50 100
LET
Set predefined constant. Useful to define system size.
LET N 100
CONST
Constant array. Must be numerical array. Constant arrays cannot be modified.
Constant arrays can be of any dimensions. Useful for arrays of small sizes.
CONST MY_ARRAY[2][3] { {1.1, 1.2, 1.3}, {2.1, 2.2, 2.3} }
FILE
Constant array from file. Syntax:
FILE varname filename { nrow, ncol, sep }
where nrow ncol are the optional numbers of rows and column to scan from filename. filename is a text file containing a Ar sep delimited array of doubles. Example
FILE my_array my_datafile.cav { nrow = 13, ncol = 2, sep = "," }
will load the first 13 rows and first 2 columns of a comma-separated of the file my_datafile.csv.
FUN
User-defined function. Simple, one-line functions can be defined this way
FUN my_fun_name (x, y, z) = x*x+y+z
This is interpreted in C as
double my_fun_name(double x,double y, double z) = { return x*x+y+z; }
Array can be passed as pointers,
FUN mean(*x) = sum(x,LENTGH_X)/LENTGH_X
is interpreted in C as
double mean(double *x) { return sum(x,LENTGH_X)/LENTGH_X; }
More complex function can be defined on multiple lines. Definition is terminated by the keyword 'end'.
FUN myatan( x, *p)
double a = *p;
return atan(a*x);
end
is interpreted as
**double myatan**(*double x*, *double *p*)
{
double a = *p;
return atan(a*x);
}
The function sum() is a helper function (see below for a list of helper functions).
%BIRTH
Particle (de novo) birth rate. Examples
%BIRTH 0.1 # set birth rate to 0.1 per unit time
%BIRTH 1.0/(10 + POP_SIZE) # birth rate function on total particle number POP_SIZE
%DEATH
Particle death rate. Examples
%DEATH 0.01 # constant particle death rate
%DEATH death_rate # set death rate to death_rate
%REPLI
Particle replication rate.
%C
Coupling term.
This is of the form
PSI[i] = 1/POP_SIZE*sum_{j=1}^POP_SIZE **phi**(*x[j]*, *x[i]*)
,
where phi() is a function of two variables. The declaration is
%C PSI phi (OY(x),MY(x))
The coupling term PSI takes a value for each particle.
%M
Mean field.
This is of the form
MF = 1/POP_SIZE * sum_{j=1}^POP_SIZE **phi**(*x[j]*)
,
where phi depends only on one variable. Example,
%M MF phi(MY(x)) # average phi(my dynamical variable x) over all particles
Since mean fields are averaged over the total particle number POP_SIZE, to get the total particle number, use
%M TOTAL POP_SIZE # not numerically efficient but ok
Alternatively, a mean field can be computed without looping through all particles, by using the attribute vect
%M TOTAL POP_SIZE {vect} # no loop, faster
DWDT
Gaussian, uncorrelated white noise ~ N(0,1/h), with h the timestep, as the derivative of the Wiener process. The stochastic differential equation
dx/dt = -theta(x - mu)*x + sigma*DWDT
would have as a solution x(t) the Ornstein-Uhlenbeck process, centered at mu, with sigma a diffusion constant and theta a dissipation rate constant.
POP_SIZE
Total number of particles.
MU(par)
Used anywhere to access the value of parameter with name par.
OY(var), OE(var), OA(var)
Used in %C to iterate over all particles; is a dynamical variable (OY), expression (OE) or auxiliary variable (OA).
MY(var,) ME(var), MA(var), MF(var)
Used in %C and %M to denote the current particle; var is a dynamical variable (MY), expression (ME), or auxiliary variable (MA) or a mean field (MF).
SY(var), SE(var,) SA(var)
Value of the current particle var's sister. Useful to specify what happens when particle replicates; var is a dynamical variable (SY), expression (SE) or auxiliary variable (SA).
ATBIRTH
logical variable indicating that the particle is just born (i.e. has no parent).
ATREPLI
logical variable indicating that the particle is replicating.
ISDAUGHTER
logical variable indicating if the particle is the daughter. This is nonzero only at replication (ATREPLI = 1). The daughter particle is the newly formed particle. At replication, the daughter particle is created from the mother particle by copy. Then, the mother particle is updated and becomes the sister particle. The daughter is then updated, and can refer to the sister particle with SE and SY.
ISMOTHER
logical variable indicating if the particle is the mother. This is nonzero only at replication (ATREPLI = 1).
MID
Current particle ID. ID's are unique and indicate the order of creation of the particle. ID's are not recycled.
See the list of options with line command lo.
x
variable to plot on the X-axis (default T). Short: x. Default value:
y
variable to plot on the Y-axis (default [0]). Short: y. Default value:
z
variable to plot on the Z-axis (default [1]). Short: z. Default value:
plot3d
plot in 3d (default 0). Short: 3d. Default value: 0
indvar
name of the INDependent variable {time}. Short: ind. Default value: time
hold
HOld (1) or replace ({0}) variable on plot. Short: ho. Default value: 0
curves
add (1) or replace ({0}) cUrves on plot. Short: u. Default value: 0
style
plot STyle {lines} | points | dots | linespoints .... Short: st. Default value: lines
realtime
plot in Real Time | {0} | 1 (not implemented). Short: rt. Default value: 0
xscale
X-axis Scale {linear} | log. Short: xs. Default value: linear
yscale
Y-axis Scale {linear} | log. Short: ys. Default value: linear
zscale
Z-axis Scale {linear} | log. Short: zs. Default value: linear
plotkey
plot key. Short: k. Default value:
data2plot
Data variable to Plot. Short: dp. Default value:
datastyle
dataset plotting style. Short: dsty. Default value: points
parstep
parameter STEP multiplicative increment. Short: step. Default value: 1.1
actpar
ACTive parameter. Short: act. Default value:
lasty
take Last Y as initial condition {0} | 1. Short: ly. Default value: 0
res
Resolution: nominal number of output time points. Short: r. Default value: 201
hmin
H MINimal time step. Short: hmin. Default value: 1e-5
h0
initial time step h0. Short: h0. Default value: 1e-1
abstol
ode solver ABSolute TOLerance. Short: abstol. Default value: 1e-6
reltol
ode solver RELative TOLerance. Short: reltol. Default value: 1e-6
solver
ode solver stepping METHod rk2 | rk4 | rkf45 | {rkck} | rk8pd | bsimp. Short: meth. Default value: rkck
lrabstol
Low Rank approx ABSolute TOLerance. Short: lrabstol. Default value: 1e-6
lrreltol
Low Rank approx RELolute TOLerance. Short: lrreltol. Default value: 1e-6
lrmax
Low Rank approx MAX rank. Short: lrmax. Default value: 31
popmode
Population simulation Mode single | {population}. Short: pm. Default value: population
popsize
initial population size for particle simulations. Short: ps. Default value: 1
particle
current Particle id. Short: p. Default value: 0
writefiles
*Obsolete* write individual particle files. Short: wf. Default value: 0
closefiles
*Obsolete* close individual particle files between writes. Short: cf. Default value: 0
ssahmin
SSA/tau-leap relative step threshold. Short: ssahmin. Default value: 0.0
aleap
tau-leaping factor. Short: aleap. Default value: 0.01
particlestyle
Particle STYLE. Short: pstyle. Default value: circles fill transparent solid 0.1 noborder
particleid
display Particle ID in particle plots. Short: pid. Default value: 1
kdensity2d
display bivariate (2D) kernel density estimate. Short: k2d. Default value: 0
kdensity2dgrid
kernel density grid resolution. Short: k2dgrid. Default value: 25
kdensity2dscale
kernel density scale parameter. Short: k2dscale. Default value: 0.5
timeframe
particle plot time frame first | {last} | previous | next | frame <n>. Short: tframe. Default value: last
particleweight
particle particle weight (expression) | {none}. Short: pweight. Default value: none
seed
seed for the random number generator. Short: seed. Default value: 3141592
reseed
Reset rng to Seed at each run 0 | {1}. Short: rs. Default value: 1
maxfail
max number of starting guesses for steady states. Short: maxfail. Default value: 10000
nlabstol
absolute tolerance for finding steady states. Short: nlabstol. Default value: 1e-6
nlreltol
relative tolerance for finding steady states. Short: nlreltol. Default value: 1e-6
nlrange
search range [0, v*var value]. Short: nlrange. Default value: 1000.0
nlminr
search range [0, v*var value]. Short: nlminr. Default value: 0.0
hc0
initial parameter continuation step. Short: hc0. Default value: 0.01
hcmax
maximal parameter continuation step. Short: hcmax. Default value: 0.05
par0
initial parameter value for range. Short: par0. Default value: 0.0
par1
final parameter value for range. Short: par1. Default value: 1.0
rmstep
parameter range multiplicative increment. Short: rmstep. Default value: 1.0
rastep
parameter range additive increment. Short: rastep. Default value: 0.1
rmic
initial condition multiplicative factor for range. Short: rmic. Default value: 1.0
raic
initial condition additive factor for range. Short: raic. Default value: 0.10
rric
reset initial conditions at each iteration for range. Short: rric. Default value: 0
font
gnuplot FOnt. Short: fo. Default value: Helvetica
fontsize
gnuplot Font Size. Short: fs. Default value: 13
terminal
gnuplot TERMinal. Short: term. Default value: qt noraise
printsettings
gnuplot PRINT settings. Short: print. Default value: postscript eps color
palette
color palette acid | qual | {apple}. Short: pal. Default value: apple
togglekey
switch key on/off. Short: key. Default value: 1
background
terminal background {none} | fancy. Short: bg. Default value: none
loudness
LouDness mode silent | quiet | {loud} (silent not implemented). Short: ld. Default value: loud
fix
number of digits after decimal point {4}. Short: fx. Default value: 4
progress
print PRogress 0 | {1} | 2 | 3. Short: pr. Default value: 1
wintitle
Window TItle. Short: wti. Default value:
runonstartup
Run On Startup. Short: ros. Default value: 1
runfirst
Run 1st, command to execute after startup. Short: r1st. Default value:
sum(double *array, long len)
Sum the elements of the array array of length len. Return the sum of the array.
sumstep(double, *array", long len, long step)
Sum only the step array of length len.
prod(double *array, long len)
Product of the elements of the array array of length len.
dotprod(double *x, double *y, long len)
Scalar product of two arrays x and y of lengths len
conv(double *u, double *v, long len)
convolution product between arrays u and v , each of length len
minus(double x, double y)
Subtraction. Used with sumxy.
plus(double x, double y)
Addition. Used with sumxy.
sumxy(long len, double (*f)(double), double (*g)(double,double), const double *x, const double yi)
Sum over j of f(g(x[j], yi)).
kern(double *Wi, double (*f)(double, double, double *), double xi, const double *x, double *p, long len)
linchaindelay(double root, double *chain, size_t link, double delay, size_t len)
This returns the link AP th element of a linear chain
beta*(chain[link-1] - chain[link]),
if link > 0, and
beta*(root - chain [0])
if link = 0.
There is a shortcut to specify a delayed variable. If z is a dynamical variable, then
LAG ztau1 {root = z, mean = tau, len = 1000, init = 0.2}
defines the dynamical variable ztau1 as the delayed version of z with a linear chain of length 1000 and mean tau. All intermediate variables, including ztau1, have initial condition 0.2.
Coupling term (%C) are evaluated by default in O(N^2) where N is the system size. When the right-hand side is equal to lrexp in a coupling declaration, an adaptative low rank expansion is used to approximate the coupling function g given in the attribute fun over the variable given in attribute var.
The coupling function g must be of the form g(u, *p) = gg(s*u) where the pointer p points to the scalar value s.
The following code calls the expansion method for the coupling term sin(xj-xi). (The auxiliary term TH is introduced to force the values of theta between 0 and 2 * PI.)
%C coupling lrexp {var = TH, fun = cpling_fun}
AUX TH theta - ( (int) (theta/2/PI) * 2 * PI )
fun cpling_fun(x, *p)
double scale = *(double *)p;
x *= scale;
return sin(x);
end
For more complex low-rank expansion, use lrwkern, on the right-hand side. lrwexp uses a matrix W = U*V as weights in the coupling term:
y = sum_j W_ij g(x_j - x_i)
For the low-rank expansion method to work, the matrix W must be itself low-rank, and admit a decomposition U*V. If N is the total system size, and R is the rank of W, U (NxR) and V (RxN) are rectangular matrices. The syntax is
%C cpl lrwexp {fun = g, U = U[0], V = V[0], rank = R, var = x }
The term cpl is the a vector of size N, and U[0] and V[0] are pointers to the first rows of U and V.
rk2
GSL Explicit embedded Runge-Kutta (2, 3) method
rk4
GSL Explicit 4th order (classical) Runge-Kutta
rkf45
GSL Explicit embedded Runge-Kutta-Fehlberg (4, 5) method.
rkck
GSL Explicit embedded Runge-Kutta Cash-Karp (4, 5) method.
rk8pd
GSL Explicit embedded Runge-Kutta Prince-Dormand (8, 9) method.
bsimp
GSL Implicit Bulirsch-Stoer method of Bader and Deuflhard.
fe
Explicit Forward Euler with fixed time steps. Combined the macro DWDT, this is the Euler-Maruyama scheme.
iteration
Not an ODE stepper. The stepper assigns the RHS of the equation to the updated state variable.
There are two primary output files: traj.dat and stats.dat. The file stats.dat stores at each time step the following information
TIME MFs N EVENTs
where TIME is the time (double), MFs are all the mean fields (double), is the number of particles (int). EVENTs have three int columns describing birth/death/replication events: PARENT_ID, EVENT, CHILD_ID. EVENT is 1 if birth or replication, -1 if death, and 0 if no event occurred (a fixed output time steps) PARENT_ID is the ID of particle that dies or replicate, -1 if EVENT is a birth, and 0 if no event occurred. CHILD_ID is the ID of the newly created particle, if EVENT = 1, -1 if a particle dies and 0 otherwise.
The file traj.dat lists at each time step all particles, and has columns
STEP ID TIME DYN AUX CPL MF EXPR
Here is an example of an odexp file for the Lotka-Volterra equations.
## file lotka.pop
## a simple nonlinear ODE system
# all lines starting with ## are printed with the command ld
PAR a 0.2
PAR b 0.3
dx/dt = x*(y - a) # equation on x
dy/dt = y*(b - x) # equation on y
INIT x 0.1 # initial condition for x
INIT y 0.2 # initial condition for y
TIMESPAN 0 10 # timespan is 0 to 10
# end of file
To print the file current.plot formatted, use
hexdump -e '"%f " "%f " "%f " "\n"' current.plot
DARWIN16 - May 3, 2021