Recipe function for specifying dynamic functions using formulas

1 | ```
prep.formulaDynamics(formula, startval, isContinuousTime = FALSE, jacobian)
``` |

`formula` |
a list of formulas specifying the drift or state-transition equations for the latent variables in continuous or discrete time, respectively. |

`startval` |
a named vector of starting values of the parameters in the formulas for estimation with parameter names as its name. |

`isContinuousTime` |
if True, the left hand side of the formulas represent the first-order derivatives of the specified variables; if False, the left hand side of the formulas represent the current state of the specified variable while the same variable on the righ hand side is its previous state. |

`jacobian` |
(optional) a list of formulas specifying the analytic jacobian matrices containing the analytic differentiation function of the dynamic functions with respect to the latent variables. If this is not provided, dynr will invoke an automatic differentiation procedure to compute the jacobian functions. |

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | ```
#Not run:
#For a full demo example that uses user-supplied analytic jacobian functions see:
#demo(RSNonlinearDiscrete, package="dynr")
formula=list(list(x1~a1*x1,x2~a2*x2),list(x1~a1*x1+c12*(exp(abs(x2)))/(1+exp(abs(x2)))*x2,
x2~a2*x2+c21*(exp(abs(x1)))/(1+exp(abs(x1)))*x1))
jacob=list(
list(x1~x1~a1,
x2~x2~a2),
list(x1~x1~a1,
x1~x2~c12*(exp(abs(x2))/(exp(abs(x2))+1)+x2*sign(x2)*exp(abs(x2))/(1+exp(abs(x2))^2)),
x2~x2~a2,
x2~x1~c21*(exp(abs(x1))/(exp(abs(x1))+1)+x1*sign(x1)*exp(abs(x1))/(1+exp(abs(x1))^2))))
dynm<-prep.formulaDynamics(formula=formula,startval=c(a1=.3,a2=.4,c12=-.5,c21=-.5),
isContinuousTime=FALSE,jacobian=jacob)
#For a full demo example that uses automatic jacobian functions see:
#demo(RSNonlinearODE , package="dynr")
formula=list(prey~ a*prey - b*prey*predator, predator~ -c*predator + d*prey*predator)
dynm<-prep.formulaDynamics(formula=formula,
startval=c(a = 2.1, c = 0.8, b = 1.9, d = 1.1),
isContinuousTime=TRUE)
``` |

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