polyPdmpModel-class: Class polyPdmpModel
In CharlotteJana/pdmppoly: Moment Approximation for Polynomial PDMPs
Description
Slots
Ratepolys
Dynpolys
Note
Examples
Description
An S4 class to represent polynomial piecewisc deterministic markov processes
(polynomial PDMPs). These processes are PDMPs with polynomial rate functions
and polynomial dynamics. This makes it possible to approximate the moments of
the process without the need of simulation, see momApp. On the
downside, simulations take much longer than simulations of the same PDMP
represented as pdmpModel.
The class is based on the pdmpModel class of package
pdmpsim but introduces additional slots that replace the slots
dynfunc and ratefunc, namely dynpolys, dynsprays,
ratepolys and ratesprays. Only slots dynpolys and
ratepolys have to be defined by the user. The other slots (including
the still existing dynfunc and ratefunc) will be set
automatically. To represent polynomials in R, package spray is
used, which stores the coefficient matrices of polynomials as sparse arrays.
Slots
dynpolysan object of class language, more precisely a quoted
list. Every element of this list contains the ODE for one of the continous
variables. These ODEs are given as spray objects and can be defined
in two different ways. See section dynpolys for further information.
ratepolysan object of class language, more precisely a quoted
list.This list contains the rates for every jumptype. Every element is
itself a list, its length is determined by the number of different values
of the discrete variable (length(discStates(obj)[[1]])). See section
ratepolys for further information.
dynspraysa nested list of spray objects. This slot is generated
automatically out of slot dynpolys. Do not edit it by hand.
ratespraysa nested list of spray objects. This slot is generated
automatically out of slot ratepolys. Do not edit it by hand.
Ratepolys
Slot ratepolys is a quted list. The length of the list determines the number
of existing jumptypes (jumptypes are used in slot jumpfunc to
determine the next state the process jumps too). It contains the rates
determining the probability of a jump to be of type 1, 2, and so on. The
rates are polynomials that usually depend on the value of the discrete
variable at the time when the jump occurs. They are given as a list of spray
objects or numbers, for every possible discrete state separately (in the same
order as the states are given in slot discStates).
For example, let's assume that we have three different jumptypes and a
discrete variable d that can take the values 0 or 1 (so slot
discStates would be defined as list(d = 0:1)). Then slot
ratepolys will be given as follows:
1
2
3
4
5
Every rate of jtype i with d = j is a spray object, for example
linear(1:3).
Dynpolys
Slot dynpolys is a quoted list. The length of the list equals the number of
continuous variables of the model. Every element contains the ODE for one of
the continuous variables, given in the same order as in slot init and
given as spray objects.
The ODEs usually depend on the discrete variable,
lets call it d. An example would be df/dt =
-3f if d = 0 and df/dt = -3f + 1 if
d = 1. Here, f is the only continous variable of the model.
Every ODE can be defined in two different ways:
variant 1:
a list whose length equals the number of different states for d. Every entry is a
polynomial with d taking a fixed value. The order of the entries corresponds
to the order of discrete states given in slot discStates.
variant 2:
a list of two variables:
a variable overall which contains a polynomial that is independent
of fixed values for d and is therefore the same for all states
(attention: overall can contain d as a formal variable),
a variable specific which contains the rest of the term.
This is a list of the same form as in variant 1.
In our example, we get
Variant 1:
quote(list(list(-3*lone(1,2), -3*lone(1,2) + 1)))
Variant 2:
quote(list(list(overall = linear(c(-3, 0)), specific = list(0, 1))))
Variant 2 with one formula:
quote(list(list(overall = linear(c(-3, 1))))
The last variant is only possible, because in this example we have the
possiblity to write both ODEs in one formula: df/dt = -3f + d.
Note
Currently, all methods only work for PDMPs with a single discrete
variable. Some methods require the discrete variable to be the last
entry in slot init. Note that it is always possible to redefine a
PDMP with multiple discrete variables in a way that only one discrete
variable is necessary.
Examples
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#### a simple PDMP ####
#------ pdmpModel version -----
simplePdmp <- new("pdmpModel",
descr = "A simple PDMP",
init = c(f = 0, d = 0),
discStates = list(d = c(-1, 0, 1)),
times = c(from = 0, to = 10, by = 0.01),
dynfunc = function(t, x, parms) c(x["d"], 0),
ratefunc = function(t, x, parms) c(1+x["d"], 1-x["d"]),
jumpfunc = function(t, x, parms, jtype){
c(0, switch(jtype, x["d"]-1, x["d"]+1))
}
)
#------ polyPdmpModel version -----
library("spray")
simplePoly <- new("polyPdmpModel",
descr = "polyModel with two jumptypes",
init = c(f = 0, d = 0),
times = c(from = 0, to = 10, by = 0.01),
discStates = list(d = -1:1),
dynpolys = quote(list(
list(overall = lone(2,2)) # variant 2
)),
ratepolys = quote(list(
list(0, 1, 2), # first jumptype
list(2, 1, 0) # second jumptype
)),
jumpfunc = function(t, x, parms, jtype){
c(0, switch(jtype, x["d"]-1, x["d"]+1))
}
)
#------- comparison of the models --------------
identical(sim(simplePoly, outSlot = FALSE, seed = 5),
sim(simplePdmp, outSlot = FALSE, seed = 5))
#### the toggleSwitch model ####
#------ pdmpModel version -----
genePdmpT <- new("pdmpModel",
descr = "toggleswitch with two promotors",
parms = list(bA = 0.5, bB = 0.5, aA = 2, aB = 4,
k01A = 0.5, k10A = 2, k01B = 0.3, k10B = 3),
init = c(fA = 0.5, fB = 0.5, d = 4),
discStates = list(d = 1:4),
dynfunc = function(t, x, parms) {
df <- with(as.list(c(x, parms)),
c(-bA * fA, -bB * fB) + switch(d,
c(0, 0),
c(aA, 0),
c(0, aB),
c(aA, aB)))
return(c(df, 0))
},
ratefunc = function(t, x, parms) {
return(with(as.list(c(x, parms)),
c(switch(d, k01B, k01B, k10B*fA, k10B*fA),
switch(d, k01A, k10A*fB, k01A, k10A*fB))))
},
jumpfunc = function(t, x, parms, jtype) {
c(x[1:2], switch(jtype,
switch(x[3], 3, 4, 1, 2),
switch(x[3], 2, 1, 4, 3)))
},
times = c(from = 0, to = 20, by = 0.01),
solver = "lsodar")
#------ polyPdmpModel version -----
genePolyT <- new("polyPdmpModel",
descr = "toggleswitch with two promotors (polynomial version)",
parms = list(bA = 0.5, bB = 0.5, aA = 2, aB = 4,
k01A = 0.5, k10A = 2, k01B = 0.3, k10B = 3),
init = c(fA = 0.5, fB = 0.5, d = 4),
discStates = list(d = 1:4),
dynpolys = quote(list(
list(overall = -bA*lone(1,3), specific = list(0, aA, 0, aA)),
list(overall = -bB*lone(2,3), specific = list(0, 0, aB, aB))
)),
ratepolys = quote(list(
list(k01B, k01B, k10B*lone(1,3), k10B*lone(1,3)),
list(k01A, k10A*lone(2,3), k01A, k10A*lone(2,3))
)),
jumpfunc = function(t, x, parms, jtype) {
c(x[1:2], switch(jtype,
switch(x[3], 3, 4, 1, 2),
switch(x[3], 2, 1, 4, 3)))
},
times = c(from = 0, to = 20, by = 0.01),
solver = "lsodar")
#------- comparison of the models --------------
identical(sim(genePdmpT, outSlot = FALSE, seed = 10),
sim(genePolyT, outSlot = FALSE, seed = 10))
data("toggleSwitch")
times(toggleSwitch) <- c(from = 0, to = 20, by = 0.01)
all.equal(sim(genePdmpT, outSlot = FALSE, seed = 20)[, c("fA", "fB")],
sim(toggleSwitch, outSlot = FALSE, seed = 20)[, c("fA", "fB")],
check.attributes = FALSE)
CharlotteJana/pdmppoly documentation built on Sept. 4, 2019, 4:40 p.m.
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Description Slots Ratepolys Dynpolys Note Examples
Description
An S4 class to represent polynomial piecewisc deterministic markov processes
(polynomial PDMPs). These processes are PDMPs with polynomial rate functions
and polynomial dynamics. This makes it possible to approximate the moments of
the process without the need of simulation, see momApp. On the
downside, simulations take much longer than simulations of the same PDMP
represented as pdmpModel.
The class is based on the pdmpModel class of package
pdmpsim but introduces additional slots that replace the slots
dynfunc and ratefunc, namely dynpolys, dynsprays,
ratepolys and ratesprays. Only slots dynpolys and
ratepolys have to be defined by the user. The other slots (including
the still existing dynfunc and ratefunc) will be set
automatically. To represent polynomials in R, package spray is
used, which stores the coefficient matrices of polynomials as sparse arrays.
Slots
dynpolysan object of class
language, more precisely a quoted list. Every element of this list contains the ODE for one of the continous variables. These ODEs are given assprayobjects and can be defined in two different ways. See section dynpolys for further information.ratepolysan object of class
language, more precisely a quoted list.This list contains the rates for every jumptype. Every element is itself a list, its length is determined by the number of different values of the discrete variable (length(discStates(obj)[[1]])). See section ratepolys for further information.dynspraysa nested list of spray objects. This slot is generated automatically out of slot
dynpolys. Do not edit it by hand.ratespraysa nested list of spray objects. This slot is generated automatically out of slot
ratepolys. Do not edit it by hand.
Ratepolys
Slot ratepolys is a quted list. The length of the list determines the number
of existing jumptypes (jumptypes are used in slot jumpfunc to
determine the next state the process jumps too). It contains the rates
determining the probability of a jump to be of type 1, 2, and so on. The
rates are polynomials that usually depend on the value of the discrete
variable at the time when the jump occurs. They are given as a list of spray
objects or numbers, for every possible discrete state separately (in the same
order as the states are given in slot discStates).
For example, let's assume that we have three different jumptypes and a
discrete variable d that can take the values 0 or 1 (so slot
discStates would be defined as list(d = 0:1)). Then slot
ratepolys will be given as follows:
1 2 3 4 5 |
Every rate of jtype i with d = j is a spray object, for example
linear(1:3).
Dynpolys
Slot dynpolys is a quoted list. The length of the list equals the number of
continuous variables of the model. Every element contains the ODE for one of
the continuous variables, given in the same order as in slot init and
given as spray objects.
The ODEs usually depend on the discrete variable,
lets call it d. An example would be df/dt =
-3f if d = 0 and df/dt = -3f + 1 if
d = 1. Here, f is the only continous variable of the model.
Every ODE can be defined in two different ways:
variant 1:
a list whose length equals the number of different states for d. Every entry is a polynomial with d taking a fixed value. The order of the entries corresponds to the order of discrete states given in slotdiscStates.variant 2:
a list of two variables:a variable
overallwhich contains a polynomial that is independent of fixed values fordand is therefore the same for all states (attention:overallcan containdas a formal variable),a variable
specificwhich contains the rest of the term. This is a list of the same form as in variant 1.
In our example, we get
Variant 1:
quote(list(list(-3*lone(1,2), -3*lone(1,2) + 1)))Variant 2:
quote(list(list(overall = linear(c(-3, 0)), specific = list(0, 1))))Variant 2 with one formula:
quote(list(list(overall = linear(c(-3, 1))))
The last variant is only possible, because in this example we have the possiblity to write both ODEs in one formula: df/dt = -3f + d.
Note
Currently, all methods only work for PDMPs with a single discrete
variable. Some methods require the discrete variable to be the last
entry in slot init. Note that it is always possible to redefine a
PDMP with multiple discrete variables in a way that only one discrete
variable is necessary.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 | #### a simple PDMP ####
#------ pdmpModel version -----
simplePdmp <- new("pdmpModel",
descr = "A simple PDMP",
init = c(f = 0, d = 0),
discStates = list(d = c(-1, 0, 1)),
times = c(from = 0, to = 10, by = 0.01),
dynfunc = function(t, x, parms) c(x["d"], 0),
ratefunc = function(t, x, parms) c(1+x["d"], 1-x["d"]),
jumpfunc = function(t, x, parms, jtype){
c(0, switch(jtype, x["d"]-1, x["d"]+1))
}
)
#------ polyPdmpModel version -----
library("spray")
simplePoly <- new("polyPdmpModel",
descr = "polyModel with two jumptypes",
init = c(f = 0, d = 0),
times = c(from = 0, to = 10, by = 0.01),
discStates = list(d = -1:1),
dynpolys = quote(list(
list(overall = lone(2,2)) # variant 2
)),
ratepolys = quote(list(
list(0, 1, 2), # first jumptype
list(2, 1, 0) # second jumptype
)),
jumpfunc = function(t, x, parms, jtype){
c(0, switch(jtype, x["d"]-1, x["d"]+1))
}
)
#------- comparison of the models --------------
identical(sim(simplePoly, outSlot = FALSE, seed = 5),
sim(simplePdmp, outSlot = FALSE, seed = 5))
#### the toggleSwitch model ####
#------ pdmpModel version -----
genePdmpT <- new("pdmpModel",
descr = "toggleswitch with two promotors",
parms = list(bA = 0.5, bB = 0.5, aA = 2, aB = 4,
k01A = 0.5, k10A = 2, k01B = 0.3, k10B = 3),
init = c(fA = 0.5, fB = 0.5, d = 4),
discStates = list(d = 1:4),
dynfunc = function(t, x, parms) {
df <- with(as.list(c(x, parms)),
c(-bA * fA, -bB * fB) + switch(d,
c(0, 0),
c(aA, 0),
c(0, aB),
c(aA, aB)))
return(c(df, 0))
},
ratefunc = function(t, x, parms) {
return(with(as.list(c(x, parms)),
c(switch(d, k01B, k01B, k10B*fA, k10B*fA),
switch(d, k01A, k10A*fB, k01A, k10A*fB))))
},
jumpfunc = function(t, x, parms, jtype) {
c(x[1:2], switch(jtype,
switch(x[3], 3, 4, 1, 2),
switch(x[3], 2, 1, 4, 3)))
},
times = c(from = 0, to = 20, by = 0.01),
solver = "lsodar")
#------ polyPdmpModel version -----
genePolyT <- new("polyPdmpModel",
descr = "toggleswitch with two promotors (polynomial version)",
parms = list(bA = 0.5, bB = 0.5, aA = 2, aB = 4,
k01A = 0.5, k10A = 2, k01B = 0.3, k10B = 3),
init = c(fA = 0.5, fB = 0.5, d = 4),
discStates = list(d = 1:4),
dynpolys = quote(list(
list(overall = -bA*lone(1,3), specific = list(0, aA, 0, aA)),
list(overall = -bB*lone(2,3), specific = list(0, 0, aB, aB))
)),
ratepolys = quote(list(
list(k01B, k01B, k10B*lone(1,3), k10B*lone(1,3)),
list(k01A, k10A*lone(2,3), k01A, k10A*lone(2,3))
)),
jumpfunc = function(t, x, parms, jtype) {
c(x[1:2], switch(jtype,
switch(x[3], 3, 4, 1, 2),
switch(x[3], 2, 1, 4, 3)))
},
times = c(from = 0, to = 20, by = 0.01),
solver = "lsodar")
#------- comparison of the models --------------
identical(sim(genePdmpT, outSlot = FALSE, seed = 10),
sim(genePolyT, outSlot = FALSE, seed = 10))
data("toggleSwitch")
times(toggleSwitch) <- c(from = 0, to = 20, by = 0.01)
all.equal(sim(genePdmpT, outSlot = FALSE, seed = 20)[, c("fA", "fB")],
sim(toggleSwitch, outSlot = FALSE, seed = 20)[, c("fA", "fB")],
check.attributes = FALSE)
|
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