Hello,
I am new to Julia, started using it in R to solve SDEs. I am trying to solve this system of SDEs, dX = (-X*a + (Y-X) b + h)dt + g dW and dY = (-Y a + (X-Y)*b)dt for time [0,200], a=0.30, b=0.2, g=1 and h is 1 for time [50,70] and 0 otherwise. I have the following code for the system for constant h=1:
(The code is from R)
library(diffeqr) ##for solving ODEs SDEs DDEs..
library(deSolve)
library(Julia) ##used for the sde
library(JuliaCall)
library(data.table)
library(minpack.lm)
tryCatch(system2(file.path(JULIA_HOME, "julia"),
"-E \"try println(JULIA_HOME) catch e println(Sys.BINDIR) end;\"", stdout = TRUE)[1],
warning = function(war) {},
error = function(err) NULL)
julia_setup(JULIA_HOME ="/home/tim/.local/share/R/JuliaCall/julia/v1.5.0/bin")
##calling Julia
JuliaCall:::julia_locate(JULIA_HOME = "/home/tim/.local/share/R/JuliaCall/julia/v1.5.0/bin")
## setup of the packages
de <- diffeqr::diffeq_setup()
julia <- julia_setup()
#u0 is the starting value for the vector
#func1 is the ODE TO SOLVE
#f is the drift part in the sde
#g is the diffusion part in the sde
#p are the parameters associated to the sde
# noise_rate_prototype is a sparse matrix by making a dense matrix and setting some values as not zero
#starting value for the three variables
u0<-c(0,0)
## parameters
a=0.33;
b=0.2;
g=1;
h=1;
## parameters of the sde
p<-c(a, b, g, h)
## drift part in the SDE
f <- JuliaCall::julia_eval("
function f(dy,y,p,t)
dy[1] = -y[1]*p[1] + (y[2]-y[1])*p[2] + p[4]
dy[2] = -y[2]*p[1] + (y[1]-y[2])*p[2]
end")
## diffusion part in the SDE
g <- JuliaCall::julia_eval("
function g(dy,y,p,t)
dy[1,1] = p[3]
dy[2,1] = 0
end")
## matrix associated to the noise
noise_rate_prototype <- matrix(rep(1,2), nrow = 2, ncol = 1)
tspan <- c(0.,200)
JuliaCall::julia_assign("u0", u0); ## initial value
JuliaCall::julia_assign("tspan", tspan); ## grid
JuliaCall::julia_assign("p", p); ## parameters
JuliaCall::julia_assign("noise_rate_prototype", noise_rate_prototype); ## matrix associated to the noise
## call the SDE problem
prob <- JuliaCall::julia_eval("SDEProblem(f, g, u0,tspan,p, noise_rate_prototype=noise_rate_prototype)");
sol <- de$solve(prob)
udf <- as.data.frame(t(sapply(sol$u,identity)))
#plot the 2 figures,
plot(sol$t,udf$V1,type="l",col="purple", ylab="Y1") #L
lines(sol$t,udf$V2,col="red",ylab="Y2") #R
I am not sure how to include the time dependence of h, I tried to do it by including a forcing variable (in the form of ‘signal’) but I got a lengthy Julia error (stating that h is not defined- code below) . So perhaps thats not the way to go. I’d appreciate any help regarding this.
The chunk of the code I changed to include the time dependent parameters is this (the new or changes lines have an arrow to their right):
## drift part in the SDE
f <- JuliaCall::julia_eval("
function f(dy,y,p,t)
MU <- signal(t) # <-
dy[1] = -y[1]*p[1] + (y[2]-y[1])*p[2] + MU # <-
dy[2] = -y[2]*p[1] + (y[1]-y[2])*p[2]
end")
signal <- approxfun(x = c(0, 35, 125, 200), # <-
y = c(0, 1, 0, 0),
method = "constant", rule = 2)
## diffusion part in the SDE
g <- JuliaCall::julia_eval("
function g(dy,y,p,t)
dy[1,1] = p[3]
dy[2,1] = 0
end")
## matrix associated to the noise
noise_rate_prototype <- matrix(rep(1,2), nrow = 2, ncol = 1)
tspan <- c(0,200)
JuliaCall::julia_assign("u0", u0); ## initial value
JuliaCall::julia_assign("tspan", tspan); ## grid
JuliaCall::julia_assign("p", p); ## parameters
JuliaCall::julia_assign("signal", signal); # <-
JuliaCall::julia_assign("noise_rate_prototype", noise_rate_prototype); ## matrix associated to the noise
## call the SDE problem
prob <- JuliaCall::julia_eval("SDEProblem(f, g, u0,tspan,p, noise_rate_prototype=noise_rate_prototype, signal=signal)"); # <-
The rest of the code remained the same. Please help me correct this.