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Monad_S_map_demo.Rmd
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Monad_S_map_demo.Rmd
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## Preamble
```{r}
library(tidyverse)
library(deSolve)
library(rgl)
library(rEDM)
library(gridExtra)
library(colorspace)
```
## Seasonal Monad
Ref: Huppert A., Blasius B., Olinky R., and Stone L. A model for seasonal phytoplankton blooms
Figure 10 c,d. The classical Monad equations with seasonal growth rate.
### Model Definition
```{r}
sim_Monad <- function(params,
x0,
sim_length = 50,
burn_length = 10,
tau = 1/48){
dF <- function(t,x,params){
with(as.list(c(params,x)),{
# beta <- 1 + delta_*ifelse(sin(2*pi*t)>0,1,-1)
beta <- 1 + delta_*(sin(2*pi*t))
dN <- I_ - b_*beta*(N*P)/(k_+N) - q_*N
dP <- c_*beta*N*P/(k_+N) - d_*P
return(list(c(dN,dP),beta=beta))
}) # with({})
} # dF
out <- ode(y = x0,
times = seq(-burn_length,sim_length,by=tau),
func = dF,
parms = params)
out <- as.data.frame(out) %>%
filter(time > 0)
return(out)
}
```
Parameters
```{r}
mu_Monad_ab <- c(I_ = 1500,
b_ = 0.0000204,
c_ = 83,
d_ = 73,
q_ = 0.1,
k_ = 65,
delta_ = 0.12)
mu_Monad_cd <- c(I_ = 720,
b_ = 0.0000204,
c_ = 83,
d_ = 73,
q_ = 0.1,
k_ = 65,
delta_ = 0.08)
x0 <- c(N=800,P=10^3)
```
Generate data and normalize.
```{r}
data_Monad <- sim_Monad(params = mu_Monad_cd,x0 = x0,burn_length = 70,sim_length = 50)
block_Monad <- data_Monad %>%
filter(row_number() %% 2 == 0) %>%
mutate_at(vars(-time),list(~ ./max(.,na.rm=TRUE)))
```
Define plotting function to visualize S-map weighting scheme.
```{r}
plot_attractor_and_smapweight <- function(block_3d,index_target=nrow(block_3d)-1,theta=0,n_colors=99,no_lines=FALSE){
# names(block_3d) <- c("x","y","z")
dist_to_target <- map_dbl(1:nrow(block_3d), ~ norm(block_3d[.,2:4] - block_3d[index_target,2:4],type="2"))
w_smap <- exp(-theta*dist_to_target/mean(dist_to_target))
# df_plot <- bind_cols(block_3d,data.frame(w_smap=w_smap)) %>%
# mutate(color_s_map = cut(w_smap,
# # breaks=c(-999,seq(0,1,length.out=n_colors)),
# breaks = seq(0,1,length.out=n_colors+1),
# labels=diverge_hcl(n_colors)))
df_plot <- bind_cols(block_3d,data.frame(w_smap=w_smap))
rgl::open3d()
for(i in 1:(NROW(df_plot)-1)){
if(i == index_target){
points3d(df_plot[i,2],
df_plot[i,3],
df_plot[i,4],
color="red",
size=9
)
}else{
points3d(df_plot[i,2],
df_plot[i,3],
df_plot[i,4],
alpha=df_plot[i,'w_smap'])
if(!no_lines){
lines3d(df_plot[(i):(i+1),2],
df_plot[(i):(i+1),3],
df_plot[(i):(i+1),4],
alpha=df_plot[i,'w_smap'])
}
}
} # for(i)
return(df_plot)
}
```
Define a viewpoint for rgl.
```{r}
# a <- 1/15
a <- 2/15
M_1 <- diag(4) %*% matrix(c(1,0,0,0 ,
0,cospi(a),-sinpi(a),0,
0,sinpi(a),cospi(a),0,
0,0,0,1),byrow = TRUE,nrow=4)
M_2 <- rbind( c( 0.95376158, -0.006761581 , -0.3004880 , 0),
c(-0.09048322, 0.946909606, -0.3085050, 0),
c(0.28662089, 0.321429372, 0.9025141, 0),
c(0.0000000, 0.00000000, 0.0000000, 1) )
```
Generate sequential weighting panels.
```{r}
dir_frames <- "FIGURES/SMAP_WEIGHTING/"
file_root <- "monad_smap_weighting"
t_0 = 27 + 2/12
# t_0 = 7 + 3/12
block_Monad_polar3d <- block_Monad %>%
filter(time <= t_0) %>%
mutate(x = N*sin(time*2*pi),y=P,z=N*cos(time*2*pi)) %>%
select(time,x,y,z)
theta_list <- c(0,0.1,0.3,1,3,10)
# theta_list <- c(0,3)
for(i.theta in 1:length(theta_list)){
theta_i <- theta_list[i.theta]
filename_i <- paste0(dir_frames,file_root,"theta=",formatC(theta_i,digits=2,flag="0",format="f"),".svg")
dump_plot <- plot_attractor_and_smapweight(block_Monad_polar3d,index_target = nrow(block_Monad_polar3d)-1,theta=theta_i)
## decorate polar
lines3d(c(0,0),c(0,1),c(0,0))
text3d(0,1.1,0,"P",cex=2)
# phi_labels=c('Jan','Feb','Mar','Apr','May','Jun','Jul','Aug','Sep','Oct','Nov','Dec')
phi_labels=c('Jan','Feb','','Apr','May','Jun','Jul','Aug','Sep','Oct','Nov','Dec')
# lines3d(c(0,1),c(0,0),c(0,0))
# lines3d(c(0,-1),c(0,0),c(0,0))
lines3d(c(0,1)*sin(pi/2),c(0,0),c(0,1)*cos(pi/2))
text3d(1.1*sin(pi/2),c(0,0),1.1*cos(pi/2),"N",cex=2)
# lines3d(c(0,1)*sin(ratio_i*(pi) + pi/2),c(0,0),c(0,1)*cos(ratio_i*(pi) + pi/2))
text3d(1,1,0,paste(intToUtf8(952),"=",theta_i),cex=2)
for(i.season in 1:12){
phi.i <- 2*pi*i.season/12
lines3d(c(0,1)*sin(phi.i),c(0,0),c(0,1)*cos(phi.i))
text3d(1.1*sin(phi.i),0,1.1*cos(phi.i),phi_labels[i.season])
}
par3d(userMatrix=M_1)
par3d(windowRect=c(80,100,690,650))
rgl.postscript( filename_i, fmt="svg", drawText = T )
}
```
```