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helpers_num_phase_diag.R
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gen_coef_from_df <- function(row,sp,Ns){
spr <- sp[row,]
coefs_s12_s23 <- expand.grid(
p = spr$p,
a12 = spr$a12,
a23 = spr$a23,
s12 = seq(.8*min(sp$ms12),1.25*max(sp$Ms12),length.out = Ns),
s13 = spr$s13,
s23 = seq(.8*min(sp$ms23),1.25*max(sp$Ms23),length.out = Ns)) %>%
mutate(
d = p/a12/a23
) %>%
as.matrix
coefs_s12_s13 <- expand.grid(
p = spr$p,
a12 = spr$a12,
a23 = spr$a23,
s12 = seq(.8*min(sp$ms12),1.25*max(sp$Ms12),length.out = Ns),
s13 = seq(.8*min(sp$ms13),1.25*max(sp$Ms13),length.out = Ns),
s23 = spr$s23) %>%
mutate(
d = p/a12/a23
) %>%
as.matrix
coefs_s23_s13 <- expand.grid(
p = spr$p,
a12 = spr$a12,
a23 = spr$a23,
s12 = spr$s12,
s13 = seq(.8*min(sp$ms13),1.25*max(sp$Ms13),length.out = Ns),
s23 = seq(.8*min(sp$ms23),1.25*max(sp$Ms23),length.out = Ns)) %>%
mutate(
d = p/a12/a23
) %>%
as.matrix
coefs_a12_a23 <- expand.grid(
p = spr$p,
a12 = seq(.8*min(sp$ma12),1.25*max(sp$Ma12),length.out = Ns),
a23 = seq(.8*min(sp$ma23),1.25*max(sp$Ma23),length.out = Ns),
s12 = spr$s12,
s13 = spr$s13,
s23 = spr$s23) %>%
mutate(
d = p/a12/a23
) %>%
as.matrix
r <- list('s12_s23' = coefs_s12_s23,
's12_s13' = coefs_s12_s13,
's23_s13' = coefs_s23_s13,
'a12_a23' = coefs_a12_a23)
return(r)
}
evol_to_stable_state <- function(row_c,coefsi,U0 = NULL){
coef_vec <- coefsi[row_c,]
weight_matrix <- construct_weight_matrix_from_coefs_3x3(coef_vec)
if(is.null(U0)){
U0 <- rep(0.5,3)
names(U0) <- paste('Y',1:3,sep='')
}
parms_ap <- prepare_parms_approx(
weight_matrix = weight_matrix,
dem_coef = c(0,0,coef_vec['d']),
prod_coef = c(coef_vec['p'],0,0),
epsilon = 1e-6
)
times_parms <- list(length = 6e3,tMax=5,tMin=0)
U <- simulate_exact_system(
U0 = U0, dU = dU_exact, parms = parms_ap,
times_parms = times_parms
) %>%
as.data.frame()
test_stability <- U %>%
tail(n = 10) %>%
mutate(dY1 = Y1 - lag(Y1,2),
dY2 = Y2 - lag(Y2,2),
dY3 = Y3 - lag(Y3,2),
dt = time - lag(time,2)) %>%
mutate(Y1p = dY1/dt,Y2p = dY2/dt, Y3p = dY2/dt) %>%
tail() %>%
summarise(modul = mean(sqrt(Y1p**2+Y2p**2+Y3p**2))) %>%
unlist() %>%
{. < 1e-4}
while(!test_stability){
U0 <- tail(U,n=1)[c('Y1','Y2','Y3')] %>% as.matrix %>% c
names(U0) <- c('Y1','Y2','Y3')
U <- simulate_exact_system(
U0 = U0, dU = dU_exact, parms = parms_ap,
times_parms = times_parms
) %>%
as.data.frame
test_stability <- U %>%
tail(n = 10) %>%
mutate(dY1 = Y1 - lag(Y1,2),
dY2 = Y2 - lag(Y2,2),
dY3 = Y3 - lag(Y3,2),
dt = time - lag(time,2)) %>%
mutate(Y1p = dY1/dt,Y2p = dY2/dt, Y3p = dY2/dt) %>%
tail() %>%
summarise(modul = mean(sqrt(Y1p**2+Y2p**2+Y3p**2))) %>%
unlist() %>%
{. < 1e-4}
}
U <- U %>%
tail(n=1) %>%
mutate(row_c = row_c) %>%
bind_cols(as.data.frame(t(as.data.frame(coef_vec))))
rownames(U) <- NULL
return(U)
}
gen_coef_for_failures <- function(sc,df){
N1 <- df %>% filter(scenario == sc,Var1 == 'refinery') %>% select(Freq) %>% unlist %>% as.numeric
N2 <- df %>% filter(scenario == sc,Var1 == 'terminal') %>% select(Freq) %>% unlist %>% as.numeric
N3 <- df %>% filter(scenario == sc,Var1 == 'gas_station') %>% select(Freq) %>% unlist %>% as.numeric
fgs_ref <- (df %>% filter(scenario == sc,Var1 == 'gas_station-refinery-road') %>% select(Freq) %>% unlist %>% as.numeric)/(df %>% filter(scenario == '0',Var1 == 'gas_station-refinery-road') %>% select(Freq) %>% unlist %>% as.numeric)
fgs_term <- (df %>% filter(scenario == sc,Var1 == 'terminal-gas_station-road') %>% select(Freq) %>% unlist %>% as.numeric)/(df %>% filter(scenario == '0',Var1 == 'terminal-gas_station-road') %>% select(Freq) %>% unlist %>% as.numeric)
fref_term <- (df %>% filter(scenario == sc,Var1 == 'terminal-refinery-road') %>% select(Freq) %>% unlist %>% as.numeric)/(df %>% filter(scenario == '0',Var1 == 'terminal-refinery-road') %>% select(Freq) %>% unlist %>% as.numeric)
Mpipe <- df %>% filter(scenario == sc) %>% select(min_cut) %>% unlist %>% as.numeric %>% unique
C1 <- seq(1,1.5,2.5e-2) * 38.2 # MillonGallons
C2 <- seq(1,2,2.5e-2) * 31 # MillonGallons
C3 <- 35 * 10**-3 # MillonGallons
P <- 18.9 * 5 / N1 # MillionGallons Per Week
W12M12pipe <- seq(2,4,length.out = 10) * 7 * Mpipe # MillonGallons Per Week
W12M12truck <- seq(3,7,length.out = 10) * 10**-3 * 7 * (N1*N2-Mpipe) * fref_term# MillonGallons Per Week
W13M13 <- seq(3,11.6,length.out = 10) * 10**-3 * 7 * N1*200 * fgs_ref # MillonGallons Per Week
W23M23 <- seq(3,7,length.out = 10) * 10**-3 * 7 * 5000 * fgs_term # MillonGallons Per Week
W12M12 <- seq(min(W12M12pipe+W12M12truck),max(W12M12pipe+W12M12truck),length.out = 10)
coef1 <- expand.grid(
N1 = N1,
N2 = N2,
N3 = N3,
C1 = C1,
C2 = C2,
C3 = C3,
P = P)
coef2 <- expand.grid(
W12M12 = W12M12,
W13M13 = W13M13,
W23M23 = W23M23,
P = P)
a_function <- function(x){
sp <- x %>% summarise(
p = mean(p),
s12 = mean(s12),
s13=mean(s13),
s23=mean(s23),
a12 = mean(a12),
a23 = mean(a23)
)
lapply(
seq(0,100,2.5),
function(f){
x %>%
summarise(
u = mean(p*f/100 <= s13 + ifelse(s12 < a12*s23,s12,a12*s23)
)) %>%
setNames(paste('survivor',f,sep=''))
}) %>%
bind_cols(sp,.) %>%
return()
}
left_join(coef1,coef2,by='P') %>%
mutate(
p = P/C1,
a12 = N2*C2 / (N1 * C1),
a23 = N3*C3 / (N2 * C2),
s12 = W12M12/(N1*C1),
s13 = W13M13/(N1*C1),
s23 = W23M23/(N2*C2),
d = p / (a12 * a23),
D = C3*d
) %>%
as.matrix() %>%
return()
}