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Update main.Rmd #2

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328 changes: 221 additions & 107 deletions main.Rmd
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Original file line number Diff line number Diff line change
Expand Up @@ -2,17 +2,27 @@
title: "FamiliaR with Dynamics"
output:
flexdashboard::flex_dashboard:
orientation: columns
orientation: column
social: menu
source_code: embed
theme: spacelab
runtime: shiny
---

<style>

.form-control {
width: 90%;
}

</style>


```{r global, include=FALSE}
# load data in 'global' chunk so it can be shared by all users of the dashboard
library(datasets)
library(ggplot2)
library(bslib)
options(shiny.maxRequestSize = 30*1024^2)
data(faithful)
Solow1 <- function(s,k,a){
Expand Down Expand Up @@ -75,10 +85,9 @@ conditionalPanel("input.model == 'Solow'",
sliderInput("d", label = "Depreciation:", min = 0, max = 1, value =0.02, step = 0.01),
sliderInput("n", label = "Population growth rate:", min = 0, max = 1, value =0.5, step = 0.01),
sliderInput("t", label = "Time", min = 0, max = 100, value =20, step = 5),
numericInput('k0', 'Initial capital, k0:', 3, min=0.5, max=200),
actionButton("go","(Re)start Numeric Simulation")
numericInput('k0', 'Initial capital, k0:', 3, min=0.5, max=200)

)

conditionalPanel("input.model == 'Ramsey'",
sliderInput("t", label = "Time", min = 0, max = 200, value = 50, step = 5),
sliderInput("c", label = "Consumption, dc/dt",min = 0, max = 5, value = 3, step = 0.05),
Expand All @@ -89,97 +98,190 @@ conditionalPanel("input.model == 'Ramsey'",
sliderInput("alpha", label = "Elasticity parameter (measuring the responsiveness of the output production to changes in the input capital):", min = 0, max = 1, value = 0.3, step = 0.01),

)
```

Column
-----------------------------------------------------------------------


### Initial values {data-height=350}
```{r}

####################################################
#Conditional panel for initial values for Solow model#
####################################################
conditionalPanel("input.model == 'Solow'",
sliderInput("initial_values", label="initial values", min=1, max=5, value=1, step=1),
conditionalPanel("input.initial_values == 1",
numericInput('aa1', 'a', 1 )),
conditionalPanel("input.initial_values == 2",
fillRow(numericInput('aa2', 'a', 1),
numericInput('bb2', 'b', 1))),
conditionalPanel("input.initial_values == 3",
fillRow(numericInput('aa3', 'a', 1),
numericInput('bb3', 'b', 1),
numericInput('cc3', 'c', 1))),
conditionalPanel("input.initial_values == 4",
fillRow(
numericInput('aa4', 'a', 1),
numericInput('bb4', 'b', 1),
numericInput('cc4', 'c', 1),
numericInput('dd4', 'd', 1))
),

conditionalPanel("input.initial_values == 5",
fillRow(
numericInput('aa5', 'a', 1),
numericInput('bb5', 'b', 1),
numericInput('cc5', 'c', 1),
numericInput('dd5', 'd', 1),
numericInput('ee5', 'e', 1))
),
actionButton("go","(Re)start Numeric Simulation", style="background-color: #ec7063 ; border-radius: 10px !important; border: none; position:absolute; bottom: 5px; margin: auto;"
))

######################################################
#Conditional panel for initial values for Goodwin model#
#####################################################
#y0 <- matrix(c(0.2, 1, 0.6, 1, 1.1, 1), ncol = 2, nrow = 3, byrow = TRUE)
conditionalPanel("input.model == 'Goodwin'",
fluidPage(
fluidRow(
sliderInput("initial_values_g",
label="initial values",
min=1,
max=3,
value=1,
step=1)
),
fluidRow(
conditionalPanel("input.initial_values_g == 1",
numericInput('gaa1', 'a', 0.2 ),
numericInput('gbb1', 'b', 1)),
conditionalPanel("input.initial_values_g == 2",
column(6,
numericInput('gaa2', 'a1', 0.2),
numericInput('gbb2', 'b1', 1)),
column(6,
numericInput('gcc2', 'a2',0.6),
numericInput('gdd2', 'b2',1))),
conditionalPanel("input.initial_values_g == 3",
column(4,
numericInput('gaa3', 'a1', 0.2),
numericInput('gbb3', 'b1', 1)),
column(4,
numericInput('gcc3', 'a2', 0.6),
numericInput('gdd3', 'b2', 1)),
column(4,
numericInput('gee3', 'a3', 0.8),
numericInput('gff3', 'b3', 1)))),
fluidRow(
actionButton("go2",
"(Re)start Numeric Simulation",
style="background-color: #ec7063 ; border-radius: 10px !important; border: none; position:absolute; bottom: 5px; margin: auto;"))))

```

Column
-----------------------------------------------------------------------




### Numerical Simulations

```{r}
renderPlot({
if (input$model == "Solow") {
req(input$go)
phaseR::flowField(solow_de,
xlim = c(0.0001, input$t),
ylim = c(0.0001, input$k),
parameters = c(input$s,input$a,input$d),
points=10,
system = 'one.dim',
add = F,
xlab = 't',
ylab = 'dk/dt')

phaseR::nullclines(solow_de,
xlim = c(0.0001, input$t),
ylim <- c(0.0001,input$k),
parameters = c(input$s,input$a,input$d),
system = "one.dim",
state.names = 'k')

phaseR::trajectory(solow_de,
y0 = input$k0,
tlim = c(0,500),
parameters = c(input$s,input$a,input$d),
system = "one.dim",
colour = rep("black"),
add = T)
}
else if (input$model == "Goodwin") {
parameters <- c(a = 1.5,
b = 1.8,
c = 0.8,
d = 0.8,
sigma=0.8)
state <- c(V = 0.5,
U = 1,
Q = 1)
times <- seq(0, 20, by = 0.01)
out <- deSolve::ode(y = state, times = times, func = goodwin2, parms = parameters)
par(oma = c(0, 0, 3, 0))
plot(out, xlab = "time", ylab = "-")
}

else if (input$model == "Ramsey"){
ramsey.flowField <- phaseR::flowField(
ramsey,
xlim = c(0.01,input$k),
ylim = c(0.01,input$c),
parameters = c(0.2,0.03,0.1,0.3),
points = 10,
add=F
)
grid()

ramsey.nullclines <- phaseR::nullclines(
ramsey,
xlim = c(0,input$k),
ylim = c(0.01,input$c),
state.names = c('k','c'),
parameters = c(0.2,0.03,0.1,0.3),
points = 500,
col = c("blue","red"),
add.legend=T
)

}

})
```
initial_val <- eventReactive(input$go, {
print(typeof(input$initial_values))
nval <- input$initial_values
print(paste("nval=",nval))
if(nval==1){return(c(input$aa1))}
else if (nval==2){return(c(input$aa2,input$bb2))}
else if(nval==3){return(c(input$aa3,input$bb3,input$cc3))}
else if(nval==4){return(c(input$aa4,input$bb4,input$cc4,input$dd4))}
else {return(c(input$aa5,input$bb5,input$cc5,input$dd5,input$ee5))}

# ifelse(nval==1, c(a),
# ifelse(nval==2, c(a,b),
# ifelse(nval==3, c(a,b,c),
# ifelse(nval==4, c(a,b,c,d),
# c(a,b,c,d,e)))))
})
initial_val_g <- eventReactive(input$go2, {
return(c(input$gaa2,input$gbb2))})

conditionalPanel("input.model == 'Solow'",
renderPlot({
ini <- initial_val()
phaseR::flowField(solow_de,
xlim = c(0.0001, input$t),
ylim = c(0.0001, input$k),
parameters = c(input$s,input$a,input$d),
points=10,
system = 'one.dim',
add = F,
xlab = 't',
ylab = 'dk/dt')
phaseR::nullclines(solow_de,
xlim = c(0.0001, input$t),
ylim <- c(0.0001,input$k),
parameters = c(input$s,input$a,input$d),
system = "one.dim",
state.names = 'k')
phaseR::trajectory(solow_de,
y0 = ini,
tlim = c(0, input$t),
parameters = c(input$s,input$a,input$d),
system = "one.dim",
add = T)}),
style="position: absolute; aspect-ratio: auto")

conditionalPanel("input.model == 'Goodwin'",
renderPlot({
ini_g <- initial_val_g()
parameters <- c(a = 1.5,
b = 1.8,
c = 0.8,
d = 0.8,
sigma=0.8)
state <- c(V = ini_g[1], #0.5
U = ini_g[2], #1
Q = 1)
times <- seq(0, 20, by = 0.01)
out <- deSolve::ode(y = state, times = times, func = goodwin2, parms = parameters)
par(oma = c(0, 0, 3, 0))
plot(out, xlab = "time", ylab = "-")}),
style="position: absolute; aspect-ratio: auto")

conditionalPanel("input.model == 'Ramsey'",
renderPlot({
phaseR::flowField(
ramsey,
xlim = c(0.01,input$k),
ylim = c(0.01,input$c),
parameters = c(0.2,0.03,0.1,0.3),
points = 10,
add=F)
#grid()
phaseR::nullclines(
ramsey,
xlim = c(0,input$k),
ylim = c(0.01,input$c),
state.names = c('k','c'),
parameters = c(0.2,0.03,0.1,0.3),
points = 500,
col = c("blue","red"),
add.legend=T)}),
style="position: absolute; aspect-ratio: auto")
```

Column {.tabset}
-----------------------------------------------------------------------
--------------------------------------------------------------------

### Dynamics

```{r}
#renderPrint(input$model)
#uiOutput("dynamic")
conditionalPanel("input.model == 'Solow'",
renderPlot({
k <- 1:input$k
if (input$model == "Solow") {
Expand All @@ -190,42 +292,54 @@ renderPlot({
#plot(k,Solow(input$s,k, input$a), type="l")
#lines(k,Solow(input$s,k, -input$a), type="l")
}
})
}),style="position: absolute; aspect-ratio: auto")
```

### Phase Portrait/Phase Diagram

```{r}
renderPlot({
if (input$model == "Solow"){
phaseR::phasePortrait(solow_de,
ylim <- c(0.5,input$k),
parameters = c(input$s,input$a,input$d),
col = 'black',
add.grid = T,
xlab='k',
ylab='dk/dt')
}
if (input$model == "Goodwin"){
phaseR::flowField(goodwin,
xlim = c(0,1.5),
ylim = c(0, 1.5),
parameters = c(0.25, 0.6, 0.2, 0.3, 0.4),
points = 19,
add = FALSE)
phaseR::nullclines(goodwin,
xlim = c(0,1.5),
ylim = c(0, 1.5),
parameters = c(0.25, 0.6, 0.2, 0.3, 0.4),
points = 500)
y0 <- matrix(c(0.2, 1, 0.6, 1, 1.1, 1), ncol = 2, nrow = 3, byrow = TRUE)
phaseR::trajectory(goodwin,
y0 = y0,
tlim = c(0,10),
parameters = c(0.25, 0.6, 0.2, 0.3, 0.4),
colour = rep("black", 3))
}
})
y_in <- eventReactive(input$go2, {
print(input$initial_values_g)
print(c(input$aa3, input$bb3, input$cc3, input$dd3, input$ee3, input$ff3))
if(input$initial_values_g==1){
return(matrix(c(input$gaa1, input$gbb1), ncol = 1, nrow = 2, byrow = TRUE))}
else if(input$initial_values_g==2){
return(matrix(c(input$gaa2, input$gbb2, input$gcc2, input$gdd2), ncol = 2, nrow = 2, byrow = TRUE))}
else{return(matrix(c(input$gaa3, input$gbb3, input$gcc3, input$gdd3, input$gee3, input$gff3), ncol = 3, nrow = 2, byrow = TRUE))}})

conditionalPanel("input.model == 'Solow'",
renderPlot({
phaseR::phasePortrait(solow_de,
ylim <- c(0.5,input$k),
parameters = c(input$s,input$a,input$d),
col = 'black',
add.grid = T,
xlab='k',
ylab='dk/dt')}),
style="position: absolute; aspect-ratio: auto")

conditionalPanel("input.model == 'Goodwin'",
renderPlot({
y0 <- y_in()
phaseR::flowField(goodwin,
xlim = c(0,1.5),
ylim = c(0, 1.5),
parameters = c(0.25, 0.6, 0.2, 0.3, 0.4),
points = 19,
add = FALSE,
xlab = "a",
ylab = "b")
phaseR::nullclines(goodwin,
xlim = c(0,1.5),
ylim = c(0, 1.5),
parameters = c(0.25, 0.6, 0.2, 0.3, 0.4),
points = 500)
phaseR::trajectory(goodwin,
y0 = y0,
tlim = c(0,10),
parameters = c(0.25, 0.6, 0.2, 0.3, 0.4),
colour = rep("black", 3))}),
style="position: absolute; aspect-ratio: auto")
```


Expand Down