sobol_ode: Wrapper around 'deSolve' 'ode'.

In sensobol: Computation of Variance-Based Sensitivity Indices

Wrapper around deSolve ode.

Description

It solves a system of ordinary differential equations and extracts the model output at the selected times.

Usage

sobol_ode(d, times, timeOutput, state, func, ...)

Arguments

d	Character vector with the name of the model inputs.
times	Time sequence as defined by ode.
timeOutput	Numeric vector determining the time steps at which the output is wanted.
state	Initial values of the state variables.
func	An R function as defined by ode.
...	Additional arguments passed to ode.

Value

A matrix with the output values.

Examples

# Define the model: the Lotka-Volterra system of equations
lotka_volterra_fun <- function(t, state, parameters) {
with(as.list(c(state, parameters)), {
  dX <- r * X * (1 - X / K) - alpha * X * Y
  dY <- -m * Y + theta * X * Y
  list(c(dX, dY))
 })
 }

# Define the settings of the sensitivity analysis
N <- 2 ^ 5 # Sample size of sample matrix
params <- c("r", "alpha", "m", "theta", "K", "X", "Y") # Parameters

# Define the times
 times <- seq(5, 20, 1)

 # Define the times at which the output is wanted
 timeOutput <- c(10, 15)

# Construct the sample matrix
mat <- sobol_matrices(N = N, params = params)

# Transform to appropriate distributions
mat[, "r"] <- qunif(mat[, "r"], 0.8, 1.8)
mat[, "alpha"] <- qunif(mat[, "alpha"], 0.2, 1)
mat[, "m"] <- qunif(mat[, "m"], 0.6, 1)
mat[, "theta"] <- qunif(mat[, "theta"], 0.05, 0.15)
mat[, "K"] <- qunif(mat[, "K"], 47, 53)
mat[, "X"] <- floor(mat[, "X"] * (15 - 8 + 1) + 8)
mat[, "Y"] <- floor(mat[, "Y"] * (2 - 6 + 1) + 6)

# Run the model
y <- list()
for (i in 1:nrow(mat)) {
  y[[i]] <- sobol_ode(d = mat[i, ],
                     times = times,
                     timeOutput = timeOutput,
                     state = c(X = mat[[i, "X"]], Y = mat[[i, "Y"]]),
                     func = lotka_volterra_fun)
}

sensobol documentation built on April 6, 2023, 5:22 p.m.