fastIsoboles: Grid refinement algorithm to calculate isoboles

In IntiQuan/populationIsoboles: Calculate isoboles efficiently

Description

Grid refinement algorithm to calculate isoboles

Usage

fastIsoboles(
  objfun,
  objvalue = 0.95,
  gridmin = c(x = 0, y = 0),
  gridmax = c(x = 1, y = 1),
  imin = 5,
  imax = 7,
  FLAGverbose = FALSE,
  k = NULL,
  .outputFolder = NULL,
  areaterm = 1.01
)

Arguments

objfun	Function(x,y) returning a vector of the same length with the corresponding objvalue values. Combined with objvalue, this could be called the objective function
objvalue	The value for which the contour lines are calculated. E.g. 0.95
gridmin	General grid parameters: Vectors with names x and y c(x = 0, y = 0)
gridmax	General grid parameters: Vectors with names x and y c(x = 0, y = 0)
imin, imax	minimum/maximum number of iterations
FLAGverbose	Print messages to the console
k	index of population for outputting the current isobole iteration to the disk
.outputFolder	Path to store results in. See output_gridrefinement_results
areaterm	Terminate when the area above the curve (bounded by the grid) doesn't change more than this value (on relative scale)

Value

list with * grid: Exact objvalue values where the objvalue has been evaluated * path: The last isobole path * pathlist: The paths of all iterations * itermax: The number of iterations used * areas: The areas above the isobole (To analyze the convergence) * times: proc.time - stamps. The first entry is before iteration 0, the second is after iteration 1 etc.

Author(s)

Daniel Lill, IntiQuan [e-mail]

See Also

Other Grid refinement functions for isoboles: arrange_isobole_internal(), fastIsoboles_iteration0(), fastIsoboles_iteration(), get_gridlens(), get_isobole_path()

Examples

library(populationIsoboles)
library(data.table)
library(ggplot2)

# Two drugs on different scales
objfun1 <- function(x,y) {sqrt((0.001)^2 * x^2 + (0.1)^2 * y^2)}
gridmin <- c(x = 0, y = 0) + 0.0001
gridmax <- c(x = 10*2^7, y = 0.1*2^7) + 0.0001

# Quick plot of function
testobjvalue = data.table(expand.grid(
  x = populationIsoboles:::seqminmax(
      gridmin["x"], gridmax["x"], (gridmax["x"] - gridmin["x"])/(2^6)),
  y = populationIsoboles:::seqminmax(
      gridmin["y"], gridmax["y"], (gridmax["y"] - gridmin["y"])/(2^6))))
testobjvalue[,`:=`(objvalue1 = objfun1(x,y))]
ggplot(testobjvalue, aes(x,y, z = objvalue1)) +
  geom_contour(aes(color = ..level..))

# Run algorithm
isobole <- fastIsoboles( objfun1,0.95,gridmin, gridmax, 5,7)
# Plot algo results
ggplot() + geom_tile(data = isobole$grid, aes(x,y,fill = objvalueCum)) +
  geom_path(data = isobole$pathlist[[5]], aes(xp,yp)) +
  geom_path(data = isobole$pathlist[[1]], aes(xp,yp), linetype = 2) +
  scale_fill_viridis_c()

# Plot grid iterations
grd <- copy(isobole$grid)
grd[,`:=`(objvalue0 = NULL, evaluated0 = NULL, objvalueCum = NULL, evaluatedCum = NULL)]
grd <- melt(grd,c("x", "y"), measure = patterns("^evaluated", "objvalue"),
            variable.name = "iteration", value.name = c("evaluated","objvalue"),
            variable.factor = FALSE)
grd[,`:=`(iteration = as.numeric(as.character(iteration)))]
grd <- grd[!is.na(objvalue)]
grd[evaluated == 0 ,`:=`(evaluated = NA)]
ggplot() +
  geom_tile(data = grd, aes(x,y,fill = factor(evaluated * iteration))) +
  geom_point(data = grd, aes(x,y,shape = factor(evaluated * iteration))) +
  geom_path(data = isobole$pathlist[[5]], aes(xp,yp))

# Run algorithm - different objvalue - Level
isobole <- fastIsoboles(objfun1, 0.5,gridmin, gridmax, 5,7)
# Plot algo results
ggplot() + geom_tile(data = isobole$grid, aes(x,y,fill = objvalueCum)) +
  geom_path(data = isobole$pathlist[[5]], aes(xp,yp)) + scale_fill_viridis_c()

# Run algorithm - lower imin
isobole <- fastIsoboles(objfun1,0.95, gridmin, gridmax, 3,7)
isobole$itermax
# Plot algo results
ggplot() + geom_tile(data = isobole$grid, aes(x,y,fill = objvalueCum)) +
  geom_path(data = isobole$pathlist[[3]], aes(xp,yp)) + scale_fill_viridis_c()

# Run algorithm - lower imin & imax
isobole <- fastIsoboles(objfun1,0.95, gridmin, gridmax, 3,3)
isobole$itermax
# Plot algo results
ggplot() + geom_tile(data = isobole$grid, aes(x,y,fill = objvalueCum)) +
  geom_path(data = isobole$pathlist[[3]], aes(xp,yp)) + scale_fill_viridis_c()

# Run algorithm - Different function
objfun2 <- function(x,y) {(x+500)*(y+5)/(80^2)}
isobole <- fastIsoboles(objfun2,0.95, gridmin, gridmax, 3,7)
isobole$itermax
# Plot algo results
ggplot() + geom_tile(data = isobole$grid, aes(x,y,fill = objvalueCum)) +
  geom_path(data = isobole$pathlist[[3]], aes(xp,yp)) + scale_fill_viridis_c()

IntiQuan/populationIsoboles documentation built on Jan. 13, 2022, 8:29 p.m.