dfswmodel: Make step-wise linear distribution function
In obreschkow/dftools: Fitting distribution functions such as galaxy mass functions

Description Usage Arguments Value Author(s) See Also Examples

View source: R/dfswmodel.R

This function converts a continuous one-dimensional distribution function (DF), such as a galaxy mass function, into a step-wise DF on an arbitrary number of bins.

dfswmodel(
  gdf = function(x) dfmodel(x, dfmodel(output = "initial"), "density"),
  xedges = seq(6, 12, 0.5),
  method = "linear",
  extrapolate = TRUE
)

`gdf`	is the one-dimensional generative DF to be converted into a step-wise DF.
`xedges`	is a vector of observables x defining the edges of the bins for the step-wise DF.
`method`	specifies the interpolation method to be used. Choices are "constant", "linear" and "spline". In the latter two cases the generative distribution function is linearly extrapolated beyond the range of `xedges`.
`extrapolate`	is a logical flag. If `TRUE`, the step-wise DF is linearly extraplated outside the range of `xedges`. This extrapolation is useful when fitting the stepw-wise DF to data.

dfswmodel returns a list with two components gdf and p.initial. The first component is a function of log-masses x and a parameter vector p. The second component is the initial parameter-vector producing a step-wise mass function that closely matches the Schechter function specified by p.

Danail Obreschkow

dffit

# For an overall illustration run
dfexample(3)

# The follwoing is a step-by-step example.
# First, define and visulize a smooth Schechter function (a special type of galaxy mass function)
p.true = c(-2,11,-1.4) # Schechter function parameters
gdf = function(x) dfmodel(x, p.true, type='Schechter') # Schechter function
x = seq(5.8,12,0.01) # plotting range
plot(10^x, gdf(x), type='l', log='xy', ylim=c(1e-5,2))

# Define the edges of non-equal bins
xbin = c(6,7,7.5,seq(8,9,0.2),seq(9.5,11,0.5),11.8) # edges of bins

# Make and plot step-wise constant function
swconstant = dfswmodel(gdf, xbin, 'constant') # step-wise constant function
lines(10^x, swconstant$gdf(x, swconstant$p.initial), col='blue', lwd=3)

# Make and plot step-wise linear function
swlinear = dfswmodel(gdf, xbin, 'linear') # step-wise linear function
lines(10^x, swlinear$gdf(x, swlinear$p.initial), col='orange', lwd=2)

# Make and plot step-wise spline function
swspline = dfswmodel(gdf, xbin, 'spline') # step-wise linear function
lines(10^x, swspline$gdf(x, swspline$p.initial), col='red')

# Plot mid-points of bins
points(10^swconstant$xmid, 10^swconstant$p.initial, pch=20)