Create randomized raster with frequency distribution of second raster

Question

I want to calculate resistance distance based on circuit theory for a set of species for the city of Berlin, GER. For the city area I use land cover, sealed soil and building height data. This data is freely available via http://fbinter.stadt-berlin.de/fb/index.jsp. I use ArcMap 10.3.
As proposed by Koen et al. 2010 (http://dx.doi.org/10.1371/journal.pone.0011785 ). To sum up the paper, I want to create a buffer around Berlin to account for edge effects. This buffer should show the same frequency distribution of resistance values as the city raster.

For example:
Scenario - Frequency Distribution (low/medium/high)

Berlin - (46/50/98)
Random - (46/50/98)

I started an attempt using R 3.3.3 on MacOS 10.11.6. So far I can import the sealed.tif (which is the city area), transform to a matrix and get the frequency distribution. I then created a new randomized matrix with values from 0 to 100.

setwd("/Users/franzxaverpoellinger/Desktop/Statistics/Raster/raster")

library(raster) 
library(sp)
library(rgdal)
library(raster)

str_name<-'sealed.tif' 
sealed=raster(str_name)
plot(sealed)

# convert from .tif to a matrix
sealed.matrix <- as.matrix(sealed)

seal.cut = cut(sealed.matrix, breaks = seq(0, 100, by = 10), right=FALSE)
seal.cut.freq = table(seal.cut)
(seal.cut.freq/sum(seal.cut.freq))*100 # this is the aimed frequency

# and now the same for the buffer .tif
str_name.buffer <-'buffer.tif' 
buffer=raster(str_name.buffer)
buffer.matrix <- as.matrix(buffer)
str(buffer.matrix)

# create a matrix the same size as buffer.hist
new.buffer.matrix <- matrix(sample.int(100, size= 457*537, replace = TRUE), nrow = 457, ncol = 537)
new.buffer.matrix

buffer.cut = cut(new.buffer.matrix, breaks = seq(0, 100, by = 10), right=FALSE)
buffer.cut.freq = table(buffer.cut)
(buffer.cut.freq/sum(buffer.cut.freq))*100

Now I want the new.buffer.matrix to show the same frequency distribution of as does sealing.matrix. If I had the same distribution I would (somehow) go back from matrix to .tif and then just clip it to the extend that I need.

Answer 1

I have a definite answer now, from input .tif down to exporting a .tif file for further use in QGIS or ArcGIS.

setwd("")

library(raster)
library(rgdal)

input_tif <-'any_tif_should_run.tif' # loading .tif file
input_raster <- raster(input_tif)
buffer_area <- readOGR('buffer_area.shp') # load shapefile of buffer if randomized area should be clipped to a certain extent
# if not remove masking in line 68

#### convert from .tif to a matrix
{
 input_matrix <- as.matrix(input_raster)
 run.projection  <- projection(input_raster)
 rows <- nrow(input_matrix) # number of rows
 cols <- ncol(input_matrix) # number of columns
 length.input_matrix <- length(input_matrix) # number of values in the input matrix
 input_matrix.cut <- cut(input_matrix, breaks = seq(0, 100, by = 10), right=FALSE) # cuts the matrix values by 10
 input_matrix.cut.freq <- table(input_matrix.cut) 
 str.input_matrix.cut.freq <- (input_matrix.cut.freq/sum(input_matrix.cut.freq))*100 # calculate relative frequency of values

# this produces the vector to fill the output.raster
 vector_10 <- c(1,11,21,31,41,51,61,71,81,91) # create vector
 input_matrix.freq.absolut <- round((str.input_matrix.cut.freq/100)*(length.input_matrix))
 input_vector <- rep(vector_10, input_matrix.freq.absolut) # vector with the values of
 # vector.10 with the absolute frequency of values of str.seal.cut.freq.absolut
 input_vector.sampled <- sample(input_vector) # randomize the vector values
}

# here the length of the vector to fill the raster with randomized values is cropped or extended
# to the number of values e.g. length in the matrix
if (length(input_vector.sampled) > length.input_matrix) {
 input_vector.sampled_out <- input_vector.sampled[1:length.input_matrix]
 } else if (length(input_vector.sampled) < length.input_matrix) {
 to.fill <- length.input_matrix-length(input_vector.sampled)
 appendix.vector <- rep(1, to.fill)
 input_vector.sampled.out <- c(input_vector.sampled, appendix.vector)
} else {
 input_vector.sampled.out <- input_vector.sampled
}
# create a matrix from input_vector.sampled.out in order to compare the frequency distribution with the input .tif/raster/matrix
{
approx.matrix <- matrix(input_vector.sampled.out,nrow = rows, ncol = cols) # create a matrix from vector to test relative frequency of classes
approx.cut <- cut(approx.matrix, breaks = seq(0, 100, by = 10), right=FALSE)
approx.cut.freq <- table(approx.cut)
str.input_vector <- (approx.cut.freq/sum(approx.cut.freq))*100
}
str.input_matrix.cut.freq    # compare distribution of input matrix and vector for raster conversion
str.input_vector

# convert matrix to raster
{
 x <- raster()
 ncol(x) <- cols
 nrow(x) <- rows
 projection(x) <- run.projection
 x <- setValues(x, input_vector.sampled.out) # fill with values of input_vector.sampled.out with random values
 new.x <- projectRaster(x, input_raster) # apply extent etc. of input raster
 new.x <- setValues(new.x, input_vector.sampled.out)
 covered.raster <- cover(input_raster, new.x) # cover NA's of 'sealed' with the random values of raster 'new.x'
 clipped <- mask(covered.raster, buffer_area) # clip covered.raster by buffer_area.shp
 plot(clipped)
}
writeRaster(clipped, filename = "output_raster.tif")

I wrote this script in a manner that it should run with any kind of .tif input.