Cartograflow

Description of functions

1. Preparing flow data sets:

1.1 General functions
You can use long “L” or matrix “M” [n*n] flow dataset formats.

– flowtabmat() is to transform “L” to “M” formats, also to build an empty square matrix from spatial codes.

– flowcarre() is to square a matrix.

– flowjointure() is to performs a spatial join between a flow dataset and a spatial features layer or an external matrix.

– flowstructmat() fixes an unpreviously codes shift in the flow dataset “M” format. If necessary this function is to be used with flowjointure and flowtabmat.

1.2. Flow computation:

– flowtype() is to compute several types of flow from an asymmetric matrix:
x= flux for remaining initial flow (Fij)
x= transpose for reverse flow value (Fji)
x= bivolum for bilateral volum, as gross flow (FSij)
x= bibal for bilateral balance, as net flow (FBij)
x= biasym for asymetry of bilateral flow (FAij)
x= bimin for minimum of bilateral flow (minFij)
x= bimax for maximum of bilateral flow (maxFij)
x= birange for bilateral flow range (rangeFij)
x= bidisym for bilateral disymetry as (FDij)

– flowplaces() is to compute several types of flow places oriented from an asymmetric:
ie. as a dataframe that describes the flows from Origin / destination point of view
x= ini for the number of incoming links (as in-degree)
x= outi for the number of outcoming links (as out-degree)
x= degi for the total number of links (as in and out degrees)
x= intra for total intra zonal interaction (if main diagonal is not empty
x= Dj for the total flows received by (j) place
x= voli for the total volume of flow per place
x= bali for the net balance of flow per place
x= asyi for the asymetry of flow per place
x= allflowplaces for computing all the above indicators

1.3. Flow reduction:

– flowlowup() is to extracts the upper or the lower triangular part of a matrix - preferably for symmetrical matrixes.

x= up for the part above the main diagonal
x= low for the part below the main diagonal

– flowreduct() is to reduce the flow dataset regarding another matrix, e.g. distances travelled.

metric is the metric of the distance matrix :
- metric= continuous (e.g. for kilometers)
- metric= ordinal (e.g. for k contiguity)

If the metric is continuous (e.g for filtering flows by kilometric distances travelled), use:

d.criteria is for selecting the minimum or the maximum distance criteria
- d.criteria= dmin for keeping only flows up to a dmin criterion in km
- d.criteria= dmax for selecting values less than a dmax criterion in km

d is the value of the selected dmin or dmax criteria.

Notice that these arguments can be used as a filter criterion in flowmap().

See Cartograflow_distance and Cartograflow_ordinal_distance Vignettes for examples.
URL: https://github.com/fbahoken/cartogRaflow/tree/master/vignettes

2. Flows filtering:

2.1. Filtering from flow concentration analysis

Flow concentration analysis:

– flowgini() performs a Gini’s concentration analysis of the flow features, by computing Gini coefficient and plotting interactive Lorenz curve.

To be use before flowanalysis()

See Cartograflow_concentration Vignette for example.
URL: https://github.com/fbahoken/cartogRaflow/tree/master/vignettes

Flow filtering according to a concentration criterion:

– flowanalysis() computes filters criterions based on:

• argument critflow is to filter the flows according to their significativity (% of total of flow information) ;
  
• argument critlink is to filter the flows according to their density (% of total features)
  

These arguments can be used as filter criterion in flowmap().

See Cartograflow_concentration Vignette for example.
URL: https://github.com/fbahoken/cartogRaflow/tree/master/vignettes

2.2. Spatial / territorial filtering of flows

Flow filtering based on a continuous distance criterion

– flowdist() computes a continous distance matrix from spatial features (area or points). The result is a matrix of the distances travelled between ODs, with flows filtered or not.

See Cartograflow_distance Vignette for example.
URL: https://github.com/fbahoken/cartogRaflow/tree/master/vignettes

Flow filtering based on an ordinal distance / neighbourhood criterion:

– flowcontig() compute an ordinal distance matrix from spatial features (area). The result is a matrix of adjacency or k-contiguity of the ODs.

• background is the areal spatial features ;
  
• code` is the spatial features codes ;
  
• k is to enter the number (k:1,2,…,k) of the contiguity matrix to be constructed : if (k=1), ODs places are adjacent, then the flow have to cross only 1 boundary, else (k=k) ODs places are distant from n borders ;
  
• algo is the algorithm to use for ordinal distance calculation (also Default is “automatic” for “Dijkstra’s”) ;
  

Notice that the function automatically returns the maximum (k) number of the spatial layer.

See Cartograflow_distance_ordinal Vignette for example.

3. Flow mapping

– flowmap() is to plot flows as segments or arrows, by acting on the following arguments:

• filter is to filter or not flow’s information or features
  
• threshold is used to set the filtering level of the flows when filter=“True”
  
• taille is the value of the width of the flow feature
  
• a.head is the arrow head parameter (in, out, in and out)
  
• a.length is the length of the edges of the arrow head (in inches)
  
• a.angle is the angle from the shaft of the arrow to the edge of the arrow head
  
• a.col is the arrow’s color
  
• plota is to add spatial features as map background to the flows’s plot
  
• add is to allow to overlay flow features on external spatial features background
  

Examples of applications

– Useful packages Best external R package to use: {dplyr} {sf} {igraph} {rlang} {cartography}

1. Load datasets

Flow dataset

# Load Statistical information
tabflow<-read.csv2("./data/MOBPRO_ETP.csv", header=TRUE, sep=";",stringsAsFactors=FALSE,
                   encoding="UTF-8", dec=".",check.names=FALSE)

## 'data.frame':    121 obs. of  4 variables:
##  $ i    : chr  "T1" "T1" "T1" "T1" ...
##  $ j    : chr  "T1" "T10" "T11" "T12" ...
##  $ Fij  : num  291058 8297 3889 17064 12163 ...
##  $ count: num  351 43 13 77 52 55 134 63 53 14 ...

Select variable and change matrix format

# Selecting useful variables for changing format
tabflow<-tabflow %>% select(i,j,Fij)

# From list (L) to matrix (M) format
matflow <-flowtabmat(tabflow,matlist="M")
head(matflow[1:4,1:4])

##         T1   T10   T11   T12
## T1  291058  8297  3889 17064
## T10  73743 19501 11707  4931
## T11  22408  9359 12108  6084
## T12  68625  1906  7269 46515

dim(matflow)

## [1] 12 12

Geographical dataset

2. Flow types computing

Compute bilateral flows types : eg. volum, balance, bilateral maximum and all types

# Bilateral volum (gross) FSij:  
tabflow_vol<-flowtype(tabflow, format="L", origin="i", destination="j", fij="Fij",  x= "bivolum" )
# Matrix format (M= : matflow_vol<-flowtype(matflow, format="M", "bivolum")

# Bilateral balance (net ) FBij:  
tabflow_net<-flowtype(tabflow, format="L", origin="i", destination="j", fij="Fij", x="bibal")

# Bilateral maximum (maxFij): 
tabflow_max<-flowtype(tabflow, format="L", origin="i", destination="j", fij="Fij", x="bimax")

# Compute all types of bilateral flows, in one 11 columns
tabflow_all<-flowtype(tabflow,format="L", origin="i", destination="j", fij="Fij", x="alltypes")
head(tabflow_all) 

##    i   j    Fij    Fji   FSij  FBij      FAij minFij maxFij rangeFij      FDij
## 1 T1  T1 291058 291058 582116     0 0.0000000 291058 291058        0 0.0000000
## 2 T1 T10   8297  73743  82040 65446 0.7977328   8297  73743    65446 0.7977328
## 3 T1 T11   3889  22408  26297 18519 0.7042248   3889  22408    18519 0.7042248
## 4 T1 T12  17064  68625  85689 51561 0.6017225  17064  68625    51561 0.6017225
## 5 T1  T2  12163  47427  59590 35264 0.5917771  12163  47427    35264 0.5917771
## 6 T1  T3  32682  45772  78454 13090 0.1668494  32682  45772    13090 0.1668494

3. Direct flow mapping

3.1. Plot all origin-destination without any filtering criterion The result will reveal a graphic complexity (“spaghetti-effect”")

Plot links

library(sf)
map<-st_read("./data/MGP_TER.shp")

## Reading layer `MGP_TER' from data source `/tmp/RtmpmeYsUo/Rbuild751f7853470a/cartograflow/vignettes/data/MGP_TER.shp' using driver `ESRI Shapefile'
## Simple feature collection with 12 features and 14 fields
## geometry type:  POLYGON
## dimension:      XY
## bbox:           xmin: 637297.4 ymin: 6838629 xmax: 671752.1 ymax: 6879246
## projected CRS:  Lambert_Conformal_Conic

# Add and overlay spatial background 
par(bg = "NA")

# Graphic parameters
par(mar=c(0,0,1,0))
extent <- c(2800000, 1340000, 6400000, 4800000)
resolution<-150

plot(st_geometry(map), col = NA, border=NA, bg="#dfe6e1")
plot(st_geometry(map), col = "light grey", add=TRUE)

# Flowmapping of all links

flowmap(tab=tabflow,
        fij="Fij",
        origin.f = "i",
        destination.f = "j",
        bkg = map,
        code="EPT_NUM",
        nodes.X="X",
        nodes.Y = "Y",
        filter=FALSE,
        add=TRUE
        )

library(cartography)

# Map cosmetics
layoutLayer(title = "All origin-destination for commuting in Greater Paris, 2017",
           coltitle ="black",
           author = "Cartograflow, 2020",
           sources = "Data : INSEE, 2017 ; Basemap : APUR, RIATE, 2018.",
           scale = 2,
           tabtitle = FALSE,
           frame = TRUE,
           col = "grey"
            )
# North arrow
north("topright")

3.2. Plot the above-average flows

library(sf)
map<-st_read("./data/MGP_TER.shp")

## Reading layer `MGP_TER' from data source `/tmp/RtmpmeYsUo/Rbuild751f7853470a/cartograflow/vignettes/data/MGP_TER.shp' using driver `ESRI Shapefile'
## Simple feature collection with 12 features and 14 fields
## geometry type:  POLYGON
## dimension:      XY
## bbox:           xmin: 637297.4 ymin: 6838629 xmax: 671752.1 ymax: 6879246
## projected CRS:  Lambert_Conformal_Conic

# Add and overlay spatial background 
par(bg = "NA")

# Graphic parameters
par(mar=c(0,0,1,0))
extent <- c(2800000, 1340000, 6400000, 4800000)
resolution<-150

plot(st_geometry(map), col = NA, border=NA, bg="#dfe6e1")
plot(st_geometry(map), col = "light grey", add=TRUE)

# Flow mapping above-average flows
flowmap(tab=tabflow,
        fij="Fij",
        origin.f = "i",
        destination.f = "j",
        bkg = map,
        code="EPT_NUM",
        nodes.X="X",
        nodes.Y = "Y",
        filter=TRUE,
        threshold =(mean(tabflow$Fij)),  #mean value is the level of threshold
        taille=20,           
        a.head = 1,
        a.length = 0.11,
        a.angle = 30,
        a.col="#138913",
        add=TRUE)

# Map Legend
legendPropLines(pos="topleft",
                title.txt="Commuters > 13220 ",
                title.cex=0.8,   
                cex=0.5,
                values.cex= 0.7,  
                var=c(mean(tabflow$Fij),max(tabflow$Fij)), 
                lwd=5, 
                frame = FALSE,
                col="#138913",
                values.rnd = 0
                )

#Map cosmetic

layoutLayer(title = "Commuters up to above-average in Greater Paris",
           coltitle ="black",
           author = "Cartograflow, 2020",
           sources = "Data : INSEE, 2017 ; Basemap : APUR, RIATE, 2018.",
           scale = 2,
           tabtitle = FALSE,
           frame = TRUE,
           col = "grey"
            )

# North arrow
north("topright")

3.3. Plot the net flows of bilateral flows

#library(sf)
map<-st_read("./data/MGP_TER.shp")

## Reading layer `MGP_TER' from data source `/tmp/RtmpmeYsUo/Rbuild751f7853470a/cartograflow/vignettes/data/MGP_TER.shp' using driver `ESRI Shapefile'
## Simple feature collection with 12 features and 14 fields
## geometry type:  POLYGON
## dimension:      XY
## bbox:           xmin: 637297.4 ymin: 6838629 xmax: 671752.1 ymax: 6879246
## projected CRS:  Lambert_Conformal_Conic

# Net matrix reduction
tabflow_net <- tabflow_net %>% filter(.data$FBij>=0)

# Net matrix thresholding
Q80<-quantile(tabflow_net$FBij,0.95)


# Add and overlay spatial background 
par(bg = "NA")

# Graphic parameters
par(mar=c(0,0,1,0))
extent <- c(2800000, 1340000, 6400000, 4800000)
resolution<-150

plot(st_geometry(map), col = NA, border=NA, bg="#dfe6e1")
plot(st_geometry(map), col = "light grey", add=TRUE)

# Flow mapping above-average flows
flowmap(tab=tabflow_net,
        fij="FBij",
        origin.f = "i",
        destination.f = "j",
        bkg = map,
        code="EPT_NUM",
        nodes.X="X",
        nodes.Y = "Y",
        filter=TRUE,
        threshold = Q80,
        taille=12,           
        a.head = 1, 
        a.length = 0.11,
        a.angle = 30,
        a.col="#4e8ef5",
        add=TRUE)

# Map Legend
legendPropLines(pos="topleft",
                title.txt="Commuters > 5722 ",
                title.cex=0.8,   
                cex=0.5,
                values.cex= 0.7,  
                var=c(Q80,max(tabflow_net$FBij)), 
                lwd=12, 
                frame = FALSE,
                col="#4e8ef5",
                values.rnd = 0
                )

#Map cosmetic

layoutLayer(title = "Net commuters in Greater Paris (20% strongest)",
           coltitle ="black",
           author = "Cartograflow, 2020",
           sources = "Data : INSEE, 2017 ; Basemap : APUR, RIATE, 2018.",
           scale = 2,
           tabtitle = FALSE,
           frame = TRUE,
           col = "grey"
            )

# North arrow
north("topright")

Sample datasets

– Statistical dataset : - INSEE - Base flux de mobilité (2015) - URL : https://www.insee.fr/fr/statistiques/fichier/3566008/rp2015_mobpro_txt.zip

– Geographical dataset :

• municipalities : IGN, GEOFLA 2015 v2.1
• Greater Paris : APUR, UMS 2414 RIATE, 2018.

See also

https://github.com/fbahoken/cartogRaflow/tree/master/vignettes

– cartograflow_general.html
– cartograflow_concentration.html
– cartograflow_distance.html
– cartograflow_ordinal_distance.hmtl

Reference

– Bahoken Francoise (2016), Programmes pour R/Rtudio annexés, in : Contribution à la cartographie d’une matrix de flux, Thèse de doctorat, Université Paris 7, pp. 325-346. URL : https://halshs.archives-ouvertes.fr/tel-01273776, pp. 480-520.