Generate grid neighborhood as prerequisites in Makefile - makefile

Question

I am trying to (ab)use a Makefile to describe a process of data generation. My data are a raster data mosaic tiles covering the world, in chunks of 30°×20° (longitude×latitude), where the tile labels are derived from the GMTED names:
lat := 70S 50S 30S 10S 10N 30N 50N 70N
lon := 180W 150W 120W 090W 060W 030W 000E 030E 060E 090E 120E 150E
tiles := $(foreach LAT,$(lat),$(foreach LON,$(lon),$(LAT)$(LON)))
For some step in the computation, each tile and its 8 neighbors are needed. So for example, one rule is
distances-extended-50S180W.tif: distances-50S180W.tif distances-70S150W.tif distances-70S150E.tif distances-50S150W.tif distances-50S150E.tif distances-30S150W.tif distances-30S150E.tif distances-70S180W.tif distances-30S180W.tif
python extend 50S180W
(so the lons wrap, but for the lats, the extremes have just 6 instead of 9 prerequisites.) How can I make this more concise than generating all these 96 rules externally and including them into the makefile?

Answer 1

Here is a list-oriented method:
lat := southpole 70S 50S 30S 10S 10N 30N 50N 70N northpole
lon := 180W 150W 120W 090W 060W 030W 000E 030E 060E 090E 120E 150E
# rotate-repeat(list,n,len):
# do "n" times: output the first "len" elements of "list", then rotate "list" one left
# "list" must be >= "len"
rotate-repeat = $(if $2,$(wordlist 1,$3,$1) $(call rotate-repeat,$(wordlist 2,$(words $1),$1) $(firstword $1),$(wordlist 2,1000,$2),$3))
# create repeated list of latitudes (including poles)
lat_ := $(foreach _,$(lon),$(lat))
# create repeated and shifted list of longitudes
lon_ := $(call rotate-repeat,$(lon),$(lon),$(words $(lat)))
# triple-cartprod(list1,list2,func)
# create the cartesian product of the two leading triples in the given
# lists and call func with them, then recurse until lists empty
triple-cartprod = $(call $3,\
$(word 1,$1)$(word 1,$2) $(word 2,$1)$(word 1,$2) $(word 3,$1)$(word 1,$2) \
$(word 1,$1)$(word 2,$2) $(word 2,$1)$(word 2,$2) $(word 3,$1)$(word 2,$2) \
$(word 1,$1)$(word 3,$2) $(word 2,$1)$(word 3,$2) $(word 3,$1)$(word 3,$2)) \
$(if $(word 4,$1),$(call triple-cartprod,$(wordlist 2,1000,$1),$(wordlist 2,1000,$2),$3))
# how to make a rule: we throw away rules for the poles and filter
# them out from the prereqs
make-rule = $(if $(findstring pole,$(word 5,$1)),,$(info $(word 5,$1) : $(filter-out %pole,$(wordlist 1,4,$1) $(wordlist 6,9,$1))))
# main:
$(call triple-cartprod,$(lon_),$(lat_),make-rule)

Answer 2

Not sure it's worth the effort but if you use GNU make a slightly simpler and less error prone solution than the full enumeration could be something like:
##################
# utility macros #
##################
# cross-product of two lists; $1: first list; $2: second list
define xp
$(sort $(foreach a,$1,$(foreach b,$2,$a$b)))
endef
#############
# variables #
#############
lat := 70S 70S 50S 30S 10S 10N 30N 50N 70N 70N
ilat := 2 3 4 5 6 7 8 9
lon := 150E 180W 150W 120W 090W 060W 030W 000E 030E 060E 090E 120E 150E 180W
ilon := 2 3 4 5 6 7 8 9 10 11 12 13
# compute north (n-LAT), central (c-LAT) and south (s-LAT) of all latitudes; $1: integer latitude
define ncs
n-$1 := $$(word $$(shell expr $1 + 1),$(lat))
c-$1 := $$(word $1,$(lat))
s-$1 := $$(word $$(shell expr $1 - 1),$(lat))
endef
$(foreach l,$(ilat),$(eval $(call ncs,$l)))
# compute west (w-LON), middle (m-LON) and east (e-LON) of all longitudes; $1: interger longitude
define wme
w-$1 := $$(word $$(shell expr $1 - 1),$(lon))
m-$1 := $$(word $1,$(lon))
e-$1 := $$(word $$(shell expr $1 + 1),$(lon))
endef
$(foreach l,$(ilon),$(eval $(call wme,$l)))
# instantiate tile rule; $1: integer latitude, $2: integer longitude
define tile-rule
$1-$2-point := $$(c-$1)$$(m-$2)
$1-$2-prereq := $$(call xp,$$(n-$1) $$(c-$1) $$(s-$1),$$(w-$2) $$(m-$2) $$(e-$2))
distances-extended-$$($1-$2-point).tif: $$(patsubst %,distances-%.tif,$$($1-$2-prereq))
python extend $$($1-$2-point)
endef
$(foreach la,$(ilat),$(foreach lo,$(ilon),$(eval $(call tile-rule,$(la),$(lo)))))
Latitudes and longitudes are represented not only as labels but also as integers (variables ilat and ilon), which simplifies the computation of north, south, west and east of positions.
The word function is used to convert integers to labels.
The saturation of latitudes (north of 70N is 70N and south of 70S is 70S) are guaranteed by left and right extensions of the lat variable and by the bounds of the ilat variable. Same for the wrapping of longitudes with the extended lon variable and the bounds of the ilon variable.
The tile-rule macro instantiates all rules. The only subtlety here is the use of the sort function in the xp macro. It sorts but also removes duplicates (for extremes).
Demo with a modified tile-rule macro to create the files and print the instantiated rules:
$ cat Makefile
...
.PHONY: all clean
# instantiate tile rule; $1: integer latitude, $2: integer longitude
define tile-rule
$1-$2-point := $$(c-$1)$$(m-$2)
distances-$$($1-$2-point).tif:
#touch "$$#"
$1-$2-prereq := $$(call xp,$$(n-$1) $$(c-$1) $$(s-$1),$$(w-$2) $$(m-$2) $$(e-$2))
distances-extended-$$($1-$2-point).tif: $$(patsubst %,distances-%.tif,$$($1-$2-prereq))
#printf '%s:' "$$#"
#printf ' %s' "$$^"
#printf '\n\tpython extend $$($1-$2-point)\n'
#touch "$$#"
all: distances-extended-$$($1-$2-point).tif
clean::
#rm -f distances-$$($1-$2-point).tif distances-extended-$$($1-$2-point).tif
endef
$(foreach la,$(ilat),$(foreach lo,$(ilon),$(eval $(call tile-rule,$(la),$(lo)))))
$ make clean
$ make -j1 all
make -j1 all
distances-extended-70S180W.tif: distances-50S150E.tif distances-50S150W.tif distances-50S180W.tif distances-70S150E.tif distances-70S150W.tif distances-70S180W.tif
python extend 70S180W
...
distances-extended-50S180W.tif: distances-30S150E.tif distances-30S150W.tif distances-30S180W.tif distances-50S150E.tif distances-50S150W.tif distances-50S180W.tif distances-70S150E.tif distances-70S150W.tif distances-70S180W.tif
python extend 50S180W
...