Module:Math

--[[ This module is intended to replace the functionality of °N, °W and related templates. It provides several methods, including

coordinate values.

degree values to DMS format.

to decimal degree format.



]]

require('Module:No globals')

local math_mod = require("Module:Math") local coordinates = {};

local current_page = mw.title.getCurrentTitle local page_name = mw.uri.encode( current_page.prefixedText, 'WIKI' ); local coord_link = '//geohack.toolforge.org/geohack.php?pagename=' .. page_name .. '&params=' local templatestyles = 'Module:Coordinates/styles.css'

-- Helper function, replacement for local function displaytitle(s, notes) local l = "Coordinates: " .. s	local co = ' ' .. l .. notes .. ' ';	return ' ' .. co .. ' '; end

-- Helper function, Replacement for local function displayinline(s, notes) return s .. notes end

-- Helper function, used in detecting DMS formatting local function dmsTest(first, second) if type(first) ~= 'string' or type(second) ~= 'string' then return nil end local s = (first .. second):upper return s:find('^[NS][EW]$') or s:find('^[EW][NS]$') end

-- Wrapper function to grab args, see Module:Arguments for this function's documentation. local function makeInvokeFunc(funcName) return function (frame) local args = require('Module:Arguments').getArgs(frame, {			wrappers = 'Template:Coord'		}) return coordinates[funcName](args, frame) end end

-- Helper function, handle optional args. local function optionalArg(arg, supplement) return arg and arg .. supplement or '' end

-- Formats any error messages generated for display local function errorPrinter(errors) local result = "" for i,v in ipairs(errors) do local errorHTML = ' Coordinates: ' .. v[2] .. ' '		result = result .. errorHTML .. " "	end return result end

--[[ Determine the required CSS class to display coordinates

Usually geo-nondefault is hidden by CSS, unless a user has overridden this for himself default is the mode as specificied by the user when calling the °N, °W template mode is the display mode (dec or dms) that we will need to determine the css class for ]] local function displayDefault(default, mode) if default == "" then default = "dec" end

if default == mode then return "geo-default" else return "geo-nondefault" end end

--[[ specPrinter

Output formatter. Takes the structure generated by either parseDec or parseDMS and formats it for inclusion on Wikipedia. ]] local function specPrinter(args, coordinateSpec) local uriComponents = coordinateSpec["param"] if uriComponents == "" then -- RETURN error, should never be empty or nil return "ERROR param was empty" end if args["name"] then uriComponents = uriComponents .. "&title=" .. mw.uri.encode(coordinateSpec["name"]) end

local geodmshtml = '' .. ' ' .. coordinateSpec["dms-lat"] .. ' '			.. ' ' ..coordinateSpec["dms-long"] .. ' '			.. ' '

local lat = tonumber( coordinateSpec["dec-lat"] ) or 0 local geodeclat if lat < 0 then -- FIXME this breaks the pre-existing precision geodeclat = tostring(coordinateSpec["dec-lat"]):sub(2) .. "°S" else geodeclat = (coordinateSpec["dec-lat"] or 0) .. "°N" end

local long = tonumber( coordinateSpec["dec-long"] ) or 0 local geodeclong if long < 0 then -- FIXME does not handle unicode minus geodeclong = tostring(coordinateSpec["dec-long"]):sub(2) .. "°W" else geodeclong = (coordinateSpec["dec-long"] or 0) .. "°E" end

local geodechtml = '' .. geodeclat .. ' '			.. geodeclong .. ' '

local geonumhtml = ' ' .. coordinateSpec["dec-lat"] .. '; '			.. coordinateSpec["dec-long"] .. ' '

local inner = '' .. geodmshtml .. ' '				.. ' &#xfeff; / &#xfeff; ' .. '';

if not args["name"] then inner = inner .. geodechtml .. ' &#xfeff; / ' .. geonumhtml .. ' '	else inner = inner .. ' ' .. geodechtml .. ' &#xfeff; / ' .. geonumhtml .. ' '				.. ' &#xfeff; ( '				.. args["name"] .. ' )  ' end

return mw.getCurrentFrame:extensionTag{ name = 'templatestyles', args = { src = templatestyles} } .. ' '	      .. '[' .. coord_link .. uriComponents .. ' ' .. inner .. ']'	      .. ' ' end

-- Helper function, convert decimal to degrees local function convert_dec2dms_d(coordinate) local d = math_mod._round( coordinate, 0 ) .. "°"	return d .. "" end

-- Helper function, convert decimal to degrees and minutes local function convert_dec2dms_dm(coordinate) coordinate = math_mod._round( coordinate * 60, 0 ); local m = coordinate % 60; coordinate = math.floor( (coordinate - m) / 60 ); local d = coordinate % 360 .."°"

return d .. string.format( "%02d′", m ) end

-- Helper function, convert decimal to degrees, minutes, and seconds local function convert_dec2dms_dms(coordinate) coordinate = math_mod._round( coordinate * 60 * 60, 0 ); local s = coordinate % 60 coordinate = math.floor( (coordinate - s) / 60 ); local m = coordinate % 60 coordinate = math.floor( (coordinate - m) / 60 ); local d = coordinate % 360 .."°"

return d .. string.format( "%02d′", m ) .. string.format( "%02d″", s ) end

-- Helper function, convert decimal latitude or longitude to degrees, minutes, and seconds format based on the specified precision. local function convert_dec2dms(coordinate, firstPostfix, secondPostfix, precision) local coord = tonumber(coordinate) local postfix if coord >= 0 then postfix = firstPostfix else postfix = secondPostfix end

precision = precision:lower; if precision == "dms" then return convert_dec2dms_dms( math.abs( coord ) ) .. postfix; elseif precision == "dm" then return convert_dec2dms_dm( math.abs( coord ) ) .. postfix; elseif precision == "d" then return convert_dec2dms_d( math.abs( coord ) ) .. postfix; end end

-- Convert DMS format into a N or E decimal coordinate local function convert_dms2dec(direction, degrees_str, minutes_str, seconds_str) local degrees = tonumber(degrees_str) local minutes = tonumber(minutes_str) or 0 local seconds = tonumber(seconds_str) or 0

local factor = 1 if direction == "S" or direction == "W" then factor = -1 end

local precision = 0 if seconds_str then precision = 5 + math.max( math_mod._precision(seconds_str), 0 ); elseif minutes_str and minutes_str ~= '' then precision = 3 + math.max( math_mod._precision(minutes_str), 0 ); else precision = math.max( math_mod._precision(degrees_str), 0 ); end

local decimal = factor * (degrees+(minutes+seconds/60)/60) return string.format( "%." .. precision .. "f", decimal ) -- not tonumber since this whole thing is string based. end

-- Checks input values to for out of range errors. local function validate( lat_d, lat_m, lat_s, long_d, long_m, long_s, source, strong ) local errors = {}; lat_d = tonumber( lat_d ) or 0; lat_m = tonumber( lat_m ) or 0; lat_s = tonumber( lat_s ) or 0; long_d = tonumber( long_d ) or 0; long_m = tonumber( long_m ) or 0; long_s = tonumber( long_s ) or 0;

if strong then if lat_d < 0 then table.insert(errors, {source, "latitude degrees < 0 with hemisphere flag"}) end if long_d < 0 then table.insert(errors, {source, "longitude degrees < 0 with hemisphere flag"}) end --[[		#coordinates is inconsistent about whether this is an error. If globe: is		specified, it won't error on this condition, but otherwise it will.

For not simply disable this check.

if long_d > 180 then table.insert(errors, {source, "longitude degrees > 180 with hemisphere flag"}) end ]]	end

if lat_d > 90 then table.insert(errors, {source, "latitude degrees > 90"}) end if lat_d < -90 then table.insert(errors, {source, "latitude degrees < -90"}) end if lat_m >= 60 then table.insert(errors, {source, "latitude minutes >= 60"}) end if lat_m < 0 then table.insert(errors, {source, "latitude minutes < 0"}) end if lat_s >= 60 then table.insert(errors, {source, "latitude seconds >= 60"}) end if lat_s < 0 then table.insert(errors, {source, "latitude seconds < 0"}) end if long_d >= 360 then table.insert(errors, {source, "longitude degrees >= 360"}) end if long_d <= -360 then table.insert(errors, {source, "longitude degrees <= -360"}) end if long_m >= 60 then table.insert(errors, {source, "longitude minutes >= 60"}) end if long_m < 0 then table.insert(errors, {source, "longitude minutes < 0"}) end if long_s >= 60 then table.insert(errors, {source, "longitude seconds >= 60"}) end if long_s < 0 then table.insert(errors, {source, "longitude seconds < 0"}) end

return errors; end

--[[ parseDec

Transforms decimal format latitude and longitude into the structure to be used in displaying coordinates ]] local function parseDec( lat, long, format ) local coordinateSpec = {} local errors = {}

if not long then return nil, elseif not tonumber(long) then return nil, end

errors = validate( lat, nil, nil, long, nil, nil, 'parseDec', false ); coordinateSpec["dec-lat"] = lat; coordinateSpec["dec-long"] = long;

local mode = coordinates.determineMode( lat, long ); coordinateSpec["dms-lat"] = convert_dec2dms( lat, "N", "S", mode)  -- coordinateSpec["dms-long"] = convert_dec2dms( long, "E", "W", mode) --

if format then coordinateSpec.default = format else coordinateSpec.default = "dec" end

return coordinateSpec, errors end

--[[ parseDMS

Transforms degrees, minutes, seconds format latitude and longitude into the a structure to be used in displaying coordinates ]] local function parseDMS( lat_d, lat_m, lat_s, lat_f, long_d, long_m, long_s, long_f, format ) local coordinateSpec, errors, backward = {}, {}

lat_f = lat_f:upper; long_f = long_f:upper;

-- Check if specified backward if lat_f == 'E' or lat_f == 'W' then lat_d, long_d, lat_m, long_m, lat_s, long_s, lat_f, long_f, backward = long_d, lat_d, long_m, lat_m, long_s, lat_s, long_f, lat_f, true; end

errors = validate( lat_d, lat_m, lat_s, long_d, long_m, long_s, 'parseDMS', true ); if not long_d then return nil, elseif not tonumber(long_d) then return nil, end

if not lat_m and not lat_s and not long_m and not long_s and #errors == 0 then if math_mod._precision( lat_d ) > 0 or math_mod._precision( long_d ) > 0 then if lat_f:upper == 'S' then lat_d = '-' .. lat_d; end if long_f:upper == 'W' then long_d = '-' .. long_d; end

return parseDec( lat_d, long_d, format ); end end

coordinateSpec["dms-lat"] = lat_d.."°"..optionalArg(lat_m,"′") .. optionalArg(lat_s,"″") .. lat_f coordinateSpec["dms-long"] = long_d.."°"..optionalArg(long_m,"′") .. optionalArg(long_s,"″") .. long_f coordinateSpec["dec-lat"] = convert_dms2dec(lat_f, lat_d, lat_m, lat_s) -- coordinateSpec["dec-long"] = convert_dms2dec(long_f, long_d, long_m, long_s) --

if format then coordinateSpec.default = format else coordinateSpec.default = "dms" end

return coordinateSpec, errors, backward end

-- Check the input arguments for coord to determine the kind of data being provided and then make the necessary processing. local function formatTest(args) local result, errors local backward, primary = false, false

local function getParam(args, lim) local ret = {} for i = 1, lim do			ret[i] = args[i] or '' end return table.concat(ret, '_') end

if not args[1] then -- no lat logic return errorPrinter elseif not tonumber(args[1]) then -- bad lat logic return errorPrinter elseif not args[4] and not args[5] and not args[6] then -- dec logic result, errors = parseDec(args[1], args[2], args.format) if not result then return errorPrinter(errors); end -- formatting for geohack: geohack expects D_N_D_E notation or D;D notation -- wikiminiatlas doesn't support D;D notation -- #coordinates parserfunction doesn't support negative decimals with NSWE result.param = table.concat({			math.abs(tonumber(args[1])),			((tonumber(args[1]) or 0) < 0) and 'S' or 'N',			math.abs(tonumber(args[2])),			((tonumber(args[2]) or 0) < 0) and 'W' or 'E',			args[3] or ''}, '_') elseif dmsTest(args[4], args[8]) then -- dms logic result, errors, backward = parseDMS(args[1], args[2], args[3], args[4],			args[5], args[6], args[7], args[8], args.format) if args[10] then table.insert(errors, {'formatTest', 'Extra unexpected parameters'}) end if not result then return errorPrinter(errors) end result.param = getParam(args, 9) elseif dmsTest(args[3], args[6]) then -- dm logic result, errors, backward = parseDMS(args[1], args[2], nil, args[3],			args[4], args[5], nil, args[6], args['format']) if args[8] then table.insert(errors, {'formatTest', 'Extra unexpected parameters'}) end if not result then return errorPrinter(errors) end result.param = getParam(args, 7) elseif dmsTest(args[2], args[4]) then -- d logic result, errors, backward = parseDMS(args[1], nil, nil, args[2],			args[3], nil, nil, args[4], args.format) if args[6] then table.insert(errors, {'formatTest', 'Extra unexpected parameters'}) end if not result then return errorPrinter(errors) end result.param = getParam(args, 5) else -- Error return errorPrinter .. ''	end result.name = args.name

local extra_param = {'dim', 'globe', 'scale', 'region', 'source', 'type'} for _, v in ipairs(extra_param) do		if args[v] then table.insert(errors, {'formatTest', 'Parameter: "' .. v .. '=" should be "' .. v .. ':"' }) end end

local ret = specPrinter(args, result) if #errors > 0 then ret = ret .. ' ' .. errorPrinter(errors) .. ''	end return ret, backward end

-- Generate Wikidata tracking categories. local function makeWikidataCategories(qid) local ret local qid = qid or mw.wikibase.getEntityIdForCurrentPage if mw.wikibase and current_page.namespace == 0 then if qid and mw.wikibase.entityExists(qid) and mw.wikibase.getBestStatements(qid, "P625") and mw.wikibase.getBestStatements(qid, "P625")[1] then local snaktype = mw.wikibase.getBestStatements(qid, "P625")[1].mainsnak.snaktype if snaktype == 'value' then -- coordinates exist both here and on Wikidata, and can be compared. ret = 'Coordinates on Wikidata' elseif snaktype == 'somevalue' then ret = 'Coordinates on Wikidata set to unknown value' elseif snaktype == 'novalue' then ret = 'Coordinates on Wikidata set to no value' end else -- We have to either import the coordinates to Wikidata or remove them here. ret = 'Coordinates not on Wikidata' end end if ret then return string.format('', ret) else return '' end end

--[[ link

Simple function to export the coordinates link for other uses.

Usage:

]] function coordinates.link(frame) return coord_link; end

--[[ dec2dms

Wrapper to allow templates to call dec2dms directly.

Usage:

decimal_coordinate is converted to DMS format. If positive, the positive_suffix is appended (typical N or E), if negative, the negative suffix is appended. The specified precision is one of 'D', 'DM', or 'DMS' to specify the level of detail to use. ]] coordinates.dec2dms = makeInvokeFunc('_dec2dms') function coordinates._dec2dms(args) local coordinate = args[1] local firstPostfix = args[2] or '' local secondPostfix = args[3] or '' local precision = args[4] or ''

return convert_dec2dms(coordinate, firstPostfix, secondPostfix, precision) end

-- Helper function to determine whether to use D, DM, or DMS format depending on the precision of the decimal input. function coordinates.determineMode( value1, value2 ) local precision = math.max( math_mod._precision( value1 ), math_mod._precision( value2 ) ); if precision <= 0 then return 'd'	elseif precision <= 2 then return 'dm'; else return 'dms'; end end

--[[ dms2dec

Wrapper to allow templates to call dms2dec directly.

Usage:

Converts DMS values specified as degrees, minutes, seconds too decimal format. direction_flag is one of N, S, E, W, and determines whether the output is positive (i.e. N and E) or negative (i.e. S and W). ]] coordinates.dms2dec = makeInvokeFunc('_dms2dec') function coordinates._dms2dec(args) local direction = args[1] local degrees = args[2] local minutes = args[3] local seconds = args[4]

return convert_dms2dec(direction, degrees, minutes, seconds) end

--[[ coord

Main entry point for Lua function to replace °N, °W

Usage: ...

Refer to °N, °W documentation page for many additional parameters and configuration options.

Note: This function provides the visual display elements of °N, °W. In order to load coordinates into the database, the parser function must also be called, this is done automatically in the Lua version of °N, °W. ]] coordinates.coord = makeInvokeFunc('_coord') function coordinates._coord(args) if not tonumber(args[1]) and not args[2] then args[3] = args[1]; args[1] = nil local entity = mw.wikibase.getEntityObject(args.qid) if entity and entity.claims and entity.claims.P625 and entity.claims.P625[1].mainsnak.snaktype == 'value' then local precision = entity.claims.P625[1].mainsnak.datavalue.value.precision args[1] = entity.claims.P625[1].mainsnak.datavalue.value.latitude args[2] = entity.claims.P625[1].mainsnak.datavalue.value.longitude if precision then precision = -math_mod._round(math.log(precision)/math.log(10),0) args[1] = math_mod._round(args[1],precision) args[2] = math_mod._round(args[2],precision) end end end

local contents, backward = formatTest(args) local Notes = args.notes or '' local Display = args.display and args.display:lower or 'inline'

local function isInline(s) -- Finds whether coordinates are displayed inline. return s:find('inline') ~= nil or s == 'i' or s == 'it' or s == 'ti' end local function isInTitle(s) -- Finds whether coordinates are displayed in the title. return s:find('title') ~= nil or s == 't' or s == 'it' or s == 'ti' end

local function coord_wrapper(in_args) -- Calls the parser function. return mw.getCurrentFrame:callParserFunction('#coordinates', in_args) or '' end

local text = '' if isInline(Display) then text = text .. displayinline(contents, Notes) end if isInTitle(Display) then text = text .. displaytitle(contents, Notes) .. makeWikidataCategories(args.qid) end if not args.nosave then local page_title, count = mw.title.getCurrentTitle, 1 if backward then local tmp = {} while not string.find((args[count-1] or ), '[EW]') do tmp[count] = (args[count] or ); count = count+1 end tmp.count = count; count = 2*(count-1) while count >= tmp.count do table.insert(tmp, 1, (args[count] or '')); count = count-1 end for i, v in ipairs(tmp) do args[i] = v end else while count <= 9 do args[count] = (args[count] or ''); count = count+1 end end if isInTitle(Display) and not page_title.isTalkPage and page_title.subpageText ~= 'doc' and page_title.subpageText ~= 'testcases' then args[10] = 'primary' end args.notes, args.format, args.display = nil text = text .. coord_wrapper(args) end return text end

--[[ coord2text

Extracts a single value from a transclusion of °N, °W. IF THE GEOHACK LINK SYNTAX CHANGES THIS FUNCTION MUST BE MODIFIED.

Usage:

Valid values for the second parameter are: lat (signed integer), long (signed integer), type, scale, dim, region, globe, source

]] function coordinates.coord2text(frame) if frame.args[1] ==  or frame.args[2] ==  or not frame.args[2] then return nil end frame.args[2] = mw.text.trim(frame.args[2]) if frame.args[2] == 'lat' or frame.args[2] == 'long' then local result, negative = mw.text.split((mw.ustring.match(frame.args[1],'[%.%d]+°[NS] [%.%d]+°[EW]') or ''), ' ') if frame.args[2] == 'lat' then result, negative = result[1], 'S'		else result, negative = result[2], 'W'		end result = mw.text.split(result, '°') if result[2] == negative then result[1] = '-'..result[1] end return result[1] else return mw.ustring.match(frame.args[1], 'params=.-_'..frame.args[2]..':(.-)[ _]') end end

--[[ coordinsert

Injects some text into the Geohack link of a transclusion of °N, °W (if that text isn't already in the transclusion). Outputs the modified transclusion of °N, °W. IF THE GEOHACK LINK SYNTAX CHANGES THIS FUNCTION MUST BE MODIFIED.

Usage:

Do not make Geohack unhappy by inserting something which isn't mentioned in the °N, °W documentation.

]] function coordinates.coordinsert(frame) for i, v in ipairs(frame.args) do		if i ~= 1 then if not mw.ustring.find(frame.args[1], (mw.ustring.match(frame.args[i], '^(.-:)') or '')) then frame.args[1] = mw.ustring.gsub(frame.args[1], '(params=.-)_? ', '%1_'..frame.args[i]..' ') end end end if frame.args.name then if not mw.ustring.find(frame.args[1], ' ') then local namestr = frame.args.name frame.args[1] = mw.ustring.gsub(frame.args[1],				'(]*>[^<>]* ]*>[^<>]*]*>[^<>]* )',				'%1 %2 &#xfeff; ( ' .. namestr .. ' ) %3')			frame.args[1] = mw.ustring.gsub(frame.args[1], '(&params=[^&"<>%[%] ]*) ', '%1&title=' .. mw.uri.encode(namestr) .. ' ')		end	end	return frame.args[1] end

return coordinates