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222 lines
7.3 KiB
222 lines
7.3 KiB
--
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-- Determine the Jenks classifications from a numeric array
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--
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-- @param in_array A numeric array of numbers to determine the best
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-- bins based on the Jenks method.
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--
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-- @param breaks The number of bins you want to find.
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--
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-- @param iterations The number of different starting positions to test.
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--
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-- @param invert Optional wheter to return the top of each bin (default)
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-- or the bottom. BOOLEAN, default=FALSE.
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--
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--
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CREATE OR REPLACE FUNCTION CDB_JenksBins ( in_array NUMERIC[], breaks INT, iterations INT DEFAULT 5, invert BOOLEAN DEFAULT FALSE) RETURNS NUMERIC[] as $$
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DECLARE
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element_count INT4;
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arr_mean NUMERIC;
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bot INT;
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top INT;
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tops INT[];
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classes INT[][];
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i INT := 1; j INT := 1;
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curr_result NUMERIC[];
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best_result NUMERIC[];
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seedtarget TEXT;
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quant NUMERIC[];
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shuffles INT;
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BEGIN
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-- get the total size of our row
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element_count := array_length(in_array, 1); --array_upper(in_array, 1) - array_lower(in_array, 1);
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-- ensure the ordering of in_array
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SELECT array_agg(e) INTO in_array FROM (SELECT unnest(in_array) e ORDER BY e) x;
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-- stop if no rows
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IF element_count IS NULL THEN
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RETURN NULL;
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END IF;
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-- stop if our breaks are more than our input array size
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IF element_count < breaks THEN
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RETURN in_array;
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END IF;
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shuffles := LEAST(GREATEST(floor(2500000.0/(element_count::float*iterations::float)), 1), 750)::int;
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-- get our mean value
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SELECT avg(v) INTO arr_mean FROM ( SELECT unnest(in_array) as v ) x;
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-- assume best is actually Quantile
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SELECT CDB_QuantileBins(in_array, breaks) INTO quant;
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-- if data is very very large, just return quant and be done
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IF element_count > 5000000 THEN
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RETURN quant;
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END IF;
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-- change quant into bottom, top markers
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LOOP
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IF i = 1 THEN
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bot = 1;
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ELSE
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-- use last top to find this bot
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bot = top+1;
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END IF;
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IF i = breaks THEN
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top = element_count;
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ELSE
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SELECT count(*) INTO top FROM ( SELECT unnest(in_array) as v) x WHERE v <= quant[i];
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END IF;
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IF i = 1 THEN
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classes = ARRAY[ARRAY[bot,top]];
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ELSE
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classes = ARRAY_CAT(classes,ARRAY[bot,top]);
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END IF;
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IF i > breaks THEN EXIT; END IF;
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i = i+1;
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END LOOP;
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best_result = CDB_JenksBinsIteration( in_array, breaks, classes, invert, element_count, arr_mean, shuffles);
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--set the seed so we can ensure the same results
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SELECT setseed(0.4567) INTO seedtarget;
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--loop through random starting positions
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LOOP
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IF j > iterations-1 THEN EXIT; END IF;
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i = 1;
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tops = ARRAY[element_count];
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LOOP
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IF i = breaks THEN EXIT; END IF;
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SELECT array_agg(distinct e) INTO tops FROM (SELECT unnest(array_cat(tops, ARRAY[floor(random()*element_count::float)::int])) as e ORDER BY e) x WHERE e != 1;
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i = array_length(tops, 1);
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END LOOP;
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i = 1;
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LOOP
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IF i > breaks THEN EXIT; END IF;
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IF i = 1 THEN
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bot = 1;
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ELSE
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bot = top+1;
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END IF;
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top = tops[i];
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IF i = 1 THEN
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classes = ARRAY[ARRAY[bot,top]];
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ELSE
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classes = ARRAY_CAT(classes,ARRAY[bot,top]);
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END IF;
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i := i+1;
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END LOOP;
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curr_result = CDB_JenksBinsIteration( in_array, breaks, classes, invert, element_count, arr_mean, shuffles);
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IF curr_result[1] > best_result[1] THEN
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best_result = curr_result;
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j = j-1; -- if we found a better result, add one more search
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END IF;
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j = j+1;
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END LOOP;
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RETURN (best_result)[2:array_upper(best_result, 1)];
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END;
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$$ language plpgsql IMMUTABLE;
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--
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-- Perform a single iteration of the Jenks classification
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--
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CREATE OR REPLACE FUNCTION CDB_JenksBinsIteration ( in_array NUMERIC[], breaks INT, classes INT[][], invert BOOLEAN, element_count INT4, arr_mean NUMERIC, max_search INT DEFAULT 50) RETURNS NUMERIC[] as $$
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DECLARE
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tmp_val numeric;
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new_classes int[][];
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tmp_class int[];
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i INT := 1;
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j INT := 1;
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side INT := 2;
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sdam numeric;
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gvf numeric := 0.0;
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new_gvf numeric;
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arr_gvf numeric[];
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class_avg numeric;
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class_max_i INT;
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class_min_i INT;
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class_max numeric;
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class_min numeric;
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reply numeric[];
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BEGIN
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-- Calculate the sum of squared deviations from the array mean (SDAM).
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SELECT sum((arr_mean - e)^2) INTO sdam FROM ( SELECT unnest(in_array) as e ) x;
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--Identify the breaks for the lowest GVF
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LOOP
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i = 1;
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LOOP
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-- get our mean
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SELECT avg(e) INTO class_avg FROM ( SELECT unnest(in_array[classes[i][1]:classes[i][2]]) as e) x;
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-- find the deviation
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SELECT sum((class_avg-e)^2) INTO tmp_val FROM ( SELECT unnest(in_array[classes[i][1]:classes[i][2]]) as e ) x;
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IF i = 1 THEN
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arr_gvf = ARRAY[tmp_val];
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-- init our min/max map for later
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class_max = arr_gvf[i];
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class_min = arr_gvf[i];
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class_min_i = 1;
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class_max_i = 1;
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ELSE
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arr_gvf = array_append(arr_gvf, tmp_val);
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END IF;
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i := i+1;
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IF i > breaks THEN EXIT; END IF;
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END LOOP;
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-- calculate our new GVF
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SELECT sdam-sum(e) INTO new_gvf FROM ( SELECT unnest(arr_gvf) as e ) x;
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-- if no improvement was made, exit
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IF new_gvf < gvf THEN EXIT; END IF;
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gvf = new_gvf;
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IF j > max_search THEN EXIT; END IF;
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j = j+1;
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i = 1;
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LOOP
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--establish directionality (uppward through classes or downward)
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IF arr_gvf[i] < class_min THEN
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class_min = arr_gvf[i];
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class_min_i = i;
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END IF;
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IF arr_gvf[i] > class_max THEN
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class_max = arr_gvf[i];
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class_max_i = i;
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END IF;
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i := i+1;
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IF i > breaks THEN EXIT; END IF;
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END LOOP;
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IF class_max_i > class_min_i THEN
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class_min_i = class_max_i - 1;
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ELSE
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class_min_i = class_max_i + 1;
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END IF;
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--Move from higher class to a lower gid order
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IF class_max_i > class_min_i THEN
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classes[class_max_i][1] = classes[class_max_i][1] + 1;
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classes[class_min_i][2] = classes[class_min_i][2] + 1;
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ELSE -- Move from lower class UP into a higher class by gid
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classes[class_max_i][2] = classes[class_max_i][2] - 1;
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classes[class_min_i][1] = classes[class_min_i][1] - 1;
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END IF;
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END LOOP;
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i = 1;
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LOOP
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IF invert = TRUE THEN
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side = 1; --default returns bottom side of breaks, invert returns top side
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END IF;
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reply = array_append(reply, in_array[classes[i][side]]);
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i = i+1;
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IF i > breaks THEN EXIT; END IF;
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END LOOP;
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RETURN array_prepend(gvf, reply);
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END;
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$$ language plpgsql IMMUTABLE;
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