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Jenks: Fix multiple bugs

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This commit is contained in:
Raul Marin 2018-09-10 13:16:54 +02:00
parent fcc06e82bf
commit 0e7d797400
1 changed files with 261 additions and 154 deletions
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415
scripts-available/CDB_JenksBins.sql
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@ -10,212 +10,319 @@
--
-- @param invert Optional wheter to return the top of each bin (default)
-- or the bottom. BOOLEAN, default=FALSE.
--
--
--
CREATE OR REPLACE FUNCTION CDB_JenksBins(in_array NUMERIC[], breaks INT, iterations INT DEFAULT 0, invert BOOLEAN DEFAULT FALSE)
RETURNS NUMERIC[] as
$$
DECLARE
in_matrix NUMERIC[][];
in_unique_count BIGINT;
CREATE OR REPLACE FUNCTION CDB_JenksBins ( in_array NUMERIC[], breaks INT, iterations INT DEFAULT 5, invert BOOLEAN DEFAULT FALSE) RETURNS NUMERIC[] as $$
DECLARE
element_count INT4;
shuffles INT;
arr_mean NUMERIC;
sdam NUMERIC;
i INT;
bot INT;
top INT;
tops INT[];
classes INT[][];
i INT := 1; j INT := 1;
j INT := 1;
curr_result NUMERIC[];
best_result NUMERIC[];
seedtarget TEXT;
quant NUMERIC[];
shuffles INT;
BEGIN
-- get the total size of our row
element_count := array_length(in_array, 1); --array_upper(in_array, 1) - array_lower(in_array, 1);
-- ensure the ordering of in_array
SELECT array_agg(e) INTO in_array FROM (SELECT unnest(in_array) e ORDER BY e) x;
-- stop if no rows
IF element_count IS NULL THEN
RETURN NULL;
END IF;
-- stop if our breaks are more than our input array size
IF element_count < breaks THEN
RETURN in_array;
END IF;
-- We clean the input array (remove NULLs) and create 2 arrays
-- [1] contains the unique values in in_array
-- [2] contains the number of appearances of those unique values
SELECT ARRAY[array_agg(value), array_agg(count)] FROM
(
SELECT value, count(1)::numeric as count
FROM unnest(in_array) AS value
WHERE value is NOT NULL
GROUP BY value
ORDER BY value
) __clean_array_q INTO in_matrix;
shuffles := LEAST(GREATEST(floor(2500000.0/(element_count::float*iterations::float)), 1), 750)::int;
-- get our mean value
SELECT avg(v) INTO arr_mean FROM ( SELECT unnest(in_array) as v ) x;
-- Get the number of unique values
in_unique_count := array_length(in_matrix[1:1], 2);
RAISE INFO 'Unique %', in_unique_count;
-- assume best is actually Quantile
SELECT CDB_QuantileBins(in_array, breaks) INTO quant;
-- if data is very very large, just return quant and be done
IF element_count > 5000000 THEN
RETURN quant;
IF in_unique_count IS NULL THEN
RETURN NULL;
END IF;
-- change quant into bottom, top markers
LOOP
IF i = 1 THEN
bot = 1;
ELSE
-- use last top to find this bot
bot = top+1;
END IF;
IF i = breaks THEN
top = element_count;
ELSE
SELECT count(*) INTO top FROM ( SELECT unnest(in_array) as v) x WHERE v <= quant[i];
END IF;
IF i = 1 THEN
classes = ARRAY[ARRAY[bot,top]];
ELSE
classes = ARRAY_CAT(classes,ARRAY[bot,top]);
END IF;
IF i > breaks THEN EXIT; END IF;
i = i+1;
END LOOP;
IF in_unique_count <= breaks THEN
-- There isn't enough distinct values for the requested breaks
RETURN ARRAY(Select unnest(in_matrix[1:1])) _a;
END IF;
best_result = CDB_JenksBinsIteration( in_array, breaks, classes, invert, element_count, arr_mean, shuffles);
-- If not declated explicitly we iterate based on the length of the array
IF iterations < 1 THEN
-- This is based on a 'looks fine' heuristic
iterations := log(in_unique_count)::integer + 1;
END IF;
RAISE INFO 'Iterations: %', iterations;
-- We set the number of shuffles per iteration as the number of unique values but
-- this is just another 'looks fine' heuristic
shuffles := in_unique_count;
RAISE INFO 'Suffles %', shuffles;
-- Get the mean value of the whole vector (already ignores NULLs)
SELECT avg(v) INTO arr_mean FROM ( SELECT unnest(in_array) as v ) x;
RAISE INFO 'Mean %', arr_mean;
-- Calculate the sum of squared deviations from the array mean (SDAM).
SELECT sum(((arr_mean - v)^2) * w) INTO sdam FROM (
SELECT unnest(in_matrix[1:1]) as v, unnest(in_matrix[2:2]) as w
) x;
RAISE INFO 'Deviation %', sdam;
-- To start, we create ranges with approximately the same amount of different values
top := 0;
i := 1;
LOOP
bot := top + 1;
top := ROUND(i * in_unique_count::numeric / breaks::NUMERIC);
IF i = 1 THEN
classes = ARRAY[ARRAY[bot,top]];
ELSE
classes = ARRAY_CAT(classes, ARRAY[bot,top]);
END IF;
i := i + 1;
IF i > breaks THEN EXIT; END IF;
END LOOP;
RAISE INFO 'Initial classes %', classes;
best_result = CDB_JenksBinsIteration(in_matrix, breaks, classes, invert, sdam, shuffles);
--set the seed so we can ensure the same results
SELECT setseed(0.4567) INTO seedtarget;
--loop through random starting positions
LOOP
IF j > iterations-1 THEN EXIT; END IF;
IF j > iterations-1 THEN EXIT; END IF;
i = 1;
tops = ARRAY[element_count];
tops = ARRAY[in_unique_count];
LOOP
IF i = breaks THEN EXIT; END IF;
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;
i = array_length(tops, 1);
END LOOP;
IF i = breaks THEN EXIT; END IF;
SELECT array_agg(distinct e) INTO tops FROM (
SELECT unnest(array_cat(tops, ARRAY[trunc(random() * in_unique_count::float8)::int + 1])) as e ORDER BY e
) x;
i = array_length(tops, 1);
END LOOP;
RAISE INFO 'Tops %', tops;
top := 0;
i = 1;
LOOP
IF i > breaks THEN EXIT; END IF;
IF i = 1 THEN
bot = 1;
ELSE
bot = top+1;
END IF;
LOOP
bot := top + 1;
top = tops[i];
IF i = 1 THEN
classes = ARRAY[ARRAY[bot,top]];
ELSE
classes = ARRAY_CAT(classes,ARRAY[bot,top]);
IF i = 1 THEN
classes = ARRAY[ARRAY[bot,top]];
ELSE
classes = ARRAY_CAT(classes, ARRAY[bot,top]);
END IF;
i := i+1;
END LOOP;
curr_result = CDB_JenksBinsIteration( in_array, breaks, classes, invert, element_count, arr_mean, shuffles);
i := i+1;
IF i > breaks THEN EXIT; END IF;
END LOOP;
RAISE INFO 'Classes %', classes;
curr_result = CDB_JenksBinsIteration(in_matrix, breaks, classes, invert, sdam, shuffles);
IF curr_result[1] > best_result[1] THEN
best_result = curr_result;
j = j-1; -- if we found a better result, add one more search
END IF;
j = j+1;
END LOOP;
RETURN (best_result)[2:array_upper(best_result, 1)];
END;
$$ language plpgsql VOLATILE PARALLEL RESTRICTED;
$$ LANGUAGE PLPGSQL IMMUTABLE PARALLEL RESTRICTED;
--
-- Perform a single iteration of the Jenks classification
--
-- Returns an array with:
-- - First element: gvf
-- - Second to 2+n: Category limits
DROP FUNCTION IF EXISTS CDB_JenksBinsIteration ( in_matrix NUMERIC[], breaks INT, classes INT[], invert BOOLEAN, element_count INT4, arr_mean NUMERIC, max_search INT); -- Old signature
CREATE OR REPLACE FUNCTION CDB_JenksBinsIteration ( in_matrix NUMERIC[], breaks INT, classes INT[], invert BOOLEAN, sdam NUMERIC, max_search INT DEFAULT 50) RETURNS NUMERIC[] as $$
DECLARE
i INT;
iterations INT = 0;
CREATE OR REPLACE FUNCTION CDB_JenksBinsIteration ( in_array NUMERIC[], breaks INT, classes INT[][], invert BOOLEAN, element_count INT4, arr_mean NUMERIC, max_search INT DEFAULT 50) RETURNS NUMERIC[] as $$
DECLARE
tmp_val numeric;
new_classes int[][];
tmp_class int[];
i INT := 1;
j INT := 1;
side INT := 2;
sdam numeric;
gvf numeric := 0.0;
new_gvf numeric;
arr_gvf numeric[];
class_avg numeric;
class_max_i INT;
class_min_i INT;
class_max numeric;
class_min numeric;
reply numeric[];
BEGIN
-- Calculate the sum of squared deviations from the array mean (SDAM).
SELECT sum((arr_mean - e)^2) INTO sdam FROM ( SELECT unnest(in_array) as e ) x;
--Identify the breaks for the lowest GVF
LOOP
i = 1;
LOOP
-- get our mean
SELECT avg(e) INTO class_avg FROM ( SELECT unnest(in_array[classes[i][1]:classes[i][2]]) as e) x;
-- find the deviation
SELECT sum((class_avg-e)^2) INTO tmp_val FROM ( SELECT unnest(in_array[classes[i][1]:classes[i][2]]) as e ) x;
IF i = 1 THEN
arr_gvf = ARRAY[tmp_val];
-- init our min/max map for later
class_max = arr_gvf[i];
class_min = arr_gvf[i];
class_min_i = 1;
class_max_i = 1;
ELSE
arr_gvf = array_append(arr_gvf, tmp_val);
END IF;
i := i+1;
IF i > breaks THEN EXIT; END IF;
END LOOP;
-- calculate our new GVF
SELECT sdam-sum(e) INTO new_gvf FROM ( SELECT unnest(arr_gvf) as e ) x;
-- if no improvement was made, exit
IF new_gvf < gvf THEN EXIT; END IF;
gvf = new_gvf;
IF j > max_search THEN EXIT; END IF;
j = j+1;
i = 1;
LOOP
--establish directionality (uppward through classes or downward)
IF arr_gvf[i] < class_min THEN
class_min = arr_gvf[i];
class_min_i = i;
END IF;
IF arr_gvf[i] > class_max THEN
class_max = arr_gvf[i];
class_max_i = i;
END IF;
i := i+1;
IF i > breaks THEN EXIT; END IF;
END LOOP;
IF class_max_i > class_min_i THEN
class_min_i = class_max_i - 1;
gvf numeric := 0.0;
new_gvf numeric;
arr_gvf numeric[];
arr_avg numeric[];
class_avg numeric;
class_dev numeric;
class_max_i INT;
class_min_i INT;
dev_max numeric;
dev_min numeric;
best_classes INT[] = classes;
reply numeric[];
BEGIN
-- We fill the arrays with the initial values
i = 0;
LOOP
IF i = breaks THEN EXIT; END IF;
i = i + 1;
RAISE INFO 'Loop %', i;
-- Get class mean
SELECT (sum(v * w) / sum(w)) INTO class_avg FROM (
SELECT unnest(in_matrix[1:1][classes[i][1]:classes[i][2]]) as v,
unnest(in_matrix[2:2][classes[i][1]:classes[i][2]]) as w
) x;
-- Get class deviation
SELECT sum((class_avg - v)^2 * w) INTO class_dev FROM (
SELECT unnest(in_matrix[1:1][classes[i][1]:classes[i][2]]) as v,
unnest(in_matrix[2:2][classes[i][1]:classes[i][2]]) as w
) x;
IF i = 1 THEN
arr_avg = ARRAY[class_avg];
arr_gvf = ARRAY[class_dev];
ELSE
class_min_i = class_max_i + 1;
arr_avg = array_append(arr_avg, class_avg);
arr_gvf = array_append(arr_gvf, class_dev);
END IF;
--Move from higher class to a lower gid order
IF class_max_i > class_min_i THEN
classes[class_max_i][1] = classes[class_max_i][1] + 1;
classes[class_min_i][2] = classes[class_min_i][2] + 1;
ELSE -- Move from lower class UP into a higher class by gid
classes[class_max_i][2] = classes[class_max_i][2] - 1;
classes[class_min_i][1] = classes[class_min_i][1] - 1;
END LOOP;
iterations = 0;
LOOP
IF iterations = max_search THEN EXIT; END IF;
iterations = iterations + 1;
-- calculate our new GVF
SELECT sdam - sum(e) INTO new_gvf FROM ( SELECT unnest(arr_gvf) as e ) x;
-- if no improvement was made, exit
IF new_gvf <= gvf OR class_max_i = class_min_i THEN EXIT; END IF;
-- We search for classes with the min and max deviation
i = 1;
class_min_i = 1;
class_max_i = 1;
dev_max = arr_gvf[1];
dev_min = arr_gvf[1];
LOOP
IF i = breaks THEN EXIT; END IF;
i = i + 1;
IF arr_gvf[i] < dev_min THEN
dev_min = arr_gvf[i];
class_min_i = i;
ELSE
IF arr_gvf[i] > dev_max THEN
dev_max = arr_gvf[i];
class_max_i = i;
END IF;
END IF;
END LOOP;
END LOOP;
-- Save best values for comparison and output
gvf = new_gvf;
best_classes = classes;
RAISE INFO 'Deviations %', arr_gvf;
RAISE INFO 'Min %. Max %', class_min_i, class_max_i;
-- Iterate by moving an element from class_max_i to class_min_i
IF class_min_i < class_max_i THEN
i := class_min_i;
LOOP
IF i = class_max_i THEN EXIT; END IF;
classes[i][2] = classes[i][2] + 1;
i := i + 1;
END LOOP;
i := class_max_i;
LOOP
IF i = class_min_i THEN EXIT; END IF;
classes[i][1] = classes[i][1] + 1;
i := i - 1;
END LOOP;
ELSE
i := class_min_i;
LOOP
IF i = class_max_i THEN EXIT; END IF;
classes[i][1] = classes[i][1] - 1;
i := i - 1;
END LOOP;
i := class_max_i;
LOOP
IF i = class_min_i THEN EXIT; END IF;
classes[i][2] = classes[i][2] - 1;
i := i + 1;
END LOOP;
END IF;
RAISE INFO 'Classes %', classes;
-- Recalculate avg and deviation for the affected classes
i = LEAST(class_min_i, class_max_i);
class_max_i = GREATEST(class_min_i, class_max_i);
LOOP
-- Get class mean
SELECT (sum(v * w) / sum(w)) INTO class_avg FROM (
SELECT unnest(in_matrix[1:1][classes[i][1]:classes[i][2]]) as v,
unnest(in_matrix[2:2][classes[i][1]:classes[i][2]]) as w
) x;
-- Get class deviation
SELECT sum((class_avg - v)^2 * w) INTO class_dev FROM (
SELECT unnest(in_matrix[1:1][classes[i][1]:classes[i][2]]) as v,
unnest(in_matrix[2:2][classes[i][1]:classes[i][2]]) as w
) x;
arr_avg[i] = class_avg;
arr_gvf[i] = class_dev;
IF i = class_max_i THEN EXIT; END IF;
i = i + 1;
END LOOP;
END LOOP;
i = 1;
LOOP
LOOP
IF invert = TRUE THEN
side = 1; --default returns bottom side of breaks, invert returns top side
END IF;
reply = array_append(reply, in_array[classes[i][side]]);
i = i+1;
IF i > breaks THEN EXIT; END IF;
END LOOP;
RETURN array_prepend(gvf, reply);
reply = array_append(reply, unnest(in_matrix[1:1][best_classes[i][side]:best_classes[i][side]]));
i = i+1;
IF i > breaks THEN EXIT; END IF;
END LOOP;
END;
$$ language plpgsql IMMUTABLE PARALLEL SAFE;
reply = array_prepend(gvf, reply);
RAISE INFO 'Reply: %', reply;
RETURN reply;
END;
$$ LANGUAGE PLPGSQL IMMUTABLE PARALLEL SAFE;