tdigest
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javascript implementation of Dunning's T-Digest for streaming quantile approximation
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JavaScript
// test the discrete distribution behavior, in which TDigest merging is
// disabled and mass is accumulated at points and reported exactly.
//
var TDigest = require('../tdigest').TDigest;
var assert = require('better-assert');
assert.deepEqual = require('chai').assert.deepEqual;
describe('discrete digests', function(){
it('consumes increasing-valued points', function(){
var tdigest = new TDigest(false);
var i, N = 100;
for (i = 0 ; i < N ; i += 1) {
tdigest.push(i*10);
}
var points = tdigest.toArray(true);
for (i = 0 ; i < N ; i += 1) {
assert(points[i].mean === i*10);
}
});
it('consumes decreasing-valued points', function(){
var tdigest = new TDigest(false);
var i, N = 100;
for (i = N - 1 ; i >= 0 ; i = i - 1) {
tdigest.push(i*10);
}
var points = tdigest.toArray(true);
for (i = 0 ; i < N ; i += 1) {
assert(points[i].mean === i*10);
}
});
it('consumes nonnumeric points', function(){
var tdigest = new TDigest(false);
tdigest.push("foo");
tdigest.push("bar");
tdigest.push("baz");
tdigest.push("foo");
tdigest.push("freen");
tdigest.push("bork");
tdigest.push("bork");
tdigest.push("bork");
tdigest.push("books");
var points = tdigest.toArray();
assert.deepEqual(points, [
{mean:"bar", n:1},
{mean:"baz", n:1},
{mean:"books", n:1},
{mean:"bork", n:3},
{mean:"foo", n:2},
{mean:"freen", n:1},
]);
});
it('consumes same-valued points into a single point', function(){
var tdigest = new TDigest(false);
var i, N = 100;
for (i = 0 ; i < N ; i = i + 1) {
tdigest.push(1000);
}
var points = tdigest.toArray();
assert.deepEqual(points, [{mean: 1000, n:N}]);
});
it('selects a run of duplicates containing the percentile', function(){
var tdigest = new TDigest(false);
tdigest.push([ 5, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
3, 0, 0, 0, 0, 6, 1, 0, 6, 5, 3, 6, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0 ]);
assert(tdigest.percentile(0.5) === 0);
});
it('handles multiple duplicates', function(){
var tdigest = new TDigest(false);
var i, N = 10;
for (i = 0 ; i < N ; i++) {
tdigest.push(0.0);
tdigest.push(1.0);
tdigest.push(0.5);
}
assert.deepEqual(
tdigest.toArray(),
[{mean:0.0, n:N},
{mean:0.5, n:N},
{mean:1.0, n:N}]
);
});
});
describe('discrete percentile ranks', function(){
it('from a single point', function(){
var tdigest = new TDigest(false);
tdigest.push(0);
var x = [-0.5, 0, 0.5, 1.0, 1.5];
var q = [0, 1, 1, 1, 1];
assert.deepEqual(tdigest.p_rank(x), q);
});
it('from two points', function(){
var tdigest = new TDigest(false);
tdigest.push([0, 1]);
var x = [-0.5, 0, 0.5, 1.0, 1.5];
var q = [0, 0.5, 0.5, 1.0, 1.0];
assert.deepEqual(tdigest.p_rank(x), q);
});
it('from three points', function(){
var tdigest = new TDigest(false);
tdigest.push([-1, 0, 1] );
var x = [-1.5, -1.0, -0.5, 0, 0.5, 1.0, 1.5];
var q = [0, 1/3, 1/3, 2/3, 2/3, 1, 1];
assert.deepEqual(tdigest.p_rank(x), q);
});
it('from three points is same as from multiples of those points', function(){
var tdigest = new TDigest(false);
tdigest.push([0,1,-1]);
var x = [-1.5, -1.0, -0.5, 0, 0.5, 1.0, 1.5];
var result1 = tdigest.p_rank(x);
tdigest.push([0,1,-1]);
tdigest.push([0,1,-1]);
var result2 = tdigest.p_rank(x);
assert.deepEqual(result1, result2);
});
it('from four points away from the origin', function(){
var tdigest = new TDigest(false);
tdigest.push([10,11,12,13]);
var x = [9, 10, 11, 12, 13, 14];
var q = [0, 1/4, 2/4, 3/4, 1, 1];
assert.deepEqual(tdigest.p_rank(x), q);
});
it('from four points is same as from multiples of those points', function(){
var tdigest = new TDigest(false);
tdigest.push([10,11,12,13]);
var x = [9, 10, 11, 12, 13, 14];
var result1 = tdigest.p_rank(x);
tdigest.push([10,11,12,13]);
tdigest.push([10,11,12,13]);
var result2 = tdigest.p_rank(x);
assert.deepEqual(result1, result2);
});
it('from nonnumeric points', function(){
var tdigest = new TDigest(false);
tdigest.push("foo");
tdigest.push("bar");
tdigest.push("baz");
tdigest.push("freen");
var x = ["bar", "baz", "foo", "freen"];
var q = [1/4, 2/4, 3/4, 4/4];
assert.deepEqual(tdigest.p_rank(x), q);
});
});
describe('discrete percentiles', function(){
it('from a single point', function(){
var tdigest = new TDigest(false);
tdigest.push(0);
var p = [0, 0.5, 1.0];
var x = [0, 0, 0];
assert.deepEqual(tdigest.percentile(p), x);
});
it('from two points', function(){
var tdigest = new TDigest(false);
tdigest.push([0, 10]);
var p = [0, 1/4, 1/2, 3/4, 1];
var x = [0, 0, 0, 10, 10];
assert.deepEqual(tdigest.percentile(p), x);
});
it('from three points', function(){
var tdigest = new TDigest(false);
tdigest.push([0, 5, 10]);
var p = [0, 1/4, 1/2.9, 1/2, 2/3, 3/4, 1];
var x = [0, 0, 5, 5, 5, 10, 10];
assert.deepEqual(tdigest.percentile(p), x);
});
it('from four points away from the origin', function(){
var tdigest = new TDigest(false);
tdigest.push([10,11,12,13]);
var p = [0, 1/4, 1/2, 3/4, 1];
var x = [10, 10, 11, 12, 13];
assert.deepEqual(tdigest.percentile(p), x);
});
it('from nonnumeric points', function(){
var tdigest = new TDigest(false);
tdigest.push("foo");
tdigest.push("bar");
tdigest.push("baz");
tdigest.push("freen");
var p = [0, 1/4, 1/2, 3/4, 1];
var x = ["bar", "bar", "baz", "foo", "freen"];
assert.deepEqual(tdigest.percentile(p), x);
});
});