From 6b1a62d0757e297be174cfa04d90a6f0941bce2b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Tom=C3=A1s=20Senart?= <tsenart@gmail.com>
Date: Sun, 12 Aug 2018 01:41:14 +0200
Subject: [PATCH] lttb: Checkin

---
 lib/lttb/lttb.go      |    96 +
 lib/lttb/lttb_test.go | 14100 ++++++++++++++++++++++++++++++++++++++++
 2 files changed, 14196 insertions(+)
 create mode 100644 lib/lttb/lttb.go
 create mode 100644 lib/lttb/lttb_test.go

diff --git a/lib/lttb/lttb.go b/lib/lttb/lttb.go
new file mode 100644
index 00000000..687c0258
--- /dev/null
+++ b/lib/lttb/lttb.go
@@ -0,0 +1,96 @@
+package lttb
+
+import "errors"
+
+// A Point in a line chart.
+type Point struct{ X, Y float64 }
+
+// An Iter represents an iterator function that returns
+// count number of Points or an error.
+type Iter func(count int) ([]Point, error)
+
+// Downsample `count` number of data points retrieved from the given iterator
+// function to contain only `threshold` number of points while maintaining close
+// visual similarity to the original data. The algorithm is called
+// Largest-Triangle-Three-Buckets and is described in:
+// https://skemman.is/bitstream/1946/15343/3/SS_MSthesis.pdf
+//
+// This implementation grew out of https://github.com/dgryski/go-lttb
+// to limit memory usage by leveraging iterators.
+func Downsample(count, threshold int, it Iter) ([]Point, error) {
+	if threshold >= count || threshold == 0 {
+		points, err := it(count)
+		return points, err
+	}
+
+	if threshold < 3 {
+		return nil, errors.New("lttb: min threshold is 3")
+	}
+
+	// Bucket size. Leave room for start and end data points
+	size := float64(count-2) / float64(threshold-2)
+
+	// Get the first point and the current bucket.
+	points, err := it(int(1 + size))
+	if err != nil {
+		return nil, err
+	}
+
+	samples := make([]Point, 0, threshold)
+	samples = append(samples, points[0]) // Always add the first point
+	current := points[1:]
+
+	for i := 0; i < threshold-2; i++ {
+		// Calculate bucket boundaries (non inclusive hi)
+		lo := int(float64(i+1)*size) + 1
+		hi := int(float64(i+2)*size) + 1
+
+		next, err := it(hi - lo)
+		if err != nil {
+			return nil, err
+		}
+
+		samples = append(samples, sample(samples[len(samples)-1], current, next))
+		current = next
+	}
+
+	// Always add the last point unmodified
+	if points, err = it(count - len(samples)); err != nil {
+		return nil, err
+	} else if len(points) == 0 {
+		points = current
+	}
+
+	if len(points) > 0 {
+		samples = append(samples, points[len(points)-1])
+	}
+
+	return samples, nil
+}
+
+func sample(a Point, current, next []Point) (b Point) {
+	// Calculate point c as the average point of all points in the next bucket.
+	var c Point
+	for i := range next {
+		c.X, c.Y = c.X+next[i].X, c.Y+next[i].Y
+	}
+
+	length := float64(len(next))
+	c.X, c.Y = c.X/length, c.Y/length
+
+	// Find index of point b that together with points a and c forms the largest triangle
+	// amongst all points in the current bucket.
+	var largest float64
+	var index int
+	for i, p := range current {
+		// Calculate triangle area over three buckets
+		area := (a.X-c.X)*(p.Y-a.Y) - (a.X-p.X)*(c.Y-a.Y)
+
+		// We only care about the relative area here. Calling math.Abs() is slower than squaring.
+		if area *= area; area > largest {
+			largest, index = area, i
+		}
+	}
+
+	return current[index]
+}
diff --git a/lib/lttb/lttb_test.go b/lib/lttb/lttb_test.go
new file mode 100644
index 00000000..6357917c
--- /dev/null
+++ b/lib/lttb/lttb_test.go
@@ -0,0 +1,14100 @@
+package lttb
+
+import (
+	"fmt"
+	"reflect"
+	"testing"
+	"unsafe"
+
+	golttb "github.com/dgryski/go-lttb"
+	"github.com/google/go-cmp/cmp"
+)
+
+func TestDownsample(t *testing.T) {
+	for _, threshold := range []int{0, len(points[0]), len(points[0]) + 1} {
+		threshold := threshold
+		t.Run(fmt.Sprintf("threshold-%d", threshold), func(t *testing.T) {
+			t.Parallel()
+
+			have, err := Downsample(len(points[0]), threshold, newIterator(points[0]))
+			if err != nil {
+				t.Fatalf("got err: %v", err)
+			}
+
+			want := points[0]
+			if diff := cmp.Diff(have, want, cmp.AllowUnexported(Point{})); diff != "" {
+				t.Error(diff)
+			}
+		})
+	}
+
+	for i := 1; i < 3; i++ {
+		threshold := i
+		t.Run(fmt.Sprintf("bad-threshold-%d", threshold), func(t *testing.T) {
+			t.Parallel()
+
+			_, err := Downsample(len(points[0]), threshold, newIterator(points[0]))
+			if have, want := fmt.Sprint(err), "lttb: min threshold is 3"; have != want {
+				t.Errorf("have err: %v, want %v", have, want)
+			}
+		})
+	}
+
+	for i, ps := range points {
+		for threshold := 3; threshold < len(ps); threshold++ {
+			ps, threshold := ps, threshold
+			t.Run(fmt.Sprintf("points=%d len=%d threshold=%d", i, len(ps), threshold), func(t *testing.T) {
+				t.Parallel()
+
+				ours, err := Downsample(len(ps), threshold, newIterator(ps))
+				if err != nil {
+					t.Fatalf("error: %v", err)
+				}
+
+				if have, want := len(ours), threshold; have != want {
+					t.Errorf("len(samples) != threshold: have %d, want %d", have, want)
+				}
+
+				if have, want := ours[0], ps[0]; have != want {
+					t.Errorf("samples[0] != data[0]: have %v, want %v", have, want)
+				}
+
+				if have, want := ours[len(ours)-1], ps[len(ps)-1]; have != want {
+					t.Errorf("samples[-1] != data[-1]: have %v, want %v", have, want)
+				}
+
+				// Test LTTB algorithm's equivalence to dgrisky/go-lttb
+				in := *(*[]golttb.Point)(unsafe.Pointer(&ps))
+				out := golttb.LTTB(in, threshold)
+				theirs := *(*[]Point)(unsafe.Pointer(&out))
+
+				if !reflect.DeepEqual(ours, theirs) {
+					t.Error(cmp.Diff(ours, theirs, cmp.AllowUnexported(Point{})))
+				}
+			})
+		}
+	}
+}
+
+func BenchmarkLTTB(b *testing.B) {
+	data := *(*[]golttb.Point)(unsafe.Pointer(&points[0]))
+	b.Run("dgryski", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			golttb.LTTB(data, 1000)
+		}
+	})
+
+	b.Run("tsenart", func(b *testing.B) {
+		for i := 0; i < b.N; i++ {
+			Downsample(len(data), 1000, newIterator(points[0]))
+		}
+	})
+}
+
+func newIterator(data []Point) Iter {
+	return func(count int) ([]Point, error) {
+		if count > len(data) {
+			count = len(data)
+		}
+		ps := data[:count]
+		data = data[count:]
+		return ps, nil
+	}
+}
+
+// From https://raw.githubusercontent.com/sveinn-steinarsson/flot-downsample/master/demo_data.js
+var points = [][]Point{
+	{
+		{0, 29.357995947822218},
+		{1, 29.40932479606209},
+		{2, 29.28168582006162},
+		{3, 30.409965579108867},
+		{4, 30.7726859735917},
+		{5, 30.839942247539028},
+		{6, 30.760611642264667},
+		{7, 31.203663004229718},
+		{8, 31.38899603525572},
+		{9, 30.890299916955737},
+		{10, 30.467811944911556},
+		{11, 30.596837868069542},
+		{12, 30.59789593509767},
+		{13, 30.19693062465079},
+		{14, 29.89081330734553},
+		{15, 29.54668002901058},
+		{16, 29.54890739422219},
+		{17, 30.53743760171474},
+		{18, 30.74066032317061},
+		{19, 30.3774450601516},
+		{20, 30.095148889986568},
+		{21, 30.057979182917986},
+		{22, 30.364655421168525},
+		{23, 30.293450053773604},
+		{24, 30.14578230340987},
+		{25, 30.277772879951996},
+		{26, 30.3711931235659},
+		{27, 30.355932660992572},
+		{28, 29.994740831603046},
+		{29, 29.938012885023657},
+		{30, 29.557268760451187},
+		{31, 29.16161297604625},
+		{32, 29.6921163421055},
+		{33, 30.246270628292226},
+		{34, 30.210955154680928},
+		{35, 29.382964668934058},
+		{36, 29.52892023906641},
+		{37, 29.719742065732202},
+		{38, 30.013856636945924},
+		{39, 29.818636169776926},
+		{40, 27.931224826933345},
+		{41, 28.103057873678374},
+		{42, 28.276025902356782},
+		{43, 28.193497487789774},
+		{44, 28.22099171488288},
+		{45, 28.06872431241809},
+		{46, 27.239835885250365},
+		{47, 26.606504358317906},
+		{48, 27.220308136213916},
+		{49, 25.80790898978574},
+		{50, 26.060334838062595},
+		{51, 25.89611036822564},
+		{52, 25.824433242208308},
+		{53, 25.89212193260212},
+		{54, 27.28963669872412},
+		{55, 27.208259984780806},
+		{56, 27.298211480886604},
+		{57, 27.056163307023077},
+		{58, 26.434701869643924},
+		{59, 26.21938188318228},
+		{60, 26.402877759468772},
+		{61, 26.326019357967294},
+		{62, 27.592635104460253},
+		{63, 27.597468405434316},
+		{64, 27.533410081050647},
+		{65, 27.30713964830731},
+		{66, 27.170789712751404},
+		{67, 27.610166301145746},
+		{68, 27.619847332319885},
+		{69, 27.55974343996647},
+		{70, 28.168803492093716},
+		{71, 28.284229862452584},
+		{72, 28.292638086760352},
+		{73, 28.523718178262335},
+		{74, 28.52268591410558},
+		{75, 28.576637206595993},
+		{76, 27.763715461946813},
+		{77, 27.48488075310065},
+		{78, 27.304006460281794},
+		{79, 26.902025619666333},
+		{80, 26.690162079132378},
+		{81, 26.52277286738866},
+		{82, 26.09406789919051},
+		{83, 26.029039984983562},
+		{84, 26.145181108429618},
+		{85, 24.75335912549342},
+		{86, 24.787772395126176},
+		{87, 24.966652093726385},
+		{88, 25.33621421606084},
+		{89, 25.29283081429076},
+		{90, 25.427452306231707},
+		{91, 25.34334450564347},
+		{92, 25.971939771661045},
+		{93, 25.907910638400836},
+		{94, 25.971895864171003},
+		{95, 26.448419417928317},
+		{96, 26.461057396494514},
+		{97, 26.332417666691025},
+		{98, 26.17395667752311},
+		{99, 25.318121919340044},
+		{100, 26.092918888834987},
+		{101, 26.080903284583307},
+		{102, 26.65713935644778},
+		{103, 26.90227335392346},
+		{104, 27.14904791481757},
+		{105, 27.45775156727039},
+		{106, 28.476933177720472},
+		{107, 27.899526884805073},
+		{108, 27.274094274806096},
+		{109, 27.007320452528134},
+		{110, 27.767594298696466},
+		{111, 28.669197835798027},
+		{112, 28.78287095361503},
+		{113, 28.744062941208348},
+		{114, 29.266136201836588},
+		{115, 29.29631346563548},
+		{116, 29.30576721224685},
+		{117, 28.92417256867908},
+		{118, 29.172020952087326},
+		{119, 29.36572118529946},
+		{120, 29.407882394097168},
+		{121, 29.24581675687127},
+		{122, 30.374496989862006},
+		{123, 29.75867484229172},
+		{124, 29.724977349500893},
+		{125, 29.766232845230032},
+		{126, 29.755425025733203},
+		{127, 29.891515813029994},
+		{128, 29.224842590902917},
+		{129, 29.19894861750696},
+		{130, 28.877260649054524},
+		{131, 29.100160763856657},
+		{132, 29.11303194254891},
+		{133, 29.471499370130353},
+		{134, 29.725430707066725},
+		{135, 29.875645922022283},
+		{136, 29.32336837740634},
+		{137, 29.659223458914788},
+		{138, 29.916122460150415},
+		{139, 29.947591268372232},
+		{140, 29.912720660976237},
+		{141, 30.030001305562784},
+		{142, 30.01603062688162},
+		{143, 30.206305874273855},
+		{144, 29.654798308068155},
+		{145, 29.51005186796388},
+		{146, 29.479249298103124},
+		{147, 29.50465455692649},
+		{148, 28.668390496723326},
+		{149, 29.70235193454973},
+		{150, 29.651621644229916},
+		{151, 29.514646394709878},
+		{152, 29.506006233800203},
+		{153, 29.85094476486748},
+		{154, 29.815453456016304},
+		{155, 29.942433471924208},
+		{156, 29.690047803042003},
+		{157, 29.081114874079432},
+		{158, 29.064499954878283},
+		{159, 29.17427761652929},
+		{160, 28.48135454514647},
+		{161, 28.43614347392514},
+		{162, 28.615830690136196},
+		{163, 27.244815449582045},
+		{164, 28.030839937141593},
+		{165, 28.09433740820739},
+		{166, 28.134090510807432},
+		{167, 28.333335545414524},
+		{168, 28.187860385951467},
+		{169, 28.275647207865163},
+		{170, 28.110663780904385},
+		{171, 27.941108395946074},
+		{172, 27.155839334130572},
+		{173, 27.486338387798014},
+		{174, 27.822551655905976},
+		{175, 27.863745721980674},
+		{176, 27.51492123912736},
+		{177, 27.83845450366903},
+		{178, 27.143346163904276},
+		{179, 26.470510229480666},
+		{180, 27.030260699355054},
+		{181, 26.530046883178517},
+		{182, 26.061343714664623},
+		{183, 26.451944204073293},
+		{184, 26.430516873002972},
+		{185, 27.54560649645601},
+		{186, 27.607455732128237},
+		{187, 27.3151823435893},
+		{188, 27.015508353290546},
+		{189, 27.564104270774138},
+		{190, 27.401004407024764},
+		{191, 27.158236015306873},
+		{192, 27.15560082391509},
+		{193, 27.052060260660955},
+		{194, 27.170854273897024},
+		{195, 27.764649442110628},
+		{196, 28.37485762180034},
+		{197, 28.693644963914128},
+		{198, 28.639988945921225},
+		{199, 28.55415913033328},
+		{200, 28.227269873938933},
+		{201, 28.17193587609251},
+		{202, 28.326544342536973},
+		{203, 27.64207374329132},
+		{204, 28.28132114918632},
+		{205, 28.87895845286964},
+		{206, 28.188530355189847},
+		{207, 27.543826104728634},
+		{208, 27.518668557969406},
+		{209, 27.501005443892083},
+		{210, 27.4034023213343},
+		{211, 27.81919230719886},
+		{212, 28.51752545491846},
+		{213, 28.45642871817993},
+		{214, 28.281434136230057},
+		{215, 28.955222450571647},
+		{216, 28.817758413114476},
+		{217, 28.512855374048605},
+		{218, 28.53649013938214},
+		{219, 28.037741647416063},
+		{220, 28.758762367232816},
+		{221, 28.411225526795217},
+		{222, 28.081382658095393},
+		{223, 28.018197966678386},
+		{224, 27.669840575416934},
+		{225, 27.729482622798493},
+		{226, 27.44804950151258},
+		{227, 27.057357503159633},
+		{228, 27.02667664651584},
+		{229, 26.99034079421472},
+		{230, 27.624460374012415},
+		{231, 26.6107079586933},
+		{232, 26.586632740266342},
+		{233, 26.50503068257422},
+		{234, 26.528094947562206},
+		{235, 27.42586110225183},
+		{236, 27.58607997646959},
+		{237, 27.119751888180552},
+		{238, 27.08687612699868},
+		{239, 26.50890594997075},
+		{240, 27.31126847238326},
+		{241, 27.241646652930587},
+		{242, 27.206837899664286},
+		{243, 27.806910729195003},
+		{244, 27.943871889687294},
+		{245, 27.682133734768627},
+		{246, 27.717567280916626},
+		{247, 28.50754775235408},
+		{248, 28.522618646129153},
+		{249, 28.119450170073687},
+		{250, 28.142446798473102},
+		{251, 27.493875384325104},
+		{252, 27.232866008532874},
+		{253, 26.815819408391537},
+		{254, 26.66806605894335},
+		{255, 26.832795316319906},
+		{256, 26.6709072973403},
+		{257, 26.805339614467922},
+		{258, 25.87709141573906},
+		{259, 25.78663848060838},
+		{260, 26.292688529709856},
+		{261, 26.13540568260593},
+		{262, 26.950679537489023},
+		{263, 26.74360016328177},
+		{264, 25.880978465490344},
+		{265, 26.625349316487267},
+		{266, 27.726596358113618},
+		{267, 27.678660195691705},
+		{268, 27.712915567796777},
+		{269, 27.721698306913026},
+		{270, 27.905267233295028},
+		{271, 27.957187159455156},
+		{272, 27.858194094400584},
+		{273, 28.081932932040928},
+		{274, 27.735044748607958},
+		{275, 27.032793497721116},
+		{276, 27.507939311361685},
+		{277, 27.574645954142067},
+		{278, 27.574051095225684},
+		{279, 27.759761781417595},
+		{280, 27.365795276665352},
+		{281, 26.617667215269847},
+		{282, 26.798097033417232},
+		{283, 26.195989054524656},
+		{284, 26.976938134909243},
+		{285, 26.89198848346594},
+		{286, 27.147250351373707},
+		{287, 27.43948527543756},
+		{288, 28.0008367927751},
+		{289, 28.231697069321097},
+		{290, 28.7967810312443},
+		{291, 29.512759843423506},
+		{292, 29.41555351035952},
+		{293, 30.70537467842703},
+		{294, 30.332009655179892},
+		{295, 30.368538690398843},
+		{296, 30.73440265654596},
+		{297, 30.967799052657455},
+		{298, 31.22392323854322},
+		{299, 31.122470949743033},
+		{300, 31.140432351354303},
+		{301, 31.13729855237942},
+		{302, 30.716789453632746},
+		{303, 31.055606178854195},
+		{304, 31.025310612429436},
+		{305, 30.746317663776093},
+		{306, 31.16989662941391},
+		{307, 29.623226075091324},
+		{308, 29.11707721446215},
+		{309, 29.671462419401518},
+		{310, 29.32656872224774},
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