/usr/share/gocode/src/github.com/influxdata/influxdb/influxql/functions.go is in golang-github-influxdb-influxdb-dev 1.1.1+dfsg1-4.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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import (
"math"
"time"
"github.com/influxdata/influxdb/influxql/neldermead"
)
// FloatMeanReducer calculates the mean of the aggregated points.
type FloatMeanReducer struct {
sum float64
count uint32
}
// NewFloatMeanReducer creates a new FloatMeanReducer.
func NewFloatMeanReducer() *FloatMeanReducer {
return &FloatMeanReducer{}
}
// AggregateFloat aggregates a point into the reducer.
func (r *FloatMeanReducer) AggregateFloat(p *FloatPoint) {
if p.Aggregated >= 2 {
r.sum += p.Value * float64(p.Aggregated)
r.count += p.Aggregated
} else {
r.sum += p.Value
r.count++
}
}
// Emit emits the mean of the aggregated points as a single point.
func (r *FloatMeanReducer) Emit() []FloatPoint {
return []FloatPoint{{
Time: ZeroTime,
Value: r.sum / float64(r.count),
Aggregated: r.count,
}}
}
// IntegerMeanReducer calculates the mean of the aggregated points.
type IntegerMeanReducer struct {
sum int64
count uint32
}
// NewIntegerMeanReducer creates a new IntegerMeanReducer.
func NewIntegerMeanReducer() *IntegerMeanReducer {
return &IntegerMeanReducer{}
}
// AggregateInteger aggregates a point into the reducer.
func (r *IntegerMeanReducer) AggregateInteger(p *IntegerPoint) {
if p.Aggregated >= 2 {
r.sum += p.Value * int64(p.Aggregated)
r.count += p.Aggregated
} else {
r.sum += p.Value
r.count++
}
}
// Emit emits the mean of the aggregated points as a single point.
func (r *IntegerMeanReducer) Emit() []FloatPoint {
return []FloatPoint{{
Time: ZeroTime,
Value: float64(r.sum) / float64(r.count),
Aggregated: r.count,
}}
}
// FloatDerivativeReducer calculates the derivative of the aggregated points.
type FloatDerivativeReducer struct {
interval Interval
prev FloatPoint
curr FloatPoint
isNonNegative bool
ascending bool
}
// NewFloatDerivativeReducer creates a new FloatDerivativeReducer.
func NewFloatDerivativeReducer(interval Interval, isNonNegative, ascending bool) *FloatDerivativeReducer {
return &FloatDerivativeReducer{
interval: interval,
isNonNegative: isNonNegative,
ascending: ascending,
prev: FloatPoint{Nil: true},
curr: FloatPoint{Nil: true},
}
}
// AggregateFloat aggregates a point into the reducer and updates the current window.
func (r *FloatDerivativeReducer) AggregateFloat(p *FloatPoint) {
// Skip past a point when it does not advance the stream. A joined series
// may have multiple points at the same time so we will discard anything
// except the first point we encounter.
if !r.curr.Nil && r.curr.Time == p.Time {
return
}
r.prev = r.curr
r.curr = *p
}
// Emit emits the derivative of the reducer at the current point.
func (r *FloatDerivativeReducer) Emit() []FloatPoint {
if !r.prev.Nil {
// Calculate the derivative of successive points by dividing the
// difference of each value by the elapsed time normalized to the interval.
diff := r.curr.Value - r.prev.Value
elapsed := r.curr.Time - r.prev.Time
if !r.ascending {
elapsed = -elapsed
}
value := diff / (float64(elapsed) / float64(r.interval.Duration))
// Mark this point as read by changing the previous point to nil.
r.prev.Nil = true
// Drop negative values for non-negative derivatives.
if r.isNonNegative && diff < 0 {
return nil
}
return []FloatPoint{{Time: r.curr.Time, Value: value}}
}
return nil
}
// IntegerDerivativeReducer calculates the derivative of the aggregated points.
type IntegerDerivativeReducer struct {
interval Interval
prev IntegerPoint
curr IntegerPoint
isNonNegative bool
ascending bool
}
// NewIntegerDerivativeReducer creates a new IntegerDerivativeReducer.
func NewIntegerDerivativeReducer(interval Interval, isNonNegative, ascending bool) *IntegerDerivativeReducer {
return &IntegerDerivativeReducer{
interval: interval,
isNonNegative: isNonNegative,
ascending: ascending,
prev: IntegerPoint{Nil: true},
curr: IntegerPoint{Nil: true},
}
}
// AggregateInteger aggregates a point into the reducer and updates the current window.
func (r *IntegerDerivativeReducer) AggregateInteger(p *IntegerPoint) {
// Skip past a point when it does not advance the stream. A joined series
// may have multiple points at the same time so we will discard anything
// except the first point we encounter.
if !r.curr.Nil && r.curr.Time == p.Time {
return
}
r.prev = r.curr
r.curr = *p
}
// Emit emits the derivative of the reducer at the current point.
func (r *IntegerDerivativeReducer) Emit() []FloatPoint {
if !r.prev.Nil {
// Calculate the derivative of successive points by dividing the
// difference of each value by the elapsed time normalized to the interval.
diff := float64(r.curr.Value - r.prev.Value)
elapsed := r.curr.Time - r.prev.Time
if !r.ascending {
elapsed = -elapsed
}
value := diff / (float64(elapsed) / float64(r.interval.Duration))
// Mark this point as read by changing the previous point to nil.
r.prev.Nil = true
// Drop negative values for non-negative derivatives.
if r.isNonNegative && diff < 0 {
return nil
}
return []FloatPoint{{Time: r.curr.Time, Value: value}}
}
return nil
}
// FloatDifferenceReducer calculates the derivative of the aggregated points.
type FloatDifferenceReducer struct {
prev FloatPoint
curr FloatPoint
}
// NewFloatDifferenceReducer creates a new FloatDifferenceReducer.
func NewFloatDifferenceReducer() *FloatDifferenceReducer {
return &FloatDifferenceReducer{
prev: FloatPoint{Nil: true},
curr: FloatPoint{Nil: true},
}
}
// AggregateFloat aggregates a point into the reducer and updates the current window.
func (r *FloatDifferenceReducer) AggregateFloat(p *FloatPoint) {
// Skip past a point when it does not advance the stream. A joined series
// may have multiple points at the same time so we will discard anything
// except the first point we encounter.
if !r.curr.Nil && r.curr.Time == p.Time {
return
}
r.prev = r.curr
r.curr = *p
}
// Emit emits the difference of the reducer at the current point.
func (r *FloatDifferenceReducer) Emit() []FloatPoint {
if !r.prev.Nil {
// Calculate the difference of successive points.
value := r.curr.Value - r.prev.Value
// Mark this point as read by changing the previous point to nil.
r.prev.Nil = true
return []FloatPoint{{Time: r.curr.Time, Value: value}}
}
return nil
}
// IntegerDifferenceReducer calculates the derivative of the aggregated points.
type IntegerDifferenceReducer struct {
prev IntegerPoint
curr IntegerPoint
}
// NewIntegerDifferenceReducer creates a new IntegerDifferenceReducer.
func NewIntegerDifferenceReducer() *IntegerDifferenceReducer {
return &IntegerDifferenceReducer{
prev: IntegerPoint{Nil: true},
curr: IntegerPoint{Nil: true},
}
}
// AggregateInteger aggregates a point into the reducer and updates the current window.
func (r *IntegerDifferenceReducer) AggregateInteger(p *IntegerPoint) {
// Skip past a point when it does not advance the stream. A joined series
// may have multiple points at the same time so we will discard anything
// except the first point we encounter.
if !r.curr.Nil && r.curr.Time == p.Time {
return
}
r.prev = r.curr
r.curr = *p
}
// Emit emits the difference of the reducer at the current point.
func (r *IntegerDifferenceReducer) Emit() []IntegerPoint {
if !r.prev.Nil {
// Calculate the difference of successive points.
value := r.curr.Value - r.prev.Value
// Mark this point as read by changing the previous point to nil.
r.prev.Nil = true
return []IntegerPoint{{Time: r.curr.Time, Value: value}}
}
return nil
}
// FloatMovingAverageReducer calculates the moving average of the aggregated points.
type FloatMovingAverageReducer struct {
pos int
sum float64
time int64
buf []float64
}
// NewFloatMovingAverageReducer creates a new FloatMovingAverageReducer.
func NewFloatMovingAverageReducer(n int) *FloatMovingAverageReducer {
return &FloatMovingAverageReducer{
buf: make([]float64, 0, n),
}
}
// AggregateFloat aggregates a point into the reducer and updates the current window.
func (r *FloatMovingAverageReducer) AggregateFloat(p *FloatPoint) {
if len(r.buf) != cap(r.buf) {
r.buf = append(r.buf, p.Value)
} else {
r.sum -= r.buf[r.pos]
r.buf[r.pos] = p.Value
}
r.sum += p.Value
r.time = p.Time
r.pos++
if r.pos >= cap(r.buf) {
r.pos = 0
}
}
// Emit emits the moving average of the current window. Emit should be called
// after every call to AggregateFloat and it will produce one point if there
// is enough data to fill a window, otherwise it will produce zero points.
func (r *FloatMovingAverageReducer) Emit() []FloatPoint {
if len(r.buf) != cap(r.buf) {
return []FloatPoint{}
}
return []FloatPoint{
{
Value: r.sum / float64(len(r.buf)),
Time: r.time,
Aggregated: uint32(len(r.buf)),
},
}
}
// IntegerMovingAverageReducer calculates the moving average of the aggregated points.
type IntegerMovingAverageReducer struct {
pos int
sum int64
time int64
buf []int64
}
// NewIntegerMovingAverageReducer creates a new IntegerMovingAverageReducer.
func NewIntegerMovingAverageReducer(n int) *IntegerMovingAverageReducer {
return &IntegerMovingAverageReducer{
buf: make([]int64, 0, n),
}
}
// AggregateInteger aggregates a point into the reducer and updates the current window.
func (r *IntegerMovingAverageReducer) AggregateInteger(p *IntegerPoint) {
if len(r.buf) != cap(r.buf) {
r.buf = append(r.buf, p.Value)
} else {
r.sum -= r.buf[r.pos]
r.buf[r.pos] = p.Value
}
r.sum += p.Value
r.time = p.Time
r.pos++
if r.pos >= cap(r.buf) {
r.pos = 0
}
}
// Emit emits the moving average of the current window. Emit should be called
// after every call to AggregateInteger and it will produce one point if there
// is enough data to fill a window, otherwise it will produce zero points.
func (r *IntegerMovingAverageReducer) Emit() []FloatPoint {
if len(r.buf) != cap(r.buf) {
return []FloatPoint{}
}
return []FloatPoint{
{
Value: float64(r.sum) / float64(len(r.buf)),
Time: r.time,
Aggregated: uint32(len(r.buf)),
},
}
}
// FloatCumulativeSumReducer cumulates the values from each point.
type FloatCumulativeSumReducer struct {
curr FloatPoint
}
// NewFloatCumulativeSumReducer creates a new FloatCumulativeSumReducer.
func NewFloatCumulativeSumReducer() *FloatCumulativeSumReducer {
return &FloatCumulativeSumReducer{
curr: FloatPoint{Nil: true},
}
}
func (r *FloatCumulativeSumReducer) AggregateFloat(p *FloatPoint) {
r.curr.Value += p.Value
r.curr.Time = p.Time
r.curr.Nil = false
}
func (r *FloatCumulativeSumReducer) Emit() []FloatPoint {
var pts []FloatPoint
if !r.curr.Nil {
pts = []FloatPoint{r.curr}
}
return pts
}
// IntegerCumulativeSumReducer cumulates the values from each point.
type IntegerCumulativeSumReducer struct {
curr IntegerPoint
}
// NewIntegerCumulativeSumReducer creates a new IntegerCumulativeSumReducer.
func NewIntegerCumulativeSumReducer() *IntegerCumulativeSumReducer {
return &IntegerCumulativeSumReducer{
curr: IntegerPoint{Nil: true},
}
}
func (r *IntegerCumulativeSumReducer) AggregateInteger(p *IntegerPoint) {
r.curr.Value += p.Value
r.curr.Time = p.Time
r.curr.Nil = false
}
func (r *IntegerCumulativeSumReducer) Emit() []IntegerPoint {
var pts []IntegerPoint
if !r.curr.Nil {
pts = []IntegerPoint{r.curr}
}
return pts
}
// FloatHoltWintersReducer forecasts a series into the future.
// This is done using the Holt-Winters damped method.
// 1. Using the series the initial values are calculated using a SSE.
// 2. The series is forecasted into the future using the iterative relations.
type FloatHoltWintersReducer struct {
// Season period
m int
seasonal bool
// Horizon
h int
// Interval between points
interval int64
// interval / 2 -- used to perform rounding
halfInterval int64
// Whether to include all data or only future values
includeFitData bool
// NelderMead optimizer
optim *neldermead.Optimizer
// Small difference bound for the optimizer
epsilon float64
y []float64
points []FloatPoint
}
const (
// Arbitrary weight for initializing some intial guesses.
// This should be in the range [0,1]
hwWeight = 0.5
// Epsilon value for the minimization process
hwDefaultEpsilon = 1.0e-4
// Define a grid of initial guesses for the parameters: alpha, beta, gamma, and phi.
// Keep in mind that this grid is N^4 so we should keep N small
// The starting lower guess
hwGuessLower = 0.3
// The upper bound on the grid
hwGuessUpper = 1.0
// The step between guesses
hwGuessStep = 0.4
)
// NewFloatHoltWintersReducer creates a new FloatHoltWintersReducer.
func NewFloatHoltWintersReducer(h, m int, includeFitData bool, interval time.Duration) *FloatHoltWintersReducer {
seasonal := true
if m < 2 {
seasonal = false
}
return &FloatHoltWintersReducer{
h: h,
m: m,
seasonal: seasonal,
includeFitData: includeFitData,
interval: int64(interval),
halfInterval: int64(interval) / 2,
optim: neldermead.New(),
epsilon: hwDefaultEpsilon,
}
}
func (r *FloatHoltWintersReducer) aggregate(time int64, value float64) {
r.points = append(r.points, FloatPoint{
Time: time,
Value: value,
})
}
// AggregateFloat aggregates a point into the reducer and updates the current window.
func (r *FloatHoltWintersReducer) AggregateFloat(p *FloatPoint) {
r.aggregate(p.Time, p.Value)
}
// AggregateInteger aggregates a point into the reducer and updates the current window.
func (r *FloatHoltWintersReducer) AggregateInteger(p *IntegerPoint) {
r.aggregate(p.Time, float64(p.Value))
}
func (r *FloatHoltWintersReducer) roundTime(t int64) int64 {
// Overflow safe round function
remainder := t % r.interval
if remainder > r.halfInterval {
// Round up
return (t/r.interval + 1) * r.interval
}
// Round down
return (t / r.interval) * r.interval
}
// Emit returns the points generated by the HoltWinters algorithm.
func (r *FloatHoltWintersReducer) Emit() []FloatPoint {
if l := len(r.points); l < 2 || r.seasonal && l < r.m || r.h <= 0 {
return nil
}
// First fill in r.y with values and NaNs for missing values
start, stop := r.roundTime(r.points[0].Time), r.roundTime(r.points[len(r.points)-1].Time)
count := (stop - start) / r.interval
if count <= 0 {
return nil
}
r.y = make([]float64, 1, count)
r.y[0] = r.points[0].Value
t := r.roundTime(r.points[0].Time)
for _, p := range r.points[1:] {
rounded := r.roundTime(p.Time)
if rounded <= t {
// Drop values that occur for the same time bucket
continue
}
t += r.interval
// Add any missing values before the next point
for rounded != t {
// Add in a NaN so we can skip it later.
r.y = append(r.y, math.NaN())
t += r.interval
}
r.y = append(r.y, p.Value)
}
// Seasonality
m := r.m
// Starting guesses
// NOTE: Since these values are guesses
// in the cases where we were missing data,
// we can just skip the value and call it good.
l0 := 0.0
if r.seasonal {
for i := 0; i < m; i++ {
if !math.IsNaN(r.y[i]) {
l0 += (1 / float64(m)) * r.y[i]
}
}
} else {
l0 += hwWeight * r.y[0]
}
b0 := 0.0
if r.seasonal {
for i := 0; i < m && m+i < len(r.y); i++ {
if !math.IsNaN(r.y[i]) && !math.IsNaN(r.y[m+i]) {
b0 += 1 / float64(m*m) * (r.y[m+i] - r.y[i])
}
}
} else {
if !math.IsNaN(r.y[1]) {
b0 = hwWeight * (r.y[1] - r.y[0])
}
}
var s []float64
if r.seasonal {
s = make([]float64, m)
for i := 0; i < m; i++ {
if !math.IsNaN(r.y[i]) {
s[i] = r.y[i] / l0
} else {
s[i] = 0
}
}
}
parameters := make([]float64, 6+len(s))
parameters[4] = l0
parameters[5] = b0
o := len(parameters) - len(s)
for i := range s {
parameters[i+o] = s[i]
}
// Determine best fit for the various parameters
minSSE := math.Inf(1)
var bestParams []float64
for alpha := hwGuessLower; alpha < hwGuessUpper; alpha += hwGuessStep {
for beta := hwGuessLower; beta < hwGuessUpper; beta += hwGuessStep {
for gamma := hwGuessLower; gamma < hwGuessUpper; gamma += hwGuessStep {
for phi := hwGuessLower; phi < hwGuessUpper; phi += hwGuessStep {
parameters[0] = alpha
parameters[1] = beta
parameters[2] = gamma
parameters[3] = phi
sse, params := r.optim.Optimize(r.sse, parameters, r.epsilon, 1)
if sse < minSSE || bestParams == nil {
minSSE = sse
bestParams = params
}
}
}
}
}
// Forecast
forecasted := r.forecast(r.h, bestParams)
var points []FloatPoint
if r.includeFitData {
start := r.points[0].Time
points = make([]FloatPoint, 0, len(forecasted))
for i, v := range forecasted {
if !math.IsNaN(v) {
t := start + r.interval*(int64(i))
points = append(points, FloatPoint{
Value: v,
Time: t,
})
}
}
} else {
stop := r.points[len(r.points)-1].Time
points = make([]FloatPoint, 0, r.h)
for i, v := range forecasted[len(r.y):] {
if !math.IsNaN(v) {
t := stop + r.interval*(int64(i)+1)
points = append(points, FloatPoint{
Value: v,
Time: t,
})
}
}
}
// Clear data set
r.y = r.y[0:0]
return points
}
// Using the recursive relations compute the next values
func (r *FloatHoltWintersReducer) next(alpha, beta, gamma, phi, phiH, yT, lTp, bTp, sTm, sTmh float64) (yTh, lT, bT, sT float64) {
lT = alpha*(yT/sTm) + (1-alpha)*(lTp+phi*bTp)
bT = beta*(lT-lTp) + (1-beta)*phi*bTp
sT = gamma*(yT/(lTp+phi*bTp)) + (1-gamma)*sTm
yTh = (lT + phiH*bT) * sTmh
return
}
// Forecast the data h points into the future.
func (r *FloatHoltWintersReducer) forecast(h int, params []float64) []float64 {
// Constrain parameters
r.constrain(params)
yT := r.y[0]
phi := params[3]
phiH := phi
lT := params[4]
bT := params[5]
sT := 0.0
// seasonals is a ring buffer of past sT values
var seasonals []float64
var m, so int
if r.seasonal {
seasonals = params[6:]
m = len(params[6:])
if m == 1 {
seasonals[0] = 1
}
// Season index offset
so = m - 1
}
forecasted := make([]float64, len(r.y)+h)
forecasted[0] = yT
l := len(r.y)
var hm int
stm, stmh := 1.0, 1.0
for t := 1; t < l+h; t++ {
if r.seasonal {
hm = t % m
stm = seasonals[(t-m+so)%m]
stmh = seasonals[(t-m+hm+so)%m]
}
yT, lT, bT, sT = r.next(
params[0], // alpha
params[1], // beta
params[2], // gamma
phi,
phiH,
yT,
lT,
bT,
stm,
stmh,
)
phiH += math.Pow(phi, float64(t))
if r.seasonal {
seasonals[(t+so)%m] = sT
so++
}
forecasted[t] = yT
}
return forecasted
}
// Compute sum squared error for the given parameters.
func (r *FloatHoltWintersReducer) sse(params []float64) float64 {
sse := 0.0
forecasted := r.forecast(0, params)
for i := range forecasted {
// Skip missing values since we cannot use them to compute an error.
if !math.IsNaN(r.y[i]) {
// Compute error
if math.IsNaN(forecasted[i]) {
// Penalize forecasted NaNs
return math.Inf(1)
}
diff := forecasted[i] - r.y[i]
sse += diff * diff
}
}
return sse
}
// Constrain alpha, beta, gamma, phi in the range [0, 1]
func (r *FloatHoltWintersReducer) constrain(x []float64) {
// alpha
if x[0] > 1 {
x[0] = 1
}
if x[0] < 0 {
x[0] = 0
}
// beta
if x[1] > 1 {
x[1] = 1
}
if x[1] < 0 {
x[1] = 0
}
// gamma
if x[2] > 1 {
x[2] = 1
}
if x[2] < 0 {
x[2] = 0
}
// phi
if x[3] > 1 {
x[3] = 1
}
if x[3] < 0 {
x[3] = 0
}
}
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