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more iterating on macd, need to get a better handle on how to test.

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This commit is contained in:
Will Charczuk 2016-07-17 11:10:04 -07:00
parent 7858457772
commit 32dd907bf8
9 changed files with 464 additions and 246 deletions
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2
bollinger_band_series.go
View file

@ -37,7 +37,7 @@ func (bbs BollingerBandsSeries) GetWindowSize(defaults ...int) int {
if len(defaults) > 0 {
return defaults[0]
}
return DefaultMovingAverageWindowSize
return DefaultSimpleMovingAveragePeriod
}
return bbs.WindowSize
}

4
bollinger_band_series_test.go
View file

@ -46,6 +46,6 @@ func TestBollingerBandLastValue(t *testing.T) {
x, y1, y2 := bbs.GetLastBoundedValue()
assert.Equal(100.0, x)
assert.Equal(100, math.Floor(y1))
assert.Equal(95, math.Floor(y2))
assert.Equal(101, math.Floor(y1))
assert.Equal(83, math.Floor(y2))
}

98
ema_series.go Normal file
View file

@ -0,0 +1,98 @@
package chart
const (
// DefaultEMASigma is the default exponential smoothing factor.
DefaultEMASigma = 0.25
)
// EMASeries is a computed series.
type EMASeries struct {
Name string
Style Style
YAxis YAxisType
// Sigma is the 'smoothing factor' parameter.
Sigma float64
Period int
InnerSeries ValueProvider
}
// GetName returns the name of the time series.
func (ema EMASeries) GetName() string {
return ema.Name
}
// GetStyle returns the line style.
func (ema EMASeries) GetStyle() Style {
return ema.Style
}
// GetYAxis returns which YAxis the series draws on.
func (ema EMASeries) GetYAxis() YAxisType {
return ema.YAxis
}
// GetPeriod returns the window size.
func (ema EMASeries) GetPeriod(defaults ...int) int {
if ema.Period == 0 {
if len(defaults) > 0 {
return defaults[0]
}
return ema.InnerSeries.Len()
}
return ema.Period
}
// Len returns the number of elements in the series.
func (ema EMASeries) Len() int {
return ema.InnerSeries.Len()
}
// GetSigma returns the smoothing factor for the serise.
func (ema EMASeries) GetSigma(defaults ...float64) float64 {
if ema.Sigma == 0 {
if len(defaults) > 0 {
return defaults[0]
}
return DefaultEMASigma
}
return ema.Sigma
}
// GetValue gets a value at a given index.
func (ema EMASeries) GetValue(index int) (x float64, y float64) {
if ema.InnerSeries == nil {
return
}
vx, _ := ema.InnerSeries.GetValue(index)
x = vx
y = ema.compute(ema.GetPeriod(), index)
return
}
// GetLastValue computes the last moving average value but walking back window size samples,
// and recomputing the last moving average chunk.
func (ema EMASeries) GetLastValue() (x float64, y float64) {
if ema.InnerSeries == nil {
return
}
lastIndex := ema.InnerSeries.Len() - 1
x, _ = ema.InnerSeries.GetValue(lastIndex)
y = ema.compute(ema.GetPeriod(), lastIndex)
return
}
func (ema EMASeries) compute(period, index int) float64 {
_, v := ema.InnerSeries.GetValue(index)
if period == 1 || index == 0 {
return v
}
sig := ema.GetSigma()
return sig*v + ((1.0 - sig) * ema.compute(period-1, index-1))
}
// Render renders the series.
func (ema EMASeries) Render(r Renderer, canvasBox Box, xrange, yrange Range, defaults Style) {
style := ema.Style.WithDefaultsFrom(defaults)
DrawLineSeries(r, canvasBox, xrange, yrange, style, ema)
}

4
exp_moving_average_series_test.go → ema_series_test.go
View file

@ -7,7 +7,7 @@ import (
"github.com/blendlabs/go-assert"
)
func TestExponentialMovingAverageSeries(t *testing.T) {
func TestEMASeries(t *testing.T) {
assert := assert.New(t)
mockSeries := mockValueProvider{
@ -16,7 +16,7 @@ func TestExponentialMovingAverageSeries(t *testing.T) {
}
assert.Equal(10, mockSeries.Len())
mas := &ExponentialMovingAverageSeries{
mas := &EMASeries{
InnerSeries: mockSeries,
}

94
exp_moving_average_series.go
View file

@ -1,94 +0,0 @@
package chart
const (
// DefaultExponentialMovingAverageSigma is the default exponential smoothing factor.
DefaultExponentialMovingAverageSigma = 0.25
)
// ExponentialMovingAverageSeries is a computed series.
type ExponentialMovingAverageSeries struct {
Name string
Style Style
YAxis YAxisType
// Sigma is the 'smoothing factor' parameter.
Sigma float64
InnerSeries ValueProvider
valueBuffer []float64
}
// GetName returns the name of the time series.
func (mas ExponentialMovingAverageSeries) GetName() string {
return mas.Name
}
// GetStyle returns the line style.
func (mas ExponentialMovingAverageSeries) GetStyle() Style {
return mas.Style
}
// GetYAxis returns which YAxis the series draws on.
func (mas ExponentialMovingAverageSeries) GetYAxis() YAxisType {
return mas.YAxis
}
// Len returns the number of elements in the series.
func (mas *ExponentialMovingAverageSeries) Len() int {
return mas.InnerSeries.Len()
}
// GetSigma returns the smoothing factor for the serise.
func (mas ExponentialMovingAverageSeries) GetSigma(defaults ...float64) float64 {
if mas.Sigma == 0 {
if len(defaults) > 0 {
return defaults[0]
}
return DefaultExponentialMovingAverageSigma
}
return mas.Sigma
}
// GetValue gets a value at a given index.
func (mas *ExponentialMovingAverageSeries) GetValue(index int) (x float64, y float64) {
if mas.InnerSeries == nil {
return
}
if mas.valueBuffer == nil || index == 0 {
mas.valueBuffer = make([]float64, mas.InnerSeries.Len())
}
vx, vy := mas.InnerSeries.GetValue(index)
x = vx
if index == 0 {
mas.valueBuffer[0] = vy
y = vy
return
}
sig := mas.GetSigma()
mas.valueBuffer[index] = sig*vy + ((1.0 - sig) * mas.valueBuffer[index-1])
y = mas.valueBuffer[index]
return
}
// GetLastValue computes the last moving average value but walking back window size samples,
// and recomputing the last moving average chunk.
func (mas ExponentialMovingAverageSeries) GetLastValue() (x float64, y float64) {
if mas.InnerSeries == nil {
return
}
seriesLength := mas.InnerSeries.Len()
for index := 0; index < seriesLength; index++ {
x, _ = mas.GetValue(index)
}
y = mas.valueBuffer[seriesLength-1]
return
}
// Render renders the series.
func (mas *ExponentialMovingAverageSeries) Render(r Renderer, canvasBox Box, xrange, yrange Range, defaults Style) {
style := mas.Style.WithDefaultsFrom(defaults)
DrawLineSeries(r, canvasBox, xrange, yrange, style, mas)
}

287
macd_series.go
View file

@ -1,37 +1,45 @@
package chart
const (
// DefaultMACDWindowPrimary is the long window.
DefaultMACDWindowPrimary = 26
// DefaultMACDWindowSecondary is the short window.
DefaultMACDWindowSecondary = 12
// DefaultMACDPeriodPrimary is the long window.
DefaultMACDPeriodPrimary = 26
// DefaultMACDPeriodSecondary is the short window.
DefaultMACDPeriodSecondary = 12
// DefaultMACDSignalPeriod is the signal period to compute for the MACD.
DefaultMACDSignalPeriod = 9
)
// MACDSeries (or Moving Average Convergence Divergence) is a special type of series that
// computes the difference between two different EMA values for a given index, as denoted by WindowPrimary(26) and WindowSecondary(12).
// MACDSeries computes the difference between the MACD line and the MACD Signal line.
// It is used in technical analysis and gives a lagging indicator of momentum.
type MACDSeries struct {
Name string
Style Style
YAxis YAxisType
InnerSeries ValueProvider
WindowPrimary int
WindowSecondary int
PrimaryPeriod int
SecondaryPeriod int
SignalPeriod int
Sigma float64
}
// GetWindows returns the primary and secondary window sizes.
func (macd MACDSeries) GetWindows() (w1, w2 int) {
if macd.WindowPrimary == 0 {
w1 = DefaultMACDWindowPrimary
// GetPeriods returns the primary and secondary periods.
func (macd MACDSeries) GetPeriods() (w1, w2, sig int) {
if macd.PrimaryPeriod == 0 {
w1 = DefaultMACDPeriodPrimary
} else {
w1 = macd.WindowPrimary
w1 = macd.PrimaryPeriod
}
if macd.WindowSecondary == 0 {
w2 = DefaultMACDWindowSecondary
if macd.SecondaryPeriod == 0 {
w2 = DefaultMACDPeriodSecondary
} else {
w2 = macd.WindowSecondary
w2 = macd.SecondaryPeriod
}
if macd.SignalPeriod == 0 {
sig = DefaultMACDSignalPeriod
} else {
sig = macd.SignalPeriod
}
return
}
@ -42,7 +50,7 @@ func (macd MACDSeries) GetSigma(defaults ...float64) float64 {
if len(defaults) > 0 {
return defaults[0]
}
return DefaultExponentialMovingAverageSigma
return DefaultEMASigma
}
return macd.Sigma
}
@ -68,7 +76,7 @@ func (macd MACDSeries) Len() int {
return 0
}
w1, _ := macd.GetWindows()
w1, _, _ := macd.GetPeriods()
innerLen := macd.InnerSeries.Len()
if innerLen > w1 {
return innerLen - w1
@ -76,35 +84,250 @@ func (macd MACDSeries) Len() int {
return 0
}
// GetValue gets a value at a given index.
// GetValue gets a value at a given index. For MACD it is the signal value.
func (macd MACDSeries) GetValue(index int) (x float64, y float64) {
if macd.InnerSeries == nil {
return
}
w1, w2 := macd.GetWindows()
w1, w2, sig := macd.GetPeriods()
sigma := macd.GetSigma()
effectiveIndex := index + w1
x, _ = macd.InnerSeries.GetValue(effectiveIndex)
ema1 := macd.computeEMA(w1, effectiveIndex)
ema2 := macd.computeEMA(w2, effectiveIndex)
signal := EMASeries{
InnerSeries: MACDLineSeries{
InnerSeries: macd.InnerSeries,
PrimaryPeriod: w1,
SecondaryPeriod: w2,
Sigma: sigma,
},
Sigma: sigma,
Period: sig,
}
macdl := MACDLineSeries{
InnerSeries: macd.InnerSeries,
PrimaryPeriod: w1,
SecondaryPeriod: w2,
Sigma: sigma,
}
_, sv := signal.GetValue(index)
_, lv := macdl.GetValue(index)
y = lv - sv
y = ema1 - ema2
return
}
func (macd MACDSeries) computeEMA(windowSize int, index int) float64 {
_, v := macd.InnerSeries.GetValue(index)
if windowSize == 1 {
return v
// MACDSignalSeries computes the EMA of the MACDLineSeries.
type MACDSignalSeries struct {
Name string
Style Style
YAxis YAxisType
InnerSeries ValueProvider
PrimaryPeriod int
SecondaryPeriod int
SignalPeriod int
Sigma float64
}
// GetPeriods returns the primary and secondary periods.
func (macds MACDSignalSeries) GetPeriods() (w1, w2, sig int) {
if macds.PrimaryPeriod == 0 {
w1 = DefaultMACDPeriodPrimary
} else {
w1 = macds.PrimaryPeriod
}
sig := macd.GetSigma()
return sig*v + ((1.0 - sig) * macd.computeEMA(windowSize-1, index-1))
if macds.SecondaryPeriod == 0 {
w2 = DefaultMACDPeriodSecondary
} else {
w2 = macds.SecondaryPeriod
}
if macds.SignalPeriod == 0 {
sig = DefaultMACDSignalPeriod
} else {
sig = macds.SignalPeriod
}
return
}
// GetSigma returns the smoothing factor for the serise.
func (macds MACDSignalSeries) GetSigma(defaults ...float64) float64 {
if macds.Sigma == 0 {
if len(defaults) > 0 {
return defaults[0]
}
return DefaultEMASigma
}
return macds.Sigma
}
// GetName returns the name of the time series.
func (macds MACDSignalSeries) GetName() string {
return macds.Name
}
// GetStyle returns the line style.
func (macds MACDSignalSeries) GetStyle() Style {
return macds.Style
}
// GetYAxis returns which YAxis the series draws on.
func (macds MACDSignalSeries) GetYAxis() YAxisType {
return macds.YAxis
}
// Len returns the number of elements in the series.
func (macds MACDSignalSeries) Len() int {
if macds.InnerSeries == nil {
return 0
}
w1, _, _ := macds.GetPeriods()
innerLen := macds.InnerSeries.Len()
if innerLen > w1 {
return innerLen - w1
}
return 0
}
// GetValue gets a value at a given index. For MACD it is the signal value.
func (macds MACDSignalSeries) GetValue(index int) (x float64, y float64) {
if macds.InnerSeries == nil {
return
}
w1, w2, sig := macds.GetPeriods()
sigma := macds.GetSigma()
effectiveIndex := index + w1
x, _ = macds.InnerSeries.GetValue(effectiveIndex)
signal := EMASeries{
InnerSeries: MACDLineSeries{
InnerSeries: macds.InnerSeries,
PrimaryPeriod: w1,
SecondaryPeriod: w2,
Sigma: sigma,
},
Sigma: sigma,
Period: sig,
}
_, y = signal.GetValue(index)
return
}
// Render renders the series.
func (macd MACDSeries) Render(r Renderer, canvasBox Box, xrange, yrange Range, defaults Style) {
style := macd.Style.WithDefaultsFrom(defaults)
DrawLineSeries(r, canvasBox, xrange, yrange, style, macd)
func (macds MACDSignalSeries) Render(r Renderer, canvasBox Box, xrange, yrange Range, defaults Style) {
style := macds.Style.WithDefaultsFrom(defaults)
DrawLineSeries(r, canvasBox, xrange, yrange, style, macds)
}
// MACDLineSeries is a series that computes the inner ema1-ema2 value as a series.
type MACDLineSeries struct {
Name string
Style Style
YAxis YAxisType
InnerSeries ValueProvider
PrimaryPeriod int
SecondaryPeriod int
Sigma float64
}
// GetName returns the name of the time series.
func (macdl MACDLineSeries) GetName() string {
return macdl.Name
}
// GetStyle returns the line style.
func (macdl MACDLineSeries) GetStyle() Style {
return macdl.Style
}
// GetYAxis returns which YAxis the series draws on.
func (macdl MACDLineSeries) GetYAxis() YAxisType {
return macdl.YAxis
}
// GetPeriods returns the primary and secondary periods.
func (macdl MACDLineSeries) GetPeriods() (w1, w2 int) {
if macdl.PrimaryPeriod == 0 {
w1 = DefaultMACDPeriodPrimary
} else {
w1 = macdl.PrimaryPeriod
}
if macdl.SecondaryPeriod == 0 {
w2 = DefaultMACDPeriodSecondary
} else {
w2 = macdl.SecondaryPeriod
}
return
}
// Len returns the number of elements in the series.
func (macdl MACDLineSeries) Len() int {
if macdl.InnerSeries == nil {
return 0
}
w1, _ := macdl.GetPeriods()
innerLen := macdl.InnerSeries.Len()
if innerLen > w1 {
return innerLen - w1
}
return 0
}
// GetSigma returns the smoothing factor for the serise.
func (macdl MACDLineSeries) GetSigma(defaults ...float64) float64 {
if macdl.Sigma == 0 {
if len(defaults) > 0 {
return defaults[0]
}
return DefaultEMASigma
}
return macdl.Sigma
}
// GetValue gets a value at a given index. For MACD it is the signal value.
func (macdl MACDLineSeries) GetValue(index int) (x float64, y float64) {
if macdl.InnerSeries == nil {
return
}
w1, w2 := macdl.GetPeriods()
effectiveIndex := index + w1
x, _ = macdl.InnerSeries.GetValue(effectiveIndex)
ema1 := EMASeries{
InnerSeries: macdl.InnerSeries,
Period: w1,
Sigma: macdl.GetSigma(),
}
ema2 := EMASeries{
InnerSeries: macdl.InnerSeries,
Period: w2,
Sigma: macdl.GetSigma(),
}
_, emav1 := ema1.GetValue(index)
_, emav2 := ema2.GetValue(index)
y = emav1 - emav2
return
}
// Render renders the series.
func (macdl MACDLineSeries) Render(r Renderer, canvasBox Box, xrange, yrange Range, defaults Style) {
style := macdl.Style.WithDefaultsFrom(defaults)
DrawLineSeries(r, canvasBox, xrange, yrange, style, macdl)
}

105
simple_moving_average_series.go
View file

@ -1,105 +0,0 @@
package chart
const (
// DefaultMovingAverageWindowSize is the default number of values to average.
DefaultMovingAverageWindowSize = 5
)
// SimpleMovingAverageSeries is a computed series.
type SimpleMovingAverageSeries struct {
Name string
Style Style
YAxis YAxisType
WindowSize int
InnerSeries ValueProvider
valueBuffer *RingBuffer
}
// GetName returns the name of the time series.
func (mas SimpleMovingAverageSeries) GetName() string {
return mas.Name
}
// GetStyle returns the line style.
func (mas SimpleMovingAverageSeries) GetStyle() Style {
return mas.Style
}
// GetYAxis returns which YAxis the series draws on.
func (mas SimpleMovingAverageSeries) GetYAxis() YAxisType {
return mas.YAxis
}
// Len returns the number of elements in the series.
func (mas *SimpleMovingAverageSeries) Len() int {
return mas.InnerSeries.Len()
}
// GetValue gets a value at a given index.
func (mas *SimpleMovingAverageSeries) GetValue(index int) (x float64, y float64) {
if mas.InnerSeries == nil {
return
}
if mas.valueBuffer == nil || index == 0 {
mas.valueBuffer = NewRingBufferWithCapacity(mas.GetWindowSize())
}
if mas.valueBuffer.Len() >= mas.GetWindowSize() {
mas.valueBuffer.Dequeue()
}
px, py := mas.InnerSeries.GetValue(index)
mas.valueBuffer.Enqueue(py)
x = px
y = mas.getAverage(mas.valueBuffer)
return
}
// GetLastValue computes the last moving average value but walking back window size samples,
// and recomputing the last moving average chunk.
func (mas SimpleMovingAverageSeries) GetLastValue() (x float64, y float64) {
if mas.InnerSeries == nil {
return
}
windowSize := mas.GetWindowSize()
seriesLength := mas.InnerSeries.Len()
startAt := seriesLength - windowSize
if startAt < 0 {
startAt = 0
}
vb := NewRingBufferWithCapacity(windowSize)
for index := startAt; index < seriesLength; index++ {
xn, yn := mas.InnerSeries.GetValue(index)
vb.Enqueue(yn)
x = xn
}
y = mas.getAverage(vb)
return
}
// GetWindowSize returns the window size.
func (mas SimpleMovingAverageSeries) GetWindowSize(defaults ...int) int {
if mas.WindowSize == 0 {
if len(defaults) > 0 {
return defaults[0]
}
return DefaultMovingAverageWindowSize
}
return mas.WindowSize
}
func (mas SimpleMovingAverageSeries) getAverage(valueBuffer *RingBuffer) float64 {
var accum float64
valueBuffer.Each(func(v interface{}) {
if typed, isTyped := v.(float64); isTyped {
accum += typed
}
})
return accum / float64(valueBuffer.Len())
}
// Render renders the series.
func (mas *SimpleMovingAverageSeries) Render(r Renderer, canvasBox Box, xrange, yrange Range, defaults Style) {
style := mas.Style.WithDefaultsFrom(defaults)
DrawLineSeries(r, canvasBox, xrange, yrange, style, mas)
}

90
sma_series.go Normal file
View file

@ -0,0 +1,90 @@
package chart
const (
// DefaultSimpleMovingAveragePeriod is the default number of values to average.
DefaultSimpleMovingAveragePeriod = 16
)
// SMASeries is a computed series.
type SMASeries struct {
Name string
Style Style
YAxis YAxisType
Period int
InnerSeries ValueProvider
}
// GetName returns the name of the time series.
func (sma SMASeries) GetName() string {
return sma.Name
}
// GetStyle returns the line style.
func (sma SMASeries) GetStyle() Style {
return sma.Style
}
// GetYAxis returns which YAxis the series draws on.
func (sma SMASeries) GetYAxis() YAxisType {
return sma.YAxis
}
// Len returns the number of elements in the series.
func (sma SMASeries) Len() int {
return sma.InnerSeries.Len()
}
// GetValue gets a value at a given index.
func (sma SMASeries) GetValue(index int) (x float64, y float64) {
if sma.InnerSeries == nil {
return
}
px, _ := sma.InnerSeries.GetValue(index)
x = px
y = sma.getAverage(index)
return
}
// GetLastValue computes the last moving average value but walking back window size samples,
// and recomputing the last moving average chunk.
func (sma SMASeries) GetLastValue() (x float64, y float64) {
if sma.InnerSeries == nil {
return
}
seriesLen := sma.InnerSeries.Len()
px, _ := sma.InnerSeries.GetValue(seriesLen - 1)
x = px
y = sma.getAverage(seriesLen - 1)
return
}
// GetPeriod returns the window size.
func (sma SMASeries) GetPeriod(defaults ...int) int {
if sma.Period == 0 {
if len(defaults) > 0 {
return defaults[0]
}
return DefaultSimpleMovingAveragePeriod
}
return sma.Period
}
func (sma SMASeries) getAverage(index int) float64 {
period := sma.GetPeriod()
floor := MaxInt(0, index-period)
var accum float64
var count float64
for x := index; x >= floor; x-- {
_, vy := sma.InnerSeries.GetValue(x)
accum += vy
count += 1.0
}
return accum / count
}
// Render renders the series.
func (sma *SMASeries) Render(r Renderer, canvasBox Box, xrange, yrange Range, defaults Style) {
style := sma.Style.WithDefaultsFrom(defaults)
DrawLineSeries(r, canvasBox, xrange, yrange, style, sma)
}

26
simple_moving_average_series_test.go → sma_series_test.go
View file

@ -16,12 +16,18 @@ func (m mockValueProvider) Len() int {
}
func (m mockValueProvider) GetValue(index int) (x, y float64) {
if index < 0 {
panic("negative index at GetValue()")
}
if index > MinInt(len(m.X), len(m.Y)) {
panic("index is outside the length of m.X or m.Y")
}
x = m.X[index]
y = m.Y[index]
return
}
func TestSimpleMovingAverageSeriesGetValue(t *testing.T) {
func TestSMASeriesGetValue(t *testing.T) {
assert := assert.New(t)
mockSeries := mockValueProvider{
@ -30,9 +36,9 @@ func TestSimpleMovingAverageSeriesGetValue(t *testing.T) {
}
assert.Equal(10, mockSeries.Len())
mas := &SimpleMovingAverageSeries{
mas := &SMASeries{
InnerSeries: mockSeries,
WindowSize: 10,
Period: 10,
}
var yvalues []float64
@ -52,7 +58,7 @@ func TestSimpleMovingAverageSeriesGetValue(t *testing.T) {
assert.Equal(6.0, yvalues[8])
}
func TestSimpleMovingAverageSeriesGetLastValueWindowOverlap(t *testing.T) {
func TestSMASeriesGetLastValueWindowOverlap(t *testing.T) {
assert := assert.New(t)
mockSeries := mockValueProvider{
@ -61,9 +67,9 @@ func TestSimpleMovingAverageSeriesGetLastValueWindowOverlap(t *testing.T) {
}
assert.Equal(10, mockSeries.Len())
mas := &SimpleMovingAverageSeries{
mas := &SMASeries{
InnerSeries: mockSeries,
WindowSize: 15,
Period: 15,
}
var yvalues []float64
@ -78,7 +84,7 @@ func TestSimpleMovingAverageSeriesGetLastValueWindowOverlap(t *testing.T) {
assert.Equal(yvalues[len(yvalues)-1], ly)
}
func TestSimpleMovingAverageSeriesGetLastValue(t *testing.T) {
func TestSMASeriesGetLastValue(t *testing.T) {
assert := assert.New(t)
mockSeries := mockValueProvider{
@ -87,9 +93,9 @@ func TestSimpleMovingAverageSeriesGetLastValue(t *testing.T) {
}
assert.Equal(100, mockSeries.Len())
mas := &SimpleMovingAverageSeries{
mas := &SMASeries{
InnerSeries: mockSeries,
WindowSize: 10,
Period: 10,
}
var yvalues []float64
@ -100,6 +106,6 @@ func TestSimpleMovingAverageSeriesGetLastValue(t *testing.T) {
lx, ly := mas.GetLastValue()
assert.Equal(100.0, lx)
assert.Equal(5.5, ly)
assert.Equal(6, ly)
assert.Equal(yvalues[len(yvalues)-1], ly)
}