mirror of
https://github.com/c9s/bbgo.git
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366 lines
7.5 KiB
Go
366 lines
7.5 KiB
Go
package bbgo
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import (
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"fmt"
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"math"
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"github.com/pkg/errors"
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)
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type Scale interface {
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Solve() error
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Formula() string
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FormulaOf(x float64) string
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Call(x float64) (y float64)
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}
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func init() {
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_ = Scale(&ExponentialScale{})
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_ = Scale(&LogarithmicScale{})
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_ = Scale(&LinearScale{})
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_ = Scale(&QuadraticScale{})
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}
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// y := ab^x
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// shift xs[0] to 0 (x - h)
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// a = y1
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//
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// y := ab^(x-h)
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// y2/a = b^(x2-h)
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// y2/y1 = b^(x2-h)
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//
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// also posted at https://play.golang.org/p/JlWlwZjoebE
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type ExponentialScale struct {
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Domain [2]float64 `json:"domain"`
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Range [2]float64 `json:"range"`
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a float64
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b float64
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h float64
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}
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func (s *ExponentialScale) Solve() error {
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s.h = s.Domain[0]
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s.a = s.Range[0]
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s.b = math.Pow(s.Range[1]/s.Range[0], 1/(s.Domain[1]-s.h))
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return nil
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}
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func (s *ExponentialScale) String() string {
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return s.Formula()
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}
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func (s *ExponentialScale) Formula() string {
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return fmt.Sprintf("f(x) = %f * %f ^ (x - %f)", s.a, s.b, s.h)
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}
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func (s *ExponentialScale) FormulaOf(x float64) string {
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return fmt.Sprintf("f(%f) = %f * %f ^ (%f - %f)", x, s.a, s.b, x, s.h)
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}
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func (s *ExponentialScale) Call(x float64) (y float64) {
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if x < s.Domain[0] {
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x = s.Domain[0]
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} else if x > s.Domain[1] {
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x = s.Domain[1]
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}
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y = s.a * math.Pow(s.b, x-s.h)
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return y
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}
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type LogarithmicScale struct {
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Domain [2]float64 `json:"domain"`
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Range [2]float64 `json:"range"`
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h float64
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s float64
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a float64
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}
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func (s *LogarithmicScale) Call(x float64) (y float64) {
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if x < s.Domain[0] {
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x = s.Domain[0]
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} else if x > s.Domain[1] {
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x = s.Domain[1]
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}
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// y = a * log(x - h) + s
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y = s.a*math.Log(x-s.h) + s.s
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return y
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}
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func (s *LogarithmicScale) String() string {
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return s.Formula()
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}
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func (s *LogarithmicScale) Formula() string {
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return fmt.Sprintf("f(x) = %f * log(x - %f) + %f", s.a, s.h, s.s)
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}
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func (s *LogarithmicScale) FormulaOf(x float64) string {
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return fmt.Sprintf("f(%f) = %f * log(%f - %f) + %f", x, s.a, x, s.h, s.s)
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}
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func (s *LogarithmicScale) Solve() error {
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// f(x) = a * log2(x - h) + s
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//
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// log2(1) = 0
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//
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// h = x1 - 1
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// s = y1
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//
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// y2 = a * log(x2 - h) + s
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// y2 = a * log(x2 - h) + y1
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// y2 - y1 = a * log(x2 - h)
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// a = (y2 - y1) / log(x2 - h)
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s.h = s.Domain[0] - 1
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s.s = s.Range[0]
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s.a = (s.Range[1] - s.Range[0]) / math.Log(s.Domain[1]-s.h)
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return nil
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}
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type LinearScale struct {
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Domain [2]float64 `json:"domain"`
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Range [2]float64 `json:"range"`
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a, b float64
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}
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func (s *LinearScale) Solve() error {
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xs := s.Domain
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ys := s.Range
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// y1 = a * x1 + b
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// y2 = a * x2 + b
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// y2 - y1 = (a * x2 + b) - (a * x1 + b)
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// y2 - y1 = (a * x2) - (a * x1)
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// y2 - y1 = a * (x2 - x1)
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// a = (y2 - y1) / (x2 - x1)
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// b = y1 - (a * x1)
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s.a = (ys[1] - ys[0]) / (xs[1] - xs[0])
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s.b = ys[0] - (s.a * xs[0])
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return nil
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}
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func (s *LinearScale) Call(x float64) (y float64) {
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if x < s.Domain[0] {
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x = s.Domain[0]
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} else if x > s.Domain[1] {
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x = s.Domain[1]
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}
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y = s.a*x + s.b
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return y
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}
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func (s *LinearScale) String() string {
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return s.Formula()
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}
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func (s *LinearScale) Formula() string {
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return fmt.Sprintf("f(x) = %f * x + %f", s.a, s.b)
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}
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func (s *LinearScale) FormulaOf(x float64) string {
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return fmt.Sprintf("f(%f) = %f * %f + %f", x, s.a, x, s.b)
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}
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// see also: http://www.vb-helper.com/howto_find_quadratic_curve.html
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type QuadraticScale struct {
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Domain [3]float64 `json:"domain"`
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Range [3]float64 `json:"range"`
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a, b, c float64
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}
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func (s *QuadraticScale) Solve() error {
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xs := s.Domain
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ys := s.Range
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s.a = ((ys[1]-ys[0])*(xs[0]-xs[2]) + (ys[2]-ys[0])*(xs[1]-xs[0])) /
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((xs[0]-xs[2])*(math.Pow(xs[1], 2)-math.Pow(xs[0], 2)) + (xs[1]-xs[0])*(math.Pow(xs[2], 2)-math.Pow(xs[0], 2)))
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s.b = ((ys[1] - ys[0]) - s.a*(math.Pow(xs[1], 2)-math.Pow(xs[0], 2))) / (xs[1] - xs[0])
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s.c = ys[1] - s.a*math.Pow(xs[1], 2) - s.b*xs[1]
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return nil
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}
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func (s *QuadraticScale) Call(x float64) (y float64) {
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if x < s.Domain[0] {
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x = s.Domain[0]
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} else if x > s.Domain[2] {
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x = s.Domain[2]
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}
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// y = a * log(x - h) + s
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y = s.a*math.Pow(x, 2) + s.b*x + s.c
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return y
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}
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func (s *QuadraticScale) String() string {
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return s.Formula()
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}
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func (s *QuadraticScale) Formula() string {
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return fmt.Sprintf("f(x) = %f * x ^ 2 + %f * x + %f", s.a, s.b, s.c)
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}
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func (s *QuadraticScale) FormulaOf(x float64) string {
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return fmt.Sprintf("f(%f) = %f * %f ^ 2 + %f * %f + %f", x, s.a, x, s.b, x, s.c)
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}
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type SlideRule struct {
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// Scale type could be one of "log", "exp", "linear", "quadratic"
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// this is similar to the d3.scale
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LinearScale *LinearScale `json:"linear"`
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LogScale *LogarithmicScale `json:"log"`
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ExpScale *ExponentialScale `json:"exp"`
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QuadraticScale *QuadraticScale `json:"quadratic"`
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}
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func (rule *SlideRule) Range() ([2]float64, error) {
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if rule.LogScale != nil {
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return rule.LogScale.Range, nil
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}
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if rule.ExpScale != nil {
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return rule.ExpScale.Range, nil
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}
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if rule.LinearScale != nil {
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return rule.LinearScale.Range, nil
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}
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if rule.QuadraticScale != nil {
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r := rule.QuadraticScale.Range
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return [2]float64{r[0], r[len(r)-1]}, nil
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}
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return [2]float64{}, errors.New("no any scale domain is defined")
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}
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func (rule *SlideRule) Scale() (Scale, error) {
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if rule.LogScale != nil {
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return rule.LogScale, nil
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}
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if rule.ExpScale != nil {
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return rule.ExpScale, nil
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}
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if rule.LinearScale != nil {
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return rule.LinearScale, nil
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}
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if rule.QuadraticScale != nil {
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return rule.QuadraticScale, nil
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}
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return nil, errors.New("no any scale is defined")
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}
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// LayerScale defines the scale DSL for maker layers, e.g.,
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//
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// quantityScale:
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// byLayer:
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// exp:
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// domain: [1, 5]
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// range: [0.01, 1.0]
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//
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// and
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//
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// quantityScale:
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// byLayer:
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// linear:
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// domain: [1, 3]
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// range: [0.01, 1.0]
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type LayerScale struct {
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LayerRule *SlideRule `json:"byLayer"`
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}
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func (s *LayerScale) Scale(layer int) (quantity float64, err error) {
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if s.LayerRule == nil {
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err = errors.New("either price or volume scale is not defined")
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return
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}
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scale, err := s.LayerRule.Scale()
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if err != nil {
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return 0, err
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}
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if err := scale.Solve(); err != nil {
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return 0, err
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}
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return scale.Call(float64(layer)), nil
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}
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// PriceVolumeScale defines the scale DSL for strategy, e.g.,
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//
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// quantityScale:
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// byPrice:
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// exp:
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// domain: [10_000, 50_000]
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// range: [0.01, 1.0]
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//
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// and
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//
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// quantityScale:
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// byVolume:
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// linear:
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// domain: [10_000, 50_000]
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// range: [0.01, 1.0]
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type PriceVolumeScale struct {
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ByPriceRule *SlideRule `json:"byPrice"`
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ByVolumeRule *SlideRule `json:"byVolume"`
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}
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func (s *PriceVolumeScale) Scale(price float64, volume float64) (quantity float64, err error) {
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if s.ByPriceRule != nil {
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quantity, err = s.ScaleByPrice(price)
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return
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} else if s.ByVolumeRule != nil {
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quantity, err = s.ScaleByVolume(volume)
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} else {
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err = errors.New("either price or volume scale is not defined")
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}
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return
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}
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// ScaleByPrice scale quantity by the given price
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func (s *PriceVolumeScale) ScaleByPrice(price float64) (float64, error) {
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if s.ByPriceRule == nil {
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return 0, errors.New("byPrice scale is not defined")
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}
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scale, err := s.ByPriceRule.Scale()
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if err != nil {
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return 0, err
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}
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if err := scale.Solve(); err != nil {
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return 0, err
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}
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return scale.Call(price), nil
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}
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// ScaleByVolume scale quantity by the given volume
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func (s *PriceVolumeScale) ScaleByVolume(volume float64) (float64, error) {
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if s.ByVolumeRule == nil {
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return 0, errors.New("byVolume scale is not defined")
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}
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scale, err := s.ByVolumeRule.Scale()
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if err != nil {
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return 0, err
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}
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if err := scale.Solve(); err != nil {
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return 0, err
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}
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return scale.Call(volume), nil
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}
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