Documentation
¶
Overview ¶
Package dual provides the dual numeric type and functions. Dual numbers are an extension of the real numbers in the form a+bϵ where ϵ^2=0, but ϵ≠0.
See https://en.wikipedia.org/wiki/Dual_number for details of their properties and uses.
Index ¶
- type Number
- func Abs(d Number) Number
- func Acos(d Number) Number
- func Acosh(d Number) Number
- func Add(x, y Number) Number
- func Asin(d Number) Number
- func Asinh(d Number) Number
- func Atan(d Number) Number
- func Atanh(d Number) Number
- func Cos(d Number) Number
- func Cosh(d Number) Number
- func Exp(d Number) Number
- func Inv(d Number) Number
- func Log(d Number) Number
- func Mul(x, y Number) Number
- func Pow(d, p Number) Number
- func PowReal(d Number, p float64) Number
- func Scale(f float64, d Number) Number
- func Sin(d Number) Number
- func Sinh(d Number) Number
- func Sqrt(d Number) Number
- func Sub(x, y Number) Number
- func Tan(d Number) Number
- func Tanh(d Number) Number
Examples ¶
Constants ¶
This section is empty.
Variables ¶
This section is empty.
Functions ¶
This section is empty.
Types ¶
type Number ¶
type Number struct {
Real, Emag float64
}
Number is a float64 precision dual number.
Example (Fike) ¶
package main
import (
"fmt"
"gonum.org/v1/gonum/num/dual"
)
func main() {
// Calculate the value and derivative of the function
// e^x/(sqrt(sin(x)^3 + cos(x)^3)).
fn := func(x dual.Number) dual.Number {
return dual.Mul(
dual.Exp(x),
dual.Inv(dual.Sqrt(
dual.Add(
dual.PowReal(dual.Sin(x), 3),
dual.PowReal(dual.Cos(x), 3)))))
}
v := fn(dual.Number{Real: 1.5, Emag: 1})
fmt.Printf("v=%.4f\n", v)
fmt.Printf("fn(1.5)=%.4f\nfn'(1.5)=%.4f\n", v.Real, v.Emag)
}
Output: v=(4.4978+4.0534ϵ) fn(1.5)=4.4978 fn'(1.5)=4.0534
func Acos ¶
Acos returns the inverse cosine of d.
Special cases are:
Acos(-1) = (Pi-Infϵ) Acos(1) = (0-Infϵ) Acos(x) = NaN if x < -1 or x > 1
func Acosh ¶
Acosh returns the inverse hyperbolic cosine of d.
Special cases are:
Acosh(+Inf) = +Inf Acosh(1) = (0+Infϵ) Acosh(x) = NaN if x < 1 Acosh(NaN) = NaN
func Asin ¶
Asin returns the inverse sine of d.
Special cases are:
Asin(±0) = (±0+Nϵ) Asin(±1) = (±Inf+Infϵ) Asin(x) = NaN if x < -1 or x > 1
func Asinh ¶
Asinh returns the inverse hyperbolic sine of d.
Special cases are:
Asinh(±0) = (±0+Nϵ) Asinh(±Inf) = ±Inf Asinh(NaN) = NaN
func Atan ¶
Atan returns the inverse tangent of d.
Special cases are:
Atan(±0) = (±0+Nϵ) Atan(±Inf) = (±Pi/2+0ϵ)
func Atanh ¶
Atanh returns the inverse hyperbolic tangent of d.
Special cases are:
Atanh(1) = +Inf Atanh(±0) = (±0+Nϵ) Atanh(-1) = -Inf Atanh(x) = NaN if x < -1 or x > 1 Atanh(NaN) = NaN
func Cosh ¶
Cosh returns the hyperbolic cosine of d.
Special cases are:
Cosh(±0) = 1 Cosh(±Inf) = +Inf Cosh(NaN) = NaN
func Exp ¶
Exp returns e**q, the base-e exponential of d.
Special cases are:
Exp(+Inf) = +Inf Exp(NaN) = NaN
Very large values overflow to 0 or +Inf. Very small values underflow to 1.
func Inv ¶
Inv returns the dual inverse of d.
Special cases are:
Inv(±Inf) = ±0-0ϵ Inv(±0) = ±Inf-Infϵ
func Log ¶
Log returns the natural logarithm of d.
Special cases are:
Log(+Inf) = (+Inf+0ϵ) Log(0) = (-Inf±Infϵ) Log(x < 0) = NaN Log(NaN) = NaN
func PowReal ¶
PowReal returns x**p, the base-x exponential of p.
Special cases are (in order):
PowReal(NaN+xϵ, ±0) = 1+NaNϵ for any x PowReal(x, ±0) = 1 for any x PowReal(1+xϵ, y) = 1+xyϵ for any y PowReal(x, 1) = x for any x PowReal(NaN+xϵ, y) = NaN+NaNϵ PowReal(x, NaN) = NaN+NaNϵ PowReal(±0, y) = ±Inf for y an odd integer < 0 PowReal(±0, -Inf) = +Inf PowReal(±0, +Inf) = +0 PowReal(±0, y) = +Inf for finite y < 0 and not an odd integer PowReal(±0, y) = ±0 for y an odd integer > 0 PowReal(±0, y) = +0 for finite y > 0 and not an odd integer PowReal(-1, ±Inf) = 1 PowReal(x+0ϵ, +Inf) = +Inf+NaNϵ for |x| > 1 PowReal(x+yϵ, +Inf) = +Inf for |x| > 1 PowReal(x, -Inf) = +0+NaNϵ for |x| > 1 PowReal(x, +Inf) = +0+NaNϵ for |x| < 1 PowReal(x+0ϵ, -Inf) = +Inf+NaNϵ for |x| < 1 PowReal(x, -Inf) = +Inf-Infϵ for |x| < 1 PowReal(+Inf, y) = +Inf for y > 0 PowReal(+Inf, y) = +0 for y < 0 PowReal(-Inf, y) = Pow(-0, -y) PowReal(x, y) = NaN+NaNϵ for finite x < 0 and finite non-integer y
func Sin ¶
Sin returns the sine of d.
Special cases are:
Sin(±0) = (±0+Nϵ) Sin(±Inf) = NaN Sin(NaN) = NaN
func Sinh ¶
Sinh returns the hyperbolic sine of d.
Special cases are:
Sinh(±0) = (±0+Nϵ) Sinh(±Inf) = ±Inf Sinh(NaN) = NaN
func Sqrt ¶
Sqrt returns the square root of d.
Special cases are:
Sqrt(+Inf) = +Inf Sqrt(±0) = (±0+Infϵ) Sqrt(x < 0) = NaN Sqrt(NaN) = NaN
func Tan ¶
Tan returns the tangent of d.
Special cases are:
Tan(±0) = (±0+Nϵ) Tan(±Inf) = NaN Tan(NaN) = NaN
Source Files