v/vlib/math/complex/complex.v

507 lines
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V

// Copyright (c) 2019-2020 Alexander Medvednikov. All rights reserved.
// Use of this source code is governed by an MIT license
// that can be found in the LICENSE file.
module complex
import math
pub struct Complex {
pub:
re f64
im f64
}
pub fn complex(re f64, im f64) Complex {
return Complex{re, im}
}
// To String method
pub fn (c Complex) str() string {
mut out := '$c.re'
out += if c.im >= 0 {
'+$c.im'
}
else {
'$c.im'
}
out += 'i'
return out
}
// Complex Modulus value
// mod() and abs() return the same
pub fn (c Complex) abs() f64 {
return C.hypot(c.re, c.im)
}
pub fn (c Complex) mod() f64 {
return c.abs()
}
// Complex Angle
pub fn (c Complex) angle() f64 {
return math.atan2(c.im, c.re)
}
// Complex Addition c1 + c2
pub fn (c1 Complex) + (c2 Complex) Complex {
return Complex{c1.re + c2.re, c1.im + c2.im}
}
// Complex Substraction c1 - c2
pub fn (c1 Complex) - (c2 Complex) Complex {
return Complex{c1.re - c2.re, c1.im - c2.im}
}
// Complex Multiplication c1 * c2
pub fn (c1 Complex) * (c2 Complex) Complex {
return Complex{
(c1.re * c2.re) + ((c1.im * c2.im) * -1),
(c1.re * c2.im) + (c1.im * c2.re)
}
}
// Complex Division c1 / c2
pub fn (c1 Complex) / (c2 Complex) Complex {
denom := (c2.re * c2.re) + (c2.im * c2.im)
return Complex {
((c1.re * c2.re) + ((c1.im * -c2.im) * -1))/denom,
((c1.re * -c2.im) + (c1.im * c2.re))/denom
}
}
// Complex Addition c1.add(c2)
pub fn (c1 Complex) add(c2 Complex) Complex {
return c1 + c2
}
// Complex Subtraction c1.subtract(c2)
pub fn (c1 Complex) subtract(c2 Complex) Complex {
return c1 - c2
}
// Complex Multiplication c1.multiply(c2)
pub fn (c1 Complex) multiply(c2 Complex) Complex {
return Complex{
(c1.re * c2.re) + ((c1.im * c2.im) * -1),
(c1.re * c2.im) + (c1.im * c2.re)
}
}
// Complex Division c1.divide(c2)
pub fn (c1 Complex) divide(c2 Complex) Complex {
denom := (c2.re * c2.re) + (c2.im * c2.im)
return Complex {
((c1.re * c2.re) + ((c1.im * -c2.im) * -1)) / denom,
((c1.re * -c2.im) + (c1.im * c2.re)) / denom
}
}
// Complex Conjugate
pub fn (c Complex) conjugate() Complex{
return Complex{c.re, -c.im}
}
// Complex Additive Inverse
// Based on
// http://tutorial.math.lamar.edu/Extras/ComplexPrimer/Arithmetic.aspx
pub fn (c Complex) addinv() Complex {
return Complex{-c.re, -c.im}
}
// Complex Multiplicative Inverse
// Based on
// http://tutorial.math.lamar.edu/Extras/ComplexPrimer/Arithmetic.aspx
pub fn (c Complex) mulinv() Complex {
return Complex {
c.re / (c.re * c.re + c.im * c.im),
-c.im / (c.re * c.re + c.im * c.im)
}
}
// Complex Power
// Based on
// https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers/multiplying-and-dividing-complex-numbers-in-polar-form/a/complex-number-polar-form-review
pub fn (c Complex) pow(n f64) Complex {
r := math.pow(c.abs(), n)
angle := c.angle()
return Complex {
r * math.cos(n * angle),
r * math.sin(n * angle)
}
}
// Complex nth root
pub fn (c Complex) root(n f64) Complex {
return c.pow(1.0 / n)
}
// Complex Exponential
// Using Euler's Identity
// Based on
// https://www.math.wisc.edu/~angenent/Free-Lecture-Notes/freecomplexnumbers.pdf
pub fn (c Complex) exp() Complex {
a := math.exp(c.re)
return Complex {
a * math.cos(c.im),
a * math.sin(c.im)
}
}
// Complex Natural Logarithm
// Based on
// http://www.chemistrylearning.com/logarithm-of-complex-number/
pub fn (c Complex) ln() Complex {
return Complex {
math.log(c.abs()),
c.angle()
}
}
// Complex Log Base Complex
// Based on
// http://www.milefoot.com/math/complex/summaryops.htm
pub fn (c Complex) log(base Complex) Complex {
return base.ln().divide(c.ln())
}
// Complex Argument
// Based on
// http://mathworld.wolfram.com/ComplexArgument.html
pub fn (c Complex) arg() f64 {
return math.atan2(c.im,c.re)
}
// Complex raised to Complex Power
// Based on
// http://mathworld.wolfram.com/ComplexExponentiation.html
pub fn (c Complex) cpow(p Complex) Complex {
a := c.arg()
b := math.pow(c.re,2) + math.pow(c.im,2)
d := p.re * a + (1.0/2) * p.im * math.log(b)
t1 := math.pow(b,p.re/2) * math.exp(-p.im*a)
return Complex{
t1 * math.cos(d),
t1 * math.sin(d)
}
}
// Complex Sin
// Based on
// http://www.milefoot.com/math/complex/functionsofi.htm
pub fn (c Complex) sin() Complex {
return Complex{
math.sin(c.re) * math.cosh(c.im),
math.cos(c.re) * math.sinh(c.im)
}
}
// Complex Cosine
// Based on
// http://www.milefoot.com/math/complex/functionsofi.htm
pub fn (c Complex) cos() Complex {
return Complex{
math.cos(c.re) * math.cosh(c.im),
-(math.sin(c.re) * math.sinh(c.im))
}
}
// Complex Tangent
// Based on
// http://www.milefoot.com/math/complex/functionsofi.htm
pub fn (c Complex) tan() Complex {
return c.sin().divide(c.cos())
}
// Complex Cotangent
// Based on
// http://www.suitcaseofdreams.net/Trigonometric_Functions.htm
pub fn (c Complex) cot() Complex {
return c.cos().divide(c.sin())
}
// Complex Secant
// Based on
// http://www.suitcaseofdreams.net/Trigonometric_Functions.htm
pub fn (c Complex) sec() Complex {
return complex(1,0).divide(c.cos())
}
// Complex Cosecant
// Based on
// http://www.suitcaseofdreams.net/Trigonometric_Functions.htm
pub fn (c Complex) csc() Complex {
return complex(1,0).divide(c.sin())
}
// Complex Arc Sin / Sin Inverse
// Based on
// http://www.milefoot.com/math/complex/summaryops.htm
pub fn (c Complex) asin() Complex {
return complex(0,-1).multiply(
complex(0,1)
.multiply(c)
.add(
complex(1,0)
.subtract(c.pow(2))
.root(2)
)
.ln()
)
}
// Complex Arc Consine / Consine Inverse
// Based on
// http://www.milefoot.com/math/complex/summaryops.htm
pub fn (c Complex) acos() Complex {
return complex(0,-1).multiply(
c.add(
complex(0,1)
.multiply(
complex(1,0)
.subtract(c.pow(2))
.root(2)
)
)
.ln()
)
}
// Complex Arc Tangent / Tangent Inverse
// Based on
// http://www.milefoot.com/math/complex/summaryops.htm
pub fn (c Complex) atan() Complex {
i := complex(0,1)
return complex(0,1.0/2).multiply(
i.add(c)
.divide(
i.subtract(c)
)
.ln()
)
}
// Complex Arc Cotangent / Cotangent Inverse
// Based on
// http://www.suitcaseofdreams.net/Inverse_Functions.htm
pub fn (c Complex) acot() Complex {
return complex(1,0).divide(c).atan()
}
// Complex Arc Secant / Secant Inverse
// Based on
// http://www.suitcaseofdreams.net/Inverse_Functions.htm
pub fn (c Complex) asec() Complex {
return complex(1,0).divide(c).acos()
}
// Complex Arc Cosecant / Cosecant Inverse
// Based on
// http://www.suitcaseofdreams.net/Inverse_Functions.htm
pub fn (c Complex) acsc() Complex {
return complex(1,0).divide(c).asin()
}
// Complex Hyperbolic Sin
// Based on
// http://www.milefoot.com/math/complex/functionsofi.htm
pub fn (c Complex) sinh() Complex {
return Complex{
math.cos(c.im) * math.sinh(c.re),
math.sin(c.im) * math.cosh(c.re)
}
}
// Complex Hyperbolic Cosine
// Based on
// http://www.milefoot.com/math/complex/functionsofi.htm
pub fn (c Complex) cosh() Complex {
return Complex{
math.cos(c.im) * math.cosh(c.re),
math.sin(c.im) * math.sinh(c.re)
}
}
// Complex Hyperbolic Tangent
// Based on
// http://www.milefoot.com/math/complex/functionsofi.htm
pub fn (c Complex) tanh() Complex {
return c.sinh().divide(c.cosh())
}
// Complex Hyperbolic Cotangent
// Based on
// http://www.suitcaseofdreams.net/Hyperbolic_Functions.htm
pub fn (c Complex) coth() Complex {
return c.cosh().divide(c.sinh())
}
// Complex Hyperbolic Secant
// Based on
// http://www.suitcaseofdreams.net/Hyperbolic_Functions.htm
pub fn (c Complex) sech() Complex {
return complex(1,0).divide(c.cosh())
}
// Complex Hyperbolic Cosecant
// Based on
// http://www.suitcaseofdreams.net/Hyperbolic_Functions.htm
pub fn (c Complex) csch() Complex {
return complex(1,0).divide(c.sinh())
}
// Complex Hyperbolic Arc Sin / Sin Inverse
// Based on
// http://www.suitcaseofdreams.net/Inverse__Hyperbolic_Functions.htm
pub fn (c Complex) asinh() Complex {
return c.add(
c.pow(2)
.add(complex(1,0))
.root(2)
).ln()
}
// Complex Hyperbolic Arc Consine / Consine Inverse
// Based on
// http://www.suitcaseofdreams.net/Inverse__Hyperbolic_Functions.htm
pub fn (c Complex) acosh() Complex {
if c.re > 1 {
return c.add(
c.pow(2)
.subtract(complex(1,0))
.root(2)
).ln()
}
else {
one := complex(1,0)
return c.add(
c.add(one)
.root(2)
.multiply(
c.subtract(one)
.root(2)
)
).ln()
}
}
// Complex Hyperbolic Arc Tangent / Tangent Inverse
// Based on
// http://www.suitcaseofdreams.net/Inverse__Hyperbolic_Functions.htm
pub fn (c Complex) atanh() Complex {
one := complex(1,0)
if c.re < 1 {
return complex(1.0/2,0).multiply(
one
.add(c)
.divide(
one
.subtract(c)
)
.ln()
)
}
else {
return complex(1.0/2,0).multiply(
one
.add(c)
.ln()
.subtract(
one
.subtract(c)
.ln()
)
)
}
}
// Complex Hyperbolic Arc Cotangent / Cotangent Inverse
// Based on
// http://www.suitcaseofdreams.net/Inverse__Hyperbolic_Functions.htm
pub fn (c Complex) acoth() Complex {
one := complex(1,0)
if c.re < 0 || c.re > 1 {
return complex(1.0/2,0).multiply(
c
.add(one)
.divide(
c.subtract(one)
)
.ln()
)
}
else {
div := one.divide(c)
return complex(1.0/2,0).multiply(
one
.add(div)
.ln()
.subtract(
one
.subtract(div)
.ln()
)
)
}
}
// Complex Hyperbolic Arc Secant / Secant Inverse
// Based on
// http://www.suitcaseofdreams.net/Inverse__Hyperbolic_Functions.htm
// For certain scenarios, Result mismatch in crossverification with Wolfram Alpha - analysis pending
// pub fn (c Complex) asech() Complex {
// one := complex(1,0)
// if(c.re < -1.0) {
// return one.subtract(
// one.subtract(
// c.pow(2)
// )
// .root(2)
// )
// .divide(c)
// .ln()
// }
// else {
// return one.add(
// one.subtract(
// c.pow(2)
// )
// .root(2)
// )
// .divide(c)
// .ln()
// }
// }
// Complex Hyperbolic Arc Cosecant / Cosecant Inverse
// Based on
// http://www.suitcaseofdreams.net/Inverse__Hyperbolic_Functions.htm
pub fn (c Complex) acsch() Complex {
one := complex(1,0)
if c.re < 0 {
return one.subtract(
one.add(
c.pow(2)
)
.root(2)
)
.divide(c)
.ln()
} else {
return one.add(
one.add(
c.pow(2)
)
.root(2)
)
.divide(c)
.ln()
}
}
// Complex Equals
pub fn (c1 Complex) equals(c2 Complex) bool {
return (c1.re == c2.re) && (c1.im == c2.im)
}