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