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math: additional complex operations with tests

This commit is contained in:
Archan Patkar 2019-07-08 23:11:37 +05:30 committed by Alexander Medvednikov
parent 7b1be8a2bd
commit 3f916efb64
2 changed files with 188 additions and 0 deletions

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@ -92,6 +92,69 @@ pub fn (c1 Complex) conjugate() Complex{
return Complex{c1.re,-c1.im}
}
// Complex Additive Inverse
// Based on
// http://tutorial.math.lamar.edu/Extras/ComplexPrimer/Arithmetic.aspx
pub fn (c1 Complex) addinv() Complex {
return Complex{-c1.re,-c1.im}
}
// Complex Multiplicative Inverse
// Based on
// http://tutorial.math.lamar.edu/Extras/ComplexPrimer/Arithmetic.aspx
pub fn (c1 Complex) mulinv() Complex {
return Complex {
c1.re / (pow(c1.re,2) + pow(c1.im,2)),
-c1.im / (pow(c1.re,2) + pow(c1.im,2))
}
}
// Complex Mod or Absolute
// Based on
// http://tutorial.math.lamar.edu/Extras/ComplexPrimer/ConjugateModulus.aspx
pub fn (c1 Complex) mod() f64 {
return sqrt(pow(c1.re,2)+pow(c1.im,2))
}
// 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 (c1 Complex) pow(n f64) Complex {
r := pow(c1.mod(),n)
angle := atan2(c1.im,c1.re)
return Complex {
r * cos(n*angle),
r * sin(n*angle)
}
}
// Complex nth root
pub fn (c1 Complex) root(n f64) Complex {
return c1.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 (c1 Complex) exp() Complex {
a := exp(c1.re)
return Complex {
a * cos(c1.im),
a * sin(c1.im)
}
}
// Complex Natural Logarithm
// Based on
// http://www.chemistrylearning.com/logarithm-of-complex-number/
pub fn (c1 Complex) ln() Complex {
return Complex {
log(c1.mod()),
atan2(c1.im,c1.re)
}
}
// Complex Equals
pub fn (c1 Complex) equals(c2 Complex) bool {
return (c1.re == c2.re) && (c1.im == c2.im)

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@ -117,3 +117,128 @@ fn test_complex_angle(){
mut cc := c.conjugate()
assert cc.angle() + c.angle() == 0
}
fn test_complex_addinv() {
// Tests were also verified on Wolfram Alpha
mut c1 := math.complex(5,7)
mut c2 := math.complex(-5,-7)
mut result := c1.addinv()
assert result.equals(c2)
c1 = math.complex(-3,4)
c2 = math.complex(3,-4)
result = c1.addinv()
assert result.equals(c2)
c1 = math.complex(-1,-2)
c2 = math.complex(1,2)
result = c1.addinv()
assert result.equals(c2)
}
fn test_complex_mulinv() {
// Tests were also verified on Wolfram Alpha
mut c1 := math.complex(5,7)
mut c2 := math.complex(0.067568,-0.094595)
mut result := c1.mulinv()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
c1 = math.complex(-3,4)
c2 = math.complex(-0.12,-0.16)
result = c1.mulinv()
assert result.str().eq(c2.str())
c1 = math.complex(-1,-2)
c2 = math.complex(-0.2,0.4)
result = c1.mulinv()
assert result.equals(c2)
}
fn test_complex_mod() {
// Tests were also verified on Wolfram Alpha
mut c1 := math.complex(5,7)
mut result := c1.mod()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq('8.602325')
c1 = math.complex(-3,4)
result = c1.mod()
assert result == 5
c1 = math.complex(-1,-2)
result = c1.mod()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq('2.236068')
}
fn test_complex_pow() {
// Tests were also verified on Wolfram Alpha
mut c1 := math.complex(5,7)
mut c2 := math.complex(-24.0,70.0)
mut result := c1.pow(2)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
c1 = math.complex(-3,4)
c2 = math.complex(117,44)
result = c1.pow(3)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
c1 = math.complex(-1,-2)
c2 = math.complex(-7,-24)
result = c1.pow(4)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
}
fn test_complex_root() {
// Tests were also verified on Wolfram Alpha
mut c1 := math.complex(5,7)
mut c2 := math.complex(2.607904,1.342074)
mut result := c1.root(2)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
c1 = math.complex(-3,4)
c2 = math.complex(1.264953,1.150614)
result = c1.root(3)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
c1 = math.complex(-1,-2)
c2 = math.complex(1.068059,-0.595482)
result = c1.root(4)
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
}
fn test_complex_exp() {
// Tests were also verified on Wolfram Alpha
mut c1 := math.complex(5,7)
mut c2 := math.complex(111.889015,97.505457)
mut result := c1.exp()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
c1 = math.complex(-3,4)
c2 = math.complex(-0.032543,-0.037679)
result = c1.exp()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
c1 = math.complex(-1,-2)
c2 = math.complex(-0.153092,-0.334512)
result = c1.exp()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
}
fn test_complex_ln() {
// Tests were also verified on Wolfram Alpha
mut c1 := math.complex(5,7)
mut c2 := math.complex(2.152033,0.950547)
mut result := c1.ln()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
c1 = math.complex(-3,4)
c2 = math.complex(1.609438,2.214297)
result = c1.ln()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
c1 = math.complex(-1,-2)
c2 = math.complex(0.804719,-2.034444)
result = c1.ln()
// Some issue with precision comparison in f64 using == operator hence serializing to string
assert result.str().eq(c2.str())
}