math: additional complex operations with tests

vlib/math/complex.v

@@ -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)

vlib/math/complex_test.v

@@ -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())
+}