Adds most of the toolsHEADmaster

1 files changed, 374 insertions, 0 deletions

diff --git a/v_windows/v/vlib/math/complex/complex.v b/v_windows/v/vlib/math/complex/complex.v
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+// Copyright (c) 2019-2021 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 := '${c.re:.6f}'
+	out += if c.im >= 0 { '+${c.im:.6f}' } else { '${c.im:.6f}' }
+	out += 'i'
+	return out
+}
+
+// Complex Modulus value
+// mod() and abs() return the same
+pub fn (c Complex) abs() f64 {
+	return math.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)
+}