From b276ad9e72279a90e38c204d9e5f2cf1eec5d4e7 Mon Sep 17 00:00:00 2001 From: Marcus Cuda Date: Tue, 11 Aug 2009 20:05:18 +0800 Subject: [PATCH] Trig: added missing file Signed-off-by: Marcus Cuda --- src/Managed/Trigonometry.cs | 931 ++++++++++++++++++++++++++++++++++++ 1 file changed, 931 insertions(+) create mode 100644 src/Managed/Trigonometry.cs diff --git a/src/Managed/Trigonometry.cs b/src/Managed/Trigonometry.cs new file mode 100644 index 00000000..b691e979 --- /dev/null +++ b/src/Managed/Trigonometry.cs @@ -0,0 +1,931 @@ +// +// Math.NET Numerics, part of the Math.NET Project +// http://mathnet.opensourcedotnet.info +// Copyright (c) 2009 Math.NET +// Permission is hereby granted, free of charge, to any person +// obtaining a copy of this software and associated documentation +// files (the "Software"), to deal in the Software without +// restriction, including without limitation the rights to use, +// copy, modify, merge, publish, distribute, sublicense, and/or sell +// copies of the Software, and to permit persons to whom the +// Software is furnished to do so, subject to the following +// conditions: +// The above copyright notice and this permission notice shall be +// included in all copies or substantial portions of the Software. +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, +// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES +// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND +// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT +// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, +// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING +// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR +// OTHER DEALINGS IN THE SOFTWARE. +// + +namespace MathNet.Numerics +{ + using System; + + /// + /// Double-precision trigonometry toolkit. + /// + public static class Trig + { + /// + /// Constant to convert a degree to grad. + /// + private const double DegreeToGradConstant = 10.0 / 9.0; + + /// + /// Trigonometric Cosecant of an angle in radian. + /// + /// + /// The angle in radian. + /// + /// + /// Cosecant of an angle in radian. + /// + public static double Cosecant(double radian) + { + return 1 / Math.Sin(radian); + } + + /// + /// Trigonometric Cosecant of a Complex number. + /// + /// + /// The complex value. + /// + /// + /// The cosecant of a complex number. + /// + public static Complex Cosecant(this Complex value) + { + if (value.IsReal) + { + return new Complex(Cosecant(value.Real), 0d); + } + + var sinr = Sine(value.Real); + var sinhi = HyperbolicSine(value.Imaginary); + var denom = (sinr * sinr) + (sinhi * sinhi); + + return new Complex(sinr * HyperbolicCosine(value.Imaginary) / denom, -Cosine(value.Real) * sinhi / denom); + } + + /// + /// Trigonometric Cosine of an angle in radian. + /// + /// + /// The angle in radian. + /// + /// + /// The cosine of an angle in radian. + /// + public static double Cosine(double radian) + { + return Math.Cos(radian); + } + + /// + /// Trigonometric Cosine of a Complex number. + /// + /// + /// The complex value. + /// + /// + /// The cosine of a complex number. + /// + public static Complex Cosine(this Complex value) + { + if (value.IsReal) + { + return new Complex(Cosine(value.Real), 0.0); + } + + return new Complex( + Cosine(value.Real) * HyperbolicCosine(value.Imaginary), + -Sine(value.Real) * HyperbolicSine(value.Imaginary)); + } + + /// + /// Trigonometric Cotangent of an angle in radian. + /// + /// + /// The angle in radian. + /// + /// + /// The cotangent of an angle in radian. + /// + public static double Cotangent(double radian) + { + return 1 / Math.Tan(radian); + } + + /// + /// Trigonometric Cotangent of a Complex number. + /// + /// + /// The complex value. + /// + /// + /// The cotangent of the complex number. + /// + public static Complex Cotangent(this Complex value) + { + if (value.IsReal) + { + return new Complex(Cotangent(value.Real), 0d); + } + + var sinr = Sine(value.Real); + var sinhi = HyperbolicSine(value.Imaginary); + var denom = (sinr * sinr) + (sinhi * sinhi); + + return new Complex(sinr * Cosine(value.Real) / denom, -sinhi * HyperbolicCosine(value.Imaginary) / denom); + } + + /// + /// Converts a degree (360-periodic) angle to a grad (400-periodic) angle. + /// + /// + /// The degree to convert. + /// + /// + /// The converted grad angle. + /// + public static double DegreeToGrad(double degree) + { + return degree * DegreeToGradConstant; + } + + /// + /// Converts a degree (360-periodic) angle to a radian (2*Pi-periodic) angle. + /// + /// + /// The degree to convert. + /// + /// + /// The converted radian angle. + /// + public static double DegreeToRadian(double degree) + { + return degree * Constants.Degree; + } + + /// + /// Converts a grad (400-periodic) angle to a degree (360-periodic) angle. + /// + /// + /// The grad to convert. + /// + /// + /// The converted degree. + /// + public static double GradToDegree(double grad) + { + return grad * 0.9; + } + + /// + /// Converts a grad (400-periodic) angle to a radian (2*Pi-periodic) angle. + /// + /// + /// The grad to convert. + /// + /// + /// The converted radian. + /// + public static double GradToRadian(double grad) + { + return grad * Constants.Grad; + } + + /// + /// Trigonometric Hyperbolic Cosecant + /// + /// + /// The angle in radian. + /// + /// + /// The hyperbolic cosecant of the radian angle. + /// + public static double HyperbolicCosecant(double radian) + { + return 1 / HyperbolicSine(radian); + } + + /// + /// Trigonometric Hyperbolic Cosecant of a Complex number. + /// + /// + /// The complex value. + /// + /// + /// The hyperbolic cosecant of a complex number. + /// + public static Complex HyperbolicCosecant(this Complex value) + { + if (value.IsReal) + { + return new Complex(HyperbolicCosecant(value.Real), 0.0); + } + + var exp = value.Exponential(); + return 2 * exp / (exp.Square() - 1); + } + + /// + /// Trigonometric Hyperbolic Cosine + /// + /// + /// The angle in radian. + /// + /// + /// The hyperbolic Cosine of the radian angle. + /// + public static double HyperbolicCosine(double radian) + { + return (Math.Exp(radian) + Math.Exp(-radian)) / 2; + } + + /// + /// Trigonometric Hyperbolic Cosine of a Complex number. + /// + /// + /// The complex value. + /// + /// + /// The hyperbolic cosine of a complex number. + /// + public static Complex HyperbolicCosine(this Complex value) + { + if (value.IsReal) + { + return new Complex(HyperbolicCosine(value.Real), 0.0); + } + + return new Complex( + HyperbolicCosine(value.Real) * Cosine(value.Imaginary), + HyperbolicSine(value.Real) * Sine(value.Imaginary)); + } + + /// + /// Trigonometric Hyperbolic Cotangent + /// + /// + /// The angle in radian angle. + /// + /// + /// The hyperbolic cotangent of the radian angle. + /// + public static double HyperbolicCotangent(double radian) + { + if (radian > 19.115) + { + return 1.0; + } + + if (radian < -19.115) + { + return -1; + } + + var e1 = Math.Exp(radian); + var e2 = Math.Exp(-radian); + return (e1 + e2) / (e1 - e2); + } + + /// + /// Trigonometric Hyperbolic Cotangent of a Complex number. + /// + /// + /// The complex value. + /// + /// + /// The hyperbolic cotangent of a complex number. + /// + public static Complex HyperbolicCotangent(this Complex value) + { + if (value.IsReal) + { + return new Complex(HyperbolicCotangent(value.Real), 0.0); + } + + var sini = Sine(value.Imaginary); + var sinhr = HyperbolicSine(value.Real); + var denom = (sini * sini) + (sinhr * sinhr); + + return new Complex(sinhr * HyperbolicCosine(value.Real) / denom, sini * Cosine(value.Imaginary) / denom); + } + + /// + /// Trigonometric Hyperbolic Secant + /// + /// + /// The angle in radian angle. + /// + /// + /// The hyperbolic secant of the radian angle. + /// + public static double HyperbolicSecant(double radian) + { + return 1 / HyperbolicCosine(radian); + } + + /// + /// Trigonometric Hyperbolic Secant of a Complex number. + /// + /// + /// The complex value. + /// + /// + /// The hyperbolic secant of a complex number. + /// + public static Complex HyperbolicSecant(this Complex value) + { + if (value.IsReal) + { + return new Complex(HyperbolicSecant(value.Real), 0.0); + } + + var exp = value.Exponential(); + return 2 * exp / (exp.Square() + 1); + } + + /// + /// Trigonometric Hyperbolic Sine + /// + /// + /// The angle in radian angle. + /// + /// + /// The hyperbolic sine of the radian angle. + /// + public static double HyperbolicSine(double radian) + { + return (Math.Exp(radian) - Math.Exp(-radian)) / 2; + } + + /// + /// Trigonometric Hyperbolic Sine of a Complex number. + /// + /// + /// The complex value. + /// + /// + /// The hyperbolic sine of a complex number. + /// + public static Complex HyperbolicSine(this Complex value) + { + if (value.IsReal) + { + return new Complex(HyperbolicSine(value.Real), 0.0); + } + + return new Complex( + HyperbolicSine(value.Real) * Cosine(value.Imaginary), + HyperbolicCosine(value.Real) * Sine(value.Imaginary)); + } + + /// + /// Trigonometric Hyperbolic Tangent in radian + /// + /// + /// The angle in radian angle. + /// + /// + /// The hyperbolic tangent of the radian angle. + /// + public static double HyperbolicTangent(double radian) + { + if (radian > 19.1) + { + return 1.0; + } + + if (radian < -19.1) + { + return -1; + } + + var e1 = Math.Exp(radian); + var e2 = Math.Exp(-radian); + return (e1 - e2) / (e1 + e2); + } + + /// + /// Trigonometric Hyperbolic Tangent of a Complex number. + /// + /// + /// The complex value. + /// + /// + /// The hyperbolic tangent of a complex number. + /// + public static Complex HyperbolicTangent(this Complex value) + { + if (value.IsReal) + { + return new Complex(HyperbolicTangent(value.Real), 0.0); + } + + var cosi = Cosine(value.Imaginary); + var sinhr = HyperbolicSine(value.Real); + var denom = (cosi * cosi) + (sinhr * sinhr); + + return new Complex(HyperbolicCosine(value.Real) * sinhr / denom, cosi * Sine(value.Imaginary) / denom); + } + + /// + /// Trigonometric Arc Cosecant in radian + /// + /// + /// The angle in radian angle. + /// + /// + /// The inverse cosecant of the radian angle. + /// + /// + /// if -1 < < 1. + /// + public static double InverseCosecant(double radian) + { + return Math.Asin(1 / radian); + } + + /// + /// Trigonometric Arc Cosecant of this Complex number. + /// + /// + /// The complex value. + /// + /// + /// The arc cosecant of a complex number. + /// + public static Complex InverseCosecant(this Complex value) + { + var inv = 1 / value; + return -Complex.I * ((Complex.I * inv) + (1 - inv.Square()).SquareRoot()).NaturalLogarithm(); + } + + /// + /// Trigonometric Arc Cosine in radian + /// + /// + /// The angle in radian angle. + /// + /// + /// The inverse cosine of the radian angle. + /// + /// + /// if 1 < or < -1. + /// + public static double InverseCosine(double radian) + { + return Math.Acos(radian); + } + + /// + /// Trigonometric Arc Cosine of this Complex number. + /// + /// + /// The complex value. + /// + /// + /// The arc cosine of a complex number. + /// + public static Complex InverseCosine(this Complex value) + { + return -Complex.I * (value + (Complex.I * (1 - value.Square()).SquareRoot())).NaturalLogarithm(); + } + + /// + /// Trigonometric Arc Cotangent in radian + /// + /// + /// The angle in radian angle. + /// + /// + /// The inverse cotangent of the radian angle. + /// + public static double InverseCotangent(double radian) + { + return Math.Atan(1 / radian); + } + + /// + /// Trigonometric Arc Cotangent of this Complex number. + /// + /// + /// The complex value. + /// + /// + /// The arc cotangent of a complex number. + /// + public static Complex InverseCotangent(this Complex value) + { + if (value.IsZero) + { + return Math.PI / 2.0; + } + + var inv = Complex.I / value; + return (Complex.I * 0.5) * ((1.0 - inv).NaturalLogarithm() - (1.0 + inv).NaturalLogarithm()); + } + + /// + /// Trigonometric Hyperbolic Arc Cosecant + /// + /// + /// The angle in radian angle. + /// + /// + /// The inverse hyperbolic cosecant of the radian angle. + /// + public static double InverseHyperbolicCosecant(double radian) + { + return InverseHyperbolicSine(1 / radian); + } + + /// + /// Trigonometric Hyperbolic Arc Cosecant of this Complex number. + /// + /// + /// The complex value. + /// + /// + /// The hyperbolic arc cosecant of a complex number. + /// + public static Complex InverseHyperbolicCosecant(this Complex value) + { + var inv = 1 / value; + return (inv + (inv.Square() + 1).SquareRoot()).NaturalLogarithm(); + } + + /// + /// Trigonometric Hyperbolic Area Cosine + /// + /// + /// The angle in radian angle. + /// + /// + /// The inverse hyperbolic cosine of the radian angle. + /// + public static double InverseHyperbolicCosine(double radian) + { + return Math.Log(radian + (Math.Sqrt(radian - 1) * Math.Sqrt(radian + 1)), Math.E); + } + + /// + /// Trigonometric Hyperbolic Arc Cosine of this Complex number. + /// + /// + /// The complex value. + /// + /// + /// The hyperbolic arc cosine of a complex number. + /// + public static Complex InverseHyperbolicCosine(this Complex value) + { + return (value + ((value - 1).SquareRoot() * (value + 1).SquareRoot())).NaturalLogarithm(); + } + + /// + /// Trigonometric Hyperbolic Arc Cotangent + /// + /// + /// The angle in radian angle. + /// + /// + /// The inverse hyperbolic cotangent of the radian angle. + /// + public static double InverseHyperbolicCotangent(double radian) + { + return 0.5 * Math.Log((radian + 1) / (radian - 1), Math.E); + } + + /// + /// Trigonometric Hyperbolic Arc Cotangent of this Complex number. + /// + /// + /// The complex value. + /// + /// + /// The hyperbolic arc cotangent of a complex number. + /// + public static Complex InverseHyperbolicCotangent(this Complex value) + { + var inv = 1.0 / value; + return 0.5 * ((1.0 + inv).NaturalLogarithm() - (1.0 - inv).NaturalLogarithm()); + } + + /// + /// Trigonometric Hyperbolic Area Secant + /// + /// + /// The angle in radian angle. + /// + /// + /// The inverse hyperbolic secant of the radian angle. + /// + public static double InverseHyperbolicSecant(double radian) + { + return InverseHyperbolicCosine(1 / radian); + } + + /// + /// Trigonometric Hyperbolic Arc Secant of this Complex number. + /// + /// + /// The complex value. + /// + /// + /// The hyperbolic arc secant of a complex number. + /// + public static Complex InverseHyperbolicSecant(this Complex value) + { + var inv = 1 / value; + return (inv + ((inv - 1).SquareRoot() * (inv + 1).SquareRoot())).NaturalLogarithm(); + } + + /// + /// Trigonometric Hyperbolic Area Sine + /// + /// + /// The angle in radian angle. + /// + /// + /// The inverse hyperbolic sine of the radian angle. + /// + public static double InverseHyperbolicSine(double radian) + { + return Math.Log(radian + Math.Sqrt((radian * radian) + 1), Math.E); + } + + /// + /// Trigonometric Hyperbolic Arc Sine of this Complex number. + /// + /// + /// The complex value. + /// + /// + /// The hyperbolic arc sine of a complex number. + /// + public static Complex InverseHyperbolicSine(this Complex value) + { + return (value + (value.Square() + 1).SquareRoot()).NaturalLogarithm(); + } + + /// + /// Trigonometric Hyperbolic Area Tangent + /// + /// + /// The angle in radian angle. + /// + /// + /// The inverse hyperbolic tangent of the radian angle. + /// + public static double InverseHyperbolicTangent(double radian) + { + return 0.5 * Math.Log((1 + radian) / (1 - radian), Math.E); + } + + /// + /// Trigonometric Hyperbolic Arc Tangent of this Complex number. + /// + /// + /// The complex value. + /// + /// + /// The hyperbolic arc tangent of a complex number. + /// + public static Complex InverseHyperbolicTangent(this Complex value) + { + return 0.5 * ((1 + value).NaturalLogarithm() - (1 - value).NaturalLogarithm()); + } + + /// + /// Trigonometric Arc Secant in radian + /// + /// + /// The angle in radian angle. + /// + /// + /// The inverse secant of the radian angle. + /// + public static double InverseSecant(double radian) + { + return Math.Acos(1 / radian); + } + + /// + /// Trigonometric Arc Secant of this Complex number. + /// + /// + /// The complex value. + /// + /// + /// The arc secant of a complex number. + /// + public static Complex InverseSecant(this Complex value) + { + var inv = 1 / value; + return -Complex.I * (inv + (Complex.I * (1 - inv.Square()).SquareRoot())).NaturalLogarithm(); + } + + /// + /// Trigonometric Arc Sine in radian + /// + /// + /// The angle in radian angle. + /// + /// + /// The inverse sine of the radian angle. + /// + public static double InverseSine(double radian) + { + return Math.Asin(radian); + } + + /// + /// Trigonometric Arc Sine of this Complex number. + /// + /// + /// The complex value. + /// + /// + /// The arc sine of a complex number. + /// + public static Complex InverseSine(this Complex value) + { + return -Complex.I * ((1 - value.Square()).SquareRoot() + (Complex.I * value)).NaturalLogarithm(); + } + + /// + /// Trigonometric Arc Tangent in radian + /// + /// + /// The angle in radian angle. + /// + /// + /// The inverse tangent of the radian angle. + /// + public static double InverseTangent(double radian) + { + return Math.Atan(radian); + } + + /// + /// Trigonometric Arc Tangent of this Complex number. + /// + /// + /// The complex value. + /// + /// + /// The arc tangent of a complex number. + /// + public static Complex InverseTangent(this Complex value) + { + var iz = new Complex(-value.Imaginary, value.Real); // I*this + return new Complex(0, 0.5) * ((1 - iz).NaturalLogarithm() - (1 + iz).NaturalLogarithm()); + } + + /// + /// Converts a radian (2*Pi-periodic) angle to a degree (360-periodic) angle. + /// + /// + /// The radian to convert. + /// + /// + /// The converted degree. + /// + public static double RadianToDegree(double radian) + { + return radian / Constants.Degree; + } + + /// + /// Converts a radian (2*Pi-periodic) angle to a grad (400-periodic) angle. + /// + /// + /// The radian to convert. + /// + /// + /// The converted grad. + /// + public static double RadianToGrad(double radian) + { + return radian / Constants.Grad; + } + + /// + /// Trigonometric Secant of an angle in radian + /// + /// + /// The angle in radian. + /// + /// + /// The secant of the radian angle. + /// + public static double Secant(double radian) + { + return 1 / Math.Cos(radian); + } + + /// + /// Trigonometric Secant of a Complex number. + /// + /// + /// The complex value. + /// + /// + /// The secant of the complex number. + /// + public static Complex Secant(this Complex value) + { + if (value.IsReal) + { + return new Complex(Secant(value.Real), 0d); + } + + var cosr = Cosine(value.Real); + var sinhi = HyperbolicSine(value.Imaginary); + var denom = (cosr * cosr) + (sinhi * sinhi); + + return new Complex(cosr * HyperbolicCosine(value.Imaginary) / denom, Sine(value.Real) * sinhi / denom); + } + + /// + /// Trigonometric Sine of an angle in radian + /// + /// + /// The angle in radian. + /// + /// + /// The sine of the radian angle. + /// + public static double Sine(double radian) + { + return Math.Sin(radian); + } + + /// + /// Trigonometric Sine of a Complex number. + /// + /// + /// The complex value. + /// + /// + /// The sine of the complex number. + /// + public static Complex Sine(this Complex value) + { + if (value.IsReal) + { + return new Complex(Sine(value.Real), 0.0); + } + + return new Complex( + Sine(value.Real) * HyperbolicCosine(value.Imaginary), + Cosine(value.Real) * HyperbolicSine(value.Imaginary)); + } + + /// + /// Trigonometric Tangent of an angle in radian + /// + /// + /// The angle in radian. + /// + /// + /// The tangent of the radian angle. + /// + public static double Tangent(double radian) + { + return Math.Tan(radian); + } + + /// + /// Trigonometric Tangent of a Complex number. + /// + /// + /// The complex value. + /// + /// + /// The tangent of the complex number. + /// + public static Complex Tangent(this Complex value) + { + if (value.IsReal) + { + return new Complex(Tangent(value.Real), 0.0); + } + + var cosr = Cosine(value.Real); + var sinhi = HyperbolicSine(value.Imaginary); + var denom = (cosr * cosr) + (sinhi * sinhi); + + return new Complex(Sine(value.Real) * cosr / denom, sinhi * HyperbolicCosine(value.Imaginary) / denom); + } + } +} \ No newline at end of file