#region Math.NET Iridium (LGPL) by Ruegg

// Math.NET Iridium, part of the Math.NET Project

// http://mathnet.opensourcedotnet.info

//

// Copyright (c) 2002-2008, Christoph Rüegg, http://christoph.ruegg.name

//

// This program is free software; you can redistribute it and/or modify

// it under the terms of the GNU Lesser General Public License as published 

// by the Free Software Foundation; either version 2 of the License, or

// (at your option) any later version.

//

// This program is distributed in the hope that it will be useful,

// but WITHOUT ANY WARRANTY; without even the implied warranty of

// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

// GNU Lesser General Public License for more details.

//

// You should have received a copy of the GNU Lesser General Public 

// License along with this program; if not, write to the Free Software

// Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.

#endregion



using System;



namespace MathNet.Numerics

{

    /// <summary>

    /// Double-precision trigonometry toolkit.

    /// </summary>

    public static class Trig

    {

        #region Angle Conversion



        /// <summary>

        /// Converts a degree (360-periodic) angle to a radian (2*Pi-periodic) angle.

        /// </summary>

        public static

        double

        DegreeToRadian(

            double degree

            )

        {

            return degree * Constants.Degree;

        }



        /// <summary>

        /// Converts a radian (2*Pi-periodic) angle to a degree (360-periodic) angle.

        /// </summary>

        public static

        double

        RadianToDegree(

            double radian

            )

        {

            return radian / Constants.Degree;

        }



        /// <summary>

        /// Converts a newgrad (400-periodic) angle to a radian (2*Pi-periodic) angle.

        /// </summary>

        public static

        double

        GradToRadian(

            double newgrad

            )

        {

            return newgrad * Constants.Grad;

        }



        /// <summary>

        /// Converts a radian (2*Pi-periodic) angle to a newgrad (400-periodic) angle.

        /// </summary>

        public static

        double

        RadianToGrad(

            double radian

            )

        {

            return radian / Constants.Grad;

        }



        /// <summary>

        /// Converts a degree (360-periodic) angle to a newgrad (400-periodic) angle.

        /// </summary>

        public static

        double

        DegreeToGrad(

            double degree

            )

        {

            return degree / 9 * 10;

        }



        /// <summary>

        /// Converts a newgrad (400-periodic) angle to a degree (360-periodic) angle.

        /// </summary>

        public static

        double

        GradToDegree(

            double newgrad

            )

        {

            return newgrad / 10 * 9;

        }



        #endregion



        #region Trigonometric Functions



        /// <summary>

        /// Trigonometric Sine (Sinus) of an angle in radian

        /// </summary>

        public static

        double

        Sine(

            double radian

            )

        {

            return Math.Sin(radian);

        }



        /// <summary>

        /// Trigonometric Cosine (Cosinus) of an angle in radian

        /// </summary>

        public static

        double

        Cosine(

            double radian

            )

        {

            return Math.Cos(radian);

        }



        /// <summary>

        /// Trigonometric Tangent (Tangens) of an angle in radian

        /// </summary>

        public static

        double

        Tangent(

            double radian

            )

        {

            return Math.Tan(radian);

        }



        /// <summary>

        /// Trigonometric Cotangent (Cotangens) of an angle in radian

        /// </summary>

        public static

        double

        Cotangent(

            double radian

            )

        {

            return 1 / Math.Tan(radian);

        }



        /// <summary>

        /// Trigonometric Secant (Sekans) of an angle in radian

        /// </summary>

        public static

        double

        Secant(

            double radian

            )

        {

            return 1 / Math.Cos(radian);

        }



        /// <summary>

        /// Trigonometric Cosecant (Cosekans) of an angle in radian

        /// </summary>

        public static

        double

        Cosecant(

            double radian

            )

        {

            return 1 / Math.Sin(radian);

        }



        #endregion



        #region Trigonometric Inverse Functions



        /// <summary>

        /// Trigonometric Arcus Sine (Arkussinus) in radian

        /// </summary>

        public static

        double

        InverseSine(

            double real

            )

        {

            return Math.Asin(real);

        }



        /// <summary>

        /// Trigonometric Arcus Cosine (Arkuscosinus) in radian

        /// </summary>

        public static

        double

        InverseCosine(

            double real

            )

        {

            return Math.Acos(real);

        }



        /// <summary>

        /// Trigonometric Arcus Tangent (Arkustangens) in radian

        /// </summary>

        public static

        double

        InverseTangent(

            double real

            )

        {

            return Math.Atan(real);

        }



        /// <summary>

        /// The principal argument (in radian) of the complex number x+I*y

        /// </summary>

        /// <param name="nominator">y</param>

        /// <param name="denominator">x</param>

        public static

        double

        InverseTangentFromRational(

            double nominator,

            double denominator

            )

        {

            return Math.Atan2(nominator, denominator);

        }



        /// <summary>

        /// Trigonometric Arcus Cotangent (Arkuscotangens) in radian

        /// </summary>

        public static

        double

        InverseCotangent(

            double real

            )

        {

            return Math.Atan(1 / real);

        }



        /// <summary>

        /// Trigonometric Arcus Secant (Arkussekans) in radian

        /// </summary>

        public static

        double

        InverseSecant(

            double real

            )

        {

            return Math.Acos(1 / real);

        }



        /// <summary>

        /// Trigonometric Arcus Cosecant (Arkuscosekans) in radian

        /// </summary>

        public static

        double

        InverseCosecant(

            double real

            )

        {

            return Math.Asin(1 / real);

        }



        #endregion



        #region Hyperbolic Functions



        /// <summary>

        /// Trigonometric Hyperbolic Sine (Sinus hyperbolicus)

        /// </summary>

        public static

        double

        HyperbolicSine(

            double radian

            )

        {

            // NOT SUPPORTED BY COMPACT FRAMEWORK!!???

            // return Math.Sinh(x)

            return (Math.Exp(radian) - Math.Exp(-radian)) / 2;

        }



        /// <summary>

        /// Trigonometric Hyperbolic Cosine (Cosinus hyperbolicus)

        /// </summary>

        public static

        double

        HyperbolicCosine(

            double radian

            )

        {

            // NOT SUPPORTED BY COMPACT FRAMEWORK!!???

            // return Math.Cosh(x);

            return (Math.Exp(radian) + Math.Exp(-radian)) / 2;

        }



        /// <summary>

        /// Trigonometric Hyperbolic Tangent (Tangens hyperbolicus)

        /// </summary>

        public static

        double

        HyperbolicTangent(

            double radian

            )

        {

            // NOT SUPPORTED BY COMPACT FRAMEWORK!!???

            // return Math.Tanh(x);

            double e1 = Math.Exp(radian);

            double e2 = Math.Exp(-radian);

            return (e1 - e2) / (e1 + e2);

        }



        /// <summary>

        /// Trigonometric Hyperbolic Cotangent (Cotangens hyperbolicus)

        /// </summary>

        public static

        double

        HyperbolicCotangent(

            double radian

            )

        {

            // NOT SUPPORTED BY COMPACT FRAMEWORK!!???

            // return 1/Math.Tanh(x);

            double e1 = Math.Exp(radian);

            double e2 = Math.Exp(-radian);

            return (e1 + e2) / (e1 - e2);

        }



        /// <summary>

        /// Trigonometric Hyperbolic Secant (Sekans hyperbolicus)

        /// </summary>

        public static

        double

        HyperbolicSecant(

            double radian

            )

        {

            return 1 / HyperbolicCosine(radian);

        }



        /// <summary>

        /// Trigonometric Hyperbolic Cosecant (Cosekans hyperbolicus)

        /// </summary>

        public static

        double

        HyperbolicCosecant(

            double radian

            )

        {

            return 1 / HyperbolicSine(radian);

        }



        #endregion



        #region Hyperbolic Area Functions



        /// <summary>

        /// Trigonometric Hyperbolic Area Sine (Areasinus hyperbolicus)

        /// </summary>

        public static

        double

        InverseHyperbolicSine(

            double real

            )

        {

            return Math.Log(

                real + Math.Sqrt(real * real + 1),

                Math.E

                );

        }



        /// <summary>

        /// Trigonometric Hyperbolic Area Cosine (Areacosinus hyperbolicus)

        /// </summary>

        public static

        double

        InverseHyperbolicCosine(

            double real

            )

        {

            return Math.Log(

                real + Math.Sqrt(real - 1) * Math.Sqrt(real + 1),

                Math.E

                );

        }



        /// <summary>

        /// Trigonometric Hyperbolic Area Tangent (Areatangens hyperbolicus)

        /// </summary>

        public static

        double

        InverseHyperbolicTangent(

            double real

            )

        {

            return 0.5 * Math.Log(

                (1 + real) / (1 - real),

                Math.E

                );

        }



        /// <summary>

        /// Trigonometric Hyperbolic Area Cotangent (Areacotangens hyperbolicus)

        /// </summary>

        public static

        double

        InverseHyperbolicCotangent(

            double real

            )

        {

            return 0.5 * Math.Log(

                (real + 1) / (real - 1),

                Math.E

                );

        }



        /// <summary>

        /// Trigonometric Hyperbolic Area Secant (Areasekans hyperbolicus)

        /// </summary>

        public static

        double

        InverseHyperbolicSecant(

            double real

            )

        {

            return InverseHyperbolicCosine(1 / real);

        }



        /// <summary>

        /// Trigonometric Hyperbolic Area Cosecant (Areacosekans hyperbolicus)

        /// </summary>

        public static

        double

        InverseHyperbolicCosecant(

            double real

            )

        {

            return InverseHyperbolicSine(1 / real);

        }



        #endregion

    }

}