233 lines
8.3 KiB
VB.net
233 lines
8.3 KiB
VB.net
#Region "Microsoft.VisualBasic::b040327637042e7f47b204fa6b7081ca, Microsoft.VisualBasic.Core\Extensions\Math\Trigonometric\Trigonometric2.vb"
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' Author:
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'
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' asuka (amethyst.asuka@gcmodeller.org)
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' xie (genetics@smrucc.org)
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' xieguigang (xie.guigang@live.com)
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'
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' Copyright (c) 2018 GPL3 Licensed
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'
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'
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' GNU GENERAL PUBLIC LICENSE (GPL3)
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'
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'
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' This program is free software: you can redistribute it and/or modify
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' it under the terms of the GNU General Public License as published by
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' the Free Software Foundation, either version 3 of the License, or
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' (at your option) any later version.
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'
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' This program is distributed in the hope that it will be useful,
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' but WITHOUT ANY WARRANTY; without even the implied warranty of
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' MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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' GNU General Public License for more details.
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'
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' You should have received a copy of the GNU General Public License
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' along with this program. If not, see <http://www.gnu.org/licenses/>.
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' /********************************************************************************/
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' Summaries:
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' Module Trigonometric
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'
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' Function: Arccos, Arccosec, Arccotan, Arcsec, Arcsin
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' Cosec, Cotan, HArccos, HArccosec, HArccotan
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' HArcsec, HArcsin, Harctan, HCos, HCosec
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' HCotan, HSec, HSin, HTan, Sec
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'
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'
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' /********************************************************************************/
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#End Region
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Imports sys = System.Math
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Namespace Math
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Partial Module Trigonometric
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''' <summary>
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''' Secant（正割） ``Sec(X) = 1 / Cos(X)``
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''' </summary>
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''' <param name="x"></param>
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''' <returns></returns>
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Public Function Sec(x As Double) As Double
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Return 1 / sys.Cos(x)
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End Function
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''' <summary>
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''' Cosecant（余割） ``Cosec(X) = 1 / Sin(X)``
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''' </summary>
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''' <param name="x"></param>
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''' <returns></returns>
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Public Function Cosec(x As Double) As Double
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Return 1 / sys.Sin(x)
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End Function
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''' <summary>
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''' Cotangent（余切） ``Cotan(X) = 1 / Tan(X)``
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''' </summary>
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''' <param name="x"></param>
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''' <returns></returns>
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Public Function Cotan(x As Double) As Double
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Return 1 / sys.Tan(x)
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End Function
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''' <summary>
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''' Inverse Sine（反正弦） ``Arcsin(X) = Atn(X / Sqr(-X * X + 1))``
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''' </summary>
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''' <param name="x"></param>
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''' <returns></returns>
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Public Function Arcsin(x As Double) As Double
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Return Atn(x / sys.Sqrt(-x * x + 1))
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End Function
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''' <summary>
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''' Inverse Cosine（反余弦） ``Arccos(X) = Atn(-X / Sqr(-X * X + 1)) + 2 * Atn(1)``
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''' </summary>
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''' <param name="x"></param>
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''' <returns></returns>
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Public Function Arccos(x As Double) As Double
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Return Atn(-x / sys.Sqrt(-x * x + 1)) + 2 * Atn(1)
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End Function
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''' <summary>
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''' Inverse Secant（反正割） ``Arcsec(X) = Atn(X / Sqr(X * X - 1)) + Sgn((X) - 1) * (2 * Atn(1))``
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''' </summary>
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''' <param name="x"></param>
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''' <returns></returns>
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Public Function Arcsec(x As Double) As Double
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Return Atn(x / sys.Sqrt(x * x - 1)) + sys.Sign((x) - 1) * (2 * Atn(1))
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End Function
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''' <summary>
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''' Inverse Cosecant（反余割） ``Arccosec(X) = Atn(X / Sqr(X * X - 1)) + (Sgn(X) - 1) * (2 * Atn(1))``
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''' </summary>
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''' <param name="x"></param>
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''' <returns></returns>
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Public Function Arccosec(x As Double) As Double
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Return Atn(x / sys.Sqrt(x * x - 1)) + (sys.Sign(x) - 1) * (2 * Atn(1))
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End Function
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''' <summary>
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''' Inverse Cotangent（反余切） ``Arccotan(X) = Atn(X) + 2 * Atn(1)``
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''' </summary>
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''' <param name="x"></param>
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''' <returns></returns>
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Public Function Arccotan(x As Double) As Double
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Return Atn(x) + 2 * Atn(1)
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End Function
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''' <summary>
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''' Hyperbolic Sine（双曲正弦） ``HSin(X) = (Exp(X) - Exp(-X)) / 2``
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''' </summary>
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''' <param name="x"></param>
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''' <returns></returns>
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Public Function HSin(x As Double) As Double
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Return (sys.Exp(x) - sys.Exp(-x)) / 2
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End Function
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''' <summary>
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''' Hyperbolic Cosine（双曲余弦） ``HCos(X) = (Exp(X) + Exp(-X)) / 2``
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''' </summary>
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''' <param name="x"></param>
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''' <returns></returns>
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Public Function HCos(x As Double) As Double
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Return (sys.Exp(x) + sys.Exp(-x)) / 2
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End Function
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''' <summary>
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''' Hyperbolic Tangent（双曲正切） ``HTan(X) = (Exp(X) - Exp(-X)) / (Exp(X) + Exp(-X))``
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''' </summary>
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''' <param name="x"></param>
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''' <returns></returns>
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Public Function HTan(x As Double) As Double
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Return (sys.Exp(x) - sys.Exp(-x)) / (sys.Exp(x) + sys.Exp(-x))
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End Function
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''' <summary>
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''' Hyperbolic Secant（双曲正割） ``HSec(X) = 2 / (Exp(X) + Exp(-X))``
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''' </summary>
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''' <param name="x"></param>
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''' <returns></returns>
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Public Function HSec(x As Double) As Double
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Return 2 / (sys.Exp(x) + sys.Exp(-x))
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End Function
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''' <summary>
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''' Hyperbolic Cosecant（双曲余割） ``HCosec(X) = 2 / (Exp(X) - Exp(-X))``
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''' </summary>
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''' <param name="x"></param>
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''' <returns></returns>
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Public Function HCosec(x As Double) As Double
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Return 2 / (sys.Exp(x) - sys.Exp(-x))
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End Function
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''' <summary>
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''' Hyperbolic Cotangent（双曲余切） ``HCotan(X) = (Exp(X) + Exp(-X)) / (Exp(X) - Exp(-X))``
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''' </summary>
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''' <param name="x"></param>
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''' <returns></returns>
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Public Function HCotan(x As Double) As Double
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Return (sys.Exp(x) + sys.Exp(-x)) / (sys.Exp(x) - sys.Exp(-x))
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End Function
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''' <summary>
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''' Inverse Hyperbolic Sine（反双曲正弦） ``HArcsin(X) = Log(X + Sqr(X * X + 1))``
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''' </summary>
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''' <param name="x"></param>
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''' <returns></returns>
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Public Function HArcsin(x As Double) As Double
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Return sys.Log(x + sys.Sqrt(x * x + 1))
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End Function
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''' <summary>
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''' Inverse Hyperbolic Cosine（反双曲余弦） ``HArccos(X) = Log(X + Sqr(X * X - 1))``
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''' </summary>
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''' <param name="x"></param>
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''' <returns></returns>
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Public Function HArccos(x As Double) As Double
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Return sys.Log(x + sys.Sqrt(x * x - 1))
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End Function
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''' <summary>
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''' Inverse Hyperbolic Tangent（反双曲正切） ``HArctan(X) = Log((1 + X) / (1 - X)) / 2``
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''' </summary>
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''' <param name="x"></param>
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''' <returns></returns>
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Public Function Harctan(x As Double) As Double
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Return sys.Log((1 + x) / (1 - x)) / 2
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End Function
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''' <summary>
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''' Inverse Hyperbolic Secant（反双曲正割） ``HArcsec(X) = Log((Sqr(-X * X + 1) + 1) / X)``
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''' </summary>
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''' <param name="x"></param>
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''' <returns></returns>
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Public Function HArcsec(x As Double) As Double
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Return sys.Log((sys.Sqrt(-x * x + 1) + 1) / x)
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End Function
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''' <summary>
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''' Inverse Hyperbolic Cosecant（反双曲余割） ``HArccosec(X) = Log((Sgn(X) * Sqr(X * X + 1) + 1) / X)``
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''' </summary>
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''' <param name="x"></param>
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''' <returns></returns>
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Public Function HArccosec(x As Double) As Double
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Return sys.Log((sys.Sign(x) * sys.Sqrt(x * x + 1) + 1) / x)
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End Function
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''' <summary>
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''' Inverse Hyperbolic Cotangent（反双曲余切） ``HArccotan(X) = Log((X + 1) / (X - 1)) / 2``
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''' </summary>
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''' <param name="x"></param>
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''' <returns></returns>
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Public Function HArccotan(x As Double) As Double
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Return sys.Log((x + 1) / (x - 1)) / 2
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End Function
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End Module
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End Namespace
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