public static ComplexD Sqrt(ComplexD a)
{
ComplexD result = ComplexD.Zero;
if ((a.Real == 0.0) && (a.Imaginary == 0.0))
{
return(result);
}
else if (a.Imaginary == 0.0)
{
result.Real = System.Math.Sqrt(a.Real);
result.Imaginary = 0.0;
}
else
{
double modulus = a.GetModulus();
result.Real = System.Math.Sqrt(0.5 * (modulus + a.Real));
result.Imaginary = System.Math.Sqrt(0.5 * (modulus + a.Real));
if (a.Imaginary < 0.0)
{
result.Imaginary = -result.Imaginary;
}
}
return(result);
}
public static ComplexD Log(ComplexD a)
{
ComplexD result = ComplexD.Zero;
if ((a.Real > 0.0) && (a.Imaginary == 0.0))
{
result.Real = System.Math.Log(a.Real);
result.Imaginary = 0.0;
}
else if (a.Real == 0.0)
{
if (a.Imaginary > 0.0)
{
result.Real = System.Math.Log(a.Imaginary);
result.Imaginary = MathFunctions.HalfPI;
}
else
{
result.Real = System.Math.Log(-(a.Imaginary));
result.Imaginary = -MathFunctions.HalfPI;
}
}
else
{
result.Real = System.Math.Log(a.GetModulus());
result.Imaginary = System.Math.Atan2(a.Imaginary, a.Real);
}
return(result);
}
/// <summary>
/// Multiplies two complex numbers.
/// </summary>
/// <param name="a">A <see cref="ComplexD"/> instance.</param>
/// <param name="b">A <see cref="ComplexD"/> instance.</param>
/// <returns>A new <see cref="ComplexD"/> instance containing the result.</returns>
public static ComplexD Multiply(ComplexD a, ComplexD b)
{
// (x + yi)(u + vi) = (xu � yv) + (xv + yu)i.
double x = a.Real, y = a.Imaginary;
double u = b.Real, v = b.Imaginary;
return(new ComplexD(x * u - y * v, x * v + y * u));
}
/// <summary>
/// Tests whether two complex numbers are approximately equal given a tolerance value.
/// </summary>
/// <param name="a">A <see cref="ComplexD"/> instance.</param>
/// <param name="b">A <see cref="ComplexD"/> instance.</param>
/// <param name="tolerance">The tolerance value used to test approximate equality.</param>
/// <returns>True if the two vectors are approximately equal; otherwise, False.</returns>
public static bool ApproxEqual(ComplexD a, ComplexD b, double tolerance)
{
return
(
(System.Math.Abs(a.Real - b.Real) <= tolerance) &&
(System.Math.Abs(a.Imaginary - b.Imaginary) <= tolerance)
);
}
/// <summary>
/// Multiplies two complex numbers and put the result in a third complex number.
/// </summary>
/// <param name="a">A <see cref="ComplexD"/> instance.</param>
/// <param name="b">A <see cref="ComplexD"/> instance.</param>
/// <param name="result">A <see cref="ComplexD"/> instance to hold the result.</param>
public static void Multiply(ComplexD a, ComplexD b, ComplexD result)
{
// (x + yi)(u + vi) = (xu � yv) + (xv + yu)i.
double x = a.Real, y = a.Imaginary;
double u = b.Real, v = b.Imaginary;
result.Real = x * u - y * v;
result.Imaginary = x * v + y * u;
}
/// <summary>
/// Returns a value indicating whether this instance is equal to
/// the specified object.
/// </summary>
/// <param name="obj">An object to compare to this instance.</param>
/// <returns>True if <paramref name="obj"/> is a <see cref="ComplexD"/> and has the same values as this instance; otherwise, False.</returns>
public override bool Equals(object obj)
{
if (obj is ComplexD)
{
ComplexD c = (ComplexD)obj;
return((this.Real == c.Real) && (this.Imaginary == c.Imaginary));
}
return(false);
}
/// <summary>
/// Converts the given object to the type of this converter, using the specified context and culture information.
/// </summary>
/// <param name="context">An <see cref="ITypeDescriptorContext"/> that provides a format context.</param>
/// <param name="culture">The <see cref="System.Globalization.CultureInfo"/> to use as the current culture. </param>
/// <param name="value">The <see cref="Object"/> to convert.</param>
/// <returns>An <see cref="Object"/> that represents the converted value.</returns>
/// <exception cref="ParseException">Failed parsing from string.</exception>
public override object ConvertFrom(ITypeDescriptorContext context, System.Globalization.CultureInfo culture, object value)
{
if (value.GetType() == typeof(string))
{
return(ComplexD.Parse((string)value));
}
return(base.ConvertFrom(context, culture, value));
}
/// <summary>
/// Divides a scalar by a complex.
/// </summary>
/// <param name="a">A <see cref="ComplexD"/> instance.</param>
/// <param name="s">A scalar.</param>
/// <returns>A new <see cref="ComplexD"/> instance containing the result.</returns>
public static ComplexD Divide(double s, ComplexD a)
{
if ((a.Real == 0) || (a.Imaginary == 0))
{
throw new DivideByZeroException();
}
return(new ComplexD(
s / a.Real,
s / a.Imaginary));
}
public static ComplexD Exp(ComplexD a)
{
ComplexD result = ComplexD.Zero;
double r = System.Math.Exp(a.Real);
result.Real = r * System.Math.Cos(a.Imaginary);
result.Imaginary = r * System.Math.Sin(a.Imaginary);
return(result);
}
/// <summary>
/// Divides a complex by a scalar.
/// </summary>
/// <param name="a">A <see cref="ComplexD"/> instance.</param>
/// <param name="s">A scalar.</param>
/// <returns>A new <see cref="ComplexD"/> instance containing the result.</returns>
public static ComplexD Divide(ComplexD a, double s)
{
if (s == 0)
{
throw new DivideByZeroException();
}
return(new ComplexD(
a.Real / s,
a.Imaginary / s));
}
/// <summary>
/// Converts the given value object to the specified type, using the specified context and culture information.
/// </summary>
/// <param name="context">An <see cref="ITypeDescriptorContext"/> that provides a format context.</param>
/// <param name="culture">A <see cref="System.Globalization.CultureInfo"/> object. If a null reference (Nothing in Visual Basic) is passed, the current culture is assumed.</param>
/// <param name="value">The <see cref="Object"/> to convert.</param>
/// <param name="destinationType">The Type to convert the <paramref name="value"/> parameter to.</param>
/// <returns>An <see cref="Object"/> that represents the converted value.</returns>
public override object ConvertTo(ITypeDescriptorContext context, System.Globalization.CultureInfo culture, object value, Type destinationType)
{
if ((destinationType == typeof(string)) && (value is ComplexD))
{
ComplexD c = (ComplexD)value;
return(c.ToString());
}
return(base.ConvertTo(context, culture, value, destinationType));
}
/// <summary>
/// Divides a complex by a scalar and put the result into another complex number.
/// </summary>
/// <param name="a">A <see cref="ComplexD"/> instance.</param>
/// <param name="s">A scalar.</param>
/// <param name="result">A <see cref="ComplexD"/> instance to hold the result.</param>
public static void Divide(ComplexD a, double s, ComplexD result)
{
if (s == 0)
{
throw new DivideByZeroException();
}
result.Real = a.Real / s;
result.Imaginary = a.Imaginary / s;
}
/// <summary>
/// Divides a scalar by a complex and put the result into another complex number.
/// </summary>
/// <param name="a">A <see cref="ComplexD"/> instance.</param>
/// <param name="s">A scalar.</param>
/// <param name="result">A <see cref="ComplexD"/> instance to hold the result.</param>
public static void Divide(double s, ComplexD a, ComplexD result)
{
if ((a.Real == 0) || (a.Imaginary == 0))
{
throw new DivideByZeroException();
}
result.Real = s / a.Real;
result.Imaginary = s / a.Imaginary;
}
/// <summary>
/// Divides a complex by a complex and put the result in a third complex number.
/// </summary>
/// <param name="a">A <see cref="ComplexD"/> instance.</param>
/// <param name="b">A <see cref="ComplexD"/> instance.</param>
/// <param name="result">A <see cref="ComplexD"/> instance to hold the result.</param>
public static void Divide(ComplexD a, ComplexD b, ComplexD result)
{
double x = a.Real, y = a.Imaginary;
double u = b.Real, v = b.Imaginary;
double modulusSquared = u * u + v * v;
if (modulusSquared == 0)
{
throw new DivideByZeroException();
}
double invModulusSquared = 1 / modulusSquared;
result.Real = (x * u + y * v) * invModulusSquared;
result.Imaginary = (y * u - x * v) * invModulusSquared;
}
/// <summary>
/// Divides a complex by a complex.
/// </summary>
/// <param name="a">A <see cref="ComplexD"/> instance.</param>
/// <param name="b">A <see cref="ComplexD"/> instance.</param>
/// <returns>A new <see cref="ComplexD"/> instance containing the result.</returns>
public static ComplexD Divide(ComplexD a, ComplexD b)
{
double x = a.Real, y = a.Imaginary;
double u = b.Real, v = b.Imaginary;
double modulusSquared = u * u + v * v;
if (modulusSquared == 0)
{
throw new DivideByZeroException();
}
double invModulusSquared = 1 / modulusSquared;
return(new ComplexD(
(x * u + y * v) * invModulusSquared,
(y * u - x * v) * invModulusSquared));
}
public static ComplexD Cos(ComplexD a)
{
ComplexD result = ComplexD.Zero;
if (a.Imaginary == 0.0)
{
result.Real = System.Math.Cos(a.Real);
result.Imaginary = 0.0;
}
else
{
result.Real = System.Math.Cos(a.Real) * System.Math.Cosh(a.Imaginary);
result.Imaginary = -System.Math.Sin(a.Real) * System.Math.Sinh(a.Imaginary);
}
return(result);
}
public static ComplexD Tan(ComplexD a)
{
ComplexD result = ComplexD.Zero;
if (a.Imaginary == 0.0)
{
result.Real = System.Math.Tan(a.Real);
result.Imaginary = 0.0;
}
else
{
double real2 = 2 * a.Real;
double imag2 = 2 * a.Imaginary;
double denom = System.Math.Cos(real2) + System.Math.Cosh(real2);
result.Real = System.Math.Sin(real2) / denom;
result.Imaginary = System.Math.Sinh(imag2) / denom;
}
return(result);
}
public static ComplexD Acot(ComplexD complex)
{
ComplexD tmp = new ComplexD(-complex.Imaginary, complex.Real);
return (new ComplexD(0, 0.5)) * (ComplexD.Log(1 + tmp) - ComplexD.Log(1 - tmp)) + MathFunctions.HalfPI;
}
/// <summary>
/// Calculates the hyperbolic cosine of the specified complex number.
/// </summary>
/// <param name="complex">A <see cref="ComplexD"/> instance.</param>
/// <returns>Returns the hyperbolic cosine of the specified complex number.</returns>
public static ComplexD Cosh(ComplexD complex)
{
if (complex.IsReal)
{
return new ComplexD(System.Math.Cosh(complex.Real), 0.0);
}
return new ComplexD(
System.Math.Cosh(complex.Real) * System.Math.Cos(complex.Imaginary),
System.Math.Sinh(complex.Real) * System.Math.Sin(complex.Imaginary)
);
}
/// <summary>
/// Calculates the cosecant of the specified complex number.
/// </summary>
/// <param name="complex">A <see cref="ComplexD"/> instance.</param>
/// <returns>The cosecant of <paramref name="complex"/>.</returns>
public static ComplexD Csc(ComplexD complex)
{
ComplexD result = ComplexD.Zero;
if (complex.IsReal)
{
result.Real = MathFunctions.Csc(complex.Real);
}
else
{
double sinr = MathFunctions.Sin(complex.Real);
double sinhi = MathFunctions.Sinh(complex.Imaginary);
double denom = sinr * sinr + sinhi * sinhi;
result.Real = (sinr * MathFunctions.Cosh(complex.Imaginary)) / denom;
result.Imaginary = (-MathFunctions.Cos(complex.Real) * sinhi) / denom;
}
return result;
}
public static ComplexD Acos(ComplexD complex)
{
ComplexD result = 1 - ComplexD.Square(complex);
result = ComplexD.Sqrt(result);
result = ComplexD.I * result;
result = complex + result;
result = ComplexD.Log(result);
result = -ComplexD.I * result;
return result;
}
/// <summary>
/// Calculates a specified complex number raised by a specified power.
/// </summary>
/// <param name="complex">A <see cref="ComplexD"/> representing the number to raise.</param>
/// <param name="power">A <see cref="ComplexD"/> representing the power.</param>
/// <returns>The complex <paramref name="complex"/> raised by <paramref name="power"/>.</returns>
public static ComplexD Pow(ComplexD complex, ComplexD power)
{
return Exp(power * Log(complex));
}
/// <summary>
/// Calculates the cosine of the specified complex number.
/// </summary>
/// <param name="complex">A <see cref="ComplexD"/> instance.</param>
/// <returns>The cosine of <paramref name="complex"/>.</returns>
public static ComplexD Cos(ComplexD complex)
{
ComplexD result = ComplexD.Zero;
if (complex.IsReal)
{
result.Real = System.Math.Cos(complex.Real);
result.Imaginary = 0.0;
}
else
{
result.Real = System.Math.Cos(complex.Real) * System.Math.Cosh(complex.Imaginary);
result.Imaginary = -System.Math.Sin(complex.Real) * System.Math.Sinh(complex.Imaginary);
}
return result;
}
/// <summary>
/// Negates a complex number.
/// </summary>
/// <param name="a">A <see cref="ComplexD"/> instance.</param>
/// <returns>A new <see cref="ComplexD"/> instance containing the negated values.</returns>
public static ComplexD Negate(ComplexD a)
{
return(new ComplexD(-a.Real, -a.Imaginary));
}
/// <summary>
/// Divides a complex by a complex and put the result in a third complex number.
/// </summary>
/// <param name="left">A <see cref="ComplexD"/> instance.</param>
/// <param name="right">A <see cref="ComplexD"/> instance.</param>
/// <param name="result">A <see cref="ComplexD"/> instance to hold the result.</param>
/// <remarks>See http://mathworld.wolfram.com/ComplexDivision.html for further details.</remarks>
public static void Divide(ComplexD left, ComplexD right, ref ComplexD result)
{
double x = left.Real, y = left.Imaginary;
double u = right.Real, v = right.Imaginary;
double modulusSquared = u * u + v * v;
if (modulusSquared == 0)
{
throw new DivideByZeroException();
}
double invModulusSquared = 1 / modulusSquared;
result.Real = (x * u + y * v) * invModulusSquared;
result.Imaginary = (y * u - x * v) * invModulusSquared;
}
/// <summary>
/// Divides a complex by a scalar.
/// </summary>
/// <param name="complex">A <see cref="ComplexD"/> instance.</param>
/// <param name="scalar">A double-precision floating-point value.</param>
/// <returns>A new <see cref="ComplexD"/> instance containing the result.</returns>
public static ComplexD Divide(ComplexD complex, double scalar)
{
if (scalar == 0)
{
throw new DivideByZeroException();
}
return new ComplexD(
complex.Real / scalar,
complex.Imaginary / scalar);
}
/// <summary>
/// Tests whether two complex numbers are approximately equal using default tolerance value.
/// </summary>
/// <param name="a">A <see cref="ComplexD"/> instance.</param>
/// <param name="b">A <see cref="ComplexD"/> instance.</param>
/// <returns>True if the two vectors are approximately equal; otherwise, False.</returns>
public static bool ApproxEqual(ComplexD a, ComplexD b)
{
return(ApproxEqual(a, b, MathFunctions.EpsilonD));
}
/// <summary>
/// Calculates the hyperbolic cotangent of the specified complex number.
/// </summary>
/// <param name="complex">A <see cref="ComplexD"/> instance.</param>
/// <returns>Returns the hyperbolic cotangent of the specified complex number.</returns>
public static ComplexD Coth(ComplexD complex)
{
if (complex.IsReal)
{
return new ComplexD(MathFunctions.Coth(complex.Real), 0.0);
}
//return ComplexD.Divide(Cosh(complex), Sinh(complex));
double sini = -System.Math.Sin(complex.Imaginary);
double sinhr = System.Math.Sinh(complex.Real);
double denom = (sini * sini) + (sinhr * sinhr);
return new ComplexD(
(sinhr * System.Math.Cosh(complex.Real)) / denom,
(sini * System.Math.Cos(complex.Imaginary)) / denom
);
}
public static ComplexD Asinh(ComplexD complex)
{
ComplexD result = ComplexD.Sqrt(ComplexD.Square(complex) + 1);
result = ComplexD.Log(complex + result);
return result;
}
/// <summary>
/// Divides a scalar by a complex and put the result into another complex number.
/// </summary>
/// <param name="complex">A <see cref="ComplexD"/> instance.</param>
/// <param name="scalar">A double-precision floating-point value.</param>
/// <param name="result">A <see cref="ComplexD"/> instance to hold the result.</param>
public static void Divide(double scalar, ComplexD complex, ref ComplexD result)
{
if ((complex.Real == 0) || (complex.Imaginary == 0))
{
throw new DivideByZeroException();
}
result.Real = scalar / complex.Real;
result.Imaginary = scalar / complex.Imaginary;
}
/// <summary>
/// Divides a complex by a complex.
/// </summary>
/// <param name="left">A <see cref="ComplexD"/> instance.</param>
/// <param name="right">A <see cref="ComplexD"/> instance.</param>
/// <returns>A new <see cref="ComplexD"/> instance containing the result.</returns>
/// <remarks>See http://mathworld.wolfram.com/ComplexDivision.html for further details.</remarks>
public static ComplexD Divide(ComplexD left, ComplexD right)
{
double x = left.Real, y = left.Imaginary;
double u = right.Real, v = right.Imaginary;
double modulusSquared = u * u + v * v;
if (modulusSquared == 0)
{
throw new DivideByZeroException();
}
double invModulusSquared = 1 / modulusSquared;
return new ComplexD(
(x * u + y * v) * invModulusSquared,
(y * u - x * v) * invModulusSquared);
}
/// <summary>
/// Tests whether two complex numbers are approximately equal using default tolerance value.
/// </summary>
/// <param name="left">A <see cref="ComplexD"/> instance.</param>
/// <param name="right">A <see cref="ComplexD"/> instance.</param>
/// <returns><see langword="true"/> if the two vectors are approximately equal; otherwise, <see langword="false"/>.</returns>
public static bool ApproxEqual(ComplexD left, ComplexD right)
{
return ApproxEqual(left, right, MathFunctions.EpsilonD);
}
/// <summary>
/// Divides a scalar by a complex.
/// </summary>
/// <param name="complex">A <see cref="ComplexD"/> instance.</param>
/// <param name="scalar">A double-precision floating-point value.</param>
/// <returns>A new <see cref="ComplexD"/> instance containing the result.</returns>
public static ComplexD Divide(double scalar, ComplexD complex)
{
if ((complex.Real == 0) || (complex.Imaginary == 0))
{
throw new DivideByZeroException();
}
return new ComplexD(
scalar / complex.Real,
scalar / complex.Imaginary);
}
/// <summary>
/// Calculates the square root of a complex number.
/// </summary>
/// <param name="complex">A <see cref="ComplexD"/> instance.</param>
/// <returns>The square root of the complex number given in <paramref name="complex"/>.</returns>
/// <remarks>See http://mathworld.wolfram.com/SquareRoot.html for further details.</remarks>
public static ComplexD Sqrt(ComplexD complex)
{
ComplexD result = ComplexD.Zero;
if ((complex.Real == 0.0) && (complex.Imaginary == 0.0))
{
return result;
}
else if (complex.IsReal)
{
result.Real = (complex.Real > 0) ? System.Math.Sqrt(complex.Real) : System.Math.Sqrt(-complex.Real);
result.Imaginary = 0.0;
}
else
{
double modulus = complex.Modulus;
result.Real = System.Math.Sqrt(0.5 * (modulus + complex.Real));
result.Imaginary = System.Math.Sqrt(0.5 * (modulus - complex.Real));
if (complex.Imaginary < 0.0)
result.Imaginary = -result.Imaginary;
}
return result;
}
/// <summary>
/// Divides a complex by a scalar and put the result into another complex number.
/// </summary>
/// <param name="complex">A <see cref="ComplexD"/> instance.</param>
/// <param name="scalar">A double-precision floating-point value.</param>
/// <param name="result">A <see cref="ComplexD"/> instance to hold the result.</param>
public static void Divide(ComplexD complex, double scalar, ref ComplexD result)
{
if (scalar == 0)
{
throw new DivideByZeroException();
}
result.Real = complex.Real / scalar;
result.Imaginary = complex.Imaginary / scalar;
}
/// <summary>
/// Calculates the logarithm of a specified complex number.
/// Calculates the natural (base e) logarithm of a specified complex number.
/// </summary>
/// <param name="complex">A <see cref="ComplexD"/> instance.</param>
/// <returns>The natural (base e) logarithm of the complex number given in <paramref name="complex"/>.</returns>
public static ComplexD Log(ComplexD complex)
{
ComplexD result = ComplexD.Zero;
if ((complex.Real > 0.0) && (complex.Imaginary == 0.0))
{
result.Real = System.Math.Log(complex.Real);
result.Imaginary = 0.0;
}
else if (complex.Real == 0.0)
{
if (complex.Imaginary > 0.0)
{
result.Real = System.Math.Log(complex.Imaginary);
result.Imaginary = MathFunctions.HalfPI;
}
else
{
result.Real = System.Math.Log(-(complex.Imaginary));
result.Imaginary = -MathFunctions.HalfPI;
}
}
else
{
result.Real = System.Math.Log(complex.Modulus);
result.Imaginary = System.Math.Atan2(complex.Imaginary, complex.Real);
}
return result;
}
/// <summary>
/// Negates a complex number.
/// </summary>
/// <param name="complex">A <see cref="ComplexD"/> instance.</param>
/// <returns>A new <see cref="ComplexD"/> instance containing the negated values.</returns>
public static ComplexD Negate(ComplexD complex)
{
return new ComplexD(-complex.Real, -complex.Imaginary);
}
/// <summary>
/// Negates the complex number.
/// </summary>
/// <param name="a">A <see cref="ComplexD"/> instance.</param>
/// <returns>A new <see cref="ComplexD"/> instance containing the negated values.</returns>
public static ComplexD operator -(ComplexD a)
{
return(ComplexD.Negate(a));
}
/// <summary>
/// Tests whether two complex numbers are approximately equal given a tolerance value.
/// </summary>
/// <param name="left">A <see cref="ComplexD"/> instance.</param>
/// <param name="right">A <see cref="ComplexD"/> instance.</param>
/// <param name="tolerance">The tolerance value used to test approximate equality.</param>
/// <returns><see langword="true"/> if the two vectors are approximately equal; otherwise, <see langword="false"/>.</returns>
public static bool ApproxEqual(ComplexD left, ComplexD right, double tolerance)
{
return
(
(System.Math.Abs(left.Real - right.Real) <= tolerance) &&
(System.Math.Abs(left.Imaginary - right.Imaginary) <= tolerance)
);
}
/// <summary>
/// Adds two complex numbers.
/// </summary>
/// <param name="a">A <see cref="ComplexD"/> instance.</param>
/// <param name="b">A <see cref="ComplexD"/> instance.</param>
/// <returns>A new <see cref="ComplexD"/> instance containing the sum.</returns>
public static ComplexD operator +(ComplexD a, ComplexD b)
{
return(ComplexD.Add(a, b));
}
/// <summary>
/// Initializes a new instance of the <see cref="ComplexD"/> class using values from a given complex instance.
/// </summary>
/// <param name="c">A complex number to get values from.</param>
public ComplexD(ComplexD c)
{
_real = c.Real;
_image = c.Imaginary;
}
/// <summary>
/// Adds a complex number and a scalar.
/// </summary>
/// <param name="a">A <see cref="ComplexD"/> instance.</param>
/// <param name="s">A scalar.</param>
/// <returns>A new <see cref="ComplexD"/> instance containing the sum.</returns>
public static ComplexD operator +(double s, ComplexD a)
{
return(ComplexD.Add(a, s));
}
/// <summary>
/// Calculates the exponential of a specified complex number.
/// </summary>
/// <param name="complex">A <see cref="ComplexD"/> instance.</param>
/// <returns>The exponential of the complex number given in <paramref name="complex"/>.</returns>
public static ComplexD Exp(ComplexD complex)
{
ComplexD result = ComplexD.Zero;
double r = System.Math.Exp(complex.Real);
result.Real = r * System.Math.Cos(complex.Imaginary);
result.Imaginary = r * System.Math.Sin(complex.Imaginary);
return result;
}
/// <summary>
/// Subtracts a complex from a complex.
/// </summary>
/// <param name="a">A <see cref="ComplexD"/> instance.</param>
/// <param name="b">A <see cref="ComplexD"/> instance.</param>
/// <returns>A new <see cref="ComplexD"/> instance containing the difference.</returns>
public static ComplexD operator -(ComplexD a, ComplexD b)
{
return(ComplexD.Subtract(a, b));
}
/// <summary>
/// Calculates the square of the specified complex number.
/// </summary>
/// <param name="complex">A <see cref="ComplexD"/> instance.</param>
/// <returns>The square of the given complex number.</returns>
public static ComplexD Square(ComplexD complex)
{
if (complex.IsReal)
{
return new ComplexD(complex.Real * complex.Real, 0.0);
}
double real = complex.Real;
double imag = complex.Imaginary;
return new ComplexD(real * real - imag * imag, 2 * real * imag);
}
/// <summary>
/// Subtracts a scalar from a complex.
/// </summary>
/// <param name="a">A <see cref="ComplexD"/> instance.</param>
/// <param name="s">A scalar.</param>
/// <returns>A new <see cref="ComplexD"/> instance containing the difference.</returns>
public static ComplexD operator -(ComplexD a, double s)
{
return(ComplexD.Subtract(a, s));
}
/// <summary>
/// Calculates the tangent of the specified complex number.
/// </summary>
/// <param name="complex">A <see cref="ComplexD"/> instance.</param>
/// <returns>The tangent of <paramref name="complex"/>.</returns>
public static ComplexD Tan(ComplexD complex)
{
ComplexD result = ComplexD.Zero;
if (complex.IsReal)
{
result.Real = System.Math.Tan(complex.Real);
result.Imaginary = 0.0;
}
else
{
double cosr = System.Math.Cos(complex.Real);
double sinhi = System.Math.Sinh(complex.Imaginary);
double denom = cosr * cosr + sinhi * sinhi;
result.Real = System.Math.Sin(complex.Real) * cosr / denom;
result.Imaginary = sinhi * System.Math.Cosh(complex.Imaginary) / denom;
}
return result;
}
/// <summary>
/// Subtracts a complex from a scalar.
/// </summary>
/// <param name="a">A <see cref="ComplexD"/> instance.</param>
/// <param name="s">A scalar.</param>
/// <returns>A new <see cref="ComplexD"/> instance containing the difference.</returns>
public static ComplexD operator -(double s, ComplexD a)
{
return(ComplexD.Subtract(s, a));
}
public static ComplexD Asin(ComplexD complex)
{
ComplexD result = 1 - ComplexD.Square(complex);
result = ComplexD.Sqrt(result);
result = result + (ComplexD.I * complex);
result = ComplexD.Log(result);
result = -ComplexD.I * result;
return result;
}
/// <summary>
/// Multiplies two complex numbers.
/// </summary>
/// <param name="a">A <see cref="ComplexD"/> instance.</param>
/// <param name="b">A <see cref="ComplexD"/> instance.</param>
/// <returns>A new <see cref="ComplexD"/> instance containing the result.</returns>
public static ComplexD operator *(ComplexD a, ComplexD b)
{
return(ComplexD.Multiply(a, b));
}
public static ComplexD Atan(ComplexD complex)
{
ComplexD tmp = new ComplexD(-complex.Imaginary, complex.Real);
return (new ComplexD(0, 0.5)) * (ComplexD.Log(1 - tmp) - ComplexD.Log(1 + tmp));
}
/// <summary>
/// Multiplies a complex by a scalar.
/// </summary>
/// <param name="a">A <see cref="ComplexD"/> instance.</param>
/// <param name="s">A scalar.</param>
/// <returns>A new <see cref="ComplexD"/> instance containing the result.</returns>
public static ComplexD operator *(ComplexD a, double s)
{
return(ComplexD.Multiply(a, s));
}
public static ComplexD Acsc(ComplexD complex)
{
ComplexD inverse = 1 / complex;
return (-ComplexD.I) * ComplexD.Log(ComplexD.I * inverse + ComplexD.Sqrt(1 - ComplexD.Square(inverse)));
}
/// <summary>
/// Divides a complex by a complex.
/// </summary>
/// <param name="a">A <see cref="ComplexD"/> instance.</param>
/// <param name="b">A <see cref="ComplexD"/> instance.</param>
/// <returns>A new <see cref="ComplexD"/> instance containing the result.</returns>
public static ComplexD operator /(ComplexD a, ComplexD b)
{
return(ComplexD.Divide(a, b));
}
/// <summary>
/// Calculates the hyperbolic tangent of the specified complex number.
/// </summary>
/// <param name="complex">A <see cref="ComplexD"/> instance.</param>
/// <returns>Returns the hyperbolic tangent of the specified complex number.</returns>
public static ComplexD Tanh(ComplexD complex)
{
if (complex.IsReal)
{
return new ComplexD(System.Math.Tanh(complex.Real), 0.0);
}
double cosi = System.Math.Cos(complex.Imaginary);
double sinhr = System.Math.Sinh(complex.Real);
double denom = (cosi * cosi) + (sinhr * sinhr);
return new ComplexD(
(sinhr* System.Math.Cosh(complex.Real)) / denom,
(cosi * System.Math.Sin(complex.Imaginary)) / denom
);
}
/// <summary>
/// Divides a complex by a scalar.
/// </summary>
/// <param name="a">A <see cref="ComplexD"/> instance.</param>
/// <param name="s">A scalar.</param>
/// <returns>A new <see cref="ComplexD"/> instance containing the result.</returns>
public static ComplexD operator /(ComplexD a, double s)
{
return(ComplexD.Divide(a, s));
}
/// <summary>
/// Calculates the hyperbolic cosecant of the specified complex number.
/// </summary>
/// <param name="complex">A <see cref="ComplexD"/> instance.</param>
/// <returns>Returns the hyperbolic cosecant of the specified complex number.</returns>
public static ComplexD Csch(ComplexD complex)
{
if (complex.IsReal)
{
return new ComplexD(MathFunctions.Csch(complex.Real), 0.0);
}
ComplexD exp = ComplexD.Exp(complex);
return (2 * exp) / (ComplexD.Square(exp) - 1);
}
/// <summary>
/// Divides a scalar by a complex.
/// </summary>
/// <param name="a">A <see cref="ComplexD"/> instance.</param>
/// <param name="s">A scalar.</param>
/// <returns>A new <see cref="ComplexD"/> instance containing the result.</returns>
public static ComplexD operator /(double s, ComplexD a)
{
return(ComplexD.Divide(s, a));
}
public static ComplexD Acosh(ComplexD complex)
{
ComplexD result = ComplexD.Sqrt(complex - 1) * ComplexD.Sqrt(complex + 1);
result = complex + result;
result = ComplexD.Log(result);
return result;
}
/// <summary>
/// Multiplies a complex by a scalar and put the result into another complex number.
/// </summary>
/// <param name="complex">A <see cref="ComplexD"/> instance.</param>
/// <param name="scalar">A double-precision floating-point value.</param>
/// <param name="result">A <see cref="ComplexD"/> instance to hold the result.</param>
public static void Multiply(ComplexD complex, double scalar, ref ComplexD result)
{
result.Real = complex.Real * scalar;
result.Imaginary = complex.Imaginary * scalar;
}