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);
}
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 = (a.Real > 0) ? System.Math.Sqrt(a.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);
}
/// <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><see langword="true"/> if the two vectors are approximately equal; otherwise, <see langword="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.
/// </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>
/// 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><see langword="true"/> if <paramref name="obj"/> is a <see cref="ComplexD"/> and has the same values as this instance; otherwise, <see langword="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>
/// 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, ref 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>
/// 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 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, ref 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 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, ref 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.
/// </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));
}
/// <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));
}
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 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, ref 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);
}
/// <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>
/// 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>
/// 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));
}
/// <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));
}
/// <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));
}
/// <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>
/// 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>
/// 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>
/// 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>
/// 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>
/// 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));
}
/// <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>
/// 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><see langword="true"/> if the two vectors are approximately equal; otherwise, <see langword="false"/>.</returns>
public static bool ApproxEqual(ComplexD a, ComplexD b)
{
return(ApproxEqual(a, b, MathFunctions.EpsilonD));
}