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)); }