Represents a complex number with double-precision floating point components More...

Inheritance diagram for BGC.Mathematics.Complex64:

Collaboration diagram for BGC.Mathematics.Complex64:

Public Member Functions
	Complex64 (double real, double imaginary)
	Initializes a new Complex64 structure using the specified real and imaginary values. More...

Complex64	Square ()
	The Square (power 2) of this Complex64 More...

Complex64	Rotation (double phase)
	Retuns the Complex64 number, rotated by phase radians, or exp(i*phase) More...

double	RealRotation (double phase)
	Retuns the real value of the Complex64 number after rotation by phase radians, or exp(i*phase) More...

bool	Equals (in Complex64 value)
	Returns a value that indicates whether the current instance and a specified complex number have the same value. More...

bool IEquatable< Complex64 >.	Equals (Complex64 other)
	Returns a value that indicates whether the current instance and a specified complex number have the same value. More...

override bool	Equals (object obj)
	Returns a value that indicates whether the current instance and a specified object have the same value. More...

override int	GetHashCode ()
	Returns the hash code for the current Complex64 object. More...

string	ToString (string format)
	Converts the value of the current complex number to its equivalent string representation in Cartesian form by using the specified format for its real and imaginary parts. More...

string	ToString (IFormatProvider provider)
	Converts the value of the current complex number to its equivalent string representation in Cartesian form by using the specified culture-specific formatting information. More...

string	ToString (string format, IFormatProvider provider)
	Converts the value of the current complex number to its equivalent string representation in Cartesian form by using the specified format and culture-specific format information for its real and imaginary parts. More...

override string	ToString ()
	Converts the value of the current complex number to its equivalent string representation in Cartesian form. More...

bool	IsReal ()
	Gets a value indicating whether the provided Complex64 is real. More...

bool	IsRealNonNegative ()
	Gets a value indicating whether the provided Complex64 is real and not negative, that is >= 0. More...

bool	IsZero ()
	Gets a value indicating whether the Complex64 is zero. More...

bool	IsOne ()
	Gets a value indicating whether the Complex64 is one. More...

bool	IsImaginaryOne ()
	Gets a value indicating whether the Complex64 is the imaginary unit. More...

bool	IsInfinity ()
	Gets a value indicating whether the provided Complex64 evaluates to an infinite value. More...

bool	IsNaN ()
	Gets a value indicating whether the provided Complex64evaluates to a value that is not a number. More...

Complex64	Power (in Complex64 exponent)
	Raise this Complex64 to the given value. More...

Complex64	NaturalLogarithm ()
	Natural Logarithm of this Complex64 (Base E). More...

Complex64	CommonLogarithm ()
	Common Logarithm of this Complex64 (Base 10). More...

Complex64	Logarithm (double baseValue)
	Logarithm of this Complex64 with custom base. More...

Complex64	Exponential ()
	Exponential of this Complex64 (exp(x), E^x). More...

double	RealProduct (in Complex64 other)
	Returns the real component of the product of this Complex64 with other. More...

Complex64	Conjugate ()
	Computes the conjugate of a complex number and returns the result. More...

Complex64	Reciprocal ()
	Returns the multiplicative inverse of a complex number. More...

Complex64	SquareRoot ()
	The Square Root (power 1/2) of this Complex64 More...

Static Public Member Functions
static double	Abs (in Complex64 value)
	Gets the absolute value (or magnitude) of a complex number. More...

static Complex64	Acos (in Complex64 value)
	Trigonometric principal Arc Cosine of this Complex64 number. More...

static Complex64	Add (in Complex64 left, in Complex64 right)
	Returns the sum of the two Complex64 inputs More...

static Complex64	Asin (in Complex64 value)
	Trigonometric principal Arc Sine of this Complex64 number. More...

static Complex64	Atan (in Complex64 value)
	Trigonometric principal Arc Tangent of this Complex64 number. More...

static Complex64	Conjugate (in Complex64 value)
	Computes the conjugate of a complex number and returns the result. More...

static Complex64	Cos (in Complex64 value)
	Trigonometric Cosine of a Complex64 number. More...

static Complex64	Cosh (in Complex64 value)
	Hyperbolic Cosine of a Complex64 number. More...

static Complex64	Divide (in Complex64 dividend, in Complex64 divisor)
	Divides one complex number by another and returns the result. More...

static Complex64	Exp (in Complex64 value)
	Returns e raised to the power specified by a complex number. More...

static Complex64	FromPolarCoordinates (double magnitude, double phase)
	Creates a complex number from a point's polar coordinates. More...

static Complex64	Log (in Complex64 value)
	Returns the natural (base e) logarithm of a specified complex number. More...

static Complex64	Log (in Complex64 value, double baseValue)
	Returns the logarithm of a specified complex number in a specified base. More...

static Complex64	Log10 (in Complex64 value)
	Returns the base-10 logarithm of a specified complex number. More...

static Complex64	Multiply (in Complex64 left, in Complex64 right)
	Returns the product of two complex numbers. More...

static Complex64	Negate (in Complex64 value)
	Returns the additive inverse of a specified complex number. More...

static Complex64	Pow (in Complex64 value, double power)
	Returns a specified complex number raised to a power specified by a double-precision doubleing-point number. More...

static Complex64	Pow (in Complex64 value, in Complex64 power)
	Returns a specified complex number raised to a power specified by a complex number. More...

static Complex64	Reciprocal (in Complex64 value)
	Returns the multiplicative inverse of a complex number. More...

static Complex64	Sin (in Complex64 value)
	Trigonometric Sine of a Complex64 number. More...

static Complex64	Sinh (in Complex64 value)
	Hyperbolic Sine of a Complex64 number. More...

static Complex64	Sqrt (in Complex64 value)
	The Square Root of a complex number More...

static Complex64	Subtract (in Complex64 left, Complex64 right)
	The difference between two Complex64 numbers; More...

static Complex64	Tan (in Complex64 value)
	Trigonometric Tangent of a Complex64 number. More...

static Complex64	Tanh (in Complex64 value)
	Hyperbolic Tangent of a Complex64 number. More...

static Complex64	operator+ (in Complex64 left, in Complex64 right)
	Adds two complex numbers. More...

static Complex64	operator- (in Complex64 value)
	Returns the additive inverse of a specified complex number. More...

static Complex64	operator- (in Complex64 left, in Complex64 right)
	Subtracts a complex number from another complex number. More...

static Complex64	operator* (in Complex64 left, in Complex64 right)
	Multiplies two specified complex numbers. More...

static Complex64	operator/ (in Complex64 dividend, in Complex64 divisor)
	Divides a specified complex number by another specified complex number. More...

static bool	operator== (in Complex64 left, in Complex64 right)
	Returns a value that indicates whether two complex numbers are equal. More...

static bool	operator!= (in Complex64 left, in Complex64 right)
	Returns a value that indicates whether two complex numbers are not equal. More...

static implicit	operator Complex64 (Complex32 value)
	Defines an implicit conversion of an unsigned byte to a complex number. More...

static implicit	operator Complex64 (byte value)
	Defines an implicit conversion of an unsigned byte to a complex number. More...

static implicit	operator Complex64 (float value)
	Defines an implicit conversion of a single-precision floating-point number to a complex number. More...

static implicit	operator Complex64 (double value)
	Defines an implicit conversion of a double-precision floating-point number to a complex number. More...

static implicit	operator Complex64 (sbyte value)
	Defines an implicit conversion of a signed byte to a complex number. More...

static implicit	operator Complex64 (ulong value)
	Defines an implicit conversion of a 64-bit unsigned integer to a complex number. More...

static implicit	operator Complex64 (uint value)
	Defines an implicit conversion of a 32-bit unsigned integer to a complex number. More...

static implicit	operator Complex64 (ushort value)
	Defines an implicit conversion of a 16-bit unsigned integer to a complex number. More...

static implicit	operator Complex64 (long value)
	Defines an implicit conversion of a 64-bit signed integer to a complex number. More...

static implicit	operator Complex64 (int value)
	Defines an implicit conversion of a 32-bit signed integer to a complex number. More...

static implicit	operator Complex64 (short value)
	Defines an implicit conversion of a 16-bit signed integer to a complex number. More...

static	operator Complex64 (decimal value)
	Defines an explicit conversion of a System.Decimal value to a complex number. More...

Data Fields
double	Imaginary => _imag
	Gets the imaginary component of the current System.Numerics.Complex64 object. More...

double	Real => _real
	Gets the real component of the current System.Numerics.Complex64 object. More...

double	Phase => _imag == 0.0 && _real < 0.0 ? Math.PI : Math.Atan2(_imag, _real)
	Gets the phase of a complex number in radians. More...

double	MagnitudeSquared => (_real * _real) + (_imag * _imag)
	Gets the squared magnitude (or squared absolute value) of a complex number. More...

Static Public Attributes
static readonly Complex64	Zero = new Complex64(0.0, 0.0)
	Returns a new Complex64 instance with a real number equal to zero and an imaginary number equal to zero. More...

static readonly Complex64	One = new Complex64(1.0, 0.0)
	Returns a new Complex64 instance with a real number equal to one and an imaginary number equal to zero. More...

static readonly Complex64	ImaginaryOne = new Complex64(0.0, 1.0)
	Returns a new Complex64 instance with a real number equal to zero and an imaginary number equal to one. More...

static readonly Complex64	PositiveInfinity = new Complex64(double.PositiveInfinity, double.PositiveInfinity)
	Returns a new Complex64 instance with real and imaginary numbers positive infinite. More...

static readonly Complex64	NaN = new Complex64(double.NaN, double.NaN)
	Returns a new Complex64 instance with real and imaginary numbers not a number. More...

Properties
double	Magnitude `[get]`
	Gets the magnitude (or absolute value) of a complex number. More...

Static Private Member Functions
static Complex64	InternalDiv (double a, double b, double c, double d, bool swapped)
	Helper method for dividing. More...

Private Attributes
readonly double	_real
	The real component of the complex number. More...

readonly double	_imag
	The imaginary component of the complex number. More...

Detailed Description

Represents a complex number with double-precision floating point components

Definition at line 39 of file Complex64.cs.

Constructor & Destructor Documentation

◆ Complex64()

BGC.Mathematics.Complex64.Complex64	(	double	real,
		double	imaginary
	)

inline

Initializes a new Complex64 structure using the specified real and imaginary values.

Definition at line 82 of file Complex64.cs.

         {
             _real = real;
             _imag = imaginary;
         }

Member Function Documentation

◆ Abs()

static double BGC.Mathematics.Complex64.Abs ( in Complex64 value )

static

Gets the absolute value (or magnitude) of a complex number.

Referenced by BGC.Mathematics.Complex64.SquareRoot().

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◆ Acos()

static Complex64 BGC.Mathematics.Complex64.Acos ( in Complex64 value )

inlinestatic

Trigonometric principal Arc Cosine of this Complex64 number.

Parameters

value The complex value.

Returns: The arc cosine of a complex number.

Definition at line 152 of file Complex64.cs.

         {
             if (value.Imaginary < 0.0 || value.Imaginary == 0.0 && value.Real > 0.0)
             {
                 return Math.PI - Acos(-value);
             }
 
             return -ImaginaryOne * (value + (ImaginaryOne * (1.0 - value.Square()).SquareRoot())).NaturalLogarithm();
         }

◆ Add()

static Complex64 BGC.Mathematics.Complex64.Add	(	in Complex64	left,
		in Complex64	right
	)

static

Returns the sum of the two Complex64 inputs

◆ Asin()

static Complex64 BGC.Mathematics.Complex64.Asin ( in Complex64 value )

inlinestatic

Trigonometric principal Arc Sine of this Complex64 number.

Parameters

value The complex value.

Returns: The arc sine of a complex number.

Definition at line 173 of file Complex64.cs.

         {
             if (value.Imaginary > 0.0 || value.Imaginary == 0.0 && value.Real < 0.0)
             {
                 return -Asin(-value);
             }
 
             return -ImaginaryOne * ((1.0 - value.Square()).SquareRoot() + (ImaginaryOne * value)).NaturalLogarithm();
         }

◆ Atan()

static Complex64 BGC.Mathematics.Complex64.Atan ( in Complex64 value )

inlinestatic

Trigonometric principal Arc Tangent of this Complex64 number.

Parameters

value The complex value.

Returns: The arc tangent of a complex number.

Definition at line 189 of file Complex64.cs.

References BGC.Mathematics.Complex64.Conjugate().

         {
             Complex64 iz = new Complex64(-value.Imaginary, value.Real); // I*this
             return new Complex64(0.0, 0.5) * ((1.0 - iz).NaturalLogarithm() - (1.0 + iz).NaturalLogarithm());
         }

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◆ CommonLogarithm()

Complex64 BGC.Mathematics.Complex64.CommonLogarithm ( )

inline

Common Logarithm of this Complex64 (Base 10).

Returns: The common logarithm of this complex number.

Definition at line 766 of file Complex64.cs.

References BGC.Mathematics.Complex64.Log().

Referenced by BGC.Mathematics.Complex64.Cosh().

         {
             if (IsRealNonNegative())
             {
                 return new Complex64(Math.Log10(_real), 0.0);
             }
 
             return new Complex64(0.5 * Math.Log10(MagnitudeSquared), Phase);
         }

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◆ Conjugate() [1/2]

static Complex64 BGC.Mathematics.Complex64.Conjugate ( in Complex64 value )

static

Computes the conjugate of a complex number and returns the result.

Referenced by BGC.Mathematics.Complex64.Atan(), and BGC.Mathematics.Fourier.BluesteinForward().

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◆ Conjugate() [2/2]

Complex64 BGC.Mathematics.Complex64.Conjugate ( )

Computes the conjugate of a complex number and returns the result.

◆ Cos()

static Complex64 BGC.Mathematics.Complex64.Cos ( in Complex64 value )

inlinestatic

Trigonometric Cosine of a Complex64 number.

Parameters

value The complex value.

Returns: The cosine of a complex number.

Definition at line 206 of file Complex64.cs.

References BGC.Mathematics.GeneralMath.Cosh(), and BGC.Mathematics.GeneralMath.Sinh().

Referenced by BGC.Audio.Filters.PhaseVocoder.PhaseVocoder(), and BGC.Mathematics.Complex64.Rotation().

         {
             if (value.IsReal())
             {
                 return new Complex64(Math.Cos(value.Real), 0.0);
             }
 
             return new Complex64(
                 Math.Cos(value.Real) * GeneralMath.Cosh(value.Imaginary),
                 -Math.Sin(value.Real) * GeneralMath.Sinh(value.Imaginary));
         }

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◆ Cosh()

static Complex64 BGC.Mathematics.Complex64.Cosh ( in Complex64 value )

inlinestatic

Hyperbolic Cosine of a Complex64 number.

Parameters

value The complex value.

Returns: The hyperbolic cosine of a complex number.

Definition at line 224 of file Complex64.cs.

References BGC.Mathematics.Complex64.CommonLogarithm(), BGC.Mathematics.GeneralMath.Cosh(), BGC.Mathematics.Complex64.Exponential(), BGC.Mathematics.Complex64.Logarithm(), BGC.Mathematics.Complex64.NaturalLogarithm(), BGC.Mathematics.Complex64.Power(), BGC.Mathematics.Complex64.Reciprocal(), and BGC.Mathematics.GeneralMath.Sinh().

         {
             if (value.IsReal())
             {
                 return new Complex64(GeneralMath.Cosh(value.Real), 0.0);
             }
 
             // cosh(x + j*y) = cosh(x)*cos(y) + j*sinh(x)*sin(y)
             // if x > huge, cosh(x + j*y) = exp(|x|)/2*cos(y) + j*sign(x)*exp(|x|)/2*sin(y)
 
             if (Math.Abs(value.Real) >= 22.0) // Taken from the msun library in FreeBSD
             {
                 double h = Math.Exp(Math.Abs(value.Real)) * 0.5;
                 return new Complex64(
                     h * Math.Cos(value.Imaginary),
                     Math.Sign(value.Real) * h * Math.Sin(value.Imaginary));
             }
 
             return new Complex64(
                 GeneralMath.Cosh(value.Real) * Math.Cos(value.Imaginary),
                 GeneralMath.Sinh(value.Real) * Math.Sin(value.Imaginary));
         }

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◆ Divide()

static Complex64 BGC.Mathematics.Complex64.Divide	(	in Complex64	dividend,
		in Complex64	divisor
	)

static

Divides one complex number by another and returns the result.

◆ Equals() [1/3]

bool BGC.Mathematics.Complex64.Equals ( in Complex64 value )

inline

Returns a value that indicates whether the current instance and a specified complex number have the same value.

Definition at line 467 of file Complex64.cs.

References BGC.Mathematics.GeneralMath.Approximately().

         {
             if (IsNaN() || value.IsNaN())
             {
                 return false;
             }
 
             if (IsInfinity() && value.IsInfinity())
             {
                 return true;
             }
 
             return GeneralMath.Approximately(_real, value._real) &&
                 GeneralMath.Approximately(_imag, value._imag);
         }

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◆ Equals() [2/3]

bool IEquatable<Complex64>. BGC.Mathematics.Complex64.Equals ( Complex64 other )

Returns a value that indicates whether the current instance and a specified complex number have the same value.

◆ Equals() [3/3]

override bool BGC.Mathematics.Complex64.Equals ( object obj )

Returns a value that indicates whether the current instance and a specified object have the same value.

◆ Exp()

static Complex64 BGC.Mathematics.Complex64.Exp ( in Complex64 value )

static

Returns e raised to the power specified by a complex number.

Referenced by BGC.Mathematics.Complex64.Exponential().

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◆ Exponential()

Complex64 BGC.Mathematics.Complex64.Exponential ( )

inline

Exponential of this Complex64 (exp(x), E^x).

Returns: The exponential of this complex number.

Definition at line 788 of file Complex64.cs.

References BGC.Mathematics.Complex64._real, and BGC.Mathematics.Complex64.Exp().

Referenced by BGC.Mathematics.Complex64.Cosh().

         {
             double exp = Math.Exp(_real);
             if (IsReal())
             {
                 return new Complex64(exp, 0.0);
             }
 
             return new Complex64(exp * Math.Cos(_imag), exp * Math.Sin(_imag));
         }

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◆ FromPolarCoordinates()

static Complex64 BGC.Mathematics.Complex64.FromPolarCoordinates	(	double	magnitude,
		double	phase
	)

static

Creates a complex number from a point's polar coordinates.

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◆ GetHashCode()

override int BGC.Mathematics.Complex64.GetHashCode ( )

inline

Returns the hash code for the current Complex64 object.

Definition at line 496 of file Complex64.cs.

         {
             int hash = 27;
             hash = (13 * hash) + _real.GetHashCode();
             hash = (13 * hash) + _imag.GetHashCode();
             return hash;
         }

◆ InternalDiv()

static Complex64 BGC.Mathematics.Complex64.InternalDiv	(	double	a,
		double	b,
		double	c,
		double	d,
		bool	swapped
	)

inlinestaticprivate

Helper method for dividing.

Parameters

a	Re first
b	Im first
c	Re second
d	Im second

Definition at line 870 of file Complex64.cs.

         {
             double r = d / c;
             double t = 1 / (c + d * r);
             double e, f;
 
             if (r != 0.0) // one can use r >= double.Epsilon || r <= double.Epsilon instead
             {
                 e = (a + b * r) * t;
                 f = (b - a * r) * t;
             }
             else
             {
                 e = (a + d * (b / c)) * t;
                 f = (b - d * (a / c)) * t;
             }
 
             if (swapped)
             {
                 f = -f;
             }
 
             return new Complex64(e, f);
         }

◆ IsImaginaryOne()

bool BGC.Mathematics.Complex64.IsImaginaryOne ( )

Gets a value indicating whether the Complex64 is the imaginary unit.

Returns: true if this instance is ImaginaryOne; otherwise, false.

◆ IsInfinity()

bool BGC.Mathematics.Complex64.IsInfinity ( )

Gets a value indicating whether the provided Complex64 evaluates to an infinite value.

Returns: true if this instance is infinite; otherwise, false.

True if it either evaluates to a complex infinity or to a directed infinity.

◆ IsNaN()

bool BGC.Mathematics.Complex64.IsNaN ( )

Gets a value indicating whether the provided Complex64evaluates to a value that is not a number.

Returns: true if this instance is NaN; otherwise, false.

◆ IsOne()

bool BGC.Mathematics.Complex64.IsOne ( )

Gets a value indicating whether the Complex64 is one.

Returns: true if this instance is one; otherwise, false.

◆ IsReal()

bool BGC.Mathematics.Complex64.IsReal ( )

Gets a value indicating whether the provided Complex64 is real.

Returns: true if this instance is a real number; otherwise, false.

◆ IsRealNonNegative()

bool BGC.Mathematics.Complex64.IsRealNonNegative ( )

Gets a value indicating whether the provided Complex64 is real and not negative, that is >= 0.

Returns: true if this instance is real nonnegative number; otherwise, false.

◆ IsZero()

bool BGC.Mathematics.Complex64.IsZero ( )

Gets a value indicating whether the Complex64 is zero.

Returns: true if this instance is zero; otherwise, false.

◆ Log() [1/2]

static Complex64 BGC.Mathematics.Complex64.Log ( in Complex64 value )

static

Returns the natural (base e) logarithm of a specified complex number.

Referenced by BGC.Audio.Synthesis.STMAudioClip._Initialize(), and BGC.Mathematics.Complex64.CommonLogarithm().

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◆ Log() [2/2]

static Complex64 BGC.Mathematics.Complex64.Log	(	in Complex64	value,
		double	baseValue
	)

static

Returns the logarithm of a specified complex number in a specified base.

◆ Log10()

static Complex64 BGC.Mathematics.Complex64.Log10 ( in Complex64 value )

static

Returns the base-10 logarithm of a specified complex number.

◆ Logarithm()

Complex64 BGC.Mathematics.Complex64.Logarithm ( double baseValue )

Logarithm of this Complex64 with custom base.

Returns: The logarithm of this complex number.

Referenced by BGC.Mathematics.Complex64.Cosh().

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◆ Multiply()

static Complex64 BGC.Mathematics.Complex64.Multiply	(	in Complex64	left,
		in Complex64	right
	)

static

Returns the product of two complex numbers.

◆ NaturalLogarithm()

Complex64 BGC.Mathematics.Complex64.NaturalLogarithm ( )

inline

Natural Logarithm of this Complex64 (Base E).

Returns: The natural logarithm of this complex number.

Definition at line 752 of file Complex64.cs.

Referenced by BGC.Mathematics.Complex64.Cosh().

         {
             if (IsRealNonNegative())
             {
                 return new Complex64(Math.Log(_real), 0.0);
             }
 
             return new Complex64(0.5 * Math.Log(MagnitudeSquared), Phase);
         }

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◆ Negate()

static Complex64 BGC.Mathematics.Complex64.Negate ( in Complex64 value )

static

Returns the additive inverse of a specified complex number.

◆ operator Complex64() [1/12]

static implicit BGC.Mathematics.Complex64.operator Complex64 ( Complex32 value )

static

Defines an implicit conversion of an unsigned byte to a complex number.

◆ operator Complex64() [2/12]

static implicit BGC.Mathematics.Complex64.operator Complex64 ( byte value )

static

Defines an implicit conversion of an unsigned byte to a complex number.

◆ operator Complex64() [3/12]

static implicit BGC.Mathematics.Complex64.operator Complex64 ( float value )

static

Defines an implicit conversion of a single-precision floating-point number to a complex number.

◆ operator Complex64() [4/12]

static implicit BGC.Mathematics.Complex64.operator Complex64 ( double value )

static

Defines an implicit conversion of a double-precision floating-point number to a complex number.

Parameters

value

◆ operator Complex64() [5/12]

static implicit BGC.Mathematics.Complex64.operator Complex64 ( sbyte value )

static

Defines an implicit conversion of a signed byte to a complex number.

◆ operator Complex64() [6/12]

static implicit BGC.Mathematics.Complex64.operator Complex64 ( ulong value )

static

Defines an implicit conversion of a 64-bit unsigned integer to a complex number.

◆ operator Complex64() [7/12]

static implicit BGC.Mathematics.Complex64.operator Complex64 ( uint value )

static

Defines an implicit conversion of a 32-bit unsigned integer to a complex number.

◆ operator Complex64() [8/12]

static implicit BGC.Mathematics.Complex64.operator Complex64 ( ushort value )

static

Defines an implicit conversion of a 16-bit unsigned integer to a complex number.

◆ operator Complex64() [9/12]

static implicit BGC.Mathematics.Complex64.operator Complex64 ( long value )

static

Defines an implicit conversion of a 64-bit signed integer to a complex number.

◆ operator Complex64() [10/12]

static implicit BGC.Mathematics.Complex64.operator Complex64 ( int value )

static

Defines an implicit conversion of a 32-bit signed integer to a complex number.

◆ operator Complex64() [11/12]

static implicit BGC.Mathematics.Complex64.operator Complex64 ( short value )

static

Defines an implicit conversion of a 16-bit signed integer to a complex number.

◆ operator Complex64() [12/12]

static BGC.Mathematics.Complex64.operator Complex64 ( decimal value )

explicitstatic

Defines an explicit conversion of a System.Decimal value to a complex number.

◆ operator!=()

static bool BGC.Mathematics.Complex64.operator!=	(	in Complex64	left,
		in Complex64	right
	)

static

Returns a value that indicates whether two complex numbers are not equal.

◆ operator*()

static Complex64 BGC.Mathematics.Complex64.operator*	(	in Complex64	left,
		in Complex64	right
	)

static

Multiplies two specified complex numbers.

◆ operator+()

static Complex64 BGC.Mathematics.Complex64.operator+	(	in Complex64	left,
		in Complex64	right
	)

static

Adds two complex numbers.

◆ operator-() [1/2]

static Complex64 BGC.Mathematics.Complex64.operator- ( in Complex64 value )

static

Returns the additive inverse of a specified complex number.

◆ operator-() [2/2]

static Complex64 BGC.Mathematics.Complex64.operator-	(	in Complex64	left,
		in Complex64	right
	)

static

Subtracts a complex number from another complex number.

◆ operator/()

static Complex64 BGC.Mathematics.Complex64.operator/	(	in Complex64	dividend,
		in Complex64	divisor
	)

inlinestatic

Divides a specified complex number by another specified complex number.

Definition at line 556 of file Complex64.cs.

References BGC.Mathematics.Complex32.Imaginary, BGC.Mathematics.Complex64.Real, and BGC.Mathematics.Complex32.Real.

         {
             if (dividend.IsZero() && divisor.IsZero())
             {
                 return NaN;
             }
 
             if (divisor.IsZero())
             {
                 return PositiveInfinity;
             }
 
             double a = dividend.Real;
             double b = dividend.Imaginary;
             double c = divisor.Real;
             double d = divisor.Imaginary;
             if (Math.Abs(d) <= Math.Abs(c))
             {
                 return InternalDiv(a, b, c, d, false);
             }
 
             return InternalDiv(b, a, d, c, true);
         }

◆ operator==()

static bool BGC.Mathematics.Complex64.operator==	(	in Complex64	left,
		in Complex64	right
	)

static

Returns a value that indicates whether two complex numbers are equal.

◆ Pow() [1/2]

static Complex64 BGC.Mathematics.Complex64.Pow	(	in Complex64	value,
		double	power
	)

static

Returns a specified complex number raised to a power specified by a double-precision doubleing-point number.

◆ Pow() [2/2]

static Complex64 BGC.Mathematics.Complex64.Pow	(	in Complex64	value,
		in Complex64	power
	)

static

Returns a specified complex number raised to a power specified by a complex number.

◆ Power()

Complex64 BGC.Mathematics.Complex64.Power ( in Complex64 exponent )

inline

Raise this Complex64 to the given value.

Parameters

exponent The exponent.

Returns: The complex number raised to the given exponent.

Definition at line 721 of file Complex64.cs.

References BGC.Mathematics.Complex64.Imaginary.

Referenced by BGC.Mathematics.Complex64.Cosh().

         {
             if (IsZero())
             {
                 if (exponent.IsZero())
                 {
                     return One;
                 }
 
                 if (exponent.Real > 0.0)
                 {
                     return Zero;
                 }
 
                 if (exponent.Real < 0.0)
                 {
                     return exponent.Imaginary == 0.0
                         ? new Complex64(double.PositiveInfinity, 0.0)
                         : new Complex64(double.PositiveInfinity, double.PositiveInfinity);
                 }
 
                 return NaN;
             }
 
             return (exponent * NaturalLogarithm()).Exponential();
         }

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◆ RealProduct()

double BGC.Mathematics.Complex64.RealProduct ( in Complex64 other )

Returns the real component of the product of this Complex64 with other.

Returns: The real component of the product.

Referenced by BGC.Audio.Filters.FrequencyModulationFilter.Read().

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◆ RealRotation()

double BGC.Mathematics.Complex64.RealRotation ( double phase )

Retuns the real value of the Complex64 number after rotation by phase radians, or exp(i*phase)

◆ Reciprocal() [1/2]

static Complex64 BGC.Mathematics.Complex64.Reciprocal ( in Complex64 value )

static

Returns the multiplicative inverse of a complex number.

Referenced by BGC.Mathematics.Complex64.Cosh().

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◆ Reciprocal() [2/2]

Complex64 BGC.Mathematics.Complex64.Reciprocal ( )

Returns the multiplicative inverse of a complex number.

◆ Rotation()

Complex64 BGC.Mathematics.Complex64.Rotation ( double phase )

inline

Retuns the Complex64 number, rotated by phase radians, or exp(i*phase)

Definition at line 450 of file Complex64.cs.

References BGC.Mathematics.Complex64.Cos(), and BGC.Mathematics.Complex64.Sin().

         {
             double cosPhase = Math.Cos(phase);
             double sinePhase = Math.Sin(phase);
             return new Complex64(
                 _real * cosPhase - _imag * sinePhase,
                 _real * sinePhase + _imag * cosPhase);
         }

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◆ Sin()

static Complex64 BGC.Mathematics.Complex64.Sin ( in Complex64 value )

inlinestatic

Trigonometric Sine of a Complex64 number.

Parameters

value The complex value.

Returns: The sine of the complex number.

Definition at line 309 of file Complex64.cs.

References BGC.Mathematics.GeneralMath.Cosh(), and BGC.Mathematics.GeneralMath.Sinh().

Referenced by BGC.Mathematics.Complex64.Rotation().

         {
             if (value.IsReal())
             {
                 return new Complex64(Math.Sin(value.Real), 0.0);
             }
 
             return new Complex64(
                 Math.Sin(value.Real) * GeneralMath.Cosh(value.Imaginary),
                 Math.Cos(value.Real) * GeneralMath.Sinh(value.Imaginary));
         }

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◆ Sinh()

static Complex64 BGC.Mathematics.Complex64.Sinh ( in Complex64 value )

inlinestatic

Hyperbolic Sine of a Complex64 number.

Parameters

value The complex value.

Returns: The hyperbolic sine of a complex number.

Definition at line 327 of file Complex64.cs.

References BGC.Mathematics.GeneralMath.Cosh(), and BGC.Mathematics.GeneralMath.Sinh().

         {
             if (value.IsReal())
             {
                 return new Complex64(GeneralMath.Sinh(value.Real), 0.0);
             }
 
             // sinh(x + j y) = sinh(x)*cos(y) + j*cosh(x)*sin(y)
             // if x > huge, sinh(x + jy) = sign(x)*exp(|x|)/2*cos(y) + j*exp(|x|)/2*sin(y)
 
             if (Math.Abs(value.Real) >= 22.0) // Taken from the msun library in FreeBSD
             {
                 double h = Math.Exp(Math.Abs(value.Real)) * 0.5;
                 return new Complex64(
                     Math.Sign(value.Real) * h * Math.Cos(value.Imaginary),
                     h * Math.Sin(value.Imaginary));
             }
 
             return new Complex64(
                 GeneralMath.Sinh(value.Real) * Math.Cos(value.Imaginary),
                 GeneralMath.Cosh(value.Real) * Math.Sin(value.Imaginary));
         }

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◆ Sqrt()

static Complex64 BGC.Mathematics.Complex64.Sqrt ( in Complex64 value )

static

The Square Root of a complex number

Referenced by BGC.Audio.FrequencyDomain.Populate().

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◆ Square()

Complex64 BGC.Mathematics.Complex64.Square ( )

inline

The Square (power 2) of this Complex64

Returns: The square of this complex number.

Definition at line 356 of file Complex64.cs.

References BGC.Mathematics.Complex64.SquareRoot().

         {
             if (IsReal())
             {
                 return new Complex64(_real * _real, 0.0);
             }
 
             return new Complex64((_real * _real) - (_imag * _imag), 2 * _real * _imag);
         }

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◆ SquareRoot()

Complex64 BGC.Mathematics.Complex64.SquareRoot ( )

inline

The Square Root (power 1/2) of this Complex64

Returns: The square root of this complex number.

Definition at line 824 of file Complex64.cs.

References BGC.Mathematics.Complex64.Abs().

Referenced by BGC.Mathematics.Complex64.Square().

         {
             if (IsRealNonNegative())
             {
                 return new Complex64(Math.Sqrt(_real), 0.0);
             }
 
             Complex64 result;
 
             double absReal = Math.Abs(Real);
             double absImag = Math.Abs(Imaginary);
             double w;
             if (absReal >= absImag)
             {
                 double ratio = Imaginary / Real;
                 w = Math.Sqrt(absReal) * Math.Sqrt(0.5 * (1.0 + Math.Sqrt(1.0 + (ratio * ratio))));
             }
             else
             {
                 double ratio = Real / Imaginary;
                 w = Math.Sqrt(absImag) * Math.Sqrt(0.5 * (Math.Abs(ratio) + Math.Sqrt(1.0 + (ratio * ratio))));
             }
 
             if (Real >= 0.0)
             {
                 result = new Complex64(w, (Imaginary / (2.0 * w)));
             }
             else if (Imaginary >= 0.0)
             {
                 result = new Complex64((absImag / (2.0 * w)), w);
             }
             else
             {
                 result = new Complex64((absImag / (2.0 * w)), -w);
             }
 
             return result;
         }

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◆ Subtract()

static Complex64 BGC.Mathematics.Complex64.Subtract	(	in Complex64	left,
		Complex64	right
	)

static

The difference between two Complex64 numbers;

Returns: The complex difference.

◆ Tan()

static Complex64 BGC.Mathematics.Complex64.Tan ( in Complex64 value )

inlinestatic

Trigonometric Tangent of a Complex64 number.

Parameters

value The complex value.

Returns: The tangent of the complex number.

Definition at line 385 of file Complex64.cs.

References BGC.Mathematics.Complex64.Imaginary, and BGC.Mathematics.Complex64.Real.

Referenced by BGC.Mathematics.Complex64.Tanh().

         {
             if (value.IsReal())
             {
                 return new Complex64(Math.Tan(value.Real), 0.0);
             }
 
             // tan(z) = - j*tanh(j*z)
 
             Complex64 z = Tanh(new Complex64(-value.Imaginary, value.Real));
             return new Complex64(z.Imaginary, -z.Real);
         }

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◆ Tanh()

static Complex64 BGC.Mathematics.Complex64.Tanh ( in Complex64 value )

inlinestatic

Hyperbolic Tangent of a Complex64 number.

Parameters

value The complex value.

Returns: The hyperbolic tangent of a complex number.

Definition at line 404 of file Complex64.cs.

References BGC.Mathematics.GeneralMath.Cosh(), BGC.Mathematics.GeneralMath.Sinh(), BGC.Mathematics.Complex64.Tan(), and BGC.Mathematics.GeneralMath.Tanh().

         {
             if (value.IsReal())
             {
                 return new Complex64(GeneralMath.Tanh(value.Real), 0.0);
             }
 
             // tanh(x + j*y) = (cosh(x)*sinh(x)/cos^2(y) + j*tan(y))/(1 + sinh^2(x)/cos^2(y))
             // if |x| > huge, tanh(z) = sign(x) + j*4*cos(y)*sin(y)*exp(-2*|x|)
             // if exp(-|x|) = 0, tanh(z) = sign(x)
             // if tan(y) = +/- oo or 1/cos^2(y) = 1 + tan^2(y) = oo, tanh(z) = cosh(x)/sinh(x)
             //
             // The algorithm is based on Kahan.
 
             if (Math.Abs(value.Real) >= 22) // Taken from the msun library in FreeBSD
             {
                 double e = Math.Exp(-Math.Abs(value.Real));
                 if (e == 0.0)
                 {
                     return new Complex64(Math.Sign(value.Real), 0.0);
                 }
                 else
                 {
                     return new Complex64(
                         Math.Sign(value.Real),
                         4.0 * Math.Cos(value.Imaginary) * Math.Sin(value.Imaginary) * e * e);
                 }
             }
 
             double tani = Math.Tan(value.Imaginary);
             double beta = 1 + tani * tani; // beta = 1/cos^2(y) = 1 + t^2
             double sinhr = GeneralMath.Sinh(value.Real);
             double coshr = GeneralMath.Cosh(value.Real);
 
             if (double.IsInfinity(tani))
             {
                 return new Complex64(coshr / sinhr, 0.0);
             }
 
             double denom = 1.0 + beta * sinhr * sinhr;
             return new Complex64(beta * coshr * sinhr / denom, tani / denom);
         }

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◆ ToString() [1/4]

string BGC.Mathematics.Complex64.ToString ( string format )

Converts the value of the current complex number to its equivalent string representation in Cartesian form by using the specified format for its real and imaginary parts.

◆ ToString() [2/4]

string BGC.Mathematics.Complex64.ToString ( IFormatProvider provider )

Converts the value of the current complex number to its equivalent string representation in Cartesian form by using the specified culture-specific formatting information.

◆ ToString() [3/4]

string BGC.Mathematics.Complex64.ToString	(	string	format,
		IFormatProvider	provider
	)

Converts the value of the current complex number to its equivalent string representation in Cartesian form by using the specified format and culture-specific format information for its real and imaginary parts.

◆ ToString() [4/4]

override string BGC.Mathematics.Complex64.ToString ( )

Converts the value of the current complex number to its equivalent string representation in Cartesian form.

Returns

Field Documentation

◆ _imag

readonly double BGC.Mathematics.Complex64._imag

private

The imaginary component of the complex number.

Definition at line 51 of file Complex64.cs.

◆ _real

readonly double BGC.Mathematics.Complex64._real

private

The real component of the complex number.

Definition at line 45 of file Complex64.cs.

Referenced by BGC.Mathematics.Complex64.Exponential().

◆ Imaginary

double BGC.Mathematics.Complex64.Imaginary => _imag

Gets the imaginary component of the current System.Numerics.Complex64 object.

Definition at line 91 of file Complex64.cs.

Referenced by BGC.Mathematics.Complex64.Power(), and BGC.Mathematics.Complex64.Tan().

◆ ImaginaryOne

readonly Complex64 BGC.Mathematics.Complex64.ImaginaryOne = new Complex64(0.0, 1.0)

static

Returns a new Complex64 instance with a real number equal to zero and an imaginary number equal to one.

Definition at line 67 of file Complex64.cs.

◆ MagnitudeSquared

double BGC.Mathematics.Complex64.MagnitudeSquared => (_real * _real) + (_imag * _imag)

Gets the squared magnitude (or squared absolute value) of a complex number.

Returns: The squared magnitude of the current instance.

Definition at line 710 of file Complex64.cs.

◆ NaN

readonly Complex64 BGC.Mathematics.Complex64.NaN = new Complex64(double.NaN, double.NaN)

static

Returns a new Complex64 instance with real and imaginary numbers not a number.

Definition at line 77 of file Complex64.cs.

◆ One

readonly Complex64 BGC.Mathematics.Complex64.One = new Complex64(1.0, 0.0)

static

Returns a new Complex64 instance with a real number equal to one and an imaginary number equal to zero.

Definition at line 62 of file Complex64.cs.

◆ Phase

double BGC.Mathematics.Complex64.Phase => _imag == 0.0 && _real < 0.0 ? Math.PI : Math.Atan2(_imag, _real)

Gets the phase of a complex number in radians.

Definition at line 139 of file Complex64.cs.

◆ PositiveInfinity

readonly Complex64 BGC.Mathematics.Complex64.PositiveInfinity = new Complex64(double.PositiveInfinity, double.PositiveInfinity)

static

Returns a new Complex64 instance with real and imaginary numbers positive infinite.

Definition at line 72 of file Complex64.cs.

◆ Real

double BGC.Mathematics.Complex64.Real => _real

Gets the real component of the current System.Numerics.Complex64 object.

Definition at line 96 of file Complex64.cs.

Referenced by BGC.Audio.Synthesis.NoiseAudioClip._Initialize(), BGC.Audio.AnalyticStreams.AnalyticStreamExtensions.CalculateRMS(), BGC.Audio.AnalyticStreams.AnalyticNoiseStream.Initialize(), BGC.Mathematics.Complex64.operator/(), BGC.Audio.Filters.AllPassFilter.ProcessSample(), and BGC.Mathematics.Complex64.Tan().

◆ Zero

readonly Complex64 BGC.Mathematics.Complex64.Zero = new Complex64(0.0, 0.0)

static

Returns a new Complex64 instance with a real number equal to zero and an imaginary number equal to zero.

Definition at line 57 of file Complex64.cs.

Property Documentation

◆ Magnitude

double BGC.Mathematics.Complex64.Magnitude

get

Gets the magnitude (or absolute value) of a complex number.

Definition at line 102 of file Complex64.cs.

The documentation for this struct was generated from the following file:

Mathematics/Complex64.cs

Public Member Functions

Static Public Member Functions

Data Fields

Static Public Attributes

Properties

Static Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Complex64()

Member Function Documentation

◆ Abs()

◆ Acos()

◆ Add()

◆ Asin()

◆ Atan()

◆ CommonLogarithm()

◆ Conjugate() [1/2]

◆ Conjugate() [2/2]

◆ Cos()

◆ Cosh()

◆ Divide()

◆ Equals() [1/3]

◆ Equals() [2/3]

◆ Equals() [3/3]

◆ Exp()

◆ Exponential()

◆ FromPolarCoordinates()

◆ GetHashCode()

◆ InternalDiv()

◆ IsImaginaryOne()

◆ IsInfinity()

◆ IsNaN()

◆ IsOne()

◆ IsReal()

◆ IsRealNonNegative()

◆ IsZero()

◆ Log() [1/2]

◆ Log() [2/2]

◆ Log10()

◆ Logarithm()

◆ Multiply()

◆ NaturalLogarithm()

◆ Negate()

◆ operator Complex64() [1/12]

◆ operator Complex64() [2/12]

◆ operator Complex64() [3/12]

◆ operator Complex64() [4/12]

◆ operator Complex64() [5/12]

◆ operator Complex64() [6/12]

◆ operator Complex64() [7/12]

◆ operator Complex64() [8/12]

◆ operator Complex64() [9/12]

◆ operator Complex64() [10/12]

◆ operator Complex64() [11/12]

◆ operator Complex64() [12/12]

◆ operator!=()

◆ operator*()

◆ operator+()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator/()

◆ operator==()

◆ Pow() [1/2]

◆ Pow() [2/2]

◆ Power()

◆ RealProduct()

◆ RealRotation()

◆ Reciprocal() [1/2]

◆ Reciprocal() [2/2]

◆ Rotation()

◆ Sin()

◆ Sinh()

◆ Sqrt()

◆ Square()

◆ SquareRoot()

◆ Subtract()

◆ Tan()

◆ Tanh()

◆ ToString() [1/4]