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

Inheritance diagram for BGC.Mathematics.Complex32:

Collaboration diagram for BGC.Mathematics.Complex32:

Public Member Functions
	Complex32 (float real, float imaginary)
	Initializes a new Complex32 structure using the specified real and imaginary values. More...

Complex32	Square ()
	The Square (power 2) of this Complex32 More...

Complex32	Rotation (float phase)
	Retuns the Complex32 number, rotated by phase radians, or exp(i*phase) More...

float	RealRotation (float phase)
	Retuns the real value of the Complex32 number after rotation by phase radians, or exp(i*phase) More...

bool	Equals (in Complex32 value)
	Returns a value that indicates whether the current instance and a specified complex number have the same value. More...

bool IEquatable< Complex32 >.	Equals (Complex32 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 Complex32 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 Complex32 is real. More...

bool	IsRealNonNegative ()
	Gets a value indicating whether the provided Complex32 is real and not negative, that is >= 0. More...

bool	IsZero ()
	Gets a value indicating whether the Complex32 is zero. More...

bool	IsOne ()
	Gets a value indicating whether the Complex32 is one. More...

bool	IsImaginaryOne ()
	Gets a value indicating whether the Complex32 is the imaginary unit. More...

bool	IsInfinity ()
	Gets a value indicating whether the provided Complex32 evaluates to an infinite value. More...

bool	IsNaN ()
	Gets a value indicating whether the provided Complex32evaluates to a value that is not a number. More...

Complex32	Power (in Complex32 exponent)
	Raise this Complex32 to the given value. More...

Complex32	NaturalLogarithm ()
	Natural Logarithm of this Complex32 (Base E). More...

Complex32	CommonLogarithm ()
	Common Logarithm of this Complex32 (Base 10). More...

Complex32	Logarithm (float baseValue)
	Logarithm of this Complex32 with custom base. More...

Complex32	Exponential ()
	Exponential of this Complex32 (exp(x), E^x). More...

float	RealProduct (in Complex32 other)
	Returns the real component of the product of this Complex32 with other. More...

Complex32	Conjugate ()
	Computes the conjugate of a complex number and returns the result. More...

Complex32	Reciprocal ()
	Returns the multiplicative inverse of a complex number. More...

Complex32	SquareRoot ()
	The Square Root (power 1/2) of this Complex32 More...

Static Public Member Functions
static float	Abs (in Complex32 value)
	Gets the absolute value (or magnitude) of a complex number. More...

static Complex32	Acos (in Complex32 value)
	Trigonometric principal Arc Cosine of this Complex32 number. More...

static Complex32	Add (in Complex32 left, in Complex32 right)
	Returns the sum of the two Complex32 inputs More...

static Complex32	Asin (in Complex32 value)
	Trigonometric principal Arc Sine of this Complex32 number. More...

static Complex32	Atan (in Complex32 value)
	Trigonometric principal Arc Tangent of this Complex32 number. More...

static Complex32	Conjugate (in Complex32 value)
	Computes the conjugate of a complex number and returns the result. More...

static Complex32	Cos (in Complex32 value)
	Trigonometric Cosine of a Complex32 number. More...

static Complex32	Cosh (in Complex32 value)
	Hyperbolic Cosine of a Complex32 number. More...

static Complex32	Divide (in Complex32 dividend, in Complex32 divisor)
	Divides one complex number by another and returns the result. More...

static Complex32	Exp (in Complex32 value)
	Returns e raised to the power specified by a complex number. More...

static Complex32	FromPolarCoordinates (float magnitude, float phase)
	Creates a complex number from a point's polar coordinates. More...

static Complex32	FromPolarCoordinates (double magnitude, double phase)
	Creates a complex number from a point's polar coordinates. More...

static Complex32	Log (in Complex32 value)
	Returns the natural (base e) logarithm of a specified complex number. More...

static Complex32	Log (in Complex32 value, float baseValue)
	Returns the logarithm of a specified complex number in a specified base. More...

static Complex32	Log10 (in Complex32 value)
	Returns the base-10 logarithm of a specified complex number. More...

static Complex32	Multiply (in Complex32 left, in Complex32 right)
	Returns the product of two complex numbers. More...

static Complex32	Negate (in Complex32 value)
	Returns the additive inverse of a specified complex number. More...

static Complex32	Pow (in Complex32 value, float power)
	Returns a specified complex number raised to a power specified by a float-precision floating-point number. More...

static Complex32	Pow (in Complex32 value, in Complex32 power)
	Returns a specified complex number raised to a power specified by a complex number. More...

static Complex32	Reciprocal (in Complex32 value)
	Returns the multiplicative inverse of a complex number. More...

static Complex32	Sin (in Complex32 value)
	Trigonometric Sine of a Complex32 number. More...

static Complex32	Sinh (in Complex32 value)
	Hyperbolic Sine of a Complex32 number. More...

static Complex32	Sqrt (in Complex32 value)
	The Square Root of a complex number More...

static Complex32	Subtract (in Complex32 left, Complex32 right)
	The difference between two Complex32 numbers; More...

static Complex32	Tan (in Complex32 value)
	Trigonometric Tangent of a Complex32 number. More...

static Complex32	Tanh (in Complex32 value)
	Hyperbolic Tangent of a Complex32 number. More...

static Complex32	operator+ (in Complex32 left, in Complex32 right)
	Adds two complex numbers. More...

static Complex32	operator- (in Complex32 value)
	Returns the additive inverse of a specified complex number. More...

static Complex32	operator- (in Complex32 left, in Complex32 right)
	Subtracts a complex number from another complex number. More...

static Complex32	operator* (in Complex32 left, in Complex32 right)
	Multiplies two specified complex numbers. More...

static Complex32	operator/ (in Complex32 dividend, in Complex32 divisor)
	Divides a specified complex number by another specified complex number. More...

static bool	operator== (in Complex32 left, in Complex32 right)
	Returns a value that indicates whether two complex numbers are equal. More...

static bool	operator!= (in Complex32 left, in Complex32 right)
	Returns a value that indicates whether two complex numbers are not equal. More...

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

static implicit	operator Complex32 (float value)
	Defines an implicit conversion of a single-precision floating-point number to a complex number. More...

static implicit	operator Complex32 (double value)
	Defines an implicit conversion of a double-precision floating-point number to a complex number. More...

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

static implicit	operator Complex32 (ulong value)
	Defines an implicit conversion of a 64-bit unsigned integer to a complex number. More...

static implicit	operator Complex32 (uint value)
	Defines an implicit conversion of a 32-bit unsigned integer to a complex number. More...

static implicit	operator Complex32 (ushort value)
	Defines an implicit conversion of a 16-bit unsigned integer to a complex number. More...

static implicit	operator Complex32 (long value)
	Defines an implicit conversion of a 64-bit signed integer to a complex number. More...

static implicit	operator Complex32 (int value)
	Defines an implicit conversion of a 32-bit signed integer to a complex number. More...

static implicit	operator Complex32 (short value)
	Defines an implicit conversion of a 16-bit signed integer to a complex number. More...

static	operator Complex32 (decimal value)
	Defines an explicit conversion of a System.Decimal value to a complex number. More...

Data Fields
float	Imaginary => _imag
	Gets the imaginary component of the current System.Numerics.Complex32 object. More...

float	Real => _real
	Gets the real component of the current System.Numerics.Complex32 object. More...

float	Phase => _imag == 0f && _real < 0f ? Mathf.PI : Mathf.Atan2(_imag, _real)
	Gets the phase of a complex number in radians. More...

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

Static Public Attributes
static readonly Complex32	Zero = new Complex32(0f, 0f)
	Returns a new Complex32 instance with a real number equal to zero and an imaginary number equal to zero. More...

static readonly Complex32	One = new Complex32(1f, 0f)
	Returns a new Complex32 instance with a real number equal to one and an imaginary number equal to zero. More...

static readonly Complex32	ImaginaryOne = new Complex32(0f, 1f)
	Returns a new Complex32 instance with a real number equal to zero and an imaginary number equal to one. More...

static readonly Complex32	PositiveInfinity = new Complex32(float.PositiveInfinity, float.PositiveInfinity)
	Returns a new Complex32 instance with real and imaginary numbers positive infinite. More...

static readonly Complex32	NaN = new Complex32(float.NaN, float.NaN)
	Returns a new Complex32 instance with real and imaginary numbers not a number. More...

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

Static Private Member Functions
static Complex32	InternalDiv (float a, float b, float c, float d, bool swapped)
	Helper method for dividing. More...

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

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

Detailed Description

Represents a complex number with single-precision floating point components

Definition at line 41 of file Complex32.cs.

Constructor & Destructor Documentation

◆ Complex32()

BGC.Mathematics.Complex32.Complex32	(	float	real,
		float	imaginary
	)

inline

Initializes a new Complex32 structure using the specified real and imaginary values.

Definition at line 84 of file Complex32.cs.

         {
             _real = real;
             _imag = imaginary;
         }

Member Function Documentation

◆ Abs()

static float BGC.Mathematics.Complex32.Abs ( in Complex32 value )

static

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

Referenced by BGC.Mathematics.Complex32.SquareRoot().

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◆ Acos()

static Complex32 BGC.Mathematics.Complex32.Acos ( in Complex32 value )

inlinestatic

Trigonometric principal Arc Cosine of this Complex32 number.

Parameters

value The complex value.

Returns: The arc cosine of a complex number.

Definition at line 155 of file Complex32.cs.

         {
             if (value.Imaginary < 0f || value.Imaginary == 0f && value.Real > 0f)
             {
                 return Mathf.PI - Acos(-value);
             }
 
             return -ImaginaryOne * (value + (ImaginaryOne * (1f - value.Square()).SquareRoot())).NaturalLogarithm();
         }

◆ Add()

static Complex32 BGC.Mathematics.Complex32.Add	(	in Complex32	left,
		in Complex32	right
	)

static

Returns the sum of the two Complex32 inputs

◆ Asin()

static Complex32 BGC.Mathematics.Complex32.Asin ( in Complex32 value )

inlinestatic

Trigonometric principal Arc Sine of this Complex32 number.

Parameters

value The complex value.

Returns: The arc sine of a complex number.

Definition at line 176 of file Complex32.cs.

         {
             if (value.Imaginary > 0f || value.Imaginary == 0f && value.Real < 0f)
             {
                 return -Asin(-value);
             }
 
             return -ImaginaryOne * ((1f - value.Square()).SquareRoot() + (ImaginaryOne * value)).NaturalLogarithm();
         }

◆ Atan()

static Complex32 BGC.Mathematics.Complex32.Atan ( in Complex32 value )

inlinestatic

Trigonometric principal Arc Tangent of this Complex32 number.

Parameters

value The complex value.

Returns: The arc tangent of a complex number.

Definition at line 192 of file Complex32.cs.

References BGC.Mathematics.Complex32.Conjugate().

         {
             Complex32 iz = new Complex32(-value.Imaginary, value.Real); // I*this
             return new Complex32(0f, 0.5f) * ((1f - iz).NaturalLogarithm() - (1f + iz).NaturalLogarithm());
         }

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◆ CommonLogarithm()

Complex32 BGC.Mathematics.Complex32.CommonLogarithm ( )

inline

Common Logarithm of this Complex32 (Base 10).

Returns: The common logarithm of this complex number.

Definition at line 771 of file Complex32.cs.

References BGC.Mathematics.Complex32.Log().

Referenced by BGC.Mathematics.Complex32.Cosh().

         {
             if (IsRealNonNegative())
             {
                 return new Complex32(Mathf.Log10(_real), 0f);
             }
 
             return new Complex32(0.5f * Mathf.Log10(MagnitudeSquared), Phase);
         }

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◆ Conjugate() [1/2]

static Complex32 BGC.Mathematics.Complex32.Conjugate ( in Complex32 value )

static

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

Referenced by BGC.Mathematics.Complex32.Atan(), and BGC.Mathematics.Fourier.BluesteinForward().

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◆ Conjugate() [2/2]

Complex32 BGC.Mathematics.Complex32.Conjugate ( )

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

◆ Cos()

static Complex32 BGC.Mathematics.Complex32.Cos ( in Complex32 value )

inlinestatic

Trigonometric Cosine of a Complex32 number.

Parameters

value The complex value.

Returns: The cosine of a complex number.

Definition at line 209 of file Complex32.cs.

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

Referenced by BGC.Mathematics.Complex32.Rotation().

         {
             if (value.IsReal())
             {
                 return new Complex32(Mathf.Cos(value.Real), 0f);
             }
 
             return new Complex32(
                 Mathf.Cos(value.Real) * GeneralMath.Cosh(value.Imaginary),
                 -Mathf.Sin(value.Real) * GeneralMath.Sinh(value.Imaginary));
         }

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◆ Cosh()

static Complex32 BGC.Mathematics.Complex32.Cosh ( in Complex32 value )

inlinestatic

Hyperbolic Cosine of a Complex32 number.

Parameters

value The complex value.

Returns: The hyperbolic cosine of a complex number.

Definition at line 227 of file Complex32.cs.

References BGC.Mathematics.Complex32.CommonLogarithm(), BGC.Mathematics.GeneralMath.Cosh(), BGC.Mathematics.Complex32.Exp(), BGC.Mathematics.Complex32.Exponential(), BGC.Mathematics.Complex32.Logarithm(), BGC.Mathematics.Complex32.NaturalLogarithm(), BGC.Mathematics.Complex32.Power(), BGC.Mathematics.Complex32.Reciprocal(), and BGC.Mathematics.GeneralMath.Sinh().

         {
             if (value.IsReal())
             {
                 return new Complex32(GeneralMath.Cosh(value.Real), 0f);
             }
 
             // 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 (Mathf.Abs(value.Real) >= 22f) // Taken from the msun library in FreeBSD
             {
                 float h = Mathf.Exp(Mathf.Abs(value.Real)) * 0.5f;
                 return new Complex32(
                     h * Mathf.Cos(value.Imaginary),
                     Mathf.Sign(value.Real) * h * Mathf.Sin(value.Imaginary));
             }
 
             return new Complex32(
                 GeneralMath.Cosh(value.Real) * Mathf.Cos(value.Imaginary),
                 GeneralMath.Sinh(value.Real) * Mathf.Sin(value.Imaginary));
         }

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◆ Divide()

static Complex32 BGC.Mathematics.Complex32.Divide	(	in Complex32	dividend,
		in Complex32	divisor
	)

static

Divides one complex number by another and returns the result.

◆ Equals() [1/3]

bool BGC.Mathematics.Complex32.Equals ( in Complex32 value )

inline

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

Definition at line 477 of file Complex32.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<Complex32>. BGC.Mathematics.Complex32.Equals ( Complex32 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.Complex32.Equals ( object obj )

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

◆ Exp()

static Complex32 BGC.Mathematics.Complex32.Exp ( in Complex32 value )

static

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

Referenced by BGC.Mathematics.Complex32.Cosh(), BGC.Mathematics.Complex32.Exponential(), BGC.Mathematics.Complex32.Sinh(), and BGC.Mathematics.Complex32.Tanh().

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◆ Exponential()

Complex32 BGC.Mathematics.Complex32.Exponential ( )

inline

Exponential of this Complex32 (exp(x), E^x).

Returns: The exponential of this complex number.

Definition at line 793 of file Complex32.cs.

References BGC.Mathematics.Complex32._real, and BGC.Mathematics.Complex32.Exp().

Referenced by BGC.Mathematics.Complex32.Cosh().

         {
             float exp = Mathf.Exp(_real);
             if (IsReal())
             {
                 return new Complex32(exp, 0f);
             }
 
             return new Complex32(exp * Mathf.Cos(_imag), exp * Mathf.Sin(_imag));
         }

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◆ FromPolarCoordinates() [1/2]

static Complex32 BGC.Mathematics.Complex32.FromPolarCoordinates	(	float	magnitude,
		float	phase
	)

static

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

◆ FromPolarCoordinates() [2/2]

static Complex32 BGC.Mathematics.Complex32.FromPolarCoordinates	(	double	magnitude,
		double	phase
	)

static

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

◆ GetHashCode()

override int BGC.Mathematics.Complex32.GetHashCode ( )

inline

Returns the hash code for the current Complex32 object.

Definition at line 506 of file Complex32.cs.

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

◆ InternalDiv()

static Complex32 BGC.Mathematics.Complex32.InternalDiv	(	float	a,
		float	b,
		float	c,
		float	d,
		bool	swapped
	)

inlinestaticprivate

Helper method for dividing.

Parameters

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

Definition at line 875 of file Complex32.cs.

         {
             float r = d / c;
             float t = 1 / (c + d * r);
             float e, f;
 
             if (r != 0f) // one can use r >= float.Epsilon || r <= float.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 Complex32(e, f);
         }

◆ IsImaginaryOne()

bool BGC.Mathematics.Complex32.IsImaginaryOne ( )

Gets a value indicating whether the Complex32 is the imaginary unit.

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

◆ IsInfinity()

bool BGC.Mathematics.Complex32.IsInfinity ( )

Gets a value indicating whether the provided Complex32 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.Complex32.IsNaN ( )

Gets a value indicating whether the provided Complex32evaluates to a value that is not a number.

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

◆ IsOne()

bool BGC.Mathematics.Complex32.IsOne ( )

Gets a value indicating whether the Complex32 is one.

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

◆ IsReal()

bool BGC.Mathematics.Complex32.IsReal ( )

Gets a value indicating whether the provided Complex32 is real.

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

◆ IsRealNonNegative()

bool BGC.Mathematics.Complex32.IsRealNonNegative ( )

Gets a value indicating whether the provided Complex32 is real and not negative, that is >= 0.

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

◆ IsZero()

bool BGC.Mathematics.Complex32.IsZero ( )

Gets a value indicating whether the Complex32 is zero.

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

◆ Log() [1/2]

static Complex32 BGC.Mathematics.Complex32.Log ( in Complex32 value )

static

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

Referenced by BGC.Mathematics.Complex32.CommonLogarithm().

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◆ Log() [2/2]

static Complex32 BGC.Mathematics.Complex32.Log	(	in Complex32	value,
		float	baseValue
	)

static

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

◆ Log10()

static Complex32 BGC.Mathematics.Complex32.Log10 ( in Complex32 value )

static

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

◆ Logarithm()

Complex32 BGC.Mathematics.Complex32.Logarithm ( float baseValue )

Logarithm of this Complex32 with custom base.

Returns: The logarithm of this complex number.

Referenced by BGC.Mathematics.Complex32.Cosh().

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◆ Multiply()

static Complex32 BGC.Mathematics.Complex32.Multiply	(	in Complex32	left,
		in Complex32	right
	)

static

Returns the product of two complex numbers.

◆ NaturalLogarithm()

Complex32 BGC.Mathematics.Complex32.NaturalLogarithm ( )

inline

Natural Logarithm of this Complex32 (Base E).

Returns: The natural logarithm of this complex number.

Definition at line 757 of file Complex32.cs.

Referenced by BGC.Mathematics.Complex32.Cosh().

         {
             if (IsRealNonNegative())
             {
                 return new Complex32(Mathf.Log(_real), 0f);
             }
 
             return new Complex32(0.5f * Mathf.Log(MagnitudeSquared), Phase);
         }

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◆ Negate()

static Complex32 BGC.Mathematics.Complex32.Negate ( in Complex32 value )

static

Returns the additive inverse of a specified complex number.

◆ operator Complex32() [1/11]

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

static

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

◆ operator Complex32() [2/11]

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

static

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

◆ operator Complex32() [3/11]

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

static

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

Parameters

value

◆ operator Complex32() [4/11]

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

static

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

◆ operator Complex32() [5/11]

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

static

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

◆ operator Complex32() [6/11]

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

static

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

◆ operator Complex32() [7/11]

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

static

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

◆ operator Complex32() [8/11]

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

static

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

◆ operator Complex32() [9/11]

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

static

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

◆ operator Complex32() [10/11]

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

static

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

◆ operator Complex32() [11/11]

static BGC.Mathematics.Complex32.operator Complex32 ( decimal value )

explicitstatic

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

◆ operator!=()

static bool BGC.Mathematics.Complex32.operator!=	(	in Complex32	left,
		in Complex32	right
	)

static

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

◆ operator*()

static Complex32 BGC.Mathematics.Complex32.operator*	(	in Complex32	left,
		in Complex32	right
	)

static

Multiplies two specified complex numbers.

◆ operator+()

static Complex32 BGC.Mathematics.Complex32.operator+	(	in Complex32	left,
		in Complex32	right
	)

static

Adds two complex numbers.

◆ operator-() [1/2]

static Complex32 BGC.Mathematics.Complex32.operator- ( in Complex32 value )

static

Returns the additive inverse of a specified complex number.

◆ operator-() [2/2]

static Complex32 BGC.Mathematics.Complex32.operator-	(	in Complex32	left,
		in Complex32	right
	)

static

Subtracts a complex number from another complex number.

◆ operator/()

static Complex32 BGC.Mathematics.Complex32.operator/	(	in Complex32	dividend,
		in Complex32	divisor
	)

inlinestatic

Divides a specified complex number by another specified complex number.

Definition at line 566 of file Complex32.cs.

References BGC.Mathematics.Complex32.Real.

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

◆ operator==()

static bool BGC.Mathematics.Complex32.operator==	(	in Complex32	left,
		in Complex32	right
	)

static

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

◆ Pow() [1/2]

static Complex32 BGC.Mathematics.Complex32.Pow	(	in Complex32	value,
		float	power
	)

static

Returns a specified complex number raised to a power specified by a float-precision floating-point number.

◆ Pow() [2/2]

static Complex32 BGC.Mathematics.Complex32.Pow	(	in Complex32	value,
		in Complex32	power
	)

static

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

◆ Power()

Complex32 BGC.Mathematics.Complex32.Power ( in Complex32 exponent )

inline

Raise this Complex32 to the given value.

Parameters

exponent The exponent.

Returns: The complex number raised to the given exponent.

Definition at line 726 of file Complex32.cs.

References BGC.Mathematics.Complex32.Imaginary.

Referenced by BGC.Mathematics.Complex32.Cosh().

         {
             if (IsZero())
             {
                 if (exponent.IsZero())
                 {
                     return One;
                 }
 
                 if (exponent.Real > 0f)
                 {
                     return Zero;
                 }
 
                 if (exponent.Real < 0f)
                 {
                     return exponent.Imaginary == 0f
                         ? new Complex32(float.PositiveInfinity, 0f)
                         : new Complex32(float.PositiveInfinity, float.PositiveInfinity);
                 }
 
                 return NaN;
             }
 
             return (exponent * NaturalLogarithm()).Exponential();
         }

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◆ RealProduct()

float BGC.Mathematics.Complex32.RealProduct ( in Complex32 other )

Returns the real component of the product of this Complex32 with other.

Returns: The real component of the product.

◆ RealRotation()

float BGC.Mathematics.Complex32.RealRotation ( float phase )

Retuns the real value of the Complex32 number after rotation by phase radians, or exp(i*phase)

◆ Reciprocal() [1/2]

static Complex32 BGC.Mathematics.Complex32.Reciprocal ( in Complex32 value )

static

Returns the multiplicative inverse of a complex number.

Referenced by BGC.Mathematics.Complex32.Cosh().

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◆ Reciprocal() [2/2]

Complex32 BGC.Mathematics.Complex32.Reciprocal ( )

Returns the multiplicative inverse of a complex number.

◆ Rotation()

Complex32 BGC.Mathematics.Complex32.Rotation ( float phase )

inline

Retuns the Complex32 number, rotated by phase radians, or exp(i*phase)

Definition at line 459 of file Complex32.cs.

References BGC.Mathematics.Complex32.Cos(), and BGC.Mathematics.Complex32.Sin().

         {
             float cosPhase = Mathf.Cos(phase);
             float sinePhase = Mathf.Sin(phase);
             return new Complex32(
                 _real * cosPhase - _imag * sinePhase,
                 _real * sinePhase + _imag * cosPhase);
         }

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◆ Sin()

static Complex32 BGC.Mathematics.Complex32.Sin ( in Complex32 value )

inlinestatic

Trigonometric Sine of a Complex32 number.

Parameters

value The complex value.

Returns: The sine of the complex number.

Definition at line 318 of file Complex32.cs.

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

Referenced by BGC.Mathematics.Complex32.Rotation().

         {
             if (value.IsReal())
             {
                 return new Complex32(Mathf.Sin(value.Real), 0f);
             }
 
             return new Complex32(
                 Mathf.Sin(value.Real) * GeneralMath.Cosh(value.Imaginary),
                 Mathf.Cos(value.Real) * GeneralMath.Sinh(value.Imaginary));
         }

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◆ Sinh()

static Complex32 BGC.Mathematics.Complex32.Sinh ( in Complex32 value )

inlinestatic

Hyperbolic Sine of a Complex32 number.

Parameters

value The complex value.

Returns: The hyperbolic sine of a complex number.

Definition at line 336 of file Complex32.cs.

References BGC.Mathematics.GeneralMath.Cosh(), BGC.Mathematics.Complex32.Exp(), and BGC.Mathematics.GeneralMath.Sinh().

         {
             if (value.IsReal())
             {
                 return new Complex32(GeneralMath.Sinh(value.Real), 0f);
             }
 
             // 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 (Mathf.Abs(value.Real) >= 22f) // Taken from the msun library in FreeBSD
             {
                 float h = Mathf.Exp(Mathf.Abs(value.Real)) * 0.5f;
                 return new Complex32(
                     Mathf.Sign(value.Real) * h * Mathf.Cos(value.Imaginary),
                     h * Mathf.Sin(value.Imaginary));
             }
 
             return new Complex32(
                 GeneralMath.Sinh(value.Real) * Mathf.Cos(value.Imaginary),
                 GeneralMath.Cosh(value.Real) * Mathf.Sin(value.Imaginary));
         }

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◆ Sqrt()

static Complex32 BGC.Mathematics.Complex32.Sqrt ( in Complex32 value )

static

The Square Root of a complex number

◆ Square()

Complex32 BGC.Mathematics.Complex32.Square ( )

inline

The Square (power 2) of this Complex32

Returns: The square of this complex number.

Definition at line 365 of file Complex32.cs.

References BGC.Mathematics.Complex32.SquareRoot().

         {
             if (IsReal())
             {
                 return new Complex32(_real * _real, 0.0f);
             }
 
             return new Complex32((_real * _real) - (_imag * _imag), 2 * _real * _imag);
         }

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◆ SquareRoot()

Complex32 BGC.Mathematics.Complex32.SquareRoot ( )

inline

The Square Root (power 1/2) of this Complex32

Returns: The square root of this complex number.

Definition at line 829 of file Complex32.cs.

References BGC.Mathematics.Complex32.Abs().

Referenced by BGC.Mathematics.Complex32.Square().

         {
             if (IsRealNonNegative())
             {
                 return new Complex32(Mathf.Sqrt(_real), 0f);
             }
 
             Complex32 result;
 
             float absReal = Mathf.Abs(Real);
             float absImag = Mathf.Abs(Imaginary);
             float w;
             if (absReal >= absImag)
             {
                 float ratio = Imaginary / Real;
                 w = Mathf.Sqrt(absReal) * Mathf.Sqrt(0.5f * (1f + Mathf.Sqrt(1f + (ratio * ratio))));
             }
             else
             {
                 float ratio = Real / Imaginary;
                 w = Mathf.Sqrt(absImag) * Mathf.Sqrt(0.5f * (Mathf.Abs(ratio) + Mathf.Sqrt(1f + (ratio * ratio))));
             }
 
             if (Real >= 0f)
             {
                 result = new Complex32(w, (Imaginary / (2f * w)));
             }
             else if (Imaginary >= 0f)
             {
                 result = new Complex32((absImag / (2f * w)), w);
             }
             else
             {
                 result = new Complex32((absImag / (2f * w)), -w);
             }
 
             return result;
         }

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◆ Subtract()

static Complex32 BGC.Mathematics.Complex32.Subtract	(	in Complex32	left,
		Complex32	right
	)

static

The difference between two Complex32 numbers;

Returns: The complex difference.

◆ Tan()

static Complex32 BGC.Mathematics.Complex32.Tan ( in Complex32 value )

inlinestatic

Trigonometric Tangent of a Complex32 number.

Parameters

value The complex value.

Returns: The tangent of the complex number.

Definition at line 394 of file Complex32.cs.

Referenced by BGC.Mathematics.Complex32.Tanh().

         {
             if (value.IsReal())
             {
                 return new Complex32(Mathf.Tan(value.Real), 0f);
             }
 
             // tan(z) = - j*tanh(j*z)
 
             Complex32 z = Tanh(new Complex32(-value.Imaginary, value.Real));
             return new Complex32(z.Imaginary, -z.Real);
         }

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◆ Tanh()

static Complex32 BGC.Mathematics.Complex32.Tanh ( in Complex32 value )

inlinestatic

Hyperbolic Tangent of a Complex32 number.

Parameters

value The complex value.

Returns: The hyperbolic tangent of a complex number.

Definition at line 413 of file Complex32.cs.

References BGC.Mathematics.GeneralMath.Cosh(), BGC.Mathematics.Complex32.Exp(), BGC.Mathematics.GeneralMath.Sinh(), BGC.Mathematics.Complex32.Tan(), and BGC.Mathematics.GeneralMath.Tanh().

         {
             if (value.IsReal())
             {
                 return new Complex32(GeneralMath.Tanh(value.Real), 0f);
             }
 
             // 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) >= 22f) // Taken from the msun library in FreeBSD
             {
                 float e = Mathf.Exp(-Mathf.Abs(value.Real));
                 if (e == 0f)
                 {
                     return new Complex32(Mathf.Sign(value.Real), 0f);
                 }
                 else
                 {
                     return new Complex32(
                         Mathf.Sign(value.Real),
                         4f * Mathf.Cos(value.Imaginary) * Mathf.Sin(value.Imaginary) * e * e);
                 }
             }
 
             float tani = Mathf.Tan(value.Imaginary);
             float beta = 1 + tani * tani; // beta = 1/cos^2(y) = 1 + t^2
             float sinhr = GeneralMath.Sinh(value.Real);
             float coshr = GeneralMath.Cosh(value.Real);
 
             if (float.IsInfinity(tani))
             {
                 return new Complex32(coshr / sinhr, 0f);
             }
 
             float denom = 1f + beta * sinhr * sinhr;
             return new Complex32(beta * coshr * sinhr / denom, tani / denom);
         }

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◆ ToString() [1/4]

string BGC.Mathematics.Complex32.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.Complex32.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.Complex32.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.Complex32.ToString ( )

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

Returns

Field Documentation

◆ _imag

readonly float BGC.Mathematics.Complex32._imag

private

The imaginary component of the complex number.

Definition at line 53 of file Complex32.cs.

◆ _real

readonly float BGC.Mathematics.Complex32._real

private

The real component of the complex number.

Definition at line 47 of file Complex32.cs.

Referenced by BGC.Mathematics.Complex32.Exponential().

◆ Imaginary

float BGC.Mathematics.Complex32.Imaginary => _imag

Gets the imaginary component of the current System.Numerics.Complex32 object.

Definition at line 93 of file Complex32.cs.

Referenced by BGC.Mathematics.Complex64.operator/(), and BGC.Mathematics.Complex32.Power().

◆ ImaginaryOne

readonly Complex32 BGC.Mathematics.Complex32.ImaginaryOne = new Complex32(0f, 1f)

static

Returns a new Complex32 instance with a real number equal to zero and an imaginary number equal to one.

Definition at line 69 of file Complex32.cs.

◆ MagnitudeSquared

float BGC.Mathematics.Complex32.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 715 of file Complex32.cs.

◆ NaN

readonly Complex32 BGC.Mathematics.Complex32.NaN = new Complex32(float.NaN, float.NaN)

static

Returns a new Complex32 instance with real and imaginary numbers not a number.

Definition at line 79 of file Complex32.cs.

◆ One

readonly Complex32 BGC.Mathematics.Complex32.One = new Complex32(1f, 0f)

static

Returns a new Complex32 instance with a real number equal to one and an imaginary number equal to zero.

Definition at line 64 of file Complex32.cs.

◆ Phase

float BGC.Mathematics.Complex32.Phase => _imag == 0f && _real < 0f ? Mathf.PI : Mathf.Atan2(_imag, _real)

Gets the phase of a complex number in radians.

Definition at line 142 of file Complex32.cs.

◆ PositiveInfinity

readonly Complex32 BGC.Mathematics.Complex32.PositiveInfinity = new Complex32(float.PositiveInfinity, float.PositiveInfinity)

static

Returns a new Complex32 instance with real and imaginary numbers positive infinite.

Definition at line 74 of file Complex32.cs.

◆ Real

float BGC.Mathematics.Complex32.Real => _real

Gets the real component of the current System.Numerics.Complex32 object.

Definition at line 98 of file Complex32.cs.

Referenced by BGC.Mathematics.Complex64.operator/(), and BGC.Mathematics.Complex32.operator/().

◆ Zero

readonly Complex32 BGC.Mathematics.Complex32.Zero = new Complex32(0f, 0f)

static

Returns a new Complex32 instance with a real number equal to zero and an imaginary number equal to zero.

Definition at line 59 of file Complex32.cs.

Property Documentation

◆ Magnitude

float BGC.Mathematics.Complex32.Magnitude

get

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

Definition at line 104 of file Complex32.cs.

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

Mathematics/Complex32.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

◆ Complex32()

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() [1/2]

◆ FromPolarCoordinates() [2/2]

◆ GetHashCode()

◆ InternalDiv()

◆ IsImaginaryOne()

◆ IsInfinity()

◆ IsNaN()

◆ IsOne()

◆ IsReal()

◆ IsRealNonNegative()

◆ IsZero()

◆ Log() [1/2]

◆ Log() [2/2]

◆ Log10()

◆ Logarithm()

◆ Multiply()

◆ NaturalLogarithm()

◆ Negate()

◆ operator Complex32() [1/11]

◆ operator Complex32() [2/11]

◆ operator Complex32() [3/11]

◆ operator Complex32() [4/11]

◆ operator Complex32() [5/11]

◆ operator Complex32() [6/11]

◆ operator Complex32() [7/11]

◆ operator Complex32() [8/11]

◆ operator Complex32() [9/11]

◆ operator Complex32() [10/11]

◆ operator Complex32() [11/11]

◆ 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]