ComplexMath (FsODE)

FsODE

Documentation for 0.0.2

ComplexMath Type

Namespace: Altaxo.Calc
Assembly: AltaxoCore.Redist.dll
Base Type: obj

Various mathematical functions for complex numbers.

Static members

Static member	Description
`ComplexMath.Abs(c)` Full Usage: `ComplexMath.Abs(c)` Parameters: c : `Complex` - The complex argument. Returns: `float` The absolute value (also called modulus, length, euclidean norm) of the complex number.	The absolute value (modulus) of complex number. Only for completeness, you can also use c.GetModulus() c : `Complex` The complex argument. Returns: `float` The absolute value (also called modulus, length, euclidean norm) of the complex number.
`ComplexMath.Abs2(c)` Full Usage: `ComplexMath.Abs2(c)` Parameters: c : `Complex` - The complex argument. Returns: `float` The squared modulus (length^2) of the complex number.	The squared modulus (length^2) of the complex number Only for completeness, you can also use c.GetModulusSquared() c : `Complex` The complex argument. Returns: `float` The squared modulus (length^2) of the complex number.
`ComplexMath.Absolute(c)` Full Usage: `ComplexMath.Absolute(c)` Parameters: c : `Complex` Returns: `float`	Return the absolute value of a complex type calculated as the euclidean norm Same as ComplexMath.Abs and provided here for compatibility with some libraries. c : `Complex` Returns: `float`
`ComplexMath.Absolute(c)` Full Usage: `ComplexMath.Absolute(c)` Parameters: c : `ComplexFloat` Returns: `float32`	Return the absolute value of a complex type calculated as the euclidean norm Same as ComplexMath.Abs and provided here for compatibility with some libraries. c : `ComplexFloat` Returns: `float32`
`ComplexMath.Acos(a)` Full Usage: `ComplexMath.Acos(a)` Parameters: a : `Complex` - The function argument. Returns: `Complex` The complex arccosine of the complex number a.	This function returns the complex arccosine of the complex number a, arccos(a). The branch cuts are on the real axis, less than -1 and greater than 1. a : `Complex` The function argument. Returns: `Complex` The complex arccosine of the complex number a.
`ComplexMath.Acos(a)` Full Usage: `ComplexMath.Acos(a)` Parameters: a : `ComplexFloat` - The function argument. Returns: `ComplexFloat` The complex arccosine of the complex number a.	This function returns the complex arccosine of the complex number a, arccos(a). The branch cuts are on the real axis, less than -1 and greater than 1. a : `ComplexFloat` The function argument. Returns: `ComplexFloat` The complex arccosine of the complex number a.
`ComplexMath.Acos(a)` Full Usage: `ComplexMath.Acos(a)` Parameters: a : `float` - The function argument. Returns: `Complex` The complex arccosine of the real number a.	This function returns the complex arccosine of the real number a, arccos(a). For a between -1 and 1, the function returns a real value in the range [0,pi]. For a less than -1 the result has a real part of pi/2 and a negative imaginary part. For a greater than 1 the result is purely imaginary and positive. a : `float` The function argument. Returns: `Complex` The complex arccosine of the real number a.
`ComplexMath.Acosh(a)` Full Usage: `ComplexMath.Acosh(a)` Parameters: a : `Complex` - Function argument. Returns: `Complex` The complex hyperbolic arccosine of the complex number a.	This function returns the complex hyperbolic arccosine of the complex number a, arccosh(a). The branch cut is on the real axis, less than 1. a : `Complex` Function argument. Returns: `Complex` The complex hyperbolic arccosine of the complex number a.
`ComplexMath.Acosh(a)` Full Usage: `ComplexMath.Acosh(a)` Parameters: a : `ComplexFloat` - Function argument. Returns: `ComplexFloat` The complex hyperbolic arccosine of the complex number a.	This function returns the complex hyperbolic arccosine of the complex number a, arccosh(a). The branch cut is on the real axis, less than 1. a : `ComplexFloat` Function argument. Returns: `ComplexFloat` The complex hyperbolic arccosine of the complex number a.
`ComplexMath.Acosh(a)` Full Usage: `ComplexMath.Acosh(a)` Parameters: a : `float` - Function argument. Returns: `Complex` The complex hyperbolic arccosine of the real number a.	This function returns the complex hyperbolic arccosine of the real number a, arccosh(a). a : `float` Function argument. Returns: `Complex` The complex hyperbolic arccosine of the real number a.
`ComplexMath.Acot(a)` Full Usage: `ComplexMath.Acot(a)` Parameters: a : `Complex` - Function argument. Returns: `Complex` The complex arccotangent of the complex number a.	This function returns the complex arccotangent of the complex number a, arccot(a) = arctan(1/a). a : `Complex` Function argument. Returns: `Complex` The complex arccotangent of the complex number a.
`ComplexMath.Acoth(a)` Full Usage: `ComplexMath.Acoth(a)` Parameters: a : `Complex` - Function argument. Returns: `Complex` The complex hyperbolic arccotangent of the complex number a.	This function returns the complex hyperbolic arccotangent of the complex number a, arccoth(a) = arctanh(1/a). a : `Complex` Function argument. Returns: `Complex` The complex hyperbolic arccotangent of the complex number a.
`ComplexMath.Acsc(a)` Full Usage: `ComplexMath.Acsc(a)` Parameters: a : `Complex` - Function argument. Returns: `Complex` The complex arccosecant of the complex number a.	This function returns the complex arccosecant of the complex number a, arccsc(a) = arcsin(1/a). a : `Complex` Function argument. Returns: `Complex` The complex arccosecant of the complex number a.
`ComplexMath.Acsc(a)` Full Usage: `ComplexMath.Acsc(a)` Parameters: a : `float` - Function argument. Returns: `Complex` The complex arccosecant of the real number a.	This function returns the complex arccosecant of the real number a, arccsc(a) = arcsin(1/a). a : `float` Function argument. Returns: `Complex` The complex arccosecant of the real number a.
`ComplexMath.Acsch(a)` Full Usage: `ComplexMath.Acsch(a)` Parameters: a : `Complex` - Function argument. Returns: `Complex` The complex hyperbolic arccosecant of the complex number a.	This function returns the complex hyperbolic arccosecant of the complex number a, arccsch(a) = arcsin(1/a). a : `Complex` Function argument. Returns: `Complex` The complex hyperbolic arccosecant of the complex number a.
`ComplexMath.Arg(c)` Full Usage: `ComplexMath.Arg(c)` Parameters: c : `Complex` - The complex number. Returns: `float` The argument (also called phase) of the complex number.	The argument value (also called phase) of a complex number. Only for completeness, you can also use c.GetArgument() c : `Complex` The complex number. Returns: `float` The argument (also called phase) of the complex number.
`ComplexMath.Arg(c)` Full Usage: `ComplexMath.Arg(c)` Parameters: c : `ComplexFloat` - The complex number. Returns: `float` The argument (also called phase) of the complex number.	The argument value (also called phase) of a complex number. Only for completeness, you can also use c.GetArgument() c : `ComplexFloat` The complex number. Returns: `float` The argument (also called phase) of the complex number.
`ComplexMath.Argument(value)` Full Usage: `ComplexMath.Argument(value)` Parameters: value : `Complex` Returns: `float`	Calculate the complex argument of a complex type. Also commonly refered to as the phase. value : `Complex` Returns: `float`
`ComplexMath.Argument(value)` Full Usage: `ComplexMath.Argument(value)` Parameters: value : `ComplexFloat` Returns: `float32`	Calculate the complex argument of a complex type. Also commonly refered to as the phase. value : `ComplexFloat` Returns: `float32`
`ComplexMath.Argument2(value)` Full Usage: `ComplexMath.Argument2(value)` Parameters: value : `Complex` Returns: `float`	Calculate the 2-argument of a complex type. value : `Complex` Returns: `float`
`ComplexMath.Argument2(value)` Full Usage: `ComplexMath.Argument2(value)` Parameters: value : `ComplexFloat` Returns: `float32`	Calculate the 2-argument of a complex type. value : `ComplexFloat` Returns: `float32`
`ComplexMath.Asec(a)` Full Usage: `ComplexMath.Asec(a)` Parameters: a : `Complex` - Function argument. Returns: `Complex` The complex arcsecant of the complex number a.	This function returns the complex arcsecant of the complex number a, arcsec(a) = arccos(1/a). a : `Complex` Function argument. Returns: `Complex` The complex arcsecant of the complex number a.
`ComplexMath.Asec(a)` Full Usage: `ComplexMath.Asec(a)` Parameters: a : `float` - Function argument. Returns: `Complex` The complex arcsecant of the real number a.	This function returns the complex arcsecant of the real number a, arcsec(a) = arccos(1/a). a : `float` Function argument. Returns: `Complex` The complex arcsecant of the real number a.
`ComplexMath.Asech(a)` Full Usage: `ComplexMath.Asech(a)` Parameters: a : `Complex` - Function argument. Returns: `Complex` The complex hyperbolic arcsecant of the complex number a.	This function returns the complex hyperbolic arcsecant of the complex number a, arcsech(a) = arccosh(1/a). a : `Complex` Function argument. Returns: `Complex` The complex hyperbolic arcsecant of the complex number a.
`ComplexMath.Asin(a)` Full Usage: `ComplexMath.Asin(a)` Parameters: a : `Complex` - The function argument. Returns: `Complex` the complex arcsine of the complex number a.	This function returns the complex arcsine of the complex number a, arcsin(a)}. The branch cuts are on the real axis, less than -1 and greater than 1. a : `Complex` The function argument. Returns: `Complex` the complex arcsine of the complex number a.
`ComplexMath.Asin(a)` Full Usage: `ComplexMath.Asin(a)` Parameters: a : `ComplexFloat` - The function argument. Returns: `ComplexFloat` the complex arcsine of the complex number a.	This function returns the complex arcsine of the complex number a, arcsin(a)}. The branch cuts are on the real axis, less than -1 and greater than 1. a : `ComplexFloat` The function argument. Returns: `ComplexFloat` the complex arcsine of the complex number a.
`ComplexMath.Asin(a)` Full Usage: `ComplexMath.Asin(a)` Parameters: a : `float` - The function argument. Returns: `Complex` The complex arcsine of the real number a.	This function returns the complex arcsine of the real number a, arcsin(a). For a between -1 and 1, the function returns a real value in the range -(pi,pi]. For a less than -1 the result has a real part of -pi/2 and a positive imaginary part. For a greater than 1 the result has a real part of pi/2 and a negative imaginary part. a : `float` The function argument. Returns: `Complex` The complex arcsine of the real number a.
`ComplexMath.Asinh(a)` Full Usage: `ComplexMath.Asinh(a)` Parameters: a : `Complex` - Function argument. Returns: `Complex` The complex hyperbolic arcsine of the complex number a.	This function returns the complex hyperbolic arcsine of the complex number a, arcsinh(a). The branch cuts are on the imaginary axis, below -i and above i. a : `Complex` Function argument. Returns: `Complex` The complex hyperbolic arcsine of the complex number a.
`ComplexMath.Asinh(a)` Full Usage: `ComplexMath.Asinh(a)` Parameters: a : `ComplexFloat` - Function argument. Returns: `ComplexFloat` The complex hyperbolic arcsine of the complex number a.	This function returns the complex hyperbolic arcsine of the complex number a, arcsinh(a). The branch cuts are on the imaginary axis, below -i and above i. a : `ComplexFloat` Function argument. Returns: `ComplexFloat` The complex hyperbolic arcsine of the complex number a.
`ComplexMath.Atan(a)` Full Usage: `ComplexMath.Atan(a)` Parameters: a : `Complex` - The function argument. Returns: `Complex` The complex arctangent of the complex number a.	This function returns the complex arctangent of the complex number a, arctan(a)}. The branch cuts are on the imaginary axis, below -i and above i . a : `Complex` The function argument. Returns: `Complex` The complex arctangent of the complex number a.
`ComplexMath.Atan(a)` Full Usage: `ComplexMath.Atan(a)` Parameters: a : `ComplexFloat` - The function argument. Returns: `ComplexFloat` The complex arctangent of the complex number a.	This function returns the complex arctangent of the complex number a, arctan(a)}. The branch cuts are on the imaginary axis, below -i and above i . a : `ComplexFloat` The function argument. Returns: `ComplexFloat` The complex arctangent of the complex number a.
`ComplexMath.Atanh(a)` Full Usage: `ComplexMath.Atanh(a)` Parameters: a : `Complex` - Function argument. Returns: `Complex` The complex hyperbolic arctangent of the complex number a.	This function returns the complex hyperbolic arctangent of the complex number a, arctanh(a). The branch cuts are on the real axis, less than -1 and greater than 1. a : `Complex` Function argument. Returns: `Complex` The complex hyperbolic arctangent of the complex number a.
`ComplexMath.Atanh(a)` Full Usage: `ComplexMath.Atanh(a)` Parameters: a : `ComplexFloat` - Function argument. Returns: `ComplexFloat` The complex hyperbolic arctangent of the complex number a.	This function returns the complex hyperbolic arctangent of the complex number a, arctanh(a). The branch cuts are on the real axis, less than -1 and greater than 1. a : `ComplexFloat` Function argument. Returns: `ComplexFloat` The complex hyperbolic arctangent of the complex number a.
`ComplexMath.Atanh(a)` Full Usage: `ComplexMath.Atanh(a)` Parameters: a : `float` - Function argument. Returns: `Complex` The complex hyperbolic arctangent of the real number a.	This function returns the complex hyperbolic arctangent of the real number a, arctanh(a). a : `float` Function argument. Returns: `Complex` The complex hyperbolic arctangent of the real number a.
`ComplexMath.Conjugate(a)` Full Usage: `ComplexMath.Conjugate(a)` Parameters: a : `Complex` Returns: `Complex`	Return the complex conjugate of a complex type a : `Complex` Returns: `Complex`
`ComplexMath.Conjugate(a)` Full Usage: `ComplexMath.Conjugate(a)` Parameters: a : `ComplexFloat` Returns: `ComplexFloat`	Return the complex conjugate of a complex type a : `ComplexFloat` Returns: `ComplexFloat`
`ComplexMath.Cos(z)` Full Usage: `ComplexMath.Cos(z)` Parameters: z : `Complex` - Function argument. Returns: `Complex` The cosine of the specified complex function argument z.	Returns the cosine of the specified complex function argument z. z : `Complex` Function argument. Returns: `Complex` The cosine of the specified complex function argument z.
`ComplexMath.Cos(z)` Full Usage: `ComplexMath.Cos(z)` Parameters: z : `ComplexFloat` - Function argument. Returns: `ComplexFloat` The cosine of the specified complex function argument z.	Returns the cosine of the specified complex function argument z. z : `ComplexFloat` Function argument. Returns: `ComplexFloat` The cosine of the specified complex function argument z.
`ComplexMath.Cosh(a)` Full Usage: `ComplexMath.Cosh(a)` Parameters: a : `Complex` - Function argument. Returns: `Complex` The hyperbolic cosine of the specified complex function argument z.	This function returns the complex hyperbolic cosine of the complex number a, cosh(a) = (exp(a) + exp(-z))/2. a : `Complex` Function argument. Returns: `Complex` The hyperbolic cosine of the specified complex function argument z.