IGLib
1.7.2
The IGLib base library EXTENDED - with other lilbraries and applications.
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Provides simple functions of complex arguments. More...
Static Public Member Functions | |
static double | Abs (Complex z) |
Computes the absolute value of a complex number. More... | |
static double | Arg (Complex z) |
Computes the phase of a complex number. More... | |
static Complex | Exp (Complex z) |
Computes e raised to the power of a complex number. More... | |
static Complex | Log (Complex z) |
Computes the natrual logarithm of a complex number. More... | |
static Complex | Sqr (Complex z) |
Computes the square of a complex number. More... | |
static Complex | Sqrt (Complex z) |
Computes the square root of a complex number. More... | |
static Complex | Sin (Complex z) |
Computes the sine of a complex number. More... | |
static Complex | Sinh (Complex z) |
Computes the hyperbolic sine of a complex number. More... | |
static Complex | Cos (Complex z) |
Computes the cosine of a complex number. More... | |
static Complex | Cosh (Complex z) |
Computes the hyperbolic cosine of a complex number. More... | |
static Complex | Tan (Complex z) |
Computes the tangent of a complex number. More... | |
static Complex | Tanh (Complex z) |
Computes the hyperbolic tangent of a complex number. More... | |
static Complex | Pow (Complex z, double p) |
Raises a complex number to an arbitrary real power. More... | |
static Complex | Pow (double x, Complex z) |
Raises a real number to an arbitrary complex power. More... | |
static Complex | Pow (Complex z, int n) |
Raises a complex number to an integer power. More... | |
Properties | |
static Complex | I [get] |
Gets the unit imaginary number I. More... | |
Provides simple functions of complex arguments.
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inlinestatic |
Computes the absolute value of a complex number.
z | The argument. |
The absolute value of a complex number is the distance of the number from the origin in the complex plane. This is a compatible generalization of the definition of the absolute value of a real number.
References Meta.Numerics.MoreMath.Hypot(), Meta.Numerics.Complex.Im, and Meta.Numerics.Complex.Re.
Referenced by Test.BugTests.Bug5504(), Test.AdvancedComplexMathTest.ComplexGammaInequality(), Test.ComplexMathTest.ComplexMagnitude(), Test.ComplexMathTest.ComplexSqrt(), Test.BugTests.DifficultEigenvalue(), Meta.Numerics.Functions.AdvancedComplexMath.DiLog(), Meta.Numerics.Functions.AdvancedComplexMath.Erf(), Meta.Numerics.Functions.AdvancedComplexMath.Faddeeva(), Test.FourierTest.FourierSpecialCases(), Meta.Numerics.Functions.AdvancedComplexMath.LogGamma(), Test.MultiIntegrateTest.RambleIntegral(), and Meta.Numerics.Functions.AdvancedComplexMath.RiemannZeta().
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inlinestatic |
Computes the phase of a complex number.
z | The argument. |
The phase of a complex number is the angle between the line joining it to the origin and the real axis of the complex plane.
The phase of complex numbers in the upper complex plane lies between 0 and π. The phase of complex numbers in the lower complex plane lies between 0 and -π. The phase of a real number is zero.
References Meta.Numerics.Complex.Im, and Meta.Numerics.Complex.Re.
Referenced by Test.BugTests.Bug5504(), Test.ComplexMathTest.ComplexLogSum(), Test.ComplexMathTest.ComplexSqrt(), and Test.BugTests.DifficultEigenvalue().
Computes e raised to the power of a complex number.
z | The argument. |
References Meta.Numerics.MoreMath.Cos(), Meta.Numerics.Complex.Im, Meta.Numerics.Complex.Re, and Meta.Numerics.MoreMath.Sin().
Referenced by Test.AdvancedComplexMathTest.ComplexDiLogClausen(), Test.AdvancedComplexMathTest.ComplexErfFaddevaAgreement(), Test.ComplexMathTest.ComplexExpReflection(), Test.ComplexMathTest.ComplexExpSpecialCase(), Test.ComplexMathTest.ComplexExpSumTest(), Test.ComplexMathTest.ComplexLogExp(), Test.ComplexMathTest.ComplexPowExponent(), Test.ComplexMathTest.ComplexRealAgreement(), Meta.Numerics.Functions.AdvancedComplexMath.Erf(), Meta.Numerics.Functions.AdvancedComplexMath.Faddeeva(), Meta.Numerics.Functions.AdvancedComplexMath.Gamma(), Meta.Numerics.Functions.AdvancedComplexMath.IntegeralE1_ContinuedFraction(), and Meta.Numerics.Functions.AdvancedComplexMath.IntegralEi_AsymptoticSeries().
Computes the natrual logarithm of a complex number.
z | The argument. |
Referenced by Test.AdvancedComplexMathTest.ComplexDiLogSymmetry(), Test.ComplexMathTest.ComplexLogExp(), Test.ComplexMathTest.ComplexLogSpecialCase(), Test.ComplexMathTest.ComplexLogSum(), Test.ComplexMathTest.ComplexRealAgreement(), Meta.Numerics.Functions.AdvancedComplexMath.DiLog(), Meta.Numerics.Functions.AdvancedComplexMath.DiLog_Log_Series(), Meta.Numerics.Functions.AdvancedComplexMath.DiLog_Series_1(), Meta.Numerics.Functions.AdvancedComplexMath.Ein(), and Meta.Numerics.Functions.AdvancedComplexMath.LogGamma_Stirling().
Computes the square of a complex number.
z | The argument. |
Referenced by Test.ComplexMathTest.ComplexSqrt().
Computes the square root of a complex number.
z | The argument. |
References Meta.Numerics.Complex.Im, and Meta.Numerics.Complex.Re.
Referenced by Test.ComplexMathTest.ComplexIDefinition(), Test.ComplexMathTest.ComplexPowOneHalf(), Test.ComplexMathTest.ComplexRealAgreement(), and Test.ComplexMathTest.ComplexSqrt().
Computes the sine of a complex number.
z | The argument. |
References Meta.Numerics.MoreMath.Cos(), Meta.Numerics.Complex.Im, Meta.Numerics.Complex.Re, and Meta.Numerics.MoreMath.Sin().
Referenced by Test.ComplexMathTest.ComplexAngleAdditionTest(), Test.ComplexMathTest.ComplexDoubleAngle(), Test.ComplexMathTest.ComplexNegativeAngles(), Test.ComplexMathTest.ComplexPythagorean(), Test.ComplexMathTest.ComplexSinSinh(), Test.ComplexMathTest.ComplexTrigPeriodicity(), and Meta.Numerics.Functions.AdvancedComplexMath.Gamma().
Computes the hyperbolic sine of a complex number.
z | The argument. |
References Meta.Numerics.Complex.Im, and Meta.Numerics.Complex.Re.
Referenced by Test.ComplexMathTest.ComplexSinhCoshRelation(), and Test.ComplexMathTest.ComplexSinSinh().
Computes the cosine of a complex number.
z | The argument. |
References Meta.Numerics.MoreMath.Cos(), Meta.Numerics.Complex.Im, Meta.Numerics.Complex.Re, and Meta.Numerics.MoreMath.Sin().
Referenced by Test.ComplexMathTest.ComplexAngleAdditionTest(), Test.ComplexMathTest.ComplexCosCosh(), Test.ComplexMathTest.ComplexDoubleAngle(), Test.ComplexMathTest.ComplexNegativeAngles(), Test.ComplexMathTest.ComplexPythagorean(), Test.ComplexMathTest.ComplexSecTanTest(), Test.ComplexMathTest.ComplexTrigPeriodicity(), and Meta.Numerics.Functions.AdvancedComplexMath.RiemannZeta().
Computes the hyperbolic cosine of a complex number.
z | The argument. |
References Meta.Numerics.Complex.Im, and Meta.Numerics.Complex.Re.
Referenced by Test.ComplexMathTest.ComplexCosCosh(), and Test.ComplexMathTest.ComplexSinhCoshRelation().
Computes the tangent of a complex number.
z | The argument. |
References Meta.Numerics.MoreMath.Cos(), Meta.Numerics.Complex.Im, Meta.Numerics.Complex.Re, and Meta.Numerics.MoreMath.Sin().
Referenced by Test.ComplexMathTest.ComplexNegativeAngles(), Test.ComplexMathTest.ComplexSecTanTest(), Test.ComplexMathTest.ComplexTanTanh(), and Meta.Numerics.Functions.AdvancedComplexMath.Psi().
Computes the hyperbolic tangent of a complex number.
z | The argument. |
References Meta.Numerics.Complex.Im, and Meta.Numerics.Complex.Re.
Referenced by Test.ComplexMathTest.ComplexTanTanh().
Raises a complex number to an arbitrary real power.
z | The argument. |
p | The power. |
References Meta.Numerics.MoreMath.Cos(), and Meta.Numerics.MoreMath.Sin().
Referenced by Test.ComplexMathTest.ComplexPowExponent(), Test.ComplexMathTest.ComplexPowMultiplication(), Test.ComplexMathTest.ComplexPowOneHalf(), Test.ComplexMathTest.ComplexPowSpecialCases(), Test.AdvancedComplexMathTest.ComplexReimannZetaPrimesTest(), Meta.Numerics.ComplexMath.Pow(), Meta.Numerics.Functions.AdvancedComplexMath.RiemannZeta(), and Meta.Numerics.Functions.AdvancedComplexMath.RiemannZeta_EulerMaclaurin().
Raises a real number to an arbitrary complex power.
x | The real base, which must be non-negative. |
z | The complex exponent. |
References Meta.Numerics.MoreMath.Cos(), Meta.Numerics.Complex.Im, Meta.Numerics.Complex.One, Meta.Numerics.Complex.Re, Meta.Numerics.MoreMath.Sin(), and Meta.Numerics.Complex.Zero.
Raises a complex number to an integer power.
z | The argument. |
n | The power. |
References Meta.Numerics.ComplexMath.Pow().
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staticget |
Gets the unit imaginary number I.
Referenced by Meta.Numerics.Functions.AdvancedMath.Bessel_CF2(), Test.ComplexMathTest.ComplexCosCosh(), Test.AdvancedComplexMathTest.ComplexDiLogBranchCut(), Test.AdvancedComplexMathTest.ComplexDiLogClausen(), Test.AdvancedComplexMathTest.ComplexDiLogUnitCircle(), Test.AdvancedComplexMathTest.ComplexErfFaddevaAgreement(), Test.AdvancedComplexMathTest.ComplexErfFresnel(), Test.ComplexMathTest.ComplexLogSpecialCase(), Test.ComplexMathTest.ComplexSinSinh(), Test.ComplexMathTest.ComplexTanTanh(), Meta.Numerics.Functions.AdvancedMath.Coulomb_CF2(), Meta.Numerics.Functions.AdvancedComplexMath.Erf(), Meta.Numerics.Functions.AdvancedComplexMath.Faddeeva(), Meta.Numerics.Functions.AdvancedComplexMath.Faddeeva_ContinuedFraction(), Meta.Numerics.Functions.AdvancedComplexMath.Faddeeva_Taylor(), and Meta.Numerics.Functions.AdvancedComplexMath.Faddeeva_Weideman().