Modelica.ComplexMath

Information

This package contains basic mathematical functions operating on complex numbers (such as sin(..)), as well as functions operating on vectors of complex numbers.

Package Content

Name	Description
j=Complex(0, 1)	Imaginary unit
Vectors	Library of functions operating on complex vectors
sin	Sine of complex number
cos	Cosine of complex number
tan	Tangent of complex number
asin	Arc-sine of complex number
acos	Arc-cosine of complex number
atan	Arc-tangent of complex number
sinh	Hyperbolic-sine of complex number
cosh	Hyperbolic-cosine of complex number
tanh	Hyperbolic-tangent of complex number
asinh	Area-hyperbolic-sine of complex number
acosh	Area-hyperbolic-cosine of complex number
atanh	Area-hyperbolic-tangent of complex number
exp	Exponential of complex number
log	Logarithm of complex number
'abs'	Absolute value of complex number
arg	Phase angle of complex number
conj	Conjugate of complex number
real	Real part of complex number
imag	Imaginary part of complex number
fromPolar	Complex from polar representation
'sqrt'	Square root of complex number
'max'	Return maximum element of complex vector
'min'	Return minimum element of complex vector
'sum'	Return sum of complex vector
'product'	Return product of complex vector

Modelica.ComplexMath.sin

Information

This function returns the Complex sine of the Complex input.

Inputs

Name	Description
c1	Complex number

Outputs

Name	Description
c2	sin(c1)

Modelica.ComplexMath.cos

Information

This function returns the Complex cosine of the Complex input.

Inputs

Name	Description
c1	Complex number

Outputs

Name	Description
c2	= cos(c1)

Modelica.ComplexMath.tan

Information

This function returns the Complex tangent of the Complex input.

Inputs

Name	Description
c1	Complex number

Outputs

Name	Description
c2	= tan(c1)

Modelica.ComplexMath.asin

Information

This function returns the inverse Complex sine of the Complex input.

Inputs

Name	Description
c1	Complex number

Outputs

Name	Description
c2	arc_sin(c1)

Modelica.ComplexMath.acos

Information

This function returns the inverse Complex cosine of the Complex input.

Inputs

Name	Description
c1	Complex number

Outputs

Name	Description
c2	= arc_cos(c1)

Modelica.ComplexMath.atan

Information

This function returns the inverse Complex tangent of the Complex input.

Inputs

Name	Description
c1	Complex number

Outputs

Name	Description
c2	= arc_tan(c1)

Modelica.ComplexMath.sinh

Information

This function returns the Complex hyperbolic sine of the Complex input.

Inputs

Name	Description
c1	Complex number

Outputs

Name	Description
c2	sinh(c1)

Modelica.ComplexMath.cosh

Information

This function returns the Complex hyperbolic cosine of the Complex input.

Inputs

Name	Description
c1	Complex number

Outputs

Name	Description
c2	= cosh(c1)

Modelica.ComplexMath.tanh

Information

This function returns the Complex hyperbolic tangent of the Complex input.

Inputs

Name	Description
c1	Complex number

Outputs

Name	Description
c2	= tanh(c1)

Modelica.ComplexMath.asinh

Information

This function returns the inverse Complex hyperbolic sine of the Complex input.

Inputs

Name	Description
c1	Complex number

Outputs

Name	Description
c2	ar_sinh(c1)

Modelica.ComplexMath.acosh

Information

This function returns the inverse Complex hyperbolic cosine of the Complex input.

Inputs

Name	Description
c1	Complex number

Outputs

Name	Description
c2	= ar_cosh(c1)

Modelica.ComplexMath.atanh

Information

This function returns the inverse Complex hyperbolic tangent of the Complex input.

Inputs

Name	Description
c1	Complex number

Outputs

Name	Description
c2	= ar_tanh(c1)

Modelica.ComplexMath.exp

Information

This function returns the Complex natural exponential of the Complex input.

Inputs

Name	Description
c1	Complex number

Outputs

Name	Description
c2	= exp(c1)

Modelica.ComplexMath.log

Information

This function returns the Complex natural logarithm of the Complex input.

Inputs

Name	Description
c1	Complex number

Outputs

Name	Description
c2	= log(c1)

Modelica.ComplexMath.'abs'

Information

This function returns the Real absolute of the Complex input, i.e., its length.

Inputs

Name	Description
c	Complex number

Outputs

Name	Description
result	= abs(c)

Modelica.ComplexMath.arg

Information

This function returns the Real argument of the Complex input, i.e., its angle.

Inputs

Name	Description
c	Complex number
phi0	Phase angle phi shall be in the range: -pi < phi-phi0 < pi [rad]

Outputs

Name	Description
phi	= phase angle of c [rad]

Modelica.ComplexMath.conj

Information

This function returns the Complex conjugate of the Complex input.

Inputs

Name	Description
c1	Complex number

Outputs

Name	Description
c2	= c1.re - j*c1.im

Modelica.ComplexMath.real

Information

This function returns the real part of the Complex input.

Inputs

Name	Description
c	Complex number

Outputs

Name	Description
r	= c.re

Modelica.ComplexMath.imag

Information

This function returns the imaginary part of the Complex input.

Inputs

Name	Description
c	Complex number

Outputs

Name	Description
r	= c.im

Modelica.ComplexMath.fromPolar

Information

This function constructs a Complex number from its length (absolute) and angle (argument).

Inputs

Name	Description
len	abs of complex
phi	arg of complex [rad]

Outputs

Name	Description
c	= len*cos(phi) + j*len*sin(phi)

Modelica.ComplexMath.'sqrt'

Information

This function returns the Complex square root of the Complex input.

Inputs

Name	Description
c1	Complex number

Outputs

Name	Description
c2	= sqrt(c1)

Modelica.ComplexMath.'max'

Information

This function returns the largest element of the Complex input vector, defined by the Complex absolute.

Inputs

Name	Description
v[:]	Vector

Outputs

Name	Description
result	Element of v with largest absolute value
index	v[index] has the largest absolute value

Modelica.ComplexMath.'min'

Information

This function returns the smallest element of the Complex input vector, defined by the Complex absolute.

Inputs

Name	Description
v[:]	Vector

Outputs

Name	Description
result	Element of v with smallest absolute value
index	v[index] has the smallest absolute value

Modelica.ComplexMath.'sum'

Information

This function returns the Complex sum of the Complex input vector

Inputs

Name	Description
v[:]	Vector

Outputs

Name	Description
result	Complex sum of vector elements

Modelica.ComplexMath.'product'

Information

This function returns the Complex product of the Complex input vector

Inputs

Name	Description
v[:]	Vector

Outputs

Name	Description
result	Complex product of vector elements