Modelica.ComplexMath

Library of complex mathematical functions (e.g., sin, cos) and of functions operating on complex vectors and matrices

Information

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

Extends from Modelica.Icons.Package (Icon for standard packages).

Package Content

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

Modelica.ComplexMath.sin Modelica.ComplexMath.sin

Sine of complex number

Information

This function returns the Complex sine of the Complex input.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
c1Complex number

Outputs

NameDescription
c2sin(c1)

Modelica.ComplexMath.cos Modelica.ComplexMath.cos

Cosine of complex number

Information

This function returns the Complex cosine of the Complex input.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
c1Complex number

Outputs

NameDescription
c2= cos(c1)

Modelica.ComplexMath.tan Modelica.ComplexMath.tan

Tangent of complex number

Information

This function returns the Complex tangent of the Complex input.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
c1Complex number

Outputs

NameDescription
c2= tan(c1)

Modelica.ComplexMath.asin Modelica.ComplexMath.asin

Arc-sine of complex number

Information

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

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
c1Complex number

Outputs

NameDescription
c2arc_sin(c1)

Modelica.ComplexMath.acos Modelica.ComplexMath.acos

Arc-cosine of complex number

Information

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

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
c1Complex number

Outputs

NameDescription
c2= arc_cos(c1)

Modelica.ComplexMath.atan Modelica.ComplexMath.atan

Arc-tangent of complex number

Information

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

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
c1Complex number

Outputs

NameDescription
c2= arc_tan(c1)

Modelica.ComplexMath.sinh Modelica.ComplexMath.sinh

Hyperbolic-sine of complex number

Information

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

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
c1Complex number

Outputs

NameDescription
c2sinh(c1)

Modelica.ComplexMath.cosh Modelica.ComplexMath.cosh

Hyperbolic-cosine of complex number

Information

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

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
c1Complex number

Outputs

NameDescription
c2= cosh(c1)

Modelica.ComplexMath.tanh Modelica.ComplexMath.tanh

Hyperbolic-tangent of complex number

Information

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

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
c1Complex number

Outputs

NameDescription
c2= tanh(c1)

Modelica.ComplexMath.asinh Modelica.ComplexMath.asinh

Area-hyperbolic-sine of complex number

Information

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

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
c1Complex number

Outputs

NameDescription
c2ar_sinh(c1)

Modelica.ComplexMath.acosh Modelica.ComplexMath.acosh

Area-hyperbolic-cosine of complex number

Information

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

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
c1Complex number

Outputs

NameDescription
c2= ar_cosh(c1)

Modelica.ComplexMath.atanh Modelica.ComplexMath.atanh

Area-hyperbolic-tangent of complex number

Information

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

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
c1Complex number

Outputs

NameDescription
c2= ar_tanh(c1)

Modelica.ComplexMath.exp Modelica.ComplexMath.exp

Exponential of complex number

Information

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

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
c1Complex number

Outputs

NameDescription
c2= exp(c1)

Modelica.ComplexMath.log Modelica.ComplexMath.log

Logarithm of complex number

Information

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

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
c1Complex number

Outputs

NameDescription
c2= log(c1)

Modelica.ComplexMath.'abs' Modelica.ComplexMath.'abs'

Absolute value of complex number

Information

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

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
cComplex number

Outputs

NameDescription
result= abs(c)

Modelica.ComplexMath.arg Modelica.ComplexMath.arg

Phase angle of complex number

Information

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

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
cComplex number
phi0Phase angle phi shall be in the range: -pi < phi-phi0 < pi [rad]

Outputs

NameDescription
phi= phase angle of c [rad]

Modelica.ComplexMath.conj Modelica.ComplexMath.conj

Conjugate of complex number

Information

This function returns the Complex conjugate of the Complex input.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
c1Complex number

Outputs

NameDescription
c2= c1.re - j*c1.im

Modelica.ComplexMath.real Modelica.ComplexMath.real

Real part of complex number

Information

This function returns the real part of the Complex input.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
cComplex number

Outputs

NameDescription
r= c.re

Modelica.ComplexMath.imag Modelica.ComplexMath.imag

Imaginary part of complex number

Information

This function returns the imaginary part of the Complex input.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
cComplex number

Outputs

NameDescription
r= c.im

Modelica.ComplexMath.fromPolar Modelica.ComplexMath.fromPolar

Complex from polar representation

Information

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

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
lenabs of complex
phiarg of complex [rad]

Outputs

NameDescription
c= len*cos(phi) + j*len*sin(phi)

Modelica.ComplexMath.'sqrt' Modelica.ComplexMath.'sqrt'

Square root of complex number

Information

This function returns the Complex square root (principal square root) of the Complex input.

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
c1Complex number

Outputs

NameDescription
c2= sqrt(c1)

Modelica.ComplexMath.'max' Modelica.ComplexMath.'max'

Return maximum element of complex vector

Information

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

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
v[:]Vector

Outputs

NameDescription
resultElement of v with largest absolute value
indexv[index] has the largest absolute value

Modelica.ComplexMath.'min' Modelica.ComplexMath.'min'

Return minimum element of complex vector

Information

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

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
v[:]Vector

Outputs

NameDescription
resultElement of v with smallest absolute value
indexv[index] has the smallest absolute value

Modelica.ComplexMath.'sum' Modelica.ComplexMath.'sum'

Return sum of complex vector

Information

This function returns the Complex sum of the Complex input vector

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
v[:]Vector

Outputs

NameDescription
resultComplex sum of vector elements

Modelica.ComplexMath.'product' Modelica.ComplexMath.'product'

Return product of complex vector

Information

This function returns the Complex product of the Complex input vector

Extends from Modelica.Icons.Function (Icon for functions).

Inputs

NameDescription
v[:]Vector

Outputs

NameDescription
resultComplex product of vector elements
Automatically generated Mon Oct 1 14:51:23 2018.