Vectors
sin
cos
tan
asin
acos
atan
sinh
cosh
tanh
asinh
acosh
atanh
exp
log
'abs'
arg
conj
real
imag
fromPolar
'sqrt'
'max'
'min'
'sum'
'product'
Library of complex mathematical functions (e.g., sin, cos) and of functions operating on complex vectors and matrices
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).
| 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.sinSine of complex number
This function returns the Complex sine of the Complex input.
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| c1 | Complex number |
| Name | Description |
|---|---|
| c2 | sin(c1) |
Modelica.ComplexMath.cosCosine of complex number
This function returns the Complex cosine of the Complex input.
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| c1 | Complex number |
| Name | Description |
|---|---|
| c2 | = cos(c1) |
Modelica.ComplexMath.tanTangent of complex number
This function returns the Complex tangent of the Complex input.
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| c1 | Complex number |
| Name | Description |
|---|---|
| c2 | = tan(c1) |
Modelica.ComplexMath.asinArc-sine of complex number
This function returns the inverse Complex sine of the Complex input.
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| c1 | Complex number |
| Name | Description |
|---|---|
| c2 | arc_sin(c1) |
Modelica.ComplexMath.acosArc-cosine of complex number
This function returns the inverse Complex cosine of the Complex input.
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| c1 | Complex number |
| Name | Description |
|---|---|
| c2 | = arc_cos(c1) |
Modelica.ComplexMath.atanArc-tangent of complex number
This function returns the inverse Complex tangent of the Complex input.
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| c1 | Complex number |
| Name | Description |
|---|---|
| c2 | = arc_tan(c1) |
Modelica.ComplexMath.sinhHyperbolic-sine of complex number
This function returns the Complex hyperbolic sine of the Complex input.
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| c1 | Complex number |
| Name | Description |
|---|---|
| c2 | sinh(c1) |
Modelica.ComplexMath.coshHyperbolic-cosine of complex number
This function returns the Complex hyperbolic cosine of the Complex input.
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| c1 | Complex number |
| Name | Description |
|---|---|
| c2 | = cosh(c1) |
Modelica.ComplexMath.tanhHyperbolic-tangent of complex number
This function returns the Complex hyperbolic tangent of the Complex input.
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| c1 | Complex number |
| Name | Description |
|---|---|
| c2 | = tanh(c1) |
Modelica.ComplexMath.asinhArea-hyperbolic-sine of complex number
This function returns the inverse Complex hyperbolic sine of the Complex input.
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| c1 | Complex number |
| Name | Description |
|---|---|
| c2 | ar_sinh(c1) |
Modelica.ComplexMath.acoshArea-hyperbolic-cosine of complex number
This function returns the inverse Complex hyperbolic cosine of the Complex input.
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| c1 | Complex number |
| Name | Description |
|---|---|
| c2 | = ar_cosh(c1) |
Modelica.ComplexMath.atanhArea-hyperbolic-tangent of complex number
This function returns the inverse Complex hyperbolic tangent of the Complex input.
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| c1 | Complex number |
| Name | Description |
|---|---|
| c2 | = ar_tanh(c1) |
Modelica.ComplexMath.expExponential of complex number
This function returns the Complex natural exponential of the Complex input.
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| c1 | Complex number |
| Name | Description |
|---|---|
| c2 | = exp(c1) |
Modelica.ComplexMath.logLogarithm of complex number
This function returns the Complex natural logarithm of the Complex input.
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| c1 | Complex number |
| Name | Description |
|---|---|
| c2 | = log(c1) |
Modelica.ComplexMath.'abs'Absolute value of complex number
This function returns the Real absolute of the Complex input, i.e., its length.
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| c | Complex number |
| Name | Description |
|---|---|
| result | = abs(c) |
Modelica.ComplexMath.argPhase angle of complex number
This function returns the Real argument of the Complex input, i.e., its angle.
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| c | Complex number |
| phi0 | Phase angle phi shall be in the range: -pi < phi-phi0 < pi [rad] |
| Name | Description |
|---|---|
| phi | = phase angle of c [rad] |
Modelica.ComplexMath.conjConjugate of complex number
This function returns the Complex conjugate of the Complex input.
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| c1 | Complex number |
| Name | Description |
|---|---|
| c2 | = c1.re - j*c1.im |
Modelica.ComplexMath.realReal part of complex number
This function returns the real part of the Complex input.
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| c | Complex number |
| Name | Description |
|---|---|
| r | = c.re |
Modelica.ComplexMath.imagImaginary part of complex number
This function returns the imaginary part of the Complex input.
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| c | Complex number |
| Name | Description |
|---|---|
| r | = c.im |
Modelica.ComplexMath.fromPolarComplex from polar representation
This function constructs a Complex number from its length (absolute) and angle (argument).
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| len | abs of complex |
| phi | arg of complex [rad] |
| Name | Description |
|---|---|
| c | = len*cos(phi) + j*len*sin(phi) |
Modelica.ComplexMath.'sqrt'Square root of complex number
This function returns the Complex square root (principal square root) of the Complex input.
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| c1 | Complex number |
| Name | Description |
|---|---|
| c2 | = sqrt(c1) |
Modelica.ComplexMath.'max'Return maximum element of complex vector
This function returns the largest element of the Complex input vector, defined by the Complex absolute.
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| v[:] | Vector |
| Name | Description |
|---|---|
| result | Element of v with largest absolute value |
| index | v[index] has the largest absolute value |
Modelica.ComplexMath.'min'Return minimum element of complex vector
This function returns the smallest element of the Complex input vector, defined by the Complex absolute.
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| v[:] | Vector |
| Name | Description |
|---|---|
| result | Element of v with smallest absolute value |
| index | v[index] has the smallest absolute value |
Modelica.ComplexMath.'sum'Return sum of complex vector
This function returns the Complex sum of the Complex input vector
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| v[:] | Vector |
| Name | Description |
|---|---|
| result | Complex sum of vector elements |
Modelica.ComplexMath.'product'Return product of complex vector
This function returns the Complex product of the Complex input vector
Extends from Modelica.Icons.Function (Icon for functions).
| Name | Description |
|---|---|
| v[:] | Vector |
| Name | Description |
|---|---|
| result | Complex product of vector elements |