Derivative of Math.Special.erf

[AHaumer]

I suppose the derivative of Math.Special.erf should be defined, like: annotation(derivative=derf);
and implementing the derivative;

function derf "Derivative of error function"
input Real u;
input Real deru;
output Real y;
algorithm
y:=2/sqrt(Modelica.Constants.pi)*exp(-u^2)*deru;
annotation(Inline=true);
end derf;

Usefull at least when a tool tries to differentiate for index reduction.

Additonally, the inverse-annotation (erfInv) is missing.

Same remarks for erfc and erfcInv.

[thorade]

I also recently noticed that sinh() and asinh() could be declared as inverses of each other, is there any reason to not have the inverses defined?
https://github.com/modelica/ModelicaStandardLibrary/blob/master/Modelica/Math/package.mo#L11359

[AHaumer]

see also #3844

[AHaumer]

Also missing: Modelica.Math.{sin, cos, tan, sinh, cosh, tanh. exp} (not only sinh).
Maybe more functions in MSL?

[HansOlsson]

I guess we could add this for erf (and erfc), even though I'm not sure how much it is used.

[HansOlsson]

Also missing: Modelica.Math.{sin, cos, tan, sinh, cosh, tanh. exp} (not only sinh). Maybe more functions in MSL?

Tools may also already have that built-in as they are basically built-in functions, so even if they are used I doubt that adding them will actually provide any benefit in practice.

Additionally, for derivatives it is a bit messy, as cos-derivative is -sin, and we don't have anything for that sign (yet); and it would seem odd to only have a derivative for sin and not for cos, and defining a new function for -sin would seem odd (and then it would need derivative etc).

There's also a bit of problem for the inverses, as e.g., sin is not bijective and one output correspond to multiple inputs.
Dymola (and possibly other tools) tries to find the best inverse among them - so any specified inverse would just be ignored.

[thorade]

Also missing: Modelica.Math.{sin, cos, tan, sinh, cosh, tanh. exp} (not only sinh). Maybe more functions in MSL?

Tools may also already have that built-in as they are basically built-in functions, so even if they are used I doubt that adding them will actually provide any benefit in practice.

Additionally, for derivatives it is a bit messy, as cos-derivative is -sin, and we don't have anything for that sign (yet); and it would seem odd to only have a derivative for sin and not for cos, and defining a new function for -sin would seem odd (and then it would need derivative etc).

There's also a bit of problem for the inverses, as e.g., sin is not bijective and one output correspond to multiple inputs. Dymola (and possibly other tools) tries to find the best inverse among them - so any specified inverse would just be ignored.

I tried for sinh and asinh, here is a small test model that should ideally have 0 nonlinear equations after manipulation:

model invert_sinh
  Real x;
  Real y1, y2;
equation
  x = time;
  x=Modelica.Math.sinh(y1);
  x=Modelica.Math.asinh(y2);
end invert_sinh;

[HansOlsson]

Also missing: Modelica.Math.{sin, cos, tan, sinh, cosh, tanh. exp} (not only sinh). Maybe more functions in MSL?

Tools may also already have that built-in as they are basically built-in functions, so even if they are used I doubt that adding them will actually provide any benefit in practice.
Additionally, for derivatives it is a bit messy, as cos-derivative is -sin, and we don't have anything for that sign (yet); and it would seem odd to only have a derivative for sin and not for cos, and defining a new function for -sin would seem odd (and then it would need derivative etc).
There's also a bit of problem for the inverses, as e.g., sin is not bijective and one output correspond to multiple inputs. Dymola (and possibly other tools) tries to find the best inverse among them - so any specified inverse would just be ignored.

I tried for sinh and asinh, here is a small test model that should ideally have 0 nonlinear equations after manipulation:

model invert_sinh
  Real x;
  Real y1, y2;
equation
  x = time;
  x=Modelica.Math.sinh(y1);
  x=Modelica.Math.asinh(y2);
end invert_sinh;

I was thinking of sin/cos, where asin/acos are also built in the Modelica language.
For some reason asinh isn't, but I'm sure that could be handled as well.

[AHaumer]

@HansOlsson you are right (my mistake) talking about the built-in functions, but there are some special ones, especially Math.Special.{erf, erc, erfInv, ercInv}. These could be usefill. I'll prepare a PR.