I have function the needs to enable some Optional parameters and an OptionsPattern. The issue I am facing is that the options are being matched to the optional parameters when the optional parameters are excluded.

How do I specify that the optional parameters should use their default when not provided without making multiple function definitions.

With

ClearAll[f] f[ts_, maxError_, fitAlgorithm_: LinearModelFit, algorithmParams_: {\[FormalX], \[FormalX]},    opts : OptionsPattern[]] :=  <|"fitAlgorithm" -> fitAlgorithm, "algorithmParams" -> algorithmParams, "opts" -> {opts}|> 

Then all optional defaults and no options works.

f[1, 2] 

<|"fitAlgorithm" -> LinearModelFit, "algorithmParams" -> {\[FormalX], \[FormalX]}, "opts" -> {}|> 

However, any additional parameters are misinterpreted

f[1, 2, StepMonitor :> (a = # &)] 

<|"fitAlgorithm" -> StepMonitor :> (a = #1 &), "algorithmParams" -> {\[FormalX], \[FormalX]}, "opts" -> {}|> 

The StepMonitor option should be the first item in opts. Instead it is taken to be the fitAlgorithm parameter.

I know multiple function defintions will work. For example:

ClearAll[f] f[ts_, maxError_, fitAlgorithm_, algorithmParams_,    opts : OptionsPattern[]] :=  <|"fitAlgorithm" -> fitAlgorithm, "algorithmParams" -> algorithmParams, "opts" -> {opts}|> f[ts_, maxError_, opts : OptionsPattern[]] :=   f[ts, maxError, LinearModelFit, {\[FormalX], \[FormalX]}, opts] f[ts_, maxError_, fitAlgorithm_, opts : OptionsPattern[]] :=   f[ts, maxError, fitAlgorithm, {\[FormalX], \[FormalX]}, opts] 

But this is not actually creating optional parameters with default values.