Expose additional normal_id_glm pointwise signatures

[andrjohns]

The current normal_id_glm signatures for use with a univariate outcome y only support matrix type inputs for x, for example:

real normal_id_glm_lpdf(real y | matrix x, real alpha, vector beta, real sigma)

For pointwise usage, it would be great to add corresponding row_vector signatures:

real normal_id_glm_lpdf(real y | row_vector x, real alpha, vector beta, real sigma)

As the current signatures require calling to_matrix() at each iteration:

generated quantities {
  vector[N] log_lik;

  for (n in 1:N) {
    log_lik[n] = normal_id_glm_lpdf(y[n] | to_matrix(x[n]), alpha, beta, sigma);
  }
}

[WardBrian]

Is this just for convenience or do we expect different performance? I thought to_matrix was essentially free for eigen types

[andrjohns]

Mostly convenience, since the majority of use-cases with a univariate outcome would be a single set of predictors (e.g., pointwise log-likelihood), so a real y and row_vector x combo would be more common than a real y and matrix x

[Pranavchiku]

I would be happy to help in this, if any reference PR or code exists please share.

[WardBrian]

Hi @Pranavchiku --

It appears that the C++ math library already supports this, so the change in the compiler would be relatively tiny. The existing code in the compiler is here:

stanc3/src/middle/Stan_math_signatures.ml

Line 273 in 96e409a

; ([Lpdf], "normal_id_glm", [DVector; DMatrix; DReal; DVector; DReal], SoA)

We want to change DMatrix there to another option. Here are the current ones:

stanc3/src/middle/Stan_math_signatures.ml

Lines 13 to 31 in 96e409a

	type dimensionality =
	| DInt
	| DReal
	| DVector
	| DMatrix
	| DIntArray
	(* Vectorizable int *)
	| DVInt
	(* Vectorizable real *)
	| DVReal
	| DVComplex
	(* DEPRECATED; vectorizable ints or reals *)
	| DIntAndReals
	(* Vectorizable vectors - for multivariate functions *)
	| DVectors
	| DDeepVectorized
	| DComplexVectors
	| DDeepComplexVectorized
	[@@warning "-37"]

It looks like none of these are exactly what we want, so we'd create a new enum variant. I'd suggest the name DEigenTypes. And then we need to update expand_arg:

stanc3/src/middle/Stan_math_signatures.ml

Line 53 in 96e409a

let rec expand_arg = function

such that DEigenTypes gets expanded to [UMatrix; UVector; URowVector]

Finally, to test that this all compiles, we'd then add calls to all the new overloads (including existing permutations) to this file:
https://github.com/stan-dev/stanc3/blob/master/test/integration/good/function-signatures/distributions/univariate/continuous/normal/normal_id_glm.stan