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Documentation for the Stan language and CmdStan

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#### Summary: Add user-facing documentation for new adaptive sampler argument `save_metric` introduced by CmdStan PR https://github.com/stan-dev/cmdstan/pull/1203. #### Description: Document argument, JSON output. #### Current Version: v2.34.0.

enhancement

It's an easy fix as the unconstrained $y$ is first constrained to be positive and then the ordered vector constraint is applied.

enhancement
feature

In https://mc-stan.org/docs/stan-users-guide/fit-gp.html#automatic-relevance-determination The function signature is written ```stan matrix L_cov_exp_quad_ARD(vector[] x, real alpha, vector rho, real delta) ``` But that `vector[] x` now needs to be `array[] vector x`.

#### Summary: Stan supports MAP estimation now so this part of the doc on clustering should be updated: https://github.com/stan-dev/docs/blob/cc4a208700cbb76bb4bea79f75b0513ff26c3d7d/src/stan-users-guide/clustering.Rmd#L559-L560 #### Current Version: v2.33.0

#### Summary: Add a note in functions reference for the `log1p_exp` function noting that it's also known as `softplus`. #### Current Version: v2.18.0

enhancement

This came up in cmdstanr issue [#826](https://github.com/stan-dev/cmdstanr/issues/826) from @ksvanhorn: > It's worth noting the the columns in the output aren't documented anywhere that I can find. I can guess what...

#### Summary: Section 21.1 ("Custom Probability Function" > "Examples" > "Triangle distribution") give an incorrect formula for the pdf of the triangle distribution. #### Description: The text gives for formula...

#### Summary: A colleague has mentioned that it would be helpful for the manual to be more explicit about Stan's behaviour with range indexing that involves operations. For example: ```stan...

#### Summary: [Ravi Sastry](https://discourse.mc-stan.org/u/Ravi_Sastry) on Discourse pointed out an inconsistency in the *User's Guide*: > In the Stan User’s Guide v2.32, the last line in Section 2.4 recommends adding a...

enhancement

In https://mc-stan.org/docs/stan-users-guide/change-point.html there is a dynamic programming version for 1 change pt but not for 2. It's a bit confusing because the text says that in the case of 2...