add test for from_cmdstanpy to distinguish between vectors of length 1 and scalars

EDIT (@OriolAbril): See https://github.com/arviz-devs/arviz/issues/1646#issuecomment-1125464400 for an up to date description of the issue.

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Describe the bug When fitting a model using cmdstanpy and reading it into an arviz.InferenceData object, I sometimes end up with a vector parameter with length 1.

When this happens, the io_cmdstanpy code incorrectly ignores the last dimension, causing an error when I provide coord/dims for that parameter.

To Reproduce I have created a reproducible example here:

# To add a new cell, type '# %%'
# To add a new markdown cell, type '# %% [markdown]'
# %%

import cmdstanpy
import arviz as az

# %% [markdown]
# # Review Stan model code

# %%
model_code = '''
// from https://arviz-devs.github.io/arviz/notebooks/InferenceDataCookbook.html#From-CmdStanPy
data {
    int<lower=0> J;
    real y[J];
    real<lower=0> sigma[J];
    int<lower = 0, upper=1> prior_only;
}
parameters {
    real mu;
    real<lower=0> tau;
    real theta_tilde[J];
}
transformed parameters {
    real theta[J];
    for (j in 1:J)
        theta[j] = mu + tau * theta_tilde[j];
}
model {
    mu ~ normal(0, 5);
    tau ~ cauchy(0, 5);
    theta_tilde ~ normal(0, 1);
    if (prior_only == 0) {
        y ~ normal(theta, sigma);
    }
}
generated quantities {
    vector[J] log_lik;
    vector[J] y_hat;
    for (j in 1:J) {
        log_lik[j] = normal_lpdf(y[j] | theta[j], sigma[j]);
        y_hat[j] = normal_rng(theta[j], sigma[j]);
    }
}
'''

# %% [markdown]
# # Fitting the model using cmdstanpy

# %%
stan_file = "eight_schools.stan"
with open(stan_file, 'x') as f:
    f.write(model_code)
model = cmdstanpy.CmdStanModel(stan_file = stan_file)


# %%
stan_data8 = dict(
            J=8,
            y=[28, 8, -3, 7, -1, 1, 18, 12],
            sigma=[15, 10, 16, 11, 9, 11, 10, 18],
            prior_only=0,
        )
stan_data1 = dict(
            J=1,
            y=[28],
            sigma=[15],
            prior_only=0,
        )
coords8 = dict(school=["A", "B", "C", "D", "E", "F", "G", "H"])
coords1 = dict(school=["a"])
dims= dict(
        theta=["school"],
        y=["school"],
        log_lik=["school"],
        y_hat=["school"],
        theta_tilde=["school"],
    )
# %%
fit8 = model.sample(data=stan_data8)
fit1 = model.sample(data=stan_data1)

# %% [markdown]
# ## Construct arviz.InferenceData object

# %%
idata8 = az.from_cmdstanpy(fit8, coords = coords8, dims = dims,
    posterior_predictive = ["y_hat"],
    prior_predictive = ['y_hat'],
    log_likelihood = ["log_lik"])

## fails!
idata1 = az.from_cmdstanpy(fit1, coords = coords1, dims = dims,
    posterior_predictive = ["y_hat"],
    prior_predictive = ['y_hat'],
    log_likelihood = ["log_lik"])

The error looks like this:

/Users/jburos/.local/share/virtualenvs/workflow2-PgZLfFHB/src/arviz/arviz/data/base.py:129: UserWarning: In variable theta_tilde, there are more dims (1) given than exist (0). Passed array should have shape (chain,draw, *shape)
  warnings.warn(
Traceback (most recent call last):
  File "/Users/jburos/projects/workflow2/docs/test_arviz_cmdstanpy.py", line 93, in <module>
    idata1 = az.from_cmdstanpy(fit1, coords = coords1, dims = dims,
  File "/Users/jburos/.local/share/virtualenvs/workflow2-PgZLfFHB/src/arviz/arviz/data/io_cmdstanpy.py", line 763, in from_cmdstanpy
    return CmdStanPyConverter(
  File "/Users/jburos/.local/share/virtualenvs/workflow2-PgZLfFHB/src/arviz/arviz/data/io_cmdstanpy.py", line 408, in to_inference_data
    "posterior": self.posterior_to_xarray(),
  File "/Users/jburos/.local/share/virtualenvs/workflow2-PgZLfFHB/src/arviz/arviz/data/base.py", line 64, in wrapped
    return func(cls)
  File "/Users/jburos/.local/share/virtualenvs/workflow2-PgZLfFHB/src/arviz/arviz/data/io_cmdstanpy.py", line 111, in posterior_to_xarray
    dict_to_dataset(
  File "/Users/jburos/.local/share/virtualenvs/workflow2-PgZLfFHB/src/arviz/arviz/data/base.py", line 302, in dict_to_dataset
    data_vars[key] = numpy_to_data_array(
  File "/Users/jburos/.local/share/virtualenvs/workflow2-PgZLfFHB/src/arviz/arviz/data/base.py", line 249, in numpy_to_data_array
    return xr.DataArray(ary, coords=coords, dims=dims)
  File "/Users/jburos/.local/share/virtualenvs/workflow2-PgZLfFHB/lib/python3.8/site-packages/xarray/core/dataarray.py", line 409, in __init__
    coords, dims = _infer_coords_and_dims(data.shape, coords, dims)
  File "/Users/jburos/.local/share/virtualenvs/workflow2-PgZLfFHB/lib/python3.8/site-packages/xarray/core/dataarray.py", line 126, in _infer_coords_and_dims
    raise ValueError(
ValueError: different number of dimensions on data and dims: 2 vs 3
deleting tmpfiles dir: /var/folders/18/st_852gs77d86c3srp0jgrnw0000gn/T/tmpfmrn2a4u
done

I think this is happening in this line: https://github.com/arviz-devs/arviz/blob/main/arviz/data/io_cmdstanpy.py#L594-L595

Expected behavior The from_cmdstanpy method should ideally know (from the dims) that this is a 1d vector or array, and label it as such.

Additional context

arviz version: 0.11.2 (github hash: 23e14fb645431014e73ba35f940b613850d59f30) cmdstanpy version: 0.9.68 python version: 3.8.7 (default, Feb 3 2021, 06:31:03) \n[Clang 12.0.0 (clang-1200.0.32.29)]

[OriolAbril]

And we should probably test on length 0 arrays for sampling wrappers and reloo

[ahartikainen]

There was probably some reason for the logic.

code should check if the variable is ‘scalar’ or nD object.

@mitzimorris @OriolAbril