test: Verify a model with many parameters works

Check that a schools model with many parameters (160) works.  Prompted
by a unusual macOS bug in late 2020 (#163).

tests/test_eight_schools_large.py

@@ -0,0 +1,52 @@
+"""Test a "large" version of the schools model.
+
+Introduced in response to a macOS bug that only
+triggered when a larger number of parameters were used.
+"""
+import pytest
+
+import stan
+
+program_code = """
+    data {
+      int<lower=0> J; // number of schools
+      real y[J]; // estimated treatment effects
+      real<lower=0> sigma[J]; // s.e. of effect estimates
+    }
+    parameters {
+      real mu;
+      real<lower=0> tau;
+      real eta[J];
+    }
+    transformed parameters {
+      real theta[J];
+      for (j in 1:J)
+        theta[j] = mu + tau * eta[j];
+    }
+    model {
+      target += normal_lpdf(eta | 0, 1);
+      target += normal_lpdf(y | theta, sigma);
+    }
+"""
+schools_data = {
+    "J": 8 * 20,
+    "y": (28, 8, -3, 7, -1, 1, 18, 12) * 20,
+    "sigma": (15, 10, 16, 11, 9, 11, 10, 18) * 20,
+}
+
+
+@pytest.fixture(scope="module")
+def posterior():
+    """Build (compile) a simple model."""
+    return stan.build(program_code, data=schools_data)
+
+
+def test_eight_schools_large_sample(posterior):
+    num_chains, num_samples = 2, 200
+    fit = posterior.sample(num_chains=num_chains, num_samples=num_samples, num_warmup=num_samples)
+    num_flat_params = schools_data["J"] * 2 + 2
+    assert fit.values.shape == (len(fit.sample_and_sampler_param_names) + num_flat_params, num_samples, num_chains,)
+    df = fit.to_frame()
+    assert "eta.1" in df.columns
+    assert len(df["eta.1"]) == num_samples * num_chains
+    assert fit["eta"].shape == (schools_data["J"], num_chains * num_samples)