gp_periodic_cov() unexpected output for fixed period

[mhollanders]

Good day,

I was experimenting with gp_periodic_cov() yesterday after getting some unexpected results in a model. I noticed that when I provide an integer for the period parameter I get different results than if I provide the same value as a real. For both Stan programs, I use the following R code to sample:

library(cmdstanr)
options(mc.cores = 4)
set.seed(1)
mod <- cmdstan_model("mod.stan")
N <- 20
x <- rlnorm(N)
fit <- mod$sample(list(N = N, x = x), seed = 1)

In the following Stan program, period is given as 4:

data {
  int N;
  array[N] real x;
}

parameters {
  real<lower=0> sigma, ell;
}

transformed parameters {
  matrix[N, N] K = gp_periodic_cov(x, sigma, ell, 4);
}

model {
  sigma ~ exponential(1);
  ell ~ exponential(1);
}

I get:

> fit$summary("K")
# A tibble: 400 × 10
   variable  mean median    sd   mad      q5   q95  rhat ess_bulk ess_tail
   <chr>    <dbl>  <dbl> <dbl> <dbl>   <dbl> <dbl> <dbl>    <dbl>    <dbl>
 1 K[1,1]    1.92  0.464  4.18 0.665 0.00239  8.97  1.00    1662.    1186.
 2 K[2,1]    1.92  0.464  4.18 0.665 0.00239  8.97  1.00    1662.    1186.
 3 K[3,1]    1.92  0.464  4.18 0.665 0.00239  8.97  1.00    1662.    1186.
 4 K[4,1]    1.92  0.464  4.18 0.665 0.00239  8.97  1.00    1662.    1186.
 5 K[5,1]    1.92  0.464  4.18 0.665 0.00239  8.97  1.00    1662.    1186.
 6 K[6,1]    1.92  0.464  4.18 0.665 0.00239  8.97  1.00    1662.    1186.
 7 K[7,1]    1.92  0.464  4.18 0.665 0.00239  8.97  1.00    1662.    1186.
 8 K[8,1]    1.92  0.464  4.18 0.665 0.00239  8.97  1.00    1662.    1186.
 9 K[9,1]    1.92  0.464  4.18 0.665 0.00239  8.97  1.00    1662.    1186.
10 K[10,1]   1.92  0.464  4.18 0.665 0.00239  8.97  1.00    1662.    1186.

When instead I provide period as 4.0:

data {
  int N;
  array[N] real x;
}

parameters {
  real<lower=0> sigma, ell;
}

transformed parameters {
  matrix[N, N] K = gp_periodic_cov(x, sigma, ell, 4.0);
}

model {
  sigma ~ exponential(1);
  ell ~ exponential(1);
}

I get:

> fit$summary("K")
# A tibble: 400 × 10
   variable  mean median    sd    mad        q5   q95  rhat ess_bulk ess_tail
   <chr>    <dbl>  <dbl> <dbl>  <dbl>     <dbl> <dbl> <dbl>    <dbl>    <dbl>
 1 K[1,1]   1.92  0.464   4.18 0.665  2.39e-  3  8.97  1.00    1662.    1186.
 2 K[2,1]   0.629 0.0250  2.43 0.0371 1.57e- 76  3.00  1.00    1368.    1647.
 3 K[3,1]   0.720 0.0427  2.57 0.0634 2.67e- 56  3.46  1.00    1372.    1632.
 4 K[4,1]   1.58  0.332   3.77 0.487  1.21e-  4  7.22  1.00    1586.    1539.
 5 K[5,1]   1.39  0.250   3.50 0.370  6.89e-  7  6.27  1.00    1508.    1627.
 6 K[6,1]   0.679 0.0342  2.51 0.0508 1.14e- 64  3.27  1.00    1367.    1647.
 7 K[7,1]   1.01  0.115   2.98 0.171  1.24e- 21  4.77  1.00    1407.    1621.
 8 K[8,1]   1.03  0.124   3.01 0.183  2.50e- 20  4.81  1.00    1409.    1621.
 9 K[9,1]   0.530 0.0112  2.27 0.0166 5.69e-108  2.56  1.00    1374.    1647.
10 K[10,1]  1.49  0.287   3.63 0.422  1.31e-  5  6.79  1.00    1542.    1530.

I suspect it has to do with ints vs reals.

Cheers,

Matt