Integrate_ode data only arguments inconsistency

[VMatthijs]

Summary:

There is an inconsistency between the data only restrictions for the arguments to the ODE integrators between what is described in the manual and what is actually implemented in Stan.

Description:

Currently, the third and fourth arguments to all ODE integrators are enforced to be data only by the Stan type checker. However, nothing is said about that in the manual.

Reproducible Steps:

Try to compile the model

functions {
  real[] sho(real t,
             real[] y, 
             real[] theta,
             real[] x,
             int[] x_int) {
    real dydt[2];
    dydt[1] = y[2];
    dydt[2] = -y[1] - theta[1] * y[2];
    return dydt;
  }
}
data {
  int<lower=1> T;
  real y0_d[2];
  real ts[T];
  real theta_d[1];
  real x[0];
  int x_int[0];
}
parameters {
  real t0;
  real y0_p[2];
  real theta_p[1];
}
model {
  real y_hat[T,2];
  y_hat = integrate_ode_rk45(sho, y0_d, t0, ts, theta_d, x, x_int);
  y_hat = integrate_ode_rk45(sho, y0_d, t0, ts, theta_p, x, x_int);
  y_hat = integrate_ode_rk45(sho, y0_p, t0, ts, theta_d, x, x_int);
  y_hat = integrate_ode_rk45(sho, y0_p, t0, ts, theta_p, x, x_int);
  y_hat = integrate_ode_rk45(sho, y0_d, t0, ts, theta_d, x, x_int, 1e-10, 1e-10, 1e8);
  y_hat = integrate_ode_rk45(sho, y0_d, t0, ts, theta_p, x, x_int, 1e-10, 1e-10, 1e8);
  y_hat = integrate_ode_rk45(sho, y0_p, t0, ts, theta_d, x, x_int, 1e-10, 1e-10, 1e8);
  y_hat = integrate_ode_rk45(sho, y0_p, t0, ts, theta_p, x, x_int, 1e-10, 1e-10, 1e8);
}
generated quantities {
  real y_hat[T,2];
  y_hat = integrate_ode_rk45(sho, y0_d, t0, ts, theta_d, x, x_int);
  y_hat = integrate_ode_rk45(sho, y0_d, t0, ts, theta_p, x, x_int);
  y_hat = integrate_ode_rk45(sho, y0_p, t0, ts, theta_d, x, x_int);
  y_hat = integrate_ode_rk45(sho, y0_p, t0, ts, theta_p, x, x_int);
  y_hat = integrate_ode_rk45(sho, y0_d, t0, ts, theta_d, x, x_int, 1e-10, 1e-10, 1e8);
  y_hat = integrate_ode_rk45(sho, y0_d, t0, ts, theta_p, x, x_int, 1e-10, 1e-10, 1e8);
  y_hat = integrate_ode_rk45(sho, y0_p, t0, ts, theta_d, x, x_int, 1e-10, 1e-10, 1e8);
  y_hat = integrate_ode_rk45(sho, y0_p, t0, ts, theta_p, x, x_int, 1e-10, 1e-10, 1e8);
}

or

functions {
  real[] sho(real t,
             real[] y, 
             real[] theta,
             real[] x,
             int[] x_int) {
    real dydt[2];
    dydt[1] = y[2];
    dydt[2] = -y[1] - theta[1] * y[2];
    return dydt;
  }
}
data {
  int<lower=1> T;
  real y0_d[2];
  real t0;
  real theta_d[1];
  real x[0];
  int x_int[0];
}
parameters {
  real ts[T];
  real y0_p[2];
  real theta_p[1];
}
model {
  real y_hat[T,2];
  y_hat = integrate_ode_rk45(sho, y0_d, t0, ts, theta_d, x, x_int);
  y_hat = integrate_ode_rk45(sho, y0_d, t0, ts, theta_p, x, x_int);
  y_hat = integrate_ode_rk45(sho, y0_p, t0, ts, theta_d, x, x_int);
  y_hat = integrate_ode_rk45(sho, y0_p, t0, ts, theta_p, x, x_int);
  y_hat = integrate_ode_rk45(sho, y0_d, t0, ts, theta_d, x, x_int, 1e-10, 1e-10, 1e8);
  y_hat = integrate_ode_rk45(sho, y0_d, t0, ts, theta_p, x, x_int, 1e-10, 1e-10, 1e8);
  y_hat = integrate_ode_rk45(sho, y0_p, t0, ts, theta_d, x, x_int, 1e-10, 1e-10, 1e8);
  y_hat = integrate_ode_rk45(sho, y0_p, t0, ts, theta_p, x, x_int, 1e-10, 1e-10, 1e8);
}
generated quantities {
  real y_hat[T,2];
  y_hat = integrate_ode_rk45(sho, y0_d, t0, ts, theta_d, x, x_int);
  y_hat = integrate_ode_rk45(sho, y0_d, t0, ts, theta_p, x, x_int);
  y_hat = integrate_ode_rk45(sho, y0_p, t0, ts, theta_d, x, x_int);
  y_hat = integrate_ode_rk45(sho, y0_p, t0, ts, theta_p, x, x_int);
  y_hat = integrate_ode_rk45(sho, y0_d, t0, ts, theta_d, x, x_int, 1e-10, 1e-10, 1e8);
  y_hat = integrate_ode_rk45(sho, y0_d, t0, ts, theta_p, x, x_int, 1e-10, 1e-10, 1e8);
  y_hat = integrate_ode_rk45(sho, y0_p, t0, ts, theta_d, x, x_int, 1e-10, 1e-10, 1e8);
  y_hat = integrate_ode_rk45(sho, y0_p, t0, ts, theta_p, x, x_int, 1e-10, 1e-10, 1e8);
}

Both should be correct, according to the manual, but the Stan compiler complains that the third/fourth argument to ODE solvers should be data only. The same happens for other ODE solvers.

Current Output:

The current output. Knowing what is the current behavior is useful.

Expected Output:

I do not know which of the two is correct, but the inconsistency should be resolved.

Current Version:

v2.18.0

[VMatthijs]

From looking at the Stan Math source, I conclude that the manual is wrong in this case. The third and fourth arguments need to be data only.

[bob-carpenter]

That's right---the start time (3rd arg) and requested solution times (4th arg) need to be data. That's going to change as soon as the PR to allow parameter start times gets merged.

…

On Dec 12, 2018, at 10:17 AM, Matthijs Vákár ***@***.***> wrote: From looking at the Stan Math source, I conclude that the manual is wrong in this case. The third and fourth arguments need to be data only. — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub, or mute the thread.

[wds15]

That changed! The initial time and the time can be var since 2.19 the latest.