Deprecated Functions
This appendix lists currently deprecated functionality along with how to replace it.
Starting in Stan 2.29, deprecated functions with drop in replacements (such as the renaming of get_lp or multiply_log) will be removed 3 versions later e.g., functions deprecated in Stan 2.20 will be removed in Stan 2.23 and placed in Removed Functions. The Stan compiler can automatically update these on the behalf of the user for the entire deprecation window and at least one version following the removal.
Integer division with operator/
Deprecated: Using / with two integer arguments is interpreted as integer floor division, such that
\[ 1 / 2 = 0 \]
This is deprecated due to its confusion with real-valued division, where
\[ 1.0 / 2.0 = 0.5 \]
Replacement: Use the integer division operator operator%/% instead.
integrate_ode_rk45, integrate_ode_adams, integrate_ode_bdf ODE Integrators
These ODE integrator functions have been replaced by those described in Ordinary Differential Equation (ODE) Solvers.
Specifying an ordinary differential equation as a function
A system of ODEs is specified as an ordinary function in Stan within the functions block. The ODE system function must have this function signature:
array[] real ode(real time, array[] real state, array[] real theta,
array[] real x_r, array[] int x_i);The ODE system function should return the derivative of the state with respect to time at the time provided. The length of the returned real array must match the length of the state input into the function.
The arguments to this function are:
time, the time to evaluate the ODE systemstate, the state of the ODE system at the time specifiedtheta, parameter values used to evaluate the ODE systemx_r, data values used to evaluate the ODE systemx_i, integer data values used to evaluate the ODE system.
The ODE system function separates parameter values, theta, from data values, x_r, for efficiency in computing the gradients of the ODE.
Non-stiff solver
array[,] real integrate_ode_rk45(function ode, array[] real initial_state, real initial_time, array[] real times, array[] real theta, array[] real x_r, array[] int x_i)
Solves the ODE system for the times provided using the Dormand-Prince algorithm, a 4th/5th order Runge-Kutta method.
array[,] real integrate_ode_rk45(function ode, array[] real initial_state, real initial_time, array[] real times, array[] real theta, array[] real x_r, array[] int x_i, real rel_tol, real abs_tol, int max_num_steps)
Solves the ODE system for the times provided using the Dormand-Prince algorithm, a 4th/5th order Runge-Kutta method with additional control parameters for the solver.
array[,] real integrate_ode(function ode, array[] real initial_state, real initial_time, array[] real times, array[] real theta, array[] real x_r, array[] int x_i)
Solves the ODE system for the times provided using the Dormand-Prince algorithm, a 4th/5th order Runge-Kutta method.
array[,] real integrate_ode_adams(function ode, array[] real initial_state, real initial_time, array[] real times, array[] real theta, data array[] real x_r, data array[] int x_i)
Solves the ODE system for the times provided using the Adams-Moulton method.
array[,] real integrate_ode_adams(function ode, array[] real initial_state, real initial_time, array[] real times, array[] real theta, data array[] real x_r, data array[] int x_i, data real rel_tol, data real abs_tol, data int max_num_steps)
Solves the ODE system for the times provided using the Adams-Moulton method with additional control parameters for the solver.
Stiff solver
array[,] real integrate_ode_bdf(function ode, array[] real initial_state, real initial_time, array[] real times, array[] real theta, data array[] real x_r, data array[] int x_i)
Solves the ODE system for the times provided using the backward differentiation formula (BDF) method.
array[,] real integrate_ode_bdf(function ode, array[] real initial_state, real initial_time, array[] real times, array[] real theta, data array[] real x_r, data array[] int x_i, data real rel_tol, data real abs_tol, data int max_num_steps)
Solves the ODE system for the times provided using the backward differentiation formula (BDF) method with additional control parameters for the solver.
Arguments to the ODE solvers
The arguments to the ODE solvers in both the stiff and non-stiff cases are as follows.
ode: function literal referring to a function specifying the system of differential equations with signature:
(real, array[] real, array[] real, data array[] real, data array[] int):array[] realThe arguments represent (1) time, (2) system state, (3) parameters, (4) real data, and (5) integer data, and the return value contains the derivatives with respect to time of the state,
initial_state: initial state, typearray[] real,initial_time: initial time, typeintorreal,times: solution times, typearray[] real,theta: parameters, typearray[] real,datax_r: real data, typearray[] real, data only, anddatax_i: integer data, typearray[] int, data only.
For more fine-grained control of the ODE solvers, these parameters can also be provided:
datarel_tol: relative tolerance for the ODE solver, typereal, data only,dataabs_tol: absolute tolerance for the ODE solver, typereal, data only, anddatamax_num_steps: maximum number of steps to take in the ODE solver, typeint, data only.
Return values
The return value for the ODE solvers is an array of type array[,] real, with values consisting of solutions at the specified times.
Sizes and parallel arrays
The sizes must match, and in particular, the following groups are of the same size:
state variables passed into the system function, derivatives returned by the system function, initial state passed into the solver, and rows of the return value of the solver,
solution times and number of rows of the return value of the solver,
parameters, real data and integer data passed to the solver will be passed to the system function
algebra_solver, algebra_solver_newton algebraic solvers
These algebraic solver functions have been replaced by those described in Algebraic Equation Solvers..
Specifying an algebraic equation as a function
An algebraic system is specified as an ordinary function in Stan within the function block. The algebraic system function must have this signature:
vector algebra_system(vector y, vector theta,
data array[] real x_r, array[] int x_i)The algebraic system function should return the value of the algebraic function which goes to 0, when we plug in the solution to the algebraic system.
The argument of this function are:
y, the unknowns we wish to solve fortheta, parameter values used to evaluate the algebraic systemx_r, data values used to evaluate the algebraic systemx_i, integer data used to evaluate the algebraic system
The algebraic system function separates parameter values, theta, from data values, x_r, for efficiency in propagating the derivatives through the algebraic system.
Call to the algebraic solver
vector algebra_solver(function algebra_system, vector y_guess, vector theta, data array[] real x_r, array[] int x_i)
Solves the algebraic system, given an initial guess, using the Powell hybrid algorithm.
vector algebra_solver(function algebra_system, vector y_guess, vector theta, data array[] real x_r, array[] int x_i, data real rel_tol, data real f_tol, int max_steps)
Solves the algebraic system, given an initial guess, using the Powell hybrid algorithm with additional control parameters for the solver.
Note: In future releases, the function algebra_solver will be deprecated and replaced with algebra_solver_powell.
vector algebra_solver_newton(function algebra_system, vector y_guess, vector theta, data array[] real x_r, array[] int x_i)
Solves the algebraic system, given an initial guess, using Newton’s method.
vector algebra_solver_newton(function algebra_system, vector y_guess, vector theta, data array[] real x_r, array[] int x_i, data real rel_tol, data real f_tol, int max_steps)
Solves the algebraic system, given an initial guess, using Newton’s method with additional control parameters for the solver.
Arguments to the algebraic solver
The arguments to the algebraic solvers are as follows:
algebra_system: function literal referring to a function specifying the system of algebraic equations with signature(vector, vector, array[] real, array[] int):vector. The arguments represent (1) unknowns, (2) parameters, (3) real data, and (4) integer data, and the return value contains the value of the algebraic function, which goes to 0 when we plug in the solution to the algebraic system,y_guess: initial guess for the solution, typevector,theta: parameters only, typevector,x_r: real data only, typearray[] real, andx_i: integer data only, typearray[] int.
For more fine-grained control of the algebraic solver, these parameters can also be provided:
rel_tol: relative tolerance for the algebraic solver, typereal, data only,function_tol: function tolerance for the algebraic solver, typereal, data only,max_num_steps: maximum number of steps to take in the algebraic solver, typeint, data only.
Return value
The return value for the algebraic solver is an object of type vector, with values which, when plugged in as y make the algebraic function go to 0.
Sizes and parallel arrays
Certain sizes have to be consistent. The initial guess, return value of the solver, and return value of the algebraic function must all be the same size.
The parameters, real data, and integer data will be passed from the solver directly to the system function.