Bases: odespy.solvers.Solver
This is a wrapper for radau5.f, a file containing the the radau5 FORTRAN subtroutine for the numerical solution of a stiff ODEs or differential algebraic (DAE) systems, involving first order equations on the form
The ODE system can be linearly implicit (mass-matrix \(M\) is not identity matrix) or explicit.
The method used is an implicit Runge-Kutta method (Radau IIA) of order 5 with step size control. The file radau5.f can be downloaded from http://www.unige.ch/~hairer/software.html. Details about the implementation can be found in the book “Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Problems”, by E. Hairer and G. Wanner, 2nd ed., 1996, published by Springer-Verlag (ISBN: 3-540-60452-9).
Required input arguments:
| Name | Description |
|---|---|
| f | Right-hand side f(u,t) defining the ODE. |
Optional input arguments:
| Name | Description |
|---|---|
| f_args | Extra positional arguments to f: f(u, t, *f_args, **f_kwargs). (default: ()) |
| f_kwargs | Extra keyword arguments to f: f(u, t, *f_args, **f_kwargs). (default: {}) |
| complex_valued | True if f is complex valued. (default: False) |
| disk_storage | Indicates whether u is stored in memory or in file. If string, it is the filename; if False or “”, u is kept in memory; if True, a default filename tmp_odspy.dat is used. (default: False) |
| verbose | Integer reflecting output of intermediate quantities. (default: 0) |
| u_exact | Function of t returning exact solution. (default: None) |
| f_f77 | Fortran subroutine for f. This subroutine has the signature: subroutine f_f77(neq,t,u,udot)
Cf2py intent(hide) neq
Cf2py intent(out) udot
integer neq
double precision t,u(neq),udot(neq)
udot = ...
return
end
|
| jac_f77_radau5 | Fortran subroutine for jac to be provided to Radau5. This subroutine should be defined as (note that rpar,ipar are not used): subroutine jac_f77_radau5
& (neq,t,u,dfu,ldfu,rpar,ipar)
Cf2py intent(hide) neq,rpar,ipar
Cf2py intent(in) t,u,ldfu
Cf2py intent(out) dfu
integer neq,ipar,ldfu
double precision t,u,dfu,rpar
dimension u(neq),dfu(ldfu,neq)
dfu(1,1) = ...
dfu(1,2) = ...
...
return
end
|
| atol | Absolute tolerance for solution. (default: 1e-08) |
| jac_banded | Function for Jacobian in banded matrix form. Used in Lsode, Lsoda, Lsodar. jac_banded(u,t,ml,mu) returns df/du as an array of size neq times ml+mu+1. |
| rtol | Relative tolerance for solution. (default: 1e-06) |
| nsteps | Max no of internal solver steps per time step. (default: 1000) |
| ml | Number of lower non-zero diagonals in a banded Jacobian. |
| mu | Number of upper non-zero diagonals in a banded Jacobian. |
| first_step | Suggested first time step size for an adaptive algorithm. |
| jac | Jacobian of right-hand side function f (df/du). (default: None) |
| safety | Safety factor on new step selection (default: 0.9) |
| max_step | Maximum step size for an adaptive algorithm. |
| nsteps | Max no of internal solver steps per time step. (default: 1000) |
| mas | User-supplied function to calculate the mass matrix M in the linearly implicit ODE system M*u’ = f(u, t). This function is used only when M is not I (the identity). M can be supplied as full matrix or banded matrix. The mas function returns M and takes any number of user-defined parameters as arguments, given through the parameter mas_args. If M is sparse, a banded matrix with dimensions (mlmas+mumas+1,neq) is returned, where mlmas and mumas are the lower and upper half-bandwidth of the banded matrix, and neq is the number of equations. |
| mas_f77 | Fortran subroutine for mas. This subroutine has the signature (note that rpar,ipar are not used): subroutine mas_f77(neq,mas,lmas,rpar,ipar)
Cf2py intent(hide) rpar,ipar
Cf2py intent(in) neq,lmas
Cf2py intent(out) mas
integer neq,lmas,ipar
double precision mas(lmas,neq),rpar
mas(1,1) = ...
...
return
end
|
| mlmas | Lower bandwith of mass matrix M |
| mumas | Upper bandwith of mass matrix M |
| mas_args | Extra positional arguments to the mas function (it is called as mas(*mas_args). (default: ()) |
Required input arguments:
| Name | Description |
|---|---|
| f | Right-hand side f(u,t) defining the ODE. |
Optional input arguments:
| Name | Description |
|---|---|
| f_args | Extra positional arguments to f: f(u, t, *f_args, **f_kwargs). (default: ()) |
| f_kwargs | Extra keyword arguments to f: f(u, t, *f_args, **f_kwargs). (default: {}) |
| complex_valued | True if f is complex valued. (default: False) |
| disk_storage | Indicates whether u is stored in memory or in file. If string, it is the filename; if False or “”, u is kept in memory; if True, a default filename tmp_odspy.dat is used. (default: False) |
| verbose | Integer reflecting output of intermediate quantities. (default: 0) |
| u_exact | Function of t returning exact solution. (default: None) |
| f_f77 | Fortran subroutine for f. This subroutine has the signature: subroutine f_f77(neq,t,u,udot)
Cf2py intent(hide) neq
Cf2py intent(out) udot
integer neq
double precision t,u(neq),udot(neq)
udot = ...
return
end
|
| jac_f77_radau5 | Fortran subroutine for jac to be provided to Radau5. This subroutine should be defined as (note that rpar,ipar are not used): subroutine jac_f77_radau5
& (neq,t,u,dfu,ldfu,rpar,ipar)
Cf2py intent(hide) neq,rpar,ipar
Cf2py intent(in) t,u,ldfu
Cf2py intent(out) dfu
integer neq,ipar,ldfu
double precision t,u,dfu,rpar
dimension u(neq),dfu(ldfu,neq)
dfu(1,1) = ...
dfu(1,2) = ...
...
return
end
|
| atol | Absolute tolerance for solution. (default: 1e-08) |
| jac_banded | Function for Jacobian in banded matrix form. Used in Lsode, Lsoda, Lsodar. jac_banded(u,t,ml,mu) returns df/du as an array of size neq times ml+mu+1. |
| rtol | Relative tolerance for solution. (default: 1e-06) |
| nsteps | Max no of internal solver steps per time step. (default: 1000) |
| ml | Number of lower non-zero diagonals in a banded Jacobian. |
| mu | Number of upper non-zero diagonals in a banded Jacobian. |
| first_step | Suggested first time step size for an adaptive algorithm. |
| jac | Jacobian of right-hand side function f (df/du). (default: None) |
| safety | Safety factor on new step selection (default: 0.9) |
| max_step | Maximum step size for an adaptive algorithm. |
| nsteps | Max no of internal solver steps per time step. (default: 1000) |
| mas | User-supplied function to calculate the mass matrix M in the linearly implicit ODE system M*u’ = f(u, t). This function is used only when M is not I (the identity). M can be supplied as full matrix or banded matrix. The mas function returns M and takes any number of user-defined parameters as arguments, given through the parameter mas_args. If M is sparse, a banded matrix with dimensions (mlmas+mumas+1,neq) is returned, where mlmas and mumas are the lower and upper half-bandwidth of the banded matrix, and neq is the number of equations. |
| mas_f77 | Fortran subroutine for mas. This subroutine has the signature (note that rpar,ipar are not used): subroutine mas_f77(neq,mas,lmas,rpar,ipar)
Cf2py intent(hide) rpar,ipar
Cf2py intent(in) neq,lmas
Cf2py intent(out) mas
integer neq,lmas,ipar
double precision mas(lmas,neq),rpar
mas(1,1) = ...
...
return
end
|
| mlmas | Lower bandwith of mass matrix M |
| mumas | Upper bandwith of mass matrix M |
| mas_args | Extra positional arguments to the mas function (it is called as mas(*mas_args). (default: ()) |
Methods
| adjust_parameters() | |
| advance() | This function intends to one step forward with Radau5. |
| check_conditional_parameters() | This function is used to check whether conditional parameters are provided when specified condition fulfilled. |
| check_extra(**kwargs) | A parameter may have a keyword extra_check for user-given functions that performs consistency checks on the parameter. |
| check_input_range(**kwargs) | Check whether all existing inputs are in right specified range. |
| check_input_types(**kwargs) | Check whether all existing inputs are of right specified type. |
| compile_string_functions(f, **kwargs) | Compile functions which are supplied as Fortran strings. |
| constant_time_step() | Check if self.t has a uniform partition. |
| func_wrappers() | |
| get([parameter_name, print_info]) | Return value of specified input parameters. |
| get_parameter_info([print_info]) | Return a dictionary containing all properties of all legal parameters in current subclass (i.e., the parameters in self._parameters). |
| has_u_t_all() | Return True if self.u_all and self.t_all, defined in |
| initialize() | Import extension module _radau5 and check that it exists. |
| initialize_for_solve() | |
| set([strict]) | Assign values to one or more parameters, specified as keyword arguments. |
| set_dummy_functions() | |
| set_initial_condition(U0) | Function set_initial_condition() is used to set initial value of |
| set_tol() | Tolerance parameters, rtol & atol, can be provided as either two scalars |
| solve(time_points[, terminate]) | Compute discrete solution u of the ODE problem at time points |
| switch_to(solver_target[, print_info]) | Create a new solver instance which switch to another subclass with same values of common attributes. |
| validate_data() |
Bases: odespy.radau5.Radau5
Radau5 solver for explcit ODE problem.
Required input arguments:
| Name | Description |
|---|---|
| f | Right-hand side f(u,t) defining the ODE. |
Optional input arguments:
| Name | Description |
|---|---|
| f_args | Extra positional arguments to f: f(u, t, *f_args, **f_kwargs). (default: ()) |
| f_kwargs | Extra keyword arguments to f: f(u, t, *f_args, **f_kwargs). (default: {}) |
| complex_valued | True if f is complex valued. (default: False) |
| disk_storage | Indicates whether u is stored in memory or in file. If string, it is the filename; if False or “”, u is kept in memory; if True, a default filename tmp_odspy.dat is used. (default: False) |
| verbose | Integer reflecting output of intermediate quantities. (default: 0) |
| u_exact | Function of t returning exact solution. (default: None) |
| f_f77 | Fortran subroutine for f. This subroutine has the signature: subroutine f_f77(neq,t,u,udot)
Cf2py intent(hide) neq
Cf2py intent(out) udot
integer neq
double precision t,u(neq),udot(neq)
udot = ...
return
end
|
| jac_f77_radau5 | Fortran subroutine for jac to be provided to Radau5. This subroutine should be defined as (note that rpar,ipar are not used): subroutine jac_f77_radau5
& (neq,t,u,dfu,ldfu,rpar,ipar)
Cf2py intent(hide) neq,rpar,ipar
Cf2py intent(in) t,u,ldfu
Cf2py intent(out) dfu
integer neq,ipar,ldfu
double precision t,u,dfu,rpar
dimension u(neq),dfu(ldfu,neq)
dfu(1,1) = ...
dfu(1,2) = ...
...
return
end
|
| atol | Absolute tolerance for solution. (default: 1e-08) |
| jac_banded | Function for Jacobian in banded matrix form. Used in Lsode, Lsoda, Lsodar. jac_banded(u,t,ml,mu) returns df/du as an array of size neq times ml+mu+1. |
| rtol | Relative tolerance for solution. (default: 1e-06) |
| nsteps | Max no of internal solver steps per time step. (default: 1000) |
| ml | Number of lower non-zero diagonals in a banded Jacobian. |
| mu | Number of upper non-zero diagonals in a banded Jacobian. |
| first_step | Suggested first time step size for an adaptive algorithm. |
| jac | Jacobian of right-hand side function f (df/du). (default: None) |
| safety | Safety factor on new step selection (default: 0.9) |
| max_step | Maximum step size for an adaptive algorithm. |
| nsteps | Max no of internal solver steps per time step. (default: 1000) |
Methods
| adjust_parameters() | |
| advance() | This function intends to one step forward with Radau5. |
| check_conditional_parameters() | This function is used to check whether conditional parameters are provided when specified condition fulfilled. |
| check_extra(**kwargs) | A parameter may have a keyword extra_check for user-given functions that performs consistency checks on the parameter. |
| check_input_range(**kwargs) | Check whether all existing inputs are in right specified range. |
| check_input_types(**kwargs) | Check whether all existing inputs are of right specified type. |
| compile_string_functions(f, **kwargs) | Compile functions which are supplied as Fortran strings. |
| constant_time_step() | Check if self.t has a uniform partition. |
| func_wrappers() | |
| get([parameter_name, print_info]) | Return value of specified input parameters. |
| get_parameter_info([print_info]) | Return a dictionary containing all properties of all legal parameters in current subclass (i.e., the parameters in self._parameters). |
| has_u_t_all() | Return True if self.u_all and self.t_all, defined in |
| initialize() | Import extension module _radau5 and check that it exists. |
| initialize_for_solve() | |
| set([strict]) | Assign values to one or more parameters, specified as keyword arguments. |
| set_dummy_functions() | |
| set_initial_condition(U0) | Function set_initial_condition() is used to set initial value of |
| set_tol() | Tolerance parameters, rtol & atol, can be provided as either two scalars |
| solve(time_points[, terminate]) | Compute discrete solution u of the ODE problem at time points |
| switch_to(solver_target[, print_info]) | Create a new solver instance which switch to another subclass with same values of common attributes. |
| validate_data() |