diffeq_base Module

A collection of base types for the DIFFEQ library.


Uses


Interfaces

interface

  • public subroutine attempt_single_step(this, sys, h, x, y, f, yn, fn, yerr, k)

    Attempts an integration step for a single-step integrator.

    Arguments

    Type IntentOptional Attributes Name
    class(single_step_integrator), intent(inout) :: this

    The single_step_integrator object.
    class(ode_container), intent(inout) :: sys

    The ode_container object containing the ODE's to integrate.
    real(kind=real64), intent(in) :: h

    The current step size.
    real(kind=real64), intent(in) :: x

    The current value of the independent variable.
    real(kind=real64), intent(in), dimension(:) :: y

    An N-element array containing the current solution at x.
    real(kind=real64), intent(in), dimension(:) :: f

    An N-element array containing the values of the derivatives at x.
    real(kind=real64), intent(out), dimension(:) :: yn

    An N-element array where this routine will write the next solution estimate at x + h.
    real(kind=real64), intent(out), dimension(:) :: fn

    An N-element array where this routine will write the next derivative estimate at x + h.
    real(kind=real64), intent(out), dimension(:) :: yerr

    An N-element array where this routine will write an estimate of the error in each equation.
    real(kind=real64), intent(out), dimension(:,:) :: k

    An N-by-NSTAGES matrix containing the derivatives at each stage.

interface

  • public pure function get_single_step_logical_parameter(this) result(rst)

    Returns a logical parameter from a single_step_integrator object.

    Arguments

    Type IntentOptional Attributes Name
    class(single_step_integrator), intent(in) :: this

    The single_step_integrator object.

    Return Value logical

    The parameter.

interface

  • public pure subroutine ode(x, y, dydx)

    Arguments

    Type IntentOptional Attributes Name
    real(kind=real64), intent(in) :: x
    real(kind=real64), intent(in), dimension(:) :: y
    real(kind=real64), intent(out), dimension(:) :: dydx

interface

  • public pure function ode_integer_inquiry(this) result(rst)

    Returns an integer value from the ode_integrator object.

    Arguments

    Type IntentOptional Attributes Name
    class(ode_integrator), intent(in) :: this

    The ode_integrator object.

    Return Value integer(kind=int32)

    The requested value.

interface

  • public pure subroutine ode_jacobian(x, y, jac)

    Arguments

    Type IntentOptional Attributes Name
    real(kind=real64), intent(in) :: x
    real(kind=real64), intent(in), dimension(:) :: y
    real(kind=real64), intent(out), dimension(:,:) :: jac

interface

  • public pure subroutine ode_mass_matrix(x, y, m)

    Arguments

    Type IntentOptional Attributes Name
    real(kind=real64), intent(in) :: x
    real(kind=real64), intent(in), dimension(:) :: y
    real(kind=real64), intent(out), dimension(:,:) :: m

interface

  • public subroutine ode_solver(this, sys, x, iv, err)

    Solves the supplied system of ODE's.

    Arguments

    Type IntentOptional Attributes Name
    class(ode_integrator), intent(inout) :: this

    The ode_integrator object.
    class(ode_container), intent(inout) :: sys

    The ode_container object containing the ODE's to integrate.
    real(kind=real64), intent(in), dimension(:) :: x

    An array, of at least 2 values, defining at a minimum the starting and ending values of the independent variable integration range. If more than two values are specified, the integration results will be returned at the supplied values.
    real(kind=real64), intent(in), dimension(:) :: iv

    An array containing the initial values for each ODE.
    class(errors), intent(inout), optional, target :: err

    An optional errors-based object that if provided can be used to retrieve information relating to any errors encountered during execution. If not provided, a default implementation of the errors class is used internally to provide error handling. Possible errors and warning messages that may be encountered are as follows.

    • DIFFEQ_MEMORY_ALLOCATION_ERROR: Occurs if there is a memory allocation issue.

    • DIFFEQ_NULL_POINTER_ERROR: Occurs if no ODE function is defined.

    • DIFFEQ_ARRAY_SIZE_ERROR: Occurs if there are less than 2 values given in the independent variable array x.

interface

  • public pure function single_step_integer_inquiry(this) result(rst)

    Gets an integer from the integrator.

    Arguments

    Type IntentOptional Attributes Name
    class(single_step_integrator), intent(in) :: this

    The single_step_integrator object.

    Return Value integer(kind=int32)

    The integer value.

interface

  • public subroutine single_step_interpolate(this, x, xn, yn, fn, xn1, yn1, fn1, y)

    Provides a routine for interpolation.

    Arguments

    Type IntentOptional Attributes Name
    class(single_step_integrator), intent(in) :: this

    The single_step_integrator object.
    real(kind=real64), intent(in) :: x

    The value of the independent variable at which to compute the interpolation.
    real(kind=real64), intent(in) :: xn

    The previous value of the independent variable at which the solution is computed.
    real(kind=real64), intent(in), dimension(:) :: yn

    An N-element array containing the solution at xn.
    real(kind=real64), intent(in), dimension(:) :: fn

    An N-element array containing the derivatives at xn.
    real(kind=real64), intent(in) :: xn1

    The value of the independent variable at xn + h.
    real(kind=real64), intent(in), dimension(:) :: yn1

    An N-element array containing the solution at xn + h.
    real(kind=real64), intent(in), dimension(:) :: fn1

    An N-element array containing the derivatives at xn + h.
    real(kind=real64), intent(out), dimension(:) :: y

    An N-element array where this routine will write the solution values interpolated at x.

interface

  • public subroutine single_step_post_step_routine(this, sys, dense, x, xn, y, yn, f, fn, k)

    Provides a routine for performing any actions, such as setting up interpolation, after successful completion of a step.

    Arguments

    Type IntentOptional Attributes Name
    class(single_step_integrator), intent(inout) :: this

    The single_step_integrator object.
    class(ode_container), intent(inout) :: sys

    The ode_container object containing the ODE's to integrate.
    logical, intent(in) :: dense

    Determines if dense output is requested (true); else, false.
    real(kind=real64), intent(in) :: x

    The previous value of the independent variable.
    real(kind=real64), intent(in) :: xn

    The current value of the independent variable.
    real(kind=real64), intent(in), dimension(:) :: y

    An N-element array containing the solution at x.
    real(kind=real64), intent(in), dimension(:) :: yn

    An N-element array containing the solution at xn.
    real(kind=real64), intent(in), dimension(:) :: f

    An N-element array containing the derivatives at x.
    real(kind=real64), intent(in), dimension(:) :: fn

    An N-element array containing the derivatives at xn.
    real(kind=real64), intent(inout), dimension(:,:) :: k

    An N-by-NSTAGES matrix containing the derivatives at each stage.

interface

  • public subroutine single_step_pre_step_routine(this, prevs, sys, h, x, y, f, err)

    Provides a routine for performing any actions, such as setting up Jacobian calculations.

    Arguments

    Type IntentOptional Attributes Name
    class(single_step_integrator), intent(inout) :: this

    The single_step_integrator object.
    logical, intent(in) :: prevs

    Defines the status of the previous step. The value is true if the previous step was successful; else, false if the previous step failed.
    class(ode_container), intent(inout) :: sys

    The ode_container object containing the ODE's to integrate.
    real(kind=real64), intent(in) :: h

    The current step size.
    real(kind=real64), intent(in) :: x

    The current value of the independent variable.
    real(kind=real64), intent(in), dimension(:) :: y

    An N-element array containing the current solution at x.
    real(kind=real64), intent(in), dimension(:) :: f

    An N-element array containing the values of the derivatives at x.
    class(errors), intent(inout), optional, target :: err

    An optional errors-based object that if provided can be used to retrieve information relating to any errors encountered during execution. If not provided, a default implementation of the errors class is used internally to provide error handling.

Derived Types

type, public ::  ode_container

A container for the routine containing the ODEs to integrate.

Components

Type Visibility Attributes Name Initial
procedure(ode), public, pointer, nopass :: fcn => null()

A pointer to the routine containing the ODEs to integrate.
procedure(ode_jacobian), public, pointer, nopass :: jacobian => null()

A pointer to the routine containing the analytical Jacobian. If supplied, this routine is utilized; however, if null, a finite difference approximation is utilized.
procedure(ode_mass_matrix), public, pointer, nopass :: mass_matrix => null()

A pointer to the routine containing the mass matrix for the system. If set to null (the default), an identity mass matrix will be assumed.

Type-Bound Procedures

procedure, public :: compute_jacobian => oc_jacobian
procedure, public :: get_finite_difference_step => oc_get_fd_step
procedure, public :: get_is_mass_matrix_dependent => oc_get_is_mass_dependent
procedure, public :: get_is_ode_defined => oc_get_is_ode_defined
procedure, public :: set_finite_difference_step => oc_set_fd_step
procedure, public :: set_is_mass_matrix_dependent => oc_set_is_mass_dependent

type, public ::  ode_integrator

The most basic ODE integrator object capable of integrating systems of ODE's.

Type-Bound Procedures

procedure, public :: append_to_buffer => oi_append_to_buffer ..\..\

Appends the supplied solution point to the internal solution buffer.<\p>
procedure, public :: clear_buffer => oi_clear_buffer ..\..\

Clears the contents of the buffer.<\p>
procedure, public :: compute_error_norm => oi_estimate_error ..\..\

Computes the norm of the scaled error estimate.<\p>
procedure, public :: estimate_inital_step_size => oi_initial_step ..\..\

Computes an estimate of an initial step size.<\p>
procedure, public :: estimate_next_step_size => oi_next_step ..\..\

Estimates the next step size.<\p>
procedure, public :: get_absolute_tolerance => oi_get_abs_tol ..\..\

Gets the absolute error tolerance.<\p>
procedure, public :: get_allow_overshoot => oi_get_allow_overshoot ..\..\

Gets a value determining if the solver is allowed to overshoot the final value in the integration range.<\p>
procedure, public :: get_maximum_step_size => oi_get_max_step ..\..\

Gets the magnitude of the maximum allowed step size.<\p>
procedure, public :: get_minimum_step_size => oi_get_min_step ..\..\

Gets the magnitude of the minimum allowed step size.<\p>
procedure(ode_integer_inquiry), public, deferred, pass :: get_order ..\..\

Returns the order of the integrator.<\p>
procedure, public :: get_relative_tolerance => oi_get_abs_tol ..\..\

Gets the relative error tolerance.<\p>
procedure, public :: get_solution => oi_get_solution ..\..\

Returns the solution computed by the integrator.<\p>
procedure, public :: get_step_limit => oi_get_step_limit ..\..\

Gets the limit on the number of integration steps.<\p>
procedure, public :: get_step_size_control_parameter => oi_get_control_parameter ..\..\

Gets the step size PI control parameter.<\p>
procedure, public :: get_step_size_factor => oi_get_safety_factor ..\..\

Gets the step size safety factor.<\p>
procedure, public :: set_absolute_tolerance => oi_set_abs_tol ..\..\

Sets the absolute error tolerance.<\p>
procedure, public :: set_allow_overshoot => oi_set_allow_overshoot ..\..\

Sets a value determining if the solver is allowed to overshoot the final value in the integration range.<\p>
procedure, public :: set_maximum_step_size => oi_set_max_step ..\..\

Sets the magnitude of the maximum allowed step size.<\p>
procedure, public :: set_minimum_step_size => oi_set_min_step ..\..\

Sets the magnitude of the minimum allowed step size.<\p>
procedure, public :: set_relative_tolerance => oi_set_abs_tol ..\..\

Sets the relative error tolerance.<\p>
procedure, public :: set_step_limit => oi_set_step_limit ..\..\

Sets the limit on the number of integration steps.<\p>
procedure, public :: set_step_size_control_parameter => oi_set_control_parameter ..\..\

Sets the step size PI control parameter.<\p>
procedure, public :: set_step_size_factor => oi_set_safety_factor ..\..\

Sets the step size safety factor.<\p>
procedure(ode_solver), public, deferred, pass :: solve ..\..\

Solves the supplied system of ODE's.<\p>

type, public, extends(ode_integrator) ::  single_step_integrator

The most basic, single-step integrator object capable of integrating systems of ODE's.

Type-Bound Procedures

procedure, public :: append_to_buffer => oi_append_to_buffer ..\..\

Appends the supplied solution point to the internal solution buffer.<\p>
procedure(attempt_single_step), public, deferred, pass :: attempt_step ..\..\

Attempts an integration step for a single-step integrator.<\p>
procedure, public :: clear_buffer => oi_clear_buffer ..\..\

Clears the contents of the buffer.<\p>
procedure, public :: compute_error_norm => oi_estimate_error ..\..\

Computes the norm of the scaled error estimate.<\p>
procedure, public :: estimate_inital_step_size => oi_initial_step ..\..\

Computes an estimate of an initial step size.<\p>
procedure, public :: estimate_next_step_size => oi_next_step ..\..\

Estimates the next step size.<\p>
procedure, public :: get_absolute_tolerance => oi_get_abs_tol ..\..\

Gets the absolute error tolerance.<\p>
procedure, public :: get_allow_overshoot => oi_get_allow_overshoot ..\..\

Gets a value determining if the solver is allowed to overshoot the final value in the integration range.<\p>
procedure(get_single_step_logical_parameter), public, deferred, pass :: get_is_fsal ..\..\

Gets a logical parameter stating if this is a first-same-as-last (FSAL) integrator.<\p>
procedure, public :: get_maximum_step_size => oi_get_max_step ..\..\

Gets the magnitude of the maximum allowed step size.<\p>
procedure, public :: get_minimum_step_size => oi_get_min_step ..\..\

Gets the magnitude of the minimum allowed step size.<\p>
procedure(ode_integer_inquiry), public, deferred, pass :: get_order ..\..\

Returns the order of the integrator.<\p>
procedure, public :: get_relative_tolerance => oi_get_abs_tol ..\..\

Gets the relative error tolerance.<\p>
procedure, public :: get_solution => oi_get_solution ..\..\

Returns the solution computed by the integrator.<\p>
procedure(single_step_integer_inquiry), public, deferred, pass :: get_stage_count ..\..\

Gets the number of stages used by the integrator.<\p>
procedure, public :: get_step_limit => oi_get_step_limit ..\..\

Gets the limit on the number of integration steps.<\p>
procedure, public :: get_step_size_control_parameter => oi_get_control_parameter ..\..\

Gets the step size PI control parameter.<\p>
procedure, public :: get_step_size_factor => oi_get_safety_factor ..\..\

Gets the step size safety factor.<\p>
procedure(single_step_interpolate), public, deferred, pass :: interpolate ..\..\

Performs an interpolation to estimate the solution at the requested point.<\p>
procedure(single_step_post_step_routine), public, deferred, pass :: post_step_action ..\..\

Performs actions such as setting up interpolation after completion of a successful integration step.<\p>
procedure(single_step_pre_step_routine), public, deferred, pass :: pre_step_action ..\..\

Provides a routine for performing any actions, such as setting up Jacobian calculations.<\p>
procedure, public :: set_absolute_tolerance => oi_set_abs_tol ..\..\

Sets the absolute error tolerance.<\p>
procedure, public :: set_allow_overshoot => oi_set_allow_overshoot ..\..\

Sets a value determining if the solver is allowed to overshoot the final value in the integration range.<\p>
procedure, public :: set_maximum_step_size => oi_set_max_step ..\..\

Sets the magnitude of the maximum allowed step size.<\p>
procedure, public :: set_minimum_step_size => oi_set_min_step ..\..\

Sets the magnitude of the minimum allowed step size.<\p>
procedure, public :: set_relative_tolerance => oi_set_abs_tol ..\..\

Sets the relative error tolerance.<\p>
procedure, public :: set_step_limit => oi_set_step_limit ..\..\

Sets the limit on the number of integration steps.<\p>
procedure, public :: set_step_size_control_parameter => oi_set_control_parameter ..\..\

Sets the step size PI control parameter.<\p>
procedure, public :: set_step_size_factor => oi_set_safety_factor ..\..\

Sets the step size safety factor.<\p>
procedure, public :: solve => ssi_ode_solver ..\..\

Solves the supplied system of ODE's.<\p>