type_lorenz Module

  1. type_lorenz.f90
  2. type_lorenz
module~~type_lorenz~~UsesGraph module~type_lorenz type_lorenz IR_Precision IR_Precision IR_Precision->module~type_lorenz module~foodie foodie module~foodie->module~type_lorenz module~foodie_integrator_adams_bashforth foodie_integrator_adams_bashforth module~foodie_integrator_adams_bashforth->module~foodie module~foodie_integrator_adams_bashforth_moulton foodie_integrator_adams_bashforth_moulton module~foodie_integrator_adams_bashforth->module~foodie_integrator_adams_bashforth_moulton module~foodie_integrator_ms_runge_kutta_ssp foodie_integrator_ms_runge_kutta_ssp module~foodie_integrator_ms_runge_kutta_ssp->module~foodie module~foodie_error_codes foodie_error_codes module~foodie_error_codes->module~foodie module~foodie_error_codes->module~foodie_integrator_adams_bashforth module~foodie_error_codes->module~foodie_integrator_ms_runge_kutta_ssp module~foodie_integrator_lmm_ssp foodie_integrator_lmm_ssp module~foodie_error_codes->module~foodie_integrator_lmm_ssp module~foodie_integrator_euler_explicit foodie_integrator_euler_explicit module~foodie_error_codes->module~foodie_integrator_euler_explicit module~foodie_integrator_runge_kutta_emd foodie_integrator_runge_kutta_emd module~foodie_error_codes->module~foodie_integrator_runge_kutta_emd module~foodie_error_codes->module~foodie_integrator_adams_bashforth_moulton module~foodie_integrator_adams_moulton foodie_integrator_adams_moulton module~foodie_error_codes->module~foodie_integrator_adams_moulton module~foodie_integrator_runge_kutta_lssp foodie_integrator_runge_kutta_lssp module~foodie_error_codes->module~foodie_integrator_runge_kutta_lssp module~foodie_integrator_lmm_ssp_vss foodie_integrator_lmm_ssp_vss module~foodie_error_codes->module~foodie_integrator_lmm_ssp_vss module~foodie_integrator_runge_kutta_ssp foodie_integrator_runge_kutta_ssp module~foodie_error_codes->module~foodie_integrator_runge_kutta_ssp module~foodie_integrator_runge_kutta_low_storage foodie_integrator_runge_kutta_low_storage module~foodie_error_codes->module~foodie_integrator_runge_kutta_low_storage module~foodie_integrator_leapfrog foodie_integrator_leapfrog module~foodie_error_codes->module~foodie_integrator_leapfrog module~foodie_integrator_backward_differentiation_formula foodie_integrator_backward_differentiation_formula module~foodie_error_codes->module~foodie_integrator_backward_differentiation_formula module~foodie_integrator_lmm_ssp->module~foodie module~foodie_integrator_euler_explicit->module~foodie module~foodie_integrator_multistep_object foodie_integrator_multistep_object module~foodie_integrator_multistep_object->module~foodie module~foodie_integrator_multistep_object->module~foodie_integrator_adams_bashforth module~foodie_integrator_multistep_object->module~foodie_integrator_lmm_ssp module~foodie_integrator_multistep_object->module~foodie_integrator_adams_bashforth_moulton module~foodie_integrator_multistep_object->module~foodie_integrator_adams_moulton module~foodie_integrator_multistep_object->module~foodie_integrator_lmm_ssp_vss module~foodie_integrator_multistep_object->module~foodie_integrator_leapfrog module~foodie_integrator_multistep_object->module~foodie_integrator_backward_differentiation_formula module~foodie_integrator_runge_kutta_emd->module~foodie module~foodie_integrator_adams_bashforth_moulton->module~foodie iso_fortran_env iso_fortran_env iso_fortran_env->module~foodie iso_fortran_env->module~foodie_integrator_multistep_object module~foodie_integrator_multistage_object foodie_integrator_multistage_object iso_fortran_env->module~foodie_integrator_multistage_object module~foodie_integrator_multistage_multistep_object foodie_integrator_multistage_multistep_object iso_fortran_env->module~foodie_integrator_multistage_multistep_object module~foodie_integrator_object foodie_integrator_object iso_fortran_env->module~foodie_integrator_object penf penf penf->module~foodie penf->module~foodie_integrator_adams_bashforth penf->module~foodie_integrator_ms_runge_kutta_ssp penf->module~foodie_error_codes penf->module~foodie_integrator_lmm_ssp penf->module~foodie_integrator_euler_explicit penf->module~foodie_integrator_multistep_object penf->module~foodie_integrator_runge_kutta_emd penf->module~foodie_integrator_adams_bashforth_moulton penf->module~foodie_integrator_adams_moulton penf->module~foodie_integrator_runge_kutta_lssp penf->module~foodie_integrator_lmm_ssp_vss penf->module~foodie_integrator_runge_kutta_ssp module~foodie_integrand_object foodie_integrand_object penf->module~foodie_integrand_object penf->module~foodie_integrator_runge_kutta_low_storage penf->module~foodie_integrator_multistage_object penf->module~foodie_integrator_leapfrog penf->module~foodie_integrator_multistage_multistep_object penf->module~foodie_integrator_object penf->module~foodie_integrator_backward_differentiation_formula module~foodie_integrator_adams_moulton->module~foodie module~foodie_integrator_adams_moulton->module~foodie_integrator_adams_bashforth_moulton module~foodie_integrator_runge_kutta_lssp->module~foodie module~foodie_integrator_lmm_ssp_vss->module~foodie module~foodie_integrator_runge_kutta_ssp->module~foodie module~foodie_integrand_object->module~foodie module~foodie_integrand_object->module~foodie_integrator_adams_bashforth module~foodie_integrand_object->module~foodie_integrator_ms_runge_kutta_ssp module~foodie_integrand_object->module~foodie_integrator_lmm_ssp module~foodie_integrand_object->module~foodie_integrator_euler_explicit module~foodie_integrand_object->module~foodie_integrator_multistep_object module~foodie_integrand_object->module~foodie_integrator_runge_kutta_emd module~foodie_integrand_object->module~foodie_integrator_adams_bashforth_moulton module~foodie_integrand_object->module~foodie_integrator_adams_moulton module~foodie_integrand_object->module~foodie_integrator_runge_kutta_lssp module~foodie_integrand_object->module~foodie_integrator_lmm_ssp_vss module~foodie_integrand_object->module~foodie_integrator_runge_kutta_ssp module~foodie_integrand_object->module~foodie_integrator_runge_kutta_low_storage module~foodie_integrand_object->module~foodie_integrator_multistage_object module~foodie_integrand_object->module~foodie_integrator_leapfrog module~foodie_integrand_object->module~foodie_integrator_multistage_multistep_object module~foodie_integrand_object->module~foodie_integrator_backward_differentiation_formula module~foodie_integrator_runge_kutta_low_storage->module~foodie module~foodie_integrator_multistage_object->module~foodie module~foodie_integrator_multistage_object->module~foodie_integrator_euler_explicit module~foodie_integrator_multistage_object->module~foodie_integrator_runge_kutta_emd module~foodie_integrator_multistage_object->module~foodie_integrator_runge_kutta_lssp module~foodie_integrator_multistage_object->module~foodie_integrator_runge_kutta_ssp module~foodie_integrator_multistage_object->module~foodie_integrator_runge_kutta_low_storage module~foodie_integrator_leapfrog->module~foodie module~foodie_integrator_multistage_multistep_object->module~foodie module~foodie_integrator_multistage_multistep_object->module~foodie_integrator_ms_runge_kutta_ssp module~foodie_integrator_object->module~foodie module~foodie_integrator_object->module~foodie_integrator_adams_bashforth module~foodie_integrator_object->module~foodie_integrator_ms_runge_kutta_ssp module~foodie_integrator_object->module~foodie_integrator_lmm_ssp module~foodie_integrator_object->module~foodie_integrator_euler_explicit module~foodie_integrator_object->module~foodie_integrator_multistep_object module~foodie_integrator_object->module~foodie_integrator_runge_kutta_emd module~foodie_integrator_object->module~foodie_integrator_adams_bashforth_moulton module~foodie_integrator_object->module~foodie_integrator_adams_moulton module~foodie_integrator_object->module~foodie_integrator_runge_kutta_lssp module~foodie_integrator_object->module~foodie_integrator_lmm_ssp_vss module~foodie_integrator_object->module~foodie_integrator_runge_kutta_ssp module~foodie_integrator_object->module~foodie_integrator_runge_kutta_low_storage module~foodie_integrator_object->module~foodie_integrator_multistage_object module~foodie_integrator_object->module~foodie_integrator_leapfrog module~foodie_integrator_object->module~foodie_integrator_multistage_multistep_object module~foodie_integrator_object->module~foodie_integrator_backward_differentiation_formula module~foodie_integrator_backward_differentiation_formula->module~foodie
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Define Lorenz field that is a concrete extension of the abstract integrand type.

Used By

module~~type_lorenz~~UsedByGraph module~type_lorenz type_lorenz program~integrate_lorenz integrate_lorenz module~type_lorenz->program~integrate_lorenz
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Derived Types

Functions

Subroutines


Derived Types

type, public, extends(integrand) :: lorenz

Lorenz equations field.

Components

TypeVisibility AttributesNameInitial
real(kind=R_P), private, dimension(:), allocatable:: U

Integrand (state) variables, [1:dims].
real(kind=R_P), private :: beta =0._R_P

Lorenz \(\beta\).
integer(kind=I_P), private :: dims =0

Space dimensions.
real(kind=R_P), private, dimension(:,:), allocatable:: previous

Previous time steps states, [1:dims,1:steps].
real(kind=R_P), private :: rho =0._R_P

Lorenz \(\rho\).
real(kind=R_P), private :: sigma =0._R_P

Lorenz \(\sigma\).
integer(kind=I_P), private :: steps =0

Number of time steps stored.

Type-Bound Procedures

procedure, public, pass(lhs) :: add => add_lorenz

Lorenz + Lorenz operator.

procedure, public, pass(lhs) :: assign_integrand => lorenz_assign_lorenz

Lorenz = Lorenz.

procedure, public, pass(lhs) :: assign_real => lorenz_assign_real

Lorenz = real.

procedure, public, pass(self) :: init

Init field.

procedure, public, pass(lhs) :: integrand_multiply_integrand => lorenz_multiply_lorenz

Lorenz * Lorenz operator.

procedure, public, pass(lhs) :: integrand_multiply_real => lorenz_multiply_real

Lorenz * real operator.

procedure, public, pass(lhs) :: local_error => lorenz_local_error

Local error.

procedure, public, pass(self) :: output

Extract Lorenz field.

procedure, public, pass(self) :: previous_step

Get a previous time step.

procedure, public, pass(rhs) :: real_multiply_integrand => real_multiply_lorenz

Real * Lorenz operator.

procedure, public, pass(lhs) :: sub => sub_lorenz

Lorenz - Lorenz.

procedure, public, pass(self) :: t => dLorenz_dt

Time derivative, residuals function.

procedure, public, pass(self) :: update_previous_steps

Update previous time steps.

Functions

private function add_lorenz(lhs, rhs) result(opr)

Add two Lorenz fields.

Arguments

Type IntentOptional AttributesName
class(lorenz), intent(in) :: lhs

Left hand side.
class(integrand), intent(in) :: rhs

Right hand side.

Return Value class(integrand), allocatable

Operator result.

private function dLorenz_dt(self, t) result(dState_dt)

Time derivative of Lorenz field.

Arguments

Type IntentOptional AttributesName
class(lorenz), intent(in) :: self

Lorenz field.
real(kind=R_P), intent(in), optional :: t

Time.

Return Value class(integrand), allocatable

Lorenz field time derivative.

private function lorenz_local_error(lhs, rhs) result(error)

Estimate local truncation error between 2 lorenz approximations.

Arguments

Type IntentOptional AttributesName
class(lorenz), intent(in) :: lhs

Left hand side.
class(integrand), intent(in) :: rhs

Right hand side.

Return Value real(kind=R_P)

Error estimation.

private function lorenz_multiply_lorenz(lhs, rhs) result(opr)

Multiply a lorenz field by another one.

Arguments

Type IntentOptional AttributesName
class(lorenz), intent(in) :: lhs

Left hand side.
class(integrand), intent(in) :: rhs

Right hand side.

Return Value class(integrand), allocatable

Operator result.

private function lorenz_multiply_real(lhs, rhs) result(opr)

Multiply a Lorenz field by a real scalar.

Arguments

Type IntentOptional AttributesName
class(lorenz), intent(in) :: lhs

Left hand side.
real(kind=R_P), intent(in) :: rhs

Right hand side.

Return Value class(integrand), allocatable

Operator result.

private pure function output(self) result(state)

Output the Lorenz field state.

Arguments

Type IntentOptional AttributesName
class(lorenz), intent(in) :: self

Lorenz field.

Return Value real(kind=R_P), dimension(:), allocatable

Lorenz state vector.

private function previous_step(self, n) result(previous)

Extract previous time solution of Lorenz field.

Arguments

Type IntentOptional AttributesName
class(lorenz), intent(in) :: self

Lorenz field.
integer(kind=I_P), intent(in) :: n

Time level.

Return Value class(integrand), allocatable

Previous time solution of Lorenz field.

private function real_multiply_lorenz(lhs, rhs) result(opr)

Multiply a real scalar by a Lorenz field.

Arguments

Type IntentOptional AttributesName
real(kind=R_P), intent(in) :: lhs

Left hand side.
class(lorenz), intent(in) :: rhs

Right hand side.

Return Value class(integrand), allocatable

Operator result.

private function sub_lorenz(lhs, rhs) result(opr)

Subtract two Lorenz fields.

Arguments

Type IntentOptional AttributesName
class(lorenz), intent(in) :: lhs

Left hand side.
class(integrand), intent(in) :: rhs

Right hand side.

Return Value class(integrand), allocatable

Operator result.


Subroutines

private subroutine init(self, initial_state, sigma, rho, beta, steps)

Construct an initialized Lorenz field.

Arguments

Type IntentOptional AttributesName
class(lorenz), intent(inout) :: self

Lorenz field.
real(kind=R_P), intent(in), dimension(:):: initial_state

Initial state of Lorenz field vector.
real(kind=R_P), intent(in) :: sigma

Lorenz \(\sigma\).
real(kind=R_P), intent(in) :: rho

Lorenz \(\rho\).
real(kind=R_P), intent(in) :: beta

Lorenz \(\beta\).
integer(kind=I_P), intent(in), optional :: steps

Time steps stored.

private subroutine lorenz_assign_lorenz(lhs, rhs)

Assign one Lorenz field to another.

Arguments

Type IntentOptional AttributesName
class(lorenz), intent(inout) :: lhs

Left hand side.
class(integrand), intent(in) :: rhs

Right hand side.

private subroutine lorenz_assign_real(lhs, rhs)

Assign one real to a Lorenz field.

Arguments

Type IntentOptional AttributesName
class(lorenz), intent(inout) :: lhs

Left hand side.
real(kind=R_P), intent(in) :: rhs

Right hand side.

private subroutine update_previous_steps(self, filter, weights)

Update previous time steps.

Arguments

Type IntentOptional AttributesName
class(lorenz), intent(inout) :: self

Lorenz field.
class(integrand), intent(in), optional :: filter

Filter field displacement.
real(kind=R_P), intent(in), optional :: weights(:)

Weights for filtering the steps.

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