rksuite_90 – ISOFT

Uses

- rksuite_90_prec
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Used by

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Graph Key

Nodes of different colours represent the following:

Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses.

Interfaces

setup range_integrate step_integrate statistics global_error reset_t_end interpolate set_stop_on_fatal get_saved_fatal collect_garbage

Derived Types

rk_comm_real_1d

Functions

get_saved_state_r1 get_saved_fatal_r1 get_stop_on_fatal_r1

Subroutines

machine_const method_const setup_r1 collect_garbage_r1 range_integrate_r1 step_integrate_r1 truerr_r1 step_r1 stiff_r1 statistics_r1 global_error_r1 reset_t_end_r1 interpolate_r1 rkmsg_r1 set_saved_state_r1 set_stop_on_fatal_r1

Interfaces

public interface setup

private subroutine setup_r1(comm, t_start, y_start, t_end, tolerance, thresholds, method, task, error_assess, h_start, message)

Arguments

Type	Intent	Optional	Attributes		Name
type(rk_comm_real_1d)				::	comm
real(kind=wp),	intent(in)			::	t_start
real(kind=wp),	intent(in),		dimension(:)	::	y_start
real(kind=wp),	intent(in)			::	t_end
real(kind=wp),	intent(in)			::	tolerance
real(kind=wp),	intent(in),		dimension(:)	::	thresholds
character(len=*),	intent(in),	optional		::	method
character(len=*),	intent(in),	optional		::	task
logical,	intent(in),	optional		::	error_assess
real(kind=wp),	intent(in),	optional		::	h_start
logical,	intent(in),	optional		::	message

public interface range_integrate

private recursive subroutine range_integrate_r1(comm, f, t_want, t_got, y_got, yderiv_got, flag)

Arguments

Type

Intent

Optional

Attributes

Name

type(rk_comm_real_1d),

intent(inout)

comm

public function f(t, y)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	t
real(kind=wp),	intent(in),		dimension(:)	::	y

Return Value real(kind=wp), dimension(size(y,1))

real(kind=wp),

intent(in)

t_want

real(kind=wp),

intent(out)

t_got

real(kind=wp),

intent(out),

dimension(:)

y_got

real(kind=wp),

intent(out),

dimension(:)

yderiv_got

integer,

intent(out),

optional

flag

public interface step_integrate

private recursive subroutine step_integrate_r1(comm, f, t_now, y_now, yderiv_now, flag)

Arguments

Type

Intent

Optional

Attributes

Name

type(rk_comm_real_1d),

intent(inout)

comm

public function f(t, y)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	t
real(kind=wp),	intent(in),		dimension(:)	::	y

Return Value real(kind=wp), dimension(size(y,1))

real(kind=wp),

intent(out)

t_now

real(kind=wp),

intent(out),

dimension(:)

y_now

real(kind=wp),

intent(out),

dimension(:)

yderiv_now

integer,

intent(out),

optional

flag

public interface statistics

private subroutine statistics_r1(comm, total_f_calls, step_cost, waste, num_succ_steps, h_next, y_maxvals)

Arguments

Type	Intent	Optional	Attributes		Name
type(rk_comm_real_1d),	intent(inout)			::	comm
integer,	intent(out),	optional		::	total_f_calls
integer,	intent(out),	optional		::	step_cost
real(kind=wp),	intent(out),	optional		::	waste
integer,	intent(out),	optional		::	num_succ_steps
real(kind=wp),	intent(out),	optional		::	h_next
real(kind=wp),	intent(out),	optional	dimension(:)	::	y_maxvals

public interface global_error

private subroutine global_error_r1(comm, rms_error, max_error, t_max_error)

Arguments

Type	Intent	Optional	Attributes		Name
type(rk_comm_real_1d),	intent(inout)			::	comm
real(kind=wp),	intent(out),	optional	dimension(:)	::	rms_error
real(kind=wp),	intent(out),	optional		::	max_error
real(kind=wp),	intent(out),	optional		::	t_max_error

public interface reset_t_end

private subroutine reset_t_end_r1(comm, t_end_new)

Arguments

Type Intent Optional Attributes Name

type(rk_comm_real_1d), intent(inout) :: comm

real(kind=wp), intent(in) :: t_end_new

public interface interpolate

private subroutine interpolate_r1(comm, f, t_want, y_want, yderiv_want)

Arguments

Type

Intent

Optional

Attributes

Name

type(rk_comm_real_1d),

intent(inout),

target

comm

public function f(t, y)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	t
real(kind=wp),	intent(in),		dimension(:)	::	y

Return Value real(kind=wp), dimension(size(y,1))

real(kind=wp),

intent(in)

t_want

real(kind=wp),

intent(out),

optional

dimension(:)

y_want

real(kind=wp),

intent(out),

optional

dimension(:)

yderiv_want

public interface set_stop_on_fatal

private subroutine set_stop_on_fatal_r1(comm, action)

Arguments

Type Intent Optional Attributes Name

type(rk_comm_real_1d), intent(inout) :: comm

logical, intent(in) :: action

public interface get_saved_fatal

private function get_saved_fatal_r1(comm)

Arguments

Type Intent Optional Attributes Name

type(rk_comm_real_1d), intent(in) :: comm

Return Value logical

public interface collect_garbage

private subroutine collect_garbage_r1(comm)

Arguments

Type Intent Optional Attributes Name

type(rk_comm_real_1d) :: comm

Derived Types

type, public :: rk_comm_real_1d

Components

Type	Visibility	Attributes		Name
real(kind=wp),	private		::	t
real(kind=wp),	private		::	t_old
real(kind=wp),	private		::	t_start
real(kind=wp),	private		::	t_end
real(kind=wp),	private		::	dir
real(kind=wp),	private		::	h
real(kind=wp),	private		::	h_old
real(kind=wp),	private		::	h_start
real(kind=wp),	private		::	h_average
real(kind=wp),	private		::	tol
integer,	private		::	f_count
integer,	private		::	full_f_count
integer,	private		::	step_count
integer,	private		::	bad_step_count
logical,	private		::	at_t_start
logical,	private		::	at_t_end
real(kind=wp),	private,	dimension(:), pointer	::	thresh
real(kind=wp),	private,	dimension(:), pointer	::	weights
real(kind=wp),	private,	dimension(:), pointer	::	ymax
real(kind=wp),	private,	dimension(:), pointer	::	scratch
real(kind=wp),	private,	dimension(:), pointer	::	y
real(kind=wp),	private,	dimension(:), pointer	::	yp
real(kind=wp),	private,	dimension(:), pointer	::	y_new
real(kind=wp),	private,	dimension(:), pointer	::	y_old
real(kind=wp),	private,	dimension(:), pointer	::	yp_old
real(kind=wp),	private,	dimension(:), pointer	::	v0
real(kind=wp),	private,	dimension(:), pointer	::	v1
real(kind=wp),	private,	dimension(:), pointer	::	err_estimates
real(kind=wp),	private,	dimension(:), pointer	::	v2
real(kind=wp),	private,	dimension(:), pointer	::	v3
real(kind=wp),	private,	dimension(:), pointer	::	vtemp
real(kind=wp),	private,	dimension(:,:), pointer	::	stages
real(kind=wp),	private		::	a(13,13)
real(kind=wp),	private		::	b(13)
real(kind=wp),	private		::	c(13)
real(kind=wp),	private		::	bhat(13)
real(kind=wp),	private		::	r(11,6)
real(kind=wp),	private		::	e(7)
integer,	private		::	ptr(13)
integer,	private		::	no_of_stages
integer,	private		::	rk_method
integer,	private		::	intrp_degree
logical,	private		::	intrp_able
logical,	private		::	intrp_needs_stages
real(kind=wp),	private		::	toosml
real(kind=wp),	private		::	cost
real(kind=wp),	private		::	safety
real(kind=wp),	private		::	expon
real(kind=wp),	private		::	stability_radius
real(kind=wp),	private		::	tan_angle
real(kind=wp),	private		::	rs
real(kind=wp),	private		::	rs1
real(kind=wp),	private		::	rs2
real(kind=wp),	private		::	rs3
real(kind=wp),	private		::	rs4
integer,	private		::	order
integer,	private		::	last_stage
integer,	private		::	max_stiff_iters
integer,	private		::	no_of_ge_steps
logical,	private		::	fsal
real(kind=wp),	private		::	ge_max_contrib
real(kind=wp),	private		::	t_ge_max_contrib
integer,	private		::	ge_f_count
real(kind=wp),	private,	dimension(:), pointer	::	ge_assess
real(kind=wp),	private,	dimension(:), pointer	::	ge_y
real(kind=wp),	private,	dimension(:), pointer	::	ge_yp
real(kind=wp),	private,	dimension(:), pointer	::	ge_y_new
real(kind=wp),	private,	dimension(:), pointer	::	ge_err_estimates
real(kind=wp),	private,	dimension(:,:), pointer	::	ge_stages
logical,	private		::	erason
logical,	private		::	erasfl
real(kind=wp),	private		::	mcheps
real(kind=wp),	private		::	dwarf
real(kind=wp),	private		::	round_off
real(kind=wp),	private		::	sqrrmc
real(kind=wp),	private		::	cubrmc
real(kind=wp),	private		::	sqtiny
integer,	private		::	outch
logical,	private		::	print_message
logical,	private		::	use_range
character(len=80),	private		::	rec(10)
real(kind=wp),	private		::	tlast
real(kind=wp),	private		::	range_t_end
real(kind=wp),	private,	dimension(:), pointer	::	xstage
real(kind=wp),	private,	dimension(:), pointer	::	ytemp
real(kind=wp),	private,	dimension(:,:), pointer	::	p
integer,	private		::	stiff_bad_step_count
integer,	private		::	hit_t_end_count
real(kind=wp),	private		::	errold
logical,	private		::	chkeff
logical,	private		::	phase2
integer,	private,	dimension(7)	::	save_states
logical,	private		::	stop_on_fatal
logical,	private		::	saved_fatal_err

Functions

private function get_saved_state_r1(srname, save_states)

Arguments

Type	Intent	Optional	Attributes		Name
character(len=*),	intent(in)			::	srname
integer,	intent(inout),		dimension(7)	::	save_states

Return Value integer

private function get_saved_fatal_r1(comm)

Arguments

Type	Intent	Optional	Attributes		Name
type(rk_comm_real_1d),	intent(in)			::	comm

Return Value logical

private function get_stop_on_fatal_r1(comm)

Arguments

Type	Intent	Optional	Attributes		Name
type(rk_comm_real_1d),	intent(in)			::	comm

Return Value logical

Subroutines

private subroutine machine_const(round_off, sqrrmc, cubrmc, sqtiny, outch)

Arguments

Type	Intent		Name
real(kind=wp),	intent(out)	::	round_off
real(kind=wp),	intent(out)	::	sqrrmc
real(kind=wp),	intent(out)	::	cubrmc
real(kind=wp),	intent(out)	::	sqtiny
integer,	intent(out)	::	outch

private subroutine method_const(rk_method, a, b, c, bhat, r, e, ptr, no_of_stages, intrp_degree, intrp_able, intrp_needs_stages, cost, safety, expon, stability_radius, tan_angle, rs, rs1, rs2, rs3, rs4, order, last_stage, max_stiff_iters, no_of_ge_steps, fsal, cdiff)

Arguments

Type	Intent		Name
integer,	intent(in)	::	rk_method
real(kind=wp),	intent(out)	::	a(13,13)
real(kind=wp),	intent(out)	::	b(13)
real(kind=wp),	intent(out)	::	c(13)
real(kind=wp),	intent(out)	::	bhat(13)
real(kind=wp),	intent(out)	::	r(11,6)
real(kind=wp),	intent(out)	::	e(7)
integer,	intent(out)	::	ptr(13)
integer,	intent(out)	::	no_of_stages
integer,	intent(out)	::	intrp_degree
logical,	intent(out)	::	intrp_able
logical,	intent(out)	::	intrp_needs_stages
real(kind=wp),	intent(out)	::	cost
real(kind=wp),	intent(out)	::	safety
real(kind=wp),	intent(out)	::	expon
real(kind=wp),	intent(out)	::	stability_radius
real(kind=wp),	intent(out)	::	tan_angle
real(kind=wp),	intent(out)	::	rs
real(kind=wp),	intent(out)	::	rs1
real(kind=wp),	intent(out)	::	rs2
real(kind=wp),	intent(out)	::	rs3
real(kind=wp),	intent(out)	::	rs4
integer,	intent(out)	::	order
integer,	intent(out)	::	last_stage
integer,	intent(out)	::	max_stiff_iters
integer,	intent(out)	::	no_of_ge_steps
logical,	intent(out)	::	fsal
real(kind=wp),	intent(out)	::	cdiff

private subroutine setup_r1(comm, t_start, y_start, t_end, tolerance, thresholds, method, task, error_assess, h_start, message)

Arguments

Type	Intent	Optional	Attributes		Name
type(rk_comm_real_1d)				::	comm
real(kind=wp),	intent(in)			::	t_start
real(kind=wp),	intent(in),		dimension(:)	::	y_start
real(kind=wp),	intent(in)			::	t_end
real(kind=wp),	intent(in)			::	tolerance
real(kind=wp),	intent(in),		dimension(:)	::	thresholds
character(len=*),	intent(in),	optional		::	method
character(len=*),	intent(in),	optional		::	task
logical,	intent(in),	optional		::	error_assess
real(kind=wp),	intent(in),	optional		::	h_start
logical,	intent(in),	optional		::	message

private subroutine collect_garbage_r1(comm)

Arguments

Type	Intent	Optional	Attributes		Name
type(rk_comm_real_1d)				::	comm

private recursive subroutine range_integrate_r1(comm, f, t_want, t_got, y_got, yderiv_got, flag)

Arguments

Type

Intent

Optional

Attributes

Name

type(rk_comm_real_1d),

intent(inout)

comm

public function f(t, y)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	t
real(kind=wp),	intent(in),		dimension(:)	::	y

Return Value real(kind=wp), dimension(size(y,1))

real(kind=wp),

intent(in)

t_want

real(kind=wp),

intent(out)

t_got

real(kind=wp),

intent(out),

dimension(:)

y_got

real(kind=wp),

intent(out),

dimension(:)

yderiv_got

integer,

intent(out),

optional

flag

private recursive subroutine step_integrate_r1(comm, f, t_now, y_now, yderiv_now, flag)

Arguments

Type

Intent

Optional

Attributes

Name

type(rk_comm_real_1d),

intent(inout)

comm

public function f(t, y)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	t
real(kind=wp),	intent(in),		dimension(:)	::	y

Return Value real(kind=wp), dimension(size(y,1))

real(kind=wp),

intent(out)

t_now

real(kind=wp),

intent(out),

dimension(:)

y_now

real(kind=wp),

intent(out),

dimension(:)

yderiv_now

integer,

intent(out),

optional

flag

private subroutine truerr_r1(comm, f, ier)

Arguments

Type

Intent

Optional

Attributes

Name

type(rk_comm_real_1d),

intent(inout)

comm

public function f(t, y)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	t
real(kind=wp),	intent(in),		dimension(:)	::	y

Return Value real(kind=wp), dimension(size(y,1))

integer,

intent(inout)

ier

private subroutine step_r1(comm, f, tnow, y, yp, stages, tol, htry, y_new, errest, err, hmin, phase_2)

Arguments

Type

Intent

Optional

Attributes

Name

type(rk_comm_real_1d),

intent(inout),

target

comm

public function f(t, y)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	t
real(kind=wp),	intent(in),		dimension(:)	::	y

Return Value real(kind=wp), dimension(size(y,1))

real(kind=wp),

intent(in)

tnow

real(kind=wp),

intent(in),

dimension(:)

real(kind=wp),

intent(in),

dimension(:)

real(kind=wp),

intent(out),

dimension(:,:)

stages

real(kind=wp),

intent(in)

tol

real(kind=wp),

intent(inout)

htry

real(kind=wp),

intent(out),

dimension(:)

y_new

real(kind=wp),

intent(out),

dimension(:)

errest

real(kind=wp),

intent(out)

err

real(kind=wp),

intent(in),

optional

hmin

logical,

intent(inout),

optional

phase_2

private subroutine stiff_r1(comm, f, toomch, sure_stiff)

Arguments

Type

Intent

Optional

Attributes

Name

type(rk_comm_real_1d),

intent(inout),

target

comm

public function f(t, y)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	t
real(kind=wp),	intent(in),		dimension(:)	::	y

Return Value real(kind=wp), dimension(size(y,1))

logical,

intent(in)

toomch

logical,

intent(out)

sure_stiff

private subroutine statistics_r1(comm, total_f_calls, step_cost, waste, num_succ_steps, h_next, y_maxvals)

Arguments

Type	Intent	Optional	Attributes		Name
type(rk_comm_real_1d),	intent(inout)			::	comm
integer,	intent(out),	optional		::	total_f_calls
integer,	intent(out),	optional		::	step_cost
real(kind=wp),	intent(out),	optional		::	waste
integer,	intent(out),	optional		::	num_succ_steps
real(kind=wp),	intent(out),	optional		::	h_next
real(kind=wp),	intent(out),	optional	dimension(:)	::	y_maxvals

private subroutine global_error_r1(comm, rms_error, max_error, t_max_error)

Arguments

Type	Intent	Optional	Attributes		Name
type(rk_comm_real_1d),	intent(inout)			::	comm
real(kind=wp),	intent(out),	optional	dimension(:)	::	rms_error
real(kind=wp),	intent(out),	optional		::	max_error
real(kind=wp),	intent(out),	optional		::	t_max_error

private subroutine reset_t_end_r1(comm, t_end_new)

Arguments

Type	Intent	Optional	Attributes		Name
type(rk_comm_real_1d),	intent(inout)			::	comm
real(kind=wp),	intent(in)			::	t_end_new

private subroutine interpolate_r1(comm, f, t_want, y_want, yderiv_want)

Arguments

Type

Intent

Optional

Attributes

Name

type(rk_comm_real_1d),

intent(inout),

target

comm

public function f(t, y)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	t
real(kind=wp),	intent(in),		dimension(:)	::	y

Return Value real(kind=wp), dimension(size(y,1))

real(kind=wp),

intent(in)

t_want

real(kind=wp),

intent(out),

optional

dimension(:)

y_want

real(kind=wp),

intent(out),

optional

dimension(:)

yderiv_want

private subroutine rkmsg_r1(ier, srname, nrec, comm, flag)

Arguments

Type	Intent	Optional		Name
integer,	intent(in)		::	ier
character(len=*),	intent(in)		::	srname
integer,	intent(in)		::	nrec
type(rk_comm_real_1d),	intent(inout)		::	comm
integer,	intent(out),	optional	::	flag

private subroutine set_saved_state_r1(srname, state, comm)

Arguments

Type	Intent		Name
character(len=*),	intent(in)	::	srname
integer,	intent(in)	::	state
type(rk_comm_real_1d),	intent(inout)	::	comm

private subroutine set_stop_on_fatal_r1(comm, action)

Arguments

Type	Intent	Optional	Attributes		Name
type(rk_comm_real_1d),	intent(inout)			::	comm
logical,	intent(in)			::	action

rksuite_90 Module

Contents

Uses

Used by

Contents

Interfaces

public interface setup

private subroutine setup_r1(comm, t_start, y_start, t_end, tolerance, thresholds, method, task, error_assess, h_start, message)

Arguments

public interface range_integrate

private recursive subroutine range_integrate_r1(comm, f, t_want, t_got, y_got, yderiv_got, flag)

Arguments

public function f(t, y)

Arguments

Return Value real(kind=wp), dimension(size(y,1))

public interface step_integrate

private recursive subroutine step_integrate_r1(comm, f, t_now, y_now, yderiv_now, flag)

Arguments

public function f(t, y)

Arguments

Return Value real(kind=wp), dimension(size(y,1))

public interface statistics

private subroutine statistics_r1(comm, total_f_calls, step_cost, waste, num_succ_steps, h_next, y_maxvals)

Arguments

public interface global_error

private subroutine global_error_r1(comm, rms_error, max_error, t_max_error)

Arguments

public interface reset_t_end

private subroutine reset_t_end_r1(comm, t_end_new)

Arguments

public interface interpolate

private subroutine interpolate_r1(comm, f, t_want, y_want, yderiv_want)

Arguments

public function f(t, y)

Arguments

Return Value real(kind=wp), dimension(size(y,1))

public interface set_stop_on_fatal

private subroutine set_stop_on_fatal_r1(comm, action)

Arguments

public interface get_saved_fatal

private function get_saved_fatal_r1(comm)

Arguments

Return Value logical

public interface collect_garbage

private subroutine collect_garbage_r1(comm)

Arguments

Derived Types

type, public :: rk_comm_real_1d

Components

Functions

private function get_saved_state_r1(srname, save_states)

Arguments

Return Value integer

private function get_saved_fatal_r1(comm)

Arguments

Return Value logical

private function get_stop_on_fatal_r1(comm)

Arguments

Return Value logical

Subroutines

private subroutine machine_const(round_off, sqrrmc, cubrmc, sqtiny, outch)

Arguments

private subroutine method_const(rk_method, a, b, c, bhat, r, e, ptr, no_of_stages, intrp_degree, intrp_able, intrp_needs_stages, cost, safety, expon, stability_radius, tan_angle, rs, rs1, rs2, rs3, rs4, order, last_stage, max_stiff_iters, no_of_ge_steps, fsal, cdiff)

Arguments

private subroutine setup_r1(comm, t_start, y_start, t_end, tolerance, thresholds, method, task, error_assess, h_start, message)

Arguments

private subroutine collect_garbage_r1(comm)

Arguments

private recursive subroutine range_integrate_r1(comm, f, t_want, t_got, y_got, yderiv_got, flag)

Arguments

public function f(t, y)

Arguments

Return Value real(kind=wp), dimension(size(y,1))

private recursive subroutine step_integrate_r1(comm, f, t_now, y_now, yderiv_now, flag)

Arguments

public function f(t, y)

Arguments

Return Value real(kind=wp), dimension(size(y,1))

private subroutine truerr_r1(comm, f, ier)

Arguments