roots Module Reference

root finding subroutines More...

Data Types
type	roots_typ
	basic type for root finding functions More...

Functions/Subroutines
pure subroutine, public	initroots (this, x1, x2, f1, f2, dxacc, maxiter)
character(len=64) function, public	geterrormessage (error)
subroutine	getroot_generic (this, Stepper, func, x1, x2, dxacc, maxiter, plist, xm)
subroutine, public	getroot_newton (funcd, x1, x2, root, error, plist, xm, iterations)
subroutine, public	getroot_regulafalsi (func, x1, x2, root, error, plist, xm, iterations)
subroutine, public	getroot_pegasus (func, x1, x2, root, error, plist, xm, iterations)
subroutine, public	getroot_king (func, x1, x2, root, error, plist, xm, iterations)
subroutine, public	getroot_andersonbjoerk (func, x1, x2, root, error, plist, xm, iterations)
subroutine, public	getroot_ridder (func, x1, x2, root, error, plist, xm, iterations)
subroutine, public	getroot_brentdekker (func, x1, x2, root, error, plist, xm, iterations)
subroutine, public	getroot_bisection (func, x1, x2, root, error, plist, xm, iterations)
pure subroutine	updatebounds_bisection (this)
pure subroutine	step_bisection (this)
pure subroutine	step_newton (this)
pure subroutine	step_regulafalsi (this)
pure subroutine	step_pegasus (this)
pure subroutine	step_king (this)
pure subroutine	step_andersonbjoerk (this)
pure subroutine	step_ridder (this)
pure subroutine	step_brentdekker (this)
pure subroutine	step_secantmethod (this)
pure subroutine	saveinversequadraticinterpolation (a, b, c, fa, fb, fc, db_numer, db_denom)
pure subroutine	step_arithmeticmean (this)
pure real function	arithmeticmean (a, b)
pure real function	linearinterpolation (x1, x2, f1, f2)
pure subroutine	testconvergence (this)

Variables
integer, parameter, public	default_max_iterations = 1000
real, parameter, public	default_accuracy = 4*EPSILON(DEFAULT_ACCURACY)
character(len=64), dimension(0:4), parameter	error_message = (/ "unknown error ", "root not bracketed ", "iteration exceeds maximum ", "requested accuracy smaller than machine precission ", "upper limit for iterations should be larger than 1 " /)

Detailed Description

root finding subroutines

Author

Tobias Illenseer

1. Newton's method combined with bisection, for ill-posed problems
2. Regula falsi
3. Bisection
4. Pegasus
5. King
6. Anderson Bjoerk
7. Ridder
8. Brent Dekker (default)

The algorithms can be found in standard textbooks on numerical analysis. See e. g. [press2007] and [engeln2011] and references therein.

Function/Subroutine Documentation

arithmeticmean()

pure real function roots::arithmeticmean ( real, intent(in)  a, real, intent(in)  b  )

private

Definition at line 887 of file roots.f90.

geterrormessage()

character(len=64) function, public roots::geterrormessage

(

integer, intent(in)

error

)

Definition at line 160 of file roots.f90.

getroot_andersonbjoerk()

subroutine, public roots::getroot_andersonbjoerk	(		func,
		real, intent(in)	x1,
		real, intent(in)	x2,
		real, intent(out)	root,
		integer, intent(out)	error,
		real, dimension(:), intent(in), optional	plist,
		real, intent(in), optional	xm,
		integer, intent(out), optional	iterations
	)

Definition at line 417 of file roots.f90.

getroot_bisection()

subroutine, public roots::getroot_bisection	(		func,
		real, intent(in)	x1,
		real, intent(in)	x2,
		real, intent(out)	root,
		integer, intent(out)	error,
		real, dimension(:), intent(in), optional	plist,
		real, intent(in), optional	xm,
		integer, intent(out), optional	iterations
	)

Definition at line 519 of file roots.f90.

getroot_brentdekker()

subroutine, public roots::getroot_brentdekker	(		func,
		real, intent(in)	x1,
		real, intent(in)	x2,
		real, intent(out)	root,
		integer, intent(out)	error,
		real, dimension(:), intent(in), optional	plist,
		real, intent(in), optional	xm,
		integer, intent(out), optional	iterations
	)

Definition at line 485 of file roots.f90.

getroot_generic()

subroutine roots::getroot_generic ( type(roots_typ), intent(inout)  this,   Stepper,   func, real, intent(in)  x1, real, intent(in)  x2, real, intent(in), optional  dxacc, integer, intent(in), optional  maxiter, real, dimension(:), intent(in), optional  plist, real, intent(in), optional  xm  )

private

Definition at line 178 of file roots.f90.

getroot_king()

subroutine, public roots::getroot_king	(		func,
		real, intent(in)	x1,
		real, intent(in)	x2,
		real, intent(out)	root,
		integer, intent(out)	error,
		real, dimension(:), intent(in), optional	plist,
		real, intent(in), optional	xm,
		integer, intent(out), optional	iterations
	)

Definition at line 383 of file roots.f90.

getroot_newton()

subroutine, public roots::getroot_newton	(		funcd,
		real, intent(in)	x1,
		real, intent(in)	x2,
		real, intent(out)	root,
		integer, intent(out)	error,
		real, dimension(:), intent(in), optional	plist,
		real, intent(in), optional	xm,
		integer, intent(out), optional	iterations
	)

Definition at line 247 of file roots.f90.

getroot_pegasus()

subroutine, public roots::getroot_pegasus	(		func,
		real, intent(in)	x1,
		real, intent(in)	x2,
		real, intent(out)	root,
		integer, intent(out)	error,
		real, dimension(:), intent(in), optional	plist,
		real, intent(in), optional	xm,
		integer, intent(out), optional	iterations
	)

Definition at line 349 of file roots.f90.

getroot_regulafalsi()

subroutine, public roots::getroot_regulafalsi	(		func,
		real, intent(in)	x1,
		real, intent(in)	x2,
		real, intent(out)	root,
		integer, intent(out)	error,
		real, dimension(:), intent(in), optional	plist,
		real, intent(in), optional	xm,
		integer, intent(out), optional	iterations
	)

Definition at line 315 of file roots.f90.

getroot_ridder()

subroutine, public roots::getroot_ridder	(		func,
		real, intent(in)	x1,
		real, intent(in)	x2,
		real, intent(out)	root,
		integer, intent(out)	error,
		real, dimension(:), intent(in), optional	plist,
		real, intent(in), optional	xm,
		integer, intent(out), optional	iterations
	)

Definition at line 451 of file roots.f90.

initroots()

pure subroutine, public roots::initroots	(	type(roots_typ), intent(inout)	this,
		real, intent(in)	x1,
		real, intent(in)	x2,
		real, intent(in)	f1,
		real, intent(in)	f2,
		real, intent(in), optional	dxacc,
		integer, intent(in), optional	maxiter
	)

Definition at line 98 of file roots.f90.

linearinterpolation()

pure real function roots::linearinterpolation ( real, intent(in)  x1, real, intent(in)  x2, real, intent(in)  f1, real, intent(in)  f2  )

private

Definition at line 897 of file roots.f90.

saveinversequadraticinterpolation()

pure subroutine roots::saveinversequadraticinterpolation ( real, intent(in)  a, real, intent(in)  b, real, intent(in)  c, real, intent(in)  fa, real, intent(in)  fb, real, intent(in)  fc, real, intent(out)  db_numer, real, intent(out)  db_denom  )

private

Definition at line 842 of file roots.f90.

step_andersonbjoerk()

pure subroutine roots::step_andersonbjoerk ( type(roots_typ), intent(inout)  this )

private

Definition at line 691 of file roots.f90.

step_arithmeticmean()

pure subroutine roots::step_arithmeticmean ( type(roots_typ), intent(inout)  this )

private

Definition at line 874 of file roots.f90.

step_bisection()

pure subroutine roots::step_bisection ( type(roots_typ), intent(inout)  this )

private

Definition at line 568 of file roots.f90.

step_brentdekker()

pure subroutine roots::step_brentdekker ( type(roots_typ), intent(inout)  this )

private

Definition at line 748 of file roots.f90.

step_king()

pure subroutine roots::step_king ( type(roots_typ), intent(inout)  this )

private

Definition at line 643 of file roots.f90.

step_newton()

pure subroutine roots::step_newton ( type(roots_typ), intent(inout)  this )

private

Definition at line 578 of file roots.f90.

step_pegasus()

pure subroutine roots::step_pegasus ( type(roots_typ), intent(inout)  this )

private

Definition at line 618 of file roots.f90.

step_regulafalsi()

pure subroutine roots::step_regulafalsi ( type(roots_typ), intent(inout)  this )

private

Definition at line 604 of file roots.f90.

step_ridder()

pure subroutine roots::step_ridder ( type(roots_typ), intent(inout)  this )

private

Definition at line 717 of file roots.f90.

step_secantmethod()

pure subroutine roots::step_secantmethod ( type(roots_typ), intent(inout)  this )

private

Definition at line 811 of file roots.f90.

testconvergence()

pure subroutine roots::testconvergence ( type(roots_typ), intent(inout)  this )

private

Definition at line 907 of file roots.f90.

updatebounds_bisection()

pure subroutine roots::updatebounds_bisection ( type(roots_typ), intent(inout)  this )

private

Definition at line 550 of file roots.f90.

Variable Documentation

default_accuracy

real, parameter, public roots::default_accuracy = 4*EPSILON(DEFAULT_ACCURACY)

Definition at line 67 of file roots.f90.

default_max_iterations

integer, parameter, public roots::default_max_iterations = 1000

Definition at line 66 of file roots.f90.

error_message

character(len=64), dimension(0:4), parameter roots::error_message = (/ "unknown error ", "root not bracketed ", "iteration exceeds maximum ", "requested accuracy smaller than machine precission ", "upper limit for iterations should be larger than 1 " /)

private

Definition at line 68 of file roots.f90.