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. [41] and [13] and references therein.

Function/Subroutine Documentation

arithmeticmean()

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

private

Definition at line 886 of file roots.f90.

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geterrormessage()

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

(

integer, intent(in)

error

)

Definition at line 159 of file roots.f90.

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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 416 of file roots.f90.

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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 518 of file roots.f90.

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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 484 of file roots.f90.

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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 177 of file roots.f90.

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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 382 of file roots.f90.

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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 246 of file roots.f90.

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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 348 of file roots.f90.

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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 314 of file roots.f90.

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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 450 of file roots.f90.

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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 97 of file roots.f90.

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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 896 of file roots.f90.

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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 841 of file roots.f90.

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step_andersonbjoerk()

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

private

Definition at line 690 of file roots.f90.

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step_arithmeticmean()

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

private

Definition at line 873 of file roots.f90.

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step_bisection()

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

private

Definition at line 567 of file roots.f90.

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step_brentdekker()

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

private

Definition at line 747 of file roots.f90.

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step_king()

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

private

Definition at line 642 of file roots.f90.

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step_newton()

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

private

Definition at line 577 of file roots.f90.

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step_pegasus()

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

private

Definition at line 617 of file roots.f90.

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step_regulafalsi()

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

private

Definition at line 603 of file roots.f90.

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step_ridder()

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

private

Definition at line 716 of file roots.f90.

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step_secantmethod()

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

private

Definition at line 810 of file roots.f90.

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testconvergence()

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

private

Definition at line 906 of file roots.f90.

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updatebounds_bisection()

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

private

Definition at line 549 of file roots.f90.

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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.