optimize – TFana

public interface bisect

Find root of a function in an interval using bisection.

Parameters:

f : function to find root of
a, b : interval to search for root
xtol : absolute tolerance, optional, default 2e-12
rtol : relative tolerance, optional, default 1e-15
maxiter : maximum number of iterations, optional, default 100

Returns:

x : root of f in [a, b]
info : solver_info_t structure, optional

The function f must be continuous, and f(a) and f(b) must have opposite signs.

If the solver converges, info%converged is true and info%iterations is the number of iterations required. If the solver does not converge, info%converged is false and info%iterations is the maximum number of iterations.

The convergence criterion is abs(x - xa) < xtol + rtol*abs(x) where xa is the left endpoint of the current interval.

private function bisect_real64(f, a, b, xtol, rtol, maxiter, info) result(x)

Impementation of bisect for real64

Arguments

Type	Intent	Optional		Name
procedure(func64)			::	f	function to find root of
real(kind=rkind),	intent(in)		::	a	interval to search for root
real(kind=rkind),	intent(in)		::	b	interval to search for root
real(kind=rkind),	intent(in),	optional	::	xtol	absolute tolerance
real(kind=rkind),	intent(in),	optional	::	rtol	relative tolerance
integer,	intent(in),	optional	::	maxiter	maximum number of iterations
type(solver_info_t),	intent(out),	optional	::	info	solver info

Return Value real(kind=rkind)

private function bisect_real32(f, a, b, xtol, rtol, maxiter, info) result(x)

Impementation of bisect for real32

Arguments

Type	Intent	Optional		Name
procedure(func32)			::	f	function to find root of
real(kind=rkind),	intent(in)		::	a	interval to search for root
real(kind=rkind),	intent(in)		::	b	interval to search for root
real(kind=rkind),	intent(in),	optional	::	xtol	absolute tolerance
real(kind=rkind),	intent(in),	optional	::	rtol	relative tolerance
integer,	intent(in),	optional	::	maxiter	maximum number of iterations
type(solver_info_t),	intent(out),	optional	::	info	solver info

Return Value real(kind=rkind)

public interface newton

Find root of a function using Newton’s or secant method.

Parameters:

f : function to find root of
x0 : initial estimate of root
fprime: derivative of f, optional
xtol : absolute tolerance, optional, default 2e-12
rtol : relative tolerance, optional, default 1e-15
maxiter : maximum number of iterations, optional, default 100

Returns:

x : root of f in [a, b]
info : solver_info_t structure, optional

The function f must be continuous, x0 should be close enough to the root.

If the solver converges, info%converged is true and info%iterations is the number of iterations required. If the solver does not converge, info%converged is false and info%iterations is the maximum number of iterations.

The convergence criterion is abs(x - xa) < xtol + rtol*abs(x) where xa is the left endpoint of the current interval.

private function newton_real64(f, x0, fprime, xtol, rtol, maxiter, info) result(x)

Impementation of bisect for real64

Arguments

Type	Intent	Optional		Name
procedure(func64)			::	f	function to find root of
real(kind=rkind),	intent(in)		::	x0	initial estimate of root
procedure(func64),		optional	::	fprime	function to find root of
real(kind=rkind),	intent(in),	optional	::	xtol	absolute tolerance
real(kind=rkind),	intent(in),	optional	::	rtol	relative tolerance
integer,	intent(in),	optional	::	maxiter	maximum number of iterations
type(solver_info_t),	intent(out),	optional	::	info	solver info

Return Value real(kind=rkind)

public interface root_scalar

Find root of a function using given method

Parameters:

f : function to find root of
x0 : initial estimate of root, optional
fprime: derivative of f, optional
xtol : absolute tolerance, optional, default 2e-12
rtol : relative tolerance, optional, default 1e-15
maxiter : maximum number of iterations, optional, default 100
method : method to use, optional, default ‘bisect’

Returns:

x : root of f in [a, b], or close to x0
info : solver_info_t structure, optional

The function f must be continuous, x0 should be close enough to the root.

If the solver converges, info%converged is true and info%iterations is the number of iterations required. If the solver does not converge, info%converged is false and info%iterations is the maximum number of iterations.

The convergence criterion is abs(x - xa) < xtol + rtol*abs(x) where xa is the left endpoint of the current interval.

private function root_scalar_real64(f, x0, a, b, fprime, xtol, rtol, maxiter, method, info) result(x)

Find root of a function using given method

Arguments

Type	Intent	Optional		Name
procedure(func64)			::	f	function to find root of
real(kind=rkind),	intent(in),	optional	::	x0	initial estimate of root
real(kind=rkind),	intent(in),	optional	::	a	interval to search for root
real(kind=rkind),	intent(in),	optional	::	b	interval to search for root
procedure(func64),		optional	::	fprime	function to find root of
real(kind=rkind),	intent(in),	optional	::	xtol	absolute tolerance
real(kind=rkind),	intent(in),	optional	::	rtol	relative tolerance
integer,	intent(in),	optional	::	maxiter	maximum number of iterations
character(len=*),	intent(in),	optional	::	method	method to use
type(solver_info_t),	intent(out),	optional	::	info	solver info

optimize Module

Contents

Interfaces

Derived Types

Uses

Interfaces

public interface bisect

private function bisect_real64(f, a, b, xtol, rtol, maxiter, info) result(x)

Arguments

Return Value real(kind=rkind)

private function bisect_real32(f, a, b, xtol, rtol, maxiter, info) result(x)

Arguments

Return Value real(kind=rkind)

public interface newton

private function newton_real64(f, x0, fprime, xtol, rtol, maxiter, info) result(x)

Arguments

Return Value real(kind=rkind)

public interface root_scalar

private function root_scalar_real64(f, x0, a, b, fprime, xtol, rtol, maxiter, method, info) result(x)

Arguments

Return Value real(kind=rkind)

Derived Types

type, public :: solver_info_t

Components

Type	Visibility	Attributes		Name		Initial
logical,	public		::	converged	=	.false.	true if solver converged
integer,	public		::	iterations	=	0	number of iterations