Minimization data derived type. More...

Data Types
type	minim_type

Functions/Subroutines
subroutine	minim_compute (minim, mpl, rng)
	Minimize ensuring bounds constraints. More...

subroutine	minim_cost (minim, mpl, x, f)
	Compute cost function. More...

subroutine	minim_cost_fit_diag (minim, mpl, x, f)
	Diagnosic fit function cost. More...

subroutine	minim_cost_fit_lct (minim, mpl, x, f)
	LCT fit function cost. More...

subroutine	minim_hooke (minim, mpl, guess)
	Seeks a minimizer of a scalar function of several variables. More...

subroutine	minim_best_nearby (minim, mpl, delta, point, prevbest, funevals, minf)
	Looks for a better nearby point, one coordinate at a time. More...

subroutine	minim_praxis (minim, mpl, rng, guess)
	Seeks a minimizer of a scalar function of several variables. More...

subroutine	minim_flin (minim, mpl, jsearch, l, x, nf, v, q0, q1, qd0, qd1, qa, qb, qc, flin)
	Seeks a minimizer of a scalar function of one variable. More...

subroutine	minim_quad (minim, mpl, t, h, v, q0, q1, nl, nf, dmin, ldt, fx, qf1, qa, qb, qc, qd0, qd1)
	Minimize the scalar function F along a particular curve. More...

subroutine	minim_minny (minim, mpl, jsearch, nits, d2, x1, f1, fk, x, t, h, v, q0, q1, nl, nf, dmin, ldt, fx, qa, qb, qc, qd0, qd1)
	Minimization of a scalar function of N variables along a line. More...

subroutine	minfit (mpl, n, tol, a, q)
	Singular value decomposition of an N by N array. More...

subroutine	swap (n, a1, a2)
	Swaps the entries of two vectors More...

subroutine	svsort (n, d, v)
	Descending sorts singular values D and adjusts V. More...

subroutine	minim_vt_dir (minim, x)
	Direct variable transform. More...

subroutine	minim_vt_inv (minim, mpl, x)
	Inverse variable transform. More...

Variables
real(kind_real), parameter	machep = epsilon(1.0_kind_real)

real(kind_real), parameter	small = machep**2

real(kind_real), parameter	vsmall = small**2

real(kind_real), parameter	large = 1.0/small

real(kind_real), parameter	vlarge = 1.0/vsmall

real(kind_real), parameter	m2 = sqrt(machep)

real(kind_real), parameter	m4 = sqrt(m2)

Detailed Description

Minimization data derived type.

Function/Subroutine Documentation

◆ minfit()

subroutine type_minim::minfit	(	type(mpl_type), intent(inout)	mpl,
		integer, intent(in)	n,
		real(kind_real), intent(in)	tol,
		real(kind_real), dimension(n,n), intent(inout)	a,
		real(kind_real), dimension(n), intent(inout)	q
	)

private

Singular value decomposition of an N by N array.

Parameters

[in,out]	mpl	MPI data
[in]	n	Order of the matrix
[in]	tol	Tolerance
[in,out]	a	Matrix
[in,out]	q	Singular values

Definition at line 1016 of file type_minim.F90.

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◆ minim_best_nearby()

subroutine type_minim::minim_best_nearby	(	class(minim_type), intent(inout)	minim,
		type(mpl_type), intent(inout)	mpl,
		real(kind_real), dimension(minim%nx), intent(inout)	delta,
		real(kind_real), dimension(minim%nx), intent(inout)	point,
		real(kind_real), intent(in)	prevbest,
		integer, intent(inout)	funevals,
		real(kind_real), intent(out)	minf
	)

private

Looks for a better nearby point, one coordinate at a time.

Parameters

[in,out]	minim	Minimization data
[in,out]	mpl	MPI data
[in,out]	delta	Step
[in]	prevbest	Best existing cost
[in,out]	funevals	Number of evaluations
[out]	minf	Minimum cost

Definition at line 439 of file type_minim.F90.

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◆ minim_compute()

subroutine type_minim::minim_compute	(	class(minim_type), intent(inout)	minim,
		type(mpl_type), intent(inout)	mpl,
		type(rng_type), intent(inout)	rng
	)

private

Minimize ensuring bounds constraints.

Parameters

[in,out]	minim	Minimization data
[in,out]	mpl	MPI data
[in,out]	rng	Random number generator

Definition at line 101 of file type_minim.F90.

◆ minim_cost()

subroutine type_minim::minim_cost	(	class(minim_type), intent(in)	minim,
		type(mpl_type), intent(inout)	mpl,
		real(kind_real), dimension(minim%nx), intent(in)	x,
		real(kind_real), intent(out)	f
	)

private

Compute cost function.

Parameters

[in]	minim	Minimization data
[in,out]	mpl	MPI data
[in]	x	Control vector
[out]	f	Cost function value

Definition at line 147 of file type_minim.F90.

◆ minim_cost_fit_diag()

subroutine type_minim::minim_cost_fit_diag	(	class(minim_type), intent(in)	minim,
		type(mpl_type), intent(inout)	mpl,
		real(kind_real), dimension(minim%nx), intent(in)	x,
		real(kind_real), intent(out)	f
	)

private

Diagnosic fit function cost.

Parameters

[in]	minim	Minimization data
[in,out]	mpl	MPI data
[in]	x	Control vector
[out]	f	Cost function value

Definition at line 175 of file type_minim.F90.

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◆ minim_cost_fit_lct()

subroutine type_minim::minim_cost_fit_lct	(	class(minim_type), intent(in)	minim,
		type(mpl_type), intent(inout)	mpl,
		real(kind_real), dimension(minim%nx), intent(in)	x,
		real(kind_real), intent(out)	f
	)

private

LCT fit function cost.

Parameters

[in]	minim	Minimization data
[in,out]	mpl	MPI data
[in]	x	Control vector
[out]	f	Cost function value

Definition at line 292 of file type_minim.F90.

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◆ minim_flin()

subroutine type_minim::minim_flin	(	class(minim_type), intent(inout)	minim,
		type(mpl_type), intent(inout)	mpl,
		integer, intent(in)	jsearch,
		real(kind_real), intent(in)	l,
		real(kind_real), dimension(minim%nx), intent(in)	x,
		integer, intent(inout)	nf,
		real(kind_real), dimension(minim%nx,minim%nx), intent(in)	v,
		real(kind_real), dimension(minim%nx), intent(in)	q0,
		real(kind_real), dimension(minim%nx), intent(in)	q1,
		real(kind_real), intent(in)	qd0,
		real(kind_real), intent(in)	qd1,
		real(kind_real), intent(out)	qa,
		real(kind_real), intent(out)	qb,
		real(kind_real), intent(out)	qc,
		real(kind_real), intent(out)	flin
	)

private

Seeks a minimizer of a scalar function of one variable.

Parameters

[in,out]	minim	Minimization data
[in,out]	mpl	MPI data
[in]	jsearch	Kind of search
[in]	l	Particular point at which the function is to be evaluated
[in]	x	State
[in,out]	nf	Number of function evaluations
[in]	v	Search directions
[in]	q0	First auxiliary point
[in]	q1	Second auxiliary point
[in]	qd0	First auxiliary value
[in]	qd1	Second auxiliary value
[out]	qa	First combination coefficient
[out]	qb	Second combination coefficient
[out]	qc	Third combination coefficient
[out]	flin	Value of the function at the minimizing point

Definition at line 742 of file type_minim.F90.

◆ minim_hooke()

subroutine type_minim::minim_hooke	(	class(minim_type), intent(inout)	minim,
		type(mpl_type), intent(inout)	mpl,
		real(kind_real), dimension(minim%nx), intent(in)	guess
	)

private

Seeks a minimizer of a scalar function of several variables.

Parameters

[in,out]	minim	Minimization data
[in,out]	mpl	MPI data

Definition at line 342 of file type_minim.F90.

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◆ minim_minny()

subroutine type_minim::minim_minny	(	class(minim_type), intent(inout)	minim,
		type(mpl_type), intent(inout)	mpl,
		integer, intent(in)	jsearch,
		integer, intent(in)	nits,
		real(kind_real), intent(inout)	d2,
		real(kind_real), intent(inout)	x1,
		real(kind_real), intent(inout)	f1,
		logical, intent(in)	fk,
		real(kind_real), dimension(minim%nx), intent(inout)	x,
		real(kind_real), intent(in)	t,
		real(kind_real), intent(in)	h,
		real(kind_real), dimension(minim%nx,minim%nx), intent(in)	v,
		real(kind_real), dimension(minim%nx), intent(in)	q0,
		real(kind_real), dimension(minim%nx), intent(in)	q1,
		integer, intent(inout)	nl,
		integer, intent(inout)	nf,
		real(kind_real), intent(in)	dmin,
		real(kind_real), intent(in)	ldt,
		real(kind_real), intent(inout)	fx,
		real(kind_real), intent(inout)	qa,
		real(kind_real), intent(inout)	qb,
		real(kind_real), intent(inout)	qc,
		real(kind_real), intent(in)	qd0,
		real(kind_real), intent(in)	qd1
	)

private

Minimization of a scalar function of N variables along a line.

Parameters

[in,out]	minim	Minimization data
[in,out]	mpl	MPI data
[in]	jsearch	Kind of search
[in]	nits	Maximum number of times the interval may be halved to retry the calculation
[in,out]	d2	Approximation to the second derivative of the function halved
[in,out]	x1	Estimate of the distance from x to the minimum along v(*,j)
[in,out]	f1	?
[in]	fk	If fk is .true., then on input f1 contains the value fline(x1)
[in,out]	x	State
[in]	t	?
[in]	h	?
[in]	v	Search directions
[in]	q0	First auxiliary point
[in]	q1	Second auxiliary point
[in,out]	nl	Number of linear searches
[in,out]	nf	Number of function evaluations
[in]	dmin	Smallest eigenvalue estimate
[in]	ldt	Step length
[in,out]	fx	Function value
[in,out]	qa	First combination coefficient
[in,out]	qb	Second combination coefficient
[in,out]	qc	Third combination coefficient
[in]	qd0	First auxiliary value
[in]	qd1	Second auxiliary value

Definition at line 857 of file type_minim.F90.

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◆ minim_praxis()

subroutine type_minim::minim_praxis	(	class(minim_type), intent(inout)	minim,
		type(mpl_type), intent(inout)	mpl,
		type(rng_type), intent(inout)	rng,
		real(kind_real), dimension(minim%nx), intent(in)	guess
	)

private

Seeks a minimizer of a scalar function of several variables.

Parameters

[in,out]	minim	Minimization data
[in,out]	mpl	MPI data
[in,out]	rng	Random number generator

Definition at line 492 of file type_minim.F90.

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◆ minim_quad()

subroutine type_minim::minim_quad	(	class(minim_type), intent(inout)	minim,
		type(mpl_type), intent(inout)	mpl,
		real(kind_real), intent(in)	t,
		real(kind_real), intent(in)	h,
		real(kind_real), dimension(minim%nx,minim%nx), intent(in)	v,
		real(kind_real), dimension(minim%nx), intent(inout)	q0,
		real(kind_real), dimension(minim%nx), intent(inout)	q1,
		integer, intent(inout)	nl,
		integer, intent(inout)	nf,
		real(kind_real), intent(in)	dmin,
		real(kind_real), intent(in)	ldt,
		real(kind_real), intent(inout)	fx,
		real(kind_real), intent(inout)	qf1,
		real(kind_real), intent(inout)	qa,
		real(kind_real), intent(inout)	qb,
		real(kind_real), intent(inout)	qc,
		real(kind_real), intent(inout)	qd0,
		real(kind_real), intent(inout)	qd1
	)

private

Minimize the scalar function F along a particular curve.

Parameters

[in,out]	minim	Minimization data
[in,out]	mpl	MPI data
[in]	t	?
[in]	h	?
[in]	v	Search directions
[in,out]	q0	First auxiliary point
[in,out]	q1	Second auxiliary point
[in,out]	nl	Number of linear searches
[in,out]	nf	Number of function evaluations
[in]	dmin	Smallest eigenvalue estimate
[in]	ldt	Step length
[in,out]	fx	Function value
[in,out]	qf1	?
[in,out]	qa	First combination coefficient
[in,out]	qb	Second combination coefficient
[in,out]	qc	Third combination coefficient
[in,out]	qd0	First auxiliary value
[in,out]	qd1	Second auxiliary value

Definition at line 790 of file type_minim.F90.

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◆ minim_vt_dir()

subroutine type_minim::minim_vt_dir	(	class(minim_type), intent(in)	minim,
		real(kind_real), dimension(minim%nx), intent(inout)	x
	)

private

Direct variable transform.

Parameters

[in]	minim	Minimization data
[in,out]	x	Vector

Definition at line 1278 of file type_minim.F90.

◆ minim_vt_inv()

subroutine type_minim::minim_vt_inv	(	class(minim_type), intent(in)	minim,
		type(mpl_type), intent(inout)	mpl,
		real(kind_real), dimension(minim%nx), intent(inout)	x
	)

private

Inverse variable transform.

Parameters

[in]	minim	Minimization data
[in,out]	mpl	MPI data
[in,out]	x	Vector

Definition at line 1295 of file type_minim.F90.

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◆ svsort()

subroutine type_minim::svsort	(	integer, intent(in)	n,
		real(kind_real), dimension(n), intent(inout)	d,
		real(kind_real), dimension(n,n), intent(inout)	v
	)

private

Descending sorts singular values D and adjusts V.

Parameters

[in]	n	Vector and array size
[in,out]	d	Vector to be sorted
[in,out]	v	Array to adjust as d is sorted

Definition at line 1244 of file type_minim.F90.

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◆ swap()

subroutine type_minim::swap	(	integer, intent(in)	n,
		real(kind_real), dimension(n), intent(inout)	a1,
		real(kind_real), dimension(n), intent(inout)	a2
	)

private

Swaps the entries of two vectors

Parameters

[in]	n	Vectors size
[in,out]	a1	First vector
[in,out]	a2	Second vector

Definition at line 1221 of file type_minim.F90.

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Variable Documentation

◆ large

real(kind_real), parameter type_minim::large = 1.0/small

Definition at line 87 of file type_minim.F90.

◆ m2

real(kind_real), parameter type_minim::m2 = sqrt(machep)

Definition at line 89 of file type_minim.F90.

◆ m4

real(kind_real), parameter type_minim::m4 = sqrt(m2)

Definition at line 90 of file type_minim.F90.

◆ machep

real(kind_real), parameter type_minim::machep = epsilon(1.0_kind_real)

Definition at line 84 of file type_minim.F90.

◆ small

real(kind_real), parameter type_minim::small = machep**2

Definition at line 85 of file type_minim.F90.

◆ vlarge

real(kind_real), parameter type_minim::vlarge = 1.0/vsmall

Definition at line 88 of file type_minim.F90.

◆ vsmall

real(kind_real), parameter type_minim::vsmall = small**2

Definition at line 86 of file type_minim.F90.

Data Types

Functions/Subroutines

Variables

Detailed Description

Function/Subroutine Documentation

◆ minfit()

◆ minim_best_nearby()

◆ minim_compute()

◆ minim_cost()

◆ minim_cost_fit_diag()

◆ minim_cost_fit_lct()

◆ minim_flin()

◆ minim_hooke()

◆ minim_minny()

◆ minim_praxis()

◆ minim_quad()

◆ minim_vt_dir()

◆ minim_vt_inv()

◆ svsort()

◆ swap()

Variable Documentation

◆ large

◆ m2

◆ m4

◆ machep

◆ small

◆ vlarge

◆ vsmall