steepest_descent_cpu Module Reference

CPU backend for the steepest-descent optimizer kernels. More...

Functions/Subroutines
subroutine, public	sd_direction_cpu (s, x, xmin, xmax, n)
	Bound-projected steepest-descent direction on CPU (Eq. D22).
subroutine, public	sd_update_move_limits_cpu (delta, x, x1, x2, dec, inc, dmin, dmax, n)
	Adapt the move limits on CPU (Eq. D23).
subroutine, public	sd_update_design_cpu (x_new, x, s, delta, psi, smax, xmin, xmax, n)
	Move-limited, box-constrained design update on CPU (Eq. D24).

Detailed Description

Elementwise kernels of the steepest descent method with move limits, Appendix D of da Silva, Aage, Beck & Sigmund (2021), Eqs. D22-D24. The device backends in bcknd/device implement the same formulas.

Function/Subroutine Documentation

sd_direction_cpu()

subroutine, public steepest_descent_cpu::sd_direction_cpu	(	real(kind=rp), dimension(n), intent(inout)	s,
		real(kind=rp), dimension(n), intent(in)	x,
		real(kind=rp), intent(in)	xmin,
		real(kind=rp), intent(in)	xmax,
		integer, intent(in)	n
	)

On entry s holds the gradient G. On exit it holds S = -G, with every component that points out of the box at an active bound set to zero.

Parameters

[in,out]	s	Gradient on entry, projected direction on exit.
[in]	x	Design variables.
[in]	xmin	Lower bound of the design variables.
[in]	xmax	Upper bound of the design variables.
[in]	n	Number of design variables.

Definition at line 58 of file steepest_descent_cpu.f90.

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sd_update_design_cpu()

subroutine, public steepest_descent_cpu::sd_update_design_cpu	(	real(kind=rp), dimension(n), intent(out)	x_new,
		real(kind=rp), dimension(n), intent(in)	x,
		real(kind=rp), dimension(n), intent(in)	s,
		real(kind=rp), dimension(n), intent(in)	delta,
		real(kind=rp), intent(in)	psi,
		real(kind=rp), intent(in)	smax,
		real(kind=rp), intent(in)	xmin,
		real(kind=rp), intent(in)	xmax,
		integer, intent(in)	n
	)

Computes x_new = min(xmax, max(xmin, min(x + delta, max(x - delta, x + psi * (s / smax))))), i.e. the move limit first and the box second. This equals Eq. D24 whenever x lies in [xmin, xmax], and stays well defined for infeasible x.

Parameters

[out]	x_new	Updated design variables.
[in]	x	Current design variables.
[in]	s	Bound-projected steepest-descent direction.
[in]	delta	Move limits.
[in]	psi	Step length.
[in]	smax	Global maximum of the absolute value of s.
[in]	xmin	Lower bound of the design variables.
[in]	xmax	Upper bound of the design variables.
[in]	n	Number of design variables.

Definition at line 124 of file steepest_descent_cpu.f90.

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sd_update_move_limits_cpu()

subroutine, public steepest_descent_cpu::sd_update_move_limits_cpu	(	real(kind=rp), dimension(n), intent(inout)	delta,
		real(kind=rp), dimension(n), intent(in)	x,
		real(kind=rp), dimension(n), intent(in)	x1,
		real(kind=rp), dimension(n), intent(in)	x2,
		real(kind=rp), intent(in)	dec,
		real(kind=rp), intent(in)	inc,
		real(kind=rp), intent(in)	dmin,
		real(kind=rp), intent(in)	dmax,
		integer, intent(in)	n
	)

The move limit of a variable shrinks when its last two changes have opposite signs, grows when they have the same sign, and is then clamped to [dmin, dmax].

Parameters

[in,out]	delta	Move limits.
[in]	x	Design variables at the current iteration.
[in]	x1	Design variables one iteration back.
[in]	x2	Design variables two iterations back.
[in]	dec	Factor applied on oscillation.
[in]	inc	Factor applied on monotone progress.
[in]	dmin	Smallest allowed move limit.
[in]	dmax	Largest allowed move limit.
[in]	n	Number of design variables.

Definition at line 88 of file steepest_descent_cpu.f90.

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