ddx_constants Module Reference

Run-time constants. More...

Data Types
type	ddx_constants_type
	Container for precomputed constants. More...
type	ddx_switching_type

Functions/Subroutines
subroutine	constants_init (params, constants, ddx_error)
	Compute all necessary constants. More...
subroutine	build_itrnl (constants, params, ddx_error)
	Build the transposed neighbor list. More...
subroutine	build_l (constants, params, ddx_error)
	Allocate and build the ddCOSMO sparse matrix, only if incore is set. More...
subroutine	build_b (constants, params, ddx_error)
	Allocate and build the HSP sparse matrix, only if incore is set. More...
subroutine	mkpmat (params, constants, isph, pmat)
	Computation of P_chi. More...
subroutine	constants_geometry_init (params, constants, ddx_error)
	Initialize geometry-related constants like list of neighbouring spheres. More...
subroutine	neighbor_list_init (params, constants, ddx_error)
	Build the neighbor list using a N^2 code. More...
subroutine	neighbor_list_init_fmm (params, constants, ddx_error)
	Build the neighbor list using a linear scaling code (only if FMMs are enabled) More...
real(dp) function	fsw (t, se, eta)
	Switching function. More...
real(dp) function	dfsw (t, se, eta)
	Derivative of a switching function. More...
real(dp) function	ratio_d (d, chi)
	Bounded evaluation of d/(1 - chi_j) with \( d = \prod_k (1 - \chi_k) \). More...
subroutine	mkprec (lmax, nbasis, nsph, ngrid, eps, ui, wgrid, vgrid, vgrid_nbasis, rx_prc, ddx_error)
	Compute preconditioner assemble the diagonal blocks of the reps matrix then invert them to build the preconditioner. More...
subroutine	tree_rib_build (nsph, csph, rsph, order, cluster, children, parent, cnode, rnode, snode, ddx_error)
	Build a recursive inertial binary tree. More...
subroutine	tree_rib_node_bisect (nsph, csph, n, order, div, ddx_error)
	Divide given cluster of spheres into two subclusters by inertial bisection. More...
subroutine	tree_get_farnear_work (n, children, cnode, rnode, lwork, iwork, jwork, work, nnfar, nfar, nnnear, nnear)
	Find near and far admissible pairs of tree nodes and store it in work array. More...
subroutine	tree_get_farnear (jwork, lwork, work, n, nnfar, nfar, sfar, far, nnnear, nnear, snear, near)
	Get near and far admissible pairs from work array of tree_get_farnear_work Works only for binary tree. More...
subroutine	constants_free (constants, ddx_error)
	Deallocate the constants. More...
subroutine	switching_init (params, constants, switching, ddx_error)
subroutine	switching_free (switching, ddx_error)
real(dp) function	compute_t (params, constants, isph, jsph, n)
real(dp) function	compute_chi (params, constants, isph, jsph, n)
subroutine	compute_d_and_f (params, constants, isph, n, d, f)
real(dp) function	compute_d (params, constants, isph, n)
real(dp) function	compute_f (params, constants, isph, n)
real(dp) function	compute_omega (params, constants, isph, jsph, n)
real(dp) function	compute_u (params, constants, isph, n)
subroutine	compute_grad_i_u_i (params, constants, isph, n, grad, dr)

Detailed Description

Run-time constants.

Function/Subroutine Documentation

constants_init()

subroutine ddx_constants::constants_init	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(out)	constants,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Compute all necessary constants.

Parameters

[in]	params	Object containing all inputs.
[out]	constants	Object containing all constants.
[in,out]	ddx_error	ddX error

Definition at line 259 of file ddx_constants.f90.

build_itrnl()

subroutine ddx_constants::build_itrnl	(	type(ddx_constants_type), intent(inout)	constants,
		type(ddx_params_type), intent(in)	params,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Build the transposed neighbor list.

Definition at line 579 of file ddx_constants.f90.

build_l()

subroutine ddx_constants::build_l	(	type(ddx_constants_type), intent(inout)	constants,
		type(ddx_params_type), intent(in)	params,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Allocate and build the ddCOSMO sparse matrix, only if incore is set.

Definition at line 604 of file ddx_constants.f90.

build_b()

subroutine ddx_constants::build_b	(	type(ddx_constants_type), intent(inout)	constants,
		type(ddx_params_type), intent(in)	params,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Allocate and build the HSP sparse matrix, only if incore is set.

Definition at line 721 of file ddx_constants.f90.

mkpmat()

subroutine ddx_constants::mkpmat	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		integer, intent(in)	isph,
		real(dp), dimension(constants % nbasis, constants % nbasis0), intent(inout)	pmat
	)

Computation of P_chi.

Definition at line 849 of file ddx_constants.f90.

constants_geometry_init()

subroutine ddx_constants::constants_geometry_init	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(inout)	constants,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Initialize geometry-related constants like list of neighbouring spheres.

This routine does not check ddx_error state of params or constants as it is intended for a low-level use.

Parameters

[in]	params	Object containing all inputs.
[in,out]	constants	Object containing all constants.
[in,out]	ddx_error	ddX error

Definition at line 885 of file ddx_constants.f90.

neighbor_list_init()

subroutine ddx_constants::neighbor_list_init	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(inout)	constants,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Build the neighbor list using a N^2 code.

Definition at line 1218 of file ddx_constants.f90.

neighbor_list_init_fmm()

subroutine ddx_constants::neighbor_list_init_fmm	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(inout)	constants,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Build the neighbor list using a linear scaling code (only if FMMs are enabled)

Definition at line 1303 of file ddx_constants.f90.

fsw()

real(dp) function ddx_constants::fsw	(	real(dp), intent(in)	t,
		real(dp), intent(in)	se,
		real(dp), intent(in)	eta
	)

Switching function.

This is an implementation of \( \chi(t) \) with a shift \( se \):

\[ \chi_\eta(t) = \left\{ \begin{array}{ll} 0, & \text{if} \quad x \geq 1 \\ p_\eta(x), & \text{if} \quad 1-\eta < x < 1 \\ 1, & \text{if} \quad x \leq 1-\eta \end{array} \right. \]

where \( x = t - \frac{1+se}{2} \eta \) is a shifted coordinate and

\[ p_\eta(x) = \frac{1}{\eta^5} (1-t)^3 (6t^2 + (15\eta-12)t + (10\eta^2 -15\eta+6)) \]

is a smoothing polynomial of the 5th degree. In the case shift \( se=1 \) the switch function \( \chi_\eta(t) \) is 1 for \( t \in [0,1] \), is 0 for \( t \in [1+\eta, \infty) \) and varies in \( [1, 1+\eta] \) which is an external shift. In the case shift \( se=-1 \) the switch function \( \chi_\eta(t) \) is 1 for \( t \in [0,1-\eta] \), is 0 for \( t \in [1, \infty) \) and varies in \( [1-\eta, 1] \) which is an internal shift. In the case shift \( se=0 \) the switch function \( \chi_\eta(t) \) is 1 for \( t \in [0,1-\eta/2] \), is 0 for \( t \in [1+\eta/2, \infty) \) and varies in \( [1-\eta/2, 1+\eta/2] \) which is a centered shift.

Parameters

[in]	t	real non-negative input value
[in]	se	shift
[in]	eta	regularization parameter \( \eta \)

Definition at line 1420 of file ddx_constants.f90.

dfsw()

real(dp) function ddx_constants::dfsw	(	real(dp), intent(in)	t,
		real(dp), intent(in)	se,
		real(dp), intent(in)	eta
	)

Derivative of a switching function.

This is an implementation of \( \chi'(t) \) with a shift \( se \):

\[ \chi_\eta'(t) = \left\{ \begin{array}{ll} 0, & \text{if} \quad x \geq 1 \\ p'_\eta(x), & \text{if} \quad 1-\eta < x < 1 \\ 0, & \text{if} \quad x \leq 1-\eta \end{array} \right. \]

where \( x = t - \frac{1+se}{2} \eta \) is a shifted coordinate and

\[ p'_\eta(x) = -\frac{30}{\eta^5} (1-t)^2 (t-1+\eta)^2 \]

is a derivative of the smoothing polynomial. In the case shift \( se=1 \) the derivative \( \chi_\eta'(t) \) is 0 for \( t \in [0,1] \cup [1+\eta, \infty) \) and varies in \( [1, 1+\eta] \) which is an external shift. In the case shift \( se=-1 \) the derivative \( \chi_\eta'(t) \) is 0 for \( t \in [0,1-\eta] \cup [1, \infty) \) and varies in \( [1-\eta, 1] \) which is an internal shift. In the case shift \( se=0 \) the derivative \( \chi_\eta'(t) \) is 0 for \( t \in [0,1-\eta/2] \cup [1+\eta/2, \infty) \) and varies in \( [1-\eta/2, 1+\eta/2] \) which is a centered shift.

Parameters

[in]	t	real non-negative input value
[in]	se	shift
[in]	eta	regularization parameter \( \eta \)

Definition at line 1475 of file ddx_constants.f90.

ratio_d()

real(dp) function ddx_constants::ratio_d	(	real(dp), intent(in)	d,
		real(dp), intent(in)	chi
	)

Bounded evaluation of d/(1 - chi_j) with \( d = \prod_k (1 - \chi_k) \).

The exact ratio is \( \prod_{k \neq j} (1 - \chi_k) \in [0, 1] \). Close to the edge of the switching region, \( \chi_j \) can round to one while dfsw is not zero, or d and \( \chi_j \) can be rounded differently, so that the plain division gives 0/0 or a huge value. The ratio is therefore clamped to [0, 1]. This is an approximation there, but its error is bounded by the vanishing factor dfsw that multiplies the ratio.

Definition at line 1506 of file ddx_constants.f90.

mkprec()

subroutine ddx_constants::mkprec	(	integer, intent(in)	lmax,
		integer, intent(in)	nbasis,
		integer, intent(in)	nsph,
		integer, intent(in)	ngrid,
		real(dp), intent(in)	eps,
		real(dp), dimension(ngrid, nsph), intent(in)	ui,
		real(dp), dimension(ngrid), intent(in)	wgrid,
		real(dp), dimension(vgrid_nbasis, ngrid), intent(in)	vgrid,
		integer, intent(in)	vgrid_nbasis,
		real(dp), dimension(nbasis, nbasis, nsph), intent(out)	rx_prc,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Compute preconditioner assemble the diagonal blocks of the reps matrix then invert them to build the preconditioner.

Definition at line 1522 of file ddx_constants.f90.

tree_rib_build()

subroutine ddx_constants::tree_rib_build	(	integer, intent(in)	nsph,
		real(dp), dimension(3, nsph), intent(in)	csph,
		real(dp), dimension(nsph), intent(in)	rsph,
		integer, dimension(nsph), intent(out)	order,
		integer, dimension(2, 2*nsph-1), intent(out)	cluster,
		integer, dimension(2, 2*nsph-1), intent(out)	children,
		integer, dimension(2*nsph-1), intent(out)	parent,
		real(dp), dimension(3, 2*nsph-1), intent(out)	cnode,
		real(dp), dimension(2*nsph-1), intent(out)	rnode,
		integer, dimension(nsph), intent(out)	snode,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Build a recursive inertial binary tree.

Uses inertial bisection in a recursive manner until each leaf node has only one input sphere inside. Number of tree nodes is always 2*nsph-1.

Parameters

[in]	nsph	Number of input spheres
[in]	csph	Centers of input spheres
[in]	rsph	Radii of input spheres
[out]	order	Ordering of input spheres to make spheres of one cluster contiguous.
[out]	cluster	Indexes in order array of the first and the last spheres of each cluster
[out]	children	Indexes of the first and the last children nodes. If both indexes are equal this means there is only 1 child node and if value of the first child node is 0, there are no children nodes.
[out]	parent	Parent of each cluster. Value 0 means there is no parent node which corresponds to the root node (with index 1).
[out]	cnode	Center of a bounding sphere of each node
[out]	rnode	Radius of a bounding sphere of each node
[out]	snode	Array of leaf nodes containing input spheres
[in,out]	ddx_error	ddX error

Definition at line 1613 of file ddx_constants.f90.

tree_rib_node_bisect()

subroutine ddx_constants::tree_rib_node_bisect	(	integer, intent(in)	nsph,
		real(dp), dimension(3, nsph), intent(in)	csph,
		integer, intent(in)	n,
		integer, dimension(n), intent(inout)	order,
		integer, intent(out)	div,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Divide given cluster of spheres into two subclusters by inertial bisection.

Parameters

[in]	nsph	Number of all input spheres
[in]	csph	Centers of all input spheres
[in]	n	Number of spheres in a given cluster
[in,out]	order	Indexes of spheres in a given cluster. On exit, indexes order(1:div) correspond to the first subcluster and indexes order(div+1:n) correspond to the second subcluster.
[out]	div	Break point of order array between two clusters.
[in,out]	ddx_error	ddX error

Definition at line 1740 of file ddx_constants.f90.

tree_get_farnear_work()

subroutine ddx_constants::tree_get_farnear_work	(	integer, intent(in)	n,
		integer, dimension(2, n), intent(in)	children,
		real(dp), dimension(3, n), intent(in)	cnode,
		real(dp), dimension(n), intent(in)	rnode,
		integer, intent(in)	lwork,
		integer, intent(inout)	iwork,
		integer, intent(inout)	jwork,
		integer, dimension(3, lwork), intent(inout)	work,
		integer, intent(out)	nnfar,
		integer, dimension(n), intent(out)	nfar,
		integer, intent(out)	nnnear,
		integer, dimension(n), intent(out)	nnear
	)

Find near and far admissible pairs of tree nodes and store it in work array.

Parameters

[in]	n	number of nodes
[in]	children	first and last children of each cluster. Value 0 means no children (leaf node).
[in]	cnode	center of bounding sphere of each cluster (node) of tree
[in]	rnode	radius of bounding sphere of each cluster (node) of tree
[in]	lwork	size of work array in dimension 2
[in,out]	iwork	index of current pair of nodes that needs to be checked for admissibility. Must be 0 for the first call of this subroutine. If on exit iwork is less or equal to jwork, that means lwork was too small, please reallocate work array and copy all the values into new array and then run procedure again.
[in,out]	jwork	amount of stored possible admissible pairs of nodes. Please read iwork comments.
[in,out]	work	all the far and near pairs will be stored here
[out]	nnfar	total amount of far admissible pairs. valid only if iwork is greater than jwork on exit.
[out]	nfar	amount of far admissible pairs for each node. valid only if iwork is greater than jwork on exit.
[out]	nnnear	total amount of near admissible pairs. valid only if iwork is greater than jwork on exit
[out]	nnear	amount of near admissible pairs for each node. valid only if iwork is greater than jwork on exit

Definition at line 1848 of file ddx_constants.f90.

tree_get_farnear()

subroutine ddx_constants::tree_get_farnear	(	integer, intent(in)	jwork,
		integer, intent(in)	lwork,
		integer, dimension(3, lwork), intent(in)	work,
		integer, intent(in)	n,
		integer, intent(in)	nnfar,
		integer, dimension(n), intent(in)	nfar,
		integer, dimension(n+1), intent(out)	sfar,
		integer, dimension(nnfar), intent(out)	far,
		integer, intent(in)	nnnear,
		integer, dimension(n), intent(in)	nnear,
		integer, dimension(n+1), intent(out)	snear,
		integer, dimension(nnnear), intent(out)	near
	)

Get near and far admissible pairs from work array of tree_get_farnear_work Works only for binary tree.

Definition at line 1941 of file ddx_constants.f90.

constants_free()

subroutine ddx_constants::constants_free	(	type(ddx_constants_type), intent(out)	constants,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Deallocate the constants.

Parameters

[out]	constants	Precomputed constants
[in,out]	ddx_error	ddX error

Definition at line 2000 of file ddx_constants.f90.

switching_init()

subroutine ddx_constants::switching_init	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_switching_type), intent(inout)	switching,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Definition at line 2323 of file ddx_constants.f90.

switching_free()

subroutine ddx_constants::switching_free	(	type(ddx_switching_type), intent(inout)	switching,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Definition at line 2398 of file ddx_constants.f90.

compute_t()

real(dp) function ddx_constants::compute_t	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		integer, intent(in)	isph,
		integer, intent(in)	jsph,
		integer, intent(in)	n
	)

Definition at line 2452 of file ddx_constants.f90.

compute_chi()

real(dp) function ddx_constants::compute_chi	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		integer, intent(in)	isph,
		integer, intent(in)	jsph,
		integer, intent(in)	n
	)

Definition at line 2466 of file ddx_constants.f90.

compute_d_and_f()

subroutine ddx_constants::compute_d_and_f	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		integer, intent(in)	isph,
		integer, intent(in)	n,
		real(dp), intent(out)	d,
		real(dp), intent(out)	f
	)

Definition at line 2475 of file ddx_constants.f90.

compute_d()

real(dp) function ddx_constants::compute_d	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		integer, intent(in)	isph,
		integer, intent(in)	n
	)

Definition at line 2492 of file ddx_constants.f90.

compute_f()

real(dp) function ddx_constants::compute_f	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		integer, intent(in)	isph,
		integer, intent(in)	n
	)

Definition at line 2506 of file ddx_constants.f90.

compute_omega()

real(dp) function ddx_constants::compute_omega	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		integer, intent(in)	isph,
		integer, intent(in)	jsph,
		integer, intent(in)	n
	)

Definition at line 2519 of file ddx_constants.f90.

compute_u()

real(dp) function ddx_constants::compute_u	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		integer, intent(in)	isph,
		integer, intent(in)	n
	)

Definition at line 2531 of file ddx_constants.f90.

compute_grad_i_u_i()

subroutine ddx_constants::compute_grad_i_u_i	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		integer, intent(in)	isph,
		integer, intent(in)	n,
		real(dp), dimension(3), intent(out)	grad,
		real(dp), intent(out)	dr
	)

Definition at line 2547 of file ddx_constants.f90.