ddx_operators Module Reference

Operators shared among ddX methods. More...

Functions/Subroutines
subroutine	lx (params, constants, workspace, x, y, ddx_error)
	Single layer operator matvec. More...
subroutine	lstarx (params, constants, workspace, x, y, ddx_error)
	Adjoint single layer operator matvec. More...
subroutine	ldm1x (params, constants, workspace, x, y, ddx_error)
	Diagonal preconditioning for Lx operator. More...
subroutine	dx (params, constants, workspace, x, y, ddx_error)
	Double layer operator matvec without diagonal blocks. More...
subroutine	dx_dense (params, constants, workspace, do_diag, x, y, ddx_error)
	Baseline implementation of double layer operator. More...
subroutine	dx_fmm (params, constants, workspace, do_diag, x, y, ddx_error)
	FMM-accelerated implementation of double layer operator. More...
subroutine	dstarx (params, constants, workspace, x, y, ddx_error)
	Adjoint double layer operator matvec. More...
subroutine	dstarx_dense (params, constants, workspace, do_diag, x, y, ddx_error)
	Baseline implementation of adjoint double layer operator. More...
subroutine	dstarx_fmm (params, constants, workspace, do_diag, x, y, ddx_error)
	FMM-accelerated implementation of adjoint double layer operator. More...
subroutine	repsx (params, constants, workspace, x, y, ddx_error)
	Apply \( R_\varepsilon \) operator to spherical harmonics. More...
subroutine	repsstarx (params, constants, workspace, x, y, ddx_error)
	Apply \( R_\varepsilon^* \) operator to spherical harmonics. More...
subroutine	rinfx (params, constants, workspace, x, y, ddx_error)
	Apply \( R_\infty \) operator to spherical harmonics. More...
subroutine	rstarinfx (params, constants, workspace, x, y, ddx_error)
	Apply \( R_\infty^* \) operator to spherical harmonics. More...
subroutine	prec_repsx (params, constants, workspace, x, y, ddx_error)
	Apply preconditioner for ddPCM primal linear system. More...
subroutine	prec_repsstarx (params, constants, workspace, x, y, ddx_error)
	Apply preconditioner for ddPCM adjoint linear system. More...
subroutine	bstarx (params, constants, workspace, x, y, ddx_error)
	Adjoint HSP matrix vector product. More...
subroutine	bx (params, constants, workspace, x, y, ddx_error)
	Primal HSP matrix vector product. More...
subroutine	tstarx (params, constants, workspace, x, y, ddx_error)
	Adjoint ddLPB matrix-vector product. More...
subroutine	bx_prec (params, constants, workspace, x, y, ddx_error)
	Apply the preconditioner to the primal HSP linear system. More...
subroutine	prec_tstarx (params, constants, workspace, x, y, ddx_error)
	Apply the preconditioner to the ddLPB adjoint linear system. More...
subroutine	prec_tx (params, constants, workspace, x, y, ddx_error)
	Apply the preconditioner to the primal ddLPB linear system |Yr| = |A^-1 0 |*|Xr| |Ye| |0 B^-1 | |Xe|. More...
subroutine	cstarx (params, constants, workspace, x, y, ddx_error)
	ddLPB adjoint matrix-vector product More...
subroutine	cx (params, constants, workspace, x, y, ddx_error)
	ddLPB matrix-vector product More...

Detailed Description

Operators shared among ddX methods.

Function/Subroutine Documentation

lx()

subroutine ddx_operators::lx	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_workspace_type), intent(inout)	workspace,
		real(dp), dimension(constants % nbasis, params % nsph), intent(in)	x,
		real(dp), dimension(constants % nbasis, params % nsph), intent(out)	y,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Single layer operator matvec.

Definition at line 25 of file ddx_operators.f90.

lstarx()

subroutine ddx_operators::lstarx	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_workspace_type), intent(inout)	workspace,
		real(dp), dimension(constants % nbasis, params % nsph), intent(in)	x,
		real(dp), dimension(constants % nbasis, params % nsph), intent(out)	y,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Adjoint single layer operator matvec.

Definition at line 88 of file ddx_operators.f90.

ldm1x()

subroutine ddx_operators::ldm1x	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_workspace_type), intent(inout)	workspace,
		real(dp), dimension(constants % nbasis, params % nsph), intent(in)	x,
		real(dp), dimension(constants % nbasis, params % nsph), intent(out)	y,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Diagonal preconditioning for Lx operator.

Applies inverse diagonal (block) of the L matrix

Definition at line 154 of file ddx_operators.f90.

dx()

subroutine ddx_operators::dx	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_workspace_type), intent(inout)	workspace,
		real(dp), dimension(constants % nbasis, params % nsph), intent(in)	x,
		real(dp), dimension(constants % nbasis, params % nsph), intent(out)	y,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Double layer operator matvec without diagonal blocks.

Definition at line 185 of file ddx_operators.f90.

dx_dense()

subroutine ddx_operators::dx_dense	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_workspace_type), intent(inout)	workspace,
		integer, intent(in)	do_diag,
		real(dp), dimension(constants % nbasis, params % nsph), intent(in)	x,
		real(dp), dimension(constants % nbasis, params % nsph), intent(out)	y,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Baseline implementation of double layer operator.

Definition at line 209 of file ddx_operators.f90.

dx_fmm()

subroutine ddx_operators::dx_fmm	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_workspace_type), intent(inout)	workspace,
		integer, intent(in)	do_diag,
		real(dp), dimension(constants % nbasis, params % nsph), intent(in)	x,
		real(dp), dimension(constants % nbasis, params % nsph), intent(out)	y,
		type(ddx_error_type), intent(inout)	ddx_error
	)

FMM-accelerated implementation of double layer operator.

Definition at line 291 of file ddx_operators.f90.

dstarx()

subroutine ddx_operators::dstarx	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_workspace_type), intent(inout)	workspace,
		real(dp), dimension(constants % nbasis, params % nsph), intent(in)	x,
		real(dp), dimension(constants % nbasis, params % nsph), intent(out)	y,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Adjoint double layer operator matvec.

Definition at line 357 of file ddx_operators.f90.

dstarx_dense()

subroutine ddx_operators::dstarx_dense	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_workspace_type), intent(inout)	workspace,
		integer, intent(in)	do_diag,
		real(dp), dimension(constants % nbasis, params % nsph), intent(in)	x,
		real(dp), dimension(constants % nbasis, params % nsph), intent(out)	y,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Baseline implementation of adjoint double layer operator.

Definition at line 382 of file ddx_operators.f90.

dstarx_fmm()

subroutine ddx_operators::dstarx_fmm	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_workspace_type), intent(inout)	workspace,
		integer, intent(in)	do_diag,
		real(dp), dimension(constants % nbasis, params % nsph), intent(in)	x,
		real(dp), dimension(constants % nbasis, params % nsph), intent(out)	y,
		type(ddx_error_type), intent(inout)	ddx_error
	)

FMM-accelerated implementation of adjoint double layer operator.

Definition at line 459 of file ddx_operators.f90.

repsx()

subroutine ddx_operators::repsx	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_workspace_type), intent(inout)	workspace,
		real(dp), dimension(constants % nbasis, params % nsph), intent(in)	x,
		real(dp), dimension(constants % nbasis, params % nsph), intent(out)	y,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Apply \( R_\varepsilon \) operator to spherical harmonics.

Compute \( y = R_\varepsilon x = (2\pi(\varepsilon + 1) / (\varepsilon - 1) - D) x \).

Definition at line 527 of file ddx_operators.f90.

repsstarx()

subroutine ddx_operators::repsstarx	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_workspace_type), intent(inout)	workspace,
		real(dp), dimension(constants % nbasis, params % nsph), intent(in)	x,
		real(dp), dimension(constants % nbasis, params % nsph), intent(out)	y,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Apply \( R_\varepsilon^* \) operator to spherical harmonics.

Compute \( y = R^*_\varepsilon x = (2\pi(\varepsilon + 1) / (\varepsilon - 1) - D) x \).

Definition at line 555 of file ddx_operators.f90.

rinfx()

subroutine ddx_operators::rinfx	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_workspace_type), intent(inout)	workspace,
		real(dp), dimension(constants % nbasis, params % nsph), intent(in)	x,
		real(dp), dimension(constants % nbasis, params % nsph), intent(out)	y,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Apply \( R_\infty \) operator to spherical harmonics.

Compute \( y = R_\infty x = (2\pi - D) x \).

Parameters

[in]	ddx_data
[in]	x
[out]	y
[in,out]	ddx_error	ddX ddx_error

Definition at line 587 of file ddx_operators.f90.

rstarinfx()

subroutine ddx_operators::rstarinfx	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_workspace_type), intent(inout)	workspace,
		real(dp), dimension(constants % nbasis, params % nsph), intent(in)	x,
		real(dp), dimension(constants % nbasis, params % nsph), intent(out)	y,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Apply \( R_\infty^* \) operator to spherical harmonics.

Compute \( y = R_\infty^* x = (2\pi - D^*) x \).

Parameters

[in]	ddx_data
[in]	x
[out]	y
[in,out]	ddx_error	ddX ddx_error

Definition at line 618 of file ddx_operators.f90.

prec_repsx()

subroutine ddx_operators::prec_repsx	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_workspace_type), intent(inout)	workspace,
		real(dp), dimension(constants % nbasis, params % nsph), intent(in)	x,
		real(dp), dimension(constants % nbasis, params % nsph), intent(out)	y,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Apply preconditioner for ddPCM primal linear system.

Parameters

[in,out]

ddx_error

ddX ddx_error

Definition at line 637 of file ddx_operators.f90.

prec_repsstarx()

subroutine ddx_operators::prec_repsstarx	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_workspace_type), intent(inout)	workspace,
		real(dp), dimension(constants % nbasis, params % nsph), intent(in)	x,
		real(dp), dimension(constants % nbasis, params % nsph), intent(out)	y,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Apply preconditioner for ddPCM adjoint linear system.

Definition at line 665 of file ddx_operators.f90.

bstarx()

subroutine ddx_operators::bstarx	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_workspace_type), intent(inout)	workspace,
		real(dp), dimension(constants % nbasis, params % nsph), intent(in)	x,
		real(dp), dimension(constants % nbasis, params % nsph), intent(out)	y,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Adjoint HSP matrix vector product.

Definition at line 694 of file ddx_operators.f90.

bx()

subroutine ddx_operators::bx	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_workspace_type), intent(inout)	workspace,
		real(dp), dimension(constants % nbasis, params % nsph), intent(in)	x,
		real(dp), dimension(constants % nbasis, params % nsph), intent(out)	y,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Primal HSP matrix vector product.

Definition at line 746 of file ddx_operators.f90.

tstarx()

subroutine ddx_operators::tstarx	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_workspace_type), intent(inout)	workspace,
		real(dp), dimension(constants % nbasis, params % nsph, 2), intent(in)	x,
		real(dp), dimension(constants % nbasis, params % nsph, 2), intent(out)	y,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Adjoint ddLPB matrix-vector product.

Definition at line 786 of file ddx_operators.f90.

bx_prec()

subroutine ddx_operators::bx_prec	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_workspace_type), intent(inout)	workspace,
		real(dp), dimension(constants % nbasis, params % nsph), intent(in)	x,
		real(dp), dimension(constants % nbasis, params % nsph), intent(out)	y,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Apply the preconditioner to the primal HSP linear system.

Parameters

[in,out]

ddx_error

ddX ddx_error

Definition at line 820 of file ddx_operators.f90.

prec_tstarx()

subroutine ddx_operators::prec_tstarx	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_workspace_type), intent(inout)	workspace,
		real(dp), dimension(constants % nbasis, params % nsph, 2), intent(in)	x,
		real(dp), dimension(constants % nbasis, params % nsph, 2), intent(inout)	y,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Apply the preconditioner to the ddLPB adjoint linear system.

Definition at line 837 of file ddx_operators.f90.

prec_tx()

subroutine ddx_operators::prec_tx	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_workspace_type), intent(inout)	workspace,
		real(dp), dimension(constants % nbasis, params % nsph, 2), intent(in)	x,
		real(dp), dimension(constants % nbasis, params % nsph, 2), intent(inout)	y,
		type(ddx_error_type), intent(inout)	ddx_error
	)

Apply the preconditioner to the primal ddLPB linear system |Yr| = |A^-1 0 |*|Xr| |Ye| |0 B^-1 | |Xe|.

Parameters

[in]	ddx_data	: dd Data
[in]	x	: Input array
[out]	y	: Linear system solution at current iteration
[in,out]	ddx_error	ddX ddx_error

Definition at line 887 of file ddx_operators.f90.

cstarx()

subroutine ddx_operators::cstarx	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_workspace_type), intent(inout)	workspace,
		real(dp), dimension(constants % nbasis, params % nsph, 2), intent(in)	x,
		real(dp), dimension(constants % nbasis, params % nsph, 2), intent(out)	y,
		type(ddx_error_type), intent(inout)	ddx_error
	)

ddLPB adjoint matrix-vector product

Definition at line 934 of file ddx_operators.f90.

cx()

subroutine ddx_operators::cx	(	type(ddx_params_type), intent(in)	params,
		type(ddx_constants_type), intent(in)	constants,
		type(ddx_workspace_type), intent(inout)	workspace,
		real(dp), dimension(constants % nbasis, params % nsph, 2), intent(in)	x,
		real(dp), dimension(constants % nbasis, params % nsph, 2), intent(out)	y,
		type(ddx_error_type), intent(inout)	ddx_error
	)

ddLPB matrix-vector product

Definition at line 1049 of file ddx_operators.f90.