Reduced-coordinate parameterization of cell constraints for CELL_OPT. More...

Data Types
type	cell_manifold_type
	Active constraint set and fixed coordinate bases anchored at q0. More...

Functions/Subroutines
subroutine, public	cell_manifold_init (m, q0, mask, info, lin_w, eq_pair)
	Record constraint targets at q0, check row independence, and build [Y, Z].
subroutine, public	cell_manifold_geometry (q, s, info)
	Compute cell lengths, angles in radians, and volume s(q).
subroutine, public	cell_manifold_jacobian (q, j, info)
	Compute the analytic 7 x 6 Jacobian J = ds/dq of the geometric quantities.
subroutine, public	cell_manifold_residual (m, q, r, info)
	Evaluate the k active constraint residuals r(q).
subroutine, public	cell_manifold_active_jacobian (m, q, a, info)
	Assemble the k x 6 Jacobian A(q) = dr/dq of the active constraints.
subroutine, public	cell_manifold_chart_eval (m, u, q, info)
	Map reduced coordinates u to a canonical cell q(u) that satisfies r(q) = 0.
subroutine, public	cell_manifold_chart_inv (m, q, u)
	Map a canonical cell q back to reduced coordinates u = u0 + Z^T (q - q0).
subroutine, public	cell_manifold_chart_pullback_grad (m, q, g_q, g_u, info)
	Transform a 6-component cell gradient g_q into the reduced gradient g_u = (dq/du)^T g_q.
subroutine, public	cell_manifold_proj_pressure (m, q, g_phys, pdiff, projected, info)
	Compute the pressure residual P_constr - pres_ext along unconstrained cell directions.
pure real(kind=dp) function, dimension(n_slot), public	cell_manifold_pack_hmat (hmat)
	Pack the upper-triangular canonical cell matrix into q(1:6).
pure subroutine, public	cell_manifold_unpack_hmat (q, hmat)
	Write q(1:6) into the upper-triangular canonical cell matrix.
pure character(len=default_string_length) function, public	cell_manifold_status_label (info)
	Return a short description of a cell_manifold_utils status code.
logical function, public	cell_manifold_is_redundant (m, mask, lin_w, eq_pair)
	Test whether one candidate constraint stays zero on manifold m near q0.
subroutine, public	cell_manifold_pin_semidefinite (m, mask, is_pinned, lin_w, eq_pair)
	Pin implied directions when a candidate constraint is semidefinite at q0.

Variables
integer, parameter, public	n_slot = 6
integer, parameter, public	n_geom = 7
integer, parameter, public	slot_ax = 1
integer, parameter, public	slot_bx = 2
integer, parameter, public	slot_by = 3
integer, parameter, public	slot_cx = 4
integer, parameter, public	slot_cy = 5
integer, parameter, public	slot_cz = 6
integer, parameter, public	geom_a = 1
integer, parameter, public	geom_b = 2
integer, parameter, public	geom_c = 3
integer, parameter, public	geom_alpha = 4
integer, parameter, public	geom_beta = 5
integer, parameter, public	geom_gamma = 6
integer, parameter, public	geom_v = 7
integer, parameter, public	comp_ax = 2**0
integer, parameter, public	comp_bx = 2**1
integer, parameter, public	comp_by = 2**2
integer, parameter, public	comp_cx = 2**3
integer, parameter, public	comp_cy = 2**4
integer, parameter, public	comp_cz = 2**5
integer, parameter, public	mask_a = comp_ax
integer, parameter, public	mask_b = comp_bx + comp_by
integer, parameter, public	mask_c = comp_cx + comp_cy + comp_cz
integer, parameter, public	mask_x = comp_ax + comp_bx + comp_cx
integer, parameter, public	mask_y = comp_bx + comp_by + comp_cy
integer, parameter, public	mask_z = mask_c
integer, parameter, public	mask_xy = comp_ax + comp_bx + comp_by + comp_cx + comp_cy
integer, parameter, public	mask_xz = comp_ax + comp_bx + comp_cx + comp_cy + comp_cz
integer, parameter, public	mask_yz = comp_bx + comp_by + comp_cx + comp_cy + comp_cz
integer, parameter, public	mask_all = comp_ax + comp_bx + comp_by + comp_cx + comp_cy + comp_cz
integer, parameter, public	gfix_a = 2**6
integer, parameter, public	gfix_b = 2**7
integer, parameter, public	gfix_c = 2**8
integer, parameter, public	gfix_alpha = 2**9
integer, parameter, public	gfix_beta = 2**10
integer, parameter, public	gfix_gamma = 2**11
integer, parameter, public	gfix_v = 2**12
integer, parameter, public	gfix_all = gfix_a + gfix_b + gfix_c + gfix_alpha + gfix_beta + gfix_gamma + gfix_v
integer, parameter, public	n_constraint_bits = n_slot + n_geom
real(kind=dp), parameter, public	min_cell_length = 1.0E-8_dp
integer, parameter, public	info_ok = 0
integer, parameter, public	info_degenerate = -1
integer, parameter, public	info_licq = -2
integer, parameter, public	info_no_converge = -3
integer, parameter, public	info_bad_input = -4
external	dgeqrf

Detailed Description

Reduced-coordinate parameterization of cell constraints for CELL_OPT.

This pure-math module depends only on kinds, ieee_arithmetic, and LAPACK. It has no force_env, cell_type, or input dependencies.

Canonical cell vector: CP2K places lattice vector a along x and b in the xy plane: hmat(:, 1) = (AX, 0, 0) hmat(:, 2) = (BX, BY, 0) hmat(:, 3) = (CX, CY, CZ) The 6 upper-triangular entries form q = (AX, BX, BY, CX, CY, CZ). The 7 geometric quantities are s(q) = (a, b, c, alpha, beta, gamma, V), with angles in radians and volume V = AX * BY * CZ.

Constraint equations and reduced coordinates: Active constraints define k equations r(q) = 0 with k x 6 Jacobian A(q) = dr/dq:

Fixed cell components: q_i - q0_i = 0.
Fixed geometric quantities: s_m(q) - s_m(q0) = 0.
Equal lengths or angles: s_m(q) - s_n(q) = 0 (for example a = b).
Linear relations: w^T (q - q0) = 0 (for example AX = BY).

At the initial cell q0, QR factorization splits R^6 into two fixed orthonormal bases:

Y (6 x k) spans the constrained directions row(A(q0)).
Z (6 x ndof, ndof = 6 - k) spans the free directions ker(A(q0)).

The optimizer works only on the reduced vector u of length ndof:

Forward map (chart_eval): q(u) = q0 + Z (u - u0) + Y w(u). Newton's method solves the k x k system r(q(u)) = 0 for w(u). Linear constraints satisfy r = 0 in zero Newton iterations.
Inverse map (chart_inv): u = u0 + Z^T (q - q0), because Z^T Y = 0.
Reduced gradient (chart_pullback_grad): g_u = (dq/du)^T g_q. Implicit differentiation gives g_u = Z^T (g_q - A(q)^T lam), where (A(q) Y)^T lam = Y^T g_q.
Unconstrained case (k = 0): Z = I and u0 = q0, so u = q and g_u = g_q with zero floating-point roundoff.

Sign convention: get_dg_dh returns g_q = +d(E + pres_ext*V)/dq. Routine cell_manifold_proj_pressure maps g_q to pdiff = P_constr - pres_ext.

Function/Subroutine Documentation

◆ cell_manifold_init()

subroutine, public cell_manifold_utils::cell_manifold_init	(	type(cell_manifold_type), intent(out)	m,
		real(kind=dp), dimension(n_slot), intent(in)	q0,
		integer, intent(in)	mask,
		integer, intent(out)	info,
		real(kind=dp), dimension(:, :), intent(in), optional	lin_w,
		integer, dimension(:, :), intent(in), optional	eq_pair )

Record constraint targets at q0, check row independence, and build [Y, Z].

Parameters

m	initialized constraint state
q0	initial canonical cell components
mask	bit union of comp_* and gfix_* flags
info	info_ok, info_degenerate, info_licq, or info_bad_input
lin_w	optional 6 x n_lin linear coupling weights, one constraint per column
eq_pair	optional 2 x n_eq index pairs [m, n] in 1..6 for s_m(q) = s_n(q)

Definition at line 199 of file cell_manifold_utils.F.

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◆ cell_manifold_geometry()

subroutine, public cell_manifold_utils::cell_manifold_geometry	(	real(kind=dp), dimension(n_slot), intent(in)	q,
		real(kind=dp), dimension(n_geom), intent(out)	s,
		integer, intent(out)	info )

Compute cell lengths, angles in radians, and volume s(q).

Parameters

q	canonical cell components (AX, BX, BY, CX, CY, CZ)
s	geometric quantities (a, b, c, alpha, beta, gamma, V)
info	info_ok or info_degenerate

Definition at line 289 of file cell_manifold_utils.F.

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◆ cell_manifold_jacobian()

subroutine, public cell_manifold_utils::cell_manifold_jacobian	(	real(kind=dp), dimension(n_slot), intent(in)	q,
		real(kind=dp), dimension(n_geom, n_slot), intent(out)	j,
		integer, intent(out)	info )

Compute the analytic 7 x 6 Jacobian J = ds/dq of the geometric quantities.

Parameters

q	canonical cell components (AX, BX, BY, CX, CY, CZ)
J	Jacobian matrix ds/dq
info	info_ok or info_degenerate

Definition at line 346 of file cell_manifold_utils.F.

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◆ cell_manifold_residual()

subroutine, public cell_manifold_utils::cell_manifold_residual	(	type(cell_manifold_type), intent(in)	m,
		real(kind=dp), dimension(n_slot), intent(in)	q,
		real(kind=dp), dimension(m%k), intent(out)	r,
		integer, intent(out)	info )

Evaluate the k active constraint residuals r(q).

Parameters

m	constraint state
q	canonical cell vector
r	residual vector of length mk (zero when q satisfies all constraints)
info	info_ok or info_degenerate

Definition at line 410 of file cell_manifold_utils.F.

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◆ cell_manifold_active_jacobian()

subroutine, public cell_manifold_utils::cell_manifold_active_jacobian	(	type(cell_manifold_type), intent(in)	m,
		real(kind=dp), dimension(n_slot), intent(in)	q,
		real(kind=dp), dimension(m%k, n_slot), intent(out)	a,
		integer, intent(out)	info )

Assemble the k x 6 Jacobian A(q) = dr/dq of the active constraints.

Parameters

m	constraint state
q	canonical cell vector
A	active constraint Jacobian in the same row order as cell_manifold_residual
info	info_ok or info_degenerate

Definition at line 457 of file cell_manifold_utils.F.

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◆ cell_manifold_chart_eval()

subroutine, public cell_manifold_utils::cell_manifold_chart_eval	(	type(cell_manifold_type), intent(inout)	m,
		real(kind=dp), dimension(m%ndof), intent(in)	u,
		real(kind=dp), dimension(n_slot), intent(out)	q,
		integer, intent(out)	info )

Map reduced coordinates u to a canonical cell q(u) that satisfies r(q) = 0.

Parameters

m	constraint state. This routine updates only last_iter and last_resid.
u	reduced coordinates of length mndof
q	canonical cell vector on the constraint surface
info	info_ok, info_degenerate, info_licq, or info_no_converge

Note: For qt = q0 + Z (u - u0), Newton's method solves r(qt + Y w) = 0 for w. Linear constraints satisfy r(qt) = 0 in zero iterations. When k = 0, q copies u with zero roundoff.

Definition at line 501 of file cell_manifold_utils.F.

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◆ cell_manifold_chart_inv()

subroutine, public cell_manifold_utils::cell_manifold_chart_inv	(	type(cell_manifold_type), intent(in)	m,
		real(kind=dp), dimension(n_slot), intent(in)	q,
		real(kind=dp), dimension(m%ndof), intent(out)	u )

Map a canonical cell q back to reduced coordinates u = u0 + Z^T (q - q0).

Parameters

m	constraint state
q	canonical cell vector
u	reduced coordinates of length mndof

Note: Because Z^T Z = I and Z^T Y = 0, this affine projection is the exact inverse of cell_manifold_chart_eval. When k = 0, u is a direct copy of q.

Definition at line 596 of file cell_manifold_utils.F.

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◆ cell_manifold_chart_pullback_grad()

subroutine, public cell_manifold_utils::cell_manifold_chart_pullback_grad	(	type(cell_manifold_type), intent(in)	m,
		real(kind=dp), dimension(n_slot), intent(in)	q,
		real(kind=dp), dimension(n_slot), intent(in)	g_q,
		real(kind=dp), dimension(m%ndof), intent(out)	g_u,
		integer, intent(out)	info )

Transform a 6-component cell gradient g_q into the reduced gradient g_u = (dq/du)^T g_q.

Parameters

m	constraint state
q	current canonical cell vector
g_q	enthalpy gradient +dH/dq in canonical cell components
g_u	enthalpy gradient +dH/du in reduced coordinates
info	info_ok, info_degenerate, or info_licq

Note: Implicit differentiation of r(q(u)) = 0 gives dq/du = Z - Y (A Y)^{-1} A Z. Thus g_u = Z^T (g_q - A^T lam), where (A Y)^T lam = Y^T g_q.

Definition at line 620 of file cell_manifold_utils.F.

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◆ cell_manifold_proj_pressure()

subroutine, public cell_manifold_utils::cell_manifold_proj_pressure	(	type(cell_manifold_type), intent(in)	m,
		real(kind=dp), dimension(n_slot), intent(in)	q,
		real(kind=dp), dimension(n_slot), intent(in)	g_phys,
		real(kind=dp), intent(out)	pdiff,
		logical, intent(out)	projected,
		integer, intent(out)	info )

Compute the pressure residual P_constr - pres_ext along unconstrained cell directions.

Parameters

m	constraint state
q	current canonical cell components
g_phys	enthalpy gradient +d(E + pres_ext*V)/dq from get_dg_dh
pdiff	residual pressure P_constr - pres_ext along the allowed volume direction
projected	.TRUE. if free directions change volume, .FALSE. if volume is fixed
info	info_ok, info_degenerate, or info_licq

Note: On curved constraints, ker(A(q)) rotates as q moves from q0. This routine projects dV/dq onto ker(A(q)) at the current cell q: vt = dV/dq - A(q)^T (A(q) A(q)^T)^{-1} A(q) (dV/dq). At any constrained minimum, g_phys lies in row(A(q)) and pdiff vanishes.

Definition at line 669 of file cell_manifold_utils.F.

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◆ cell_manifold_pack_hmat()

pure real(kind=dp) function, dimension(n_slot), public cell_manifold_utils::cell_manifold_pack_hmat ( real(kind=dp), dimension(3, 3), intent(in) hmat )

Pack the upper-triangular canonical cell matrix into q(1:6).

Parameters

hmat	canonical 3x3 cell matrix (a along x, b in the xy plane)

Returns: q = (AX, BX, BY, CX, CY, CZ)

Definition at line 728 of file cell_manifold_utils.F.

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◆ cell_manifold_unpack_hmat()

pure subroutine, public cell_manifold_utils::cell_manifold_unpack_hmat	(	real(kind=dp), dimension(n_slot), intent(in)	q,
		real(kind=dp), dimension(3, 3), intent(out)	hmat )

Write q(1:6) into the upper-triangular canonical cell matrix.

Parameters

q	canonical cell vector (AX, BX, BY, CX, CY, CZ)
hmat	canonical 3x3 cell matrix with zeroed lower triangle

Definition at line 741 of file cell_manifold_utils.F.

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◆ cell_manifold_status_label()

pure character(len=default_string_length) function, public cell_manifold_utils::cell_manifold_status_label ( integer, intent(in) info )

Return a short description of a cell_manifold_utils status code.

Parameters

info	status code from a cell_manifold_* routine

Returns: diagnostic text

Definition at line 760 of file cell_manifold_utils.F.

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◆ cell_manifold_is_redundant()

logical function, public cell_manifold_utils::cell_manifold_is_redundant	(	type(cell_manifold_type), intent(in)	m,
		integer, intent(in)	mask,
		real(kind=dp), dimension(:, :), intent(in), optional	lin_w,
		integer, dimension(:, :), intent(in), optional	eq_pair )

Test whether one candidate constraint stays zero on manifold m near q0.

Parameters

m	active constraint manifold anchored at q0
mask	candidate comp_* or gfix_* bit, or 0 for a lin_w or eq_pair test
lin_w	optional 6 x 1 column of candidate linear weights
eq_pair	optional 2 x 1 index pair for a candidate equality

Returns: .TRUE. if the candidate residual stays zero along m, or .FALSE. otherwise

Definition at line 789 of file cell_manifold_utils.F.

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◆ cell_manifold_pin_semidefinite()

subroutine, public cell_manifold_utils::cell_manifold_pin_semidefinite	(	type(cell_manifold_type), intent(inout)	m,
		integer, intent(in)	mask,
		logical, intent(out)	is_pinned,
		real(kind=dp), dimension(:, :), intent(in), optional	lin_w,
		integer, dimension(:, :), intent(in), optional	eq_pair )

Pin implied directions when a candidate constraint is semidefinite at q0.

Parameters

m	active constraint manifold at q0. This routine updates m when is_pinned is .TRUE.
mask	candidate comp_* or gfix_* bit, or 0 for a lin_w or eq_pair test
is_pinned	.TRUE. if this routine pins the candidate constraint
lin_w	optional 6 x 1 column of candidate linear weights
eq_pair	optional 2 x 1 index pair for a candidate equality

Note: This routine builds the 6 x 6 Lagrangian Hessian at q0 from 4-point central differences of analytic Jacobians. When the reduced Hessian on ker(A(q0)) is nonzero and semidefinite, this routine pins the curved directions. It then verifies that the candidate stays zero.

Definition at line 886 of file cell_manifold_utils.F.

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Variable Documentation

◆ n_slot

integer, parameter, public cell_manifold_utils::n_slot = 6

Definition at line 59 of file cell_manifold_utils.F.

◆ n_geom

integer, parameter, public cell_manifold_utils::n_geom = 7

Definition at line 59 of file cell_manifold_utils.F.

◆ slot_ax

integer, parameter, public cell_manifold_utils::slot_ax = 1

Definition at line 60 of file cell_manifold_utils.F.

◆ slot_bx

integer, parameter, public cell_manifold_utils::slot_bx = 2

Definition at line 60 of file cell_manifold_utils.F.

◆ slot_by

integer, parameter, public cell_manifold_utils::slot_by = 3

Definition at line 60 of file cell_manifold_utils.F.

◆ slot_cx

integer, parameter, public cell_manifold_utils::slot_cx = 4

Definition at line 60 of file cell_manifold_utils.F.

◆ slot_cy

integer, parameter, public cell_manifold_utils::slot_cy = 5

Definition at line 60 of file cell_manifold_utils.F.

◆ slot_cz

integer, parameter, public cell_manifold_utils::slot_cz = 6

Definition at line 60 of file cell_manifold_utils.F.

◆ geom_a

integer, parameter, public cell_manifold_utils::geom_a = 1

Definition at line 66 of file cell_manifold_utils.F.

◆ geom_b

integer, parameter, public cell_manifold_utils::geom_b = 2

Definition at line 66 of file cell_manifold_utils.F.

◆ geom_c

integer, parameter, public cell_manifold_utils::geom_c = 3

Definition at line 66 of file cell_manifold_utils.F.

◆ geom_alpha

integer, parameter, public cell_manifold_utils::geom_alpha = 4

Definition at line 66 of file cell_manifold_utils.F.

◆ geom_beta

integer, parameter, public cell_manifold_utils::geom_beta = 5

Definition at line 66 of file cell_manifold_utils.F.

◆ geom_gamma

integer, parameter, public cell_manifold_utils::geom_gamma = 6

Definition at line 66 of file cell_manifold_utils.F.

◆ geom_v

integer, parameter, public cell_manifold_utils::geom_v = 7

Definition at line 66 of file cell_manifold_utils.F.

◆ comp_ax

integer, parameter, public cell_manifold_utils::comp_ax = 2**0

Definition at line 75 of file cell_manifold_utils.F.

◆ comp_bx

integer, parameter, public cell_manifold_utils::comp_bx = 2**1

Definition at line 75 of file cell_manifold_utils.F.

◆ comp_by

integer, parameter, public cell_manifold_utils::comp_by = 2**2

Definition at line 75 of file cell_manifold_utils.F.

◆ comp_cx

integer, parameter, public cell_manifold_utils::comp_cx = 2**3

Definition at line 75 of file cell_manifold_utils.F.

◆ comp_cy

integer, parameter, public cell_manifold_utils::comp_cy = 2**4

Definition at line 75 of file cell_manifold_utils.F.

◆ comp_cz

integer, parameter, public cell_manifold_utils::comp_cz = 2**5

Definition at line 75 of file cell_manifold_utils.F.

◆ mask_a

integer, parameter, public cell_manifold_utils::mask_a = comp_ax

Definition at line 81 of file cell_manifold_utils.F.

◆ mask_b

integer, parameter, public cell_manifold_utils::mask_b = comp_bx + comp_by

Definition at line 81 of file cell_manifold_utils.F.

◆ mask_c

integer, parameter, public cell_manifold_utils::mask_c = comp_cx + comp_cy + comp_cz

Definition at line 81 of file cell_manifold_utils.F.

◆ mask_x

integer, parameter, public cell_manifold_utils::mask_x = comp_ax + comp_bx + comp_cx

Definition at line 81 of file cell_manifold_utils.F.

◆ mask_y

integer, parameter, public cell_manifold_utils::mask_y = comp_bx + comp_by + comp_cy

Definition at line 81 of file cell_manifold_utils.F.

◆ mask_z

integer, parameter, public cell_manifold_utils::mask_z = mask_c

Definition at line 81 of file cell_manifold_utils.F.

◆ mask_xy

integer, parameter, public cell_manifold_utils::mask_xy = comp_ax + comp_bx + comp_by + comp_cx + comp_cy

Definition at line 81 of file cell_manifold_utils.F.

◆ mask_xz

integer, parameter, public cell_manifold_utils::mask_xz = comp_ax + comp_bx + comp_cx + comp_cy + comp_cz

Definition at line 81 of file cell_manifold_utils.F.

◆ mask_yz

integer, parameter, public cell_manifold_utils::mask_yz = comp_bx + comp_by + comp_cx + comp_cy + comp_cz

Definition at line 81 of file cell_manifold_utils.F.

◆ mask_all

integer, parameter, public cell_manifold_utils::mask_all = comp_ax + comp_bx + comp_by + comp_cx + comp_cy + comp_cz

Definition at line 81 of file cell_manifold_utils.F.

◆ gfix_a

integer, parameter, public cell_manifold_utils::gfix_a = 2**6

Definition at line 96 of file cell_manifold_utils.F.

◆ gfix_b

integer, parameter, public cell_manifold_utils::gfix_b = 2**7

Definition at line 96 of file cell_manifold_utils.F.

◆ gfix_c

integer, parameter, public cell_manifold_utils::gfix_c = 2**8

Definition at line 96 of file cell_manifold_utils.F.

◆ gfix_alpha

integer, parameter, public cell_manifold_utils::gfix_alpha = 2**9

Definition at line 96 of file cell_manifold_utils.F.

◆ gfix_beta

integer, parameter, public cell_manifold_utils::gfix_beta = 2**10

Definition at line 96 of file cell_manifold_utils.F.

◆ gfix_gamma

integer, parameter, public cell_manifold_utils::gfix_gamma = 2**11

Definition at line 96 of file cell_manifold_utils.F.

◆ gfix_v

integer, parameter, public cell_manifold_utils::gfix_v = 2**12

Definition at line 96 of file cell_manifold_utils.F.

◆ gfix_all

integer, parameter, public cell_manifold_utils::gfix_all = gfix_a + gfix_b + gfix_c + gfix_alpha + gfix_beta + gfix_gamma + gfix_v

Definition at line 103 of file cell_manifold_utils.F.

◆ n_constraint_bits

integer, parameter, public cell_manifold_utils::n_constraint_bits = n_slot + n_geom

Definition at line 105 of file cell_manifold_utils.F.

◆ min_cell_length

real(kind=dp), parameter, public cell_manifold_utils::min_cell_length = 1.0E-8_dp

Definition at line 109 of file cell_manifold_utils.F.

◆ info_ok

integer, parameter, public cell_manifold_utils::info_ok = 0

Definition at line 137 of file cell_manifold_utils.F.

◆ info_degenerate

integer, parameter, public cell_manifold_utils::info_degenerate = -1

Definition at line 138 of file cell_manifold_utils.F.

◆ info_licq

integer, parameter, public cell_manifold_utils::info_licq = -2

Definition at line 139 of file cell_manifold_utils.F.

◆ info_no_converge

integer, parameter, public cell_manifold_utils::info_no_converge = -3

Definition at line 140 of file cell_manifold_utils.F.

◆ info_bad_input

integer, parameter, public cell_manifold_utils::info_bad_input = -4

Definition at line 141 of file cell_manifold_utils.F.

◆ dgeqrf

external cell_manifold_utils::dgeqrf

Definition at line 186 of file cell_manifold_utils.F.

Data Types

Functions/Subroutines

Variables

Detailed Description

Function/Subroutine Documentation

◆ cell_manifold_init()

◆ cell_manifold_geometry()

◆ cell_manifold_jacobian()

◆ cell_manifold_residual()

◆ cell_manifold_active_jacobian()

◆ cell_manifold_chart_eval()

◆ cell_manifold_chart_inv()

◆ cell_manifold_chart_pullback_grad()

◆ cell_manifold_proj_pressure()

◆ cell_manifold_pack_hmat()

◆ cell_manifold_unpack_hmat()

◆ cell_manifold_status_label()

◆ cell_manifold_is_redundant()

◆ cell_manifold_pin_semidefinite()

Variable Documentation

◆ n_slot

◆ n_geom

◆ slot_ax

◆ slot_bx

◆ slot_by

◆ slot_cx

◆ slot_cy

◆ slot_cz

◆ geom_a

◆ geom_b

◆ geom_c

◆ geom_alpha

◆ geom_beta

◆ geom_gamma

◆ geom_v

◆ comp_ax

◆ comp_bx

◆ comp_by

◆ comp_cx

◆ comp_cy

◆ comp_cz

◆ mask_a

◆ mask_b

◆ mask_c

◆ mask_x

◆ mask_y

◆ mask_z

◆ mask_xy

◆ mask_xz

◆ mask_yz

◆ mask_all

◆ gfix_a

◆ gfix_b

◆ gfix_c

◆ gfix_alpha

◆ gfix_beta

◆ gfix_gamma

◆ gfix_v

◆ gfix_all

◆ n_constraint_bits

◆ min_cell_length

◆ info_ok

◆ info_degenerate

◆ info_licq

◆ info_no_converge

◆ info_bad_input

◆ dgeqrf