occ::mults::RigidBodyProjection Class Reference

Projection matrix for removing rigid-body modes from optimization. More...

#include <optimization_projection.h>

Public Member Functions
	RigidBodyProjection (size_t n_molecules)
	Construct projection for N rigid bodies.
size_t	full_dof () const
	Get number of original degrees of freedom (6N)
size_t	projected_dof () const
	Get number of projected degrees of freedom (6N-6)
Vec	project_gradient (const Vec &grad_full) const
	Project full gradient to reduced space.
Vec	reconstruct_full (const Vec &x_proj, const Vec &x_base) const
	Reconstruct full coordinates from projected coordinates.
Vec	project_coordinates (const Vec &x_full, const Vec &x_base) const
	Project full coordinates to reduced space.
const Mat &	projection_matrix () const
	Get projection matrix (for debugging/analysis)

Detailed Description

Projection matrix for removing rigid-body modes from optimization.

For a system of N rigid bodies with 6N degrees of freedom (3 position + 3 orientation each), there are 6 spurious modes corresponding to global translation (3) and global rotation (3). These cause the Hessian to have 6 zero eigenvalues, leading to divergence in optimization.

Orient's approach (BUILDO routine):

• Construct a projection matrix P that removes these 6 modes
• Optimize in the (6N-6) dimensional space
• Gradient projection: grad_proj = P^T * grad_full
• Coordinate reconstruction: x_full = x_base + P * x_proj

For 2 molecules (N=2):

• 12 DOF → 6 DOF (relative position + relative orientation)
• Simplest approach: Fix molecule 1 at origin with identity rotation
• Optimize only molecule 2's position and orientation relative to molecule 1

Constructor & Destructor Documentation

RigidBodyProjection()

occ::mults::RigidBodyProjection::RigidBodyProjection ( size_t  n_molecules )

explicit

Construct projection for N rigid bodies.

Parameters

n_molecules

Number of rigid bodies

Member Function Documentation

full_dof()

size_t occ::mults::RigidBodyProjection::full_dof ( ) const

inline

Get number of original degrees of freedom (6N)

project_coordinates()

Vec occ::mults::RigidBodyProjection::project_coordinates	(	const Vec &	x_full,
		const Vec &	x_base
	)		const

Project full coordinates to reduced space.

Given full coordinates, project to (6N-6) space relative to base: x_proj = P^T * (x_full - x_base)

Parameters

x_full	Coordinates in full 6N space
x_base	Base configuration

Returns

Coordinates in (6N-6) projected space

project_gradient()

Vec occ::mults::RigidBodyProjection::project_gradient

(

const Vec &

grad_full

)

const

Project full gradient to reduced space.

For optimization, we need: grad_proj = P^T * grad_full This removes components corresponding to global translation/rotation.

Parameters

grad_full

Gradient in full 6N space

Returns

Gradient in (6N-6) projected space

projected_dof()

size_t occ::mults::RigidBodyProjection::projected_dof ( ) const

inline

Get number of projected degrees of freedom (6N-6)

projection_matrix()

const Mat & occ::mults::RigidBodyProjection::projection_matrix ( ) const

inline

Get projection matrix (for debugging/analysis)

Returns

(6N-6) × 6N projection matrix

reconstruct_full()

Vec occ::mults::RigidBodyProjection::reconstruct_full	(	const Vec &	x_proj,
		const Vec &	x_base
	)		const

Reconstruct full coordinates from projected coordinates.

Given projected coordinates x_proj in (6N-6) space, reconstruct full coordinates: x_full = x_base + P * x_proj

Parameters

x_proj	Coordinates in (6N-6) projected space
x_base	Base configuration (typically initial geometry)

Returns

Coordinates in full 6N space

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The documentation for this class was generated from the following file:

• /home/runner/work/occ/occ/include/occ/mults/optimization_projection.h