CVSpace

CVSpace(variables, bounded=False)

The domain of the collective variables: grid, periodicity, boundaries.

Parameters:

Name	Type	Description	Default
variables		Sequence of collective variable descriptions. Each must expose minValue, maxValue, gridWidth and periodic; an openmm.app.BiasVariable qualifies.	required
bounded	bool	Whether non-periodic variables have reflective boundaries. When true the internal grid is tripled with mirrored copies on each side, and foldedGrid folds them back.	False

gridShape property

gridShape

Shape of the CV-space grid, slowest axis first.

numDimensions property

numDimensions

Number of collective variables.

axisDisplacement

axisDisplacement(index, start, end)

Displacement along one axis, minimum-image if that axis is periodic.

axisGridDistances

axisGridDistances(index, centers)

Distances from each of centers to every node of one axis.

A 2-D array, one row per center, matching gridDistances for a single center: minimum-image on a periodic axis, whose last node repeats the first, and over the tripled grid on a reflective axis.

axisImages

axisImages(index, value)

The images of one coordinate under the reflective walls of its axis.

value itself, plus its reflections off both walls when the space is bounded and the axis is not periodic. mirrorPositions returns every combination of these per-axis images.

closestNode

closestNode(position)

Index of the grid node nearest to position, in gridShape order.

displacement

displacement(position, endpoint)

Displacement from position to endpoint, minimum-image if periodic.

endpoint

endpoint(position, displacement)

Endpoint reached from position, wrapped into the periodic domain.

foldedAxis

foldedAxis(index, values)

Fold one axis's tripled bounded profile back onto the domain, in log space.

A kernel factorizes over the CVs, and its mirror images under the reflective walls are every combination of per-axis reflections, so folding each axis's one-dimensional profile before the outer product gives exactly what foldedGrid gives on the full tripled grid, at a fraction of the cost.

foldedAxisRows

foldedAxisRows(index, values)

Fold every row of a 2-D array of log profiles.

Applies foldedAxis row by row.

foldedGrid

foldedGrid(values)

Fold a tripled bounded grid back onto the physical domain, in log space.

gridDistances

gridDistances(position)

Per-axis distances from position to every grid node.

mirrorPositions

mirrorPositions(position)

Every image of position under the reflective boundaries.

For each non-periodic dimension, reflecting a point off both walls gives two images in addition to the point itself; the images across every dimension combine multiplicatively (a corner sees images of images). Unbounded spaces, or spaces with only periodic CVs, have no images: [position] is returned unchanged.

A kernel centered at any one of these images is, by the symmetry of reflection, exactly as far from a given query point as the original kernel is from that point's own mirror image -- so summing a kernel's density over these images is equivalent to summing the query point's images against the one true kernel, which is what the tripled evaluation grid does. Used to keep Kernel.evaluate (arbitrary points) consistent with Kernel.evaluateOnGrid.

periodicCopies

periodicCopies(values)

Make the last node along every periodic axis an exact copy of the first.

The two nodes are the same point. Evaluating them separately can round differently (a matrix product, for one, need not give equal columns equal sums), and OpenMM rejects a periodic table whose ends differ at all.