qpms.lattices2d Namespace Reference

Data Structures
class	LatticeType

Functions
def	reduceBasisSingle (b1, b2)
def	shortestBase3 (b1, b2)
def	shortestBase46 (b1, b2, tolerance=1e-13)
def	is_obtuse (b1, b2, tolerance=1e-13)
def	classifyLatticeSingle (b1, b2, tolerance=1e-13)
def	range2D (maxN, mini=1, minj=0, minN=0)
def	generateLattice (b1, b2, maxlayer=5, include_origin=False, order='leaves')
def	generateLatticeDisk (b1, b2, r, include_origin=False, order='leaves')
def	cellCornersWS (b1, b2)
def	cutWS (points, b1, b2, scale=1., tolerance=1e-13)
def	filledWS (b1, b2, density=10, scale=1.)
def	reciprocalBasis1 (*pargs)
def	reciprocalBasis2pi (*pargs)
def	filledWS2 (b1, b2, density=10, scale=1.)
def	change_basis (srcbasis, destbasis, srccoords, srccoordsaxis=-1, lattice=True)

Variables
	nx = None

Detailed Description

These functions are mostly deprecated by the C counterparts from lattices.h.
This file is still kept for reference, but might be removed in the future.

Function Documentation

cellCornersWS()

def qpms.lattices2d.cellCornersWS	(		b1,
			b2
	)

Given basis vectors, returns the corners of the Wigner-Seitz unit cell
(w1, w2, -w1, w2) for rectangular and square lattice or
(w1, w2, w3, -w1, -w2, -w3) otherwise

classifyLatticeSingle()

def qpms.lattices2d.classifyLatticeSingle	(		b1,
			b2,
			tolerance = 1e-13
	)

Given two basis vectors, returns 2D Bravais lattice type.
Tolerance is relative.
TODO doc

cutWS()

def qpms.lattices2d.cutWS	(		points,
			b1,
			b2,
			scale = 1.,
			tolerance = 1e-13
	)

From given points, return only those that are inside (or on the edge of)
the Wigner-Seitz cell of a (scale*b1, scale*b2)-based lattice.

filledWS()

def qpms.lattices2d.filledWS	(		b1,
			b2,
			density = 10,
			scale = 1.
	)

TODO doc
TODO more intelligent generation, anisotropy balancing etc.

range2D()

def qpms.lattices2d.range2D	(		maxN,
			mini = 1,
			minj = 0,
			minN = 0
	)

"Triangle indices"
Generates pairs of non-negative integer indices (i, j) such that
minN ≤ i + j ≤ maxN, i ≥ mini, j ≥ minj.
TODO doc and possibly different orderings

reduceBasisSingle()

def qpms.lattices2d.reduceBasisSingle	(		b1,
			b2
	)

Lagrange-Gauss reduction of a 2D basis.
cf. https://www.math.auckland.ac.nz/~sgal018/crypto-book/ch17.pdf
inputs and outputs are (2,)-shaped numpy arrays
The output shall satisfy |b1| <= |b2| <= |b2 - b1| 
TODO doc

TODO perhaps have the (on-demand?) guarantee of obtuse angle between b1, b2?
TODO possibility of returning the (in-order, no-obtuse angles) b as well?

shortestBase3()

def qpms.lattices2d.shortestBase3	(		b1,
			b2
	)

returns the "ordered shortest triple" of base vectors (each pair from 
the triple is a base) and there may not be obtuse angle between b1, b2
and between b2, b3