from ATK.KohnSham import *
from numpy import *

def cross (a,b):
    return array([a[1]*b[2]-a[2]*b[1],
                  a[2]*b[0]-a[0]*b[2],
                  a[0]*b[1]-a[1]*b[0]])

def invertVectors (v):
    v1 = v[0]
    v2 = v[1]
    v3 = v[2]
    norm = dot(v1,cross(v2,v3))
    r1 = cross(v2,v3)
    r2 = cross(v3,v1)
    r3 = cross(v1,v2)
    return 2.*pi*array([r1,r2,r3])/norm

def primitiveVectors (lattice):
    V = identity(3)*1.
    for i in range(3):
        for j in range(3):
            V[i,j] = lattice.primitiveVectors()[i][j].inUnitsOf(Ang)
    return V
    
def reciprocalVectors (bulk_config):
    return invertVectors(primitiveVectors(bulk_config.bravaisLattice()))
    
def convertCartesianCoordsToLattice (bulk_config,cartesian_coordinates):
    import numpy
    from numpy.linear_algebra import inverse as matrixinverse
    V = numpy.transpose(reciprocalVectors(bulk_config))
    return numpy.matrixmultiply(
        matrixinverse(V),
        numpy.transpose(
            cartesian_coordinates
            )
        )