def kpath(vecs, N=10):
"""Simple k-path. Given a set of K vectors (special points in the BZ),
generate a "fine path" of N*(K-1)+1 vectors along the path defined by the
vectors in `vecs`. The K vectors are the "vertices" of the k-path and we
construct the fine path by connecting the vertices by their distance
vectors and placing N points on each connection edge.
Parameters
----------
vecs : array (K,M)
Array with K vectors of the Brillouin zone (so M = 3 usually :)
N : int
Returns
-------
new_vecs : array (N*(K-1)+1,M)
Array with a fine grid of vectors along the path
defined by `vecs`.
Notes
-----
This is the simplest method one can think of. Points on the "fine path" are
not equally distributed. The distance between 2 vertices (k-points) doesn't
matter, you will always get N points between them. For a smooth dispersion
plot, you need N=20 or more.
"""
K = vecs.shape[0]
new_vecs = np.empty(((K - 1) * N + 1, vecs.shape[1]), dtype=float)
for i in range(1, K):
new_vecs[(i - 1) * N : i * N, :] = num.vlinspace(vecs[i - 1, :], vecs[i, :], N, endpoint=False)
new_vecs[-1, :] = vecs[-1, :]
return new_vecs
def test_vlinspace():
aa = np.array([0,0,0])
bb = np.array([1,1,1])
np.testing.assert_array_equal(vlinspace(aa,bb,1), aa[None,:])
np.testing.assert_array_equal(vlinspace(aa,bb,2),
np.array([aa,bb]))
tgt = np.array([aa, [0.5,0.5,0.5], bb])
np.testing.assert_array_equal(vlinspace(aa,bb,3), tgt)
tgt = np.array([aa, [1/3.]*3, [2/3.]*3, bb])
np.testing.assert_array_almost_equal(vlinspace(aa,bb,4), tgt)
tgt = np.array([[ 0. , 0. , 0. ],
[ 0.25, 0.25, 0.25],
[ 0.5 , 0.5 , 0.5 ],
[ 0.75, 0.75, 0.75]])
np.testing.assert_array_equal(vlinspace(aa,bb,4,endpoint=False),
tgt)
aa = np.array([-1,-1,-1])
bb = np.array([1,1,1])
tgt = np.array([[ -1. , -1. , -1. ],
[ 0, 0, 0],
[ 1, 1, 1]])
np.testing.assert_array_equal(vlinspace(aa,bb,3),
tgt)
def kpath(vecs, N=10):
"""Simple k-path. Given a set of K vectors (special points in the BZ),
generate a "fine path" of N*(K-1)+1 vectors along the path defined by the
vectors in `vecs`. The K vectors are the "vertices" of the k-path and we
construct the fine path by connecting the vertices by their distance
vectors and placing N points on each connection edge.
Parameters
----------
vecs : array (K,M)
Array with K vectors of the Brillouin zone (so M = 3 usually :)
N : int
Returns
-------
new_vecs : array (N*(K-1)+1,M)
Array with a fine grid of vectors along the path
defined by `vecs`.
Notes
-----
This is the simplest method one can think of. Points on the "fine path" are
not equally distributed. The distance between 2 vertices (k-points) doesn't
matter, you will always get N points between them. For a smooth dispersion
plot, you need N=20 or more.
"""
K = vecs.shape[0]
new_vecs = np.empty(((K - 1) * N + 1, vecs.shape[1]), dtype=float)
for i in range(1, K):
new_vecs[(i - 1) * N:i * N, :] = num.vlinspace(vecs[i - 1, :],
vecs[i, :],
N,
endpoint=False)
new_vecs[-1, :] = vecs[-1, :]
return new_vecs
def test_vlinspace():
aa = np.array([0, 0, 0])
bb = np.array([1, 1, 1])
np.testing.assert_array_equal(vlinspace(aa, bb, 1), aa[None, :])
np.testing.assert_array_equal(vlinspace(aa, bb, 2), np.array([aa, bb]))
tgt = np.array([aa, [0.5, 0.5, 0.5], bb])
np.testing.assert_array_equal(vlinspace(aa, bb, 3), tgt)
tgt = np.array([aa, [1 / 3.] * 3, [2 / 3.] * 3, bb])
np.testing.assert_array_almost_equal(vlinspace(aa, bb, 4), tgt)
tgt = np.array([[0., 0., 0.], [0.25, 0.25, 0.25], [0.5, 0.5, 0.5],
[0.75, 0.75, 0.75]])
np.testing.assert_array_equal(vlinspace(aa, bb, 4, endpoint=False), tgt)
aa = np.array([-1, -1, -1])
bb = np.array([1, 1, 1])
tgt = np.array([[-1., -1., -1.], [0, 0, 0], [1, 1, 1]])
np.testing.assert_array_equal(vlinspace(aa, bb, 3), tgt)