def test_tripoints_input_rescale(self):
# Test at single points
x = np.array([(0, 0), (-5, -5), (-5, 5), (5, 5), (2.5, 3)],
dtype=np.double)
y = np.arange(x.shape[0], dtype=np.double)
y = y - 3j * y
tri = qhull.Delaunay(x)
yi = interpnd.LinearNDInterpolator(tri.points, y)(x)
yi_rescale = interpnd.LinearNDInterpolator(tri.points, y,
rescale=True)(x)
assert_almost_equal(yi, yi_rescale)
def test_smoketest_rescale(self):
# Test at single points
x = np.array([(0, 0), (-5, -5), (-5, 5), (5, 5), (2.5, 3)],
dtype=np.double)
y = np.arange(x.shape[0], dtype=np.double)
yi = interpnd.LinearNDInterpolator(x, y, rescale=True)(x)
assert_almost_equal(y, yi)
def test_smoketest_alternate(self):
# Test at single points, alternate calling convention
x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
dtype=np.double)
y = np.arange(x.shape[0], dtype=np.double)
yi = interpnd.LinearNDInterpolator((x[:,0], x[:,1]), y)(x[:,0], x[:,1])
assert_almost_equal(y, yi)
def test_smoketest(self):
# Test at single points
x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
dtype=np.double)
y = np.arange(x.shape[0], dtype=np.double)
yi = interpnd.LinearNDInterpolator(x, y)(x)
assert_almost_equal(y, yi)
def test_square_rescale(self):
# Test barycentric interpolation on a rectangle with rescaling
# agaings the same implementation without rescaling
points = np.array([(0,0), (0,100), (10,100), (10,0)], dtype=np.double)
values = np.array([1., 2., -3., 5.], dtype=np.double)
xx, yy = np.broadcast_arrays(np.linspace(0, 10, 14)[:,None],
np.linspace(0, 100, 14)[None,:])
xx = xx.ravel()
yy = yy.ravel()
xi = np.array([xx, yy]).T.copy()
zi = interpnd.LinearNDInterpolator(points, values)(xi)
zi_rescaled = interpnd.LinearNDInterpolator(points, values,
rescale=True)(xi)
assert_almost_equal(zi, zi_rescaled)
def test_pickle(self):
# Test at single points
np.random.seed(1234)
x = np.random.rand(30, 2)
y = np.random.rand(30) + 1j * np.random.rand(30)
ip = interpnd.LinearNDInterpolator(x, y)
ip2 = pickle.loads(pickle.dumps(ip))
assert_almost_equal(ip(0.5, 0.5), ip2(0.5, 0.5))
def test_tri_input(self):
# Test at single points
x = np.array([(0,0), (-0.5,-0.5), (-0.5,0.5), (0.5, 0.5), (0.25, 0.3)],
dtype=np.double)
y = np.arange(x.shape[0], dtype=np.double)
y = y - 3j*y
tri = qhull.Delaunay(x)
yi = interpnd.LinearNDInterpolator(tri, y)(x)
assert_almost_equal(y, yi)
def test_tri_input_rescale(self):
# Test at single points
x = np.array([(0, 0), (-5, -5), (-5, 5), (5, 5), (2.5, 3)],
dtype=np.double)
y = np.arange(x.shape[0], dtype=np.double)
y = y - 3j * y
tri = qhull.Delaunay(x)
match = ("Rescaling is not supported when passing a "
"Delaunay triangulation as ``points``.")
with pytest.raises(ValueError, match=match):
interpnd.LinearNDInterpolator(tri, y, rescale=True)(x)
def test_tri_input_rescale(self):
# Test at single points
x = np.array([(0, 0), (-5, -5), (-5, 5), (5, 5), (2.5, 3)],
dtype=np.double)
y = np.arange(x.shape[0], dtype=np.double)
y = y - 3j * y
tri = qhull.Delaunay(x)
try:
interpnd.LinearNDInterpolator(tri, y, rescale=True)(x)
except ValueError as e:
if str(e) != ("Rescaling is not supported when passing a "
"Delaunay triangulation as ``points``."):
raise
except:
raise
def test_square(self):
# Test barycentric interpolation on a square against a manual
# implementation
points = np.array([(0,0), (0,1), (1,1), (1,0)], dtype=np.double)
values = np.array([1., 2., -3., 5.], dtype=np.double)
# NB: assume triangles (0, 1, 3) and (1, 2, 3)
#
# 1----2
# | \ |
# | \ |
# 0----3
def ip(x, y):
t1 = (x + y <= 1)
t2 = ~t1
x1 = x[t1]
y1 = y[t1]
x2 = x[t2]
y2 = y[t2]
z = 0*x
z[t1] = (values[0]*(1 - x1 - y1)
+ values[1]*y1
+ values[3]*x1)
z[t2] = (values[2]*(x2 + y2 - 1)
+ values[1]*(1 - x2)
+ values[3]*(1 - y2))
return z
xx, yy = np.broadcast_arrays(np.linspace(0, 1, 14)[:,None],
np.linspace(0, 1, 14)[None,:])
xx = xx.ravel()
yy = yy.ravel()
xi = np.array([xx, yy]).T.copy()
zi = interpnd.LinearNDInterpolator(points, values)(xi)
assert_almost_equal(zi, ip(xx, yy))
def __init__(self,astruct,mesh,evals,fermi_energy):
import spglib,numpy
cell=astruct_to_cell(astruct)
self.lattice=cell[0]
#celltmp=[ a if a!=float('inf') else 1.0 for a in astruct['cell']]
#self.lattice=numpy.diag(celltmp)
#print 'lattice',self.lattice
#pos=[ [ a/b if b!=float('inf') else 0.0 for a,b in zip(at.values()[0], celltmp)]for at in astruct['positions']]
#atoms=[ at.keys()[0] for at in astruct['positions']]
#ianames,iatype=numpy.unique(atoms,return_inverse=True) #[1,]*4+[2,]*4 #we should write a function for the iatype
#print 'iatype', iatype
#cell=(self.lattice,pos,iatype)
safe_print('spacegroup',spglib.get_spacegroup(cell, symprec=1e-5))
#then define the pathes and special points
import ase.dft.kpoints as ase
#we should adapt the 'cubic'
cell_tmp=astruct['cell']
#print 'cell',cell_tmp,numpy.allclose(cell_tmp,[cell_tmp[0],]*len(cell_tmp))
if numpy.allclose(cell_tmp,[cell_tmp[0],]*len(cell_tmp)):
lattice_string='cubic'
else:
lattice_string='orthorhombic'
safe_print('Lattice found:',lattice_string)
self.special_points=ase.get_special_points(lattice_string, self.lattice, eps=0.0001)
self.special_paths=ase.parse_path_string(ase.special_paths[lattice_string])
self.fermi_energy=fermi_energy
#dataset = spglib.get_symmetry_dataset(cell, symprec=1e-3)
#print dataset
#the shift has also to be put if present
mapping, grid = spglib.get_ir_reciprocal_mesh(mesh, cell, is_shift=[0, 0, 0])
lookup=[]
for ikpt in numpy.unique(mapping):
ltmp=[]
for ind, (m, g) in enumerate(zip(mapping, grid)):
if m==ikpt:
ltmp.append((g,ind))
lookup.append(ltmp)
safe_print('irreductible k-points',len(lookup))
#print 'mapping',mapping
#print 'grid',len(grid),numpy.max(grid)
coords=numpy.array(grid, dtype = numpy.float)/mesh
#print 'coords',coords
#print 'shape',coords.shape
#print grid #[ x+mesh[0]*y+mesh[0]*mesh[1]*z for x,y,z in grid]
#brillouin zone
kp=numpy.array([ k.kpt for k in evals])
ourkpt=numpy.rint(kp*(numpy.array(mesh))).astype(int)
#print ourkpt
bz=numpy.ndarray((coords.shape[0],evals[0].size),dtype=float)
#print bz
shift=(numpy.array(mesh)-1)/2
#print 'shift',shift
for ik in lookup:
irrk=None
for orbs,bzk in zip(evals,ourkpt):
for (kt,ind) in ik:
if (bzk==kt).all():
irrk=orbs
#print 'hello',orbs.kpt,kt
break
if irrk is not None: break
if irrk is None:
safe_print( 'error in ik',ik)
safe_print( 'our',ourkpt)
safe_print( 'spglib',grid)
safe_print( 'mapping',mapping)
for (kt,ind) in ik:
#r=kt+shift
#ind=numpy.argwhere([(g==kt).all() for g in grid])
#print 'ik',kt,r,ind
#print irrk.shape, bz.shape
#bz[r[0],r[1],r[2],:]=irrk.reshape(irrk.size)
bz[ind,:]=irrk.reshape(irrk.size)
#duplicate coordinates for the interpolation
bztmp=bz#.reshape((mesh[0]*mesh[1]*mesh[2], -1))
#print bztmp
ndup=7
duplicates=[[-1,0,0],[1,0,0],[0,-1,0],[0,1,0],[0,0,-1],[0,0,1]]
bztot=numpy.ndarray((ndup,bztmp.shape[0],bztmp.shape[1]))
bztot[0,:,:]=bztmp
ctot=numpy.ndarray((ndup,coords.shape[0],coords.shape[1]))
ctot[0,:,:]=coords
for i,sh in enumerate(duplicates):
bztot[i+1,:,:]=bztmp
ctot[i+1,:,:]=coords+sh
#print 'coors',coords,coords+[1.0,0,0]
bztot=bztot.reshape((ndup*bztmp.shape[0], -1))
ctot=ctot.reshape((ndup*coords.shape[0], -1))
import scipy.interpolate.interpnd as interpnd
self.interpolator=interpnd.LinearNDInterpolator(ctot,bztot)
#sanity check of the interpolation
sanity=0.0
for kpt in evals:
diff=numpy.ravel(numpy.ravel(kpt)-numpy.ravel(self.interpolator([ kpt.kpt])))
sanity=max(sanity,numpy.dot(diff,diff))
print('Interpolation bias',sanity)