Coverage for eminus/operators.py: 98.92%
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« prev ^ index » next coverage.py v7.6.4, created at 2024-11-01 11:47 +0000
1# SPDX-FileCopyrightText: 2021 The eminus developers
2# SPDX-License-Identifier: Apache-2.0
3"""Basis set dependent operators for a plane wave basis.
5These operators act on discretized wave functions, i.e., the arrays W.
7These W are column vectors. This has been chosen to let theory and code coincide, e.g.,
8W^dagger W becomes :code:`W.conj().T @ W`.
10The downside is that the i-th state will be accessed with W[:, i] instead of W[i].
11Choosing the i-th state makes the array 1d.
13These operators can act on six different options, namely
151. the real-space
162. the real-space (1d)
173. the full reciprocal space
184. the full reciprocal space (1d)
195. the active reciprocal space
206. the active reciprocal space (1d)
22The active space is the truncated reciprocal space by restricting it with a sphere given by ecut.
24Every spin dependence will be handled with handle_spin by calling the operators for each
25spin individually. The same goes for the handling of k-points, while for k-points W is represented
26as a list of arrays. This gives the final indexing for the k-point k, spin s, and state n of
27W[ik][s, :, n].
28"""
30import copy
32import numpy as np
33from scipy.fft import fftn, ifftn
35from . import config
36from .utils import handle_k, handle_spin, handle_torch
39# Spin handling is trivial for this operator
40@handle_k
41def O(atoms, W):
42 """Overlap operator.
44 This operator acts on the options 3, 4, 5, and 6.
46 Reference: Comput. Phys. Commun. 128, 1.
48 Args:
49 atoms: Atoms object.
50 W: Expansion coefficients of unconstrained wave functions in reciprocal space.
52 Returns:
53 The operator applied on W.
54 """
55 return atoms.Omega * W
58@handle_spin
59def L(atoms, W, ik=-1):
60 """Laplacian operator with k-point dependency.
62 This operator acts on options 3 and 5.
64 Reference: Comput. Phys. Commun. 128, 1.
66 Args:
67 atoms: Atoms object.
68 W: Expansion coefficients of unconstrained wave functions in reciprocal space.
70 Keyword Args:
71 ik: k-point index.
73 Returns:
74 The operator applied on W.
75 """
76 # Gk2 is a normal 1d row vector, reshape it so it can be applied to the column vector W
77 if len(W) == len(atoms.Gk2c[ik]):
78 Gk2 = atoms.Gk2c[ik][:, None]
79 else:
80 Gk2 = atoms.Gk2[ik][:, None]
81 return -atoms.Omega * Gk2 * W
84@handle_spin
85def Linv(atoms, W):
86 """Inverse Laplacian operator.
88 This operator acts on options 3 and 4.
90 Reference: Comput. Phys. Commun. 128, 1.
92 Args:
93 atoms: Atoms object.
94 W: Expansion coefficients of unconstrained wave functions in reciprocal space.
96 Returns:
97 The operator applied on W.
98 """
99 # Ignore the division by zero for the first elements
100 with np.errstate(divide="ignore", invalid="ignore"):
101 if W.ndim == 1:
102 # One could do some proper indexing with [1:] but indexing is slow
103 out = W / (atoms.G2 * -atoms.Omega)
104 out[0] = 0
105 else:
106 # G2 is a normal 1d row vector, reshape it so it can be applied to the column vector W
107 G2 = atoms.G2[:, None]
108 out = W / (G2 * -atoms.Omega)
109 out[0, :] = 0
110 return out
113@handle_torch
114@handle_k(mode="index")
115@handle_spin
116def I(atoms, W, ik=-1):
117 """Backward transformation from reciprocal space to real-space.
119 This operator acts on the options 3, 4, 5, and 6.
121 Reference: Comput. Phys. Commun. 128, 1.
123 Args:
124 atoms: Atoms object.
125 W: Expansion coefficients of unconstrained wave functions in reciprocal space.
127 Keyword Args:
128 ik: k-point index.
130 Returns:
131 The operator applied on W.
132 """
133 n = atoms.Ns
135 # If W is in the full space do nothing with W
136 if len(W) == len(atoms.Gk2[ik]):
137 Wfft = np.copy(W)
138 else:
139 # Fill with zeros if W is in the active space
140 if W.ndim == 1:
141 Wfft = np.zeros(n, dtype=W.dtype)
142 else:
143 Wfft = np.zeros((n, W.shape[-1]), dtype=W.dtype)
144 Wfft[atoms.active[ik]] = W
146 # `workers` sets the number of threads the FFT operates on
147 # `overwrite_x` allows writing in Wfft, but since we do not need Wfft later on, we can set this
148 # for a little bit of extra performance
149 # Normally, we would have to multiply by n in the end for the correct normalization, but we can
150 # ignore this step when properly setting the `norm` option for a faster operation
151 if W.ndim == 1:
152 Wfft = Wfft.reshape(atoms.s)
153 Finv = ifftn(Wfft, workers=config.threads, overwrite_x=True, norm="forward").ravel()
154 else:
155 # Here we reshape the input like in the 1d case but add an extra dimension in the end,
156 # holding the number of states
157 Wfft = Wfft.reshape(np.append(atoms.s, W.shape[-1]))
158 # Tell the function that the FFT only has to act on the first 3 axes
159 Finv = ifftn(
160 Wfft, workers=config.threads, overwrite_x=True, norm="forward", axes=(0, 1, 2)
161 ).reshape((n, W.shape[-1]))
162 return Finv
165@handle_torch
166@handle_k(mode="index")
167@handle_spin
168def J(atoms, W, ik=-1, full=True):
169 """Forward transformation from real-space to reciprocal space.
171 This operator acts on options 1 and 2.
173 Reference: Comput. Phys. Commun. 128, 1.
175 Args:
176 atoms: Atoms object.
177 W: Expansion coefficients of unconstrained wave functions in reciprocal space.
179 Keyword Args:
180 ik: k-point index.
181 full: Whether to transform in the full or in the active space.
183 Returns:
184 The operator applied on W.
185 """
186 n = atoms.Ns
187 Wfft = np.copy(W)
189 # `workers` sets the number of threads the FFT operates on
190 # `overwrite_x` allows writing in Wfft, but since we do not need Wfft later on, we can set this
191 # for a little bit of extra performance
192 # Normally, we would have to divide by n in the end for the correct normalization, but we can
193 # ignore this step when properly setting the `norm` option for a faster operation
194 if W.ndim == 1:
195 Wfft = Wfft.reshape(atoms.s)
196 F = fftn(Wfft, workers=config.threads, overwrite_x=True, norm="forward").ravel()
197 else:
198 Wfft = Wfft.reshape(np.append(atoms.s, W.shape[-1]))
199 F = fftn(
200 Wfft, workers=config.threads, overwrite_x=True, norm="forward", axes=(0, 1, 2)
201 ).reshape((n, W.shape[-1]))
203 # There is no way to know if J has to transform to the full or the active space
204 # but normally it transforms to the full space
205 if not full:
206 return F[atoms.active[ik]]
207 return F
210@handle_torch
211@handle_k(mode="index")
212@handle_spin
213def Idag(atoms, W, ik=-1, full=False):
214 """Conjugated backward transformation from real-space to reciprocal space.
216 This operator acts on options 1 and 2.
218 Reference: Comput. Phys. Commun. 128, 1.
220 Args:
221 atoms: Atoms object.
222 W: Expansion coefficients of unconstrained wave functions in reciprocal space.
224 Keyword Args:
225 ik: k-point index.
226 full: Whether to transform in the full or in the active space.
228 Returns:
229 The operator applied on W.
230 """
231 n = atoms.Ns
232 F = J(atoms, W, ik, full)
233 return F * n
236@handle_torch
237@handle_k(mode="index")
238@handle_spin
239def Jdag(atoms, W, ik=-1):
240 """Conjugated forward transformation from reciprocal space to real-space.
242 This operator acts on the options 3, 4, 5, and 6.
244 Reference: Comput. Phys. Commun. 128, 1.
246 Args:
247 atoms: Atoms object.
248 W: Expansion coefficients of unconstrained wave functions in reciprocal space.
250 Keyword Args:
251 ik: k-point index.
253 Returns:
254 The operator applied on W.
255 """
256 n = atoms.Ns
257 Finv = I(atoms, W, ik)
258 return Finv / n
261@handle_spin
262def K(atoms, W, ik):
263 """Preconditioning operator with k-point dependency.
265 This operator acts on options 3 and 5.
267 Reference: Comput. Mater. Sci. 14, 4.
269 Args:
270 atoms: Atoms object.
271 W: Expansion coefficients of unconstrained wave functions in reciprocal space.
272 ik: k-point index.
274 Returns:
275 The operator applied on W.
276 """
277 # Gk2c is a normal 1d row vector, reshape it so it can be applied to the column vector W
278 return W / (1 + atoms.Gk2c[ik][:, None])
281def T(atoms, W, dr):
282 """Translation operator.
284 This operator acts on options 5 and 6.
286 Reference: https://ccrma.stanford.edu/~jos/st/Shift_Theorem.html
288 Args:
289 atoms: Atoms object.
290 W: Expansion coefficients of unconstrained wave functions in reciprocal space.
291 ik: k-point index.
292 dr: Real-space shifting vector.
294 Returns:
295 The operator applied on W.
296 """
297 # We can not use a fancy decorator for this operator, so handle it here
298 if isinstance(W, np.ndarray) and W.ndim == 3:
299 return np.asarray([T(atoms, Wspin, dr) for Wspin in W])
301 if isinstance(W, np.ndarray):
302 atoms.kpts._assert_gamma_only()
303 if len(W) == len(atoms.Gk2c[0]):
304 G = atoms.G[atoms.active[0]]
305 elif len(W) == len(atoms.Gk2c[-1]):
306 G = atoms.G[atoms.active[-1]]
307 else:
308 G = atoms.G
309 factor = np.exp(-1j * G @ dr)
310 if W.ndim == 2:
311 factor = factor[:, None]
312 return factor * W
314 # If W is a list we have to account for k-points
315 Wshift = copy.deepcopy(W)
316 for ik in range(atoms.kpts.Nk):
317 # Do the shift by multiplying a phase factor, given by the shift theorem
318 if W[ik].shape[1] == len(atoms.Gk2c[ik]):
319 Gk = atoms.G[atoms.active[ik]] + atoms.kpts.k[ik]
320 else:
321 Gk = atoms.G + atoms.kpts.k[ik]
322 Wshift[ik] = np.exp(-1j * Gk @ dr)[:, None] * W[ik]
323 return Wshift