1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
|
!
! Copyright (C) 1996-2016 The SIESTA group
! This file is distributed under the terms of the
! GNU General Public License: see COPYING in the top directory
! or http://www.gnu.org/copyleft/gpl.txt.
! See Docs/Contributors.txt for a list of contributors.
!
subroutine pdoskp(nspin, nuo, no, maxspn, maxnh,
. maxo, numh, listhptr, listh, H, S,
. E1, E2, nhist, sigma,
. xij, indxuo, nk, kpoint, wk, eo,
. Haux, Saux, psi, dtot, dpr, nuotot )
C **********************************************************************
C Find the density of states projected onto the atomic orbitals
C D_mu(E) = Sum(n,k,nu) C(mu,n,k) C(nu,n,k) S(mu,nu,k) Delta(E-E(n,k))
C where n run over all the bands between two given energies
C Written by J. Junquera and E. Artacho. Nov' 99
C Modified version for parallel execution over K points by J.D. Gale
C March 2005
C **** INPUT *********************************************************
C integer nspin : Number of spin components (1 or 2)
C integer nuo : Number of atomic orbitals in the unit cell
C integer NO : Number of atomic orbitals in the supercell
C integer maxspn : Second dimension of eo and qo
C (maximum number of differents spin polarizations)
C integer maxnh : Maximum number of orbitals interacting
C with any orbital
C integer maxo : First dimension of eo
C integer numh(nuo) : Number of nonzero elements of each row
C of hamiltonian matrix
C integer listhptr(nuo) : Pointer to each row (-1) of the
C hamiltonian matrix
C integer listh(maxnh) : Nonzero hamiltonian-matrix element
C column indexes for each matrix row
C real*8 H(maxnh,nspin) : Hamiltonian in sparse format
C real*8 S(maxnh) : Overlap in sparse format
C real*8 E1, E2 : Energy range for density-matrix states
C (to find local density of states)
C Not used if e1 > e2
C integer nhist : Number of the subdivisions of the histogram
C real*8 sigma : Width of the gaussian to expand the eigenvectors
C real*8 xij(3,maxnh) : Vectors between orbital centers (sparse)
C (not used if only gamma point)
C integer indxuo(no) : Index of equivalent orbital in unit cell
C integer nk : Number of k points
C real*8 kpoint(3,nk) : k point vectors
C real*8 wk(nk) : Weights for k points
C real*8 eo(maxo,maxspn,nk): Eigenvalues
C integer nuotot : Total number of orbitals per unit cell
C **** AUXILIARY *****************************************************
C real*8 Haux(2,nuo,nuo) : Auxiliary space for the hamiltonian matrix
C real*8 Saux(2,nuo,nuo) : Auxiliary space for the overlap matrix
C real*8 psi(2,nuo,nuo) : Auxiliary space for the eigenvectors
C **** OUTPUT ********************************************************
C real*8 dtot(nhist,2) : Total density of states
C real*8 dpr(nhist,nuo,2): Proyected density of states
C **********************************************************************
use precision
use parallel, only : Node, Nodes
use parallelsubs, only : GetNodeOrbs, LocalToGlobalOrb
use parallelsubs, only : WhichNodeOrb, GlobalToLocalOrb
use units, only : pi
use alloc, only : re_alloc, de_alloc
#ifdef MPI
use mpi_siesta
#endif
use sys, only : die
implicit none
integer
. nspin, nuo, no, maxspn, maxnh, NK,
. maxo, nhist, nuotot
integer
. numh(nuo), listhptr(nuo), listh(maxnh),
. indxuo(no)
real(dp)
. H(maxnh,nspin), S(maxnh), E1, E2, sigma,
. xij(3,maxnh), kpoint(3,nk), eo(maxo,maxspn,nk),
. Haux(2,nuotot,nuotot), Saux(2,nuotot,nuotot),
. psi(2,nuotot,nuotot),
. dtot(nhist,2), dpr(nhist,nuotot,2), wk(nk)
C Internal variables ---------------------------------------------------
integer
. ik, is, iio, io, iuo, juo, j, jo, ihist, iband, ind, ierror,
. maxnhg, nuog, BNode
integer, dimension(:), pointer :: numhg, listhptrg, listhg
real(dp)
. kxij, Ckxij, Skxij, delta, ener, diff, pipj1, pipj2,
. pipjS1, gauss, norm, wksum
real(dp), dimension(:), pointer :: Snew
real(dp), dimension(:,:), pointer :: Hnew, xijloc
#ifdef MPI
integer :: MPIerror
real(dp), dimension(:,:,:), pointer :: Sloc
#endif
external cdiag
C Initialize some variables
delta = (E2 - E1)/nhist
C Globalise list arrays - assumes listh and listd are the same
C Allocate local memory for global list arrays
nullify( numhg )
call re_alloc( numhg, 1, nuotot, name='numhg', routine='pdoskp' )
nullify( listhptrg )
call re_alloc( listhptrg, 1, nuotot, name='listhptrg',
& routine='pdoskp' )
C Globalise numh
do io = 1,nuotot
call WhichNodeOrb(io,Nodes,BNode)
if (Node.eq.BNode) then
call GlobalToLocalOrb(io,Node,Nodes,iio)
numhg(io) = numh(iio)
endif
#ifdef MPI
call MPI_Bcast(numhg(io),1,MPI_integer,BNode,
. MPI_Comm_World,MPIerror)
#endif
enddo
C Build global listhptr
listhptrg(1) = 0
do io = 2,nuotot
listhptrg(io) = listhptrg(io-1) + numhg(io-1)
enddo
C Globalse listh
maxnhg = listhptrg(nuotot) + numhg(nuotot)
nullify( listhg )
call re_alloc( listhg, 1, maxnhg, name='listhg',
& routine='pdoskp' )
do io = 1,nuotot
call WhichNodeOrb(io,Nodes,BNode)
if (Node.eq.BNode) then
call GlobalToLocalOrb(io,Node,Nodes,iio)
do jo = 1,numhg(io)
listhg(listhptrg(io)+1:listhptrg(io)+numhg(io)) =
. listh(listhptr(iio)+1:listhptr(iio)+numh(iio))
enddo
endif
#ifdef MPI
call MPI_Bcast(listhg(listhptrg(io)+1),numhg(io),MPI_integer,
. BNode,MPI_Comm_World,MPIerror)
#endif
enddo
C Create new distribution of H and S
nuog = nuotot
nullify( Snew )
call re_alloc( Snew, 1, maxnhg, name='Snew',
& routine='pdoskp' )
nullify( Hnew )
call re_alloc( Hnew, 1, maxnhg, 1, nspin, name='Hnew',
& routine='pdoskp' )
nullify( xijloc )
call re_alloc( xijloc, 1, 3, 1, maxnhg, name='xijloc',
& routine='pdoskp' )
do io = 1,nuotot
call WhichNodeOrb(io,Nodes,BNode)
if (Node.eq.BNode) then
call GlobalToLocalOrb(io,Node,Nodes,iio)
do is = 1,nspin
do jo = 1,numh(iio)
Hnew(listhptrg(io)+jo,is) = H(listhptr(iio)+jo,is)
enddo
enddo
do jo = 1,numh(iio)
Snew(listhptrg(io)+jo) = S(listhptr(iio)+jo)
enddo
do jo = 1,numh(iio)
xijloc(1:3,listhptrg(io)+jo) = xij(1:3,listhptr(iio)+jo)
enddo
endif
#ifdef MPI
do is = 1,nspin
call MPI_Bcast(Hnew(listhptrg(io)+1,is),numhg(io),
. MPI_double_precision,BNode,MPI_Comm_World,MPIerror)
enddo
call MPI_Bcast(Snew(listhptrg(io)+1),numhg(io),
. MPI_double_precision,BNode,MPI_Comm_World,MPIerror)
call MPI_Bcast(xijloc(1,listhptrg(io)+1),3*numhg(io),
. MPI_double_precision,BNode,MPI_Comm_World,MPIerror)
#endif
enddo
C Solve eigenvalue problem for each k-point
do is = 1,nspin
do ik = 1+Node,nk,Nodes
C Initialize auxiliary variables
do iuo = 1,nuog
do juo = 1,nuotot
Saux(1,juo,iuo) = 0.0d0
Saux(2,juo,iuo) = 0.0d0
Haux(1,juo,iuo) = 0.0d0
Haux(2,juo,iuo) = 0.0d0
enddo
enddo
do io = 1,nuog
do j = 1,numhg(io)
ind = listhptrg(io) + j
jo = listhg(ind)
iuo = indxuo(io)
juo = indxuo(jo)
C Calculate the phases k*r_ij
kxij = kpoint(1,ik) * xijloc(1,ind) +
. kpoint(2,ik) * xijloc(2,ind) +
. kpoint(3,ik) * xijloc(3,ind)
Ckxij = cos(kxij)
Skxij = sin(kxij)
C Calculate the Hamiltonian and the overlap in k space
C H(k) = Sum(R) exp(i*k*R) * H(R)
Saux(1,juo,iuo) = Saux(1,juo,iuo) + Snew(ind) * Ckxij
Saux(2,juo,iuo) = Saux(2,juo,iuo) - Snew(ind) * Skxij
Haux(1,juo,iuo) = Haux(1,juo,iuo) + Hnew(ind,is) * Ckxij
Haux(2,juo,iuo) = Haux(2,juo,iuo) - Hnew(ind,is) * Skxij
enddo
enddo
C Diagonalize for each k point
call cdiag( Haux, Saux, nuotot, nuog, nuotot,
. eo(1,is,ik), psi, nuotot, 1, ierror, -1 ) !dummy blocksize
C Check error flag and take appropriate action
if (ierror.gt.0) then
call die('Terminating due to failed diagonalisation')
elseif (ierror.lt.0) then
C Repeat diagonalisation with increased memory to handle clustering
do iuo = 1,nuog
do juo = 1,nuotot
Saux(1,juo,iuo) = 0.0d0
Saux(2,juo,iuo) = 0.0d0
Haux(1,juo,iuo) = 0.0d0
Haux(2,juo,iuo) = 0.0d0
enddo
enddo
do io = 1, nuog
do j = 1, numhg(io)
ind = listhptrg(io) + j
jo = listhg(ind)
iuo = indxuo(io)
juo = indxuo(jo)
kxij = kpoint(1,ik) * xijloc(1,ind) +
. kpoint(2,ik) * xijloc(2,ind) +
. kpoint(3,ik) * xijloc(3,ind)
Ckxij = cos(kxij)
Skxij = sin(kxij)
Saux(1,juo,iuo) = Saux(1,juo,iuo) + Snew(ind)*Ckxij
Saux(2,juo,iuo) = Saux(2,juo,iuo) - Snew(ind)*Skxij
Haux(1,juo,iuo) = Haux(1,juo,iuo) + Hnew(ind,is)*Ckxij
Haux(2,juo,iuo) = Haux(2,juo,iuo) - Hnew(ind,is)*Skxij
enddo
enddo
call cdiag( Haux, Saux, nuotot, nuog, nuotot,
. eo(1,is,ik), psi, nuotot, 1, ierror, -1 ) !dummy blocksize
endif
C Recalculate again the overlap matrix in k-space
do iuo = 1,nuog
do juo = 1,nuotot
Saux(1,juo,iuo) = 0.0d0
Saux(2,juo,iuo) = 0.0d0
enddo
enddo
do io = 1,nuog
do j = 1,numhg(io)
ind = listhptrg(io) + j
jo = listhg(ind)
iuo = indxuo(io)
juo = indxuo(jo)
C Calculate the phases k*r_ij
kxij = kpoint(1,ik) * xijloc(1,ind) +
. kpoint(2,ik) * xijloc(2,ind) +
. kpoint(3,ik) * xijloc(3,ind)
ckxij = cos(kxij)
skxij = sin(kxij)
! Since we are doing element wise multiplications (and not dot-products)
! we might as well setup the transpose S(k)^T == S(-k) because this will
! mean that we can do a simpler multiplication further down
Saux(1,juo,iuo) = Saux(1,juo,iuo) + Snew(ind) * ckxij
Saux(2,juo,iuo) = Saux(2,juo,iuo) + Snew(ind) * skxij
enddo
enddo
C Loop over all the energy range
do ihist = 1,nhist
ener = E1 + (ihist - 1) * delta
do 170 iband = 1,nuog
diff = (ener - eo(iband,is,ik))**2 / (sigma**2)
if (diff .gt. 15.0d0) then
cycle
else
gauss = exp(-diff) * wk(ik)
dtot(ihist,is) = dtot(ihist,is) + gauss
do juo = 1, nuotot
do iuo = 1, nuotot
! This is: psi(iuo) * psi(juo)^*
pipj1 = psi(1,iuo,iband) * psi(1,juo,iband) +
. psi(2,iuo,iband) * psi(2,juo,iband)
pipj2 = - psi(1,iuo,iband) * psi(2,juo,iband) +
. psi(2,iuo,iband) * psi(1,juo,iband)
pipjS1 = pipj1*Saux(1,iuo,juo)-pipj2*Saux(2,iuo,juo)
dpr(ihist,juo,is) = dpr(ihist,juo,is) + pipjS1*gauss
enddo
enddo
endif
170 enddo
enddo
enddo
enddo
C Free local memory from computation of dpr
call de_alloc( xijloc, name='xijloc' )
call de_alloc( Hnew, name='Hnew' )
call de_alloc( Snew, name='Snew' )
call de_alloc( listhg, name='listhg' )
call de_alloc( listhptrg, name='listhptrg' )
call de_alloc( numhg, name='numhg' )
#ifdef MPI
C Allocate workspace array for global reduction
nullify( Sloc )
call re_alloc( Sloc, 1, nhist, 1, max(nuotot,nspin),
& 1, nspin, name='Sloc', routine='pdoskp' )
C Global reduction of dpr matrix
Sloc(1:nhist,1:nuotot,1:nspin) = 0.0d0
call MPI_AllReduce(dpr(1,1,1),Sloc(1,1,1),nhist*nuotot*nspin,
. MPI_double_precision,MPI_sum,MPI_Comm_World,MPIerror)
dpr(1:nhist,1:nuotot,1:nspin) = Sloc(1:nhist,1:nuotot,1:nspin)
C Global reduction of dtot matrix
Sloc(1:nhist,1:nspin,1) = 0.0d0
call MPI_AllReduce(dtot(1,1),Sloc(1,1,1),nhist*nspin,
. MPI_double_precision,MPI_sum,MPI_Comm_World,MPIerror)
dtot(1:nhist,1:nspin) = Sloc(1:nhist,1:nspin,1)
C Free workspace array for global reduction
call de_alloc( Sloc, name='Sloc' )
#endif
wksum = 0.0d0
do ik = 1,nk
wksum = wksum + wk(ik)
enddo
norm = sigma * sqrt(pi) * wksum
do ihist = 1,nhist
do is = 1,nspin
dtot(ihist,is) = dtot(ihist,is) / norm
do iuo = 1,nuotot
dpr(ihist,iuo,is) = dpr(ihist,iuo,is) /norm
enddo
enddo
enddo
return
end
|