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python: Commit

libtetrabz python package


Commit MetaInfo

Revision8f8c8198e91324b8d0a3a63d7102d24d2a50dec0 (tree)
Zeit2022-03-31 13:39:58
AutorMitsuaki Kawamura <kawamitsuaki@gmai...>
CommiterMitsuaki Kawamura

Log Message

Update tutorial

Ändern Zusammenfassung

  • add: doc/fig/honeycomb.svg (diff)
  • delete: setup.cfg
  • add: setup.py (diff)
  • delete: src/c/__init__.py
  • delete: src/c/libtetrabz.c
  • delete: src/c/setup.py
  • modified: src/libtetrabz/__init__.py (diff)
  • delete: src/libtetrabz/libtetrabz_common.py
  • delete: src/libtetrabz/libtetrabz_dbldelta.py
  • delete: src/libtetrabz/libtetrabz_dblstep.py
  • delete: src/libtetrabz/libtetrabz_dos.py
  • delete: src/libtetrabz/libtetrabz_fermigr.py
  • delete: src/libtetrabz/libtetrabz_occ.py
  • delete: src/libtetrabz/libtetrabz_polcmplx.py
  • delete: src/libtetrabz/libtetrabz_polstat.py
  • modified: src/libtetrabz_tutorial.ipynb (diff)

Diff

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--- a/setup.cfg
+++ /dev/null
@@ -1,24 +0,0 @@
1-[metadata]
2-name = libtetrabz
3-version = 0.0.2
4-author = Mitsuaki Kawamura
5-author_email = kawamitsuaki@gmail.com
6-description = Optimized tetrahedron method to perform brillouin-zone integral
7-long_description = file: README.md
8-long_description_content_type = text/markdown
9-url = https://libtetrabz.osdn.jp/
10-project_urls =
11- Bug Tracker = https://osdn.net/projects/libtetrabz/forums/
12-classifiers =
13- Programming Language :: Python :: 3
14- License :: OSI Approved :: MIT License
15- Operating System :: OS Independent
16-
17-[options]
18-package_dir =
19- = src
20-packages = find:
21-python_requires = >=3.6
22-
23-[options.packages.find]
24-where = src
--- /dev/null
+++ b/setup.py
@@ -0,0 +1,27 @@
1+import setuptools
2+
3+with open("README.md", "r", encoding="utf-8") as fh:
4+ long_description = fh.read()
5+
6+setuptools.setup(
7+ name="libtetrabz",
8+ version="0.0.4",
9+ author="Mitsuaki Kawamura",
10+ author_email="kawamitsuaki@gmail.com",
11+ description="Optimized tetrahedron method to perform brillouin-zone integral",
12+ long_description=long_description,
13+ long_description_content_type="text/markdown",
14+ url="https://libtetrabz.osdn.jp/",
15+ project_urls={
16+ "Bug Tracker": "https://osdn.net/projects/libtetrabz/forums/",
17+ },
18+ classifiers=[
19+ "Programming Language :: Python :: 3",
20+ "License :: OSI Approved :: MIT License",
21+ "Operating System :: OS Independent",
22+ ],
23+ package_dir={"": "src"},
24+ packages=setuptools.find_packages(where="src"),
25+ python_requires=">=3.6",
26+ ext_modules=[setuptools.Extension('libtetrabz.libtetrabzc', ['src/libtetrabz/libtetrabz.c'])]
27+)
--- a/src/c/__init__.py
+++ /dev/null
@@ -1,247 +0,0 @@
1-#
2-# Copyright (c) 2014 Mitsuaki Kawamura
3-#
4-# Permission is hereby granted, free of charge, to any person obtaining a
5-# copy of this software and associated documentation files (the
6-# "Software"), to deal in the Software without restriction, including
7-# without limitation the rights to use, copy, modify, merge, publish,
8-# distribute, sublicense, and/or sell copies of the Software, and to
9-# permit persons to whom the Software is furnished to do so, subject to
10-# the following conditions:
11-#
12-# The above copyright notice and this permission notice shall be included
13-# in all copies or substantial portions of the Software.
14-#
15-# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
16-# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
17-# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
18-# IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
19-# CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
20-# TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
21-# SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
22-#
23-from .libtetrabzc import dos_c
24-from .libtetrabzc import intdos_c
25-from .libtetrabzc import occ_c
26-from .libtetrabzc import fermieng_c
27-from .libtetrabzc import polstat_c
28-from .libtetrabzc import fermigr_c
29-from .libtetrabzc import dbldelta_c
30-from .libtetrabzc import dblstep_c
31-from .libtetrabzc import polcmplx_c
32-import numpy
33-
34-
35-def occ(bvec=numpy.array([1.0, 0.0, 0.0]), eig=numpy.array([0.0])):
36- """
37-
38- :return:
39- """
40- #
41- ng = numpy.array(eig.shape[0:3])
42- nk = ng.prod(0)
43- nb = eig.shape[3]
44- eig_c = eig.reshape(nk*nb).tolist()
45- #
46- wght_c = libtetrabzc.occ_c(ng[0], ng[1], ng[2], nk, nb,
47- bvec[0, 0], bvec[0, 1], bvec[0, 2],
48- bvec[1, 0], bvec[1, 1], bvec[1, 2],
49- bvec[2, 0], bvec[2, 1], bvec[2, 2], eig_c)
50- #
51- wght = numpy.array(wght_c).reshape([ng[0], ng[1], ng[2], nb])
52- return wght
53-
54-
55-def fermieng(bvec=numpy.array([1.0, 0.0, 0.0]), eig=numpy.array([0.0]), nelec=0.0):
56- """
57-
58- :return:
59- """
60- #
61- ng = numpy.array(eig.shape[0:3])
62- nk = ng.prod(0)
63- nb = eig.shape[3]
64- eig_c = eig.reshape(nk*nb).tolist()
65-
66- wght_c = libtetrabzc.fermieng_c(ng[0], ng[1], ng[2], nk, nb,
67- bvec[0, 0], bvec[0, 1], bvec[0, 2],
68- bvec[1, 0], bvec[1, 1], bvec[1, 2],
69- bvec[2, 0], bvec[2, 1], bvec[2, 2], eig_c, nelec)
70- #
71- ef = wght_c[nk * nb]
72- iteration = wght_c[nk*nb + 1]
73- wght = numpy.array(wght_c)[0:nk*nb].reshape([ng[0], ng[1], ng[2], nb])
74- return ef, wght, iteration
75-
76-
77-def dos(bvec=numpy.array([1.0, 0.0, 0.0]), eig=numpy.array([0.0]), e0=numpy.array([0.0])):
78- """
79-
80- :return:
81- """
82- ng = numpy.array(eig.shape[0:3])
83- nk = ng.prod(0)
84- nb = eig.shape[3]
85- ne = e0.shape[0]
86- eig_c = eig.reshape(nk*nb).tolist()
87- e0_c = e0.tolist()
88- #
89- wght_c = libtetrabzc.dos_c(ng[0], ng[1], ng[2], nk, nb, ne,
90- bvec[0, 0], bvec[0, 1], bvec[0, 2],
91- bvec[1, 0], bvec[1, 1], bvec[1, 2],
92- bvec[2, 0], bvec[2, 1], bvec[2, 2], eig_c, e0_c)
93- #
94- wght = numpy.array(wght_c).reshape([ng[0], ng[1], ng[2], nb, ne])
95- return wght
96-
97-
98-def intdos(bvec=numpy.array([1.0, 0.0, 0.0]), eig=numpy.array([0.0]), e0=numpy.array([0.0])):
99- """
100-
101- :return:
102- """
103- ng = numpy.array(eig.shape[0:3])
104- nk = ng.prod(0)
105- nb = eig.shape[3]
106- ne = e0.shape[0]
107- eig_c = eig.reshape(nk*nb).tolist()
108- e0_c = e0.tolist()
109- #
110- wght_c = libtetrabzc.intdos_c(ng[0], ng[1], ng[2], nk, nb, ne,
111- bvec[0, 0], bvec[0, 1], bvec[0, 2],
112- bvec[1, 0], bvec[1, 1], bvec[1, 2],
113- bvec[2, 0], bvec[2, 1], bvec[2, 2], eig_c, e0_c)
114- #
115- wght = numpy.array(wght_c).reshape([ng[0], ng[1], ng[2], nb, ne])
116- return wght
117-
118-
119-def dblstep(bvec=numpy.array([1.0, 0.0, 0.0]), eig1=numpy.array([0.0]), eig2=numpy.array([0.0])):
120- """
121-
122- :param bvec:
123- :param eig1:
124- :param eig2:
125- :return:
126- """
127- #
128- ng = numpy.array(eig1.shape[0:3])
129- nk = ng.prod(0)
130- nb = eig1.shape[3]
131- eig1_c = eig1.reshape(nk*nb).tolist()
132- eig2_c = eig2.reshape(nk*nb).tolist()
133-
134- wght_c = libtetrabzc.dblstep_c(ng[0], ng[1], ng[2], nk, nb,
135- bvec[0, 0], bvec[0, 1], bvec[0, 2],
136- bvec[1, 0], bvec[1, 1], bvec[1, 2],
137- bvec[2, 0], bvec[2, 1], bvec[2, 2], eig1_c, eig2_c)
138- #
139- wght = numpy.array(wght_c).reshape([ng[0], ng[1], ng[2], nb, nb])
140- return wght
141-
142-
143-def dbldelta(bvec=numpy.array([1.0, 0.0, 0.0]), eig1=numpy.array([0.0]), eig2=numpy.array([0.0])):
144- """
145-
146- :param bvec:
147- :param eig1:
148- :param eig2:
149- :return:
150- """
151- #
152- ng = numpy.array(eig1.shape[0:3])
153- nk = ng.prod(0)
154- nb = eig1.shape[3]
155- eig1_c = eig1.reshape(nk * nb).tolist()
156- eig2_c = eig2.reshape(nk * nb).tolist()
157-
158- wght_c = libtetrabzc.dbldelta_c(ng[0], ng[1], ng[2], nk, nb,
159- bvec[0, 0], bvec[0, 1], bvec[0, 2],
160- bvec[1, 0], bvec[1, 1], bvec[1, 2],
161- bvec[2, 0], bvec[2, 1], bvec[2, 2], eig1_c, eig2_c)
162- #
163- wght = numpy.array(wght_c).reshape([ng[0], ng[1], ng[2], nb, nb])
164- return wght
165-
166-
167-def polstat(bvec=numpy.array([1.0, 0.0, 0.0]), eig1=numpy.array([0.0]), eig2=numpy.array([0.0])):
168- """
169-
170- :param bvec:
171- :param eig1:
172- :param eig2:
173- :return:
174- """
175- ng = numpy.array(eig1.shape[0:3])
176- nk = ng.prod(0)
177- nb = eig1.shape[3]
178- eig1_c = eig1.reshape(nk * nb).tolist()
179- eig2_c = eig2.reshape(nk * nb).tolist()
180-
181- wght_c = libtetrabzc.polstat_c(ng[0], ng[1], ng[2], nk, nb,
182- bvec[0, 0], bvec[0, 1], bvec[0, 2],
183- bvec[1, 0], bvec[1, 1], bvec[1, 2],
184- bvec[2, 0], bvec[2, 1], bvec[2, 2], eig1_c, eig2_c)
185- #
186- wght = numpy.array(wght_c).reshape([ng[0], ng[1], ng[2], nb, nb])
187- return wght
188-
189-
190-def fermigr(bvec=numpy.array([1.0, 0.0, 0.0]),
191- eig1=numpy.array([0.0]), eig2=numpy.array([0.0]), e0=numpy.array([0.0])):
192- """
193-
194- :param bvec:
195- :param eig1:
196- :param eig2:
197- :param e0:
198- :return:
199- """
200- ng = numpy.array(eig1.shape[0:3])
201- nk = ng.prod(0)
202- nb = eig1.shape[3]
203- ne = e0.shape[0]
204- eig1_c = eig1.reshape(nk * nb).tolist()
205- eig2_c = eig2.reshape(nk * nb).tolist()
206- e0_c = e0.tolist()
207-
208- wght_c = libtetrabzc.fermigr_c(ng[0], ng[1], ng[2], nk, nb, ne,
209- bvec[0, 0], bvec[0, 1], bvec[0, 2],
210- bvec[1, 0], bvec[1, 1], bvec[1, 2],
211- bvec[2, 0], bvec[2, 1], bvec[2, 2], eig1_c, eig2_c, e0_c)
212- #
213- wght = numpy.array(wght_c).reshape([ng[0], ng[1], ng[2], nb, nb, ne])
214- return wght
215-
216-
217-def polcmplx(bvec=numpy.array([1.0, 0.0, 0.0]),
218- eig1=numpy.array([0.0]), eig2=numpy.array([0.0]), e0=numpy.array([0.0+0.0j])):
219- """
220-
221- :param bvec:
222- :param eig1:
223- :param eig2:
224- :param e0:
225- :return:
226- """
227- ng = numpy.array(eig1.shape[0:3])
228- nk = ng.prod(0)
229- nb = eig1.shape[3]
230- ne = e0.shape[0]
231- eig1_c = eig1.reshape(nk * nb).tolist()
232- eig2_c = eig2.reshape(nk * nb).tolist()
233-
234- e0_1 = numpy.empty([ne, 2], dtype=numpy.float_)
235- e0_1[:, 0] = e0[:].real
236- e0_1[:, 1] = e0[:].imag
237- e0_c = e0_1.reshape(ne * 2).tolist()
238-
239- wght_c = libtetrabzc.polcmplx_c(ng[0], ng[1], ng[2], nk, nb, ne,
240- bvec[0, 0], bvec[0, 1], bvec[0, 2],
241- bvec[1, 0], bvec[1, 1], bvec[1, 2],
242- bvec[2, 0], bvec[2, 1], bvec[2, 2], eig1_c, eig2_c, e0_c)
243- #
244- wght_1 = numpy.array(wght_c).reshape([ng[0], ng[1], ng[2], nb, nb, ne, 2])
245- #
246- wght = wght_1[:, :, :, :, :, :, 0] + 1.0j * wght_1[:, :, :, :, :, :, 1]
247- return wght
--- a/src/c/libtetrabz.c
+++ /dev/null
@@ -1,4116 +0,0 @@
1-/*
2- Copyright (c) 2014 Mitsuaki Kawamura
3-
4- Permission is hereby granted, free of charge, to any person obtaining a
5- copy of this software and associated documentation files (the
6- "Software"), to deal in the Software without restriction, including
7- without limitation the rights to use, copy, modify, merge, publish,
8- distribute, sublicense, and/or sell copies of the Software, and to
9- permit persons to whom the Software is furnished to do so, subject to
10- the following conditions:
11-
12- The above copyright notice and this permission notice shall be included
13- in all copies or substantial portions of the Software.
14-
15- THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
16- OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
17- MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
18- IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
19- CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
20- TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
21- SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
22-*/
23-#define PY_SSIZE_T_CLEAN
24-#include <Python.h>
25-#include <stdio.h>
26-#include <stdlib.h>
27-#include <math.h>
28-
29-void libtetrabz_initialize(
30- int ng[3],
31- double bvec[3][3],
32- double wlsm[20][4],
33- int **ikv
34- )
35- {
36- /*
37- define shortest diagonal line & define type of tetragonal
38- */
39- int ii, i0, i1, i2, i3, it, itype, ivvec0[4], divvec[4][4], ivvec[6][20][3], ikv0[3], nt;
40- double bvec2[3][3], bvec3[4][3], bnorm[4];
41- double wlsm1[4][4] = { {1440.0, 0.0, 30.0, 0.0},
42- {0.0, 1440.0, 0.0, 30.0},
43- {30.0, 0.0, 1440.0, 0.0},
44- {0.0, 30.0, 0.0, 1440.0} },
45- wlsm2[4][4] = {{-38.0, 7.0, 17.0, -28.0},
46- {-28.0, -38.0, 7.0, 17.0},
47- {17.0, -28.0, -38.0, 7.0},
48- {7.0, 17.0, -28.0, -38.0}},
49- wlsm3[4][4] = {{-56.0, 9.0, -46.0, 9.0},
50- {9.0, -56.0, 9.0, -46.0},
51- {-46.0, 9.0, -56.0, 9.0},
52- {9.0, -46.0, 9.0, -56.0}},
53- wlsm4[4][4] = {{-38.0, -28.0, 17.0, 7.0},
54- {7.0, -38.0, -28.0, 17.0},
55- {17.0, 7.0, -38.0, -28.0},
56- {-28.0, 17.0, 7.0, -38.0}},
57- wlsm5[4][4] = {{-18.0, -18.0, 12.0, -18.0},
58- {-18.0, -18.0, -18.0, 12.0},
59- {12.0, -18.0, -18.0, -18.0},
60- {-18.0, 12.0, -18.0, -18.0}};
61-
62- for (i1 = 0; i1 < 3; i1++)
63- for (i2 = 0; i2 < 3; i2++)
64- bvec2[i1][i2] = bvec[i1][i2] / (double) ng[i1];
65-
66- for (i1 = 0; i1 < 3; i1++) {
67- bvec3[0][i1] = -bvec2[0][i1] + bvec2[1][i1] + bvec2[2][i1];
68- bvec3[1][i1] = bvec2[0][i1] - bvec2[1][i1] + bvec2[2][i1];
69- bvec3[2][i1] = bvec2[0][i1] + bvec2[1][i1] - bvec2[2][i1];
70- bvec3[3][i1] = bvec2[0][i1] + bvec2[1][i1] + bvec2[2][i1];
71- }
72- /*
73- length of delta bvec
74- */
75- for (i1 = 0; i1 < 4; i1++) {
76- bnorm[i1] = 0.0;
77- for (i2 = 0; i2 < 3; i2++)
78- bnorm[i1] += bvec3[i1][i2] * bvec3[i1][i2];
79- }
80- itype = 0;
81- for (i1 = 1; i1 < 4; i1++)
82- if (bnorm[i1] < bnorm[itype]) itype = i1;
83- /*
84- start & last
85- */
86- for (i0 = 0; i0 < 4; i0++) {
87- ivvec0[i0] = 0;
88- for (i1 = 0; i1 < 4; i1++)divvec[i0][i1] = 0;
89- divvec[i0][i0] = 1;
90- }
91- ivvec0[itype] = 1;
92- divvec[itype][itype] = -1;
93- /*
94- Corners of tetrahedron
95- */
96- it = 0;
97- for (i0 = 0; i0 < 3; i0++) {
98- for (i1 = 0; i1 < 3; i1++) {
99- if (i1 == i0) continue;
100- for (i2 = 0; i2 < 3; i2++) {
101- if (i2 == i1 || i2 == i0) continue;
102-
103- for (i3 = 0; i3 < 3; i3++) {
104- ivvec[it][0][i3] = ivvec0[i3];
105- ivvec[it][1][i3] = ivvec[it][0][i3] + divvec[i0][i3];
106- ivvec[it][2][i3] = ivvec[it][1][i3] + divvec[i1][i3];
107- ivvec[it][3][i3] = ivvec[it][2][i3] + divvec[i2][i3];
108- }
109-
110- it += 1;
111- }
112- }
113- }
114- /*
115- Additional points
116- */
117- for (i1 = 0; i1 < 6; i1++) {
118- for (i2 = 0; i2 < 3; i2++) {
119- ivvec[i1][4][i2] = 2 * ivvec[i1][0][i2] - ivvec[i1][1][i2];
120- ivvec[i1][5][i2] = 2 * ivvec[i1][1][i2] - ivvec[i1][2][i2];
121- ivvec[i1][6][i2] = 2 * ivvec[i1][2][i2] - ivvec[i1][3][i2];
122- ivvec[i1][7][i2] = 2 * ivvec[i1][3][i2] - ivvec[i1][0][i2];
123-
124- ivvec[i1][8][i2] = 2 * ivvec[i1][0][i2] - ivvec[i1][2][i2];
125- ivvec[i1][9][i2] = 2 * ivvec[i1][1][i2] - ivvec[i1][3][i2];
126- ivvec[i1][10][i2] = 2 * ivvec[i1][2][i2] - ivvec[i1][0][i2];
127- ivvec[i1][11][i2] = 2 * ivvec[i1][3][i2] - ivvec[i1][1][i2];
128-
129- ivvec[i1][12][i2] = 2 * ivvec[i1][0][i2] - ivvec[i1][3][i2];
130- ivvec[i1][13][i2] = 2 * ivvec[i1][1][i2] - ivvec[i1][0][i2];
131- ivvec[i1][14][i2] = 2 * ivvec[i1][2][i2] - ivvec[i1][1][i2];
132- ivvec[i1][15][i2] = 2 * ivvec[i1][3][i2] - ivvec[i1][2][i2];
133-
134- ivvec[i1][16][i2] = ivvec[i1][3][i2] - ivvec[i1][0][i2] + ivvec[i1][1][i2];
135- ivvec[i1][17][i2] = ivvec[i1][0][i2] - ivvec[i1][1][i2] + ivvec[i1][2][i2];
136- ivvec[i1][18][i2] = ivvec[i1][1][i2] - ivvec[i1][2][i2] + ivvec[i1][3][i2];
137- ivvec[i1][19][i2] = ivvec[i1][2][i2] - ivvec[i1][3][i2] + ivvec[i1][0][i2];
138- }
139- }
140-
141- for (i1 = 0; i1 < 4; i1++) {
142- for (i2 = 0; i2 < 4; i2++) {
143- wlsm[i2][i1] = wlsm1[i1][i2] /= 1260.0;
144- wlsm[i2 + 4][i1] = wlsm2[i1][i2] /= 1260.0;
145- wlsm[i2 + 8][i1] = wlsm3[i1][i2] /= 1260.0;
146- wlsm[i2 + 12][i1] = wlsm4[i1][i2] /= 1260.0;
147- wlsm[i2 + 16][i1] = wlsm5[i1][i2] /= 1260.0;
148- }
149- }
150- /*
151- k-index for energy
152- */
153- nt = 0;
154- for (i2 = 0; i2 < ng[2]; i2++) {
155- for (i1 = 0; i1 < ng[1]; i1++) {
156- for (i0 = 0; i0 < ng[0]; i0++) {
157-
158- for (it = 0; it < 6; it++) {
159-
160- for (ii = 0; ii < 20; ii++) {
161- ikv0[0] = (i0 + ivvec[it][ii][0]) % ng[0];
162- ikv0[1] = (i1 + ivvec[it][ii][1]) % ng[1];
163- ikv0[2] = (i2 + ivvec[it][ii][2]) % ng[2];
164- for (i3 = 0; i3 < 3; i3++) if (ikv0[i3] < 0) ikv0[i3] += ng[i3];
165- ikv[nt][ii] = ikv0[2] + ng[2] * ikv0[1] + ng[2] * ng[1] * ikv0[0];
166- }
167- nt += 1;
168- }
169- }
170- }
171- }
172-}
173-/*
174-Cut small tetrahedron A1
175-*/
176-void libtetrabz_tsmall_a1(
177- double *e,
178- double e0,
179- double *v,
180- double tsmall[4][4]
181-) {
182- double a10, a20, a30;
183- a10 = (e0 - e[0]) / (e[1] - e[0]);
184- a20 = (e0 - e[0]) / (e[2] - e[0]);
185- a30 = (e0 - e[0]) / (e[3] - e[0]);
186-
187- *v = a10 * a20 * a30;
188-
189- tsmall[0][0] = 1.0;
190- tsmall[0][1] = 1.0 - a10;
191- tsmall[0][2] = 1.0 - a20;
192- tsmall[0][3] = 1.0 - a30;
193- tsmall[1][0] = 0.0;
194- tsmall[1][1] = a10;
195- tsmall[1][2] = 0.0;
196- tsmall[1][3] = 0.0;
197- tsmall[2][0] = 0.0;
198- tsmall[2][1] = 0.0;
199- tsmall[2][2] = a20;
200- tsmall[2][3] = 0.0;
201- tsmall[3][0] = 0.0;
202- tsmall[3][1] = 0.0;
203- tsmall[3][2] = 0.0;
204- tsmall[3][3] = a30;
205-}
206-/*
207-Cut small tetrahedron B1
208-*/
209-void libtetrabz_tsmall_b1(
210- double *e,
211- double e0,
212- double *v,
213- double tsmall[4][4]
214-)
215-{
216- double a13, a20, a30;
217- a13 = (e0 - e[3]) / (e[1] - e[3]);
218- a20 = (e0 - e[0]) / (e[2] - e[0]);
219- a30 = (e0 - e[0]) / (e[3] - e[0]);
220-
221- *v = a20 * a30 * a13;
222-
223- tsmall[0][0] = 1.0;
224- tsmall[0][1] = 1.0 - a20;
225- tsmall[0][2] = 1.0 - a30;
226- tsmall[0][3] = 0.0;
227- tsmall[1][0] = 0.0;
228- tsmall[1][1] = 0.0;
229- tsmall[1][2] = 0.0;
230- tsmall[1][3] = a13;
231- tsmall[2][0] = 0.0;
232- tsmall[2][1] = a20;
233- tsmall[2][2] = 0.0;
234- tsmall[2][3] = 0.0;
235- tsmall[3][0] = 0.0;
236- tsmall[3][1] = 0.0;
237- tsmall[3][2] = a30;
238- tsmall[3][3] = 1.0 - a13;
239-}
240-/*
241-Cut small tetrahedron B2
242-*/
243-void libtetrabz_tsmall_b2(
244- double *e,
245- double e0,
246- double *v,
247- double tsmall[4][4]
248-)
249-{
250- double a21, a31;
251- a21 = (e0 - e[1]) / (e[2] - e[1]);
252- a31 = (e0 - e[1]) / (e[3] - e[1]);
253-
254- *v = a21 * a31;
255-
256- tsmall[0][0] = 1.0;
257- tsmall[0][1] = 0.0;
258- tsmall[0][2] = 0.0;
259- tsmall[0][3] = 0.0;
260- tsmall[1][0] = 0.0;
261- tsmall[1][1] = 1.0;
262- tsmall[1][2] = 1.0 - a21;
263- tsmall[1][3] = 1.0 - a31;
264- tsmall[2][0] = 0.0;
265- tsmall[2][1] = 0.0;
266- tsmall[2][2] = a21;
267- tsmall[2][3] = 0.0;
268- tsmall[3][0] = 0.0;
269- tsmall[3][1] = 0.0;
270- tsmall[3][2] = 0.0;
271- tsmall[3][3] = a31;
272-}
273-/*
274-Cut small tetrahedron B3
275-*/
276-void libtetrabz_tsmall_b3(
277- double *e,
278- double e0,
279- double *v,
280- double tsmall[4][4]
281-)
282-{
283- double a12, a20, a31;
284- a12 = (e0 - e[2]) / (e[1] - e[2]);
285- a20 = (e0 - e[0]) / (e[2] - e[0]);
286- a31 = (e0 - e[1]) / (e[3] - e[1]);
287-
288- *v = a12 * a20 * a31;
289-
290- tsmall[0][0] = 1.0;
291- tsmall[0][1] = 1.0 - a20;
292- tsmall[0][2] = 0.0;
293- tsmall[0][3] = 0.0;
294- tsmall[1][0] = 0.0;
295- tsmall[1][1] = 0.0;
296- tsmall[1][2] = a12;
297- tsmall[1][3] = 1.0 - a31;
298- tsmall[2][0] = 0.0;
299- tsmall[2][1] = a20;
300- tsmall[2][2] = 1.0 - a12;
301- tsmall[2][3] = 0.0;
302- tsmall[3][0] = 0.0;
303- tsmall[3][1] = 0.0;
304- tsmall[3][2] = 0.0;
305- tsmall[3][3] = a31;
306-}
307-/*
308-Cut small tetrahedron C1
309-*/
310-void libtetrabz_tsmall_c1(
311- double *e,
312- double e0,
313- double *v,
314- double tsmall[4][4]
315-)
316-{
317- double a32;
318- a32 = (e0 - e[2]) / (e[3] - e[2]);
319-
320- *v = a32;
321-
322- tsmall[0][0] = 1.0;
323- tsmall[0][1] = 0.0;
324- tsmall[0][2] = 0.0;
325- tsmall[0][3] = 0.0;
326- tsmall[1][0] = 0.0;
327- tsmall[1][1] = 1.0;
328- tsmall[1][2] = 0.0;
329- tsmall[1][3] = 0.0;
330- tsmall[2][0] = 0.0;
331- tsmall[2][1] = 0.0;
332- tsmall[2][2] = 1.0;
333- tsmall[2][3] = 1.0 - a32;
334- tsmall[3][0] = 0.0;
335- tsmall[3][1] = 0.0;
336- tsmall[3][2] = 0.0;
337- tsmall[3][3] = a32;
338-}
339-/*
340-Cut small tetrahedron C2
341-*/
342-void libtetrabz_tsmall_c2(
343- double *e,
344- double e0,
345- double *v,
346- double tsmall[4][4]
347-)
348-{
349- double a23, a31;
350- a23 = (e0 - e[3]) / (e[2] - e[3]);
351- a31 = (e0 - e[1]) / (e[3] - e[1]);
352-
353- *v = a23 * a31;
354-
355- tsmall[0][0] = 1.0;
356- tsmall[0][1] = 0.0;
357- tsmall[0][2] = 0.0;
358- tsmall[0][3] = 0.0;
359- tsmall[1][0] = 0.0;
360- tsmall[1][1] = 1.0;
361- tsmall[1][2] = 1.0 - a31;
362- tsmall[1][3] = 0.0;
363- tsmall[2][0] = 0.0;
364- tsmall[2][1] = 0.0;
365- tsmall[2][2] = 0.0;
366- tsmall[2][3] = a23;
367- tsmall[3][0] = 0.0;
368- tsmall[3][1] = 0.0;
369- tsmall[3][2] = a31;
370- tsmall[3][3] = 1.0 - a23;
371-}
372-/*
373-Cut small tetrahedron C3
374-*/
375-void libtetrabz_tsmall_c3(
376- double *e,
377- double e0,
378- double *v,
379- double tsmall[4][4]
380-)
381-{
382- double a23, a13, a30;
383- a23 = (e0 - e[3]) / (e[2] - e[3]);
384- a13 = (e0 - e[3]) / (e[1] - e[3]);
385- a30 = (e0 - e[0]) / (e[3] - e[0]);
386-
387- *v = a23 * a13 * a30;
388-
389- tsmall[0][0] = 1.0;
390- tsmall[0][1] = 1.0 - a30;
391- tsmall[0][2] = 0.0;
392- tsmall[0][3] = 0.0;
393- tsmall[1][0] = 0.0;
394- tsmall[1][1] = 0.0;
395- tsmall[1][2] = a13;
396- tsmall[1][3] = 0.0;
397- tsmall[2][0] = 0.0;
398- tsmall[2][1] = 0.0;
399- tsmall[2][2] = 0.0;
400- tsmall[2][3] = a23;
401- tsmall[3][0] = 0.0;
402- tsmall[3][1] = a30;
403- tsmall[3][2] = 1.0 - a13;
404- tsmall[3][3] = 1.0 - a23;
405-}
406-/*
407-Cut triangle A1
408-*/
409-void libtetrabz_triangle_a1(
410- double *e,
411- double e0,
412- double *v,
413- double tsmall[4][3]
414-)
415-{
416- double a10, a20, a30;
417- a10 = (e0 - e[0]) / (e[1] - e[0]);
418- a20 = (e0 - e[0]) / (e[2] - e[0]);
419- a30 = (e0 - e[0]) / (e[3] - e[0]);
420-
421- *v = 3.0 * a10 * a20 / (e[3] - e[0]);
422-
423- tsmall[0][0] = 1.0 - a10;
424- tsmall[0][1] = 1.0 - a20;
425- tsmall[0][2] = 1.0 - a30;
426- tsmall[1][0] = a10;
427- tsmall[1][1] = 0.0;
428- tsmall[1][2] = 0.0;
429- tsmall[2][0] = 0.0;
430- tsmall[2][1] = a20;
431- tsmall[2][2] = 0.0;
432- tsmall[3][0] = 0.0;
433- tsmall[3][1] = 0.0;
434- tsmall[3][2] = a30;
435-}
436-/*
437-Cut triangle B1
438-*/
439-void libtetrabz_triangle_b1(
440- double *e,
441- double e0,
442- double *v,
443- double tsmall[4][3]
444-) {
445- double a30, a13, a20;
446- a30 = (e0 - e[0]) / (e[3] - e[0]);
447- a13 = (e0 - e[3]) / (e[1] - e[3]);
448- a20 = (e0 - e[0]) / (e[2] - e[0]);
449-
450- *v = 3.0 * a30 * a13 / (e[2] - e[0]);
451-
452- tsmall[0][0] = 1.0 - a20;
453- tsmall[0][1] = 1.0 - a30;
454- tsmall[0][2] = 0.0;
455- tsmall[1][0] = 0.0;
456- tsmall[1][1] = 0.0;
457- tsmall[1][2] = a13;
458- tsmall[2][0] = a20;
459- tsmall[2][1] = 0.0;
460- tsmall[2][2] = 0.0;
461- tsmall[3][0] = 0.0;
462- tsmall[3][1] = a30;
463- tsmall[3][2] = 1.0 - a13;
464-}
465-/*
466-Cut triangle B2
467-*/
468-void libtetrabz_triangle_b2(
469- double *e,
470- double e0,
471- double *v,
472- double tsmall[4][3]
473-)
474-{
475- double a12, a31, a20;
476- a12 = (e0 - e[2]) / (e[1] - e[2]);
477- a31 = (e0 - e[1]) / (e[3] - e[1]);
478- a20 = (e0 - e[0]) / (e[2] - e[0]);
479-
480- *v = 3.0 * a12 * a31 / (e[2] - e[0]);
481-
482- tsmall[0][0] = 1.0 - a20;
483- tsmall[0][1] = 0.0;
484- tsmall[0][2] = 0.0;
485- tsmall[1][0] = 0.0;
486- tsmall[1][1] = a12;
487- tsmall[1][2] = 1.0 - a31;
488- tsmall[2][0] = a20;
489- tsmall[2][1] = 1.0 - a12;
490- tsmall[2][2] = 0.0;
491- tsmall[3][0] = 0.0;
492- tsmall[3][1] = 0.0;
493- tsmall[3][2]= a31;
494-}
495-/*
496-Cut triangle C1
497-*/
498-void libtetrabz_triangle_c1(
499- double *e,
500- double e0,
501- double *v,
502- double tsmall[4][3]
503-)
504-{
505- double a03, a13, a23;
506- a03 = (e0 - e[3]) / (e[0] - e[3]);
507- a13 = (e0 - e[3]) / (e[1] - e[3]);
508- a23 = (e0 - e[3]) / (e[2] - e[3]);
509-
510- *v = 3.0 * a03 * a13 / (e[3] - e[2]);
511-
512- tsmall[0][0] = a03;
513- tsmall[0][1] = 0.0;
514- tsmall[0][2] = 0.0;
515- tsmall[1][0] = 0.0;
516- tsmall[1][1] = a13;
517- tsmall[1][2] = 0.0;
518- tsmall[2][0] = 0.0;
519- tsmall[2][1] = 0.0;
520- tsmall[2][2] = a23;
521- tsmall[3][0] = 1.0 - a03;
522- tsmall[3][1] = 1.0 - a13;
523- tsmall[3][2] = 1.0 - a23;
524-}
525-/*
526-Sort eigenvalues
527-*/
528-void eig_sort(
529- int n, //!< [in] the number of components
530- double *key, //!< [in] Variables to be sorted [n].
531- int *swap //!< [out] Order of index (sorted)
532-)
533-{
534- int i, j, k, min_loc;
535- double min_val;
536-
537- for (i = 0; i < n; ++i) swap[i] = i;
538-
539- for (i = 0; i < n - 1; ++i) {
540- min_val = key[i];
541- min_loc = i;
542- for (j = i + 1; j < n; ++j) {
543- if (min_val > key[j]) {
544- min_val = key[j];
545- min_loc = j;
546- }
547- }
548- if (key[i] > min_val) {
549- /*
550- Swap
551- */
552- key[min_loc] = key[i];
553- key[i] = min_val;
554-
555- k = swap[min_loc];
556- swap[min_loc] = swap[i];
557- swap[i] = k;
558- }
559- }/*for (i = 0; i < n - 1; ++i)*/
560-}/*eig_sort*/
561-/*
562-2nd step of tetrahedron method.
563-*/
564-static void libtetrabz_dbldelta2(
565- int nb,
566- double **ej,
567- double **w
568-) {
569- int i3, ib, indx[3];
570- double a10, a20, a02, a12, v, e[3], e_abs;
571-
572- for (ib = 0; ib < nb; ib++) {
573-
574- e_abs = 0.0;
575- for (i3 = 0; i3 < 3; i3++) {
576- e[i3] = ej[ib][i3];
577- if (e_abs < fabs(e[i3])) e_abs = fabs(e[i3]);
578- }
579- eig_sort(3, e, indx);
580-
581- if (e_abs < 1.0e-10) {
582- printf("Nesting ##\n");
583- }
584-
585- if ((e[0] < 0.0 && 0.0 <= e[1]) || (e[0] <= 0.0 && 0.0 < e[1])) {
586-
587- a10 = (0.0 - e[0]) / (e[1] - e[0]);
588- a20 = (0.0 - e[0]) / (e[2] - e[0]);
589-
590- v = a10 / (e[2] - e[0]);
591-
592- w[ib][indx[0]] = v * (2.0 - a10 - a20);
593- w[ib][indx[1]] = v * a10;
594- w[ib][indx[2]] = v * a20;
595- }
596- else if ((e[1] <= 0.0 && 0.0 < e[2]) || (e[1] < 0.0 && 0.0 <= e[2])) {
597-
598- a02 = (0.0 - e[2]) / (e[0] - e[2]);
599- a12 = (0.0 - e[2]) / (e[1] - e[2]);
600-
601- v = a12 / (e[2] - e[0]);
602-
603- w[ib][indx[0]] = v * a02;
604- w[ib][indx[1]] = v * a12;
605- w[ib][indx[2]] = v * (2.0 - a02 - a12);
606- }
607- else {
608- for (i3 = 0; i3 < 3; i3++)
609- w[ib][i3] = 0.0;
610- }
611- }
612-}
613-/*
614-Main SUBROUTINE for Delta(E1) * Delta(E2)
615-*/
616-static PyObject* dbldelta_c(PyObject* self, PyObject* args)
617-{
618- int it, ik, ib, i20, i4, j3, jb, ** ikv, indx[4], ierr, ng[3], nk, nb;
619- double wlsm[20][4], ** ei1, ** ej1, ** ej2, e[4], *** w1, **w2, v, tsmall[4][3], thr,
620- bvec[3][3], ** eig1, ** eig2, *** wght;
621- PyObject* eig1_po, * eig2_po, * wght_po;
622- /*
623- Read input from python object
624- */
625- if (!PyArg_ParseTuple(args, "iiiiidddddddddOO",
626- &ng[0], &ng[1], &ng[2], &nk, &nb,
627- &bvec[0][0], &bvec[0][1], &bvec[0][2], &bvec[1][0], &bvec[1][1], &bvec[1][2], &bvec[2][0], &bvec[2][1], &bvec[2][2],
628- &eig1_po, &eig2_po))
629- return NULL;
630- /*
631- convert python list object to array
632- */
633- eig1 = (double**)malloc(nk * sizeof(double*));
634- eig1[0] = (double*)malloc(nk * nb * sizeof(double));
635- eig2 = (double**)malloc(nk * sizeof(double*));
636- eig2[0] = (double*)malloc(nk * nb * sizeof(double));
637- wght = (double***)malloc(nk * sizeof(double**));
638- wght[0] = (double**)malloc(nk * nb * sizeof(double*));
639- wght[0][0] = (double*)malloc(nk * nb * nb * sizeof(double));
640- for (ik = 0; ik < nk; ik++) {
641- eig1[ik] = eig1[0] + ik * nb;
642- eig2[ik] = eig2[0] + ik * nb;
643- wght[ik] = wght[0] + ik * nb;
644- for (ib = 0; ib < nb; ib++) {
645- wght[ik][ib] = wght[0][0] + ik * nb * nb + ib * nb;
646- }
647- }
648-
649- for (ik = 0; ik < nk; ik++)
650- for (ib = 0; ib < nb; ib++) {
651- eig1[ik][ib] = PyFloat_AsDouble(PyList_GetItem(eig1_po, ik * nb + ib));
652- eig2[ik][ib] = PyFloat_AsDouble(PyList_GetItem(eig2_po, ik * nb + ib));
653- }
654- /*
655- Start main calculation
656- */
657- thr = 1.0e-10;
658-
659- ikv = (int**)malloc(6 * nk * sizeof(int*));
660- ikv[0] = (int*)malloc(6 * nk * 20 * sizeof(int));
661- for (ik = 0; ik < 6 * nk; ik++) {
662- ikv[ik] = ikv[0] + ik * 20;
663- }
664-
665- ei1 = (double**)malloc(4 * sizeof(double*));
666- ej1 = (double**)malloc(4 * sizeof(double*));
667- ei1[0] = (double*)malloc(4 * nb * sizeof(double));
668- ej1[0] = (double*)malloc(4 * nb * sizeof(double));
669- for (i4 = 0; i4 < 4; i4++) {
670- ei1[i4] = ei1[0] + i4 * nb;
671- ej1[i4] = ej1[0] + i4 * nb;
672- }
673-
674- w1 = (double***)malloc(nb * sizeof(double**));
675- w1[0] = (double**)malloc(nb * 4 * sizeof(double*));
676- w1[0][0] = (double*)malloc(nb * 4 * nb * sizeof(double));
677- for (ib = 0; ib < nb; ib++) {
678- w1[ib] = w1[0] + ib * 4;
679- for (i4 = 0; i4 < 4; i4++) {
680- w1[ib][i4] = w1[0][0] + ib * 4 * nb + i4 * nb;
681- }
682- }
683-
684- ej2 = (double**)malloc(nb * sizeof(double*));
685- ej2[0] = (double*)malloc(nb * 3 * sizeof(double));
686- for (ib = 0; ib < nb; ib++) {
687- ej2[ib] = ej2[0] + ib * 3;
688- }
689-
690- w2 = (double**)malloc(nb * sizeof(double*));
691- w2[0] = (double*)malloc(nb * 3 * sizeof(double));
692- for (ib = 0; ib < nb; ib++) {
693- w2[ib] = w2[0] + ib * 3;
694- }
695-
696- libtetrabz_initialize(ng, bvec, wlsm, ikv);
697-
698- for (ik = 0; ik < nk; ik++)
699- for (ib = 0; ib < nb; ib++)
700- for (jb = 0; jb < nb; jb++)
701- wght[ik][ib][jb] = 0.0;
702-
703- for (it = 0; it < 6 * nk; it++) {
704-
705- for (i4 = 0; i4 < 4; i4++)
706- for (ib = 0; ib < nb; ib++) {
707- ei1[i4][ib] = 0.0;
708- ej1[i4][ib] = 0.0;
709- }
710- for (i20 = 0; i20 < 20; i20++) {
711- for (i4 = 0; i4 < 4; i4++) {
712- for (ib = 0; ib < nb; ib++) {
713- ei1[i4][ib] += eig1[ikv[it][i20]][ib] * wlsm[i20][i4];
714- ej1[i4][ib] += eig2[ikv[it][i20]][ib] * wlsm[i20][i4];
715- }
716- }
717- }
718-
719- for (ib = 0; ib < nb; ib++) {
720-
721- for (i4 = 0; i4 < 4; i4++)
722- for (jb = 0; jb < nb; jb++)
723- w1[ib][i4][jb] = 0.0;
724-
725- for (i4 = 0; i4 < 4; i4++) e[i4] = ei1[i4][ib];
726- eig_sort(4, e, indx);
727-
728- if (e[0] < 0.0 && 0.0 <= e[1]) {
729-
730- libtetrabz_triangle_a1(e, 0.0, &v, tsmall);
731-
732- if (v > thr) {
733- for (jb = 0; jb < nb; jb++)
734- for (j3 = 0; j3 < 3; j3++) ej2[jb][j3] = 0.0;
735- for (i4 = 0; i4 < 4; i4++)
736- for (jb = 0; jb < nb; jb++)
737- for (j3 = 0; j3 < 3; j3++)
738- ej2[jb][j3] += ej1[indx[i4]][jb] * tsmall[i4][j3];
739- libtetrabz_dbldelta2(nb, ej2, w2);
740- for (i4 = 0; i4 < 4; i4++)
741- for (jb = 0; jb < nb; jb++)
742- for (j3 = 0; j3 < 3; j3++)
743- w1[ib][indx[i4]][jb] += v * tsmall[i4][j3] * w2[jb][j3];
744- }
745- }
746- else if (e[1] < 0.0 && 0.0 <= e[2]) {
747-
748- libtetrabz_triangle_b1(e, 0.0, &v, tsmall);
749-
750- if (v > thr) {
751- for (jb = 0; jb < nb; jb++)
752- for (j3 = 0; j3 < 3; j3++) ej2[jb][j3] = 0.0;
753- for (i4 = 0; i4 < 4; i4++)
754- for (jb = 0; jb < nb; jb++)
755- for (j3 = 0; j3 < 3; j3++)
756- ej2[jb][j3] += ej1[indx[i4]][jb] * tsmall[i4][j3];
757- libtetrabz_dbldelta2(nb, ej2, w2);
758- for (i4 = 0; i4 < 4; i4++)
759- for (jb = 0; jb < nb; jb++)
760- for (j3 = 0; j3 < 3; j3++)
761- w1[ib][indx[i4]][jb] += v * tsmall[i4][j3] * w2[jb][j3];
762- }
763-
764- libtetrabz_triangle_b2(e, 0.0, &v, tsmall);
765-
766- if (v > thr) {
767- for (jb = 0; jb < nb; jb++)
768- for (j3 = 0; j3 < 3; j3++) ej2[jb][j3] = 0.0;
769- for (i4 = 0; i4 < 4; i4++)
770- for (jb = 0; jb < nb; jb++)
771- for (j3 = 0; j3 < 3; j3++)
772- ej2[jb][j3] += ej1[indx[i4]][jb] * tsmall[i4][j3];
773- libtetrabz_dbldelta2(nb, ej2, w2);
774- for (i4 = 0; i4 < 4; i4++)
775- for (jb = 0; jb < nb; jb++)
776- for (j3 = 0; j3 < 3; j3++)
777- w1[ib][indx[i4]][jb] += v * tsmall[i4][j3] * w2[jb][j3];
778- }
779- }
780- else if (e[2] < 0.0 && 0.0 < e[3]) {
781-
782- libtetrabz_triangle_c1(e, 0.0, &v, tsmall);
783-
784- if (v > thr) {
785- for (jb = 0; jb < nb; jb++)
786- for (j3 = 0; j3 < 3; j3++) ej2[jb][j3] = 0.0;
787- for (i4 = 0; i4 < 4; i4++)
788- for (jb = 0; jb < nb; jb++)
789- for (j3 = 0; j3 < 3; j3++)
790- ej2[jb][j3] += ej1[indx[i4]][jb] * tsmall[i4][j3];
791- libtetrabz_dbldelta2(nb, ej2, w2);
792- for (i4 = 0; i4 < 4; i4++)
793- for (jb = 0; jb < nb; jb++)
794- for (j3 = 0; j3 < 3; j3++)
795- w1[ib][indx[i4]][jb] += v * tsmall[i4][j3] * w2[jb][j3];
796- }
797- }
798- else {
799- continue;
800- }
801- }
802- for (i20 = 0; i20 < 20; i20++)
803- for (ib = 0; ib < nb; ib++)
804- for (i4 = 0; i4 < 4; i4++)
805- for (jb = 0; jb < nb; jb++)
806- wght[ikv[it][i20]][ib][jb] += wlsm[i20][i4] * w1[ib][i4][jb];
807- }
808- for (ik = 0; ik < nk; ik++)
809- for (ib = 0; ib < nb; ib++)
810- for (jb = 0; jb < nb; jb++)
811- wght[ik][ib][jb] /= (6.0 * (double)nk);
812-
813- free(ikv[0]);
814- free(ikv);
815- free(ei1[0]);
816- free(ei1);
817- free(ej1[0]);
818- free(ej1);
819- free(ej2[0]);
820- free(ej2);
821- free(w1[0][0]);
822- free(w1[0]);
823- free(w1);
824- free(w2[0]);
825- free(w2);
826- /*
827- Convert weight to python list object
828- */
829- wght_po = PyList_New(nk * nb * nb);
830- ierr = 0;
831- for (ik = 0; ik < nk; ik++)
832- for (ib = 0; ib < nb; ib++)
833- for (jb = 0; jb < nb; jb++)
834- ierr = PyList_SetItem(wght_po, ik * nb * nb + ib * nb + jb, PyFloat_FromDouble(wght[ik][ib][jb]));
835- if (ierr != 0)printf("Error in PyList_SetItem\n");
836-
837- free(eig1[0]);
838- free(eig1);
839- free(eig2[0]);
840- free(eig2);
841- free(wght[0][0]);
842- free(wght[0]);
843- free(wght);
844-
845- return wght_po;
846-}
847-/*
848-Tetrahedron method for theta( - de)
849-*/
850-static void libtetrabz_dblstep2(
851- int nb,
852- double ei[4],
853- double **ej,
854- double **w1
855-) {
856- int i4, j4, ib, indx[4];
857- double v, thr, e[4], tsmall[4][4];
858-
859- thr = 1.0e-8;
860-
861- for (ib = 0; ib < nb; ib++) {
862-
863- for (i4 = 0; i4 < 4; i4++)
864- w1[ib][i4] = 0.0;
865-
866- for (i4 = 0; i4 < 4; i4++) e[i4] = - ei[i4] + ej[ib][i4];
867- eig_sort(4, e, indx);
868-
869- if (fabs(e[0]) < thr && fabs(e[3]) < thr) {
870- /*
871- Theta(0) = 0.5
872- */
873- v = 0.5;
874- for (i4 = 0; i4 < 4; i4++)
875- w1[ib][i4] += v * 0.25;
876- }
877- else if ((e[0] <= 0.0 && 0.0 < e[1]) || (e[0] < 0.0 && 0.0 <= e[1])) {
878- libtetrabz_tsmall_a1(e, 0.0, &v, tsmall);
879- for (i4 = 0; i4 < 4; i4++)
880- for (j4 = 0; j4 < 4; j4++)
881- w1[ib][indx[i4]] += v * tsmall[i4][j4] * 0.25;
882- }
883- else if ((e[1] <= 0.0 && 0.0 < e[2]) || (e[1] < 0.0 && 0.0 <= e[2])) {
884-
885- libtetrabz_tsmall_b1(e, 0.0, &v, tsmall);
886- for (i4 = 0; i4 < 4; i4++)
887- for (j4 = 0; j4 < 4; j4++)
888- w1[ib][indx[i4]] += v * tsmall[i4][j4] * 0.25;
889-
890- libtetrabz_tsmall_b2(e, 0.0, &v, tsmall);
891- for (i4 = 0; i4 < 4; i4++)
892- for (j4 = 0; j4 < 4; j4++)
893- w1[ib][indx[i4]] += v * tsmall[i4][j4] * 0.25;
894-
895- libtetrabz_tsmall_b3(e, 0.0, &v, tsmall);
896- for (i4 = 0; i4 < 4; i4++)
897- for (j4 = 0; j4 < 4; j4++)
898- w1[ib][indx[i4]] += v * tsmall[i4][j4] * 0.25;
899- }
900- else if ((e[2] <= 0.0 && 0.0 < e[3]) || (e[2] < 0.0 && 0.0 <= e[3])) {
901-
902- libtetrabz_tsmall_c1(e, 0.0, &v, tsmall);
903- for (i4 = 0; i4 < 4; i4++)
904- for (j4 = 0; j4 < 4; j4++)
905- w1[ib][indx[i4]] += v * tsmall[i4][j4] * 0.25;
906-
907- libtetrabz_tsmall_c2(e, 0.0, &v, tsmall);
908- for (i4 = 0; i4 < 4; i4++)
909- for (j4 = 0; j4 < 4; j4++)
910- w1[ib][indx[i4]] += v * tsmall[i4][j4] * 0.25;
911-
912- libtetrabz_tsmall_c3(e, 0.0, &v, tsmall);
913- for (i4 = 0; i4 < 4; i4++)
914- for (j4 = 0; j4 < 4; j4++)
915- w1[ib][indx[i4]] += v * tsmall[i4][j4] * 0.25;
916- }
917- else if (e[3] <= 0.0) {
918- for (i4 = 0; i4 < 4; i4++)
919- w1[ib][i4] += 0.25;
920- }
921- }
922-}
923-/*
924-Main SUBROUTINE for Theta(- E1) * Theta(E1 - E2)
925-*/
926-static PyObject* dblstep_c(PyObject* self, PyObject* args)
927-{
928- int it, ik, ib, jb, i20, i4, j4, **ikv, indx[4], ierr, ng[3], nk, nb;
929- double wlsm[20][4], **ei1, **ej1, ei2[4], ** ej2, e[4], *** w1, ** w2, v, tsmall[4][4], thr,
930- bvec[3][3], ** eig1, ** eig2, *** wght;
931- PyObject* eig1_po, * eig2_po, * wght_po;
932-
933- /*
934- Read input from python object
935- */
936- if (!PyArg_ParseTuple(args, "iiiiidddddddddOO",
937- &ng[0], &ng[1], &ng[2], &nk, &nb,
938- &bvec[0][0], &bvec[0][1], &bvec[0][2], &bvec[1][0], &bvec[1][1], &bvec[1][2], &bvec[2][0], &bvec[2][1], &bvec[2][2],
939- &eig1_po, &eig2_po))
940- return NULL;
941- /*
942- convert python list object to array
943- */
944- eig1 = (double**)malloc(nk * sizeof(double*));
945- eig1[0] = (double*)malloc(nk * nb * sizeof(double));
946- eig2 = (double**)malloc(nk * sizeof(double*));
947- eig2[0] = (double*)malloc(nk * nb * sizeof(double));
948- wght = (double***)malloc(nk * sizeof(double**));
949- wght[0] = (double**)malloc(nk * nb * sizeof(double*));
950- wght[0][0] = (double*)malloc(nk * nb * nb * sizeof(double));
951- for (ik = 0; ik < nk; ik++) {
952- eig1[ik] = eig1[0] + ik * nb;
953- eig2[ik] = eig2[0] + ik * nb;
954- wght[ik] = wght[0] + ik * nb;
955- for (ib = 0; ib < nb; ib++) {
956- wght[ik][ib] = wght[0][0] + ik * nb * nb + ib * nb;
957- }
958- }
959-
960- for (ik = 0; ik < nk; ik++)
961- for (ib = 0; ib < nb; ib++) {
962- eig1[ik][ib] = PyFloat_AsDouble(PyList_GetItem(eig1_po, ik * nb + ib));
963- eig2[ik][ib] = PyFloat_AsDouble(PyList_GetItem(eig2_po, ik * nb + ib));
964- }
965- /*
966- Start main calculation
967- */
968- ikv = (int**)malloc(6 * nk * sizeof(int*));
969- ikv[0] = (int*)malloc(6 * nk * 20 * sizeof(int));
970- for (ik = 0; ik < 6 * nk; ik++) {
971- ikv[ik] = ikv[0] + ik * 20;
972- }
973-
974- ei1 = (double**)malloc(4 * sizeof(double*));
975- ej1 = (double**)malloc(4 * sizeof(double*));
976- ei1[0] = (double*)malloc(4 * nb * sizeof(double));
977- ej1[0] = (double*)malloc(4 * nb * sizeof(double));
978- for (i4 = 0; i4 < 4; i4++) {
979- ei1[i4] = ei1[0] + i4 * nb;
980- ej1[i4] = ej1[0] + i4 * nb;
981- }
982-
983- ej2 = (double**)malloc(nb * sizeof(double*));
984- ej2[0] = (double*)malloc(nb * 4 * sizeof(double));
985- for (ib = 0; ib < nb; ib++) {
986- ej2[ib] = ej2[0] + ib * 4;
987- }
988-
989- w1 = (double***)malloc(nb * sizeof(double**));
990- w1[0] = (double**)malloc(nb * 4 * sizeof(double*));
991- w1[0][0] = (double*)malloc(nb * 4 * nb * sizeof(double));
992- for (ib = 0; ib < nb; ib++) {
993- w1[ib] = w1[0] + ib * 4;
994- for (i4 = 0; i4 < 4; i4++) {
995- w1[ib][i4] = w1[0][0] + ib * 4 * nb + i4 * nb;
996- }
997- }
998-
999- w2 = (double**)malloc(nb * sizeof(double*));
1000- w2[0] = (double*)malloc(nb * 4 * sizeof(double));
1001- for (ib = 0; ib < nb; ib++) {
1002- w2[ib] = w2[0] + ib * 4;
1003- }
1004-
1005- libtetrabz_initialize(ng, bvec, wlsm, ikv);
1006-
1007- for (ik = 0; ik < nk; ik++)
1008- for (ib = 0; ib < nb; ib++)
1009- for (jb = 0; jb < nb; jb++)
1010- wght[ik][ib][jb] = 0.0;
1011-
1012- thr = 1.0e-8;
1013-
1014- for(it = 0; it < 6*nk; it++) {
1015-
1016- for (i4 = 0; i4 < 4; i4++)
1017- for (ib = 0; ib < nb; ib++) {
1018- ei1[i4][ib] = 0.0;
1019- ej1[i4][ib] = 0.0;
1020- }
1021- for (i20 = 0; i20 < 20; i20++) {
1022- for (i4 = 0; i4 < 4; i4++) {
1023- for (ib = 0; ib < nb; ib++) {
1024- ei1[i4][ib] += eig1[ikv[it][i20]][ib] * wlsm[i20][i4];
1025- ej1[i4][ib] += eig2[ikv[it][i20]][ib] * wlsm[i20][i4];
1026- }
1027- }
1028- }
1029-
1030- for (ib = 0; ib < nb; ib++) {
1031-
1032- for (i4 = 0; i4 < 4; i4++)
1033- for (jb = 0; jb < nb; jb++)
1034- w1[ib][i4][jb] = 0.0;
1035-
1036- for (i4 = 0; i4 < 4; i4++) e[i4] = ei1[i4][ib];
1037- eig_sort(4, e, indx);
1038-
1039- if (e[0] <= 0.0 && 0.0 < e[1]) {
1040-
1041- libtetrabz_tsmall_a1(e, 0.0, &v, tsmall);
1042-
1043- if (v > thr) {
1044- for (j4 = 0; j4 < 4; j4++) {
1045- ei2[j4] = 0.0;
1046- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
1047- }
1048- for (i4 = 0; i4 < 4; i4++)
1049- for (j4 = 0; j4 < 4; j4++) {
1050- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
1051- for (jb = 0; jb < nb; jb++)
1052- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
1053- }
1054- libtetrabz_dblstep2(nb, ei2, ej2, w2);
1055- for (i4 = 0; i4 < 4; i4++)
1056- for (jb = 0; jb < nb; jb++)
1057- for (j4 = 0; j4 < 4; j4++)
1058- w1[ib][indx[i4]][jb] += v * tsmall[i4][j4] * w2[jb][j4];
1059- }
1060- }
1061- else if (e[1] <= 0.0 && 0.0 < e[2]) {
1062-
1063- libtetrabz_tsmall_b1(e, 0.0, &v, tsmall);
1064-
1065- if (v > thr) {
1066- for (j4 = 0; j4 < 4; j4++) {
1067- ei2[j4] = 0.0;
1068- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
1069- }
1070- for (i4 = 0; i4 < 4; i4++)
1071- for (j4 = 0; j4 < 4; j4++) {
1072- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
1073- for (jb = 0; jb < nb; jb++)
1074- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
1075- }
1076- libtetrabz_dblstep2(nb, ei2, ej2, w2);
1077- for (i4 = 0; i4 < 4; i4++)
1078- for (jb = 0; jb < nb; jb++)
1079- for (j4 = 0; j4 < 4; j4++)
1080- w1[ib][indx[i4]][jb] += v * tsmall[i4][j4] * w2[jb][j4];
1081- }
1082-
1083- libtetrabz_tsmall_b2(e, 0.0, &v, tsmall);
1084-
1085- if (v > thr) {
1086- for (j4 = 0; j4 < 4; j4++) {
1087- ei2[j4] = 0.0;
1088- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
1089- }
1090- for (i4 = 0; i4 < 4; i4++)
1091- for (j4 = 0; j4 < 4; j4++) {
1092- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
1093- for (jb = 0; jb < nb; jb++)
1094- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
1095- }
1096- libtetrabz_dblstep2(nb, ei2, ej2, w2);
1097- for (i4 = 0; i4 < 4; i4++)
1098- for (jb = 0; jb < nb; jb++)
1099- for (j4 = 0; j4 < 4; j4++)
1100- w1[ib][indx[i4]][jb] += v * tsmall[i4][j4] * w2[jb][j4];
1101- }
1102-
1103- libtetrabz_tsmall_b3(e, 0.0, &v, tsmall);
1104-
1105- if (v > thr) {
1106- for (j4 = 0; j4 < 4; j4++) {
1107- ei2[j4] = 0.0;
1108- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
1109- }
1110- for (i4 = 0; i4 < 4; i4++)
1111- for (j4 = 0; j4 < 4; j4++) {
1112- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
1113- for (jb = 0; jb < nb; jb++)
1114- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
1115- }
1116- libtetrabz_dblstep2(nb, ei2, ej2, w2);
1117- for (i4 = 0; i4 < 4; i4++)
1118- for (jb = 0; jb < nb; jb++)
1119- for (j4 = 0; j4 < 4; j4++)
1120- w1[ib][indx[i4]][jb] += v * tsmall[i4][j4] * w2[jb][j4];
1121- }
1122- }
1123- else if (e[2] <= 0.0 && 0.0 < e[3]) {
1124-
1125- libtetrabz_tsmall_c1(e, 0.0, &v, tsmall);
1126-
1127- if (v > thr) {
1128- for (j4 = 0; j4 < 4; j4++) {
1129- ei2[j4] = 0.0;
1130- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
1131- }
1132- for (i4 = 0; i4 < 4; i4++)
1133- for (j4 = 0; j4 < 4; j4++) {
1134- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
1135- for (jb = 0; jb < nb; jb++)
1136- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
1137- }
1138- libtetrabz_dblstep2(nb, ei2, ej2, w2);
1139- for (i4 = 0; i4 < 4; i4++)
1140- for (jb = 0; jb < nb; jb++)
1141- for (j4 = 0; j4 < 4; j4++)
1142- w1[ib][indx[i4]][jb] += v * tsmall[i4][j4] * w2[jb][j4];
1143- }
1144-
1145- libtetrabz_tsmall_c2(e, 0.0, &v, tsmall);
1146-
1147- if (v > thr) {
1148- for (j4 = 0; j4 < 4; j4++) {
1149- ei2[j4] = 0.0;
1150- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
1151- }
1152- for (i4 = 0; i4 < 4; i4++)
1153- for (j4 = 0; j4 < 4; j4++) {
1154- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
1155- for (jb = 0; jb < nb; jb++)
1156- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
1157- }
1158- libtetrabz_dblstep2(nb, ei2, ej2, w2);
1159- for (i4 = 0; i4 < 4; i4++)
1160- for (jb = 0; jb < nb; jb++)
1161- for (j4 = 0; j4 < 4; j4++)
1162- w1[ib][indx[i4]][jb] += v * tsmall[i4][j4] * w2[jb][j4];
1163- }
1164-
1165- libtetrabz_tsmall_c3(e, 0.0, &v, tsmall);
1166-
1167- if (v > thr) {
1168- for (j4 = 0; j4 < 4; j4++) {
1169- ei2[j4] = 0.0;
1170- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
1171- }
1172- for (i4 = 0; i4 < 4; i4++)
1173- for (j4 = 0; j4 < 4; j4++) {
1174- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
1175- for (jb = 0; jb < nb; jb++)
1176- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
1177- }
1178- libtetrabz_dblstep2(nb, ei2, ej2, w2);
1179- for (i4 = 0; i4 < 4; i4++)
1180- for (jb = 0; jb < nb; jb++)
1181- for (j4 = 0; j4 < 4; j4++)
1182- w1[ib][indx[i4]][jb] += v * tsmall[i4][j4] * w2[jb][j4];
1183- }
1184- }
1185- else if (e[3] <= 0.0) {
1186- for (i4 = 0; i4 < 4; i4++) {
1187- ei2[i4] = ei1[i4][ib];
1188- for (jb = 0; jb < nb; jb++)
1189- ej2[jb][i4] = ej1[i4][jb];
1190- }
1191- libtetrabz_dblstep2(nb, ei2, ej2, w2);
1192- for (i4 = 0; i4 < 4; i4++)
1193- for (jb = 0; jb < nb; jb++)
1194- w1[ib][i4][jb] += w2[jb][i4];
1195- }
1196- else {
1197- continue;
1198- }
1199- }
1200- for (i20 = 0; i20 < 20; i20++)
1201- for (ib = 0; ib < nb; ib++)
1202- for (i4 = 0; i4 < 4; i4++)
1203- for (jb = 0; jb < nb; jb++)
1204- wght[ikv[it][i20]][ib][jb] += wlsm[i20][i4] * w1[ib][i4][jb];
1205- }
1206- for (ik = 0; ik < nk; ik++)
1207- for (ib = 0; ib < nb; ib++)
1208- for (jb = 0; jb < nb; jb++)
1209- wght[ik][ib][jb] /= (6.0 * (double) nk);
1210-
1211- free(ikv[0]);
1212- free(ikv);
1213- free(ei1[0]);
1214- free(ei1);
1215- free(ej1[0]);
1216- free(ej1);
1217- free(ej2[0]);
1218- free(ej2);
1219- free(w1[0][0]);
1220- free(w1[0]);
1221- free(w1);
1222- free(w2[0]);
1223- free(w2);
1224- /*
1225- Convert weight to python list object
1226- */
1227- wght_po = PyList_New(nk * nb * nb);
1228- ierr = 0;
1229- for (ik = 0; ik < nk; ik++)
1230- for (ib = 0; ib < nb; ib++)
1231- for (jb = 0; jb < nb; jb++)
1232- ierr = PyList_SetItem(wght_po, ik * nb * nb + ib * nb + jb, PyFloat_FromDouble(wght[ik][ib][jb]));
1233- if (ierr != 0)printf("Error in PyList_SetItem\n");
1234-
1235- free(eig1[0]);
1236- free(eig1);
1237- free(eig2[0]);
1238- free(eig2);
1239- free(wght[0][0]);
1240- free(wght[0]);
1241- free(wght);
1242-
1243- return wght_po;
1244-}
1245-/*
1246-Compute Dos : Delta(E - E1)
1247-*/
1248-static PyObject* dos_c(PyObject* self, PyObject* args) {
1249- int it, ik, ib, ii, jj, ie, ** ikv, indx[4], ierr, ng[3], nk, nb, ne;
1250- double wlsm[20][4], ** ei1, e[4], *** w1, v, tsmall[4][3], bvec[3][3], ** eig, * e0, *** wght;
1251- PyObject* eig_po, * e0_po, * wght_po;
1252- /*
1253- Read input from python object
1254- */
1255- if (!PyArg_ParseTuple(args, "iiiiiidddddddddOO",
1256- &ng[0], &ng[1], &ng[2], &nk, &nb, &ne,
1257- &bvec[0][0], &bvec[0][1], &bvec[0][2], &bvec[1][0], &bvec[1][1], &bvec[1][2], &bvec[2][0], &bvec[2][1], &bvec[2][2],
1258- &eig_po, &e0_po))
1259- return NULL;
1260- /*
1261- convert python list object to array
1262- */
1263- eig = (double**)malloc(nk * sizeof(double*));
1264- eig[0] = (double*)malloc(nk * nb * sizeof(double));
1265- wght = (double***)malloc(nk * sizeof(double**));
1266- wght[0] = (double**)malloc(nk * nb * sizeof(double*));
1267- wght[0][0] = (double*)malloc(nk * nb * ne * sizeof(double));
1268- for (ik = 0; ik < nk; ik++) {
1269- eig[ik] = eig[0] + ik * nb;
1270- wght[ik] = wght[0] + ik * nb;
1271- for (ib = 0; ib < nb; ib++) {
1272- wght[ik][ib] = wght[0][0] + ik * nb * ne + ib * ne;
1273- }
1274- }
1275- e0 = (double*)malloc(ne * sizeof(double));
1276-
1277- for (ik = 0; ik < nk; ik++)
1278- for (ib = 0; ib < nb; ib++)
1279- eig[ik][ib] = PyFloat_AsDouble(PyList_GetItem(eig_po, ik * nb + ib));
1280- for (ie = 0; ie < ne; ie++)e0[ie] = PyFloat_AsDouble(PyList_GetItem(e0_po, ie));
1281- /*
1282- Start main calculation
1283- */
1284- ikv = (int**)malloc(6 * nk * sizeof(int*));
1285- ikv[0] = (int*)malloc(6 * nk * 20 * sizeof(int));
1286- for (ik = 0; ik < 6 * nk; ik++) {
1287- ikv[ik] = ikv[0] + ik * 20;
1288- }
1289-
1290- ei1 = (double**)malloc(4 * sizeof(double*));
1291- ei1[0] = (double*)malloc(4 * nb * sizeof(double));
1292- for (ii = 0; ii < 4; ii++) {
1293- ei1[ii] = ei1[0] + ii * nb;
1294- }
1295-
1296- w1 = (double***)malloc(nb * sizeof(double**));
1297- w1[0] = (double**)malloc(nb * ne * sizeof(double*));
1298- w1[0][0] = (double*)malloc(nb * ne * 4 * sizeof(double));
1299- for (ib = 0; ib < nb; ib++) {
1300- w1[ib] = w1[0] + ib * ne;
1301- for (ie = 0; ie < ne; ie++) {
1302- w1[ib][ie] = w1[0][0] + ib * ne * 4 + ie * 4;
1303- }
1304- }
1305-
1306- libtetrabz_initialize(ng, bvec, wlsm, ikv);
1307-
1308- for (ik = 0; ik < nk; ik++)
1309- for (ib = 0; ib < nb; ib++)
1310- for (ie = 0; ie < ne; ie++)
1311- wght[ik][ib][ie] = 0.0;
1312-
1313- for (it = 0; it < 6 * nk; it++) {
1314-
1315- for (ii = 0; ii < 4; ii++)
1316- for (ib = 0; ib < nb; ib++)
1317- ei1[ii][ib] = 0.0;
1318- for (jj = 0; jj < 20; jj++)
1319- for (ii = 0; ii < 4; ii++)
1320- for (ib = 0; ib < nb; ib++)
1321- ei1[ii][ib] += eig[ikv[it][jj]][ib] * wlsm[jj][ii];
1322-
1323- for (ib = 0; ib < nb; ib++) {
1324-
1325- for (ie = 0; ie < ne; ie++)
1326- for (ii = 0; ii < 4; ii++)
1327- w1[ib][ie][ii] = 0.0;
1328-
1329- for (ii = 0; ii < 4; ii++) e[ii] = ei1[ii][ib];
1330- eig_sort(4, e, indx);
1331-
1332- for (ie = 0; ie < ne; ie++) {
1333-
1334- if ((e[0] < e0[ie] && e0[ie] <= e[1]) || (e[0] <= e0[ie] && e0[ie] < e[1])) {
1335-
1336- libtetrabz_triangle_a1(e, e0[ie], &v, tsmall);
1337- for (ii = 0; ii < 4; ii++)
1338- for (jj = 0; jj < 3; jj++)
1339- w1[ib][ie][indx[ii]] += v * tsmall[ii][jj] / 3.0;
1340-
1341- }
1342- else if ((e[1] < e0[ie] && e0[ie] <= e[2]) || (e[1] <= e0[ie] && e0[ie] < e[2])) {
1343-
1344- libtetrabz_triangle_b1(e, e0[ie], &v, tsmall);
1345- for (ii = 0; ii < 4; ii++)
1346- for (jj = 0; jj < 3; jj++)
1347- w1[ib][ie][indx[ii]] += v * tsmall[ii][jj] / 3.0;
1348-
1349- libtetrabz_triangle_b2(e, e0[ie], &v, tsmall);
1350- for (ii = 0; ii < 4; ii++)
1351- for (jj = 0; jj < 3; jj++)
1352- w1[ib][ie][indx[ii]] += v * tsmall[ii][jj] / 3.0;
1353- }
1354- else if ((e[2] < e0[ie] && e0[ie] <= e[3]) || (e[2] <= e0[ie] && e0[ie] < e[3])) {
1355-
1356- libtetrabz_triangle_c1(e, e0[ie], &v, tsmall);
1357- for (ii = 0; ii < 4; ii++)
1358- for (jj = 0; jj < 3; jj++)
1359- w1[ib][ie][indx[ii]] += v * tsmall[ii][jj] / 3.0;
1360- }
1361- else {
1362- continue;
1363- }
1364- }
1365- }
1366- for (ii = 0; ii < 20; ii++)
1367- for (ib = 0; ib < nb; ib++)
1368- for (ie = 0; ie < ne; ie++)
1369- for (jj = 0; jj < 4; jj++)
1370- wght[ikv[it][ii]][ib][ie] += wlsm[ii][jj] * w1[ib][ie][jj];
1371- }
1372- for (ik = 0; ik < nk; ik++)
1373- for (ib = 0; ib < nb; ib++)
1374- for (ie = 0; ie < ne; ie++)
1375- wght[ik][ib][ie] /= (6.0 * (double)nk);
1376-
1377- free(ikv[0]);
1378- free(ikv);
1379- free(ei1[0]);
1380- free(ei1);
1381- free(w1[0][0]);
1382- free(w1[0]);
1383- free(w1);
1384- /*
1385- Convert weight to python list object
1386- */
1387- wght_po = PyList_New(nk * nb * ne);
1388- ierr = 0;
1389- for (ik = 0; ik < nk; ik++)
1390- for (ib = 0; ib < nb; ib++)
1391- for (ie = 0; ie < ne; ie++)
1392- ierr = PyList_SetItem(wght_po, ik * nb * ne + ib * ne + ie, PyFloat_FromDouble(wght[ik][ib][ie]));
1393- if (ierr != 0)printf("Error in PyList_SetItem\n");
1394-
1395- free(eig[0]);
1396- free(eig);
1397- free(wght[0][0]);
1398- free(wght[0]);
1399- free(wght);
1400- free(e0);
1401-
1402- return wght_po;
1403-}
1404-/*
1405-Compute integrated Dos : theta(E - E1)
1406-*/
1407-static PyObject* intdos_c(PyObject* self, PyObject* args) {
1408- int it, ik, ib, ii, jj, ie, ** ikv, indx[4], ierr, ng[3], nk, nb, ne;
1409- double wlsm[20][4], ** ei1, e[4], *** w1, v, tsmall[4][4], bvec[3][3], ** eig, * e0, *** wght;
1410- PyObject* eig_po, * e0_po, * wght_po;
1411- /*
1412- Read input from python object
1413- */
1414- if (!PyArg_ParseTuple(args, "iiiiiidddddddddOO",
1415- &ng[0], &ng[1], &ng[2], &nk, &nb, &ne,
1416- &bvec[0][0], &bvec[0][1], &bvec[0][2], &bvec[1][0], &bvec[1][1], &bvec[1][2], &bvec[2][0], &bvec[2][1], &bvec[2][2],
1417- &eig_po, &e0_po))
1418- return NULL;
1419- /*
1420- convert python list object to array
1421- */
1422- eig = (double**)malloc(nk * sizeof(double*));
1423- eig[0] = (double*)malloc(nk * nb * sizeof(double));
1424- wght = (double***)malloc(nk * sizeof(double**));
1425- wght[0] = (double**)malloc(nk * nb * sizeof(double*));
1426- wght[0][0] = (double*)malloc(nk * nb * ne * sizeof(double));
1427- for (ik = 0; ik < nk; ik++) {
1428- eig[ik] = eig[0] + ik * nb;
1429- wght[ik] = wght[0] + ik * nb;
1430- for (ib = 0; ib < nb; ib++) {
1431- wght[ik][ib] = wght[0][0] + ik * nb * ne + ib * ne;
1432- }
1433- }
1434- e0 = (double*)malloc(ne * sizeof(double));
1435-
1436- for (ik = 0; ik < nk; ik++)
1437- for (ib = 0; ib < nb; ib++)
1438- eig[ik][ib] = PyFloat_AsDouble(PyList_GetItem(eig_po, ik * nb + ib));
1439- for (ie = 0; ie < ne; ie++)e0[ie] = PyFloat_AsDouble(PyList_GetItem(e0_po, ie));
1440- /*
1441- Start main calculation
1442- */
1443- ikv = (int**)malloc(6 * nk * sizeof(int*));
1444- ikv[0] = (int*)malloc(6 * nk * 20 * sizeof(int));
1445- for (ik = 0; ik < 6 * nk; ik++) {
1446- ikv[ik] = ikv[0] + ik * 20;
1447- }
1448-
1449- ei1 = (double**)malloc(4 * sizeof(double*));
1450- ei1[0] = (double*)malloc(4 * nb * sizeof(double));
1451- for (ii = 0; ii < 4; ii++) {
1452- ei1[ii] = ei1[0] + ii * nb;
1453- }
1454-
1455- w1 = (double***)malloc(nb * sizeof(double**));
1456- w1[0] = (double**)malloc(nb * ne * sizeof(double*));
1457- w1[0][0] = (double*)malloc(nb * ne * 4 * sizeof(double));
1458- for (ib = 0; ib < nb; ib++) {
1459- w1[ib] = w1[0] + ib * ne;
1460- for (ie = 0; ie < ne; ie++) {
1461- w1[ib][ie] = w1[0][0] + ib * ne * 4 + ie * 4;
1462- }
1463- }
1464-
1465- libtetrabz_initialize(ng, bvec, wlsm, ikv);
1466-
1467- for (ik = 0; ik < nk; ik++)
1468- for (ib = 0; ib < nb; ib++)
1469- for (ie = 0; ie < ne; ie++)
1470- wght[ik][ib][ie] = 0.0;
1471-
1472- for (it = 0; it < 6 * nk; it++) {
1473-
1474- for (ii = 0; ii < 4; ii++)
1475- for (ib = 0; ib < nb; ib++)
1476- ei1[ii][ib] = 0.0;
1477- for (jj = 0; jj < 20; jj++)
1478- for (ii = 0; ii < 4; ii++)
1479- for (ib = 0; ib < nb; ib++)
1480- ei1[ii][ib] += eig[ikv[it][jj]][ib] * wlsm[jj][ii];
1481-
1482- for (ib = 0; ib < nb; ib++)
1483- for (ie = 0; ie < ne; ie++)
1484- for (ii = 0; ii < 4; ii++)
1485- w1[ib][ie][ii] = 0.0;
1486-
1487- for (ib = 0; ib < nb; ib++) {
1488-
1489- for (ii = 0; ii < 4; ii++) e[ii] = ei1[ii][ib];
1490- eig_sort(4, e, indx);
1491-
1492- for (ie = 0; ie < ne; ie++) {
1493-
1494- if ((e[0] <= e0[ie] && e0[ie] < e[1]) || (e[0] < e0[ie] && e0[ie] <= e[1])) {
1495- libtetrabz_tsmall_a1(e, e0[ie], &v, tsmall);
1496- for (ii = 0; ii < 4; ii++)
1497- for (jj = 0; jj < 4; jj++)
1498- w1[ib][ie][indx[ii]] += v * tsmall[ii][jj] * 0.25;
1499- }
1500- else if ((e[1] <= e0[ie] && e0[ie] < e[2]) || (e[1] < e0[ie] && e0[ie] <= e[2])) {
1501-
1502- libtetrabz_tsmall_b1(e, e0[ie], &v, tsmall);
1503- for (ii = 0; ii < 4; ii++)
1504- for (jj = 0; jj < 4; jj++)
1505- w1[ib][ie][indx[ii]] += v * tsmall[ii][jj] * 0.25;
1506-
1507- libtetrabz_tsmall_b2(e, e0[ie], &v, tsmall);
1508- for (ii = 0; ii < 4; ii++)
1509- for (jj = 0; jj < 4; jj++)
1510- w1[ib][ie][indx[ii]] += v * tsmall[ii][jj] * 0.25;
1511-
1512- libtetrabz_tsmall_b3(e, e0[ie], &v, tsmall);
1513- for (ii = 0; ii < 4; ii++)
1514- for (jj = 0; jj < 4; jj++)
1515- w1[ib][ie][indx[ii]] += v * tsmall[ii][jj] * 0.25;
1516-
1517- }
1518- else if ((e[2] <= e0[ie] && e0[ie] < e[3]) || (e[2] < e0[ie] && e0[ie] <= e[3])) {
1519-
1520- libtetrabz_tsmall_c1(e, e0[ie], &v, tsmall);
1521- for (ii = 0; ii < 4; ii++)
1522- for (jj = 0; jj < 4; jj++)
1523- w1[ib][ie][indx[ii]] += v * tsmall[ii][jj] * 0.25;
1524-
1525- libtetrabz_tsmall_c2(e, e0[ie], &v, tsmall);
1526- for (ii = 0; ii < 4; ii++)
1527- for (jj = 0; jj < 4; jj++)
1528- w1[ib][ie][indx[ii]] += v * tsmall[ii][jj] * 0.25;
1529-
1530- libtetrabz_tsmall_c3(e, e0[ie], &v, tsmall);
1531- for (ii = 0; ii < 4; ii++)
1532- for (jj = 0; jj < 4; jj++)
1533- w1[ib][ie][indx[ii]] += v * tsmall[ii][jj] * 0.25;
1534-
1535- }
1536- else if (e[3] <= e0[ie]) {
1537- for (ii = 0; ii < 4; ii++)
1538- w1[ib][ie][ii] = 0.25;
1539- }
1540- else {
1541- continue;
1542- }
1543- }
1544- }
1545-
1546- for (ii = 0; ii < 20; ii++)
1547- for (ib = 0; ib < nb; ib++)
1548- for (ie = 0; ie < ne; ie++)
1549- for (jj = 0; jj < 4; jj++)
1550- wght[ikv[it][ii]][ib][ie] += wlsm[ii][jj] * w1[ib][ie][jj];
1551- }
1552- for (ik = 0; ik < nk; ik++)
1553- for (ib = 0; ib < nb; ib++)
1554- for (ie = 0; ie < ne; ie++)
1555- wght[ik][ib][ie] /= (6.0 * (double)nk);
1556-
1557- free(ikv[0]);
1558- free(ikv);
1559- free(ei1[0]);
1560- free(ei1);
1561- free(w1[0][0]);
1562- free(w1[0]);
1563- free(w1);
1564- /*
1565- Convert weight to python list object
1566- */
1567- wght_po = PyList_New(nk * nb * ne);
1568- ierr = 0;
1569- for (ik = 0; ik < nk; ik++)
1570- for (ib = 0; ib < nb; ib++)
1571- for (ie = 0; ie < ne; ie++)
1572- ierr = PyList_SetItem(wght_po, ik * nb * ne + ib * ne + ie, PyFloat_FromDouble(wght[ik][ib][ie]));
1573- if (ierr != 0)printf("Error in PyList_SetItem\n");
1574-
1575- free(eig[0]);
1576- free(eig);
1577- free(wght[0][0]);
1578- free(wght[0]);
1579- free(wght);
1580- free(e0);
1581-
1582- return wght_po; }
1583-/*
1584- 3rd step for Fermi's golden rule
1585-*/
1586-static void libtetrabz_fermigr3(
1587- int ne,
1588- double *e0,
1589- double de[4],
1590- double **w1
1591-) {
1592- int i4, j3, ie, indx[4];
1593- double e[4], tsmall[4][3], v;
1594-
1595- for (i4 = 0; i4 < 4; i4++) e[i4] = de[i4];
1596- eig_sort(4, e, indx);
1597-
1598- for (ie = 0; ie < ne; ie++) {
1599-
1600- for (i4 = 0; i4 < 4; i4++) w1[i4][ie] = 0.0;
1601-
1602- if (e[0] < e0[ie] && e0[ie] <= e[1]) {
1603-
1604- libtetrabz_triangle_a1(e, e0[ie], &v, tsmall);
1605- for (i4 = 0; i4 < 4; i4++)
1606- for (j3 = 0; j3 < 3; j3++)
1607- w1[indx[i4]][ie] += v * tsmall[i4][j3] / 3.0;
1608- }
1609- else if (e[1] < e0[ie] && e0[ie] <= e[2]) {
1610-
1611- libtetrabz_triangle_b1(e, e0[ie], &v, tsmall);
1612- for (i4 = 0; i4 < 4; i4++)
1613- for (j3 = 0; j3 < 3; j3++)
1614- w1[indx[i4]][ie] += v * tsmall[i4][j3] / 3.0;
1615-
1616- libtetrabz_triangle_b2(e, e0[ie], &v, tsmall);
1617- for (i4 = 0; i4 < 4; i4++)
1618- for (j3 = 0; j3 < 3; j3++)
1619- w1[indx[i4]][ie] += v * tsmall[i4][j3] / 3.0;
1620- }
1621- else if (e[2] < e0[ie] && e0[ie] < e[3]) {
1622-
1623- libtetrabz_triangle_c1(e, e0[ie], &v, tsmall);
1624- for (i4 = 0; i4 < 4; i4++)
1625- for (j3 = 0; j3 < 3; j3++)
1626- w1[indx[i4]][ie] += v * tsmall[i4][j3] / 3.0;
1627- }
1628- }
1629-}
1630-/*
1631-2nd step for Fermi's golden rule
1632-*/
1633-static void libtetrabz_fermigr2(
1634- int nb,
1635- int ne,
1636- double *e0,
1637- double *ei1,
1638- double **ej1,
1639- double ***w1
1640-) {
1641- int ib, i4, j4, ie, indx[4];
1642- double e[4], tsmall[4][4], v, de[4], thr, **w2;
1643-
1644- w2 = (double**)malloc(4 * sizeof(double*));
1645- w2[0] = (double*)malloc(4 * ne * sizeof(double));
1646- for (i4 = 0; i4 < 4; i4++) {
1647- w2[i4] = w2[0] + i4 * ne;
1648- }
1649-
1650- thr = 1.0e-8;
1651-
1652- for (ib = 0; ib < nb; ib++) {
1653-
1654- for (i4 = 0; i4 < 4; i4++)
1655- for (ie = 0; ie < ne; ie++)
1656- w1[ib][i4][ie] = 0.0;
1657-
1658- for (i4 = 0; i4 < 4; i4++) e[i4] = -ej1[ib][i4];
1659- eig_sort(4, e, indx);
1660-
1661- if ((e[0] <= 0.0 && 0.0 < e[1]) || (e[0] < 0.0 && 0.0 <= e[1])) {
1662-
1663- libtetrabz_tsmall_a1(e, 0.0, &v, tsmall);
1664-
1665- if (v > thr) {
1666- for (j4 = 0; j4 < 4; j4++) de[j4] = 0.0;
1667- for (i4 = 0; i4 < 4; i4++)
1668- for (j4 = 0; j4 < 4; j4++)
1669- de[j4] += (ej1[ib][indx[i4]] - ei1[indx[i4]]) * tsmall[i4][j4];
1670- libtetrabz_fermigr3(ne, e0, de, w2);
1671- for (i4 = 0; i4 < 4; i4++)
1672- for (j4 = 0; j4 < 4; j4++)
1673- for (ie = 0; ie < ne; ie++)
1674- w1[ib][indx[i4]][ie] += v * tsmall[i4][j4] * w2[j4][ie];
1675- }
1676- }
1677- else if ((e[1] <= 0.0 && 0.0 < e[2]) || (e[1] < 0.0 && 0.0 <= e[2])) {
1678-
1679- libtetrabz_tsmall_b1(e, 0.0, &v, tsmall);
1680-
1681- if (v > thr) {
1682- for (j4 = 0; j4 < 4; j4++) de[j4] = 0.0;
1683- for (i4 = 0; i4 < 4; i4++)
1684- for (j4 = 0; j4 < 4; j4++)
1685- de[j4] += (ej1[ib][indx[i4]] - ei1[indx[i4]]) * tsmall[i4][j4];
1686- libtetrabz_fermigr3(ne, e0, de, w2);
1687- for (i4 = 0; i4 < 4; i4++)
1688- for (j4 = 0; j4 < 4; j4++)
1689- for (ie = 0; ie < ne; ie++)
1690- w1[ib][indx[i4]][ie] += v * tsmall[i4][j4] * w2[j4][ie];
1691- }
1692-
1693- libtetrabz_tsmall_b2(e, 0.0, &v, tsmall);
1694-
1695- if (v > thr) {
1696- for (j4 = 0; j4 < 4; j4++) de[j4] = 0.0;
1697- for (i4 = 0; i4 < 4; i4++)
1698- for (j4 = 0; j4 < 4; j4++)
1699- de[j4] += (ej1[ib][indx[i4]] - ei1[indx[i4]]) * tsmall[i4][j4];
1700- libtetrabz_fermigr3(ne, e0, de, w2);
1701- for (i4 = 0; i4 < 4; i4++)
1702- for (j4 = 0; j4 < 4; j4++)
1703- for (ie = 0; ie < ne; ie++)
1704- w1[ib][indx[i4]][ie] += v * tsmall[i4][j4] * w2[j4][ie];
1705- }
1706-
1707- libtetrabz_tsmall_b3(e, 0.0, &v, tsmall);
1708-
1709- if (v > thr) {
1710- for (j4 = 0; j4 < 4; j4++) de[j4] = 0.0;
1711- for (i4 = 0; i4 < 4; i4++)
1712- for (j4 = 0; j4 < 4; j4++)
1713- de[j4] += (ej1[ib][indx[i4]] - ei1[indx[i4]]) * tsmall[i4][j4];
1714- libtetrabz_fermigr3(ne, e0, de, w2);
1715- for (i4 = 0; i4 < 4; i4++)
1716- for (j4 = 0; j4 < 4; j4++)
1717- for (ie = 0; ie < ne; ie++)
1718- w1[ib][indx[i4]][ie] += v * tsmall[i4][j4] * w2[j4][ie];
1719- }
1720- }
1721- else if ((e[2] <= 0.0 && 0.0 < e[3]) || (e[2] < 0.0 && 0.0 <= e[3])) {
1722-
1723- libtetrabz_tsmall_c1(e, 0.0, &v, tsmall);
1724-
1725- if (v > thr) {
1726- for (j4 = 0; j4 < 4; j4++) de[j4] = 0.0;
1727- for (i4 = 0; i4 < 4; i4++)
1728- for (j4 = 0; j4 < 4; j4++)
1729- de[j4] += (ej1[ib][indx[i4]] - ei1[indx[i4]]) * tsmall[i4][j4];
1730- libtetrabz_fermigr3(ne, e0, de, w2);
1731- for (i4 = 0; i4 < 4; i4++)
1732- for (j4 = 0; j4 < 4; j4++)
1733- for (ie = 0; ie < ne; ie++)
1734- w1[ib][indx[i4]][ie] += v * tsmall[i4][j4] * w2[j4][ie];
1735- }
1736-
1737- libtetrabz_tsmall_c2(e, 0.0, &v, tsmall);
1738-
1739- if (v > thr) {
1740- for (j4 = 0; j4 < 4; j4++) de[j4] = 0.0;
1741- for (i4 = 0; i4 < 4; i4++)
1742- for (j4 = 0; j4 < 4; j4++)
1743- de[j4] += (ej1[ib][indx[i4]] - ei1[indx[i4]]) * tsmall[i4][j4];
1744- libtetrabz_fermigr3(ne, e0, de, w2);
1745- for (i4 = 0; i4 < 4; i4++)
1746- for (j4 = 0; j4 < 4; j4++)
1747- for (ie = 0; ie < ne; ie++)
1748- w1[ib][indx[i4]][ie] += v * tsmall[i4][j4] * w2[j4][ie];
1749- }
1750-
1751- libtetrabz_tsmall_c3(e, 0.0, &v, tsmall);
1752-
1753- if (v > thr) {
1754- for (j4 = 0; j4 < 4; j4++) de[j4] = 0.0;
1755- for (i4 = 0; i4 < 4; i4++)
1756- for (j4 = 0; j4 < 4; j4++)
1757- de[j4] += (ej1[ib][indx[i4]] - ei1[indx[i4]]) * tsmall[i4][j4];
1758- libtetrabz_fermigr3(ne, e0, de, w2);
1759- for (i4 = 0; i4 < 4; i4++)
1760- for (j4 = 0; j4 < 4; j4++)
1761- for (ie = 0; ie < ne; ie++)
1762- w1[ib][indx[i4]][ie] += v * tsmall[i4][j4] * w2[j4][ie];
1763- }
1764- }
1765- else if (e[3] <= 0.0) {
1766- for (i4 = 0; i4 < 4; i4++)
1767- de[i4] = ej1[ib][i4] - ei1[i4];
1768- libtetrabz_fermigr3(ne, e0, de, w2);
1769- for (i4 = 0; i4 < 4; i4++)
1770- for (ie = 0; ie < ne; ie++)
1771- w1[ib][i4][ie] += w2[i4][ie];
1772- }
1773- }
1774-
1775- free(w2[0]);
1776- free(w2);
1777-}
1778-/*
1779-Main SUBROUTINE for Fermi's Golden rule : Theta(- E1) * Theta(E2) * Delta(E2 - E1 - w)
1780-*/
1781-static PyObject* fermigr_c(PyObject* self, PyObject* args)
1782-{
1783- int it, ik, ib, i20, i4, j4, jb, ie, **ikv, indx[4], ierr, ng[3], nk, nb, ne;
1784- double wlsm[20][4], **ei1, **ej1, ei2[4], ** ej2, e[4], **** w1, *** w2, v, tsmall[4][4], thr,
1785- bvec[3][3], ** eig1, ** eig2, *e0, * ***wght;
1786- PyObject* eig1_po, * eig2_po, *e0_po, * wght_po;
1787- /*
1788- Read input from python object
1789- */
1790- if (!PyArg_ParseTuple(args, "iiiiiidddddddddOOO",
1791- &ng[0], &ng[1], &ng[2], &nk, &nb, &ne,
1792- &bvec[0][0], &bvec[0][1], &bvec[0][2], &bvec[1][0], &bvec[1][1], &bvec[1][2], &bvec[2][0], &bvec[2][1], &bvec[2][2],
1793- &eig1_po, &eig2_po, &e0_po))
1794- return NULL;
1795- /*
1796- convert python list object to array
1797- */
1798- eig1 = (double**)malloc(nk * sizeof(double*));
1799- eig1[0] = (double*)malloc(nk * nb * sizeof(double));
1800- eig2 = (double**)malloc(nk * sizeof(double*));
1801- eig2[0] = (double*)malloc(nk * nb * sizeof(double));
1802- wght = (double****)malloc(nk * sizeof(double***));
1803- wght[0] = (double***)malloc(nk * nb * sizeof(double**));
1804- wght[0][0] = (double**)malloc(nk * nb * nb * sizeof(double*));
1805- wght[0][0][0] = (double*)malloc(nk * nb * nb *ne *sizeof(double));
1806- for (ik = 0; ik < nk; ik++) {
1807- eig1[ik] = eig1[0] + ik * nb;
1808- eig2[ik] = eig2[0] + ik * nb;
1809- wght[ik] = wght[0] + ik * nb;
1810- for (ib = 0; ib < nb; ib++) {
1811- wght[ik][ib] = wght[0][0] + ik * nb * nb + ib * nb;
1812- for (jb = 0; jb < nb; jb++) {
1813- wght[ik][ib][jb] = wght[0][0][0]
1814- + ik * nb * nb * ne + ib * nb * ne + jb * ne;
1815- }
1816- }
1817- }
1818- e0 = (double*)malloc(ne * sizeof(double));
1819-
1820- for (ik = 0; ik < nk; ik++)
1821- for (ib = 0; ib < nb; ib++) {
1822- eig1[ik][ib] = PyFloat_AsDouble(PyList_GetItem(eig1_po, ik * nb + ib));
1823- eig2[ik][ib] = PyFloat_AsDouble(PyList_GetItem(eig2_po, ik * nb + ib));
1824- }
1825- for (ie = 0; ie < ne; ie++)e0[ie] = PyFloat_AsDouble(PyList_GetItem(e0_po, ie));
1826- /*
1827- Start main calculation
1828- */
1829- ikv = (int**)malloc(6 * nk * sizeof(int*));
1830- ikv[0] = (int*)malloc(6 * nk * 20 * sizeof(int));
1831- for (it = 0; it < 6 * nk; it++) {
1832- ikv[it] = ikv[0] + it * 20;
1833- }
1834-
1835- ei1 = (double**)malloc(4 * sizeof(double*));
1836- ej1 = (double**)malloc(4 * sizeof(double*));
1837- ei1[0] = (double*)malloc(4 * nb * sizeof(double));
1838- ej1[0] = (double*)malloc(4 * nb * sizeof(double));
1839- for (i4 = 0; i4 < 4; i4++) {
1840- ei1[i4] = ei1[0] + i4 * nb;
1841- ej1[i4] = ej1[0] + i4 * nb;
1842- }
1843-
1844- ej2 = (double**)malloc(nb * sizeof(double*));
1845- ej2[0] = (double*)malloc(nb * 4 * sizeof(double));
1846- for (ib = 0; ib < nb; ib++)
1847- ej2[ib] = ej2[0] + ib * 4;
1848-
1849- w1 = (double****)malloc(nb * sizeof(double***));
1850- w1[0] = (double***)malloc(nb * 4 * sizeof(double**));
1851- w1[0][0] = (double**)malloc(nb * 4 * nb * sizeof(double*));
1852- w1[0][0][0] = (double*)malloc(nb * 4 * nb * ne * sizeof(double));
1853- for (ib = 0; ib < nb; ib++) {
1854- w1[ib] = w1[0] + ib * 4;
1855- for (i4 = 0; i4 < 4; i4++) {
1856- w1[ib][i4] = w1[0][0] + ib * 4 * nb + i4 * nb;
1857- for (jb = 0; jb < nb; jb++) {
1858- w1[ib][i4][jb] = w1[0][0][0] + ib * 4 * nb * ne + i4 * nb * ne + jb * ne;
1859- }
1860- }
1861- }
1862-
1863- w2 = (double***)malloc(nb * sizeof(double**));
1864- w2[0] = (double**)malloc(nb * 4 * sizeof(double*));
1865- w2[0][0] = (double*)malloc(nb * 4 * ne * sizeof(double));
1866- for (ib = 0; ib < nb; ib++) {
1867- w2[ib] = w2[0] + ib * 4;
1868- for (i4 = 0; i4 < 4; i4++) {
1869- w2[ib][i4] = w2[0][0] + ib * 4 * ne + i4 * ne;
1870- }
1871- }
1872-
1873- libtetrabz_initialize(ng, bvec, wlsm, ikv);
1874-
1875- for (ik = 0; ik < nk; ik++)
1876- for (ib = 0; ib < nb; ib++)
1877- for (jb = 0; jb < nb; jb++)
1878- for (ie = 0; ie < ne; ie++)
1879- wght[ik][ib][jb][ie] = 0.0;
1880-
1881- thr = 1.0e-10;
1882-
1883- for (it = 0; it < 6*nk; it++) {
1884-
1885- for (i4 = 0; i4 < 4; i4++)
1886- for (ib = 0; ib < nb; ib++) {
1887- ei1[i4][ib] = 0.0;
1888- ej1[i4][ib] = 0.0;
1889- }
1890- for (i20 = 0; i20 < 20; i20++) {
1891- for (i4 = 0; i4 < 4; i4++) {
1892- for (ib = 0; ib < nb; ib++) {
1893- ei1[i4][ib] += eig1[ikv[it][i20]][ib] * wlsm[i20][i4];
1894- ej1[i4][ib] += eig2[ikv[it][i20]][ib] * wlsm[i20][i4];
1895- }
1896- }
1897- }
1898-
1899- for (ib = 0; ib < nb; ib++) {
1900-
1901- for (i4 = 0; i4 < 4; i4++)
1902- for (jb = 0; jb < nb; jb++)
1903- for (ie = 0; ie < ne; ie++)
1904- w1[ib][i4][jb][ie] = 0.0;
1905-
1906- for (i4 = 0; i4 < 4; i4++) e[i4] = ei1[i4][ib];
1907- eig_sort(4, e, indx);
1908-
1909- if (e[0] <= 0.0 && 0.0 < e[1]) {
1910-
1911- libtetrabz_tsmall_a1(e, 0.0, &v, tsmall);
1912-
1913- if (v > thr) {
1914- for (j4 = 0; j4 < 4; j4++) {
1915- ei2[j4] = 0.0;
1916- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
1917- }
1918- for (i4 = 0; i4 < 4; i4++)
1919- for (j4 = 0; j4 < 4; j4++) {
1920- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
1921- for (jb = 0; jb < nb; jb++)
1922- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
1923- }
1924- libtetrabz_fermigr2(nb, ne, e0, ei2, ej2, w2);
1925- for (i4 = 0; i4 < 4; i4++)
1926- for (jb = 0; jb < nb; jb++)
1927- for (j4 = 0; j4 < 4; j4++)
1928- for (ie = 0; ie < ne; ie++)
1929- w1[ib][indx[i4]][jb][ie] += v * tsmall[i4][j4] * w2[jb][j4][ie];
1930- }
1931- }
1932- else if (e[1] <= 0.0 && 0.0 < e[2]) {
1933-
1934- libtetrabz_tsmall_b1(e, 0.0, &v, tsmall);
1935-
1936- if (v > thr) {
1937- for (j4 = 0; j4 < 4; j4++) {
1938- ei2[j4] = 0.0;
1939- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
1940- }
1941- for (i4 = 0; i4 < 4; i4++)
1942- for (j4 = 0; j4 < 4; j4++) {
1943- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
1944- for (jb = 0; jb < nb; jb++)
1945- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
1946- }
1947- libtetrabz_fermigr2(nb, ne, e0, ei2, ej2, w2);
1948- for (i4 = 0; i4 < 4; i4++)
1949- for (jb = 0; jb < nb; jb++)
1950- for (j4 = 0; j4 < 4; j4++)
1951- for (ie = 0; ie < ne; ie++)
1952- w1[ib][indx[i4]][jb][ie] += v * tsmall[i4][j4] * w2[jb][j4][ie];
1953- }
1954-
1955- libtetrabz_tsmall_b2(e, 0.0, &v, tsmall);
1956-
1957- if (v > thr) {
1958- for (j4 = 0; j4 < 4; j4++) {
1959- ei2[j4] = 0.0;
1960- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
1961- }
1962- for (i4 = 0; i4 < 4; i4++)
1963- for (j4 = 0; j4 < 4; j4++) {
1964- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
1965- for (jb = 0; jb < nb; jb++)
1966- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
1967- }
1968- libtetrabz_fermigr2(nb, ne, e0, ei2, ej2, w2);
1969- for (i4 = 0; i4 < 4; i4++)
1970- for (jb = 0; jb < nb; jb++)
1971- for (j4 = 0; j4 < 4; j4++)
1972- for (ie = 0; ie < ne; ie++)
1973- w1[ib][indx[i4]][jb][ie] += v * tsmall[i4][j4] * w2[jb][j4][ie];
1974- }
1975-
1976- libtetrabz_tsmall_b3(e, 0.0, &v, tsmall);
1977-
1978- if (v > thr) {
1979- for (j4 = 0; j4 < 4; j4++) {
1980- ei2[j4] = 0.0;
1981- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
1982- }
1983- for (i4 = 0; i4 < 4; i4++)
1984- for (j4 = 0; j4 < 4; j4++) {
1985- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
1986- for (jb = 0; jb < nb; jb++)
1987- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
1988- }
1989- libtetrabz_fermigr2(nb, ne, e0, ei2, ej2, w2);
1990- for (i4 = 0; i4 < 4; i4++)
1991- for (jb = 0; jb < nb; jb++)
1992- for (j4 = 0; j4 < 4; j4++)
1993- for (ie = 0; ie < ne; ie++)
1994- w1[ib][indx[i4]][jb][ie] += v * tsmall[i4][j4] * w2[jb][j4][ie];
1995- }
1996- }
1997- else if (e[2] <= 0.0 && 0.0 < e[3]) {
1998-
1999- libtetrabz_tsmall_c1(e, 0.0, &v, tsmall);
2000-
2001- if (v > thr) {
2002- for (j4 = 0; j4 < 4; j4++) {
2003- ei2[j4] = 0.0;
2004- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
2005- }
2006- for (i4 = 0; i4 < 4; i4++)
2007- for (j4 = 0; j4 < 4; j4++) {
2008- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
2009- for (jb = 0; jb < nb; jb++)
2010- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
2011- }
2012- libtetrabz_fermigr2(nb, ne, e0, ei2, ej2, w2);
2013- for (i4 = 0; i4 < 4; i4++)
2014- for (jb = 0; jb < nb; jb++)
2015- for (j4 = 0; j4 < 4; j4++)
2016- for (ie = 0; ie < ne; ie++)
2017- w1[ib][indx[i4]][jb][ie] += v * tsmall[i4][j4] * w2[jb][j4][ie];
2018- }
2019-
2020- libtetrabz_tsmall_c2(e, 0.0, &v, tsmall);
2021-
2022- if (v > thr) {
2023- for (j4 = 0; j4 < 4; j4++) {
2024- ei2[j4] = 0.0;
2025- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
2026- }
2027- for (i4 = 0; i4 < 4; i4++)
2028- for (j4 = 0; j4 < 4; j4++) {
2029- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
2030- for (jb = 0; jb < nb; jb++)
2031- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
2032- }
2033- libtetrabz_fermigr2(nb, ne, e0, ei2, ej2, w2);
2034- for (i4 = 0; i4 < 4; i4++)
2035- for (jb = 0; jb < nb; jb++)
2036- for (j4 = 0; j4 < 4; j4++)
2037- for (ie = 0; ie < ne; ie++)
2038- w1[ib][indx[i4]][jb][ie] += v * tsmall[i4][j4] * w2[jb][j4][ie];
2039- }
2040-
2041- libtetrabz_tsmall_c3(e, 0.0, &v, tsmall);
2042-
2043- if (v > thr) {
2044- for (j4 = 0; j4 < 4; j4++) {
2045- ei2[j4] = 0.0;
2046- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
2047- }
2048- for (i4 = 0; i4 < 4; i4++)
2049- for (j4 = 0; j4 < 4; j4++) {
2050- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
2051- for (jb = 0; jb < nb; jb++)
2052- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
2053- }
2054- libtetrabz_fermigr2(nb, ne, e0, ei2, ej2, w2);
2055- for (i4 = 0; i4 < 4; i4++)
2056- for (jb = 0; jb < nb; jb++)
2057- for (j4 = 0; j4 < 4; j4++)
2058- for (ie = 0; ie < ne; ie++)
2059- w1[ib][indx[i4]][jb][ie] += v * tsmall[i4][j4] * w2[jb][j4][ie];
2060- }
2061- }
2062- else if (e[3] <= 0.0) {
2063- for (i4 = 0; i4 < 4; i4++) {
2064- ei2[i4] = ei1[i4][ib];
2065- for (jb = 0; jb < nb; jb++)
2066- ej2[jb][i4] = ej1[i4][jb];
2067- }
2068- libtetrabz_fermigr2(nb, ne, e0, ei2, ej2, w2);
2069- for (i4 = 0; i4 < 4; i4++)
2070- for (jb = 0; jb < nb; jb++)
2071- for (ie = 0; ie < ne; ie++)
2072- w1[ib][i4][jb][ie] += w2[jb][i4][ie];
2073- }
2074- else {
2075- continue;
2076- }
2077- }
2078- for (i20 = 0; i20 < 20; i20++)
2079- for (ib = 0; ib < nb; ib++)
2080- for (i4 = 0; i4 < 4; i4++)
2081- for (jb = 0; jb < nb; jb++)
2082- for (ie = 0; ie < ne; ie++)
2083- wght[ikv[it][i20]][ib][jb][ie] += wlsm[i20][i4] * w1[ib][i4][jb][ie];
2084- }
2085- for (ik = 0; ik < nk; ik++)
2086- for (ib = 0; ib < nb; ib++)
2087- for (jb = 0; jb < nb; jb++)
2088- for (ie = 0; ie < ne; ie++)
2089- wght[ik][ib][jb][ie] /= (6.0 * (double) nk);
2090-
2091- free(ikv[0]);
2092- free(ikv);
2093- free(ei1[0]);
2094- free(ei1);
2095- free(ej1[0]);
2096- free(ej1);
2097- free(ej2[0]);
2098- free(ej2);
2099- free(w1[0][0][0]);
2100- free(w1[0][0]);
2101- free(w1[0]);
2102- free(w1);
2103- free(w2[0][0]);
2104- free(w2[0]);
2105- free(w2);
2106- /*
2107- Convert weight to python list object
2108- */
2109- wght_po = PyList_New(nk * nb * nb * ne);
2110- ierr = 0;
2111- for (ik = 0; ik < nk; ik++)
2112- for (ib = 0; ib < nb; ib++)
2113- for (jb = 0; jb < nb; jb++)
2114- for (ie = 0; ie < ne; ie++)
2115- ierr = PyList_SetItem(wght_po, ik * nb * nb * ne + ib * nb * ne + jb * ne + ie,
2116- PyFloat_FromDouble(wght[ik][ib][jb][ie]));
2117- if (ierr != 0)printf("Error in PyList_SetItem\n");
2118-
2119- free(eig1[0]);
2120- free(eig1);
2121- free(eig2[0]);
2122- free(eig2);
2123- free(wght[0][0][0]);
2124- free(wght[0][0]);
2125- free(wght[0]);
2126- free(wght);
2127- free(e0);
2128-
2129- return wght_po;
2130-}
2131-/*
2132-Main SUBROUTINE for occupation : Theta(EF - E1)
2133-*/
2134-void occ_main(
2135- int nk,
2136- int nb,
2137- double** eig,
2138- int **ikv,
2139- double wlsm[20][4],
2140- double **ei1,
2141- double **w1,
2142- double **wght
2143-) {
2144- int it, ik, ib, ii, jj, indx[4];
2145- double e[4], v, tsmall[4][4];
2146-
2147- for (ik = 0; ik < nk; ik++)
2148- for (ib = 0; ib < nb; ib++)
2149- wght[ik][ib] = 0.0;
2150-
2151- for (it = 0; it < 6 * nk; it++) {
2152-
2153- for (ii = 0; ii < 4; ii++)
2154- for (ib = 0; ib < nb; ib++)
2155- ei1[ii][ib] = 0.0;
2156- for (jj = 0; jj < 20; jj++)
2157- for (ii = 0; ii < 4; ii++)
2158- for (ib = 0; ib < nb; ib++)
2159- ei1[ii][ib] += eig[ikv[it][jj]][ib] * wlsm[jj][ii];
2160-
2161- for (ib = 0; ib < nb; ib++) {
2162-
2163- for (ii = 0; ii < 4; ii++)
2164- w1[ib][ii] = 0.0;
2165-
2166- for (ii = 0; ii < 4; ii++) e[ii] = ei1[ii][ib];
2167- eig_sort(4, e, indx);
2168-
2169- if (e[0] <= 0.0 && 0.0 < e[1]) {
2170- libtetrabz_tsmall_a1(e, 0.0, &v, tsmall);
2171- for (ii = 0; ii < 4; ii++)
2172- for (jj = 0; jj < 4; jj++)
2173- w1[ib][indx[ii]] += v * tsmall[ii][jj] * 0.25;
2174- }
2175- else if (e[1] <= 0.0 && 0.0 < e[2]) {
2176-
2177- libtetrabz_tsmall_b1(e, 0.0, &v, tsmall);
2178- for (ii = 0; ii < 4; ii++)
2179- for (jj = 0; jj < 4; jj++)
2180- w1[ib][indx[ii]] += v * tsmall[ii][jj] * 0.25;
2181-
2182- libtetrabz_tsmall_b2(e, 0.0, &v, tsmall);
2183- for (ii = 0; ii < 4; ii++)
2184- for (jj = 0; jj < 4; jj++)
2185- w1[ib][indx[ii]] += v * tsmall[ii][jj] * 0.25;
2186-
2187- libtetrabz_tsmall_b3(e, 0.0, &v, tsmall);
2188- for (ii = 0; ii < 4; ii++)
2189- for (jj = 0; jj < 4; jj++)
2190- w1[ib][indx[ii]] += v * tsmall[ii][jj] * 0.25;
2191- }
2192- else if (e[2] <= 0.0 && 0.0 < e[3]) {
2193-
2194- libtetrabz_tsmall_c1(e, 0.0, &v, tsmall);
2195- for (ii = 0; ii < 4; ii++)
2196- for (jj = 0; jj < 4; jj++)
2197- w1[ib][indx[ii]] += v * tsmall[ii][jj] * 0.25;
2198-
2199- libtetrabz_tsmall_c2(e, 0.0, &v, tsmall);
2200- for (ii = 0; ii < 4; ii++)
2201- for (jj = 0; jj < 4; jj++)
2202- w1[ib][indx[ii]] += v * tsmall[ii][jj] * 0.25;
2203-
2204- libtetrabz_tsmall_c3(e, 0.0, &v, tsmall);
2205- for (ii = 0; ii < 4; ii++)
2206- for (jj = 0; jj < 4; jj++)
2207- w1[ib][indx[ii]] += v * tsmall[ii][jj] * 0.25;
2208- }
2209- else if (e[3] <= 0.0) {
2210- for (ii = 0; ii < 4; ii++)
2211- w1[ib][ii] += 0.25;
2212- }
2213- else {
2214- continue;
2215- }
2216- }
2217- for (ii = 0; ii < 20; ii++)
2218- for (ib = 0; ib < nb; ib++)
2219- for (jj = 0; jj < 4; jj++) {
2220- wght[ikv[it][ii]][ib] += wlsm[ii][jj] * w1[ib][jj];
2221- }
2222- }
2223- for (ik = 0; ik < nk; ik++)
2224- for (ib = 0; ib < nb; ib++)
2225- wght[ik][ib] /= (6.0 * (double)nk);
2226-}
2227-/*
2228-
2229-*/
2230-static PyObject* occ_c(PyObject* self, PyObject* args)
2231-{
2232- int ik, ib, ii, nk, nb, ng[3], ierr, ** ikv;
2233- double** eig, ** wght, bvec[3][3], wlsm[20][4], **ei1, **w1;
2234- PyObject* eig_po, * wght_po;
2235- /*
2236- Read input from python object
2237- */
2238- if (!PyArg_ParseTuple(args, "iiiiidddddddddO",
2239- &ng[0], &ng[1], &ng[2], &nk, &nb,
2240- &bvec[0][0], &bvec[0][1], &bvec[0][2], &bvec[1][0], &bvec[1][1], &bvec[1][2], &bvec[2][0], &bvec[2][1], &bvec[2][2],
2241- &eig_po))
2242- return NULL;
2243- /*
2244- convert python list object to array
2245- */
2246- eig = (double**)malloc(nk * sizeof(double*));
2247- eig[0] = (double*)malloc(nk * nb * sizeof(double));
2248- wght = (double**)malloc(nk * sizeof(double*));
2249- wght[0] = (double*)malloc(nk * nb * sizeof(double));
2250- for (ik = 0; ik < nk; ik++) {
2251- eig[ik] = eig[0] + ik * nb;
2252- wght[ik] = wght[0] + ik * nb;
2253- }
2254-
2255- for (ik = 0; ik < nk; ik++)
2256- for (ib = 0; ib < nb; ib++)
2257- eig[ik][ib] = PyFloat_AsDouble(PyList_GetItem(eig_po, ik * nb + ib));
2258-
2259- /*
2260- Start main calculation
2261- */
2262- ikv = (int**)malloc(6 * nk * sizeof(int*));
2263- ikv[0] = (int*)malloc(6 * nk * 20 * sizeof(int));
2264- for (ik = 0; ik < 6 * nk; ik++) {
2265- ikv[ik] = ikv[0] + ik * 20;
2266- }
2267- ei1 = (double**)malloc(4 * sizeof(double*));
2268- ei1[0] = (double*)malloc(4 * nb * sizeof(double));
2269- for (ii = 0; ii < 4; ii++) {
2270- ei1[ii] = ei1[0] + ii * nb;
2271- }
2272-
2273- w1 = (double**)malloc(nb * sizeof(double*));
2274- w1[0] = (double*)malloc(nb * 4 * sizeof(double));
2275- for (ib = 0; ib < nb; ib++) {
2276- w1[ib] = w1[0] + ib * 4;
2277- }
2278-
2279- libtetrabz_initialize(ng, bvec, wlsm, ikv);
2280-
2281- occ_main(nk, nb, eig, ikv, wlsm, ei1, w1, wght);
2282-
2283- free(ikv[0]);
2284- free(ikv);
2285- free(ei1[0]);
2286- free(ei1);
2287- free(w1[0]);
2288- free(w1);
2289- /*
2290- Convert weight to python list object
2291- */
2292- wght_po = PyList_New(nk * nb);
2293- ierr = 0;
2294- for (ik = 0; ik < nk; ik++)
2295- for (ib = 0; ib < nb; ib++)
2296- ierr = PyList_SetItem(wght_po, ik * nb + ib, PyFloat_FromDouble(wght[ik][ib]));
2297- if (ierr != 0)printf("Error in PyList_SetItem\n");
2298-
2299- free(eig[0]);
2300- free(eig);
2301- free(wght[0]);
2302- free(wght);
2303- return wght_po;
2304-}
2305-/*
2306-Calculate Fermi energy
2307-*/
2308-static PyObject* fermieng_c(PyObject* self, PyObject* args)
2309-{
2310- int maxiter, ik, ib, iteration, nk, nb, ng[3],
2311- **ikv, ii, ierr;
2312- double eps, elw, eup, **eig2, sumkmid, bvec[3][3],
2313- **eig, **wght, wlsm[20][4], **ei1, **w1, nelec, ef;
2314- PyObject* eig_po, * wght_po;
2315- /*
2316- Read input from python object
2317- */
2318- if (!PyArg_ParseTuple(args, "iiiiidddddddddOd",
2319- &ng[0], &ng[1], &ng[2], &nk, &nb,
2320- &bvec[0][0], &bvec[0][1], &bvec[0][2], &bvec[1][0], &bvec[1][1], &bvec[1][2], &bvec[2][0], &bvec[2][1], &bvec[2][2],
2321- &eig_po, &nelec))
2322- return NULL;
2323- /*
2324- convert python list object to array
2325- */
2326- eig = (double**)malloc(nk * sizeof(double*));
2327- eig[0] = (double*)malloc(nk * nb * sizeof(double));
2328- wght = (double**)malloc(nk * sizeof(double*));
2329- wght[0] = (double*)malloc(nk * nb * sizeof(double));
2330- for (ik = 0; ik < nk; ik++) {
2331- eig[ik] = eig[0] + ik * nb;
2332- wght[ik] = wght[0] + ik * nb;
2333- }
2334-
2335- for (ik = 0; ik < nk; ik++)
2336- for (ib = 0; ib < nb; ib++)
2337- eig[ik][ib] = PyFloat_AsDouble(PyList_GetItem(eig_po, ik * nb + ib));
2338-
2339- /*
2340- Start main calculation
2341- */
2342- ikv = (int**)malloc(6 * nk * sizeof(int*));
2343- ikv[0] = (int*)malloc(6 * nk * 20 * sizeof(int));
2344- for (ik = 0; ik < 6 * nk; ik++) {
2345- ikv[ik] = ikv[0] + ik * 20;
2346- }
2347- ei1 = (double**)malloc(4 * sizeof(double*));
2348- ei1[0] = (double*)malloc(4 * nb * sizeof(double));
2349- for (ii = 0; ii < 4; ii++) {
2350- ei1[ii] = ei1[0] + ii * nb;
2351- }
2352-
2353- w1 = (double**)malloc(nb * sizeof(double*));
2354- w1[0] = (double*)malloc(nb * 4 * sizeof(double));
2355- for (ib = 0; ib < nb; ib++) {
2356- w1[ib] = w1[0] + ib * 4;
2357- }
2358-
2359- libtetrabz_initialize(ng, bvec, wlsm, ikv);
2360-
2361- eig2 = (double**)malloc(nk * sizeof(double*));
2362- eig2[0] = (double*)malloc(nk * nb * sizeof(double));
2363- for (ik = 0; ik < nk; ik++) {
2364- eig2[ik] = eig2[0] + ik * nb;
2365- }
2366-
2367- maxiter = 300;
2368- eps = 1.0e-10;
2369-
2370- elw = eig[0][0];
2371- eup = eig[0][0];
2372- for (ik = 0; ik < nk; ik++) {
2373- for (ib = 0; ib < nb; ib++) {
2374- if (elw > eig[ik][ib]) elw = eig[ik][ib];
2375- if (eup < eig[ik][ib]) eup = eig[ik][ib];
2376- }
2377- }
2378- /*
2379- Bisection method
2380- */
2381- for (iteration = 0; iteration < maxiter; iteration++) {
2382-
2383- ef = (eup + elw) * 0.5;
2384- /*
2385- Calc. # of electrons
2386- */
2387- for (ik = 0; ik < nk; ik++)
2388- for (ib = 0; ib < nb; ib++)
2389- eig2[ik][ib] = eig[ik][ib] - ef;
2390- occ_main(nk, nb, eig2, ikv, wlsm, ei1, w1, wght);
2391-
2392- sumkmid = 0.0;
2393- for (ik = 0; ik < nk; ik++) {
2394- for (ib = 0; ib < nb; ib++) {
2395- sumkmid += wght[ik][ib];
2396- }
2397- }
2398- /*
2399- convergence check
2400- */
2401- if (fabs(sumkmid - nelec) < eps) {
2402- break;
2403- }
2404- else if (sumkmid < nelec)
2405- elw = ef;
2406- else
2407- eup = ef;
2408- }
2409- free(eig2);
2410- free(ikv[0]);
2411- free(ikv);
2412- free(ei1[0]);
2413- free(ei1);
2414- free(w1[0]);
2415- free(w1);
2416- /*
2417- Convert weight to python list object
2418- */
2419- wght_po = PyList_New(nk * nb+2);
2420- ierr = 0;
2421- for (ik = 0; ik < nk; ik++)
2422- for (ib = 0; ib < nb; ib++)
2423- ierr = PyList_SetItem(wght_po, ik * nb + ib, PyFloat_FromDouble(wght[ik][ib]));
2424- ierr = PyList_SetItem(wght_po, nk*nb, PyFloat_FromDouble(ef));
2425- ierr = PyList_SetItem(wght_po, nk * nb+1, PyLong_FromLong((long)iteration));
2426- if (ierr != 0)printf("Error in PyList_SetItem\n");
2427-
2428- free(eig[0]);
2429- free(eig);
2430- free(wght[0]);
2431- free(wght);
2432- return wght_po;
2433-}
2434-/*
2435-Results of Integration (1-x-y-z)/(g0+(g1-g0)x+(g2-g0)y+(g3-g0))
2436-for 0<x<1, 0<y<1-x, 0<z<1-x-y
2437-*/
2438-/*
2439-1, Different each other
2440-*/
2441-static void libtetrabz_polcmplx_1234(
2442- double g1,
2443- double g2,
2444- double g3,
2445- double g4,
2446- double* w
2447-) {
2448- double w2, w3, w4;
2449- /*
2450- Real
2451- */
2452- w2 = 2.0 * (3.0 * g2 * g2 - 1.0) * (atan(g2) - atan(g1)) +
2453- (g2 * g2 - 3.0) * g2 * log((1.0 + g2 * g2) / (1.0 + g1 * g1));
2454- w2 = -2.0 * (g2 * g2 - 1.0) + w2 / (g2 - g1);
2455- w2 = w2 / (g2 - g1);
2456- w3 = 2.0 * (3.0 * g3 * g3 - 1.0) * (atan(g3) - atan(g1)) +
2457- (g3 * g3 - 3.0) * g3 * log((1.0 + g3 * g3) / (1.0 + g1 * g1));
2458- w3 = -2.0 * (g3 * g3 - 1.0) + w3 / (g3 - g1);
2459- w3 = w3 / (g3 - g1);
2460- w4 = 2.0 * (3.0 * g4 * g4 - 1.0) * (atan(g4) - atan(g1)) +
2461- (g4 * g4 - 3.0) * g4 * log((1.0 + g4 * g4) / (1.0 + g1 * g1));
2462- w4 = -2.0 * (g4 * g4 - 1.0) + w4 / (g4 - g1);
2463- w4 = w4 / (g4 - g1);
2464- w2 = (w2 - w3) / (g2 - g3);
2465- w4 = (w4 - w3) / (g4 - g3);
2466- w[0] = (w4 - w2) / (2.0 * (g4 - g2));
2467- /*
2468- Imaginal
2469- */
2470- w2 = 2.0 * (3.0 - g2 * g2) * g2 * (atan(g2) - atan(g1)) +
2471- (3.0 * g2 * g2 - 1.0) * log((1.0 + g2 * g2) / (1.0 + g1 * g1));
2472- w2 = 4.0 * g2 - w2 / (g2 - g1);
2473- w2 = w2 / (g2 - g1);
2474- w3 = 2.0 * (3.0 - g3 * g3) * g3 * (atan(g3) - atan(g1)) +
2475- (3.0 * g3 * g3 - 1.0) * log((1.0 + g3 * g3) / (1.0 + g1 * g1));
2476- w3 = 4.0 * g3 - w3 / (g3 - g1);
2477- w3 = w3 / (g3 - g1);
2478- w4 = 2.0 * (3.0 - g4 * g4) * g4 * (atan(g4) - atan(g1)) +
2479- (3.0 * g4 * g4 - 1.0) * log((1.0 + g4 * g4) / (1.0 + g1 * g1));
2480- w4 = 4.0 * g4 - w4 / (g4 - g1);
2481- w4 = w4 / (g4 - g1);
2482- w2 = (w2 - w3) / (g2 - g3);
2483- w4 = (w4 - w3) / (g4 - g3);
2484- w[1] = (w4 - w2) / (2.0 * (g4 - g2));
2485-}
2486-/*
2487-2, g4 = g1
2488-*/
2489-static void libtetrabz_polcmplx_1231(
2490- double g1,
2491- double g2,
2492- double g3,
2493- double* w
2494-) {
2495- double w2, w3;
2496- /*
2497- Real
2498- */
2499- w2 = 2.0 * (-1.0 + 3.0 * g2 * g2) * (atan(g2) - atan(g1))
2500- + g2 * (-3.0 + g2 * g2) * log((1.0 + g2 * g2) / (1.0 + g1 * g1));
2501- w2 = 2.0 * (1.0 - g2 * g2) + w2 / (g2 - g1);
2502- w2 = -g1 + w2 / (g2 - g1);
2503- w2 = w2 / (g2 - g1);
2504- w3 = 2.0 * (-1.0 + 3.0 * g3 * g3) * (atan(g3) - atan(g1))
2505- + g3 * (-3.0 + g3 * g3) * log((1.0 + g3 * g3) / (1.0 + g1 * g1));
2506- w3 = 2.0 * (1 - g3 * g3) + w3 / (g3 - g1);
2507- w3 = -g1 + w3 / (g3 - g1);
2508- w3 = w3 / (g3 - g1);
2509- w[0] = (w3 - w2) / (2.0 * (g3 - g2));
2510- /*
2511- Imaginal
2512- */
2513- w2 = 2.0 * g2 * (3.0 - g2 * g2) * (atan(g2) - atan(g1)) +
2514- (-1.0 + 3.0 * g2 * g2) * log((1.0 + g2 * g2) / (1.0 + g1 * g1));
2515- w2 = 4.0 * g2 - w2 / (g2 - g1);
2516- w2 = 1 + w2 / (g2 - g1);
2517- w2 = w2 / (g2 - g1);
2518- w3 = 2.0 * g3 * (3.0 - g3 * g3) * (atan(g3) - atan(g1)) +
2519- (-1.0 + 3.0 * g3 * g3) * log((1.0 + g3 * g3) / (1.0 + g1 * g1));
2520- w3 = 4.0 * g3 - w3 / (g3 - g1);
2521- w3 = 1 + w3 / (g3 - g1);
2522- w3 = w3 / (g3 - g1);
2523- w[1] = (w3 - w2) / (2.0 * (g3 - g2));
2524-}
2525-/*
2526-3, g4 = g3
2527-*/
2528-static void libtetrabz_polcmplx_1233(
2529- double g1,
2530- double g2,
2531- double g3,
2532- double* w
2533-) {
2534- double w2, w3;
2535- /*
2536- Real
2537- */
2538- w2 = 2.0 * (1.0 - 3.0 * g2 * g2) * (atan(g2) - atan(g1)) +
2539- g2 * (3.0 - g2 * g2) * log((1.0 + g2 * g2) / (1.0 + g1 * g1));
2540- w2 = 2.0 * (1 - g2 * g2) - w2 / (g2 - g1);
2541- w2 = w2 / (g2 - g1);
2542- w3 = 2.0 * (1.0 - 3.0 * g3 * g3) * (atan(g3) - atan(g1)) +
2543- g3 * (3.0 - g3 * g3) * log((1.0 + g3 * g3) / (1.0 + g1 * g1));
2544- w3 = 2.0 * (1 - g3 * g3) - w3 / (g3 - g1);
2545- w3 = w3 / (g3 - g1);
2546- w2 = (w3 - w2) / (g3 - g2);
2547- w3 = 4.0 * (1.0 - 3.0 * g1 * g3) * (atan(g3) - atan(g1))
2548- + (3.0 * g1 + 3.0 * g3 - 3.0 * g1 * g3 * g3 + g3 * g3 * g3) * log((1.0 + g3 * g3) / (1.0 + g1 * g1));
2549- w3 = -4.0 * (1.0 - g1 * g1) + w3 / (g3 - g1);
2550- w3 = 4.0 * g1 + w3 / (g3 - g1);
2551- w3 = w3 / (g3 - g1);
2552- w[0] = (w3 - w2) / (2.0 * (g3 - g2));
2553- /*
2554- Imaginal
2555- */
2556- w2 = 2.0 * g2 * (3.0 - g2 * g2) * (atan(g2) - atan(g1)) +
2557- (-1.0 + 3.0 * g2 * g2) * log((1.0 + g2 * g2) / (1.0 + g1 * g1));
2558- w2 = 4.0 * g2 - w2 / (g2 - g1);
2559- w2 = w2 / (g2 - g1);
2560- w3 = 2.0 * g3 * (3.0 - g3 * g3) * (atan(g3) - atan(g1)) +
2561- (-1.0 + 3.0 * g3 * g3) * log((1.0 + g3 * g3) / (1.0 + g1 * g1));
2562- w3 = 4.0 * g3 - w3 / (g3 - g1);
2563- w3 = w3 / (g3 - g1);
2564- w2 = (w3 - w2) / (g3 - g2);
2565- w3 = (3.0 * g1 - 3.0 * g1 * g3 * g3 + 3.0 * g3 + g3 * g3 * g3) * (atan(g3) - atan(g1))
2566- + (3.0 * g1 * g3 - 1.0) * log((1.0 + g3 * g3) / (1.0 + g1 * g1));
2567- w3 = w3 / (g3 - g1) - 4.0 * g1;
2568- w3 = w3 / (g3 - g1) - 2.0;
2569- w3 = (2.0 * w3) / (g3 - g1);
2570- w[1] = (w3 - w2) / (2.0 * (g3 - g2));
2571-}
2572-/*
2573-4, g4 = g1 and g3 = g2
2574-*/
2575-static void libtetrabz_polcmplx_1221(
2576- double g1,
2577- double g2,
2578- double* w
2579-) {
2580- /*
2581- Real
2582- */
2583- w[0] = -2.0 * (-1.0 + 2.0 * g1 * g2 + g2 * g2) * (atan(g2) - atan(g1))
2584- + (g1 + 2.0 * g2 - g1 * g2 * g2) * log((1.0 + g2 * g2) / (1.0 + g1 * g1));
2585- w[0] = 2.0 * (-1.0 + g1 * g1) + w[0] / (g2 - g1);
2586- w[0] = 3.0 * g1 + w[0] / (g2 - g1);
2587- w[0] = 2.0 + (3.0 * w[0]) / (g2 - g1);
2588- w[0] = w[0] / (2.0 * (g2 - g1));
2589- /*
2590- Imaginal
2591- */
2592- w[1] = 2.0 * (g1 + 2.0 * g2 - g1 * g2 * g2) * (atan(g2) - atan(g1))
2593- + (-1.0 + 2.0 * g1 * g2 + g2 * g2) * log((1 + g2 * g2) / (1 + g1 * g1));
2594- w[1] = -4.0 * g1 + w[1] / (g2 - g1);
2595- w[1] = -3.0 + w[1] / (g2 - g1);
2596- w[1] = (3.0 * w[1]) / (2.0 * (g2 - g1) * (g2 - g1));
2597-}
2598-/*
2599-5, g4 = g3 = g2
2600-*/
2601-static void libtetrabz_polcmplx_1222(
2602- double g1,
2603- double g2,
2604- double* w
2605-) {
2606- /*
2607- Real
2608- */
2609- w[0] = 2.0 * (-1.0 + g1 * g1 + 2.0 * g1 * g2) * (atan(g2) - atan(g1))
2610- + (-2.0 * g1 - g2 + g1 * g1 * g2) * log((1.0 + g2 * g2) / (1.0 + g1 * g1));
2611- w[0] = 2.0 * (1.0 - g1 * g1) + w[0] / (g2 - g1);
2612- w[0] = g1 - w[0] / (g2 - g1);
2613- w[0] = 1.0 - (3.0 * w[0]) / (g2 - g1);
2614- w[0] = w[0] / (2.0 * (g2 - g1));
2615- /*
2616- Imaginal
2617- */
2618- w[1] = 2.0 * (-2.0 * g1 - g2 + g1 * g1 * g2) * (atan(g2) - atan(g1))
2619- + (1.0 - g1 * g1 - 2.0 * g1 * g2) * log((1.0 + g2 * g2) / (1.0 + g1 * g1));
2620- w[1] = 4.0 * g1 + w[1] / (g2 - g1);
2621- w[1] = 1.0 + w[1] / (g2 - g1);
2622- w[1] = (3.0 * w[1]) / (2.0 * (g2 - g1) * (g2 - g1));
2623-}
2624-/*
2625-6, g4 = g3 = g1
2626-*/
2627-static void libtetrabz_polcmplx_1211(
2628- double g1,
2629- double g2,
2630- double* w
2631-) {
2632- /*
2633- Real
2634- */
2635- w[0] = 2.0 * (3.0 * g2 * g2 - 1.0) * (atan(g2) - atan(g1))
2636- + g2 * (g2 * g2 - 3.0) * log((1.0 + g2 * g2) / (1.0 + g1 * g1));
2637- w[0] = 2.0 * (1.0 - g1 * g1) + w[0] / (g2 - g1);
2638- w[0] = -5.0 * g1 + w[0] / (g2 - g1);
2639- w[0] = -11.0 + (3.0 * w[0]) / (g2 - g1);
2640- w[0] = w[0] / (6.0 * (g2 - g1));
2641- /*
2642- Imaginal
2643- */
2644- w[1] = 2.0 * g2 * (-3.0 + g2 * g2) * (atan(g2) - atan(g1))
2645- + (1.0 - 3.0 * g2 * g2) * log((1.0 + g2 * g2) / (1.0 + g1 * g1));
2646- w[1] = 4.0 * g2 + w[1] / (g2 - g1);
2647- w[1] = 1.0 + w[1] / (g2 - g1);
2648- w[1] = w[1] / (2.0 * (g2 - g1) * (g2 - g1));
2649-}
2650-/*
2651-Tetrahedron method for delta(om - ep + e)
2652-*/
2653-static void libtetrabz_polcmplx3(
2654- int ne,
2655- double** e0,
2656- double de[4],
2657- double*** w1
2658-) {
2659- int i4, ir, indx[4], ie;
2660- double e[4], x[4], thr, w2[4][2], denom;
2661-
2662- for (i4 = 0; i4 < 3; i4++) e[i4] = de[i4];
2663- eig_sort(4, e, indx);
2664-
2665- for (ie = 0; ie < ne; ie++) {
2666- /*
2667- I am not sure which one is better.
2668- The former is more stable.
2669- The latter is more accurate ?
2670- */
2671- for (i4 = 0; i4 < 4; i4++) {
2672- denom = (de[i4] + e0[ie][0]) * (de[i4] + e0[ie][0]) + e0[ie][1] * e0[ie][1];
2673- w1[i4][ie][0] = 0.25 * (de[i4] + e0[ie][0]) / denom;
2674- w1[i4][ie][1] = 0.25 * (-e0[ie][1]) / denom;
2675- }
2676- continue;
2677-
2678- for (i4 = 0; i4 < 4; i4++)
2679- x[i4] = (e[i4] + e0[ie][0]) / e0[ie][1];
2680- /* thr = maxval(de(1:4)) * 1d-3*/
2681- thr = fabs(x[0]);
2682- for (i4 = 0; i4 < 4; i4++)
2683- if (thr < fabs(x[i4])) thr = fabs(x[i4]);
2684- thr = fmax(1.0e-3, thr * 1.0e-2);
2685-
2686- if (fabs(x[3] - x[2]) < thr) {
2687- if (fabs(x[3] - x[1]) < thr) {
2688- if (fabs(x[3] - x[0]) < thr) {
2689- /*
2690- e[3] = e[2] = e[1] = e[0]
2691- */
2692- w2[3][0] = 0.25 * x[3] / (1.0 + x[3] * x[3]);
2693- w2[3][1] = 0.25 / (1.0 + x[3] * x[3]);
2694- for (ir = 0; ir < 2; ir++) {
2695- w2[2][ir] = w2[3][ir];
2696- w2[1][ir] = w2[3][ir];
2697- w2[0][ir] = w2[3][ir];
2698- }
2699- }
2700- else {
2701- /*
2702- e[3] = e[2] = e[1]
2703- */
2704- libtetrabz_polcmplx_1211(x[3], x[0], w2[3]);
2705- for (ir = 0; ir < 2; ir++) {
2706- w2[2][ir] = w2[3][ir];
2707- w2[1][ir] = w2[3][ir];
2708- }
2709- libtetrabz_polcmplx_1222(x[0], x[3], w2[0]);
2710- /*
2711- # IF(ANY(w2(1:2,1:4) < 0.0)):
2712- # WRITE(*,*) ie
2713- # WRITE(*,'(100e15.5)') x[0:4]
2714- # WRITE(*,'(2e15.5)') w2(1:2,1:4)
2715- # STOP "weighting 4=3=2"
2716- */
2717- }
2718- }
2719- else if (fabs(x[1] - x[0]) < thr) {
2720- /*
2721- e[3] = e[2], e[1] = e[0]
2722- */
2723- libtetrabz_polcmplx_1221(x[3], x[1], w2[3]);
2724- for (ir = 0; ir < 2; ir++) w2[2][ir] = w2[3][ir];
2725- libtetrabz_polcmplx_1221(x[1], x[3], w2[1]);
2726- for (ir = 0; ir < 2; ir++) w2[0][ir] = w2[1][ir];
2727- /*
2728- IF(ANY(w2(1:2,1:4) < 0.0)):
2729- WRITE(*,*) ie
2730- WRITE(*,'(100e15.5)') x[0:4]
2731- WRITE(*,'(2e15.5)') w2(1:2,1:4)
2732- STOP "weighting 4=3 2=1"
2733- */
2734- }
2735- else {
2736- /*
2737- e[3] = e[2]
2738- */
2739- libtetrabz_polcmplx_1231(x[3], x[0], x[1], w2[3]);
2740- for (ir = 0; ir < 2; ir++) w2[2][ir] = w2[3][ir];
2741- libtetrabz_polcmplx_1233(x[1], x[0], x[3], w2[1]);
2742- libtetrabz_polcmplx_1233(x[0], x[1], x[3], w2[0]);
2743- /*
2744- IF(ANY(w2(1:2,1:4) < 0.0)):
2745- WRITE(*,*) ie
2746- WRITE(*,'(100e15.5)') x[0:4]
2747- WRITE(*,'(2e15.5)') w2(1:2,1:4)
2748- STOP "weighting 4=3"
2749- */
2750- }
2751- }
2752- else if (fabs(x[2] - x[1]) < thr) {
2753- if (fabs(x[2] - x[0]) < thr) {
2754- /*
2755- e[2] = e[1] = e[0]
2756- */
2757- libtetrabz_polcmplx_1222(x[3], x[2], w2[3]);
2758- libtetrabz_polcmplx_1211(x[2], x[3], w2[2]);
2759- for (ir = 0; ir < 2; ir++) w2[1][ir] = w2[2][ir];
2760- for (ir = 0; ir < 2; ir++) w2[0][ir] = w2[2][ir];
2761- /*
2762- IF(ANY(w2(1:2,1:4) < 0.0)):
2763- WRITE(*,*) ie
2764- WRITE(*,'(100e15.5)') x[0:4]
2765- WRITE(*,'(2e15.5)') w2(1:2,1:4)
2766- STOP "weighting 3=2=1"
2767- */
2768- }
2769- else {
2770- /*
2771- e[2] = e[1]
2772- */
2773- libtetrabz_polcmplx_1233(x[3], x[0], x[2], w2[3]);
2774- libtetrabz_polcmplx_1231(x[2], x[0], x[3], w2[2]);
2775- for (ir = 0; ir < 2; ir++) w2[1][ir] = w2[2][ir];
2776- libtetrabz_polcmplx_1233(x[0], x[3], x[2], w2[0]);
2777- /*
2778- IF(ANY(w2(1:2,1:4) < 0.0)):
2779- WRITE(*,*) ie
2780- WRITE(*,'(100e15.5)') x[0:4]
2781- WRITE(*,'(2e15.5)') w2(1:2,1:4)
2782- STOP "weighting 3=2"
2783- */
2784- }
2785- }
2786- else if (fabs(x[1] - x[0]) < thr) {
2787- /*
2788- e[1] = e[0]
2789- */
2790- libtetrabz_polcmplx_1233(x[3], x[2], x[1], w2[3]);
2791- libtetrabz_polcmplx_1233(x[2], x[3], x[1], w2[2]);
2792- libtetrabz_polcmplx_1231(x[1], x[2], x[3], w2[1]);
2793- for (ir = 0; ir < 2; ir++) w2[0][ir] = w2[1][ir];
2794- /*
2795- IF(ANY(w2(1:2,1:4) < 0.0)):
2796- WRITE(*,*) ie
2797- WRITE(*,'(100e15.5)') x[0:4]
2798- WRITE(*,'(2e15.5)') w2(1:2,1:4)
2799- STOP "weighting 2=1"
2800- */
2801- }
2802- else {
2803- /*
2804- Different each other.
2805- */
2806- libtetrabz_polcmplx_1234(x[3], x[0], x[1], x[2], w2[3]);
2807- libtetrabz_polcmplx_1234(x[2], x[0], x[1], x[3], w2[2]);
2808- libtetrabz_polcmplx_1234(x[1], x[0], x[2], x[3], w2[1]);
2809- libtetrabz_polcmplx_1234(x[0], x[1], x[2], x[3], w2[0]);
2810- /*
2811- IF(ANY(w2(1:2,1:4) < 0.0)):
2812- WRITE(*,*) ie
2813- WRITE(*,'(100e15.5)') x[0:4]
2814- WRITE(*,'(2e15.5)') w2(1:2,1:4)
2815- STOP "weighting"
2816- */
2817- }
2818- for (i4 = 0; i4 < 4; i4++) {
2819- w1[indx[i4]][ie][0] = w2[i4][0] / e0[ie][1];
2820- w1[indx[i4]][ie][1] = w2[i4][1] / (-e0[ie][1]);
2821- }
2822- }
2823-}
2824-/*
2825-Tetrahedron method for theta( - E2)
2826-*/
2827-static void libtetrabz_polcmplx2(
2828- int nb,
2829- int ne,
2830- double* *e0,
2831- double* ei1,
2832- double** ej1,
2833- double**** w1
2834-) {
2835- int ib, i4, j4, ir, ie, indx[4];
2836- double e[4], tsmall[4][4], v, de[4], thr, *** w2;
2837-
2838- w2 = (double***)malloc(4 * sizeof(double**));
2839- w2[0] = (double**)malloc(4 * ne * sizeof(double*));
2840- w2[0][0] = (double*)malloc(4 * ne * 2 * sizeof(double));
2841- for (i4 = 0; i4 < 4; i4++) {
2842- w2[i4] = w2[0] + i4 * ne;
2843- for (ie = 0; ie < ne; ie++) {
2844- w2[i4][ie] = w2[0][0] + i4 * ne * 2 + ie * 2;
2845- }
2846- }
2847-
2848- thr = 1.0e-8;
2849-
2850- for (ib = 0; ib < nb; ib++) {
2851-
2852- for (i4 = 0; i4 < 4; i4++)
2853- for (ie = 0; ie < ne; ie++)
2854- for (ir = 0; ir < 2; ir++)
2855- w1[ib][i4][ie][ir] = 0.0;
2856-
2857- for (i4 = 0; i4 < 4; i4++) e[i4] = -ej1[ib][i4];
2858- eig_sort(4, e, indx);
2859-
2860- if ((e[0] <= 0.0 && 0.0 < e[1]) || (e[0] < 0.0 && 0.0 <= e[1])) {
2861-
2862- libtetrabz_tsmall_a1(e, 0.0, &v, tsmall);
2863-
2864- if (v > thr) {
2865- for (j4 = 0; j4 < 4; j4++) de[j4] = 0.0;
2866- for (i4 = 0; i4 < 4; i4++)
2867- for (j4 = 0; j4 < 4; j4++)
2868- de[j4] += (ej1[ib][indx[i4]] - ei1[indx[i4]]) * tsmall[i4][j4];
2869- libtetrabz_polcmplx3(ne, e0, de, w2);
2870- for (i4 = 0; i4 < 4; i4++)
2871- for (j4 = 0; j4 < 4; j4++)
2872- for (ie = 0; ie < ne; ie++)
2873- for (ir = 0; ir < 2; ir++)
2874- w1[ib][indx[i4]][ie][ir] += v * tsmall[i4][j4] * w2[j4][ie][ir];
2875- }
2876- }
2877- else if ((e[1] <= 0.0 && 0.0 < e[2]) || (e[1] < 0.0 && 0.0 <= e[2])) {
2878-
2879- libtetrabz_tsmall_b1(e, 0.0, &v, tsmall);
2880-
2881- if (v > thr) {
2882- for (j4 = 0; j4 < 4; j4++) de[j4] = 0.0;
2883- for (i4 = 0; i4 < 4; i4++)
2884- for (j4 = 0; j4 < 4; j4++)
2885- de[j4] += (ej1[ib][indx[i4]] - ei1[indx[i4]]) * tsmall[i4][j4];
2886- libtetrabz_polcmplx3(ne, e0, de, w2);
2887- for (i4 = 0; i4 < 4; i4++)
2888- for (j4 = 0; j4 < 4; j4++)
2889- for (ie = 0; ie < ne; ie++)
2890- for (ir = 0; ir < 2; ir++)
2891- w1[ib][indx[i4]][ie][ir] += v * tsmall[i4][j4] * w2[j4][ie][ir];
2892- }
2893-
2894- libtetrabz_tsmall_b2(e, 0.0, &v, tsmall);
2895-
2896- if (v > thr) {
2897- for (j4 = 0; j4 < 4; j4++) de[j4] = 0.0;
2898- for (i4 = 0; i4 < 4; i4++)
2899- for (j4 = 0; j4 < 4; j4++)
2900- de[j4] += (ej1[ib][indx[i4]] - ei1[indx[i4]]) * tsmall[i4][j4];
2901- libtetrabz_polcmplx3(ne, e0, de, w2);
2902- for (i4 = 0; i4 < 4; i4++)
2903- for (j4 = 0; j4 < 4; j4++)
2904- for (ie = 0; ie < ne; ie++)
2905- for (ir = 0; ir < 2; ir++)
2906- w1[ib][indx[i4]][ie][ir] += v * tsmall[i4][j4] * w2[j4][ie][ir];
2907- }
2908-
2909- libtetrabz_tsmall_b3(e, 0.0, &v, tsmall);
2910-
2911- if (v > thr) {
2912- for (j4 = 0; j4 < 4; j4++) de[j4] = 0.0;
2913- for (i4 = 0; i4 < 4; i4++)
2914- for (j4 = 0; j4 < 4; j4++)
2915- de[j4] += (ej1[ib][indx[i4]] - ei1[indx[i4]]) * tsmall[i4][j4];
2916- libtetrabz_polcmplx3(ne, e0, de, w2);
2917- for (i4 = 0; i4 < 4; i4++)
2918- for (j4 = 0; j4 < 4; j4++)
2919- for (ie = 0; ie < ne; ie++)
2920- for (ir = 0; ir < 2; ir++)
2921- w1[ib][indx[i4]][ie][ir] += v * tsmall[i4][j4] * w2[j4][ie][ir];
2922- }
2923- }
2924- else if ((e[2] <= 0.0 && 0.0 < e[3]) || (e[2] < 0.0 && 0.0 <= e[3])) {
2925-
2926- libtetrabz_tsmall_c1(e, 0.0, &v, tsmall);
2927-
2928- if (v > thr) {
2929- for (j4 = 0; j4 < 4; j4++) de[j4] = 0.0;
2930- for (i4 = 0; i4 < 4; i4++)
2931- for (j4 = 0; j4 < 4; j4++)
2932- de[j4] += (ej1[ib][indx[i4]] - ei1[indx[i4]]) * tsmall[i4][j4];
2933- libtetrabz_polcmplx3(ne, e0, de, w2);
2934- for (i4 = 0; i4 < 4; i4++)
2935- for (j4 = 0; j4 < 4; j4++)
2936- for (ie = 0; ie < ne; ie++)
2937- for (ir = 0; ir < 2; ir++)
2938- w1[ib][indx[i4]][ie][ir] += v * tsmall[i4][j4] * w2[j4][ie][ir];
2939- }
2940-
2941- libtetrabz_tsmall_c2(e, 0.0, &v, tsmall);
2942-
2943- if (v > thr) {
2944- for (j4 = 0; j4 < 4; j4++) de[j4] = 0.0;
2945- for (i4 = 0; i4 < 4; i4++)
2946- for (j4 = 0; j4 < 4; j4++)
2947- de[j4] += (ej1[ib][indx[i4]] - ei1[indx[i4]]) * tsmall[i4][j4];
2948- libtetrabz_polcmplx3(ne, e0, de, w2);
2949- for (i4 = 0; i4 < 4; i4++)
2950- for (j4 = 0; j4 < 4; j4++)
2951- for (ie = 0; ie < ne; ie++)
2952- for (ir = 0; ir < 2; ir++)
2953- w1[ib][indx[i4]][ie][ir] += v * tsmall[i4][j4] * w2[j4][ie][ir];
2954- }
2955-
2956- libtetrabz_tsmall_c3(e, 0.0, &v, tsmall);
2957-
2958- if (v > thr) {
2959- for (j4 = 0; j4 < 4; j4++) de[j4] = 0.0;
2960- for (i4 = 0; i4 < 4; i4++)
2961- for (j4 = 0; j4 < 4; j4++)
2962- de[j4] += (ej1[ib][indx[i4]] - ei1[indx[i4]]) * tsmall[i4][j4];
2963- libtetrabz_polcmplx3(ne, e0, de, w2);
2964- for (i4 = 0; i4 < 4; i4++)
2965- for (j4 = 0; j4 < 4; j4++)
2966- for (ie = 0; ie < ne; ie++)
2967- for (ir = 0; ir < 2; ir++)
2968- w1[ib][indx[i4]][ie][ir] += v * tsmall[i4][j4] * w2[j4][ie][ir];
2969- }
2970- }
2971- else if (e[3] <= 0.0) {
2972- for (i4 = 0; i4 < 4; i4++)
2973- de[i4] = ej1[ib][i4] - ei1[i4];
2974- libtetrabz_polcmplx3(ne, e0, de, w2);
2975- for (i4 = 0; i4 < 4; i4++)
2976- for (ie = 0; ie < ne; ie++)
2977- for (ir = 0; ir < 2; ir++)
2978- w1[ib][i4][ie][ir] += w2[i4][ie][ir];
2979- }
2980- }
2981- free(w2[0][0]);
2982- free(w2[0]);
2983- free(w2);
2984-}
2985-/*
2986-Main SUBROUTINE for Polarization (Imaginary axis) : Theta(- E1) * Theta(E2) / (E2 - E1 - iw)
2987-*/
2988-static PyObject* polcmplx_c(PyObject* self, PyObject* args) {
2989- int it, ik, ie, ib, i4, j4, ir, jb, **ikv, indx[4], i20, ierr, ng[3], nk, nb, ne;
2990- double wlsm[20][4], **ei1, **ej1, ei2[4], ** ej2, e[4], ***** w1, **** w2, v, tsmall[4][4], thr,
2991- bvec[3][3], ** eig1, ** eig2, ** e0, ***** wght;
2992- PyObject* eig1_po, * eig2_po, * e0_po, * wght_po;
2993- /*
2994- Read input from python object
2995- */
2996- if (!PyArg_ParseTuple(args, "iiiiiidddddddddOOO",
2997- &ng[0], &ng[1], &ng[2], &nk, &nb, &ne,
2998- &bvec[0][0], &bvec[0][1], &bvec[0][2], &bvec[1][0], &bvec[1][1], &bvec[1][2], &bvec[2][0], &bvec[2][1], &bvec[2][2],
2999- &eig1_po, &eig2_po, &e0_po))
3000- return NULL;
3001- /*
3002- convert python list object to array
3003- */
3004- eig1 = (double**)malloc(nk * sizeof(double*));
3005- eig1[0] = (double*)malloc(nk * nb * sizeof(double));
3006- eig2 = (double**)malloc(nk * sizeof(double*));
3007- eig2[0] = (double*)malloc(nk * nb * sizeof(double));
3008- wght = (double*****)malloc(nk * sizeof(double****));
3009- wght[0] = (double****)malloc(nk * nb * sizeof(double***));
3010- wght[0][0] = (double***)malloc(nk * nb * nb * sizeof(double**));
3011- wght[0][0][0] = (double**)malloc(nk * nb * nb * ne * sizeof(double*));
3012- wght[0][0][0][0] = (double*)malloc(nk * nb * nb * ne * 2 * sizeof(double));
3013- for (ik = 0; ik < nk; ik++) {
3014- eig1[ik] = eig1[0] + ik * nb;
3015- eig2[ik] = eig2[0] + ik * nb;
3016- wght[ik] = wght[0] + ik * nb;
3017- for (ib = 0; ib < nb; ib++) {
3018- wght[ik][ib] = wght[0][0] + ik * nb * nb + ib * nb;
3019- for (jb = 0; jb < nb; jb++) {
3020- wght[ik][ib][jb] = wght[0][0][0]
3021- + ik * nb * nb * ne + ib * nb * ne + jb * ne;
3022- for (ie = 0; ie < ne; ie++) {
3023- wght[ik][ib][jb][ie] = wght[0][0][0][0]
3024- + ik * nb * nb * ne * 2 + ib * nb * ne * 2 + jb * ne * 2 + ie * 2;
3025- }
3026- }
3027- }
3028- }
3029- e0 = (double**)malloc(ne * sizeof(double*));
3030- e0[0] = (double*)malloc(ne * 2 * sizeof(double));
3031- for (ie = 0; ie < ne; ie++)
3032- e0[ie] = e0[0] + ie * 2;
3033-
3034- for (ik = 0; ik < nk; ik++)
3035- for (ib = 0; ib < nb; ib++) {
3036- eig1[ik][ib] = PyFloat_AsDouble(PyList_GetItem(eig1_po, ik * nb + ib));
3037- eig2[ik][ib] = PyFloat_AsDouble(PyList_GetItem(eig2_po, ik * nb + ib));
3038- }
3039- for (ie = 0; ie < ne; ie++)
3040- for (ir = 0; ir < 2; ir++)
3041- e0[ie][ir] = PyFloat_AsDouble(PyList_GetItem(e0_po, ie * 2 + ir));
3042- /*
3043- Start main calculation
3044- */
3045- ikv = (int**)malloc(6 * nk * sizeof(int*));
3046- ikv[0] = (int*)malloc(6 * nk * 20 * sizeof(int));
3047- for (it = 0; it < 6 * nk; it++) {
3048- ikv[it] = ikv[0] + it * 20;
3049- }
3050-
3051- ei1 = (double**)malloc(4 * sizeof(double*));
3052- ej1 = (double**)malloc(4 * sizeof(double*));
3053- ei1[0] = (double*)malloc(4 * nb * sizeof(double));
3054- ej1[0] = (double*)malloc(4 * nb * sizeof(double));
3055- for (i4 = 0; i4 < 4; i4++) {
3056- ei1[i4] = ei1[0] + i4 * nb;
3057- ej1[i4] = ej1[0] + i4 * nb;
3058- }
3059-
3060- ej2 = (double**)malloc(nb * sizeof(double*));
3061- ej2[0] = (double*)malloc(nb * 4 * sizeof(double));
3062- for (ib = 0; ib < nb; ib++)
3063- ej2[ib] = ej2[0] + ib * 4;
3064-
3065- w1 = (double*****)malloc(nb * sizeof(double****));
3066- w1[0] = (double****)malloc(nb * 4 * sizeof(double***));
3067- w1[0][0] = (double***)malloc(nb * 4 * nb * sizeof(double**));
3068- w1[0][0][0] = (double**)malloc(nb * 4 * nb * ne * sizeof(double*));
3069- w1[0][0][0][0] = (double*)malloc(nb * 4 * nb * ne * 2 * sizeof(double));
3070- for (ib = 0; ib < nb; ib++) {
3071- w1[ib] = w1[0] + ib * 4;
3072- for (i4 = 0; i4 < 4; i4++) {
3073- w1[ib][i4] = w1[0][0] + ib * 4 * nb + i4 * nb;
3074- for (jb = 0; jb < nb; jb++) {
3075- w1[ib][i4][jb] = w1[0][0][0] + ib * 4 * nb * ne + i4 * nb * ne + jb * ne;
3076- for (ie = 0; ie < ne; ie++) {
3077- w1[ib][i4][jb][ie] = w1[0][0][0][0] + ib * 4 * nb * ne * 2 + i4 * nb * ne * 2 + jb * ne * 2 + ie * 2;
3078- }
3079- }
3080- }
3081- }
3082-
3083- w2 = (double****)malloc(nb * sizeof(double***));
3084- w2[0] = (double***)malloc(nb * 4 * sizeof(double**));
3085- w2[0][0] = (double**)malloc(nb * 4 * ne * sizeof(double*));
3086- w2[0][0][0] = (double*)malloc(nb * 4 * ne * 2 * sizeof(double));
3087- for (ib = 0; ib < nb; ib++) {
3088- w2[ib] = w2[0] + ib * 4;
3089- for (i4 = 0; i4 < 4; i4++) {
3090- w2[ib][i4] = w2[0][0] + ib * 4 * ne + i4 * ne;
3091- for (ie = 0; ie < ne; ie++) {
3092- w2[ib][i4][ie] = w2[0][0][0] + ib * 4 * ne * 2 + i4 * ne * 2 + ie * 2;
3093- }
3094- }
3095- }
3096-
3097- libtetrabz_initialize(ng, bvec, wlsm, ikv);
3098-
3099- for (ik = 0; ik < nk; ik++)
3100- for (ib = 0; ib < nb; ib++)
3101- for (jb = 0; jb < nb; jb++)
3102- for (ie = 0; ie < ne; ie++)
3103- for (ir = 0; ir < 2; ir++)
3104- wght[ik][ib][jb][ie][ir] = 0.0;
3105-
3106- thr = 1.0e-8;
3107-
3108- for (it = 0; it < 6 * nk; it++) {
3109-
3110- for (i4 = 0; i4 < 4; i4++)
3111- for (ib = 0; ib < nb; ib++) {
3112- ei1[i4][ib] = 0.0;
3113- ej1[i4][ib] = 0.0;
3114- }
3115- for (i20 = 0; i20 < 20; i20++) {
3116- for (i4 = 0; i4 < 4; i4++) {
3117- for (ib = 0; ib < nb; ib++) {
3118- ei1[i4][ib] += eig1[ikv[it][i20]][ib] * wlsm[i20][i4];
3119- ej1[i4][ib] += eig2[ikv[it][i20]][ib] * wlsm[i20][i4];
3120- }
3121- }
3122- }
3123-
3124- for (ib = 0; ib < nb; ib++) {
3125-
3126- for (i4 = 0; i4 < 4; i4++)
3127- for (jb = 0; jb < nb; jb++)
3128- for (ie = 0; ie < ne; ie++)
3129- for (ir = 0; ir < 2; ir++)
3130- w1[ib][i4][jb][ie][ir] = 0.0;
3131-
3132- for (i4 = 0; i4 < 4; i4++) e[i4] = ei1[i4][ib];
3133- eig_sort(4, e, indx);
3134-
3135- if (e[0] <= 0.0 && 0.0 < e[1]) {
3136-
3137- libtetrabz_tsmall_a1(e, 0.0, &v, tsmall);
3138-
3139- if (v > thr) {
3140- for (j4 = 0; j4 < 4; j4++) {
3141- ei2[j4] = 0.0;
3142- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
3143- }
3144- for (i4 = 0; i4 < 4; i4++)
3145- for (j4 = 0; j4 < 4; j4++) {
3146- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
3147- for (jb = 0; jb < nb; jb++)
3148- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
3149- }
3150- libtetrabz_polcmplx2(nb, ne, e0, ei2, ej2, w2);
3151- for (i4 = 0; i4 < 4; i4++)
3152- for (jb = 0; jb < nb; jb++)
3153- for (j4 = 0; j4 < 4; j4++)
3154- for (ie = 0; ie < ne; ie++)
3155- for (ir = 0; ir < 2; ir++)
3156- w1[ib][indx[i4]][jb][ie][ir] += v * tsmall[i4][j4] * w2[jb][j4][ie][ir];
3157- }
3158- }
3159- else if (e[1] <= 0.0 && 0.0 < e[2]) {
3160-
3161- libtetrabz_tsmall_b1(e, 0.0, &v, tsmall);
3162-
3163- if (v > thr) {
3164- for (j4 = 0; j4 < 4; j4++) {
3165- ei2[j4] = 0.0;
3166- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
3167- }
3168- for (i4 = 0; i4 < 4; i4++)
3169- for (j4 = 0; j4 < 4; j4++) {
3170- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
3171- for (jb = 0; jb < nb; jb++)
3172- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
3173- }
3174- libtetrabz_polcmplx2(nb, ne, e0, ei2, ej2, w2);
3175- for (i4 = 0; i4 < 4; i4++)
3176- for (jb = 0; jb < nb; jb++)
3177- for (j4 = 0; j4 < 4; j4++)
3178- for (ie = 0; ie < ne; ie++)
3179- for (ir = 0; ir < 2; ir++)
3180- w1[ib][indx[i4]][jb][ie][ir] += v * tsmall[i4][j4] * w2[jb][j4][ie][ir];
3181- }
3182-
3183- libtetrabz_tsmall_b2(e, 0.0, &v, tsmall);
3184-
3185- if (v > thr) {
3186- for (j4 = 0; j4 < 4; j4++) {
3187- ei2[j4] = 0.0;
3188- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
3189- }
3190- for (i4 = 0; i4 < 4; i4++)
3191- for (j4 = 0; j4 < 4; j4++) {
3192- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
3193- for (jb = 0; jb < nb; jb++)
3194- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
3195- }
3196- libtetrabz_polcmplx2(nb, ne, e0, ei2, ej2, w2);
3197- for (i4 = 0; i4 < 4; i4++)
3198- for (jb = 0; jb < nb; jb++)
3199- for (j4 = 0; j4 < 4; j4++)
3200- for (ie = 0; ie < ne; ie++)
3201- for (ir = 0; ir < 2; ir++)
3202- w1[ib][indx[i4]][jb][ie][ir] += v * tsmall[i4][j4] * w2[jb][j4][ie][ir];
3203- }
3204-
3205- libtetrabz_tsmall_b3(e, 0.0, &v, tsmall);
3206-
3207- if (v > thr) {
3208- for (j4 = 0; j4 < 4; j4++) {
3209- ei2[j4] = 0.0;
3210- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
3211- }
3212- for (i4 = 0; i4 < 4; i4++)
3213- for (j4 = 0; j4 < 4; j4++) {
3214- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
3215- for (jb = 0; jb < nb; jb++)
3216- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
3217- }
3218- libtetrabz_polcmplx2(nb, ne, e0, ei2, ej2, w2);
3219- for (i4 = 0; i4 < 4; i4++)
3220- for (jb = 0; jb < nb; jb++)
3221- for (j4 = 0; j4 < 4; j4++)
3222- for (ie = 0; ie < ne; ie++)
3223- for (ir = 0; ir < 2; ir++)
3224- w1[ib][indx[i4]][jb][ie][ir] += v * tsmall[i4][j4] * w2[jb][j4][ie][ir];
3225- }
3226- }
3227- else if (e[2] <= 0.0 && 0.0 < e[3]) {
3228-
3229- libtetrabz_tsmall_c1(e, 0.0, &v, tsmall);
3230-
3231- if (v > thr) {
3232- for (j4 = 0; j4 < 4; j4++) {
3233- ei2[j4] = 0.0;
3234- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
3235- }
3236- for (i4 = 0; i4 < 4; i4++)
3237- for (j4 = 0; j4 < 4; j4++) {
3238- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
3239- for (jb = 0; jb < nb; jb++)
3240- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
3241- }
3242- libtetrabz_polcmplx2(nb, ne, e0, ei2, ej2, w2);
3243- for (i4 = 0; i4 < 4; i4++)
3244- for (jb = 0; jb < nb; jb++)
3245- for (j4 = 0; j4 < 4; j4++)
3246- for (ie = 0; ie < ne; ie++)
3247- for (ir = 0; ir < 2; ir++)
3248- w1[ib][indx[i4]][jb][ie][ir] += v * tsmall[i4][j4] * w2[jb][j4][ie][ir];
3249- }
3250-
3251- libtetrabz_tsmall_c2(e, 0.0, &v, tsmall);
3252-
3253- if (v > thr) {
3254- for (j4 = 0; j4 < 4; j4++) {
3255- ei2[j4] = 0.0;
3256- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
3257- }
3258- for (i4 = 0; i4 < 4; i4++)
3259- for (j4 = 0; j4 < 4; j4++) {
3260- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
3261- for (jb = 0; jb < nb; jb++)
3262- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
3263- }
3264- libtetrabz_polcmplx2(nb, ne, e0, ei2, ej2, w2);
3265- for (i4 = 0; i4 < 4; i4++)
3266- for (jb = 0; jb < nb; jb++)
3267- for (j4 = 0; j4 < 4; j4++)
3268- for (ie = 0; ie < ne; ie++)
3269- for (ir = 0; ir < 2; ir++)
3270- w1[ib][indx[i4]][jb][ie][ir] += v * tsmall[i4][j4] * w2[jb][j4][ie][ir];
3271- }
3272-
3273- libtetrabz_tsmall_c3(e, 0.0, &v, tsmall);
3274-
3275- if (v > thr) {
3276- for (j4 = 0; j4 < 4; j4++) {
3277- ei2[j4] = 0.0;
3278- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
3279- }
3280- for (i4 = 0; i4 < 4; i4++)
3281- for (j4 = 0; j4 < 4; j4++) {
3282- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
3283- for (jb = 0; jb < nb; jb++)
3284- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
3285- }
3286- libtetrabz_polcmplx2(nb, ne, e0, ei2, ej2, w2);
3287- for (i4 = 0; i4 < 4; i4++)
3288- for (jb = 0; jb < nb; jb++)
3289- for (j4 = 0; j4 < 4; j4++)
3290- for (ie = 0; ie < ne; ie++)
3291- for (ir = 0; ir < 2; ir++)
3292- w1[ib][indx[i4]][jb][ie][ir] += v * tsmall[i4][j4] * w2[jb][j4][ie][ir];
3293- }
3294- }
3295- else if (e[3] <= 0.0) {
3296- for (i4 = 0; i4 < 4; i4++) {
3297- ei2[i4] = ei1[i4][ib];
3298- for (jb = 0; jb < nb; jb++)
3299- ej2[jb][i4] = ej1[i4][jb];
3300- }
3301- libtetrabz_polcmplx2(nb, ne, e0, ei2, ej2, w2);
3302- for (i4 = 0; i4 < 4; i4++)
3303- for (jb = 0; jb < nb; jb++)
3304- for (ie = 0; ie < ne; ie++)
3305- for (ir = 0; ir < 2; ir++)
3306- w1[ib][i4][jb][ie][ir] += w2[jb][i4][ie][ir];
3307- }
3308- else {
3309- continue;
3310- }
3311- }
3312- for (i20 = 0; i20 < 20; i20++)
3313- for (ib = 0; ib < nb; ib++)
3314- for (i4 = 0; i4 < 4; i4++)
3315- for (jb = 0; jb < nb; jb++)
3316- for (ie = 0; ie < ne; ie++)
3317- for (ir = 0; ir < 2; ir++)
3318- wght[ikv[it][i20]][ib][jb][ie][ir] += wlsm[i20][i4] * w1[ib][i4][jb][ie][ir];
3319- }
3320- for (ik = 0; ik < nk; ik++)
3321- for (ib = 0; ib < nb; ib++)
3322- for (jb = 0; jb < nb; jb++)
3323- for (ie = 0; ie < ne; ie++)
3324- for (i4 = 0; i4 < 2; i4++)
3325- wght[ik][ib][jb][ie][i4] /= (6.0 * (double) nk);
3326-
3327- free(ikv[0]);
3328- free(ikv);
3329- free(ei1[0]);
3330- free(ei1);
3331- free(ej1[0]);
3332- free(ej1);
3333- free(ej2[0]);
3334- free(ej2);
3335- free(w1[0][0][0][0]);
3336- free(w1[0][0][0]);
3337- free(w1[0][0]);
3338- free(w1[0]);
3339- free(w1);
3340- free(w2[0][0][0]);
3341- free(w2[0][0]);
3342- free(w2[0]);
3343- free(w2);
3344- /*
3345- Convert weight to python list object
3346- */
3347- wght_po = PyList_New(nk * nb * nb * ne * 2);
3348- ierr = 0;
3349-
3350- for (ik = 0; ik < nk; ik++)
3351- for (ib = 0; ib < nb; ib++)
3352- for (jb = 0; jb < nb; jb++)
3353- for (ie = 0; ie < ne; ie++)
3354- for (ir = 0; ir < 2; ir++)
3355- ierr = PyList_SetItem(wght_po,
3356- ik * nb * nb * ne * 2 + ib * nb * ne * 2 + jb * ne * 2 + ie * 2 + ir,
3357- PyFloat_FromDouble(wght[ik][ib][jb][ie][ir]));
3358- if (ierr != 0)printf("Error in PyList_SetItem\n");
3359-
3360- free(eig1[0]);
3361- free(eig1);
3362- free(eig2[0]);
3363- free(eig2);
3364- free(wght[0][0][0][0]);
3365- free(wght[0][0][0]);
3366- free(wght[0][0]);
3367- free(wght[0]);
3368- free(wght);
3369- free(e0[0]);
3370- free(e0);
3371-
3372- return wght_po;
3373-}
3374-/*
3375- Results of Integration (1-x-y-z)/(g0+(g1-g0)x+(g2-g0)y+(g3-g0))
3376- for 0<x<1, 0<y<1-x, 0<z<1-x-y
3377-*/
3378-/*
3379-1, Different each other
3380-*/
3381-static double libtetrabz_polstat_1234(
3382- double g1,
3383- double g2,
3384- double g3,
3385- double g4,
3386- double lng1,
3387- double lng2,
3388- double lng3,
3389- double lng4)
3390-{
3391- double w2, w3, w4, w;
3392- w2 = ((lng2 - lng1) / (g2 - g1) * g2 - 1.0) * g2 / (g2 - g1);
3393- w3 = ((lng3 - lng1) / (g3 - g1) * g3 - 1.0) * g3 / (g3 - g1);
3394- w4 = ((lng4 - lng1) / (g4 - g1) * g4 - 1.0) * g4 / (g4 - g1);
3395- w2 = ((w2 - w3) * g2) / (g2 - g3);
3396- w4 = ((w4 - w3) * g4) / (g4 - g3);
3397- w = (w4 - w2) / (g4 - g2);
3398- return w;
3399-}
3400-/*
3401-2, g4 = g1
3402-*/
3403-static double libtetrabz_polstat_1231(
3404- double g1,
3405- double g2,
3406- double g3,
3407- double lng1,
3408- double lng2,
3409- double lng3
3410-) {
3411- double w2, w3, w;
3412- w2 = ((lng2 - lng1) / (g2 - g1) * g2 - 1.0) * g2 * g2 / (g2 - g1) - g1 / 2.0;
3413- w2 = w2 / (g2 - g1);
3414- w3 = ((lng3 - lng1) / (g3 - g1) * g3 - 1.0) * g3 * g3 / (g3 - g1) - g1 / 2.0;
3415- w3 = w3 / (g3 - g1);
3416- w = (w3 - w2) / (g3 - g2);
3417- return w;
3418-}
3419-/*
3420-# 3, g4 = g3
3421-*/
3422-static double libtetrabz_polstat_1233(
3423- double g1,
3424- double g2,
3425- double g3,
3426- double lng1,
3427- double lng2,
3428- double lng3
3429-) {
3430- double w2, w3, w;
3431- w2 = (lng2 - lng1) / (g2 - g1) * g2 - 1.0;
3432- w2 = (g2 * w2) / (g2 - g1);
3433- w3 = (lng3 - lng1) / (g3 - g1) * g3 - 1.0;
3434- w3 = (g3 * w3) / (g3 - g1);
3435- w2 = (w3 - w2) / (g3 - g2);
3436- w3 = (lng3 - lng1) / (g3 - g1) * g3 - 1.0;
3437- w3 = 1.0 - (2.0 * w3 * g1) / (g3 - g1);
3438- w3 = w3 / (g3 - g1);
3439- w = (g3 * w3 - g2 * w2) / (g3 - g2);
3440- return w;
3441-}
3442-/*
3443-4, g4 = g1 and g3 = g2
3444-*/
3445-static double libtetrabz_polstat_1221(
3446- double g1,
3447- double g2,
3448- double lng1,
3449- double lng2
3450-) {
3451- double w;
3452- w = 1.0 - (lng2 - lng1) / (g2 - g1) * g1;
3453- w = -1.0 + (2.0 * g2 * w) / (g2 - g1);
3454- w = -1.0 + (3.0 * g2 * w) / (g2 - g1);
3455- w = w / (2.0 * (g2 - g1));
3456- return w;
3457-}
3458-/*
3459-5, g4 = g3 = g2
3460-*/
3461-static double libtetrabz_polstat_1222(
3462- double g1,
3463- double g2,
3464- double lng1,
3465- double lng2
3466-) {
3467- double w;
3468- w = (lng2 - lng1) / (g2 - g1) * g2 - 1.0;
3469- w = (2.0 * g1 * w) / (g2 - g1) - 1.0;
3470- w = (3.0 * g1 * w) / (g2 - g1) + 1.0;
3471- w = w / (2.0 * (g2 - g1));
3472- return w;
3473-}
3474-/*
3475-6, g4 = g3 = g1
3476-*/
3477-static double libtetrabz_polstat_1211(
3478- double g1,
3479- double g2,
3480- double lng1,
3481- double lng2
3482-) {
3483- double w;
3484- w = -1.0 + (lng2 - lng1) / (g2 - g1) * g2;
3485- w = -1.0 + (2.0 * g2 * w) / (g2 - g1);
3486- w = -1.0 + (3.0 * g2 * w) / (2.0 * (g2 - g1));
3487- w = w / (3.0 * (g2 - g1));
3488- return w;
3489-}
3490-/*
3491-Tetrahedron method for delta(om - ep + e)
3492-*/
3493-static void libtetrabz_polstat3(
3494- double de[4],
3495- double w1[4]
3496-)
3497-{
3498- int i4, indx[4];
3499- double thr, thr2, e[4], ln[4];
3500-
3501- for (i4 = 0; i4 < 4; i4++) e[i4] = de[i4];
3502- eig_sort(4, e, indx);
3503-
3504- thr = e[3] * 1.0e-3;
3505- thr2 = 1.0e-8;
3506-
3507- for(i4 =0; i4 <4; i4++){
3508- if (e[i4] < thr2) {
3509- if (i4 == 3) {
3510- printf(" Nesting # \n");
3511- }
3512- ln[i4] = 0.0;
3513- e[i4] = 0.0;
3514- }
3515- else{
3516- ln[i4] = log(e[i4]);
3517- }
3518- }
3519-
3520- if (fabs(e[3] - e[2]) < thr) {
3521- if (fabs(e[3] - e[1]) < thr) {
3522- if (fabs(e[3] - e[0]) < thr) {
3523- /*
3524- e[3] = e[2] = e[1] = e[0]
3525- */
3526- w1[indx[3]] = 0.25 / e[3];
3527- w1[indx[2]] = w1[indx[3]];
3528- w1[indx[1]] = w1[indx[3]];
3529- w1[indx[0]] = w1[indx[3]];
3530- }
3531- else {
3532- /*
3533- e[3] = e[2] = e[1]
3534- */
3535- w1[indx[3]] = libtetrabz_polstat_1211(e[3], e[0], ln[3], ln[0]);
3536- w1[indx[2]] = w1[indx[3]];
3537- w1[indx[1]] = w1[indx[3]];
3538- w1[indx[0]] = libtetrabz_polstat_1222(e[0], e[3], ln[0], ln[3]);
3539- if (w1[0] < 0.0 || w1[1] < 0.0 || w1[2] < 0.0 || w1[3] < 0.0) {
3540- printf("%f %f %f %f\n", e[0], e[1], e[2], e[3]);
3541- printf("%f %f %f %f\n", w1[indx[0]], w1[indx[1]], w1[indx[2]], w1[indx[3]]);
3542- printf("weighting 4=3=2\n");
3543- }
3544- }
3545- }
3546- else if (fabs(e[1] - e[0]) < thr) {
3547- /*
3548- e[3] = e[2], e[1] = e[0]
3549- */
3550- w1[indx[3]] = libtetrabz_polstat_1221(e[3], e[1], ln[3], ln[1]);
3551- w1[indx[2]] = w1[indx[3]];
3552- w1[indx[1]] = libtetrabz_polstat_1221(e[1], e[3], ln[1], ln[3]);
3553- w1[indx[0]] = w1[indx[1]];
3554-
3555- if (w1[0] < 0.0 || w1[1] < 0.0 || w1[2] < 0.0 || w1[3] < 0.0) {
3556- printf("%f %f %f %f\n", e[0], e[1], e[2], e[3]);
3557- printf("%f %f %f %f\n", w1[indx[0]], w1[indx[1]], w1[indx[2]], w1[indx[3]]);
3558- printf("weighting 4=3 2=1\n");
3559- }
3560- }
3561- else {
3562- /*
3563- e[3] = e[2]
3564- */
3565- w1[indx[3]] = libtetrabz_polstat_1231(e[3], e[0], e[1], ln[3], ln[0], ln[1]);
3566- w1[indx[2]] = w1[indx[3]];
3567- w1[indx[1]] = libtetrabz_polstat_1233(e[1], e[0], e[3], ln[1], ln[0], ln[3]);
3568- w1[indx[0]] = libtetrabz_polstat_1233(e[0], e[1], e[3], ln[0], ln[1], ln[3]);
3569-
3570- if (w1[0] < 0.0 || w1[1] < 0.0 || w1[2] < 0.0 || w1[3] < 0.0) {
3571- printf("%f %f %f %f\n", e[0], e[1], e[2], e[3]);
3572- printf("%f %f %f %f\n", w1[indx[0]], w1[indx[1]], w1[indx[2]], w1[indx[3]]);
3573- printf("weighting 4=3\n");
3574- }
3575- }
3576- }
3577- else if (fabs(e[2] - e[1]) < thr) {
3578- if (fabs(e[2] - e[0]) < thr) {
3579- /*
3580- e[2] = e[1] = e[0]
3581- */
3582- w1[indx[3]] = libtetrabz_polstat_1222(e[3], e[2], ln[3], ln[2]);
3583- w1[indx[2]] = libtetrabz_polstat_1211(e[2], e[3], ln[2], ln[3]);
3584- w1[indx[1]] = w1[indx[2]];
3585- w1[indx[0]] = w1[indx[2]];
3586-
3587- if (w1[0] < 0.0 || w1[1] < 0.0 || w1[2] < 0.0 || w1[3] < 0.0) {
3588- printf("%f %f %f %f\n", e[0], e[1], e[2], e[3]);
3589- printf("%f %f %f %f\n", w1[indx[0]], w1[indx[1]], w1[indx[2]], w1[indx[3]]);
3590- printf("weighting 3=2=1\n");
3591- }
3592- }
3593- else {
3594- /*
3595- e[2] = e[1]
3596- */
3597- w1[indx[3]] = libtetrabz_polstat_1233(e[3], e[0], e[2], ln[3], ln[0], ln[2]);
3598- w1[indx[2]] = libtetrabz_polstat_1231(e[2], e[0], e[3], ln[2], ln[0], ln[3]);
3599- w1[indx[1]] = w1[indx[2]];
3600- w1[indx[0]] = libtetrabz_polstat_1233(e[0], e[3], e[2], ln[0], ln[3], ln[2]);
3601-
3602- if (w1[0] < 0.0 || w1[1] < 0.0 || w1[2] < 0.0 || w1[3] < 0.0) {
3603- printf("%f %f %f %f\n", e[0], e[1], e[2], e[3]);
3604- printf("%f %f %f %f\n", w1[indx[0]], w1[indx[1]], w1[indx[2]], w1[indx[3]]);
3605- printf("weighting 3=2\n");
3606- }
3607- }
3608- }
3609- else if (fabs(e[1] - e[0]) < thr) {
3610- /*
3611- e[1] = e[0]
3612- */
3613- w1[indx[3]] = libtetrabz_polstat_1233(e[3], e[2], e[1], ln[3], ln[2], ln[1]);
3614- w1[indx[2]] = libtetrabz_polstat_1233(e[2], e[3], e[1], ln[2], ln[3], ln[1]);
3615- w1[indx[1]] = libtetrabz_polstat_1231(e[1], e[2], e[3], ln[1], ln[2], ln[3]);
3616- w1[indx[0]] = w1[indx[1]];
3617-
3618- if (w1[0] < 0.0 || w1[1] < 0.0 || w1[2] < 0.0 || w1[3] < 0.0) {
3619- printf("%f %f %f %f\n", e[0], e[1], e[2], e[3]);
3620- printf("%f %f %f %f\n", w1[indx[0]], w1[indx[1]], w1[indx[2]], w1[indx[3]]);
3621- printf("weighting 2=1\n");
3622- }
3623- }
3624- else {
3625- /*
3626- Different each other.
3627- */
3628- w1[indx[3]] = libtetrabz_polstat_1234(e[3], e[0], e[1], e[2], ln[3], ln[0], ln[1], ln[2]);
3629- w1[indx[2]] = libtetrabz_polstat_1234(e[2], e[0], e[1], e[3], ln[2], ln[0], ln[1], ln[3]);
3630- w1[indx[1]] = libtetrabz_polstat_1234(e[1], e[0], e[2], e[3], ln[1], ln[0], ln[2], ln[3]);
3631- w1[indx[0]] = libtetrabz_polstat_1234(e[0], e[1], e[2], e[3], ln[0], ln[1], ln[2], ln[3]);
3632-
3633- if (w1[0] < 0.0 || w1[1] < 0.0 || w1[2] < 0.0 || w1[3] < 0.0) {
3634- printf("%f %f %f %f\n", e[0], e[1], e[2], e[3]);
3635- printf("%f %f %f %f\n", w1[indx[0]], w1[indx[1]], w1[indx[2]], w1[indx[3]]);
3636- printf("weighting\n");
3637- }
3638- }
3639-}
3640-/*
3641-Tetrahedron method for theta( - E2)
3642-*/
3643-static void libtetrabz_polstat2(
3644- int nb,
3645- double *ei1,
3646- double **ej1,
3647- double **w1
3648-) {
3649- int i4, j4, ib, indx[4];
3650- double v, thr, e[4], de[4], w2[4], tsmall[4][4];
3651-
3652- thr = 1.0e-8;
3653-
3654- for (ib = 0; ib < nb; ib++) {
3655-
3656- for (i4 = 0; i4 < 4; i4++)
3657- w1[ib][i4] = 0.0;
3658-
3659- for (i4 = 0; i4 < 4; i4++) e[i4] = -ej1[ib][i4];
3660- eig_sort(4, e, indx);
3661-
3662- if ((e[0] <= 0.0 && 0.0 < e[1]) || (e[0] < 0.0 && 0.0 <= e[1])) {
3663-
3664- libtetrabz_tsmall_a1(e, 0.0, &v, tsmall);
3665-
3666- if (v > thr) {
3667- for (j4 = 0; j4 < 4; j4++) de[j4] = 0.0;
3668- for (i4 = 0; i4 < 4; i4++)
3669- for (j4 = 0; j4 < 4; j4++)
3670- de[j4] += (ej1[ib][indx[i4]] - ei1[indx[i4]]) * tsmall[i4][j4];
3671- libtetrabz_polstat3(de, w2);
3672- for (i4 = 0; i4 < 4; i4++)
3673- for (j4 = 0; j4 < 4; j4++)
3674- w1[ib][indx[i4]] += v * tsmall[i4][j4] * w2[j4];
3675- }
3676- }
3677- else if ((e[1] <= 0.0 && 0.0 < e[2]) || (e[1] < 0.0 && 0.0 <= e[2])) {
3678-
3679- libtetrabz_tsmall_b1(e, 0.0, &v, tsmall);
3680-
3681- if (v > thr) {
3682- for (j4 = 0; j4 < 4; j4++) de[j4] = 0.0;
3683- for (i4 = 0; i4 < 4; i4++)
3684- for (j4 = 0; j4 < 4; j4++)
3685- de[j4] += (ej1[ib][indx[i4]] - ei1[indx[i4]]) * tsmall[i4][j4];
3686- libtetrabz_polstat3(de, w2);
3687- for (i4 = 0; i4 < 4; i4++)
3688- for (j4 = 0; j4 < 4; j4++)
3689- w1[ib][indx[i4]] += v * tsmall[i4][j4] * w2[j4];
3690- }
3691-
3692- libtetrabz_tsmall_b2(e, 0.0, &v, tsmall);
3693-
3694- if (v > thr) {
3695- for (j4 = 0; j4 < 4; j4++) de[j4] = 0.0;
3696- for (i4 = 0; i4 < 4; i4++)
3697- for (j4 = 0; j4 < 4; j4++)
3698- de[j4] += (ej1[ib][indx[i4]] - ei1[indx[i4]]) * tsmall[i4][j4];
3699- libtetrabz_polstat3(de, w2);
3700- for (i4 = 0; i4 < 4; i4++)
3701- for (j4 = 0; j4 < 4; j4++)
3702- w1[ib][indx[i4]] += v * tsmall[i4][j4] * w2[j4];
3703- }
3704-
3705- libtetrabz_tsmall_b3(e, 0.0, &v, tsmall);
3706-
3707- if (v > thr) {
3708- for (j4 = 0; j4 < 4; j4++) de[j4] = 0.0;
3709- for (i4 = 0; i4 < 4; i4++)
3710- for (j4 = 0; j4 < 4; j4++)
3711- de[j4] += (ej1[ib][indx[i4]] - ei1[indx[i4]]) * tsmall[i4][j4];
3712- libtetrabz_polstat3(de, w2);
3713- for (i4 = 0; i4 < 4; i4++)
3714- for (j4 = 0; j4 < 4; j4++)
3715- w1[ib][indx[i4]] += v * tsmall[i4][j4] * w2[j4];
3716- }
3717- }
3718- else if ((e[2] <= 0.0 && 0.0 < e[3]) || (e[2] < 0.0 && 0.0 <= e[3])) {
3719-
3720- libtetrabz_tsmall_c1(e, 0.0, &v, tsmall);
3721-
3722- if (v > thr) {
3723- for (j4 = 0; j4 < 4; j4++) de[j4] = 0.0;
3724- for (i4 = 0; i4 < 4; i4++)
3725- for (j4 = 0; j4 < 4; j4++)
3726- de[j4] += (ej1[ib][indx[i4]] - ei1[indx[i4]]) * tsmall[i4][j4];
3727- libtetrabz_polstat3(de, w2);
3728- for (i4 = 0; i4 < 4; i4++)
3729- for (j4 = 0; j4 < 4; j4++)
3730- w1[ib][indx[i4]] += v * tsmall[i4][j4] * w2[j4];
3731- }
3732-
3733- libtetrabz_tsmall_c2(e, 0.0, &v, tsmall);
3734-
3735- if (v > thr) {
3736- for (j4 = 0; j4 < 4; j4++) de[j4] = 0.0;
3737- for (i4 = 0; i4 < 4; i4++)
3738- for (j4 = 0; j4 < 4; j4++)
3739- de[j4] += (ej1[ib][indx[i4]] - ei1[indx[i4]]) * tsmall[i4][j4];
3740- libtetrabz_polstat3(de, w2);
3741- for (i4 = 0; i4 < 4; i4++)
3742- for (j4 = 0; j4 < 4; j4++)
3743- w1[ib][indx[i4]] += v * tsmall[i4][j4] * w2[j4];
3744- }
3745-
3746- libtetrabz_tsmall_c3(e, 0.0, &v, tsmall);
3747-
3748- if (v > thr) {
3749- for (j4 = 0; j4 < 4; j4++) de[j4] = 0.0;
3750- for (i4 = 0; i4 < 4; i4++)
3751- for (j4 = 0; j4 < 4; j4++)
3752- de[j4] += (ej1[ib][indx[i4]] - ei1[indx[i4]]) * tsmall[i4][j4];
3753- libtetrabz_polstat3(de, w2);
3754- for (i4 = 0; i4 < 4; i4++)
3755- for (j4 = 0; j4 < 4; j4++)
3756- w1[ib][indx[i4]] += v * tsmall[i4][j4] * w2[j4];
3757- }
3758- }
3759- else if (e[3] <= 0.0) {
3760- for (i4 = 0; i4 < 4; i4++)
3761- de[i4] = ej1[ib][i4] - ei1[i4];
3762- libtetrabz_polstat3(de, w2);
3763- for (i4 = 0; i4 < 4; i4++)
3764- w1[ib][i4] += w2[i4];
3765- }
3766- }
3767-}
3768-/*
3769-Compute Static polarization function
3770-*/
3771-static PyObject* polstat_c(PyObject* self, PyObject* args)
3772-{
3773- int it, ik, ib, jb, i20, i4, j4, **ikv, indx[4], ierr, ng[3], nk, nb;
3774- double wlsm[20][4], **ei1, **ej1, ei2[4], ** ej2, e[4], *** w1, ** w2, v, tsmall[4][4], thr,
3775- bvec[3][3], ** eig1, ** eig2, *** wght;
3776- PyObject* eig1_po, * eig2_po, * wght_po;
3777- /*
3778- Read input from python object
3779- */
3780- if (!PyArg_ParseTuple(args, "iiiiidddddddddOO",
3781- &ng[0], &ng[1], &ng[2], &nk, &nb,
3782- &bvec[0][0], &bvec[0][1], &bvec[0][2], &bvec[1][0], &bvec[1][1], &bvec[1][2], &bvec[2][0], &bvec[2][1], &bvec[2][2],
3783- &eig1_po, &eig2_po))
3784- return NULL;
3785- /*
3786- convert python list object to array
3787- */
3788- eig1 = (double**)malloc(nk * sizeof(double*));
3789- eig1[0] = (double*)malloc(nk * nb * sizeof(double));
3790- eig2 = (double**)malloc(nk * sizeof(double*));
3791- eig2[0] = (double*)malloc(nk * nb * sizeof(double));
3792- wght = (double***)malloc(nk * sizeof(double**));
3793- wght[0] = (double**)malloc(nk * nb * sizeof(double*));
3794- wght[0][0] = (double*)malloc(nk * nb * nb * sizeof(double));
3795- for (ik = 0; ik < nk; ik++) {
3796- eig1[ik] = eig1[0] + ik * nb;
3797- eig2[ik] = eig2[0] + ik * nb;
3798- wght[ik] = wght[0] + ik * nb;
3799- for (ib = 0; ib < nb; ib++) {
3800- wght[ik][ib] = wght[0][0] + ik * nb * nb + ib * nb;
3801- }
3802- }
3803-
3804- for (ik = 0; ik < nk; ik++)
3805- for (ib = 0; ib < nb; ib++) {
3806- eig1[ik][ib] = PyFloat_AsDouble(PyList_GetItem(eig1_po, ik * nb + ib));
3807- eig2[ik][ib] = PyFloat_AsDouble(PyList_GetItem(eig2_po, ik * nb + ib));
3808- }
3809- /*
3810- Start main calculation
3811- */
3812-
3813-
3814- thr = 1.0e-10;
3815-
3816- ikv = (int**)malloc(6 * nk * sizeof(int*));
3817- ikv[0] = (int*)malloc(6 * nk * 20 * sizeof(int));
3818- for (it = 0; it < 6 * nk; it++) {
3819- ikv[it] = ikv[0] + it * 20;
3820- }
3821-
3822- ei1 = (double**)malloc(4 * sizeof(double*));
3823- ej1 = (double**)malloc(4 * sizeof(double*));
3824- ei1[0] = (double*)malloc(4 * nb * sizeof(double));
3825- ej1[0] = (double*)malloc(4 * nb * sizeof(double));
3826- for (i4 = 0; i4 < 4; i4++) {
3827- ei1[i4] = ei1[0] + i4 * nb;
3828- ej1[i4] = ej1[0] + i4 * nb;
3829- }
3830-
3831- ej2 = (double**)malloc(nb * sizeof(double*));
3832- ej2[0] = (double*)malloc(nb * 4 * sizeof(double));
3833- for (ib = 0; ib < nb; ib++)
3834- ej2[ib] = ej2[0] + ib * 4;
3835-
3836- w1 = (double***)malloc(nb * sizeof(double**));
3837- w1[0] = (double**)malloc(nb * 4 * sizeof(double*));
3838- w1[0][0] = (double*)malloc(nb * 4 * nb * sizeof(double));
3839- for (ib = 0; ib < nb; ib++) {
3840- w1[ib] = w1[0] + ib * 4;
3841- for (i4 = 0; i4 < 4; i4++) {
3842- w1[ib][i4] = w1[0][0] + ib * 4 * nb + i4 * nb;
3843- }
3844- }
3845-
3846- w2 = (double**)malloc(nb * sizeof(double*));
3847- w2[0] = (double*)malloc(nb * 4 * sizeof(double));
3848- for (ib = 0; ib < nb; ib++) {
3849- w2[ib] = w2[0] + ib * 4;
3850- }
3851-
3852- libtetrabz_initialize(ng, bvec, wlsm, ikv);
3853-
3854- for (ik = 0; ik < nk; ik++)
3855- for (ib = 0; ib < nb; ib++)
3856- for (jb = 0; jb < nb; jb++)
3857- wght[ik][ib][jb] = 0.0;
3858-
3859- for(it = 0; it < 6*nk; it++) {
3860-
3861- for (i4 = 0; i4 < 4; i4++)
3862- for (ib = 0; ib < nb; ib++) {
3863- ei1[i4][ib] = 0.0;
3864- ej1[i4][ib] = 0.0;
3865- }
3866- for (i20 = 0; i20 < 20; i20++) {
3867- for (i4 = 0; i4 < 4; i4++) {
3868- for (ib = 0; ib < nb; ib++) {
3869- ei1[i4][ib] += eig1[ikv[it][i20]][ib] * wlsm[i20][i4];
3870- ej1[i4][ib] += eig2[ikv[it][i20]][ib] * wlsm[i20][i4];
3871- }
3872- }
3873- }
3874-
3875- for (ib = 0; ib < nb; ib++) {
3876-
3877- for (i4 = 0; i4 < 4; i4++)
3878- for (jb = 0; jb < nb; jb++)
3879- w1[ib][i4][jb] = 0.0;
3880-
3881- for (i4 = 0; i4 < 4; i4++) e[i4] = ei1[i4][ib];
3882- eig_sort(4, e, indx);
3883-
3884- if (e[0] <= 0.0 && 0.0 < e[1]) {
3885-
3886- libtetrabz_tsmall_a1(e, 0.0, &v, tsmall);
3887-
3888- if (v > thr) {
3889- for (j4 = 0; j4 < 4; j4++) {
3890- ei2[j4] = 0.0;
3891- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
3892- }
3893- for (i4 = 0; i4 < 4; i4++)
3894- for (j4 = 0; j4 < 4; j4++) {
3895- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
3896- for (jb = 0; jb < nb; jb++)
3897- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
3898- }
3899- libtetrabz_polstat2(nb, ei2, ej2, w2);
3900- for (i4 = 0; i4 < 4; i4++)
3901- for (jb = 0; jb < nb; jb++)
3902- for (j4 = 0; j4 < 4; j4++)
3903- w1[ib][indx[i4]][jb] += v * tsmall[i4][j4] * w2[jb][j4];
3904- }
3905- }
3906- else if (e[1] <= 0.0 && 0.0 < e[2]) {
3907-
3908- libtetrabz_tsmall_b1(e, 0.0, &v, tsmall);
3909-
3910- if (v > thr) {
3911- for (j4 = 0; j4 < 4; j4++) {
3912- ei2[j4] = 0.0;
3913- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
3914- }
3915- for (i4 = 0; i4 < 4; i4++)
3916- for (j4 = 0; j4 < 4; j4++) {
3917- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
3918- for (jb = 0; jb < nb; jb++)
3919- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
3920- }
3921- libtetrabz_polstat2(nb, ei2, ej2, w2);
3922- for (i4 = 0; i4 < 4; i4++)
3923- for (jb = 0; jb < nb; jb++)
3924- for (j4 = 0; j4 < 4; j4++)
3925- w1[ib][indx[i4]][jb] += v * tsmall[i4][j4] * w2[jb][j4];
3926- }
3927-
3928- libtetrabz_tsmall_b2(e, 0.0, &v, tsmall);
3929-
3930- if (v > thr) {
3931- for (j4 = 0; j4 < 4; j4++) {
3932- ei2[j4] = 0.0;
3933- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
3934- }
3935- for (i4 = 0; i4 < 4; i4++)
3936- for (j4 = 0; j4 < 4; j4++) {
3937- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
3938- for (jb = 0; jb < nb; jb++)
3939- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
3940- }
3941- libtetrabz_polstat2(nb, ei2, ej2, w2);
3942- for (i4 = 0; i4 < 4; i4++)
3943- for (jb = 0; jb < nb; jb++)
3944- for (j4 = 0; j4 < 4; j4++)
3945- w1[ib][indx[i4]][jb] += v * tsmall[i4][j4] * w2[jb][j4];
3946- }
3947-
3948- libtetrabz_tsmall_b3(e, 0.0, &v, tsmall);
3949-
3950- if (v > thr) {
3951- for (j4 = 0; j4 < 4; j4++) {
3952- ei2[j4] = 0.0;
3953- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
3954- }
3955- for (i4 = 0; i4 < 4; i4++)
3956- for (j4 = 0; j4 < 4; j4++) {
3957- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
3958- for (jb = 0; jb < nb; jb++)
3959- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
3960- }
3961- libtetrabz_polstat2(nb, ei2, ej2, w2);
3962- for (i4 = 0; i4 < 4; i4++)
3963- for (jb = 0; jb < nb; jb++)
3964- for (j4 = 0; j4 < 4; j4++)
3965- w1[ib][indx[i4]][jb] += v * tsmall[i4][j4] * w2[jb][j4];
3966- }
3967- }
3968- else if (e[2] <= 0.0 && 0.0 < e[3]) {
3969-
3970- libtetrabz_tsmall_c1(e, 0.0, &v, tsmall);
3971-
3972- if (v > thr) {
3973- for (j4 = 0; j4 < 4; j4++) {
3974- ei2[j4] = 0.0;
3975- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
3976- }
3977- for (i4 = 0; i4 < 4; i4++)
3978- for (j4 = 0; j4 < 4; j4++) {
3979- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
3980- for (jb = 0; jb < nb; jb++)
3981- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
3982- }
3983- libtetrabz_polstat2(nb, ei2, ej2, w2);
3984- for (i4 = 0; i4 < 4; i4++)
3985- for (jb = 0; jb < nb; jb++)
3986- for (j4 = 0; j4 < 4; j4++)
3987- w1[ib][indx[i4]][jb] += v * tsmall[i4][j4] * w2[jb][j4];
3988- }
3989-
3990- libtetrabz_tsmall_c2(e, 0.0, &v, tsmall);
3991-
3992- if (v > thr) {
3993- for (j4 = 0; j4 < 4; j4++) {
3994- ei2[j4] = 0.0;
3995- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
3996- }
3997- for (i4 = 0; i4 < 4; i4++)
3998- for (j4 = 0; j4 < 4; j4++) {
3999- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
4000- for (jb = 0; jb < nb; jb++)
4001- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
4002- }
4003- libtetrabz_polstat2(nb, ei2, ej2, w2);
4004- for (i4 = 0; i4 < 4; i4++)
4005- for (jb = 0; jb < nb; jb++)
4006- for (j4 = 0; j4 < 4; j4++)
4007- w1[ib][indx[i4]][jb] += v * tsmall[i4][j4] * w2[jb][j4];
4008- }
4009-
4010- libtetrabz_tsmall_c3(e, 0.0, &v, tsmall);
4011-
4012- if (v > thr) {
4013- for (j4 = 0; j4 < 4; j4++) {
4014- ei2[j4] = 0.0;
4015- for (jb = 0; jb < nb; jb++) ej2[jb][j4] = 0.0;
4016- }
4017- for (i4 = 0; i4 < 4; i4++)
4018- for (j4 = 0; j4 < 4; j4++) {
4019- ei2[j4] += ei1[indx[i4]][ib] * tsmall[i4][j4];
4020- for (jb = 0; jb < nb; jb++)
4021- ej2[jb][j4] += ej1[indx[i4]][jb] * tsmall[i4][j4];
4022- }
4023- libtetrabz_polstat2(nb, ei2, ej2, w2);
4024- for (i4 = 0; i4 < 4; i4++)
4025- for (jb = 0; jb < nb; jb++)
4026- for (j4 = 0; j4 < 4; j4++)
4027- w1[ib][indx[i4]][jb] += v * tsmall[i4][j4] * w2[jb][j4];
4028- }
4029- }
4030- else if (e[3] <= 0.0) {
4031- for (i4 = 0; i4 < 4; i4++) {
4032- ei2[i4] = ei1[i4][ib];
4033- for (jb = 0; jb < nb; jb++)
4034- ej2[jb][i4] = ej1[i4][jb];
4035- }
4036- libtetrabz_polstat2(nb, ei2, ej2, w2);
4037- for (i4 = 0; i4 < 4; i4++)
4038- for (jb = 0; jb < nb; jb++)
4039- w1[ib][i4][jb] += w2[jb][i4];
4040- }
4041- else {
4042- continue;
4043- }
4044- }
4045- for (i20 = 0; i20 < 20; i20++)
4046- for (ib = 0; ib < nb; ib++)
4047- for (i4 = 0; i4 < 4; i4++)
4048- for (jb = 0; jb < nb; jb++)
4049- wght[ikv[it][i20]][ib][jb] += wlsm[i20][i4] * w1[ib][i4][jb];
4050- }
4051- for (ik = 0; ik < nk; ik++)
4052- for (ib = 0; ib < nb; ib++)
4053- for (jb = 0; jb < nb; jb++)
4054- wght[ik][ib][jb] /= (6.0 * (double) nk);
4055-
4056- free(ikv[0]);
4057- free(ikv);
4058- free(ei1[0]);
4059- free(ei1);
4060- free(ej1[0]);
4061- free(ej1);
4062- free(ej2[0]);
4063- free(ej2);
4064- free(w1[0][0]);
4065- free(w1[0]);
4066- free(w1);
4067- free(w2[0]);
4068- free(w2);
4069- /*
4070- Convert weight to python list object
4071- */
4072- wght_po = PyList_New(nk * nb * nb);
4073- ierr = 0;
4074- for (ik = 0; ik < nk; ik++)
4075- for (ib = 0; ib < nb; ib++)
4076- for (jb = 0; jb < nb; jb++)
4077- ierr = PyList_SetItem(wght_po, ik * nb * nb + ib * nb + jb, PyFloat_FromDouble(wght[ik][ib][jb]));
4078- if (ierr != 0)printf("Error in PyList_SetItem\n");
4079-
4080- free(eig1[0]);
4081- free(eig1);
4082- free(eig2[0]);
4083- free(eig2);
4084- free(wght[0][0]);
4085- free(wght[0]);
4086- free(wght);
4087-
4088- return wght_po;
4089-}
4090-static PyMethodDef LibTetraBZCMethods[] = {
4091- {"dos_c", dos_c, METH_VARARGS, "Density of States"},
4092- {"intdos_c", intdos_c, METH_VARARGS, "Integrated density of States"},
4093- {"occ_c", occ_c, METH_VARARGS, "Occupations"},
4094- {"fermieng_c", fermieng_c, METH_VARARGS, "Fermi energy"},
4095- {"dbldelta_c", dbldelta_c, METH_VARARGS, "Double delta"},
4096- {"dblstep_c", dblstep_c, METH_VARARGS, "Double step function"},
4097- {"polstat_c", polstat_c, METH_VARARGS, "Static polarization function"},
4098- {"fermigr_c", fermigr_c, METH_VARARGS, "Fermi's golden rule"},
4099- {"polcmplx_c", polcmplx_c, METH_VARARGS, "Dynamical polarization function on complex frequency"},
4100- {NULL, NULL, 0, NULL} /* Sentinel */
4101-};
4102-
4103-static struct PyModuleDef libtetrabzcmodule = {
4104- PyModuleDef_HEAD_INIT,
4105- "libtetrabzc", /* name of module */
4106- NULL, /* module documentation, may be NULL */
4107- -1, /* size of per-interpreter state of the module,
4108- or -1 if the module keeps state in global variables. */
4109- LibTetraBZCMethods
4110-};
4111-
4112-PyMODINIT_FUNC
4113-PyInit_libtetrabzc(void)
4114-{
4115- return PyModule_Create(&libtetrabzcmodule);
4116-}
--- a/src/c/setup.py
+++ /dev/null
@@ -1,7 +0,0 @@
1-from distutils.core import setup, Extension
2-
3-setup(name='libtetrabzc',
4- version='1.0',
5- ext_modules=[Extension('libtetrabzc', ['libtetrabz.c'])]
6-)
7-
--- a/src/libtetrabz/__init__.py
+++ b/src/libtetrabz/__init__.py
@@ -20,12 +20,228 @@
2020 # TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
2121 # SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
2222 #
23-from .libtetrabz_dos import dos
24-from .libtetrabz_dos import intdos
25-from .libtetrabz_occ import occ
26-from .libtetrabz_occ import fermieng
27-from .libtetrabz_polstat import polstat
28-from .libtetrabz_fermigr import fermigr
29-from .libtetrabz_dbldelta import dbldelta
30-from .libtetrabz_dblstep import dblstep
31-from .libtetrabz_polcmplx import polcmplx
23+from .libtetrabzc import dos_c
24+from .libtetrabzc import intdos_c
25+from .libtetrabzc import occ_c
26+from .libtetrabzc import fermieng_c
27+from .libtetrabzc import polstat_c
28+from .libtetrabzc import fermigr_c
29+from .libtetrabzc import dbldelta_c
30+from .libtetrabzc import dblstep_c
31+from .libtetrabzc import polcmplx_c
32+import numpy
33+
34+
35+def occ(bvec=numpy.array([1.0, 0.0, 0.0]), eig=numpy.array([0.0])):
36+ """
37+
38+ :return:
39+ """
40+ #
41+ ng = numpy.array(eig.shape[0:3])
42+ nk = ng.prod(0)
43+ nb = eig.shape[3]
44+ eig_c = eig.reshape(nk*nb).tolist()
45+ #
46+ wght_c = libtetrabzc.occ_c(ng[0], ng[1], ng[2], nk, nb,
47+ bvec[0, 0], bvec[0, 1], bvec[0, 2],
48+ bvec[1, 0], bvec[1, 1], bvec[1, 2],
49+ bvec[2, 0], bvec[2, 1], bvec[2, 2], eig_c)
50+ #
51+ wght = numpy.array(wght_c).reshape([ng[0], ng[1], ng[2], nb])
52+ return wght
53+
54+
55+def fermieng(bvec=numpy.array([1.0, 0.0, 0.0]), eig=numpy.array([0.0]), nelec=0.0):
56+ """
57+
58+ :return:
59+ """
60+ #
61+ ng = numpy.array(eig.shape[0:3])
62+ nk = ng.prod(0)
63+ nb = eig.shape[3]
64+ eig_c = eig.reshape(nk*nb).tolist()
65+
66+ wght_c = libtetrabzc.fermieng_c(ng[0], ng[1], ng[2], nk, nb,
67+ bvec[0, 0], bvec[0, 1], bvec[0, 2],
68+ bvec[1, 0], bvec[1, 1], bvec[1, 2],
69+ bvec[2, 0], bvec[2, 1], bvec[2, 2], eig_c, nelec)
70+ #
71+ ef = wght_c[nk * nb]
72+ iteration = wght_c[nk*nb + 1]
73+ wght = numpy.array(wght_c)[0:nk*nb].reshape([ng[0], ng[1], ng[2], nb])
74+ return ef, wght, iteration
75+
76+
77+def dos(bvec=numpy.array([1.0, 0.0, 0.0]), eig=numpy.array([0.0]), e0=numpy.array([0.0])):
78+ """
79+
80+ :return:
81+ """
82+ ng = numpy.array(eig.shape[0:3])
83+ nk = ng.prod(0)
84+ nb = eig.shape[3]
85+ ne = e0.shape[0]
86+ eig_c = eig.reshape(nk*nb).tolist()
87+ e0_c = e0.tolist()
88+ #
89+ wght_c = libtetrabzc.dos_c(ng[0], ng[1], ng[2], nk, nb, ne,
90+ bvec[0, 0], bvec[0, 1], bvec[0, 2],
91+ bvec[1, 0], bvec[1, 1], bvec[1, 2],
92+ bvec[2, 0], bvec[2, 1], bvec[2, 2], eig_c, e0_c)
93+ #
94+ wght = numpy.array(wght_c).reshape([ng[0], ng[1], ng[2], nb, ne])
95+ return wght
96+
97+
98+def intdos(bvec=numpy.array([1.0, 0.0, 0.0]), eig=numpy.array([0.0]), e0=numpy.array([0.0])):
99+ """
100+
101+ :return:
102+ """
103+ ng = numpy.array(eig.shape[0:3])
104+ nk = ng.prod(0)
105+ nb = eig.shape[3]
106+ ne = e0.shape[0]
107+ eig_c = eig.reshape(nk*nb).tolist()
108+ e0_c = e0.tolist()
109+ #
110+ wght_c = libtetrabzc.intdos_c(ng[0], ng[1], ng[2], nk, nb, ne,
111+ bvec[0, 0], bvec[0, 1], bvec[0, 2],
112+ bvec[1, 0], bvec[1, 1], bvec[1, 2],
113+ bvec[2, 0], bvec[2, 1], bvec[2, 2], eig_c, e0_c)
114+ #
115+ wght = numpy.array(wght_c).reshape([ng[0], ng[1], ng[2], nb, ne])
116+ return wght
117+
118+
119+def dblstep(bvec=numpy.array([1.0, 0.0, 0.0]), eig1=numpy.array([0.0]), eig2=numpy.array([0.0])):
120+ """
121+
122+ :param bvec:
123+ :param eig1:
124+ :param eig2:
125+ :return:
126+ """
127+ #
128+ ng = numpy.array(eig1.shape[0:3])
129+ nk = ng.prod(0)
130+ nb = eig1.shape[3]
131+ eig1_c = eig1.reshape(nk*nb).tolist()
132+ eig2_c = eig2.reshape(nk*nb).tolist()
133+
134+ wght_c = libtetrabzc.dblstep_c(ng[0], ng[1], ng[2], nk, nb,
135+ bvec[0, 0], bvec[0, 1], bvec[0, 2],
136+ bvec[1, 0], bvec[1, 1], bvec[1, 2],
137+ bvec[2, 0], bvec[2, 1], bvec[2, 2], eig1_c, eig2_c)
138+ #
139+ wght = numpy.array(wght_c).reshape([ng[0], ng[1], ng[2], nb, nb])
140+ return wght
141+
142+
143+def dbldelta(bvec=numpy.array([1.0, 0.0, 0.0]), eig1=numpy.array([0.0]), eig2=numpy.array([0.0])):
144+ """
145+
146+ :param bvec:
147+ :param eig1:
148+ :param eig2:
149+ :return:
150+ """
151+ #
152+ ng = numpy.array(eig1.shape[0:3])
153+ nk = ng.prod(0)
154+ nb = eig1.shape[3]
155+ eig1_c = eig1.reshape(nk * nb).tolist()
156+ eig2_c = eig2.reshape(nk * nb).tolist()
157+
158+ wght_c = libtetrabzc.dbldelta_c(ng[0], ng[1], ng[2], nk, nb,
159+ bvec[0, 0], bvec[0, 1], bvec[0, 2],
160+ bvec[1, 0], bvec[1, 1], bvec[1, 2],
161+ bvec[2, 0], bvec[2, 1], bvec[2, 2], eig1_c, eig2_c)
162+ #
163+ wght = numpy.array(wght_c).reshape([ng[0], ng[1], ng[2], nb, nb])
164+ return wght
165+
166+
167+def polstat(bvec=numpy.array([1.0, 0.0, 0.0]), eig1=numpy.array([0.0]), eig2=numpy.array([0.0])):
168+ """
169+
170+ :param bvec:
171+ :param eig1:
172+ :param eig2:
173+ :return:
174+ """
175+ ng = numpy.array(eig1.shape[0:3])
176+ nk = ng.prod(0)
177+ nb = eig1.shape[3]
178+ eig1_c = eig1.reshape(nk * nb).tolist()
179+ eig2_c = eig2.reshape(nk * nb).tolist()
180+
181+ wght_c = libtetrabzc.polstat_c(ng[0], ng[1], ng[2], nk, nb,
182+ bvec[0, 0], bvec[0, 1], bvec[0, 2],
183+ bvec[1, 0], bvec[1, 1], bvec[1, 2],
184+ bvec[2, 0], bvec[2, 1], bvec[2, 2], eig1_c, eig2_c)
185+ #
186+ wght = numpy.array(wght_c).reshape([ng[0], ng[1], ng[2], nb, nb])
187+ return wght
188+
189+
190+def fermigr(bvec=numpy.array([1.0, 0.0, 0.0]),
191+ eig1=numpy.array([0.0]), eig2=numpy.array([0.0]), e0=numpy.array([0.0])):
192+ """
193+
194+ :param bvec:
195+ :param eig1:
196+ :param eig2:
197+ :param e0:
198+ :return:
199+ """
200+ ng = numpy.array(eig1.shape[0:3])
201+ nk = ng.prod(0)
202+ nb = eig1.shape[3]
203+ ne = e0.shape[0]
204+ eig1_c = eig1.reshape(nk * nb).tolist()
205+ eig2_c = eig2.reshape(nk * nb).tolist()
206+ e0_c = e0.tolist()
207+
208+ wght_c = libtetrabzc.fermigr_c(ng[0], ng[1], ng[2], nk, nb, ne,
209+ bvec[0, 0], bvec[0, 1], bvec[0, 2],
210+ bvec[1, 0], bvec[1, 1], bvec[1, 2],
211+ bvec[2, 0], bvec[2, 1], bvec[2, 2], eig1_c, eig2_c, e0_c)
212+ #
213+ wght = numpy.array(wght_c).reshape([ng[0], ng[1], ng[2], nb, nb, ne])
214+ return wght
215+
216+
217+def polcmplx(bvec=numpy.array([1.0, 0.0, 0.0]),
218+ eig1=numpy.array([0.0]), eig2=numpy.array([0.0]), e0=numpy.array([0.0+0.0j])):
219+ """
220+
221+ :param bvec:
222+ :param eig1:
223+ :param eig2:
224+ :param e0:
225+ :return:
226+ """
227+ ng = numpy.array(eig1.shape[0:3])
228+ nk = ng.prod(0)
229+ nb = eig1.shape[3]
230+ ne = e0.shape[0]
231+ eig1_c = eig1.reshape(nk * nb).tolist()
232+ eig2_c = eig2.reshape(nk * nb).tolist()
233+
234+ e0_1 = numpy.empty([ne, 2], dtype=numpy.float_)
235+ e0_1[:, 0] = e0[:].real
236+ e0_1[:, 1] = e0[:].imag
237+ e0_c = e0_1.reshape(ne * 2).tolist()
238+
239+ wght_c = libtetrabzc.polcmplx_c(ng[0], ng[1], ng[2], nk, nb, ne,
240+ bvec[0, 0], bvec[0, 1], bvec[0, 2],
241+ bvec[1, 0], bvec[1, 1], bvec[1, 2],
242+ bvec[2, 0], bvec[2, 1], bvec[2, 2], eig1_c, eig2_c, e0_c)
243+ #
244+ wght_1 = numpy.array(wght_c).reshape([ng[0], ng[1], ng[2], nb, nb, ne, 2])
245+ #
246+ wght = wght_1[:, :, :, :, :, :, 0] + 1.0j * wght_1[:, :, :, :, :, :, 1]
247+ return wght
--- a/src/libtetrabz/libtetrabz_common.py
+++ /dev/null
@@ -1,356 +0,0 @@
1-#
2-# Copyright (c) 2014 Mitsuaki Kawamura
3-#
4-# Permission is hereby granted, free of charge, to any person obtaining a
5-# copy of this software and associated documentation files (the
6-# "Software"), to deal in the Software without restriction, including
7-# without limitation the rights to use, copy, modify, merge, publish,
8-# distribute, sublicense, and/or sell copies of the Software, and to
9-# permit persons to whom the Software is furnished to do so, subject to
10-# the following conditions:
11-#
12-# The above copyright notice and this permission notice shall be included
13-# in all copies or substantial portions of the Software.
14-#
15-# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
16-# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
17-# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
18-# IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
19-# CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
20-# TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
21-# SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
22-#
23-import numpy
24-
25-
26-def libtetrabz_initialize(ng, bvec):
27- """
28- :param ng:
29- :param bvec:
30- :return: Weight
31-
32- define shortest diagonal line & define type of tetragonal
33- """
34- bvec2 = numpy.empty([3, 3], dtype=numpy.float_)
35- for i1 in range(3):
36- bvec2[i1, 0:3] = bvec[i1, 0:3] / ng[i1]
37- #
38- bvec3 = numpy.empty([4, 3], dtype=numpy.float_)
39- bvec3[0, 0:3] = -bvec2[0, 0:3] + bvec2[1, 0:3] + bvec2[2, 0:3]
40- bvec3[1, 0:3] = bvec2[0, 0:3] - bvec2[1, 0:3] + bvec2[2, 0:3]
41- bvec3[2, 0:3] = bvec2[0, 0:3] + bvec2[1, 0:3] - bvec2[2, 0:3]
42- bvec3[3, 0:3] = bvec2[0, 0:3] + bvec2[1, 0:3] + bvec2[2, 0:3]
43- #
44- # length of delta bvec
45- #
46- bnorm = numpy.empty(4, dtype=numpy.float_)
47- for i1 in range(4):
48- bnorm[i1] = numpy.linalg.norm(bvec3[i1, 0:3])
49- #
50- itype = bnorm.argmin(0)
51- #
52- # start & last
53- #
54- ivvec0 = numpy.zeros(4, dtype=numpy.int_)
55- #
56- divvec = numpy.identity(4, dtype=numpy.int_)
57- #
58- ivvec0[itype] = 1
59- divvec[itype, itype] = - 1
60- #
61- # Corners of tetrahedra
62- #
63- ivvec = numpy.empty([6, 20, 3], dtype=numpy.float_)
64- it = 0
65- for i1 in range(3):
66- for i2 in range(3):
67- if i2 == i1:
68- continue
69- for i3 in range(3):
70- if i3 == i1 or i3 == i2:
71- continue
72- #
73- ivvec[it, 0, 0:3] = ivvec0[0:3]
74- ivvec[it, 1, 0:3] = ivvec[it, 0, 0:3] + divvec[i1, 0:3]
75- ivvec[it, 2, 0:3] = ivvec[it, 1, 0:3] + divvec[i2, 0:3]
76- ivvec[it, 3, 0:3] = ivvec[it, 2, 0:3] + divvec[i3, 0:3]
77- #
78- it += 1
79- #
80- # Additional points
81- #
82- ivvec[0:6, 4, 0:3] = 2 * ivvec[0:6, 0, 0:3] - ivvec[0:6, 1, 0:3]
83- ivvec[0:6, 5, 0:3] = 2 * ivvec[0:6, 1, 0:3] - ivvec[0:6, 2, 0:3]
84- ivvec[0:6, 6, 0:3] = 2 * ivvec[0:6, 2, 0:3] - ivvec[0:6, 3, 0:3]
85- ivvec[0:6, 7, 0:3] = 2 * ivvec[0:6, 3, 0:3] - ivvec[0:6, 0, 0:3]
86- #
87- ivvec[0:6, 8, 0:3] = 2 * ivvec[0:6, 0, 0:3] - ivvec[0:6, 2, 0:3]
88- ivvec[0:6, 9, 0:3] = 2 * ivvec[0:6, 1, 0:3] - ivvec[0:6, 3, 0:3]
89- ivvec[0:6, 10, 0:3] = 2 * ivvec[0:6, 2, 0:3] - ivvec[0:6, 0, 0:3]
90- ivvec[0:6, 11, 0:3] = 2 * ivvec[0:6, 3, 0:3] - ivvec[0:6, 1, 0:3]
91- #
92- ivvec[0:6, 12, 0:3] = 2 * ivvec[0:6, 0, 0:3] - ivvec[0:6, 3, 0:3]
93- ivvec[0:6, 13, 0:3] = 2 * ivvec[0:6, 1, 0:3] - ivvec[0:6, 0, 0:3]
94- ivvec[0:6, 14, 0:3] = 2 * ivvec[0:6, 2, 0:3] - ivvec[0:6, 1, 0:3]
95- ivvec[0:6, 15, 0:3] = 2 * ivvec[0:6, 3, 0:3] - ivvec[0:6, 2, 0:3]
96- #
97- ivvec[0:6, 16, 0:3] = ivvec[0:6, 3, 0:3] - ivvec[0:6, 0, 0:3] + ivvec[0:6, 1, 0:3]
98- ivvec[0:6, 17, 0:3] = ivvec[0:6, 0, 0:3] - ivvec[0:6, 1, 0:3] + ivvec[0:6, 2, 0:3]
99- ivvec[0:6, 18, 0:3] = ivvec[0:6, 1, 0:3] - ivvec[0:6, 2, 0:3] + ivvec[0:6, 3, 0:3]
100- ivvec[0:6, 19, 0:3] = ivvec[0:6, 2, 0:3] - ivvec[0:6, 3, 0:3] + ivvec[0:6, 0, 0:3]
101- #
102- wlsm = numpy.empty([4, 20], dtype=numpy.float_)
103- wlsm[0:4, 0: 4] = numpy.array([[1440.0, 0.0, 30.0, 0.0],
104- [0.0, 1440.0, 0.0, 30.0],
105- [30.0, 0.0, 1440.0, 0.0],
106- [0.0, 30.0, 0.0, 1440.0]])
107- #
108- wlsm[0:4, 4: 8] = numpy.array([[-38.0, 7.0, 17.0, -28.0],
109- [-28.0, -38.0, 7.0, 17.0],
110- [17.0, -28.0, -38.0, 7.0],
111- [7.0, 17.0, -28.0, -38.0]])
112- #
113- wlsm[0:4, 8:12] = numpy.array([[-56.0, 9.0, -46.0, 9.0],
114- [9.0, -56.0, 9.0, -46.0],
115- [-46.0, 9.0, -56.0, 9.0],
116- [9.0, -46.0, 9.0, -56.0]])
117- #
118- wlsm[0:4, 12:16] = numpy.array([[-38.0, -28.0, 17.0, 7.0],
119- [7.0, -38.0, -28.0, 17.0],
120- [17.0, 7.0, -38.0, -28.0],
121- [-28.0, 17.0, 7.0, -38.0]])
122- #
123- wlsm[0:4, 16:20] = numpy.array([[-18.0, -18.0, 12.0, -18.0],
124- [-18.0, -18.0, -18.0, 12.0],
125- [12.0, -18.0, -18.0, -18.0],
126- [-18.0, 12.0, -18.0, -18.0]])
127- #
128- wlsm[0:4, 0:20] /= 1260.0
129- #
130- # k-index for energy
131- #
132- nk = ng.prod(0)
133- ikv = numpy.empty([nk*6, 20, 3], dtype=numpy.int_)
134- ikv0 = numpy.empty(3, dtype=numpy.int_)
135- nt = 0
136- for i2 in range(ng[2]):
137- for i1 in range(ng[1]):
138- for i0 in range(ng[0]):
139- #
140- for it in range(6):
141- #
142- for ii in range(20):
143- #
144- ikv0[0:3] = [i0, i1, i2] + ivvec[it, ii, 0:3]
145- ikv[nt, ii, 0:3] = ikv0[0:3] % ng[0:3]
146- #
147- nt += 1
148- return wlsm, ikv
149-
150-
151-def libtetrabz_tsmall_a1(e):
152- """Cut small tetrahedron A1
153- """
154- a10 = (0.0 - e[0]) / (e[1] - e[0])
155- a20 = (0.0 - e[0]) / (e[2] - e[0])
156- a30 = (0.0 - e[0]) / (e[3] - e[0])
157- #
158- v = a10 * a20 * a30
159- #
160- tsmall = numpy.array([[1.0, 0.0, 0.0, 0.0],
161- [1.0 - a10, a10, 0.0, 0.0],
162- [1.0 - a20, 0.0, a20, 0.0],
163- [1.0 - a30, 0.0, 0.0, a30]])
164- return v, tsmall
165-
166-
167-def libtetrabz_tsmall_b1(e):
168- """
169- Cut small tetrahedron B1
170- :param e: numpy
171- :return:
172- """
173- #
174- #
175- a13 = (0.0 - e[3]) / (e[1] - e[3])
176- a20 = (0.0 - e[0]) / (e[2] - e[0])
177- a30 = (0.0 - e[0]) / (e[3] - e[0])
178- #
179- v = a20 * a30 * a13
180- tsmall = numpy.array([[1.0, 0.0, 0.0, 0.0],
181- [1.0 - a20, 0.0, a20, 0.0],
182- [1.0 - a30, 0.0, 0.0, a30],
183- [0.0, a13, 0.0, 1.0 - a13]])
184- return v, tsmall
185-
186-
187-def libtetrabz_tsmall_b2(e):
188- """
189- Cut small tetrahedron B2
190- :param e:
191- :return:
192- """
193- a21 = (0.0 - e[1]) / (e[2] - e[1])
194- a31 = (0.0 - e[1]) / (e[3] - e[1])
195- #
196- v = a21 * a31
197- #
198- tsmall = numpy.array([[1.0, 0.0, 0.0, 0.0],
199- [0.0, 1.0, 0.0, 0.0],
200- [0.0, 1.0 - a21, a21, 0.0],
201- [0.0, 1.0 - a31, 0.0, a31]])
202- return v, tsmall
203-
204-
205-def libtetrabz_tsmall_b3(e):
206- """
207- Cut small tetrahedron B3
208- :param e:
209- :return:
210- """
211- a12 = (0.0 - e[2]) / (e[1] - e[2])
212- a20 = (0.0 - e[0]) / (e[2] - e[0])
213- a31 = (0.0 - e[1]) / (e[3] - e[1])
214- #
215- v = a12 * a20 * a31
216- #
217- tsmall = numpy.array([[1.0, 0.0, 0.0, 0.0],
218- [1.0-a20, 0.0, a20, 0.0],
219- [0.0, a12, 1.0-a12, 0.0],
220- [0.0, 1.0-a31, 0.0, a31]])
221- return v, tsmall
222-
223-
224-def libtetrabz_tsmall_c1(e):
225- """
226- Cut small tetrahedron C1
227- :param e:
228- :return:
229- """
230- a32 = (0.0 - e[2]) / (e[3] - e[2])
231- #
232- v = a32
233- #
234- tsmall = numpy.array([[1.0, 0.0, 0.0, 0.0],
235- [0.0, 1.0, 0.0, 0.0],
236- [0.0, 0.0, 1.0, 0.0],
237- [0.0, 0.0, 1.0 - a32, a32]])
238- return v, tsmall
239-
240-
241-def libtetrabz_tsmall_c2(e):
242- """
243- Cut small tetrahedron C2
244- :param e:
245- :return:
246- """
247- a23 = (0.0 - e[3]) / (e[2] - e[3])
248- a31 = (0.0 - e[1]) / (e[3] - e[1])
249- #
250- v = a23 * a31
251- #
252- tsmall = numpy.array([[1.0, 0.0, 0.0, 0.0],
253- [0.0, 1.0, 0.0, 0.0],
254- [0.0, 1.0 - a31, 0.0, a31],
255- [0.0, 0.0, a23, 1.0 - a23]])
256- return v, tsmall
257-
258-
259-def libtetrabz_tsmall_c3(e):
260- """
261- Cut small tetrahedron C3
262- :param e:
263- :return:
264- """
265- a23 = (0.0 - e[3]) / (e[2] - e[3])
266- a13 = (0.0 - e[3]) / (e[1] - e[3])
267- a30 = (0.0 - e[0]) / (e[3] - e[0])
268- #
269- v = a23 * a13 * a30
270- #
271- tsmall = numpy.array([[1.0, 0.0, 0.0, 0.0],
272- [1.0 - a30, 0.0, 0.0, a30],
273- [0.0, a13, 0.0, 1.0 - a13],
274- [0.0, 0.0, a23, 1.0 - a23]])
275- return v, tsmall
276-
277-
278-def libtetrabz_triangle_a1(e):
279- """
280- Cut triangle A1
281- :param e:
282- :return:
283- """
284- a10 = (0.0 - e[0]) / (e[1] - e[0])
285- a20 = (0.0 - e[0]) / (e[2] - e[0])
286- a30 = (0.0 - e[0]) / (e[3] - e[0])
287- #
288- # v = 3.0 * a[1,0] * a[2,0] * a[3,0] / (0.0 - e[0])
289- v = 3.0 * a10 * a20 / (e[3] - e[0])
290- #
291- tsmall = numpy.array([[1.0 - a10, a10, 0.0, 0.0],
292- [1.0 - a20, 0.0, a20, 0.0],
293- [1.0 - a30, 0.0, 0.0, a30]])
294- return v, tsmall
295-
296-
297-def libtetrabz_triangle_b1(e):
298- """
299- Cut triangle B1
300- :param e:
301- :return:
302- """
303- a30 = (0.0 - e[0]) / (e[3] - e[0])
304- a13 = (0.0 - e[3]) / (e[1] - e[3])
305- a20 = (0.0 - e[0]) / (e[2] - e[0])
306- #
307- # v = 3.0 * a[2,0] * a[3,0] * a[1,3] / (0.0 - e[0])
308- v = 3.0 * a30 * a13 / (e[2] - e[0])
309- #
310- tsmall = numpy.array([[1.0 - a20, 0.0, a20, 0.0],
311- [1.0 - a30, 0.0, 0.0, a30],
312- [0.0, a13, 0.0, 1.0 - a13]])
313- return v, tsmall
314-
315-
316-def libtetrabz_triangle_b2(e):
317- """
318-
319- :param e:
320- :returns:
321- - x - first
322- - y - second
323- """
324- a12 = (0.0 - e[2]) / (e[1] - e[2])
325- a31 = (0.0 - e[1]) / (e[3] - e[1])
326- a20 = (0.0 - e[0]) / (e[2] - e[0])
327- #
328- # v = 3.0 * a[1,2] * a[2,0] * a[3,1] / (0.0 - e[0])
329- v = 3.0 * a12 * a31 / (e[2] - e[0])
330- #
331- tsmall = numpy.array([[1.0 - a20, 0.0, a20, 0.0],
332- [0.0, a12, 1.0 - a12, 0.0],
333- [0.0, 1.0 - a31, 0.0, a31]])
334- return v, tsmall
335-
336-
337-def libtetrabz_triangle_c1(e):
338- """
339- :param ndarray(4, float) e: energy eigenvalues
340- :returns:
341- Volume
342- Vertex ratio
343-
344- Cut triangle C1
345- """
346- a03 = (0.0 - e[3]) / (e[0] - e[3])
347- a13 = (0.0 - e[3]) / (e[1] - e[3])
348- a23 = (0.0 - e[3]) / (e[2] - e[3])
349- #
350- # v = 3.0 * a[0,3] * a[1,3] * a[2,3] / (e[3] - 0.0)
351- v = 3.0 * a03 * a13 / (e[3] - e[2])
352- #
353- tsmall = numpy.array([[a03, 0.0, 0.0, 1.0 - a03],
354- [0.0, a13, 0.0, 1.0 - a13],
355- [0.0, 0.0, a23, 1.0 - a23]])
356- return v, tsmall
--- a/src/libtetrabz/libtetrabz_dbldelta.py
+++ /dev/null
@@ -1,153 +0,0 @@
1-#
2-# Copyright (c) 2014 Mitsuaki Kawamura
3-#
4-# Permission is hereby granted, free of charge, to any person obtaining a
5-# copy of this software and associated documentation files (the
6-# "Software"), to deal in the Software without restriction, including
7-# without limitation the rights to use, copy, modify, merge, publish,
8-# distribute, sublicense, and/or sell copies of the Software, and to
9-# permit persons to whom the Software is furnished to do so, subject to
10-# the following conditions:
11-#
12-# The above copyright notice and this permission notice shall be included
13-# in all copies or substantial portions of the Software.
14-#
15-# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
16-# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
17-# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
18-# IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
19-# CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
20-# TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
21-# SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
22-#
23-import numpy
24-from . import libtetrabz_common
25-
26-
27-def dbldelta(bvec, eig1, eig2):
28- """
29- Main SUBROUTINE for Delta(E1) * Delta(E2)
30- :param bvec:
31- :param eig1:
32- :param eig2:
33- :return:
34- """
35- thr = 1.0e-10
36- ng = numpy.array(eig1.shape[0:3])
37- nk = ng.prod(0)
38- nb = eig1.shape[3]
39- wlsm, ikv = libtetrabz_common.libtetrabz_initialize(ng, bvec)
40- #
41- wght = numpy.zeros([ng[0], ng[1], ng[2], nb, nb], dtype=numpy.float_)
42- #
43- for it in range(6 * nk):
44- #
45- eig1t = numpy.empty([20, nb], dtype=numpy.float_)
46- eig2t = numpy.empty([20, nb], dtype=numpy.float_)
47- for ii in range(20):
48- eig1t[ii, 0:nb] = eig1[ikv[it, ii, 0], ikv[it, ii, 1], ikv[it, ii, 2], 0:nb]
49- eig2t[ii, 0:nb] = eig2[ikv[it, ii, 0], ikv[it, ii, 1], ikv[it, ii, 2], 0:nb]
50- ei1 = wlsm.dot(eig1t)
51- ej1 = wlsm.dot(eig2t)
52- #
53- w1 = numpy.zeros([nb, nb, 4], dtype=numpy.float_)
54- w2t = numpy.zeros([nb, 4], dtype=numpy.float_)
55- for ib in range(nb):
56- #
57- e = ei1[0:4, ib].copy()
58- indx = e.argsort(0)
59- e.sort(0)
60- #
61- if e[0] < 0.0 <= e[1]:
62- #
63- v, tsmall = libtetrabz_common.libtetrabz_triangle_a1(e)
64- #
65- if v > thr:
66- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
67- w2 = libtetrabz_dbldelta2(ej2)
68- w2t[0:nb, indx[0:4]] = w2.dot(tsmall)
69- w1[ib, 0:nb, 0:4] += v * w2t
70- #
71- elif e[1] < 0.0 <= e[2]:
72- #
73- v, tsmall = libtetrabz_common.libtetrabz_triangle_b1(e)
74- #
75- if v > thr:
76- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
77- w2 = libtetrabz_dbldelta2(ej2)
78- w2t[0:nb, indx[0:4]] = w2.dot(tsmall)
79- w1[ib, 0:nb, 0:4] += v * w2t
80- #
81- v, tsmall = libtetrabz_common.libtetrabz_triangle_b2(e)
82- #
83- if v > thr:
84- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
85- w2 = libtetrabz_dbldelta2(ej2)
86- w2t[0:nb, indx[0:4]] = w2.dot(tsmall)
87- w1[ib, 0:nb, 0:4] += v * w2t
88- #
89- elif e[2] < 0.0 < e[3]:
90- #
91- v, tsmall = libtetrabz_common.libtetrabz_triangle_c1(e)
92- #
93- if v > thr:
94- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
95- w2 = libtetrabz_dbldelta2(ej2)
96- w2t[0:nb, indx[0:4]] = w2.dot(tsmall)
97- w1[ib, 0:nb, 0:4] += v * w2t
98- #
99- else:
100- continue
101- #
102- for ii in range(20):
103- wght[ikv[it, ii, 0], ikv[it, ii, 1], ikv[it, ii, 2], 0:nb, 0:nb] += w1.dot(wlsm[:, ii])
104- #
105- wght[0:ng[0], 0:ng[1], 0:ng[2], 0:nb, 0:nb] /= (6.0 * nk)
106- return wght
107-
108-
109-def libtetrabz_dbldelta2(ej):
110- """
111- 2nd step of tetrahedra method.
112- :param ej:
113- :return:
114- """
115- nb = ej.shape[1]
116- w = numpy.zeros([nb, 3], dtype=numpy.float_)
117- for ib in range(nb):
118- #
119- if abs(ej[0:3, ib]).max() < 1.0e-10:
120- raise ValueError("Nesting ##")
121- #
122- e = ej[0:3, ib].copy()
123- indx = e.argsort(0)
124- e.sort(0)
125- #
126- #for ii in range(3):
127- # a[0:3, ii] = (0.0 - e[ii]) / (e[0:3] - e[ii])
128- #
129- if e[0] < 0.0 <= e[1] or e[0] <= 0.0 < e[1]:
130- #
131- a10 = (0.0 - e[0]) / (e[1] - e[0])
132- a20 = (0.0 - e[0]) / (e[2] - e[0])
133- #
134- # v = a[1, 0] * a[2, 0] / (0.0 - e[0])
135- v = a10 / (e[2] - e[0])
136- #
137- w[ib, indx[0]] = v * (2.0 - a10 - a20)
138- w[ib, indx[1]] = v * a10
139- w[ib, indx[2]] = v * a20
140- #
141- elif e[1] <= 0.0 < e[2] or e[1] < 0.0 <= e[2]:
142- #
143- a02 = (0.0 - e[2]) / (e[0] - e[2])
144- a12 = (0.0 - e[2]) / (e[1] - e[2])
145- #
146- # v = a[1, 2] * a[1, 2] / (e[2] - 0.0)
147- v = a12 / (e[2] - e[0])
148- #
149- w[ib, indx[0]] = v * a02
150- w[ib, indx[1]] = v * a12
151- w[ib, indx[2]] = v * (2.0 - a02 - a12)
152- #
153- return w
--- a/src/libtetrabz/libtetrabz_dblstep.py
+++ /dev/null
@@ -1,201 +0,0 @@
1-#
2-# Copyright (c) 2014 Mitsuaki Kawamura
3-#
4-# Permission is hereby granted, free of charge, to any person obtaining a
5-# copy of this software and associated documentation files (the
6-# "Software"), to deal in the Software without restriction, including
7-# without limitation the rights to use, copy, modify, merge, publish,
8-# distribute, sublicense, and/or sell copies of the Software, and to
9-# permit persons to whom the Software is furnished to do so, subject to
10-# the following conditions:
11-#
12-# The above copyright notice and this permission notice shall be included
13-# in all copies or substantial portions of the Software.
14-#
15-# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
16-# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
17-# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
18-# IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
19-# CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
20-# TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
21-# SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
22-#
23-import numpy
24-from . import libtetrabz_common
25-
26-
27-def dblstep(bvec, eig1, eig2):
28- """
29- Main SUBROUTINE for Theta(- E1) * Theta(E1 - E2)
30- :param bvec:
31- :param eig1:
32- :param eig2:
33- :return:
34- """
35- ng = numpy.array(eig1.shape[0:3])
36- nk = ng.prod(0)
37- nb = eig1.shape[3]
38- wlsm, ikv = libtetrabz_common.libtetrabz_initialize(ng, bvec)
39-
40- wght = numpy.zeros([ng[0], ng[1], ng[2], nb, nb], dtype=numpy.float_)
41-
42- thr = 1.0e-8
43- #
44- for it in range(6 * nk):
45- #
46- eig1t = numpy.empty([20, nb], dtype=numpy.float_)
47- eig2t = numpy.empty([20, nb], dtype=numpy.float_)
48- for ii in range(20):
49- eig1t[ii, 0:nb] = eig1[ikv[it, ii, 0], ikv[it, ii, 1], ikv[it, ii, 2], 0:nb]
50- eig2t[ii, 0:nb] = eig2[ikv[it, ii, 0], ikv[it, ii, 1], ikv[it, ii, 2], 0:nb]
51- ei1 = wlsm.dot(eig1t)
52- ej1 = wlsm.dot(eig2t)
53- #
54- w1 = numpy.zeros([nb, nb, 4], dtype=numpy.float_)
55- w2t = numpy.zeros([nb, 4], dtype=numpy.float_)
56- for ib in range(nb):
57- #
58- e = ei1[0:4, ib].copy()
59- indx = e.argsort(0)
60- e.sort(0)
61- #
62- if e[0] <= 0.0 < e[1]:
63- #
64- v, tsmall = libtetrabz_common.libtetrabz_tsmall_a1(e)
65- #
66- if v > thr:
67- ei2 = tsmall.dot(ei1[indx[0:4], ib])
68- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
69- w2 = libtetrabz_dblstep2(ei2, ej2)
70- w2t[0:nb, indx[0:4]] = w2.dot(tsmall)
71- w1[ib, 0:nb, 0:4] += v * w2t[0:nb, 0:4]
72- #
73- elif e[1] <= 0.0 < e[2]:
74- #
75- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b1(e)
76- #
77- if v > thr:
78- ei2 = tsmall.dot(ei1[indx[0:4], ib])
79- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
80- w2 = libtetrabz_dblstep2(ei2, ej2)
81- w2t[0:nb, indx[0:4]] = w2.dot(tsmall)
82- w1[ib, 0:nb, 0:4] += v * w2t[0:nb, 0:4]
83- #
84- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b2(e)
85- #
86- if v > thr:
87- ei2 = tsmall.dot(ei1[indx[0:4], ib])
88- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
89- w2 = libtetrabz_dblstep2(ei2, ej2)
90- w2t[0:nb, indx[0:4]] = w2.dot(tsmall)
91- w1[ib, 0:nb, 0:4] += v * w2t[0:nb, 0:4]
92- #
93- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b3(e)
94- #
95- if v > thr:
96- ei2 = tsmall.dot(ei1[indx[0:4], ib])
97- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
98- w2 = libtetrabz_dblstep2(ei2, ej2)
99- w2t[0:nb, indx[0:4]] = w2.dot(tsmall)
100- w1[ib, 0:nb, 0:4] += v * w2t[0:nb, 0:4]
101- #
102- elif e[2] <= 0.0 < e[3]:
103- #
104- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c1(e)
105- #
106- if v > thr:
107- ei2 = tsmall.dot(ei1[indx[0:4], ib])
108- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
109- w2 = libtetrabz_dblstep2(ei2, ej2)
110- w2t[0:nb, indx[0:4]] = w2.dot(tsmall)
111- w1[ib, 0:nb, 0:4] += v * w2t[0:nb, 0:4]
112- #
113- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c2(e)
114- #
115- if v > thr:
116- ei2 = tsmall.dot(ei1[indx[0:4], ib])
117- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
118- w2 = libtetrabz_dblstep2(ei2, ej2)
119- w2t[0:nb, indx[0:4]] = w2.dot(tsmall)
120- w1[ib, 0:nb, 0:4] += v * w2t[0:nb, 0:4]
121- #
122- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c3(e)
123- #
124- if v > thr:
125- ei2 = tsmall.dot(ei1[indx[0:4], ib])
126- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
127- w2 = libtetrabz_dblstep2(ei2, ej2)
128- w2t[0:nb, indx[0:4]] = w2.dot(tsmall)
129- w1[ib, 0:nb, 0:4] += v * w2t[0:nb, 0:4]
130- #
131- elif e[3] <= 0.0:
132- ei2 = ei1[0:4, ib]
133- ej2 = ej1[0:4, 0:nb]
134- w2 = libtetrabz_dblstep2(ei2, ej2)
135- w1[ib, 0:nb, 0:4] += w2[0:nb, 0:4]
136- else:
137- continue
138- #
139- for ii in range(20):
140- wght[ikv[it, ii, 0], ikv[it, ii, 1], ikv[it, ii, 2], 0:nb, 0:nb] += w1.dot(wlsm[:, ii])
141- #
142- wght[0:ng[0], 0:ng[1], 0:ng[2], 0:nb, 0:nb] /= (6.0 * nk)
143- return wght
144-
145-
146-def libtetrabz_dblstep2(ei1, ej1):
147- """
148- Tetrahedra method for theta( - de)
149- :param ei1:
150- :param ej1:
151- :return:
152- """
153- thr = 1.0e-8
154- nb = ej1.shape[1]
155- w1 = numpy.zeros([nb, 4], dtype=numpy.float_)
156-
157- for ib in range(nb):
158- #
159- e = - ei1[0:4] + ej1[0:4, ib]
160- indx = e.argsort(0)
161- e.sort(0)
162- #
163- if abs(e[0]) < thr and abs(e[3]) < thr:
164- #
165- # Theta(0) = 0.5
166- #
167- v = 0.5
168- w1[ib, 0:4] += v * 0.25
169- #
170- elif e[0] <= 0.0 < e[1] or e[0] < 0.0 <= e[1]:
171- #
172- v, tsmall = libtetrabz_common.libtetrabz_tsmall_a1(e)
173- w1[ib, indx[0:4]] += v * tsmall.sum(0) * 0.25
174- #
175- elif e[1] <= 0.0 < e[2] or e[1] < 0.0 <= e[2]:
176- #
177- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b1(e)
178- w1[ib, indx[0:4]] += v * tsmall.sum(0) * 0.25
179- #
180- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b2(e)
181- w1[ib, indx[0:4]] += v * tsmall.sum(0) * 0.25
182- #
183- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b3(e)
184- w1[ib, indx[0:4]] += v * tsmall.sum(0) * 0.25
185- #
186- elif e[2] <= 0.0 < e[3] or e[2] < 0.0 <= e[3]:
187- #
188- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c1(e)
189- w1[ib, indx[0:4]] += v * tsmall.sum(0) * 0.25
190- #
191- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c2(e)
192- w1[ib, indx[0:4]] += v * tsmall.sum(0) * 0.25
193- #
194- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c3(e)
195- w1[ib, indx[0:4]] += v * tsmall.sum(0) * 0.25
196- #
197- elif e[3] <= 0.0:
198- #
199- w1[ib, 0:4] += 0.25
200- #
201- return w1
--- a/src/libtetrabz/libtetrabz_dos.py
+++ /dev/null
@@ -1,163 +0,0 @@
1-#
2-# Copyright (c) 2014 Mitsuaki Kawamura
3-#
4-# Permission is hereby granted, free of charge, to any person obtaining a
5-# copy of this software and associated documentation files (the
6-# "Software"), to deal in the Software without restriction, including
7-# without limitation the rights to use, copy, modify, merge, publish,
8-# distribute, sublicense, and/or sell copies of the Software, and to
9-# permit persons to whom the Software is furnished to do so, subject to
10-# the following conditions:
11-#
12-# The above copyright notice and this permission notice shall be included
13-# in all copies or substantial portions of the Software.
14-#
15-# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
16-# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
17-# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
18-# IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
19-# CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
20-# TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
21-# SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
22-#
23-import numpy
24-from . import libtetrabz_common
25-
26-
27-def dos(bvec, eig, e0):
28- """
29- :param bvec: ndarray([3, 3], float) Reciprocal-lattice vectors
30- :param eig: ndarray([ng0, ng1, ng2, nb], float) Energy eigenvalue
31- :param e0: ndarray(ne, float) Energy grid
32- :return : ndarray([ng0, ng1, ng2, nb, ne], float) Integration weight
33-
34- Compute Dos : Delta(E - E1)
35- """
36- ng = numpy.array(eig.shape[0:3])
37- nk = ng.prod(0)
38- nb = eig.shape[3]
39- ne = e0.shape[0]
40- wlsm, ikv = libtetrabz_common.libtetrabz_initialize(ng, bvec)
41- #
42- wght = numpy.zeros([ng[0], ng[1], ng[2], nb, ne], dtype=numpy.float_)
43- #
44- for it in range(6*nk):
45- #
46- eigt = numpy.empty([20, nb], dtype=numpy.float_)
47- for ii in range(20):
48- eigt[ii, 0:nb] = eig[ikv[it, ii, 0], ikv[it, ii, 1], ikv[it, ii, 2], 0:nb]
49- ei1 = wlsm.dot(eigt)
50- #
51- w1 = numpy.zeros([nb, ne, 4], dtype=numpy.float_)
52- #
53- for ib in range(nb):
54- #
55- e = ei1[0:4, ib].copy()
56- indx = e.argsort(0)
57- e = e[indx[0:4]]
58- #
59- for ie in range(ne):
60- #
61- if e[0] < e0[ie] <= e[1] or e[0] <= e0[ie] < e[1]:
62- #
63- v, tsmall = libtetrabz_common.libtetrabz_triangle_a1(e[0:4] - e0[ie])
64- w1[ib, ie, indx[0:4]] += v * tsmall.sum(0) / 3.0
65- #
66- elif e[1] < e0[ie] <= e[2] or e[1] <= e0[ie] < e[2]:
67- #
68- v, tsmall = libtetrabz_common.libtetrabz_triangle_b1(e[0:4] - e0[ie])
69- w1[ib, ie, indx[0:4]] += v * tsmall.sum(0) / 3.0
70- #
71- v, tsmall = libtetrabz_common.libtetrabz_triangle_b2(e[0:4] - e0[ie])
72- w1[ib, ie, indx[0:4]] += v * tsmall.sum(0) / 3.0
73- #
74- elif e[2] < e0[ie] <= e[3] or e[2] <= e0[ie] < e[3]:
75- #
76- v, tsmall = libtetrabz_common.libtetrabz_triangle_c1(e[0:4] - e0[ie])
77- w1[ib, ie, indx[0:4]] += v * tsmall.sum(0) / 3.0
78- #
79- else:
80- continue
81- #
82- #
83- #
84- for ii in range(20):
85- wght[ikv[it, ii, 0], ikv[it, ii, 1], ikv[it, ii, 2], 0:nb, 0:ne] += w1.dot(wlsm[:, ii])
86- #
87- #
88- wght[0:ng[0], 0:ng[1], 0:ng[2], 0:nb, 0:ne] /= (6.0 * nk)
89- return wght
90-
91-
92-def intdos(bvec, eig, e0):
93- """
94- Compute integrated Dos : theta(E - E1)
95- :param ndarray([3, 3], float) bvec: Reciprocal-lattice vectors
96- :param ndarray([ng0, ng1, ng2, nb], float) eig: Energy eigenvalue
97- :param ndarray(ne, float) e0: Energy grid
98- :return ndarray([ng0, ng1, ng2, nb, ne], float) wght: Weight
99- """
100- ng = numpy.array(eig.shape[0:3])
101- nk = ng.prod(0)
102- nb = eig.shape[3]
103- ne = e0.shape[0]
104- wlsm, ikv = libtetrabz_common.libtetrabz_initialize(ng, bvec)
105- #
106- wght = numpy.zeros([ng[0], ng[1], ng[2], nb, ne], dtype=numpy.float_)
107- #
108- for it in range(6*nk):
109- #
110- eigt = numpy.empty([20, nb], dtype=numpy.float_)
111- for ii in range(20):
112- eigt[ii, 0:nb] = eig[ikv[it, ii, 0], ikv[it, ii, 1], ikv[it, ii, 2], 0:nb]
113- ei1 = wlsm.dot(eigt)
114- #
115- w1 = numpy.zeros([nb, ne, 4], dtype=numpy.float_)
116- #
117- for ib in range(nb):
118- #
119- e = ei1[0:4, ib].copy()
120- indx = e.argsort(0)
121- e.sort(0)
122- #
123- for ie in range(ne):
124- #
125- if e[0] <= e0[ie] < e[1] or e[0] < e0[ie] <= e[1]:
126- #
127- v, tsmall = libtetrabz_common.libtetrabz_tsmall_a1(e - e0[ie])
128- w1[ib, ie, indx[0:4]] += v * tsmall.sum(0) * 0.25
129- #
130- elif e[1] <= e0[ie] < e[2] or e[1] < e0[ie] <= e[2]:
131- #
132- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b1(e - e0[ie])
133- w1[ib, ie, indx[0:4]] += v * tsmall.sum(0) * 0.25
134- #
135- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b2(e - e0[ie])
136- w1[ib, ie, indx[0:4]] += v * tsmall.sum(0) * 0.25
137- #
138- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b3(e - e0[ie])
139- w1[ib, ie, indx[0:4]] += v * tsmall.sum(0) * 0.25
140- #
141- elif e[2] <= e0[ie] < e[3] or e[2] < e0[ie] <= e[3]:
142- #
143- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c1(e - e0[ie])
144- w1[ib, ie, indx[0:4]] += v * tsmall.sum(0) * 0.25
145- #
146- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c2(e - e0[ie])
147- w1[ib, ie, indx[0:4]] += v * tsmall.sum(0) * 0.25
148- #
149- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c3(e - e0[ie])
150- w1[ib, ie, indx[0:4]] += v * tsmall.sum(0) * 0.25
151- #
152- elif e[3] <= e0[ie]:
153- w1[ib, ie, 0:4] = 0.25
154- else:
155- continue
156- #
157- #
158- #
159- for ii in range(20):
160- wght[ikv[it, ii, 0], ikv[it, ii, 1], ikv[it, ii, 2], 0:nb, 0:ne] += w1.dot(wlsm[:, ii])
161- #
162- wght[0:ng[0], 0:ng[1], 0:ng[2], 0:nb, 0:ne] /= (6.0 * nk)
163- return wght
--- a/src/libtetrabz/libtetrabz_fermigr.py
+++ /dev/null
@@ -1,278 +0,0 @@
1-#
2-# Copyright (c) 2014 Mitsuaki Kawamura
3-#
4-# Permission is hereby granted, free of charge, to any person obtaining a
5-# copy of this software and associated documentation files (the
6-# "Software"), to deal in the Software without restriction, including
7-# without limitation the rights to use, copy, modify, merge, publish,
8-# distribute, sublicense, and/or sell copies of the Software, and to
9-# permit persons to whom the Software is furnished to do so, subject to
10-# the following conditions:
11-#
12-# The above copyright notice and this permission notice shall be included
13-# in all copies or substantial portions of the Software.
14-#
15-# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
16-# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
17-# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
18-# IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
19-# CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
20-# TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
21-# SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
22-#
23-import numpy
24-from . import libtetrabz_common
25-
26-
27-def fermigr(bvec, eig1, eig2, e0):
28- """
29- Main SUBROUTINE for Fermi's Golden rule : Theta(- E1) * Theta(E2) * Delta(E2 - E1 - w)
30- :param bvec:
31- :param eig1:
32- :param eig2:
33- :param e0:
34- :return:
35- """
36- ng = numpy.array(eig1.shape[0:3])
37- nk = ng.prod(0)
38- nb = eig1.shape[3]
39- ne = e0.shape[0]
40- wlsm, ikv = libtetrabz_common.libtetrabz_initialize(ng, bvec)
41-
42- wght = numpy.zeros([ng[0], ng[1], ng[2], nb, nb, ne], dtype=numpy.float_)
43-
44- thr = 1.0e-10
45- #
46- for it in range(6 * nk):
47- #
48- eig1t = numpy.empty([20, nb], dtype=numpy.float_)
49- eig2t = numpy.empty([20, nb], dtype=numpy.float_)
50- for ii in range(20):
51- eig1t[ii, 0:nb] = eig1[ikv[it, ii, 0], ikv[it, ii, 1], ikv[it, ii, 2], 0:nb]
52- eig2t[ii, 0:nb] = eig2[ikv[it, ii, 0], ikv[it, ii, 1], ikv[it, ii, 2], 0:nb]
53- ei1 = wlsm.dot(eig1t)
54- ej1 = wlsm.dot(eig2t)
55- #
56- w1 = numpy.zeros([nb, nb, ne, 4], dtype=numpy.float_)
57- w2t = numpy.zeros([nb, ne, 4], dtype=numpy.float_)
58- for ib in range(nb):
59- #
60- e = ei1[0:4, ib].copy()
61- indx = e.argsort(0)
62- e.sort(0)
63- #
64- if e[0] <= 0.0 < e[1]:
65- #
66- v, tsmall = libtetrabz_common.libtetrabz_tsmall_a1(e)
67- #
68- if v > thr:
69- #
70- ei2 = tsmall.dot(ei1[indx[0:4], ib])
71- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
72- w2 = libtetrabz_fermigr2(e0, ei2, ej2)
73- w2t[0:nb, 0:ne, indx[0:4]] = w2.dot(tsmall)
74- w1[ib, 0:nb, 0:ne, 0:4] += v * w2t
75- #
76- elif e[1] <= 0.0 < e[2]:
77- #
78- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b1(e)
79- #
80- if v > thr:
81- #
82- ei2 = tsmall.dot(ei1[indx[0:4], ib])
83- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
84- w2 = libtetrabz_fermigr2(e0, ei2, ej2)
85- w2t[0:nb, 0:ne, indx[0:4]] = w2.dot(tsmall)
86- w1[ib, 0:nb, 0:ne, 0:4] += v * w2t
87- #
88- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b2(e)
89- #
90- if v > thr:
91- #
92- ei2 = tsmall.dot(ei1[indx[0:4], ib])
93- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
94- w2 = libtetrabz_fermigr2(e0, ei2, ej2)
95- w2t[0:nb, 0:ne, indx[0:4]] = w2.dot(tsmall)
96- w1[ib, 0:nb, 0:ne, 0:4] += v * w2t
97- #
98- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b3(e)
99- #
100- if v > thr:
101- #
102- ei2 = tsmall.dot(ei1[indx[0:4], ib])
103- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
104- w2 = libtetrabz_fermigr2(e0, ei2, ej2)
105- w2t[0:nb, 0:ne, indx[0:4]] = w2.dot(tsmall)
106- w1[ib, 0:nb, 0:ne, 0:4] += v * w2t
107- #
108- elif e[2] <= 0.0 < e[3]:
109- #
110- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c1(e)
111- #
112- if v > thr:
113- #
114- ei2 = tsmall.dot(ei1[indx[0:4], ib])
115- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
116- w2 = libtetrabz_fermigr2(e0, ei2, ej2)
117- w2t[0:nb, 0:ne, indx[0:4]] = w2.dot(tsmall)
118- w1[ib, 0:nb, 0:ne, 0:4] += v * w2t
119- #
120- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c2(e)
121- #
122- if v > thr:
123- #
124- ei2 = tsmall.dot(ei1[indx[0:4], ib])
125- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
126- w2 = libtetrabz_fermigr2(e0, ei2, ej2)
127- w2t[0:nb, 0:ne, indx[0:4]] = w2.dot(tsmall)
128- w1[ib, 0:nb, 0:ne, 0:4] += v * w2t
129- #
130- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c3(e)
131- #
132- if v > thr:
133- #
134- ei2 = tsmall.dot(ei1[indx[0:4], ib])
135- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
136- w2 = libtetrabz_fermigr2(e0, ei2, ej2)
137- w2t[0:nb, 0:ne, indx[0:4]] = w2.dot(tsmall)
138- w1[ib, 0:nb, 0:ne, 0:4] += v * w2t
139- #
140- elif e[3] <= 0.0:
141- #
142- ei2 = ei1[0:4, ib]
143- ej2 = ej1[0:4, 0:nb]
144- w2 = libtetrabz_fermigr2(e0, ei2, ej2)
145- w1[ib, 0:nb, 0:ne, 0:4] += w2[0:nb, 0:ne, 0:4]
146- #
147- else:
148- continue
149- #
150- for ii in range(20):
151- wght[ikv[it, ii, 0], ikv[it, ii, 1], ikv[it, ii, 2], 0:nb, 0:nb, 0:ne] += w1.dot(wlsm[:, ii])
152- #
153- wght[0:ng[0], 0:ng[1], 0:ng[2], 0:nb, 0:nb, 0:ne] /= (6.0 * nk)
154- return wght
155-
156-
157-def libtetrabz_fermigr2(e0, ei1, ej1):
158- """
159- Tetrahedra method for theta( - E2)
160- :param e0:
161- :param ei1:
162- :param ej1:
163- :return:
164- """
165- #
166- ne = e0.shape[0]
167- nb = ej1.shape[1]
168- w1 = numpy.zeros([nb, ne, 4], dtype=numpy.float_)
169- w2t = numpy.zeros([ne, 4], dtype=numpy.float_)
170- thr = 1.0e-8
171- #
172- for ib in range(nb):
173- #
174- e = -ej1[0:4, ib]
175- indx = e.argsort(0)
176- e.sort(0)
177- #
178- if e[0] <= 0.0 < e[1] or e[0] < 0.0 <= e[1]:
179- #
180- v, tsmall = libtetrabz_common.libtetrabz_tsmall_a1(e)
181- #
182- if v > thr:
183- #
184- de = tsmall.dot(ej1[indx[0:4], ib] - ei1[indx[0:4]])
185- w2 = libtetrabz_fermigr3(e0, de)
186- w2t[0:ne, indx[0:4]] = w2.dot(tsmall)
187- w1[ib, 0:ne, 0:4] += v * w2t
188- #
189- #
190- elif e[1] <= 0.0 < e[2] or e[1] < 0.0 <= e[2]:
191- #
192- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b1(e)
193- #
194- if v > thr:
195- de = tsmall.dot(ej1[indx[0:4], ib] - ei1[indx[0:4]])
196- w2 = libtetrabz_fermigr3(e0, de)
197- w2t[0:ne, indx[0:4]] = w2.dot(tsmall)
198- w1[ib, 0:ne, 0:4] += v * w2t
199- #
200- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b2(e)
201- #
202- if v > thr:
203- de = tsmall.dot(ej1[indx[0:4], ib] - ei1[indx[0:4]])
204- w2 = libtetrabz_fermigr3(e0, de)
205- w2t[0:ne, indx[0:4]] = w2.dot(tsmall)
206- w1[ib, 0:ne, 0:4] += v * w2t
207- #
208- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b3(e)
209- #
210- if v > thr:
211- de = tsmall.dot(ej1[indx[0:4], ib] - ei1[indx[0:4]])
212- w2 = libtetrabz_fermigr3(e0, de)
213- w2t[0:ne, indx[0:4]] = w2.dot(tsmall)
214- w1[ib, 0:ne, 0:4] += v * w2t
215- #
216- elif e[2] <= 0.0 < e[3] or e[2] < 0.0 <= e[3]:
217- #
218- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c1(e)
219- #
220- if v > thr:
221- de = tsmall.dot(ej1[indx[0:4], ib] - ei1[indx[0:4]])
222- w2 = libtetrabz_fermigr3(e0, de)
223- w2t[0:ne, indx[0:4]] = w2.dot(tsmall)
224- w1[ib, 0:ne, 0:4] += v * w2t
225- #
226- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c2(e)
227- #
228- if v > thr:
229- de = tsmall.dot(ej1[indx[0:4], ib] - ei1[indx[0:4]])
230- w2 = libtetrabz_fermigr3(e0, de)
231- w2t[0:ne, indx[0:4]] = w2.dot(tsmall)
232- w1[ib, 0:ne, 0:4] += v * w2t
233- #
234- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c3(e)
235- #
236- if v > thr:
237- de = tsmall.dot(ej1[indx[0:4], ib] - ei1[indx[0:4]])
238- w2 = libtetrabz_fermigr3(e0, de)
239- w2t[0:ne, indx[0:4]] = w2.dot(tsmall)
240- w1[ib, 0:ne, 0:4] += v * w2t
241- #
242- elif e[3] <= 0.0:
243- de = ej1[0:4, ib] - ei1[0:4]
244- w2 = libtetrabz_fermigr3(e0, de)
245- w1[ib, 0:ne, 0:4] += w2
246- #
247- return w1
248-
249-
250-def libtetrabz_fermigr3(e0, de):
251- #
252- ne = e0.shape[0]
253- e = de[0:4].copy()
254- indx = e.argsort(0)
255- e.sort(0)
256- w1 = numpy.zeros([ne, 4], dtype=numpy.float_)
257- #
258- for ie in range(ne):
259- #
260- if e[0] < e0[ie] <= e[1]:
261- #
262- v, tsmall = libtetrabz_common.libtetrabz_triangle_a1(e[0:4] - e0[ie])
263- w1[ie, indx[0:4]] += v * tsmall.sum(0) / 3.0
264- #
265- elif e[1] < e0[ie] <= e[2]:
266- #
267- v, tsmall = libtetrabz_common.libtetrabz_triangle_b1(e[0:4] - e0[ie])
268- w1[ie, indx[0:4]] += v * tsmall.sum(0) / 3.0
269- #
270- v, tsmall = libtetrabz_common.libtetrabz_triangle_b2(e[0:4] - e0[ie])
271- w1[ie, indx[0:4]] += v * tsmall.sum(0) / 3.0
272- #
273- elif e[2] < e0[ie] < e[3]:
274- #
275- v, tsmall = libtetrabz_common.libtetrabz_triangle_c1(e[0:4] - e0[ie])
276- w1[ie, indx[0:4]] += v * tsmall.sum(0) / 3.0
277- #
278- return w1
--- a/src/libtetrabz/libtetrabz_occ.py
+++ /dev/null
@@ -1,131 +0,0 @@
1-#
2-# Copyright (c) 2014 Mitsuaki Kawamura
3-#
4-# Permission is hereby granted, free of charge, to any person obtaining a
5-# copy of this software and associated documentation files (the
6-# "Software"), to deal in the Software without restriction, including
7-# without limitation the rights to use, copy, modify, merge, publish,
8-# distribute, sublicense, and/or sell copies of the Software, and to
9-# permit persons to whom the Software is furnished to do so, subject to
10-# the following conditions:
11-#
12-# The above copyright notice and this permission notice shall be included
13-# in all copies or substantial portions of the Software.
14-#
15-# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
16-# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
17-# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
18-# IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
19-# CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
20-# TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
21-# SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
22-#
23-import numpy
24-from . import libtetrabz_common
25-
26-
27-def fermieng(bvec, eig, nelec):
28- """
29- Calculate Fermi energy
30- :param ndarray([3, 3], float) bvec: Reciprocal-lattice vectors
31- :param ndarray([ng0, ng1, ng2, nb], float) eig: Energy eigenvalue
32- :param float nelec:
33- :return:
34- """
35- #
36- maxiter = 300
37- eps = 1.0e-10
38- #
39- elw = eig.min()
40- eup = eig.max()
41- #
42- # Bisection method
43- #
44- for iteration in range(maxiter):
45- #
46- ef = (eup + elw) * 0.5
47- #
48- # Calc. # of electrons
49- #
50- wght = occ(bvec, eig-ef)
51- sumkmid = wght.sum()
52- #
53- # convergence check
54- #
55- if abs(sumkmid - nelec) < eps:
56- return ef, wght, iteration
57- elif sumkmid < nelec:
58- elw = ef
59- else:
60- eup = ef
61- #
62- raise ValueError("libtetrabz_fermieng")
63-
64-
65-def occ(bvec=numpy.array([1.0, 0.0, 0.0]), eig=numpy.array([0.0])):
66- """
67- Main SUBROUTINE for occupation : Theta(EF - E1)
68- :param ndarray([3, 3], float) bvec: Reciprocal-lattice vectors
69- :param ndarray([ng0, ng1, ng2, nb], float) eig: Energy eigenvalue
70- :return ndarray([ng0, ng1, ng2, nb], float) wght: Weight
71- """
72- #
73- ng = numpy.array(eig.shape[0:3])
74- nk = ng.prod(0)
75- nb = eig.shape[3]
76- wlsm, ikv = libtetrabz_common.libtetrabz_initialize(ng, bvec)
77- #
78- wght = numpy.zeros([ng[0], ng[1], ng[2], nb], dtype=numpy.float_)
79- #
80- for it in range(6 * nk):
81- #
82- eigt = numpy.empty([20, nb], dtype=numpy.float_)
83- for ii in range(20):
84- eigt[ii, 0:nb] = eig[ikv[it, ii, 0], ikv[it, ii, 1], ikv[it, ii, 2], 0:nb]
85- ei1 = wlsm.dot(eigt)
86- #
87- w1 = numpy.zeros([nb, 4], dtype=numpy.float_)
88- for ib in range(nb):
89- #
90- e = ei1[0:4, ib].copy()
91- indx = e.argsort(0)
92- e.sort(0)
93- #
94- if e[0] <= 0.0 < e[1]:
95- #
96- v, tsmall = libtetrabz_common.libtetrabz_tsmall_a1(e)
97- w1[ib, indx[0:4]] += v * tsmall.sum(0) * 0.25
98- #
99- elif e[1] <= 0.0 < e[2]:
100- #
101- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b1(e)
102- w1[ib, indx[0:4]] += v * tsmall.sum(0) * 0.25
103- #
104- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b2(e)
105- w1[ib, indx[0:4]] += v * tsmall.sum(0) * 0.25
106- #
107- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b3(e)
108- w1[ib, indx[0:4]] += v * tsmall.sum(0) * 0.25
109- #
110- elif e[2] <= 0.0 < e[3]:
111- #
112- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c1(e)
113- w1[ib, indx[0:4]] += v * tsmall.sum(0) * 0.25
114- #
115- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c2(e)
116- w1[ib, indx[0:4]] += v * tsmall.sum(0) * 0.25
117- #
118- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c3(e)
119- w1[ib, indx[0:4]] += v * tsmall.sum(0) * 0.25
120- #
121- elif e[3] <= 0.0:
122- w1[ib, 0:4] = 0.25
123- else:
124- continue
125- #
126- #
127- for ii in range(20):
128- wght[ikv[it, ii, 0], ikv[it, ii, 1], ikv[it, ii, 2], 0:nb] += w1.dot(wlsm[:, ii])
129- #
130- wght[0:ng[0], 0:ng[1], 0:ng[2], 0:nb] /= (6.0 * nk)
131- return wght
--- a/src/libtetrabz/libtetrabz_polcmplx.py
+++ /dev/null
@@ -1,607 +0,0 @@
1-#
2-# Copyright (c) 2014 Mitsuaki Kawamura
3-#
4-# Permission is hereby granted, free of charge, to any person obtaining a
5-# copy of this software and associated documentation files (the
6-# "Software"), to deal in the Software without restriction, including
7-# without limitation the rights to use, copy, modify, merge, publish,
8-# distribute, sublicense, and/or sell copies of the Software, and to
9-# permit persons to whom the Software is furnished to do so, subject to
10-# the following conditions:
11-#
12-# The above copyright notice and this permission notice shall be included
13-# in all copies or substantial portions of the Software.
14-#
15-# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
16-# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
17-# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
18-# IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
19-# CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
20-# TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
21-# SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
22-#
23-import math
24-import numpy
25-from . import libtetrabz_common
26-
27-
28-def polcmplx(bvec, eig1, eig2, e0):
29- """
30- Main SUBROUTINE for Polarization (Imaginary axis) : Theta(- E1) * Theta(E2) / (E2 - E1 - iw)
31- :param bvec:
32- :param eig1:
33- :param eig2:
34- :param e0:
35- :return:
36- """
37- ng = numpy.array(eig1.shape[0:3])
38- nk = ng.prod(0)
39- nb = eig1.shape[3]
40- ne = e0.shape[0]
41- wlsm, ikv = libtetrabz_common.libtetrabz_initialize(ng, bvec)
42-
43- wght = numpy.zeros([ng[0], ng[1], ng[2], nb, nb, ne], dtype=numpy.complex_)
44- #
45- thr = 1.0e-8
46- for it in range(6 * nk):
47- #
48- eig1t = numpy.empty([20, nb], dtype=numpy.float_)
49- eig2t = numpy.empty([20, nb], dtype=numpy.float_)
50- for ii in range(20):
51- eig1t[ii, 0:nb] = eig1[ikv[it, ii, 0], ikv[it, ii, 1], ikv[it, ii, 2], 0:nb]
52- eig2t[ii, 0:nb] = eig2[ikv[it, ii, 0], ikv[it, ii, 1], ikv[it, ii, 2], 0:nb]
53- ei1 = wlsm.dot(eig1t)
54- ej1 = wlsm.dot(eig2t)
55- #
56- w1 = numpy.zeros([nb, nb, ne, 4], dtype=numpy.complex_)
57- w2t = numpy.zeros([nb, ne, 4], dtype=numpy.complex_)
58- for ib in range(nb):
59- #
60- e = ei1[0:4, ib].copy()
61- indx = e.argsort(0)
62- e.sort(0)
63- #
64- if e[0] <= 0.0 < e[1]:
65- #
66- v, tsmall = libtetrabz_common.libtetrabz_tsmall_a1(e)
67- #
68- if v > thr:
69- ei2 = tsmall.dot(ei1[indx[0:4], ib])
70- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
71- w2 = libtetrabz_polcmplx2(e0, ei2, ej2)
72- w2t[0:nb, 0:ne, indx[0:4]] = w2.dot(tsmall)
73- w1[ib, 0:nb, 0:ne, 0:4] += v * w2t
74- #
75- elif e[1] <= 0.0 < e[2]:
76- #
77- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b1(e)
78- #
79- if v > thr:
80- ei2 = tsmall.dot(ei1[indx[0:4], ib])
81- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
82- w2 = libtetrabz_polcmplx2(e0, ei2, ej2)
83- w2t[0:nb, 0:ne, indx[0:4]] = w2.dot(tsmall)
84- w1[ib, 0:nb, 0:ne, 0:4] += v * w2t
85- #
86- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b2(e)
87- #
88- if v > thr:
89- ei2 = tsmall.dot(ei1[indx[0:4], ib])
90- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
91- w2 = libtetrabz_polcmplx2(e0, ei2, ej2)
92- w2t[0:nb, 0:ne, indx[0:4]] = w2.dot(tsmall)
93- w1[ib, 0:nb, 0:ne, 0:4] += v * w2t
94- #
95- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b3(e)
96- #
97- if v > thr:
98- ei2 = tsmall.dot(ei1[indx[0:4], ib])
99- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
100- w2 = libtetrabz_polcmplx2(e0, ei2, ej2)
101- w2t[0:nb, 0:ne, indx[0:4]] = w2.dot(tsmall)
102- w1[ib, 0:nb, 0:ne, 0:4] += v * w2t
103- #
104- elif e[2] <= 0.0 < e[3]:
105- #
106- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c1(e)
107- #
108- if v > thr:
109- ei2 = tsmall.dot(ei1[indx[0:4], ib])
110- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
111- w2 = libtetrabz_polcmplx2(e0, ei2, ej2)
112- w2t[0:nb, 0:ne, indx[0:4]] = w2.dot(tsmall)
113- w1[ib, 0:nb, 0:ne, 0:4] += v * w2t
114- #
115- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c2(e)
116- #
117- if v > thr:
118- ei2 = tsmall.dot(ei1[indx[0:4], ib])
119- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
120- w2 = libtetrabz_polcmplx2(e0, ei2, ej2)
121- w2t[0:nb, 0:ne, indx[0:4]] = w2.dot(tsmall)
122- w1[ib, 0:nb, 0:ne, 0:4] += v * w2t
123- #
124- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c3(e)
125- #
126- if v > thr:
127- ei2 = tsmall.dot(ei1[indx[0:4], ib])
128- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
129- w2 = libtetrabz_polcmplx2(e0, ei2, ej2)
130- w2t[0:nb, 0:ne, indx[0:4]] = w2.dot(tsmall)
131- w1[ib, 0:nb, 0:ne, 0:4] += v * w2t
132- #
133- elif e[3] <= 0.0:
134- #
135- ei2 = ei1[0:4, ib]
136- ej2 = ej1[0:4, 0:nb]
137- w2 = libtetrabz_polcmplx2(e0, ei2, ej2)
138- w1[ib, 0:nb, 0:ne, 0:4] += w2[0:nb, 0:ne, 0:4]
139- #
140- else:
141- continue
142- #
143- for ii in range(20):
144- wght[ikv[it, ii, 0], ikv[it, ii, 1], ikv[it, ii, 2], 0:nb, 0:nb, 0:ne] += w1.dot(wlsm[:, ii])
145- #
146- wght[0:ng[0], 0:ng[1], 0:ng[2], 0:nb, 0:nb, 0:ne] /= (6.0 * nk)
147- return wght
148-
149-
150-def libtetrabz_polcmplx2(e0, ei1, ej1):
151- """
152- Tetrahedra method for theta( - E2)
153- :param e0:
154- :param ei1:
155- :param ej1:
156- :return:
157- """
158- ne = e0.shape[0]
159- nb = ej1.shape[1]
160- thr = 1.0e-8
161- w1 = numpy.zeros([nb, ne, 4], dtype=numpy.complex_)
162- w2t = numpy.zeros([ne, 4], dtype=numpy.complex_)
163-
164- for ib in range(nb):
165- #
166- e = -ej1[0:4, ib]
167- indx = e.argsort(0)
168- e.sort(0)
169- #
170- if e[0] <= 0.0 < e[1] or e[0] < 0.0 <= e[1]:
171- #
172- v, tsmall = libtetrabz_common.libtetrabz_tsmall_a1(e)
173- #
174- if v > thr:
175- de = tsmall.dot(ej1[indx[0:4], ib] - ei1[indx[0:4]])
176- w2 = libtetrabz_polcmplx3(e0, de)
177- w2t[0:ne, indx[0:4]] = w2.dot(tsmall)
178- w1[ib, 0:ne, 0:4] += v * w2t
179- #
180- elif e[1] <= 0.0 < e[2] or e[1] < 0.0 <= e[2]:
181- #
182- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b1(e)
183- #
184- if v > thr:
185- de = tsmall.dot(ej1[indx[0:4], ib] - ei1[indx[0:4]])
186- w2 = libtetrabz_polcmplx3(e0, de)
187- w2t[0:ne, indx[0:4]] = w2.dot(tsmall)
188- w1[ib, 0:ne, 0:4] += v * w2t
189- #
190- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b2(e)
191- #
192- if v > thr:
193- de = tsmall.dot(ej1[indx[0:4], ib] - ei1[indx[0:4]])
194- w2 = libtetrabz_polcmplx3(e0, de)
195- w2t[0:ne, indx[0:4]] = w2.dot(tsmall)
196- w1[ib, 0:ne, 0:4] += v * w2t
197- #
198- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b3(e)
199- #
200- if v > thr:
201- de = tsmall.dot(ej1[indx[0:4], ib] - ei1[indx[0:4]])
202- w2 = libtetrabz_polcmplx3(e0, de)
203- w2t[0:ne, indx[0:4]] = w2.dot(tsmall)
204- w1[ib, 0:ne, 0:4] += v * w2t
205- #
206- elif e[2] <= 0.0 < e[3] or e[2] < 0.0 <= e[3]:
207- #
208- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c1(e)
209- #
210- if v > thr:
211- de = tsmall.dot(ej1[indx[0:4], ib] - ei1[indx[0:4]])
212- w2 = libtetrabz_polcmplx3(e0, de)
213- w2t[0:ne, indx[0:4]] = w2.dot(tsmall)
214- w1[ib, 0:ne, 0:4] += v * w2t
215- #
216- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c2(e)
217- #
218- if v > thr:
219- de = tsmall.dot(ej1[indx[0:4], ib] - ei1[indx[0:4]])
220- w2 = libtetrabz_polcmplx3(e0, de)
221- w2t[0:ne, indx[0:4]] = w2.dot(tsmall)
222- w1[ib, 0:ne, 0:4] += v * w2t
223- #
224- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c3(e)
225- #
226- if v > thr:
227- de = tsmall.dot(ej1[indx[0:4], ib] - ei1[indx[0:4]])
228- w2 = libtetrabz_polcmplx3(e0, de)
229- w2t[0:ne, indx[0:4]] = w2.dot(tsmall)
230- w1[ib, 0:ne, 0:4] += v * w2t
231- #
232- elif e[3] <= 0.0:
233- de = ej1[0:4, ib] - ei1[0:4]
234- w2 = libtetrabz_polcmplx3(e0, de)
235- w1[ib, 0:ne, 0:4] += w2
236-
237- return w1
238-
239-
240-def libtetrabz_polcmplx3(e0, de):
241- """
242- Tetrahedron method for delta(om - ep + e)
243- :param e0:
244- :param de:
245- :return:
246- """
247- ne = e0.shape[0]
248- e = de[0:4].copy()
249- indx = e.argsort(0)
250- e.sort(0)
251- w1 = numpy.zeros([ne, 4], dtype=numpy.complex_)
252- w2 = numpy.empty([2, 4], dtype=numpy.float_)
253- #
254- for ie in range(ne):
255- #
256- # I am no sure which one is better.
257- # The former is more stable.
258- # The latter is more accurate ?
259- #
260- w1[ie, 0:4] = 0.25 / (de[0:4] + e0[ie])
261- #
262- continue
263- #
264- x = (e[0:4] + e0[ie].real) / e0[ie].imag
265- # thr = maxval(de(1:4)) * 1d-3
266- thr = max(1.0e-3, numpy.abs(x).max() * 1.0e-2)
267- #
268- if abs(x[3] - x[2]) < thr:
269- if abs(x[3] - x[1]) < thr:
270- if abs(x[3] - x[0]) < thr:
271- #
272- # e[3] = e[2] = e[1] = e[0]
273- #
274- w2[0, 3] = 0.25 * x[3] / (1.0 + x[3]**2)
275- w2[1, 3] = 0.25 / (1.0 + x[3]**2)
276- w2[0:2, 2] = w2[0:2, 3]
277- w2[0:2, 1] = w2[0:2, 3]
278- w2[0:2, 0] = w2[0:2, 3]
279- #
280- else:
281- #
282- # e[3] = e[2] = e[1]
283- #
284- w2[0:2, 3] = libtetrabz_polcmplx_1211(x[3], x[0])
285- w2[0:2, 2] = w2[0:2, 3]
286- w2[0:2, 1] = w2[0:2, 3]
287- w2[0:2, 0] = libtetrabz_polcmplx_1222(x[0], x[3])
288- #
289- # IF(ANY(w2(1:2,1:4) < 0.0)):
290- # WRITE(*,*) ie
291- # WRITE(*,'(100e15.5)') x[0:4]
292- # WRITE(*,'(2e15.5)') w2(1:2,1:4)
293- # STOP "weighting 4=3=2"
294- #
295- elif abs(x[1] - x[0]) < thr:
296- #
297- # e[3] = e[2], e[1] = e[0]
298- #
299- w2[0:2, 3] = libtetrabz_polcmplx_1221(x[3], x[1])
300- w2[0:2, 2] = w2[0:2, 3]
301- w2[0:2, 1] = libtetrabz_polcmplx_1221(x[1], x[3])
302- w2[0:2, 0] = w2[0:2, 1]
303- #
304- # IF(ANY(w2(1:2,1:4) < 0.0)):
305- # WRITE(*,*) ie
306- # WRITE(*,'(100e15.5)') x[0:4]
307- # WRITE(*,'(2e15.5)') w2(1:2,1:4)
308- # STOP "weighting 4=3 2=1"
309- #
310- else:
311- #
312- # e[3] = e[2]
313- #
314- w2[0:2, 3] = libtetrabz_polcmplx_1231(x[3], x[0], x[1])
315- w2[0:2, 2] = w2[0:2, 3]
316- w2[0:2, 1] = libtetrabz_polcmplx_1233(x[1], x[0], x[3])
317- w2[0:2, 0] = libtetrabz_polcmplx_1233(x[0], x[1], x[3])
318- #
319- # IF(ANY(w2(1:2,1:4) < 0.0)):
320- # WRITE(*,*) ie
321- # WRITE(*,'(100e15.5)') x[0:4]
322- # WRITE(*,'(2e15.5)') w2(1:2,1:4)
323- # STOP "weighting 4=3"
324- #
325- elif abs(x[2] - x[1]) < thr:
326- if abs(x[2] - x[0]) < thr:
327- #
328- # e[2] = e[1] = e[0]
329- #
330- w2[0:2, 3] = libtetrabz_polcmplx_1222(x[3], x[2])
331- w2[0:2, 2] = libtetrabz_polcmplx_1211(x[2], x[3])
332- w2[0:2, 1] = w2[0:2, 2]
333- w2[0:2, 0] = w2[0:2, 2]
334- #
335- # IF(ANY(w2(1:2,1:4) < 0.0)):
336- # WRITE(*,*) ie
337- # WRITE(*,'(100e15.5)') x[0:4]
338- # WRITE(*,'(2e15.5)') w2(1:2,1:4)
339- # STOP "weighting 3=2=1"
340- #
341- else:
342- #
343- # e[2] = e[1]
344- #
345- w2[0:2, 3] = libtetrabz_polcmplx_1233(x[3], x[0], x[2])
346- w2[0:2, 2] = libtetrabz_polcmplx_1231(x[2], x[0], x[3])
347- w2[0:2, 1] = w2[0:2, 2]
348- w2[0:2, 0] = libtetrabz_polcmplx_1233(x[0], x[3], x[2])
349- #
350- # IF(ANY(w2(1:2,1:4) < 0.0)):
351- # WRITE(*,*) ie
352- # WRITE(*,'(100e15.5)') x[0:4]
353- # WRITE(*,'(2e15.5)') w2(1:2,1:4)
354- # STOP "weighting 3=2"
355- #
356- elif abs(x[1] - x[0]) < thr:
357- #
358- # e[1] = e[0]
359- #
360- w2[0:2, 3] = libtetrabz_polcmplx_1233(x[3], x[2], x[1])
361- w2[0:2, 2] = libtetrabz_polcmplx_1233(x[2], x[3], x[1])
362- w2[0:2, 1] = libtetrabz_polcmplx_1231(x[1], x[2], x[3])
363- w2[0:2, 0] = w2[0:2, 1]
364- #
365- # IF(ANY(w2(1:2,1:4) < 0.0)):
366- # WRITE(*,*) ie
367- # WRITE(*,'(100e15.5)') x[0:4]
368- # WRITE(*,'(2e15.5)') w2(1:2,1:4)
369- # STOP "weighting 2=1"
370- #
371- else:
372- #
373- # Different each other.
374- #
375- w2[0:2, 3] = libtetrabz_polcmplx_1234(x[3], x[0], x[1], x[2])
376- w2[0:2, 2] = libtetrabz_polcmplx_1234(x[2], x[0], x[1], x[3])
377- w2[0:2, 1] = libtetrabz_polcmplx_1234(x[1], x[0], x[2], x[3])
378- w2[0:2, 0] = libtetrabz_polcmplx_1234(x[0], x[1], x[2], x[3])
379- #
380- # IF(ANY(w2(1:2,1:4) < 0.0)):
381- # WRITE(*,*) ie
382- # WRITE(*,'(100e15.5)') x[0:4]
383- # WRITE(*,'(2e15.5)') w2(1:2,1:4)
384- # STOP "weighting"
385- #
386- #
387- w1[ie, indx[0:4]] = w2[0, 0:4] / e0[ie].imag + 1.0j * w2[1, 0:4] / (- e0[ie].imag)
388- #
389- return w1
390-#
391-# Results of Integration (1-x-y-z)/(g0+(g1-g0)x+(g2-g0)y+(g3-g0))
392-# for 0<x<1, 0<y<1-x, 0<z<1-x-y
393-
394-
395-def libtetrabz_polcmplx_1234(g1, g2, g3, g4):
396- """
397- 1, Different each other
398- :param g1:
399- :param g2:
400- :param g3:
401- :param g4:
402- :return:
403- """
404- w = numpy.empty(2, dtype=numpy.float_)
405- #
406- # Real
407- #
408- w2 = 2.0*(3.0*g2**2 - 1.0)*(math.atan(g2) - math.atan(g1)) + (g2**2 - 3.0)*g2*math.log((1.0 + g2**2)/(1.0 + g1**2))
409- w2 = -2.0*(g2**2 - 1.0) + w2/(g2 - g1)
410- w2 = w2/(g2 - g1)
411- w3 = 2.0*(3.0*g3**2 - 1.0)*(math.atan(g3) - math.atan(g1)) + (g3**2 - 3.0)*g3*math.log((1.0 + g3**2)/(1.0 + g1**2))
412- w3 = -2.0*(g3**2 - 1.0) + w3/(g3 - g1)
413- w3 = w3/(g3 - g1)
414- w4 = 2.0*(3.0*g4**2 - 1.0)*(math.atan(g4) - math.atan(g1)) + (g4**2 - 3.0)*g4*math.log((1.0 + g4**2)/(1.0 + g1**2))
415- w4 = -2.0*(g4**2 - 1.0) + w4/(g4 - g1)
416- w4 = w4/(g4 - g1)
417- w2 = (w2 - w3)/(g2 - g3)
418- w4 = (w4 - w3)/(g4 - g3)
419- w[0] = (w4 - w2)/(2.0*(g4 - g2))
420- #
421- # Imaginal
422- #
423- w2 = 2.0*(3.0 - g2**2)*g2*(math.atan(g2) - math.atan(g1)) + (3.0*g2**2 - 1.0)*math.log((1.0 + g2**2)/(1.0 + g1**2))
424- w2 = 4.0*g2 - w2/(g2 - g1)
425- w2 = w2/(g2 - g1)
426- w3 = 2.0*(3.0 - g3**2)*g3*(math.atan(g3) - math.atan(g1)) + (3.0*g3**2 - 1.0)*math.log((1.0 + g3**2)/(1.0 + g1**2))
427- w3 = 4.0*g3 - w3/(g3 - g1)
428- w3 = w3/(g3 - g1)
429- w4 = 2.0*(3.0 - g4**2)*g4*(math.atan(g4) - math.atan(g1)) + (3.0*g4**2 - 1.0)*math.log((1.0 + g4**2)/(1.0 + g1**2))
430- w4 = 4.0*g4 - w4/(g4 - g1)
431- w4 = w4/(g4 - g1)
432- w2 = (w2 - w3)/(g2 - g3)
433- w4 = (w4 - w3)/(g4 - g3)
434- w[1] = (w4 - w2)/(2.0*(g4 - g2))
435- #
436- return w
437-
438-
439-def libtetrabz_polcmplx_1231(g1, g2, g3):
440- """
441- 2, g4 = g1
442- :param g1:
443- :param g2:
444- :param g3:
445- :return:
446- """
447- w = numpy.empty(2, dtype=numpy.float_)
448- #
449- # Real
450- #
451- w2 = 2.0*(-1.0 + 3.0*g2**2)*(math.atan(g2) - math.atan(g1))\
452- + g2*(-3.0 + g2**2)*math.log((1.0 + g2**2)/(1.0 + g1**2))
453- w2 = 2.0*(1.0 - g2**2) + w2/(g2 - g1)
454- w2 = -g1 + w2/(g2 - g1)
455- w2 = w2/(g2 - g1)
456- w3 = 2.0*(-1.0 + 3.0*g3**2)*(math.atan(g3) - math.atan(g1))\
457- + g3*(-3.0 + g3**2)*math.log((1.0 + g3**2)/(1.0 + g1**2))
458- w3 = 2.0*(1 - g3**2) + w3/(g3 - g1)
459- w3 = -g1 + w3/(g3 - g1)
460- w3 = w3/(g3 - g1)
461- w[0] = (w3 - w2)/(2.0*(g3 - g2))
462- #
463- # Imaginal
464- #
465- w2 = 2.0*g2*(3.0 - g2**2)*(math.atan(g2) - math.atan(g1)) + (-1.0 + 3.0*g2**2)*math.log((1.0 + g2**2)/(1.0 + g1**2))
466- w2 = 4.0*g2 - w2/(g2 - g1)
467- w2 = 1 + w2/(g2 - g1)
468- w2 = w2/(g2 - g1)
469- w3 = 2.0*g3*(3.0 - g3**2)*(math.atan(g3) - math.atan(g1)) + (-1.0 + 3.0*g3**2)*math.log((1.0 + g3**2)/(1.0 + g1**2))
470- w3 = 4.0*g3 - w3/(g3 - g1)
471- w3 = 1 + w3/(g3 - g1)
472- w3 = w3/(g3 - g1)
473- w[1] = (w3 - w2)/(2.0*(g3 - g2))
474- #
475- return w
476-
477-
478-def libtetrabz_polcmplx_1233(g1, g2, g3):
479- """
480- 3, g4 = g3
481- :param g1:
482- :param g2:
483- :param g3:
484- :return:
485- """
486- w = numpy.empty(2, dtype=numpy.float_)
487- #
488- # Real
489- #
490- w2 = 2.0*(1.0 - 3.0*g2**2)*(math.atan(g2) - math.atan(g1)) + g2*(3.0 - g2**2)*math.log((1.0 + g2**2)/(1.0 + g1**2))
491- w2 = 2.0*(1 - g2**2) - w2/(g2 - g1)
492- w2 = w2/(g2 - g1)
493- w3 = 2.0*(1.0 - 3.0*g3**2)*(math.atan(g3) - math.atan(g1)) + g3*(3.0 - g3**2)*math.log((1.0 + g3**2)/(1.0 + g1**2))
494- w3 = 2.0*(1 - g3**2) - w3/(g3 - g1)
495- w3 = w3/(g3 - g1)
496- w2 = (w3 - w2)/(g3 - g2)
497- w3 = 4.0*(1.0 - 3.0*g1*g3)*(math.atan(g3) - math.atan(g1))\
498- + (3.0*g1 + 3.0*g3 - 3.0*g1*g3**2 + g3**3) * math.log((1.0 + g3**2)/(1.0 + g1**2))
499- w3 = -4.0*(1.0 - g1**2) + w3/(g3 - g1)
500- w3 = 4.0*g1 + w3/(g3 - g1)
501- w3 = w3/(g3 - g1)
502- w[0] = (w3 - w2)/(2.0*(g3 - g2))
503- #
504- # Imaginal
505- #
506- w2 = 2.0*g2*(3.0 - g2**2)*(math.atan(g2) - math.atan(g1)) + (-1.0 + 3.0*g2**2)*math.log((1.0 + g2**2)/(1.0 + g1**2))
507- w2 = 4.0*g2 - w2/(g2 - g1)
508- w2 = w2/(g2 - g1)
509- w3 = 2.0*g3*(3.0 - g3**2)*(math.atan(g3) - math.atan(g1)) + (-1.0 + 3.0*g3**2)*math.log((1.0 + g3**2)/(1.0 + g1**2))
510- w3 = 4.0*g3 - w3/(g3 - g1)
511- w3 = w3/(g3 - g1)
512- w2 = (w3 - w2)/(g3 - g2)
513- w3 = (3.0*g1 - 3.0*g1*g3**2 + 3.0*g3 + g3**3)*(math.atan(g3) - math.atan(g1)) \
514- + (3.0*g1*g3 - 1.0)*math.log((1.0 + g3**2)/(1.0 + g1**2))
515- w3 = w3/(g3 - g1) - 4.0*g1
516- w3 = w3/(g3 - g1) - 2.0
517- w3 = (2.0*w3)/(g3 - g1)
518- w[1] = (w3 - w2)/(2.0*(g3 - g2))
519- #
520- return w
521-
522-
523-def libtetrabz_polcmplx_1221(g1, g2):
524- """
525- 4, g4 = g1 and g3 = g2
526- :param g1:
527- :param g2:
528- :return:
529- """
530- w = numpy.empty(2, dtype=numpy.float_)
531- #
532- # Real
533- #
534- w[0] = -2.0*(-1.0 + 2.0*g1*g2 + g2**2)*(math.atan(g2) - math.atan(g1)) \
535- + (g1 + 2.0*g2 - g1*g2**2)*math.log((1.0 + g2**2)/(1.0 + g1**2))
536- w[0] = 2.0*(-1.0 + g1**2) + w[0]/(g2 - g1)
537- w[0] = 3.0*g1 + w[0]/(g2 - g1)
538- w[0] = 2.0 + (3.0*w[0])/(g2 - g1)
539- w[0] = w[0]/(2.0*(g2 - g1))
540- #
541- # Imaginal
542- #
543- w[1] = 2.0*(g1 + 2.0*g2 - g1*g2**2)*(math.atan(g2) - math.atan(g1)) \
544- + (-1.0 + 2.0*g1*g2 + g2**2)*math.log((1 + g2**2)/(1 + g1**2))
545- w[1] = -4.0*g1 + w[1]/(g2 - g1)
546- w[1] = -3.0 + w[1]/(g2 - g1)
547- w[1] = (3.0*w[1])/(2.0*(g2 - g1)**2)
548- #
549- return w
550-
551-
552-def libtetrabz_polcmplx_1222(g1, g2):
553- """
554- 5, g4 = g3 = g2
555- :param g1:
556- :param g2:
557- :return:
558- """
559- w = numpy.empty(2, dtype=numpy.float_)
560- #
561- # Real
562- #
563- w[0] = 2.0*(-1.0 + g1**2 + 2.0*g1*g2)*(math.atan(g2) - math.atan(g1)) \
564- + (-2.0*g1 - g2 + g1**2*g2) * math.log((1.0 + g2**2)/(1.0 + g1**2))
565- w[0] = 2.0*(1.0 - g1**2) + w[0]/(g2 - g1)
566- w[0] = g1 - w[0]/(g2 - g1)
567- w[0] = 1.0 - (3.0*w[0])/(g2 - g1)
568- w[0] = w[0]/(2.0*(g2 - g1))
569- #
570- # Imaginal
571- #
572- w[1] = 2.0*(-2.0*g1 - g2 + g1**2*g2)*(math.atan(g2) - math.atan(g1)) \
573- + (1.0 - g1**2 - 2.0*g1*g2) * math.log((1.0 + g2**2)/(1.0 + g1**2))
574- w[1] = 4.0*g1 + w[1]/(g2 - g1)
575- w[1] = 1.0 + w[1]/(g2 - g1)
576- w[1] = (3.0*w[1])/(2.0*(g2 - g1)**2)
577- #
578- return w
579-
580-
581-def libtetrabz_polcmplx_1211(g1, g2):
582- """
583- 6, g4 = g3 = g1
584- :param g1:
585- :param g2:
586- :return:
587- """
588- w = numpy.empty(2, dtype=numpy.float_)
589- #
590- # Real
591- #
592- w[0] = 2.0*(3.0*g2**2 - 1.0)*(math.atan(g2) - math.atan(g1)) \
593- + g2*(g2**2 - 3.0)*math.log((1.0 + g2**2)/(1.0 + g1**2))
594- w[0] = 2.0*(1.0 - g1**2) + w[0]/(g2 - g1)
595- w[0] = -5.0*g1 + w[0]/(g2 - g1)
596- w[0] = -11.0 + (3.0*w[0])/(g2 - g1)
597- w[0] = w[0]/(6.0*(g2 - g1))
598- #
599- # Imaginal
600- #
601- w[1] = 2.0*g2*(-3.0 + g2**2)*(math.atan(g2) - math.atan(g1)) \
602- + (1.0 - 3.0*g2**2)*math.log((1.0 + g2**2)/(1.0 + g1**2))
603- w[1] = 4.0*g2 + w[1]/(g2 - g1)
604- w[1] = 1.0 + w[1]/(g2 - g1)
605- w[1] = w[1]/(2.0*(g2 - g1)**2)
606- #
607- return w
--- a/src/libtetrabz/libtetrabz_polstat.py
+++ /dev/null
@@ -1,488 +0,0 @@
1-#
2-# Copyright (c) 2014 Mitsuaki Kawamura
3-#
4-# Permission is hereby granted, free of charge, to any person obtaining a
5-# copy of this software and associated documentation files (the
6-# "Software"), to deal in the Software without restriction, including
7-# without limitation the rights to use, copy, modify, merge, publish,
8-# distribute, sublicense, and/or sell copies of the Software, and to
9-# permit persons to whom the Software is furnished to do so, subject to
10-# the following conditions:
11-#
12-# The above copyright notice and this permission notice shall be included
13-# in all copies or substantial portions of the Software.
14-#
15-# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
16-# OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
17-# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
18-# IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
19-# CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
20-# TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
21-# SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
22-#
23-import math
24-import numpy
25-from . import libtetrabz_common
26-
27-
28-def polstat(bvec, eig1, eig2):
29- """
30- Compute Static polarization function
31- :param bvec:
32- :param eig1:
33- :param eig2:
34- :return:
35- """
36- thr = 1.0e-10
37-
38- ng = numpy.array(eig1.shape[0:3])
39- nk = ng.prod(0)
40- nb = eig1.shape[3]
41- wlsm, ikv = libtetrabz_common.libtetrabz_initialize(ng, bvec)
42-
43- wght = numpy.zeros([ng[0], ng[1], ng[2], nb, nb], dtype=numpy.float_)
44-
45- for it in range(6 * nk):
46- #
47- eig1t = numpy.empty([20, nb], dtype=numpy.float_)
48- eig2t = numpy.empty([20, nb], dtype=numpy.float_)
49- for ii in range(20):
50- eig1t[ii, 0:nb] = eig1[ikv[it, ii, 0], ikv[it, ii, 1], ikv[it, ii, 2], 0:nb]
51- eig2t[ii, 0:nb] = eig2[ikv[it, ii, 0], ikv[it, ii, 1], ikv[it, ii, 2], 0:nb]
52- ei1 = wlsm.dot(eig1t)
53- ej1 = wlsm.dot(eig2t)
54- #
55- w1 = numpy.zeros([nb, nb, 4], dtype=numpy.float_)
56- w2t = numpy.zeros([nb, 4], dtype=numpy.float_)
57- for ib in range(nb):
58- #
59- e = ei1[0:4, ib].copy()
60- indx = e.argsort(0)
61- e.sort(0)
62- #
63- if e[0] <= 0.0 < e[1]:
64- #
65- v, tsmall = libtetrabz_common.libtetrabz_tsmall_a1(e)
66- #
67- if v > thr:
68- ei2 = tsmall.dot(ei1[indx[0:4], ib])
69- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
70- w2 = libtetrabz_polstat2(ei2, ej2)
71- w2t[0:nb, indx[0:4]] = w2.dot(tsmall)
72- w1[ib, 0:nb, 0:4] += v * w2t[0:nb, 0:4]
73- #
74- elif e[1] <= 0.0 < e[2]:
75- #
76- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b1(e)
77- #
78- if v > thr:
79- ei2 = tsmall.dot(ei1[indx[0:4], ib])
80- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
81- w2 = libtetrabz_polstat2(ei2, ej2)
82- w2t[0:nb, indx[0:4]] = w2.dot(tsmall)
83- w1[ib, 0:nb, 0:4] += v * w2t[0:nb, 0:4]
84- #
85- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b2(e)
86- #
87- if v > thr:
88- ei2 = tsmall.dot(ei1[indx[0:4], ib])
89- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
90- w2 = libtetrabz_polstat2(ei2, ej2)
91- w2t[0:nb, indx[0:4]] = w2.dot(tsmall)
92- w1[ib, 0:nb, 0:4] += v * w2t[0:nb, 0:4]
93- #
94- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b3(e)
95- #
96- if v > thr:
97- ei2 = tsmall.dot(ei1[indx[0:4], ib])
98- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
99- w2 = libtetrabz_polstat2(ei2, ej2)
100- w2t[0:nb, indx[0:4]] = w2.dot(tsmall)
101- w1[ib, 0:nb, 0:4] += v * w2t[0:nb, 0:4]
102- #
103- elif e[2] <= 0.0 < e[3]:
104- #
105- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c1(e)
106- #
107- if v > thr:
108- ei2 = tsmall.dot(ei1[indx[0:4], ib])
109- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
110- w2 = libtetrabz_polstat2(ei2, ej2)
111- w2t[0:nb, indx[0:4]] = w2.dot(tsmall)
112- w1[ib, 0:nb, 0:4] += v * w2t[0:nb, 0:4]
113- #
114- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c2(e)
115- #
116- if v > thr:
117- ei2 = tsmall.dot(ei1[indx[0:4], ib])
118- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
119- w2 = libtetrabz_polstat2(ei2, ej2)
120- w2t[0:nb, indx[0:4]] = w2.dot(tsmall)
121- w1[ib, 0:nb, 0:4] += v * w2t[0:nb, 0:4]
122- #
123- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c3(e)
124- #
125- if v > thr:
126- ei2 = tsmall.dot(ei1[indx[0:4], ib])
127- ej2 = tsmall.dot(ej1[indx[0:4], 0:nb])
128- w2 = libtetrabz_polstat2(ei2, ej2)
129- w2t[0:nb, indx[0:4]] = w2.dot(tsmall)
130- w1[ib, 0:nb, 0:4] += v * w2t[0:nb, 0:4]
131- #
132- elif e[3] <= 0.0:
133- ei2 = ei1[0:4, ib]
134- ej2 = ej1[0:4, 0:nb]
135- w2 = libtetrabz_polstat2(ei2, ej2)
136- w1[ib, 0:nb, 0:4] += w2[0:nb, 0:4]
137- else:
138- continue
139- #
140- #
141- for ii in range(20):
142- wght[ikv[it, ii, 0], ikv[it, ii, 1], ikv[it, ii, 2], 0:nb, 0:nb] += w1.dot(wlsm[:, ii])
143- #
144- wght[0:ng[0], 0:ng[1], 0:ng[2], 0:nb, 0:nb] /= (6.0 * nk)
145- return wght
146-
147-
148-def libtetrabz_polstat2(ei1, ej1):
149- """
150- Tetrahedron method for theta( - E2)
151- :param ei1:
152- :param ej1:
153- :return:
154- """
155- #
156- thr = 1.0e-8
157- nb = ej1.shape[1]
158- w1 = numpy.zeros([nb, 4], dtype=numpy.float_)
159-
160- for ib in range(nb):
161- e = -ej1[0:4, ib]
162- indx = e.argsort(0)
163- e.sort(0)
164- #
165- if e[0] <= 0.0 < e[1] or e[0] < 0.0 <= e[1]:
166- #
167- v, tsmall = libtetrabz_common.libtetrabz_tsmall_a1(e)
168- #
169- if v > thr:
170- #
171- de = tsmall.dot(ej1[indx[0:4], ib] - ei1[indx[0:4]])
172- w2 = libtetrabz_polstat3(de)
173- w1[ib, indx[0:4]] += v * w2.dot(tsmall)
174- #
175- elif e[1] <= 0.0 < e[2] or e[1] < 0.0 <= e[2]:
176- #
177- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b1(e)
178- #
179- if v > thr:
180- #
181- de = tsmall.dot(ej1[indx[0:4], ib] - ei1[indx[0:4]])
182- w2 = libtetrabz_polstat3(de)
183- w1[ib, indx[0:4]] += v * w2.dot(tsmall)
184- #
185- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b2(e)
186- #
187- if v > thr:
188- #
189- de = tsmall.dot(ej1[indx[0:4], ib] - ei1[indx[0:4]])
190- w2 = libtetrabz_polstat3(de)
191- w1[ib, indx[0:4]] += v * w2.dot(tsmall)
192- #
193- v, tsmall = libtetrabz_common.libtetrabz_tsmall_b3(e)
194- #
195- if v > thr:
196- #
197- de = tsmall.dot(ej1[indx[0:4], ib] - ei1[indx[0:4]])
198- w2 = libtetrabz_polstat3(de)
199- w1[ib, indx[0:4]] += v * w2.dot(tsmall)
200- #
201- elif e[2] <= 0.0 < e[3] or e[2] < 0.0 <= e[3]:
202- #
203- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c1(e)
204- #
205- if v > thr:
206- #
207- de = tsmall.dot(ej1[indx[0:4], ib] - ei1[indx[0:4]])
208- w2 = libtetrabz_polstat3(de)
209- w1[ib, indx[0:4]] += v * w2.dot(tsmall)
210- #
211- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c2(e)
212- #
213- if v > thr:
214- #
215- de = tsmall.dot(ej1[indx[0:4], ib] - ei1[indx[0:4]])
216- w2 = libtetrabz_polstat3(de)
217- w1[ib, indx[0:4]] += v * w2.dot(tsmall)
218- #
219- v, tsmall = libtetrabz_common.libtetrabz_tsmall_c3(e)
220- #
221- if v > thr:
222- #
223- de = tsmall.dot(ej1[indx[0:4], ib] - ei1[indx[0:4]])
224- w2 = libtetrabz_polstat3(de)
225- w1[ib, indx[0:4]] += v * w2.dot(tsmall)
226- #
227- elif e[3] <= 0.0:
228- #
229- de = ej1[0:4, ib] - ei1[0:4]
230- w2 = libtetrabz_polstat3(de)
231- w1[ib, 0:4] += w2
232- #
233- return w1
234-
235-
236-def libtetrabz_polstat3(de):
237- """
238- Tetrahedron method for delta(om - ep + e)
239- :param de:
240- :return:
241- """
242- #
243- e = de[0:4].copy()
244- indx = e.argsort(0)
245- e.sort(0)
246- #
247- thr = e.max(0) * 1.0e-3
248- thr2 = 1.0e-8
249- #
250- ln = numpy.empty(4, dtype=numpy.float_)
251- for ii in range(4):
252- if e[ii] < thr2:
253- if ii == 3:
254- raise ValueError(" Nesting # ")
255- ln[ii] = 0.0
256- e[ii] = 0.0
257- else:
258- ln[ii] = math.log(e[ii])
259- #
260- w1 = numpy.empty(4, dtype=numpy.float_)
261- if abs(e[3] - e[2]) < thr:
262- if abs(e[3] - e[1]) < thr:
263- if abs(e[3] - e[0]) < thr:
264- #
265- # e[3] = e[2] = e[1] = e[0]
266- #
267- w1[indx[3]] = 0.25 / e[3]
268- w1[indx[2]] = w1[indx[3]]
269- w1[indx[1]] = w1[indx[3]]
270- w1[indx[0]] = w1[indx[3]]
271- #
272- else:
273- #
274- # e[3] = e[2] = e[1]
275- #
276- w1[indx[3]] = libtetrabz_polstat_1211(e[3], e[0], ln[3], ln[0])
277- w1[indx[2]] = w1[indx[3]]
278- w1[indx[1]] = w1[indx[3]]
279- w1[indx[0]] = libtetrabz_polstat_1222(e[0], e[3], ln[0], ln[3])
280- #
281- if w1.min(initial=w1[0]) < 0.0:
282- print(e[0], e[1], e[2], e[3])
283- print(w1[indx[0]], w1[indx[1]], w1[indx[2]], w1[indx[3]])
284- raise ValueError("weighting 4=3=2")
285- #
286- elif abs(e[1] - e[0]) < thr:
287- #
288- # e[3] = e[2], e[1] = e[0]
289- #
290- w1[indx[3]] = libtetrabz_polstat_1221(e[3], e[1], ln[3], ln[1])
291- w1[indx[2]] = w1[indx[3]]
292- w1[indx[1]] = libtetrabz_polstat_1221(e[1], e[3], ln[1], ln[3])
293- w1[indx[0]] = w1[indx[1]]
294- #
295- if w1.min(initial=w1[0]) < 0.0:
296- print(e[0], e[1], e[2], e[3])
297- print(w1[indx[0]], w1[indx[1]], w1[indx[2]], w1[indx[3]])
298- raise ValueError("weighting 4=3 2=1")
299- #
300- else:
301- #
302- # e[3] = e[2]
303- #
304- w1[indx[3]] = libtetrabz_polstat_1231(e[3], e[0], e[1], ln[3], ln[0], ln[1])
305- w1[indx[2]] = w1[indx[3]]
306- w1[indx[1]] = libtetrabz_polstat_1233(e[1], e[0], e[3], ln[1], ln[0], ln[3])
307- w1[indx[0]] = libtetrabz_polstat_1233(e[0], e[1], e[3], ln[0], ln[1], ln[3])
308- #
309- if w1.min(initial=w1[0]) < 0.0:
310- print(e[0], e[1], e[2], e[3])
311- print(w1[indx[0]], w1[indx[1]], w1[indx[2]], w1[indx[3]])
312- raise ValueError("weighting 4=3")
313- #
314- elif abs(e[2] - e[1]) < thr:
315- if abs(e[2] - e[0]) < thr:
316- #
317- # e[2] = e[1] = e[0]
318- #
319- w1[indx[3]] = libtetrabz_polstat_1222(e[3], e[2], ln[3], ln[2])
320- w1[indx[2]] = libtetrabz_polstat_1211(e[2], e[3], ln[2], ln[3])
321- w1[indx[1]] = w1[indx[2]]
322- w1[indx[0]] = w1[indx[2]]
323- #
324- if w1.min(initial=w1[0]) < 0.0:
325- print(e[0], e[1], e[2], e[3])
326- print(w1[indx[0]], w1[indx[1]], w1[indx[2]], w1[indx[3]])
327- raise ValueError("weighting 3=2=1")
328- #
329- else:
330- #
331- # e[2] = e[1]
332- #
333- w1[indx[3]] = libtetrabz_polstat_1233(e[3], e[0], e[2], ln[3], ln[0], ln[2])
334- w1[indx[2]] = libtetrabz_polstat_1231(e[2], e[0], e[3], ln[2], ln[0], ln[3])
335- w1[indx[1]] = w1[indx[2]]
336- w1[indx[0]] = libtetrabz_polstat_1233(e[0], e[3], e[2], ln[0], ln[3], ln[2])
337- #
338- if w1.min(initial=w1[0]) < 0.0:
339- print(e[0], e[1], e[2], e[3])
340- print(w1[indx[0]], w1[indx[1]], w1[indx[2]], w1[indx[3]])
341- raise ValueError("weighting 3=2")
342- #
343- elif abs(e[1] - e[0]) < thr:
344- #
345- # e[1] = e[0]
346- #
347- w1[indx[3]] = libtetrabz_polstat_1233(e[3], e[2], e[1], ln[3], ln[2], ln[1])
348- w1[indx[2]] = libtetrabz_polstat_1233(e[2], e[3], e[1], ln[2], ln[3], ln[1])
349- w1[indx[1]] = libtetrabz_polstat_1231(e[1], e[2], e[3], ln[1], ln[2], ln[3])
350- w1[indx[0]] = w1[indx[1]]
351- #
352- if w1.min(initial=w1[0]) < 0.0:
353- print(e[0], e[1], e[2], e[3])
354- print(w1[indx[0]], w1[indx[1]], w1[indx[2]], w1[indx[3]])
355- raise ValueError("weighting 2=1")
356- #
357- else:
358- #
359- # Different each other.
360- #
361- w1[indx[3]] = libtetrabz_polstat_1234(e[3], e[0], e[1], e[2], ln[3], ln[0], ln[1], ln[2])
362- w1[indx[2]] = libtetrabz_polstat_1234(e[2], e[0], e[1], e[3], ln[2], ln[0], ln[1], ln[3])
363- w1[indx[1]] = libtetrabz_polstat_1234(e[1], e[0], e[2], e[3], ln[1], ln[0], ln[2], ln[3])
364- w1[indx[0]] = libtetrabz_polstat_1234(e[0], e[1], e[2], e[3], ln[0], ln[1], ln[2], ln[3])
365- #
366- if w1.min(initial=w1[0]) < 0.0:
367- print(e[0], e[1], e[2], e[3])
368- print(w1[indx[0]], w1[indx[1]], w1[indx[2]], w1[indx[3]])
369- raise ValueError("weighting")
370- #
371- #
372- return w1
373-#
374-# Results of Integration (1-x-y-z)/(g0+(g1-g0)x+(g2-g0)y+(g3-g0))
375-# for 0<x<1, 0<y<1-x, 0<z<1-x-y
376-#
377-
378-
379-def libtetrabz_polstat_1234(g1, g2, g3, g4, lng1, lng2, lng3, lng4):
380- """
381- 1, Different each other
382- :param g1:
383- :param g2:
384- :param g3:
385- :param g4:
386- :param lng1:
387- :param lng2:
388- :param lng3:
389- :param lng4:
390- :return:
391- """
392- w2 = ((lng2 - lng1)/(g2 - g1)*g2 - 1.0)*g2/(g2 - g1)
393- w3 = ((lng3 - lng1)/(g3 - g1)*g3 - 1.0)*g3/(g3 - g1)
394- w4 = ((lng4 - lng1)/(g4 - g1)*g4 - 1.0)*g4/(g4 - g1)
395- w2 = ((w2 - w3)*g2)/(g2 - g3)
396- w4 = ((w4 - w3)*g4)/(g4 - g3)
397- w = (w4 - w2)/(g4 - g2)
398- return w
399-
400-
401-def libtetrabz_polstat_1231(g1, g2, g3, lng1, lng2, lng3):
402- """
403- 2, g4 = g1
404- :param g1:
405- :param g2:
406- :param g3:
407- :param lng1:
408- :param lng2:
409- :param lng3:
410- :return:
411- """
412- w2 = ((lng2 - lng1)/(g2 - g1)*g2 - 1.0)*g2**2/(g2 - g1) - g1/2.0
413- w2 = w2/(g2 - g1)
414- w3 = ((lng3 - lng1)/(g3 - g1)*g3 - 1.0)*g3**2/(g3 - g1) - g1/2.0
415- w3 = w3/(g3 - g1)
416- w = (w3 - w2)/(g3 - g2)
417- return w
418-
419-
420-def libtetrabz_polstat_1233(g1, g2, g3, lng1, lng2, lng3):
421- """
422- # 3, g4 = g3
423- :param g1:
424- :param g2:
425- :param g3:
426- :param lng1:
427- :param lng2:
428- :param lng3:
429- :return:
430- """
431- w2 = (lng2 - lng1)/(g2 - g1)*g2 - 1.0
432- w2 = (g2*w2)/(g2 - g1)
433- w3 = (lng3 - lng1)/(g3 - g1)*g3 - 1.0
434- w3 = (g3*w3)/(g3 - g1)
435- w2 = (w3 - w2)/(g3 - g2)
436- w3 = (lng3 - lng1)/(g3 - g1)*g3 - 1.0
437- w3 = 1.0 - (2.0*w3*g1)/(g3 - g1)
438- w3 = w3/(g3 - g1)
439- w = (g3*w3 - g2*w2)/(g3 - g2)
440- return w
441-
442-
443-def libtetrabz_polstat_1221(g1, g2, lng1, lng2):
444- """
445- 4, g4 = g1 and g3 = g2
446- :param g1:
447- :param g2:
448- :param lng1:
449- :param lng2:
450- :return:
451- """
452- w = 1.0 - (lng2 - lng1)/(g2 - g1)*g1
453- w = -1.0 + (2.0*g2*w)/(g2 - g1)
454- w = -1.0 + (3.0*g2*w)/(g2 - g1)
455- w = w/(2.0*(g2 - g1))
456- return w
457-
458-
459-def libtetrabz_polstat_1222(g1, g2, lng1, lng2):
460- """
461- 5, g4 = g3 = g2
462- :param g1:
463- :param g2:
464- :param lng1:
465- :param lng2:
466- :return:
467- """
468- w = (lng2 - lng1)/(g2 - g1)*g2 - 1.0
469- w = (2.0*g1*w)/(g2 - g1) - 1.0
470- w = (3.0*g1*w)/(g2 - g1) + 1.0
471- w = w/(2.0*(g2 - g1))
472- return w
473-
474-
475-def libtetrabz_polstat_1211(g1, g2, lng1, lng2):
476- """
477- 6, g4 = g3 = g1
478- :param g1:
479- :param g2:
480- :param lng1:
481- :param lng2:
482- :return:
483- """
484- w = -1.0 + (lng2 - lng1)/(g2 - g1)*g2
485- w = -1.0 + (2.0*g2*w)/(g2 - g1)
486- w = -1.0 + (3.0*g2*w)/(2.0*(g2 - g1))
487- w = w/(3.0*(g2 - g1))
488- return w
--- a/src/libtetrabz_tutorial.ipynb
+++ b/src/libtetrabz_tutorial.ipynb
@@ -1,7 +1,6 @@
11 {
22 "cells": [
33 {
4- "attachments": {},
54 "cell_type": "markdown",
65 "metadata": {
76 "id": "pahorUv9vKeB"
@@ -29,7 +28,6 @@
2928 ]
3029 },
3130 {
32- "attachments": {},
3331 "cell_type": "markdown",
3432 "metadata": {
3533 "id": "dGU3CIgJipXD"
@@ -64,6 +62,13 @@
6462 ]
6563 },
6664 {
65+ "cell_type": "markdown",
66+ "metadata": {},
67+ "source": [
68+ "Simulation box of Brillouin zone (must be large enough)"
69+ ]
70+ },
71+ {
6772 "cell_type": "code",
6873 "execution_count": null,
6974 "metadata": {
@@ -76,6 +81,13 @@
7681 ]
7782 },
7883 {
84+ "cell_type": "markdown",
85+ "metadata": {},
86+ "source": [
87+ "Reciplocal lattice vector"
88+ ]
89+ },
90+ {
7991 "cell_type": "code",
8092 "execution_count": null,
8193 "metadata": {
@@ -84,8 +96,17 @@
8496 "outputs": [],
8597 "source": [
8698 "bvec = 2.0 * numpy.array([[k_max, 0.0, 0.0],\n",
87- " [0.0, k_max, 0.0],\n",
88- " [0.0, 0.0, k_max]])"
99+ " [0.0, k_max, 0.0],\n",
100+ " [0.0, 0.0, k_max]])"
101+ ]
102+ },
103+ {
104+ "cell_type": "markdown",
105+ "metadata": {},
106+ "source": [
107+ "$$\n",
108+ "\\varepsilon_{\\bf k} = \\frac{k^2}{2}\n",
109+ "$$"
89110 ]
90111 },
91112 {
@@ -138,6 +159,7 @@
138159 "cell_type": "markdown",
139160 "metadata": {},
140161 "source": [
162+ "Reasonable choice of broadening width : Average change of enegy between neighboring grid point\n",
141163 "$$\n",
142164 "\\sigma = \\left \\langle |\\nabla_k \\varepsilon_k| \\right \\rangle \\Delta k\n",
143165 "= \\left \\langle \\sqrt{2\\varepsilon_k} \\right \\rangle \\Delta k\n",
@@ -154,6 +176,15 @@
154176 ]
155177 },
156178 {
179+ "cell_type": "markdown",
180+ "metadata": {},
181+ "source": [
182+ "$$\n",
183+ "\\tilde{\\delta}(\\varepsilon)=\\frac{1}{\\sigma \\sqrt{\\pi}}\\exp\\left(-\\frac{\\varepsilon^2}{\\sigma^2}\\right)\n",
184+ "$$"
185+ ]
186+ },
187+ {
157188 "cell_type": "code",
158189 "execution_count": null,
159190 "metadata": {},
@@ -175,6 +206,18 @@
175206 ]
176207 },
177208 {
209+ "cell_type": "markdown",
210+ "metadata": {},
211+ "source": [
212+ "Analytical value\n",
213+ "$$\n",
214+ "D(\\varepsilon) = \\int d^3 k \\delta(\\epsilon - \\varepsilon_k) = \n",
215+ "4 \\pi \\int_0^\\infty dk k^2 \\delta \\left(\\epsilon - \\frac{k^2}{2}\\right)\n",
216+ "=4 \\pi \\sqrt{2 \\varepsilon}.\n",
217+ "$$"
218+ ]
219+ },
220+ {
178221 "cell_type": "code",
179222 "execution_count": null,
180223 "metadata": {},
@@ -191,7 +234,6 @@
191234 ]
192235 },
193236 {
194- "attachments": {},
195237 "cell_type": "markdown",
196238 "metadata": {},
197239 "source": [
@@ -245,13 +287,6 @@
245287 ]
246288 },
247289 {
248- "attachments": {
249- "libtetrabz.svg": {
250- "image/svg+xml": [
251- "<?xml version="1.0" encoding="UTF-8" standalone="no"?>
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256291 "metadata": {},
257292 "source": [
@@ -265,8 +300,7 @@
265300 "If we set $k_{\\rm F}=1$,\n",
266301 "$$\n",
267302 "\\chi(q) = 2 \\pi \\left(1 + \\frac{1 - q^2/4}{q} \\log\\left|\\frac{q+2}{q-2} \\right|\\right)\n",
268- "$$\n",
269- "![libtetrabz.svg](attachment:libtetrabz.svg)"
303+ "$$"
270304 ]
271305 },
272306 {
@@ -294,8 +328,7 @@
294328 "source": [
295329 "ng0 = 10\n",
296330 "nb = 1\n",
297- "ng = numpy.array([ng0, ng0, ng0])\n",
298- "eig = numpy.empty([ng[0], ng[1], ng[2], nb], dtype=numpy.float_)"
331+ "ng = numpy.array([ng0, ng0, ng0])"
299332 ]
300333 },
301334 {
@@ -318,11 +351,50 @@
318351 },
319352 "outputs": [],
320353 "source": [
321- "eig1 = numpy.empty([ng[0], ng[1], ng[2], nb], dtype=numpy.float_)\n",
322- "eig2 = numpy.empty([ng[0], ng[1], ng[2], nb], dtype=numpy.float_)\n",
323- "qx = numpy.arange(0.0, qmax, 0.4)\n",
324- "chi_t = numpy.empty(qx.shape, dtype=numpy.float_)\n",
325- "chi_s = numpy.empty(qx.shape, dtype=numpy.float_)"
354+ "qx = numpy.arange(0.0, qmax, 0.4)"
355+ ]
356+ },
357+ {
358+ "cell_type": "markdown",
359+ "metadata": {},
360+ "source": [
361+ "Reasonable choice of broadening width : Average change of enegy between neighboring grid point\n",
362+ "$$\n",
363+ "\\sigma = \\left \\langle |\\nabla_k \\varepsilon_k| \\right \\rangle \\Delta k\n",
364+ "= \\left \\langle \\sqrt{2\\varepsilon_k} \\right \\rangle \\Delta k\n",
365+ "$$"
366+ ]
367+ },
368+ {
369+ "cell_type": "code",
370+ "execution_count": null,
371+ "metadata": {},
372+ "outputs": [],
373+ "source": [
374+ "eig = numpy.empty([ng[0], ng[1], ng[2], nb], dtype=numpy.float_)\n",
375+ "for i0 in range(ng[0]):\n",
376+ " for i1 in range(ng[1]):\n",
377+ " for i2 in range(ng[2]):\n",
378+ " ikvec = numpy.array([i0, i1, i2])\n",
379+ " for ii in range(3):\n",
380+ " if ikvec[ii] * 2 >= ng[ii]:\n",
381+ " ikvec[ii] += - ng[ii]\n",
382+ " kvec = ikvec[0:3] / ng[0:3]\n",
383+ " kvec[0:3] = kvec.dot(bvec)\n",
384+ " eig[i0, i1, i2, 0] = 0.5 * kvec.dot(kvec)\n",
385+ "sigma=numpy.sqrt(2.0*eig).mean()*2.0*k_max/ng0 "
386+ ]
387+ },
388+ {
389+ "cell_type": "markdown",
390+ "metadata": {},
391+ "source": [
392+ "Broadening method\n",
393+ "$$\n",
394+ "\\chi(q) = \\int d^3 k \\frac{\\tilde{\\theta}(\\varepsilon_{\\rm F} - \\varepsilon_k) - \\tilde{\\theta}(\\varepsilon_{\\rm F} - \\varepsilon_{k+q})}{\\varepsilon_{k+q} - \\varepsilon_k} \\\\\n",
395+ "\\tilde{\\theta}(\\varepsilon) = \\frac{\\rm{erfc}(-\\varepsilon/\\sigma)}{2}=\\frac{1}{\\sqrt{\\pi}}\\int_{-\\varepsilon}^\\infty dt \\exp \\left[-\\left(\\frac{t}{\\sigma}\\right)^2\\right] \\\\\n",
396+ "\\lim_{\\varepsilon_{k+q} \\rightarrow \\varepsilon_{k}}\\frac{\\tilde{\\theta}(\\varepsilon_{\\rm F} - \\varepsilon_k) - \\tilde{\\theta}(\\varepsilon_{\\rm F} - \\varepsilon_{k+q})}{\\varepsilon_{k+q} - \\varepsilon_k} = -\\tilde{\\delta}(\\varepsilon_{\\rm F} - \\varepsilon_{k+q})\n",
397+ "$$"
326398 ]
327399 },
328400 {
@@ -332,7 +404,7 @@
332404 "outputs": [],
333405 "source": [
334406 "import math\n",
335- "sigma=numpy.sqrt(2.0*(eig1+ef)).mean()*2.0*k_max/ng0\n",
407+ "chi_s = numpy.empty(qx.shape, dtype=numpy.float_)\n",
336408 "for iq in range(qx.shape[0]):\n",
337409 " qvec = numpy.array([qx[iq], 0.0, 0.0])\n",
338410 " chi_s[iq] = 0.0\n",
@@ -358,6 +430,17 @@
358430 ]
359431 },
360432 {
433+ "cell_type": "markdown",
434+ "metadata": {},
435+ "source": [
436+ "Tetrahedron method\n",
437+ "$$\n",
438+ "\\chi(q) = \\sum_{\\bf k} w_{\\bf k}(q) \\\\\n",
439+ "\\chi(0) = D(0)\n",
440+ "$$"
441+ ]
442+ },
443+ {
361444 "cell_type": "code",
362445 "execution_count": null,
363446 "metadata": {
@@ -365,6 +448,9 @@
365448 },
366449 "outputs": [],
367450 "source": [
451+ "eig1 = numpy.empty([ng[0], ng[1], ng[2], nb], dtype=numpy.float_)\n",
452+ "eig2 = numpy.empty([ng[0], ng[1], ng[2], nb], dtype=numpy.float_)\n",
453+ "chi_t = numpy.empty(qx.shape, dtype=numpy.float_)\n",
368454 "for iq in range(qx.shape[0]):\n",
369455 " qvec = numpy.array([qx[iq], 0.0, 0.0])\n",
370456 " for i0 in range(ng[0]):\n",
@@ -390,6 +476,15 @@
390476 ]
391477 },
392478 {
479+ "cell_type": "markdown",
480+ "metadata": {},
481+ "source": [
482+ "$$\n",
483+ "\\chi(q) = 2 \\pi \\left(1 + \\frac{1 - q^2/4}{q} \\log\\left|\\frac{q+2}{q-2} \\right|\\right)\n",
484+ "$$"
485+ ]
486+ },
487+ {
393488 "cell_type": "code",
394489 "execution_count": null,
395490 "metadata": {
@@ -428,13 +523,21 @@
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530+ ]
531+ }
532+ },
431533 "cell_type": "markdown",
432534 "metadata": {
433535 "id": "mo3GriM1K9UK"
434536 },
435537 "source": [
436538 "## 4, Multiband, low dimension, and partial DOS\n",
437- "We caonsider the simple honeycomb lattice which has two orbitals (bands) in a unit cell.\n"
539+ "We caonsider the simple honeycomb lattice which has two orbitals (bands) in a unit cell.\n",
540+ "![honeycomb-2.svg](attachment:honeycomb-2.svg)"
438541 ]
439542 },
440543 {
@@ -443,12 +546,21 @@
443546 "metadata": {},
444547 "outputs": [],
445548 "source": [
446- "bvec = numpy.array([[1.0, 0.0, 0.0],\n",
447- " [0.5, 0.5*numpy.sqrt(3.0), 0.0],\n",
549+ "bvec = numpy.array([[0.5*numpy.sqrt(3.0), 0.5, 0.0],\n",
550+ " [0.5*numpy.sqrt(3.0), -0.5, 0.0],\n",
448551 " [0.0, 0.0, 10.0]])"
449552 ]
450553 },
451554 {
555+ "cell_type": "markdown",
556+ "metadata": {},
557+ "source": [
558+ "Set of ${\\bf R}=(l,m,n)$ and orbitals pair\n",
559+ "\n",
560+ "Corresponding hopping parameter"
561+ ]
562+ },
563+ {
452564 "cell_type": "code",
453565 "execution_count": null,
454566 "metadata": {},
@@ -464,6 +576,21 @@
464576 ]
465577 },
466578 {
579+ "cell_type": "markdown",
580+ "metadata": {},
581+ "source": [
582+ "Diagonalize\n",
583+ "$$\n",
584+ "H_{i j}({\\bf k}) = \\sum H_{i j} ({\\bf R}) \\exp(i{\\bf k}\\cdot{\\bf R})\n",
585+ "$$\n",
586+ "And compute projection ($|\\langle\\varphi_{n {\\bf k}} |\\varphi_{\\pm}\\rangle|^2$) onto bonding $|\\varphi_+\\rangle$ and anti-bonding $|\\varphi_-\\rangle$ orbitals, where\n",
587+ "$$\n",
588+ "|\\varphi_+\\rangle = \\frac{|\\varphi_A\\rangle + |\\varphi_B\\rangle}{\\sqrt{2}}\\\\\n",
589+ "|\\varphi_-\\rangle = \\frac{|\\varphi_A\\rangle - |\\varphi_B\\rangle}{\\sqrt{2}}\n",
590+ "$$"
591+ ]
592+ },
593+ {
467594 "cell_type": "code",
468595 "execution_count": null,
469596 "metadata": {},
@@ -558,6 +685,16 @@
558685 ]
559686 },
560687 {
688+ "cell_type": "markdown",
689+ "metadata": {},
690+ "source": [
691+ "Simple-cubic tight-binding model\n",
692+ "$$\n",
693+ "\\varepsilon_{\\bf k} = - \\{ \\cos(k_x) +\\cos(k_y) +\\cos(k_z) \\}\n",
694+ "$$"
695+ ]
696+ },
697+ {
561698 "cell_type": "code",
562699 "execution_count": null,
563700 "metadata": {},
@@ -657,13 +794,6 @@
657794 " for i2 in range(ng[2]):\n",
658795 " print(vf[i0, i1, i2, ib], file=f)"
659796 ]
660- },
661- {
662- "cell_type": "code",
663- "execution_count": null,
664- "metadata": {},
665- "outputs": [],
666- "source": []
667797 }
668798 ],
669799 "metadata": {
@@ -687,7 +817,7 @@
687817 "name": "python",
688818 "nbconvert_exporter": "python",
689819 "pygments_lexer": "ipython3",
690- "version": "3.7.8"
820+ "version": "3.8.10"
691821 }
692822 },
693823 "nbformat": 4,
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