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libtetrabz: コミット

テトラへドロン法ライブラリ


コミットメタ情報

リビジョン55312a16e45043ade4007fe9cd5e0ebf9b11ea50 (tree)
日時2018-12-20 16:43:21
作者Mitsuaki Kawamura <kawamitsuaki@gmai...>
コミッターMitsuaki Kawamura

ログメッセージ

k sum -> k integration

変更サマリ

  • modified: doc/en/index.rst (diff)
  • delete: doc/en/{libtetrabz_app_en.rst => app.rst}
  • delete: doc/en/{libtetrabz_contact_en.rst => contact.rst}
  • delete: doc/en/{libtetrabz_copy_en.rst => copy.rst}
  • delete: doc/en/{libtetrabz_install_en.rst => install.rst}
  • delete: doc/en/{libtetrabz_link_en.rst => link.rst}
  • delete: doc/en/{libtetrabz_overview_en.rst => overview.rst}
  • delete: doc/en/{libtetrabz_ref_en.rst => ref.rst}
  • delete: doc/en/{libtetrabz_routine_en.rst => routine.rst}
  • delete: doc/en/{libtetrabz_sample_en.rst => sample.rst}
  • modified: doc/ja/index.rst (diff)
  • delete: doc/ja/{libtetrabz_app_ja.rst => app.rst}
  • delete: doc/ja/{libtetrabz_contact_ja.rst => contact.rst}
  • delete: doc/ja/{libtetrabz_copy_ja.rst => copy.rst}
  • delete: doc/ja/{libtetrabz_install_ja.rst => install.rst}
  • delete: doc/ja/{libtetrabz_link_ja.rst => link.rst}
  • delete: doc/ja/{libtetrabz_overview_ja.rst => overview.rst}
  • delete: doc/ja/{libtetrabz_ref_ja.rst => ref.rst}
  • delete: doc/ja/{libtetrabz_routine_ja.rst => routine.rst}
  • delete: doc/ja/{libtetrabz_sample_ja.rst => sample.rst}

差分

--- a/doc/en/index.rst
+++ b/doc/en/index.rst
@@ -9,15 +9,15 @@ Welcome to LibTetraBZ's documentation!
99 .. toctree::
1010 :maxdepth: 3
1111
12- libtetrabz_overview_en
13- libtetrabz_install_en
14- libtetrabz_link_en
15- libtetrabz_routine_en
16- libtetrabz_sample_en
17- libtetrabz_copy_en
18- libtetrabz_contact_en
19- libtetrabz_app_en
20- libtetrabz_ref_en
12+ overview
13+ install
14+ link
15+ routine
16+ sample
17+ copy
18+ contact
19+ app
20+ ref
2121
2222 .. Indices and tables
2323 .. ==================
--- a/doc/en/libtetrabz_overview_en.rst
+++ b/doc/en/overview.rst
@@ -11,8 +11,10 @@ calculate weights :math:`w_{n n' k}` for integration such as
1111 .. math::
1212
1313 \begin{align}
14- \sum_{n n' k} F(\varepsilon_{n k}, \varepsilon_{n' k+q})X_{n n' k}
15- = \sum_{n n' k} w_{n n' k} X_{n n' k}
14+ \sum_{n n'}
15+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
16+ F(\varepsilon_{n k}, \varepsilon_{n' k+q})X_{n n' k}
17+ = \sum_{n n'} \sum_{k}^{N_k} w_{n n' k} X_{n n' k}
1618 \end{align}
1719
1820 ``libtetrabz`` supports following Brillouin-zone integrations
@@ -20,7 +22,8 @@ calculate weights :math:`w_{n n' k}` for integration such as
2022 .. math::
2123
2224 \begin{align}
23- \sum_{n k}
25+ \sum_{n}
26+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
2427 \theta(\varepsilon_{\rm F} - \varepsilon_{n k})
2528 X_{n k}
2629 \end{align}
@@ -28,7 +31,8 @@ calculate weights :math:`w_{n n' k}` for integration such as
2831 .. math::
2932
3033 \begin{align}
31- \sum_{n k}
34+ \sum_{n}
35+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
3236 \delta(\omega - \varepsilon_{n k})
3337 X_{n k}(\omega)
3438 \end{align}
@@ -36,7 +40,8 @@ calculate weights :math:`w_{n n' k}` for integration such as
3640 .. math::
3741
3842 \begin{align}
39- \sum_{n n' k}
43+ \sum_{n n'}
44+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
4045 \delta(\varepsilon_{\rm F} - \varepsilon_{n k})
4146 \delta(\varepsilon_{\rm F} - \varepsilon'_{n' k})
4247 X_{n n' k}
@@ -45,7 +50,8 @@ calculate weights :math:`w_{n n' k}` for integration such as
4550 .. math::
4651
4752 \begin{align}
48- \sum_{n n' k}
53+ \sum_{n n'}
54+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
4955 \theta(\varepsilon_{\rm F} - \varepsilon_{n k})
5056 \theta(\varepsilon_{n k} - \varepsilon'_{n' k})
5157 X_{n n' k}
@@ -54,7 +60,8 @@ calculate weights :math:`w_{n n' k}` for integration such as
5460 .. math::
5561
5662 \begin{align}
57- \sum_{n n' k}
63+ \sum_{n n'}
64+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
5865 \frac{
5966 \theta(\varepsilon_{\rm F} - \varepsilon_{n k})
6067 \theta(\varepsilon'_{n' k} - \varepsilon_{\rm F})}
@@ -65,7 +72,8 @@ calculate weights :math:`w_{n n' k}` for integration such as
6572 .. math::
6673
6774 \begin{align}
68- \sum_{n n' k}
75+ \sum_{n n'}
76+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
6977 \theta(\varepsilon_{\rm F} - \varepsilon_{n k})
7078 \theta(\varepsilon'_{n' k} - \varepsilon_{\rm F})
7179 \delta(\varepsilon'_{n' k} - \varepsilon_{n k} - \omega)
@@ -75,7 +83,8 @@ calculate weights :math:`w_{n n' k}` for integration such as
7583 .. math::
7684
7785 \begin{align}
78- \sum_{n n' k}
86+ \sum_{n n'}
87+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
7988 \frac{
8089 \theta(\varepsilon_{\rm F} - \varepsilon_{n k})
8190 \theta(\varepsilon'_{n' k} - \varepsilon_{\rm F})}
--- a/doc/en/libtetrabz_routine_en.rst
+++ b/doc/en/routine.rst
@@ -34,7 +34,9 @@ Total energy, charge density, occupations
3434 .. math::
3535
3636 \begin{align}
37- \sum_{n k} \theta(\varepsilon_{\rm F} -
37+ \sum_{n}
38+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
39+ \theta(\varepsilon_{\rm F} -
3840 \varepsilon_{n k}) X_{n k}
3941 \end{align}
4042
@@ -115,7 +117,9 @@ Fermi energy and occupations
115117 .. math::
116118
117119 \begin{align}
118- \sum_{n k} \theta(\varepsilon_{\rm F} -
120+ \sum_{n}
121+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
122+ \theta(\varepsilon_{\rm F} -
119123 \varepsilon_{n k}) X_{n k}
120124 \end{align}
121125
@@ -210,7 +214,9 @@ Partial density of states
210214 .. math::
211215
212216 \begin{align}
213- \sum_{n k} \delta(\omega - \varepsilon_{n k})
217+ \sum_{n}
218+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
219+ \delta(\omega - \varepsilon_{n k})
214220 X_{n k}(\omega)
215221 \end{align}
216222
@@ -305,7 +311,9 @@ Integrated density of states
305311 .. math::
306312
307313 \begin{align}
308- \sum_{n k} \theta(\omega - \varepsilon_{n k})
314+ \sum_{n}
315+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
316+ \theta(\omega - \varepsilon_{n k})
309317 X_{n k}(\omega)
310318 \end{align}
311319
@@ -400,7 +408,9 @@ Nesting function and Fr&oumlhlich parameter
400408 .. math::
401409
402410 \begin{align}
403- \sum_{n n' k} \delta(\varepsilon_{\rm F} -
411+ \sum_{n n'}
412+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
413+ \delta(\varepsilon_{\rm F} -
404414 \varepsilon_{n k}) \delta(\varepsilon_{\rm F} - \varepsilon'_{n' k})
405415 X_{n n' k}
406416 \end{align}
@@ -491,7 +501,9 @@ A part of DFPT calculation
491501 .. math::
492502
493503 \begin{align}
494- \sum_{n n' k} \theta(\varepsilon_{\rm F} -
504+ \sum_{n n'}
505+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
506+ \theta(\varepsilon_{\rm F} -
495507 \varepsilon_{n k}) \theta(\varepsilon_{n k} - \varepsilon'_{n' k})
496508 X_{n n' k}
497509 \end{align}
@@ -582,7 +594,9 @@ Static polarization function
582594 .. math::
583595
584596 \begin{align}
585- \sum_{n n' k} \frac{\theta(\varepsilon_{\rm F} - \varepsilon_{n k})
597+ \sum_{n n'}
598+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
599+ \frac{\theta(\varepsilon_{\rm F} - \varepsilon_{n k})
586600 \theta(\varepsilon'_{n' k} - \varepsilon_{\rm F})}
587601 {\varepsilon'_{n' k} - \varepsilon_{n k}}
588602 X_{n n' k}
@@ -674,7 +688,9 @@ Phonon linewidth
674688 .. math::
675689
676690 \begin{align}
677- \sum_{n n' k} \theta(\varepsilon_{\rm F} -
691+ \sum_{n n'}
692+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
693+ \theta(\varepsilon_{\rm F} -
678694 \varepsilon_{n k}) \theta(\varepsilon'_{n' k} - \varepsilon_{\rm F})
679695 \delta(\varepsilon'_{n' k} - \varepsilon_{n k} - \omega)
680696 X_{n n' k}(\omega)
@@ -780,7 +796,9 @@ Polarization function (complex frequency)
780796 .. math::
781797
782798 \begin{align}
783- \sum_{n n' k} \frac{\theta(\varepsilon_{\rm F} - \varepsilon_{n k})
799+ \sum_{n n'}
800+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
801+ \frac{\theta(\varepsilon_{\rm F} - \varepsilon_{n k})
784802 \theta(\varepsilon'_{n' k} - \varepsilon_{\rm F})}
785803 {\varepsilon'_{n' k} - \varepsilon_{n k} + i \omega}
786804 X_{n n' k}(\omega)
--- a/doc/ja/index.rst
+++ b/doc/ja/index.rst
@@ -9,15 +9,15 @@ Welcome to LibTetraBZ's documentation!
99 .. toctree::
1010 :maxdepth: 3
1111
12- libtetrabz_overview_ja
13- libtetrabz_install_ja
14- libtetrabz_link_ja
15- libtetrabz_routine_ja
16- libtetrabz_sample_ja
17- libtetrabz_copy_ja
18- libtetrabz_contact_ja
19- libtetrabz_app_ja
20- libtetrabz_ref_ja
12+ overview
13+ install
14+ link
15+ routine
16+ sample
17+ copy
18+ contact
19+ app
20+ ref
2121
2222 .. Indices and tables
2323 .. ==================
--- a/doc/ja/libtetrabz_overview_ja.rst
+++ b/doc/ja/overview.rst
@@ -10,8 +10,8 @@
1010 .. math::
1111
1212 \begin{align}
13- \sum_{n n' k} F(\varepsilon_{n k}, \varepsilon_{n' k+q})X_{n n' k}
14- = \sum_{n n' k} w_{n n' k} X_{n n' k}
13+ \sum_{n n'} \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}} F(\varepsilon_{n k}, \varepsilon_{n' k+q})X_{n n' k}
14+ = \sum_{n n'} \sum_{k}^{N_k} w_{n n' k} X_{n n' k}
1515 \end{align}
1616
1717 のような積分における, 積分重み :math:`w_{n n' k}` を出力するサブルーチンを,
@@ -20,7 +20,8 @@
2020 .. math::
2121
2222 \begin{align}
23- \sum_{n k}
23+ \sum_{n}
24+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
2425 \theta(\varepsilon_{\rm F} - \varepsilon_{n k})
2526 X_{n k}
2627 \end{align}
@@ -28,7 +29,8 @@
2829 .. math::
2930
3031 \begin{align}
31- \sum_{n k}
32+ \sum_{n}
33+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
3234 \delta(\omega - \varepsilon_{n k})
3335 X_{n k}(\omega)
3436 \end{align}
@@ -36,7 +38,8 @@
3638 .. math::
3739
3840 \begin{align}
39- \sum_{n n' k}
41+ \sum_{n n'}
42+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
4043 \delta(\varepsilon_{\rm F} - \varepsilon_{n k})
4144 \delta(\varepsilon_{\rm F} - \varepsilon'_{n' k})
4245 X_{n n' k}
@@ -45,7 +48,8 @@
4548 .. math::
4649
4750 \begin{align}
48- \sum_{n n' k}
51+ \sum_{n n'}
52+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
4953 \theta(\varepsilon_{\rm F} - \varepsilon_{n k})
5054 \theta(\varepsilon_{n k} - \varepsilon'_{n' k})
5155 X_{n n' k}
@@ -54,7 +58,8 @@
5458 .. math::
5559
5660 \begin{align}
57- \sum_{n n' k}
61+ \sum_{n n'}
62+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
5863 \frac{
5964 \theta(\varepsilon_{\rm F} - \varepsilon_{n k})
6065 \theta(\varepsilon'_{n' k} - \varepsilon_{\rm F})}
@@ -65,7 +70,8 @@
6570 .. math::
6671
6772 \begin{align}
68- \sum_{n n' k}
73+ \sum_{n n'}
74+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
6975 \theta(\varepsilon_{\rm F} - \varepsilon_{n k})
7076 \theta(\varepsilon'_{n' k} - \varepsilon_{\rm F})
7177 \delta(\varepsilon'_{n' k} - \varepsilon_{n k} - \omega)
@@ -75,7 +81,8 @@
7581 .. math::
7682
7783 \begin{align}
78- \sum_{n n' k}
84+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
85+ \sum_{n n'}
7986 \frac{
8087 \theta(\varepsilon_{\rm F} - \varepsilon_{n k})
8188 \theta(\varepsilon'_{n' k} - \varepsilon_{\rm F})}
--- a/doc/ja/libtetrabz_routine_ja.rst
+++ b/doc/ja/routine.rst
@@ -35,7 +35,9 @@ C言語で書かれたプログラムから呼び出す場合には次のよう
3535 .. math::
3636
3737 \begin{align}
38- \sum_{n k} \theta(\varepsilon_{\rm F} -
38+ \sum_{n}
39+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
40+ \theta(\varepsilon_{\rm F} -
3941 \varepsilon_{n k}) X_{n k}
4042 \end{align}
4143
@@ -116,7 +118,9 @@ Fermi エネルギー(占有率も同時に計算する)
116118 .. math::
117119
118120 \begin{align}
119- \sum_{n k} \theta(\varepsilon_{\rm F} -
121+ \sum_{n}
122+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
123+ \theta(\varepsilon_{\rm F} -
120124 \varepsilon_{n k}) X_{n k}
121125 \end{align}
122126
@@ -217,7 +221,9 @@ Fermi エネルギー(占有率も同時に計算する)
217221 .. math::
218222
219223 \begin{align}
220- \sum_{n k} \delta(\omega - \varepsilon_{n k})
224+ \sum_{n}
225+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
226+ \delta(\omega - \varepsilon_{n k})
221227 X_{n k}(\omega)
222228 \end{align}
223229
@@ -311,7 +317,9 @@ Fermi エネルギー(占有率も同時に計算する)
311317 .. math::
312318
313319 \begin{align}
314- \sum_{n k} \theta(\omega - \varepsilon_{n k})
320+ \sum_{n}
321+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
322+ \theta(\omega - \varepsilon_{n k})
315323 X_{n k}(\omega)
316324 \end{align}
317325
@@ -405,7 +413,9 @@ Fermi エネルギー(占有率も同時に計算する)
405413 .. math::
406414
407415 \begin{align}
408- \sum_{n n' k} \delta(\varepsilon_{\rm F} -
416+ \sum_{n n'}
417+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
418+ \delta(\varepsilon_{\rm F} -
409419 \varepsilon_{n k}) \delta(\varepsilon_{\rm F} - \varepsilon'_{n' k})
410420 X_{n n' k}
411421 \end{align}
@@ -496,7 +506,9 @@ DFPT 計算の一部
496506 .. math::
497507
498508 \begin{align}
499- \sum_{n n' k} \theta(\varepsilon_{\rm F} -
509+ \sum_{n n'}
510+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
511+ \theta(\varepsilon_{\rm F} -
500512 \varepsilon_{n k}) \theta(\varepsilon_{n k} - \varepsilon'_{n' k})
501513 X_{n n' k}
502514 \end{align}
@@ -587,7 +599,9 @@ DFPT 計算の一部
587599 .. math::
588600
589601 \begin{align}
590- \sum_{n n' k} \frac{\theta(\varepsilon_{\rm F} - \varepsilon_{n k})
602+ \sum_{n n'}
603+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
604+ \frac{\theta(\varepsilon_{\rm F} - \varepsilon_{n k})
591605 \theta(\varepsilon'_{n' k} - \varepsilon_{\rm F})}
592606 {\varepsilon'_{n' k} - \varepsilon_{n k}}
593607 X_{n n' k}
@@ -679,7 +693,9 @@ DFPT 計算の一部
679693 .. math::
680694
681695 \begin{align}
682- \sum_{n n' k} \theta(\varepsilon_{\rm F} -
696+ \sum_{n n'}
697+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
698+ \theta(\varepsilon_{\rm F} -
683699 \varepsilon_{n k}) \theta(\varepsilon'_{n' k} - \varepsilon_{\rm F})
684700 \delta(\varepsilon'_{n' k} - \varepsilon_{n k} - \omega)
685701 X_{n n' k}(\omega)
@@ -785,7 +801,9 @@ DFPT 計算の一部
785801 .. math::
786802
787803 \begin{align}
788- \sum_{n n' k} \frac{\theta(\varepsilon_{\rm F} - \varepsilon_{n k})
804+ \sum_{n n'}
805+ \int_{\rm BZ} \frac{d^3 k}{V_{\rm BZ}}
806+ \frac{\theta(\varepsilon_{\rm F} - \varepsilon_{n k})
789807 \theta(\varepsilon'_{n' k} - \varepsilon_{\rm F})}
790808 {\varepsilon'_{n' k} - \varepsilon_{n k} + i \omega}
791809 X_{n n' k}(\omega)
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