The Kitchin Research Group

Using org-entries like a database

Thu, 21 Aug 2014 20:45:07 EDT

1. Generating the entries
2. Tabulating the results in column mode
3. org-map-entries to get the data
4. Getting specific data from a calculation
5. Summary

I recently added an org export to jasp which provides an org-mode representation of a Vasp calculation. It is still a work in progress, but the main ideas are developed. The idea is to represent a calculation as an org-mode headline with tabular data, properties and tags. This will make the representation human readable, but machine accessible. Here I examine how we could use it.

1 Generating the entries

We will loop over a set of calculations that define the equation of state for two different Al-Ni alloy structures. For each calculation this code generates a level 3 headline with some tags derived from the calculation directory. I chose level 3 so they would all be nested in this level 2 headline. We write out two sets of data because later we will selectively get portions of the data.

from jasp import *
from jasp.utils import get_jasp_dirs

for d in get_jasp_dirs('10'):
    with jasp(d) as calc:
        print calc.org(level=3)

for d in get_jasp_dirs('11'):
    with jasp(d) as calc:
        print calc.org(level=3)

1.1 10/eos-exp/f+0 10 eos_dash_exp f_plus_0

	x	y	z
A0	-1.98408	0.0	-1.98408
A1	0.0	-1.98408	1.98408
A2	-3.53625	3.53625	3.53625

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-3.77549	1.79141	1.79141	0.000773	-0.000773	-0.000773	T	T	T
Al	-1.74484	-0.23924	1.74484	-0.000773	0.000773	0.000773	T	T	T
Ni	0.0	0.0	0.0	0.0	0.0	0.0	T	T	T

Parameter	Value
nbands	25
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Ni	potpaw_PBE/Ni/POTCAR	6c814bc7144b98435771aded093fb4ebe527acd9
Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2

1.2 10/eos-exp/f+10 10 eos_dash_exp f_plus_10

	x	y	z
A0	-2.04813	0.0	-2.04813
A1	0.0	-2.04813	2.04813
A2	-3.6504	3.6504	3.6504

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-3.85098179507	1.84576178527	1.83645153581	-0.012598	0.014577	-0.007395	T	T	T
Al	-1.7283215185	-0.279882546245	1.73598892646	0.000817	0.006771	0.025221	T	T	T
Ni	-5.63955668642	1.58856076097	3.61420953773	0.011781	-0.021349	-0.017826	T	T	T

Parameter	Value
nbands	25
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Ni	potpaw_PBE/Ni/POTCAR	6c814bc7144b98435771aded093fb4ebe527acd9
Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2

1.3 10/eos-exp/f+12 10 eos_dash_exp f_plus_12

	x	y	z
A0	-2.06046	0.0	-2.06046
A1	0.0	-2.06046	2.06046
A2	-3.67239	3.67239	3.67239

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-3.86530078437	1.85683453967	1.84560971979	-0.017615	0.018377	-0.00588	T	T	T
Al	-1.72555029376	-0.287469117251	1.73429429921	0.009139	-0.000441	0.020494	T	T	T
Ni	-5.66232892187	1.59473457758	3.628735981	0.008476	-0.017936	-0.014613	T	T	T

Parameter	Value
nbands	25
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Ni	potpaw_PBE/Ni/POTCAR	6c814bc7144b98435771aded093fb4ebe527acd9
Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2

1.4 10/eos-exp/f+15 10 eos_dash_exp f_plus_15

	x	y	z
A0	-2.0787	0.0	-2.0787
A1	0.0	-2.0787	2.0787
A2	-3.70489	3.70489	3.70489

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-3.88717652995	1.87379242704	1.86009271779	-0.022309	0.021755	-0.006413	T	T	T
Al	-1.72325929808	-0.297739728075	1.73317610987	0.033819	-0.022553	-0.000329	T	T	T
Ni	-5.69348417197	1.60230730103	3.64787117234	-0.01151	0.000799	0.006742	T	T	T

Parameter	Value
nbands	25
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Ni	potpaw_PBE/Ni/POTCAR	6c814bc7144b98435771aded093fb4ebe527acd9
Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2

1.5 10/eos-exp/f+2 10 eos_dash_exp f_plus_2

	x	y	z
A0	-1.99722	0.0	-1.99722
A1	0.0	-1.99722	1.99722
A2	-3.55967	3.55967	3.55967

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-3.78897262915	1.80298810692	1.80238679997	-0.00052	-0.01106	-0.017256	T	T	T
Al	-1.74283113391	-0.243416998758	1.743431885	0.011316	-0.021883	-0.005492	T	T	T
Ni	-5.54541623693	1.55504889184	3.55010131503	-0.010796	0.032943	0.022747	T	T	T

Parameter	Value
nbands	25
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Ni	potpaw_PBE/Ni/POTCAR	6c814bc7144b98435771aded093fb4ebe527acd9
Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2

1.6 10/eos-exp/f+4 10 eos_dash_exp f_plus_4

	x	y	z
A0	-2.01019	0.0	-2.01019
A1	0.0	-2.01019	2.01019
A2	-3.58278	3.58278	3.58278

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-3.80137127251	1.81395280614	1.81276515721	-0.021611	-0.002318	-0.01379	T	T	T
Al	-1.73979870776	-0.248609560277	1.74098667865	0.017491	-0.038446	-0.007248	T	T	T
Ni	-5.57213001973	1.55941675414	3.56527816415	0.004121	0.040764	0.021038	T	T	T

Parameter	Value
nbands	25
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Ni	potpaw_PBE/Ni/POTCAR	6c814bc7144b98435771aded093fb4ebe527acd9
Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2

1.7 10/eos-exp/f+6 10 eos_dash_exp f_plus_6

	x	y	z
A0	-2.02299	0.0	-2.02299
A1	0.0	-2.02299	2.02299
A2	-3.60561	3.60561	3.60561

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-3.81674368134	1.82268911017	1.81846628092	-0.03365	0.021418	0.006392	T	T	T
Al	-1.73592646487	-0.259496276667	1.73977985143	0.007575	-0.01713	0.007756	T	T	T
Ni	-5.5962598538	1.5715971665	3.58361386765	0.026075	-0.004288	-0.014148	T	T	T

Parameter	Value
nbands	25
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Ni	potpaw_PBE/Ni/POTCAR	6c814bc7144b98435771aded093fb4ebe527acd9
Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2

1.8 10/eos-exp/f+8 10 eos_dash_exp f_plus_8

	x	y	z
A0	-2.03564	0.0	-2.03564
A1	0.0	-2.03564	2.03564
A2	-3.62814	3.62814	3.62814

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-3.83039067392	1.83353256518	1.82788023062	-0.042201	0.025424	0.00725	T	T	T
Al	-1.73261729052	-0.266893248067	1.73758502884	0.008197	-0.020125	0.010395	T	T	T
Ni	-5.62110203556	1.57803068288	3.59892474053	0.034004	-0.005299	-0.017645	T	T	T

Parameter	Value
nbands	25
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Ni	potpaw_PBE/Ni/POTCAR	6c814bc7144b98435771aded093fb4ebe527acd9
Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2

1.9 10/eos-exp/f-10 10 eos_dash_exp f_dash_10

	x	y	z
A0	-1.91561	0.0	-1.91561
A1	0.0	-1.91561	1.91561
A2	-3.41421	3.41421	3.41421

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-3.69513184604	1.73676514888	1.75200457401	-0.00015	-0.016008	0.015593	T	T	T
Al	-1.76033286748	-0.198966401698	1.74405584289	0.003022	-0.015555	-0.029074	T	T	T
Ni	-0.0648652864789	0.0143712528207	0.040189583095	-0.002872	0.031562	0.013481	T	T	T

Parameter	Value
nbands	25
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Ni	potpaw_PBE/Ni/POTCAR	6c814bc7144b98435771aded093fb4ebe527acd9
Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2

1.10 10/eos-exp/f-12 10 eos_dash_exp f_dash_12

	x	y	z
A0	-1.90131	0.0	-1.90131
A1	0.0	-1.90131	1.90131
A2	-3.38873	3.38873	3.38873

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-3.67627852264	1.72365573425	1.74704265204	-0.021096	-0.003148	0.019104	T	T	T
Al	-1.76353019483	-0.189393782717	1.73913926696	-0.006667	-0.016634	-0.009534	T	T	T
Ni	-0.0805212825263	0.0179080484715	0.050068081002	0.027763	0.019782	-0.00957	T	T	T

Parameter	Value
nbands	25
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Ni	potpaw_PBE/Ni/POTCAR	6c814bc7144b98435771aded093fb4ebe527acd9
Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2

1.11 10/eos-exp/f-15 10 eos_dash_exp f_dash_15

	x	y	z
A0	-1.87946	0.0	-1.87946
A1	0.0	-1.87946	1.87946
A2	-3.34978	3.34978	3.34978

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-3.65183912264	1.70528638812	1.73537994296	-0.037051	0.019573	0.044452	T	T	T
Al	-1.76884279383	-0.178373914577	1.73770842538	0.010475	-0.025221	-0.029082	T	T	T
Ni	-0.0996480835307	0.0252575264549	0.0631616316537	0.026577	0.005648	-0.01537	T	T	T

Parameter	Value
nbands	25
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Ni	potpaw_PBE/Ni/POTCAR	6c814bc7144b98435771aded093fb4ebe527acd9
Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2

1.12 10/eos-exp/f-2 10 eos_dash_exp f_dash_2

	x	y	z
A0	-1.97076	0.0	-1.97076
A1	0.0	-1.97076	1.97076
A2	-3.51252	3.51252	3.51252

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-3.76146938751	1.7792636125	1.77972964831	0.002765	0.010416	0.018609	T	T	T
Al	-1.74832410416	-0.234109027383	1.74785846541	-0.002339	0.016333	-0.006172	T	T	T
Ni	-0.0105365083339	0.00701541488599	0.00866188628634	-0.000426	-0.026749	-0.012437	T	T	T

Parameter	Value
nbands	25
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Ni	potpaw_PBE/Ni/POTCAR	6c814bc7144b98435771aded093fb4ebe527acd9
Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2

1.13 10/eos-exp/f-4 10 eos_dash_exp f_dash_4

	x	y	z
A0	-1.95726	0.0	-1.95726
A1	0.0	-1.95726	1.95726
A2	-3.48846	3.48846	3.48846

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-3.74916407088	1.76890327148	1.76974035279	0.025717	0.002077	0.019316	T	T	T
Al	-1.75040151275	-0.230732012577	1.74956509347	-0.018564	0.049532	8.6e-05	T	T	T
Ni	-0.0207644163691	0.0139987410966	0.0169445537375	-0.007153	-0.051609	-0.019402	T	T	T

Parameter	Value
nbands	25
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Ni	potpaw_PBE/Ni/POTCAR	6c814bc7144b98435771aded093fb4ebe527acd9
Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2

1.14 10/eos-exp/f-6 10 eos_dash_exp f_dash_6

	x	y	z
A0	-1.94358	0.0	-1.94358
A1	0.0	-1.94358	1.94358
A2	-3.46406	3.46406	3.46406

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-3.73031485721	1.75693465653	1.76095910776	-0.000377	0.017266	0.043872	T	T	T
Al	-1.75673108966	-0.217813140979	1.75241474358	0.034718	-0.014395	-0.060867	T	T	T
Ni	-0.0332840531202	0.0130484844485	0.0228761486573	-0.034341	-0.002871	0.016995	T	T	T

Parameter	Value
nbands	25
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Ni	potpaw_PBE/Ni/POTCAR	6c814bc7144b98435771aded093fb4ebe527acd9
Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2

1.15 10/eos-exp/f-8 10 eos_dash_exp f_dash_8

	x	y	z
A0	-1.92969	0.0	-1.92969
A1	0.0	-1.92969	1.92969
A2	-3.43932	3.43932	3.43932

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-3.71109103713	1.74742547037	1.75920312374	-0.003371	-0.008528	0.015983	T	T	T
Al	-1.75760409593	-0.206692341706	1.74515790595	0.004847	-0.014457	-0.026033	T	T	T
Ni	-0.0516348669472	0.011436871336	0.0318889703136	-0.001476	0.022985	0.01005	T	T	T

Parameter	Value
nbands	25
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Ni	potpaw_PBE/Ni/POTCAR	6c814bc7144b98435771aded093fb4ebe527acd9
Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2

1.16 11/eos-exp/f+0 11 eos_dash_exp f_plus_0

	x	y	z
A0	-1.83341	0.0	-1.83341
A1	0.0	-1.83341	1.83341
A2	-3.44161	3.44161	3.44161

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-1.75834	-0.07507	1.75834	0.0	0.0	0.0	T	T	T
Fe	-3.39510205563	3.39510205563	3.39510205563	0.065417	-0.065417	-0.065417	T	T	T
Fe	-3.56318794437	1.72977794437	1.72977794437	-0.065417	0.065417	0.065417	T	T	T

Parameter	Value
nbands	21
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2
Fe	potpaw_PBE/Fe/POTCAR	201d71adcb39575fc20d69f0abd331ae9c01ed2e

1.17 11/eos-exp/f+10 11 eos_dash_exp f_plus_10

	x	y	z
A0	-1.89259	0.0	-1.89259
A1	0.0	-1.89259	1.89259
A2	-3.55271	3.55271	3.55271

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-1.71768562473	-0.12420477333	1.72897811362	-0.027763	-0.002052	0.049582	T	T	T
Fe	-5.29679962665	1.54076691889	3.42444208823	0.067989	-0.02176	-0.05605	T	T	T
Fe	-3.59473474862	1.74065785444	1.72979979816	-0.040226	0.023812	0.006467	T	T	T

Parameter	Value
nbands	21
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2
Fe	potpaw_PBE/Fe/POTCAR	201d71adcb39575fc20d69f0abd331ae9c01ed2e

1.18 11/eos-exp/f+12 11 eos_dash_exp f_plus_12

	x	y	z
A0	-1.90399	0.0	-1.90399
A1	0.0	-1.90399	1.90399
A2	-3.57411	3.57411	3.57411

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-1.71395551429	-0.137649234072	1.73446168186	0.003858	-0.016816	0.003362	T	T	T
Fe	-5.30314000606	1.54316547516	3.42737702355	0.034226	-0.051683	-0.060287	T	T	T
Fe	-3.60352447965	1.74030375892	1.7213812946	-0.038084	0.068499	0.056924	T	T	T

Parameter	Value
nbands	21
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2
Fe	potpaw_PBE/Fe/POTCAR	201d71adcb39575fc20d69f0abd331ae9c01ed2e

1.19 11/eos-exp/f+15 11 eos_dash_exp f_plus_15

	x	y	z
A0	-1.92084	0.0	-1.92084
A1	0.0	-1.92084	1.92084
A2	-3.60574	3.60574	3.60574

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-1.70274811209	-0.152372217551	1.72799358203	-0.001016	-0.015145	0.009612	T	T	T
Fe	-5.31888643404	1.53641622409	3.43283036647	0.011105	-0.02964	-0.037354	T	T	T
Fe	-3.61583545387	1.74492599346	1.7223960515	-0.010088	0.044785	0.027742	T	T	T

Parameter	Value
nbands	21
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2
Fe	potpaw_PBE/Fe/POTCAR	201d71adcb39575fc20d69f0abd331ae9c01ed2e

1.20 11/eos-exp/f+2 11 eos_dash_exp f_plus_2

	x	y	z
A0	-1.84555	0.0	-1.84555
A1	0.0	-1.84555	1.84555
A2	-3.4644	3.4644	3.4644

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-1.75029374339	-0.0841326953171	1.75144674035	-0.006952	-0.003547	0.01682	T	T	T
Fe	-5.24418323089	1.55674197758	3.40127583308	0.081175	-0.052085	-0.064081	T	T	T
Fe	-3.56770302572	1.73165071774	1.73049742657	-0.074224	0.055633	0.047261	T	T	T

Parameter	Value
nbands	21
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2
Fe	potpaw_PBE/Fe/POTCAR	201d71adcb39575fc20d69f0abd331ae9c01ed2e

1.21 11/eos-exp/f+4 11 eos_dash_exp f_plus_4

	x	y	z
A0	-1.85754	0.0	-1.85754
A1	0.0	-1.85754	1.85754
A2	-3.4869	3.4869	3.4869

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-1.74219271636	-0.0933112216124	1.74481701196	-0.01609	-0.003222	0.033588	T	T	T
Fe	-5.26036201118	1.55320104576	3.40867525476	0.120223	-0.071335	-0.093285	T	T	T
Fe	-3.57161527246	1.73238017585	1.72972773328	-0.104133	0.074557	0.059697	T	T	T

Parameter	Value
nbands	21
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2
Fe	potpaw_PBE/Fe/POTCAR	201d71adcb39575fc20d69f0abd331ae9c01ed2e

1.22 11/eos-exp/f+6 11 eos_dash_exp f_plus_6

	x	y	z
A0	-1.86937	0.0	-1.86937
A1	0.0	-1.86937	1.86937
A2	-3.50911	3.50911	3.50911

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-1.73452887124	-0.101697405678	1.73856189969	-0.015386	-0.012456	0.039644	T	T	T
Fe	-5.27502082144	1.54772132046	3.4142939235	0.127115	-0.055701	-0.087484	T	T	T
Fe	-3.57645030732	1.73441608522	1.73036417681	-0.111729	0.068157	0.04784	T	T	T

Parameter	Value
nbands	21
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2
Fe	potpaw_PBE/Fe/POTCAR	201d71adcb39575fc20d69f0abd331ae9c01ed2e

1.23 11/eos-exp/f+8 11 eos_dash_exp f_plus_8

	x	y	z
A0	-1.88105	0.0	-1.88105
A1	0.0	-1.88105	1.88105
A2	-3.53104	3.53104	3.53104

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-1.72649034784	-0.11573354282	1.73674863604	-0.016594	-0.002774	0.032443	T	T	T
Fe	-5.28013390733	1.54597101428	3.41783536417	0.029827	-0.01744	-0.039596	T	T	T
Fe	-3.59105574483	1.73852252854	1.7286359998	-0.013233	0.020213	0.007153	T	T	T

Parameter	Value
nbands	21
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2
Fe	potpaw_PBE/Fe/POTCAR	201d71adcb39575fc20d69f0abd331ae9c01ed2e

1.24 11/eos-exp/f-10 11 eos_dash_exp f_dash_10

	x	y	z
A0	-1.77014	0.0	-1.77014
A1	0.0	-1.77014	1.77014
A2	-3.32284	3.32284	3.32284

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-1.7975784663	-0.01829295971	1.78049380651	-0.007299	0.023676	-0.013472	T	T	T
Fe	-0.0656240800248	0.0224466618076	0.0395349460384	0.084793	-0.065991	-0.04627	T	T	T
Fe	-3.53058745368	1.7228162979	1.74035124745	-0.077494	0.042315	0.059741	T	T	T

Parameter	Value
nbands	21
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2
Fe	potpaw_PBE/Fe/POTCAR	201d71adcb39575fc20d69f0abd331ae9c01ed2e

1.25 11/eos-exp/f-12 11 eos_dash_exp f_dash_12

	x	y	z
A0	-1.75693	0.0	-1.75693
A1	0.0	-1.75693	1.75693
A2	-3.29804	3.29804	3.29804

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-1.80588201814	-0.00576933899531	1.78487378934	-0.004797	0.023557	-0.019673	T	T	T
Fe	-0.0889524804644	0.0361683086543	0.057258635695	0.086292	-0.05927	-0.035757	T	T	T
Fe	-3.52375550139	1.72137103034	1.74304757497	-0.081495	0.035713	0.05543	T	T	T

Parameter	Value
nbands	21
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2
Fe	potpaw_PBE/Fe/POTCAR	201d71adcb39575fc20d69f0abd331ae9c01ed2e

1.26 11/eos-exp/f-15 11 eos_dash_exp f_dash_15

	x	y	z
A0	-1.73673	0.0	-1.73673
A1	0.0	-1.73673	1.73673
A2	-3.26013	3.26013	3.26013

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-1.81850401219	0.0184814979188	1.7846748897	-0.013651	0.006945	0.022302	T	T	T
Fe	-0.121256908412	0.0564193466513	0.0901670119937	0.073536	-0.071854	-0.082079	T	T	T
Fe	-3.5167390794	1.71477915543	1.7482480983	-0.059885	0.064909	0.059777	T	T	T

Parameter	Value
nbands	21
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2
Fe	potpaw_PBE/Fe/POTCAR	201d71adcb39575fc20d69f0abd331ae9c01ed2e

1.27 11/eos-exp/f-2 11 eos_dash_exp f_dash_2

	x	y	z
A0	-1.8211	0.0	-1.8211
A1	0.0	-1.8211	1.8211
A2	-3.41851	3.41851	3.41851

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-1.76538350661	-0.067067453209	1.76453861606	-0.008756	0.02094	-0.003441	T	T	T
Fe	-3.39061275864	3.3875708672	3.38853117003	0.024749	-0.062564	-0.052235	T	T	T
Fe	-3.56063373475	1.72930658601	1.73015021391	-0.015993	0.041624	0.055675	T	T	T

Parameter	Value
nbands	21
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2
Fe	potpaw_PBE/Fe/POTCAR	201d71adcb39575fc20d69f0abd331ae9c01ed2e

1.28 11/eos-exp/f-4 11 eos_dash_exp f_dash_4

	x	y	z
A0	-1.80863	0.0	-1.80863
A1	0.0	-1.80863	1.80863
A2	-3.3951	3.3951	3.3951

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-1.77477734473	-0.0548385641908	1.77147863672	0.018222	-8.4e-05	-0.038433	T	T	T
Fe	-3.38991272702	3.37906159113	3.38279256816	0.054526	-0.094194	-0.078195	T	T	T
Fe	-3.55193992824	1.72558697306	1.72894879512	-0.072747	0.094278	0.116628	T	T	T

Parameter	Value
nbands	21
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2
Fe	potpaw_PBE/Fe/POTCAR	201d71adcb39575fc20d69f0abd331ae9c01ed2e

1.29 11/eos-exp/f-6 11 eos_dash_exp f_dash_6

	x	y	z
A0	-1.79598	0.0	-1.79598
A1	0.0	-1.79598	1.79598
A2	-3.37135	3.37135	3.37135

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-1.78297699606	-0.0446680285269	1.77821103953	0.028987	-0.000194	-0.062433	T	T	T
Fe	-0.0156774252598	-0.000431572871362	0.00517398273374	0.050099	-0.112472	-0.086264	T	T	T
Fe	-3.54662557868	1.7235596014	1.72848497774	-0.079085	0.112666	0.148697	T	T	T

Parameter	Value
nbands	21
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2
Fe	potpaw_PBE/Fe/POTCAR	201d71adcb39575fc20d69f0abd331ae9c01ed2e

1.30 11/eos-exp/f-8 11 eos_dash_exp f_dash_8

	x	y	z
A0	-1.78315	0.0	-1.78315
A1	0.0	-1.78315	1.78315
A2	-3.34727	3.34727	3.34727

species	x	y	z	fx	fy	fz	free x	free y	free z
Al	-1.78874833405	-0.029531043967	1.77374404304	-0.022672	0.030355	0.013661	T	T	T
Fe	-0.0461476403345	0.00738880489013	0.0220586228803	0.121535	-0.072896	-0.06196	T	T	T
Fe	-3.53446402561	1.72468223908	1.74014733408	-0.098863	0.042541	0.048299	T	T	T

Parameter	Value
nbands	21
encut	375.0
sigma	0.1
prec	Normal
kpts	[12, 12, 5]
xc	PBE
txt	-
gamma	True

Al	potpaw_PBE/Al/POTCAR	c8d9ecb0b6ebec0256c5f5072cee4de6a046dac2
Fe	potpaw_PBE/Fe/POTCAR	201d71adcb39575fc20d69f0abd331ae9c01ed2e

2 Tabulating the results in column mode

We can use column view to see the results in a tabular like form. For example, here we capture the VOLUME and TOTAL_ENERGY properties.

ITEM	VOLUME	TOTAL_ENERGY
* Using org-entries like a database
** Generating the entries
* 10/eos-exp/f+0 :10:eos_dash_exp:f_plus₀:	41.7621235495	-13.997605
* 10/eos-exp/f+10 :10:eos_dash_exp:f_plus₁₀:	45.9384934449	-13.874719
* 10/eos-exp/f+12 :10:eos_dash_exp:f_plus₁₂:	46.7733446838	-13.826981
* 10/eos-exp/f+15 :10:eos_dash_exp:f_plus₁₅:	48.0264189364	-13.744565
* 10/eos-exp/f+2 :10:eos_dash_exp:f_plus₂:	42.5973719405	-13.991505
* 10/eos-exp/f+4 :10:eos_dash_exp:f_plus₄:	43.4325784041	-13.97507
* 10/eos-exp/f+6 :10:eos_dash_exp:f_plus₆:	44.2677528152	-13.949606
* 10/eos-exp/f+8 :10:eos_dash_exp:f_plus₈:	45.10318841	-13.915655
* 10/eos-exp/f-10 :10:eos_dash_exp:f_dash₁₀:	37.5859624695	-13.819891
* 10/eos-exp/f-12 :10:eos_dash_exp:f_dash₁₂:	36.75057064	-13.730761
* 10/eos-exp/f-15 :10:eos_dash_exp:f_dash₁₅:	35.4979860465	-13.553386
* 10/eos-exp/f-2 :10:eos_dash_exp:f_dash₂:	40.9267763602	-13.991485
* 10/eos-exp/f-4 :10:eos_dash_exp:f_dash₄:	40.0914758244	-13.971902
* 10/eos-exp/f-6 :10:eos_dash_exp:f_dash₆:	39.2564933754	-13.938219
* 10/eos-exp/f-8 :10:eos_dash_exp:f_dash₈:	38.4210237246	-13.888471
* 11/eos-exp/f+0 :11:eos_dash_exp:f_plus₀:	34.7058033185	-20.281953
* 11/eos-exp/f+10 :11:eos_dash_exp:f_plus₁₀:	38.1763228931	-20.095119
* 11/eos-exp/f+12 :11:eos_dash_exp:f_plus₁₂:	38.870353968	-20.024412
* 11/eos-exp/f+15 :11:eos_dash_exp:f_plus₁₅:	39.9114994655	-19.90227
* 11/eos-exp/f+2 :11:eos_dash_exp:f_plus₂:	35.3998087733	-20.271762
* 11/eos-exp/f+4 :11:eos_dash_exp:f_plus₄:	36.0941730661	-20.24583
* 11/eos-exp/f+6 :11:eos_dash_exp:f_plus₆:	36.7882199604	-20.206804
* 11/eos-exp/f+8 :11:eos_dash_exp:f_plus₈:	37.4821566447	-20.157092
* 11/eos-exp/f-10 :11:eos_dash_exp:f_dash₁₀:	31.2353169019	-20.038179
* 11/eos-exp/f-12 :11:eos_dash_exp:f_dash₁₂:	30.5411995447	-19.912894
* 11/eos-exp/f-15 :11:eos_dash_exp:f_dash₁₅:	29.4999164187	-19.662755
* 11/eos-exp/f-2 :11:eos_dash_exp:f_dash₂:	34.0114931233	-20.275411
* 11/eos-exp/f-4 :11:eos_dash_exp:f_dash₄:	33.31756747	-20.249632
* 11/eos-exp/f-6 :11:eos_dash_exp:f_dash₆:	32.6233149155	-20.202731
* 11/eos-exp/f-8 :11:eos_dash_exp:f_dash₈:	31.9291793012	-20.133749
** Tabulating the results in column mode
** org-map-entries to get the data
** Getting specific data from a calculation
** Summary

That is more or less what we want, but we cannot use that table as a data source very directly. While you can use it as a data source, you just get a string of the whole table, e.g.

print data.__class__

<type 'str'>

You could parse that string, or try converting it to a table, but we skip that for now. In the next section we consider another approach that more directly gets at the data.

3 org-map-entries to get the data

Let us try a different approach. Here we map over headlines that match a criteria, and get specific data. We add a header of labels and horizontal line to the beginning of the table. Here we find the results tagged with 11, and that match f_dash_* (we actually use a regular expression).

(cons '(label volume energy) 
      (cons 'hline
            (org-map-entries
             (lambda ()
               (list (nth 4 (org-heading-components))
                     (org-entry-get (point) "VOLUME")
                     (org-entry-get (point) "TOTAL_ENERGY"))) 
             ;; this next line specifies headlines tagged with 11
             ;; and that match the regular expression in {}
             "+11+{f_dash_.*}")))

label	volume	energy
11/eos-exp/f-10	31.2353169019	-20.038179
11/eos-exp/f-12	30.5411995447	-19.912894
11/eos-exp/f-15	29.4999164187	-19.662755
11/eos-exp/f-2	34.0114931233	-20.275411
11/eos-exp/f-4	33.31756747	-20.249632
11/eos-exp/f-6	32.6233149155	-20.202731
11/eos-exp/f-8	31.9291793012	-20.133749

Now, since there are strings in the table (or in the results from the named code-block), we will have to cast the results to floats using a numpy array. Note it appears that we actually run the code block to get the results, they do not come from the table. The table is just helpful to know what data you are using.

import matplotlib.pyplot as plt
import numpy as np

print E

plt.plot(np.array(V), np.array(E), 'ko')
plt.xlabel('Volume $\AA^3$')
plt.ylabel('Energy (eV)')
plt.savefig('11-eos.png')

['-20.038179', '-19.912894', '-19.662755', '-20.275411', '-20.249632', '-20.202731', '-20.133749']

And here you have the figure. We extracted some data into an org-file in human readable form. Then, we extracted the data from those entries to a table, and finally plotted it.

4 Getting specific data from a calculation

Say you want the stress from some calculation. Each heading is identified by a CUSTOM_ID, so we can temporarily go to that headline, and get the property. Easy!

(save-excursion
  (org-open-link-from-string "[[#10/eos-exp/f+0]]")
  (org-entry-get (point) "STRESS"))

[-0.003191325893994518, -0.003191325893994518, -0.003191325893994518, -0.00042576435655845916, 0.00042576435655845916, 0.00042576435655845916]

Note, however, that the value returned is a string, so we need to convert it to numbers if we want to do anything with it, e.g. find the maximum component. Here, we eval the string in Python to make it a list, and then find the maximum value.

import numpy as np
print np.abs(np.array(eval(stress))).max()

0.00319132589399

Next, we get the unit cell from that calculation, so we can calculate the volume using python. The unit cell is stored in a table and we extract the unit cell vectors from it in the code block header.

import numpy as np

print('cell = {}'.format(np.array(data)))
print('Volume = {}'.format(np.linalg.det(np.array(data))))

cell = [[-1.98408  0.      -1.98408]
 [ 0.      -1.98408  1.98408]
 [-3.53625  3.53625  3.53625]]
Volume = 41.7621235495

Compare that to the volume we computed when the entry was generated, and you can see they are the same.

(save-excursion
  (org-open-link-from-string "[[#10/eos-exp/f+0]]")
  (org-entry-get (point) "VOLUME"))

41.7621235495

The last example is getting the formula for the calculation. The atoms positions are stored in a table in the entry, and the species for each atom is stored in the first column. We extract the species into a variable, then then get counts for each species, and finally construct a string representation of the formula.

(let* ((unique-species '())
      (counts))
  ;; first get unique species
  (mapcar (lambda (s) (add-to-list 'unique-species s)) species)

  ;; now get counts
  (setq counts
        (mapcar (lambda (s)
                  (--count (string= it s) species)) unique-species))

  ;; Now put them together
  (mapconcat 'identity (cl-mapcar (lambda (s n)
                  (format "%s%s" s n)) unique-species counts) ""))

Ni1Al2

Suppose we want to sort the elements alphabetically. We can make a list of cons cells of element and count, sort the list by element, and then put them back together. We do this in lisp.

(let* ((unique-species '())
      (counts))
  ;; first get unique species
  (mapcar (lambda (s) (add-to-list 'unique-species s)) species)

  ;; now get counts
  (setq counts
        (mapcar (lambda (s)
                  (--count (string= it s) species)) unique-species))

  (mapconcat (lambda (x)
               (format "%s%s" (car x) (cdr x)))
             (cl-sort
              (cl-mapcar (lambda (a b) (cons a b)) unique-species counts)
              'string-lessp :key 'car)
             ""))

Al2Ni1

That is not too bad. It is a little verbose, some of that could be put into a library to be reused. For example, here is the same code in Python for the unsorted formula

from collections import Counter
counts = Counter(species)
print ''.join(['{0}{1}'.format(x, counts[x]) for x in counts])

Ni1Al2

and for the sorted formula.

from collections import Counter
counts = Counter(species)
print ''.join(['{0}{1}'.format(x, counts[x]) for x in sorted(counts.keys())])

Al2Ni1

Obviously a lot must be happening behind the scenes in those short, dense python blocks. For example, the list comprehension syntax in Python is functionally similar to the mapcar code, and the join function is similar to the mapconcat code in lisp.

5 Summary

This has some potential. It is a hybrid approach to human and machine readable data, that enables inline analysis. You can mix programming languages, which is great if one language has unique capabilities or is just more convenient. There are some limitations, mostly that org-properties are read as strings, and they have to be converted to the right data type, e.g. numbers or lists or arrays, etc… But, these can be saved as forms that can be directly evaled in some languages. On the other hand, it is possible to do analysis on another machine where the original data does not exist.

This is a very different mental model of data than I am used to. We typically have thought about data in files, and paths to get to that data. Here, data is in headings, and we use links to get to the data. We also use different syntax to link data to code blocks. That means in some cases the code blocks cannot be run independently of this file.

org-mode source

Org-mode version = 8.2.7c

Sharing data via JSON files

Tue, 22 Oct 2013 14:39:56 EDT

1. Summary

In a previous post I discussed how to represent a single DFT calculation in a JSON file that could easily be shared, and reanalyzed. Here I look at sharing a series of calculations. I had previously run calculations to analyze an equation of state for Cu. Here we create a list of the JSON representations of each calculation, and save it in one overall JSON file. We will give the data some structure and documentation. JSON represents dictionaries very well, so we build a dictionary of the results and then "dump" that dictionary to a JSON file.

from jasp import *

LC = [3.5, 3.55, 3.6, 3.65, 3.7, 3.75]

data = {'doc':'JSON file containing a set of calculations for the equation of state of Cu'}

data['calculations'] = []

for a in LC:
    with jasp('../bulk/Cu-{0}'.format(a)) as calc:
        data['calculations'].append(calc.dict)

import json
with open('eos.json', 'wb') as f:
    f.write(json.dumps(data))

Now, you can view this eos.json file, and analyze it yourself as follows. In python we read the file in and convert it to a data structure using the json module.

import json

with open('eos.json', 'rb') as f:
    d = json.loads(f.read())

volumes =  [entry['data']['volume'] for entry in d['calculations']]
energies = [entry['data']['total_energy'] for entry in d['calculations']]

import matplotlib.pyplot as plt
plt.plot(volumes, energies)
plt.xlabel('Volume ($\AA$)')
plt.ylabel('Total energy (eV)')
plt.savefig('eos-from-json.png')
plt.show()

If you wanted to do further analysis you could. Suppose you wanted to know more detail about how that calculation was done? You can retrieve the INCAR, KPOINT, and POTCAR details for each calculation. Any parameter not listed here was not specified in the calculations.

import json

with open('eos.json', 'rb') as f:
    d = json.loads(f.read())

# print details for the first calculation in the list
print d['calculations'][0]['incar']
print d['calculations'][0]['input']
print d['calculations'][0]['potcar']

{u'doc': u'INCAR parameters', u'nbands': 9, u'encut': 350.0, u'prec': u'Normal'}
{u'kpts': [8, 8, 8], u'reciprocal': False, u'xc': u'PBE', u'kpts_nintersections': None, u'setups': None, u'txt': u'-', u'gamma': False}
[[u'Cu', u'potpaw_PBE/Cu/POTCAR', u'a44c591415026f53deb16a99ca3f06b1e69be10b']]

The POTCAR information contains the species, the path to the POTCAR, and a git-hash of the POTCAR file. That way you can tell if you used exactly the same file that I did. You can compute a git hash like this :

cat /home-research/jkitchin/src/vasp/potpaw_PBE/Cu/POTCAR | git hash-object --stdin

a44c591415026f53deb16a99ca3f06b1e69be10b

If you want to get the details of the geometry of some calculation, you do it this way:

import json

with open('eos.json', 'rb') as f:
    d = json.loads(f.read())

print d['calculations'][0]['atoms'].keys()
print 'cell = ', d['calculations'][0]['atoms']['cell']
print 'syms = ', d['calculations'][0]['atoms']['symbols']
print 'cpos = ', d['calculations'][0]['atoms']['positions']

[u'cell', u'symbols', u'positions', u'pbc', u'tags']
cell =  [[1.75, 1.75, 0.0], [0.0, 1.75, 1.75], [1.75, 0.0, 1.75]]
syms =  [u'Cu']
cpos =  [[0.0, 0.0, 0.0]]

You can do further analysis from there.

1 Summary

This looks ok as a data sharing mechanism. The json file here is pretty small (6.8 kb), and pretty easy to work with. Clearly some thought must go into how the data is structured so you know what to get, and how you get it. That could even be documented in the json file itself. For instance, each calculator has a doc element that describes what is in it. The json file we made above also has that data.

import json

with open('eos.json', 'rb') as f:
    d = json.loads(f.read())

print d['doc']
print
print d['calculations'][0]['doc']

JSON file containing a set of calculations for the equation of state of Cu

JSON representation of a VASP calculation.

energy is in eV
forces are in eV/\AA
stress is in GPa (sxx, syy, szz,  syz, sxz, sxy)
magnetic moments are in Bohr-magneton
The density of states is reported with E_f at 0 eV.
Volume is reported in \AA^3
Coordinates and cell parameters are reported in \AA

If atom-projected dos are included they are in the form:
{ados:{energy:data, {atom index: {orbital : dos}}}

For archival purposes you may want to put a creation date, contact data, etc… in the file too.

org-mode source

Integrating the Fermi distribution to compute entropy

Wed, 06 Mar 2013 09:39:42 EST

The Fermi distribution is defined by \(f(\epsilon) = \frac{1}{e^{(\epsilon - \mu)/(k T)} + 1}\). This function describes the occupation of energy levels at temperatures above absolute zero. We use this function to compute electronic entropy in a metal, which contains an integral of \(\int n(\epsilon) (f \ln f + (1 - f) \ln (1-f)) d\epsilon\), where \(n(\epsilon)\) is the electronic density of states. Here we plot the Fermi distribution function. It shows that well below the Fermi level the states are fully occupied, and well above the Fermi level, they are unoccupied. Near the Fermi level, the states go from occupied to unoccupied smoothly.

import numpy as np
import matplotlib.pyplot as plt

mu = 0
k = 8.6e-5
T = 1000

def f(e):
    return 1.0 / (np.exp((e - mu)/(k*T)) + 1)

espan = np.linspace(-10, 10, 200)
plt.plot(espan, f(espan))
plt.ylim([-0.1, 1.1])
plt.savefig('images/fermi-entropy-integrand-1.png')

Let us consider a simple density of states function, just a parabola. This could represent a s-band for example. We will use this function to explore the integral.

import numpy as np
import matplotlib.pyplot as plt

mu = 0
k = 8.6e-5
T = 1000

def f(e):
    return 1.0 / (np.exp((e - mu)/(k*T)) + 1)

def dos(e):
    d = (np.ones(e.shape) - 0.03 * e**2) 
    return d * (d > 0)
espan = np.linspace(-10, 10)

plt.plot(espan, dos(espan), label='Total dos')
plt.plot(espan, f(espan) * dos(espan), label='Occupied states')
plt.legend(loc='best')
plt.savefig('images/fermi-entropy-integrand-2.png')

Now, we consider the integral to compute the electronic entropy. The entropy is proportional to this integral.

\( \int n(\epsilon) (f \ln f + (1 - f) \ln (1-f)) d\epsilon \)

It looks straightforward to compute, but it turns out there is a wrinkle. Evaluating the integrand leads to nan elements because the ln(0) is -∞.

import numpy as np
mu = 0
k = 8.6e-5
T = 100

def fermi(e):
    return 1.0 / (np.exp((e - mu)/(k*T)) + 1)

espan = np.array([-20, -10, -5, 0.0, 5, 10])
f = fermi(espan)

print f * np.log(f)
print (1 - f) * np.log(1 - f)

[  0.00000000e+000   0.00000000e+000   0.00000000e+000  -3.46573590e-001
  -1.85216532e-250               nan]
[        nan         nan         nan -0.34657359  0.          0.        ]

In this case, these nan elements should be equal to zero (x ln(x) goes to zero as x goes to zero). So, we can just ignore those elements in the integral. Here is how to do that.

import numpy as np
import matplotlib.pyplot as plt

mu = 0
k = 8.6e-5
T = 1000

def fermi(e):
    return 1.0 / (np.exp((e - mu)/(k*T)) + 1)

def dos(e):
    d = (np.ones(e.shape) - 0.03 * e**2) 
    return d * (d > 0)

espan = np.linspace(-20, 10)
f = fermi(espan)
n = dos(espan)

g = n * (f * np.log(f) + (1 - f) * np.log(1 - f))

print np.trapz(espan, g) # nan because of the nan in the g vector
print g

plt.plot(espan, g)
plt.savefig('images/fermi-entropy-integrand-3.png')

# find the elements that are not nan
ind = np.logical_not(np.isnan(g))

# evaluate the integrand for only those points
print np.trapz(espan[ind], g[ind])

nan
[             nan              nan              nan              nan
              nan              nan              nan              nan
              nan              nan              nan              nan
              nan              nan              nan              nan
              nan              nan              nan              nan
              nan              nan              nan              nan
              nan              nan              nan              nan
  -9.75109643e-14  -1.05987106e-10  -1.04640574e-07  -8.76265644e-05
  -4.92684641e-02  -2.91047740e-01  -7.75652579e-04  -1.00962241e-06
  -1.06972936e-09  -1.00527877e-12  -8.36436686e-16  -6.48930917e-19
  -4.37946336e-22  -2.23285389e-25  -1.88578082e-29   0.00000000e+00
   0.00000000e+00   0.00000000e+00   0.00000000e+00   0.00000000e+00
   0.00000000e+00   0.00000000e+00]
0.208886080897

The integrand is pretty well behaved in the figure above. You do not see the full range of the x-axis, because the integrand evaluates to nan for very negative numbers. This causes the trapz function to return nan also. We can solve the problem by only integrating the parts that are not nan. We have to use numpy.logical_not to get an element-wise array of which elements are not nan. In this example, the integrand is not well sampled, so the area under that curve may not be very accurate.

org-mode source

The Kitchin Research Group

Using org-entries like a database

Table of Contents

1 Generating the entries

1.1 10/eos-exp/f+0 10 eos_dash_exp f_plus_0

1.2 10/eos-exp/f+10 10 eos_dash_exp f_plus_10

1.3 10/eos-exp/f+12 10 eos_dash_exp f_plus_12

1.4 10/eos-exp/f+15 10 eos_dash_exp f_plus_15

1.5 10/eos-exp/f+2 10 eos_dash_exp f_plus_2

1.6 10/eos-exp/f+4 10 eos_dash_exp f_plus_4

1.7 10/eos-exp/f+6 10 eos_dash_exp f_plus_6

1.8 10/eos-exp/f+8 10 eos_dash_exp f_plus_8

1.9 10/eos-exp/f-10 10 eos_dash_exp f_dash_10

1.10 10/eos-exp/f-12 10 eos_dash_exp f_dash_12

1.11 10/eos-exp/f-15 10 eos_dash_exp f_dash_15

1.12 10/eos-exp/f-2 10 eos_dash_exp f_dash_2

1.13 10/eos-exp/f-4 10 eos_dash_exp f_dash_4

1.14 10/eos-exp/f-6 10 eos_dash_exp f_dash_6

1.15 10/eos-exp/f-8 10 eos_dash_exp f_dash_8

1.16 11/eos-exp/f+0 11 eos_dash_exp f_plus_0

1.17 11/eos-exp/f+10 11 eos_dash_exp f_plus_10

1.18 11/eos-exp/f+12 11 eos_dash_exp f_plus_12

1.19 11/eos-exp/f+15 11 eos_dash_exp f_plus_15

1.20 11/eos-exp/f+2 11 eos_dash_exp f_plus_2

1.21 11/eos-exp/f+4 11 eos_dash_exp f_plus_4

1.22 11/eos-exp/f+6 11 eos_dash_exp f_plus_6

1.23 11/eos-exp/f+8 11 eos_dash_exp f_plus_8

1.24 11/eos-exp/f-10 11 eos_dash_exp f_dash_10

1.25 11/eos-exp/f-12 11 eos_dash_exp f_dash_12

1.26 11/eos-exp/f-15 11 eos_dash_exp f_dash_15

1.27 11/eos-exp/f-2 11 eos_dash_exp f_dash_2

1.28 11/eos-exp/f-4 11 eos_dash_exp f_dash_4

1.29 11/eos-exp/f-6 11 eos_dash_exp f_dash_6

1.30 11/eos-exp/f-8 11 eos_dash_exp f_dash_8

2 Tabulating the results in column mode

3 org-map-entries to get the data

4 Getting specific data from a calculation

5 Summary

Sharing data via JSON files

Table of Contents

1 Summary

Integrating the Fermi distribution to compute entropy