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#!/usr/bin/env python
"""\
C version: Dmitri Laikov
F77 version: Christoph van Wuellen, http://www.ccl.net
Python version: Richard P. Muller, 2002.
This subroutine is part of a set of subroutines that generate
Lebedev grids [1-6] for integration on a sphere. The original
C-code [1] was kindly provided by Dr. Dmitri N. Laikov and
translated into fortran by Dr. Christoph van Wuellen.
This subroutine was translated from C to fortran77 by hand.
Users of this code are asked to include reference [1] in their
publications, and in the user- and programmers-manuals
describing their codes.
[1] V.I. Lebedev, and D.N. Laikov
'A quadrature formula for the sphere of the 131st
algebraic order of accuracy'
Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
[2] V.I. Lebedev
'A quadrature formula for the sphere of 59th algebraic
order of accuracy'
Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.
[3] V.I. Lebedev, and A.L. Skorokhodov
'Quadrature formulas of orders 41, 47, and 53 for the sphere'
Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.
[4] V.I. Lebedev
'Spherical quadrature formulas exact to orders 25-29'
Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.
[5] V.I. Lebedev
'Quadratures on a sphere'
Computational Mathematics and Mathematical Physics, Vol. 16,
1976, pp. 10-24.
[6] V.I. Lebedev
'Values of the nodes and weights of ninth to seventeenth
order Gauss-Markov quadrature formulae invariant under the
octahedron group with inversion'
Computational Mathematics and Mathematical Physics, Vol. 15,
1975, pp. 44-51.
"""
from math import *
import numpy as np
from numpy import *
def genOh_a00(v):
"(0,0,a) etc. (6 points)"
a=1.0
v = 4.0 * np.pi * v;
return [(a,0,0,v),(-a,0,0,v),(0,a,0,v),(0,-a,0,v),(0,0,a,v),(0,0,-a,v)]
def genOh_aa0(v):
"(0,a,a) etc, a=1/sqrt(2) (12 points)"
a=sqrt(0.5)
v = 4.0 * np.pi * v;
return [(0,a,a,v),(0,-a,a,v),(0,a,-a,v),(0,-a,-a,v),
(a,0,a,v),(-a,0,a,v),(a,0,-a,v),(-a,0,-a,v),
(a,a,0,v),(-a,a,0,v),(a,-a,0,v),(-a,-a,0,v)]
def genOh_aaa(v):
"(a,a,a) etc, a=1/sqrt(3) (8 points)"
a = sqrt(1./3.)
v = 4.0 * np.pi * v;
return [(a,a,a,v),(-a,a,a,v),(a,-a,a,v),(-a,-a,a,v),
(a,a,-a,v),(-a,a,-a,v),(a,-a,-a,v),(-a,-a,-a,v)]
def genOh_aab(v,a):
"(a,a,b) etc, b=sqrt(1-2 a^2), a input (24 points)"
b = sqrt(1.0 - 2.0*a*a)
v = 4.0 * np.pi * v;
return [(a,a,b,v),(-a,a,b,v),(a,-a,b,v),(-a,-a,b,v),
(a,a,-b,v),(-a,a,-b,v),(a,-a,-b,v),(-a,-a,-b,v),
(a,b,a,v),(-a,b,a,v),(a,-b,a,v),(-a,-b,a,v),
(a,b,-a,v),(-a,b,-a,v),(a,-b,-a,v),(-a,-b,-a,v),
(b,a,a,v),(-b,a,a,v),(b,-a,a,v),(-b,-a,a,v),
(b,a,-a,v),(-b,a,-a,v),(b,-a,-a,v),(-b,-a,-a,v)]
def genOh_ab0(v,a):
"(a,b,0) etc, b=sqrt(1-a^2), a input (24 points)"
b=sqrt(1.0-a*a)
v = 4.0 * np.pi * v;
return [(a,b,0,v),(-a,b,0,v),(a,-b,0,v),(-a,-b,0,v),
(b,a,0,v),(-b,a,0,v),(b,-a,0,v),(-b,-a,0,v),
(a,0,b,v),(-a,0,b,v),(a,0,-b,v),(-a,0,-b,v),
(b,0,a,v),(-b,0,a,v),(b,0,-a,v),(-b,0,-a,v),
(0,a,b,v),(0,-a,b,v),(0,a,-b,v),(0,-a,-b,v),
(0,b,a,v),(0,-b,a,v),(0,b,-a,v),(0,-b,-a,v)]
def genOh_abc(v,a,b):
"(a,b,c) etc, c=sqrt(1-a^2-b^2), a,b input (48 points)"
c=sqrt(1.0 - a*a - b*b)
v = 4.0 * np.pi * v;
return [(a,b,c,v),(-a,b,c,v),(a,-b,c,v),(-a,-b,c,v),
(a,b,-c,v),(-a,b,-c,v),(a,-b,-c,v),(-a,-b,-c,v),
(a,c,b,v),(-a,c,b,v),(a,-c,b,v),(-a,-c,b,v),
(a,c,-b,v),(-a,c,-b,v),(a,-c,-b,v),(-a,-c,-b,v),
(b,a,c,v),(-b,a,c,v),(b,-a,c,v),(-b,-a,c,v),
(b,a,-c,v),(-b,a,-c,v),(b,-a,-c,v),(-b,-a,-c,v),
(b,c,a,v),(-b,c,a,v),(b,-c,a,v),(-b,-c,a,v),
(b,c,-a,v),(-b,c,-a,v),(b,-c,-a,v),(-b,-c,-a,v),
(c,a,b,v),(-c,a,b,v),(c,-a,b,v),(-c,-a,b,v),
(c,a,-b,v),(-c,a,-b,v),(c,-a,-b,v),(-c,-a,-b,v),
(c,b,a,v),(-c,b,a,v),(c,-b,a,v),(-c,-b,a,v),
(c,b,-a,v),(-c,b,-a,v),(c,-b,-a,v),(-c,-b,-a,v)]
def leb6():
return genOh_a00(0.1666666666666667)
def leb14():
return genOh_a00(0.06666666666666667)\
+ genOh_aaa(0.07500000000000000)
def leb26():
return genOh_a00(0.04761904761904762)\
+ genOh_aa0(0.03809523809523810) \
+ genOh_aaa(0.03214285714285714)
def leb38():
return genOh_a00(0.009523809523809524)\
+ genOh_aaa(0.3214285714285714E-1) \
+ genOh_ab0(0.2857142857142857E-1,0.4597008433809831E+0)
def leb50():
return genOh_a00(0.1269841269841270E-1)\
+ genOh_aa0(0.2257495590828924E-1) \
+ genOh_aaa(0.2109375000000000E-1) \
+ genOh_aab(0.2017333553791887E-1,0.3015113445777636E+0)
def leb74():
return genOh_a00(0.5130671797338464E-3)\
+ genOh_aa0(0.1660406956574204E-1) \
+ genOh_aaa(-0.2958603896103896E-1) \
+ genOh_aab(0.2657620708215946E-1,0.4803844614152614E+0) \
+ genOh_ab0(0.1652217099371571E-1,0.3207726489807764E+0)
def leb86():
return genOh_a00(0.1154401154401154E-1) \
+ genOh_aaa(0.1194390908585628E-1) \
+ genOh_aab(0.1111055571060340E-1,0.3696028464541502E+0) \
+ genOh_aab(0.1187650129453714E-1,0.6943540066026664E+0) \
+ genOh_ab0(0.1181230374690448E-1,0.3742430390903412E+0)
def leb110():
return genOh_a00(0.3828270494937162E-2) \
+ genOh_aaa(0.9793737512487512E-2) \
+ genOh_aab(0.8211737283191111E-2,0.1851156353447362E+0) \
+ genOh_aab(0.9942814891178103E-2,0.6904210483822922E+0) \
+ genOh_aab(0.9595471336070963E-2,0.3956894730559419E+0) \
+ genOh_ab0(0.9694996361663028E-2,0.4783690288121502E+0)
def leb146():
return genOh_a00(0.5996313688621381E-3) \
+ genOh_aa0(0.7372999718620756E-2) \
+ genOh_aaa(0.7210515360144488E-2) \
+ genOh_aab(0.7116355493117555E-2,0.6764410400114264E+0) \
+ genOh_aab(0.6753829486314477E-2,0.4174961227965453E+0) \
+ genOh_aab(0.7574394159054034E-2,0.1574676672039082E+0) \
+ genOh_abc(0.6991087353303262E-2,0.1403553811713183E+0,
0.4493328323269557E+0)
def leb170():
return genOh_a00(0.5544842902037365E-2) \
+ genOh_aa0(0.6071332770670752E-2) \
+ genOh_aaa(0.6383674773515093E-2) \
+ genOh_aab(0.5183387587747790E-2,0.2551252621114134E+0) \
+ genOh_aab(0.6317929009813725E-2,0.6743601460362766E+0) \
+ genOh_aab(0.6201670006589077E-2,0.4318910696719410E+0) \
+ genOh_ab0(0.5477143385137348E-2,0.2613931360335988E+0) \
+ genOh_abc(0.5968383987681156E-2,0.4990453161796037E+0,
0.1446630744325115E+0)
def leb194():
return genOh_a00(0.1782340447244611E-2) \
+ genOh_aa0(0.5716905949977102E-2) \
+ genOh_aaa(0.5573383178848738E-2) \
+ genOh_aab(0.5608704082587997E-2,0.6712973442695226E+0) \
+ genOh_aab(0.5158237711805383E-2,0.2892465627575439E+0) \
+ genOh_aab(0.5518771467273614E-2,0.4446933178717437E+0) \
+ genOh_aab(0.4106777028169394E-2,0.1299335447650067E+0) \
+ genOh_ab0(0.5051846064614808E-2,0.3457702197611283E+0) \
+ genOh_abc(0.5530248916233094E-2,0.1590417105383530E+0,
0.8360360154824589E+0)
def leb230():
v=-0.5522639919727325E-1;
out = genOh_a00(v);
v=0.4450274607445226E-2;
out = out + genOh_aaa(v);
a=0.4492044687397611E+0;
v=0.4496841067921404E-2;
out = out + genOh_aab(v,a);
a=0.2520419490210201E+0;
v=0.5049153450478750E-2;
out = out + genOh_aab(v,a);
a=0.6981906658447242E+0;
v=0.3976408018051883E-2;
out = out + genOh_aab(v,a);
a=0.6587405243460960E+0;
v=0.4401400650381014E-2;
out = out + genOh_aab(v,a);
a=0.4038544050097660E-1;
v=0.1724544350544401E-1;
out = out + genOh_aab(v,a);
a=0.5823842309715585E+0;
v=0.4231083095357343E-2;
out = out + genOh_ab0(v,a);
a=0.3545877390518688E+0;
v=0.5198069864064399E-2;
out = out + genOh_ab0(v,a);
a=0.2272181808998187E+0;
b=0.4864661535886647E+0;
v=0.4695720972568883E-2;
out = out + genOh_abc(v,a,b);
return out
def leb266():
v=-0.1313769127326952E-2;
out = genOh_a00(v);
v=-0.2522728704859336E-2;
out = out + genOh_aa0(v);
v=0.4186853881700583E-2;
out = out + genOh_aaa(v);
a=0.7039373391585475E+0;
v=0.5315167977810885E-2;
out = out + genOh_aab(v,a);
a=0.1012526248572414E+0;
v=0.4047142377086219E-2;
out = out + genOh_aab(v,a);
a=0.4647448726420539E+0;
v=0.4112482394406990E-2;
out = out + genOh_aab(v,a);
a=0.3277420654971629E+0;
v=0.3595584899758782E-2;
out = out + genOh_aab(v,a);
a=0.6620338663699974E+0;
v=0.4256131351428158E-2;
out = out + genOh_aab(v,a);
a=0.8506508083520399E+0;
v=0.4229582700647240E-2;
out = out + genOh_ab0(v,a);
a=0.3233484542692899E+0;
b=0.1153112011009701E+0;
v=0.4080914225780505E-2;
out = out + genOh_abc(v,a,b);
a=0.2314790158712601E+0;
b=0.5244939240922365E+0;
v=0.4071467593830964E-2;
out = out + genOh_abc(v,a,b);
return out
def leb302():
v=0.8545911725128148E-3;
out = genOh_a00(v);
v=0.3599119285025571E-2;
out = out + genOh_aaa(v);
a=0.3515640345570105E+0;
v=0.3449788424305883E-2;
out = out + genOh_aab(v,a);
a=0.6566329410219612E+0;
v=0.3604822601419882E-2;
out = out + genOh_aab(v,a);
a=0.4729054132581005E+0;
v=0.3576729661743367E-2;
out = out + genOh_aab(v,a);
a=0.9618308522614784E-1;
v=0.2352101413689164E-2;
out = out + genOh_aab(v,a);
a=0.2219645236294178E+0;
v=0.3108953122413675E-2;
out = out + genOh_aab(v,a);
a=0.7011766416089545E+0;
v=0.3650045807677255E-2;
out = out + genOh_aab(v,a);
a=0.2644152887060663E+0;
v=0.2982344963171804E-2;
out = out + genOh_ab0(v,a);
a=0.5718955891878961E+0;
v=0.3600820932216460E-2;
out = out + genOh_ab0(v,a);
a=0.2510034751770465E+0;
b=0.8000727494073952E+0;
v=0.3571540554273387E-2;
out = out + genOh_abc(v,a,b);
a=0.1233548532583327E+0;
b=0.4127724083168531E+0;
v=0.3392312205006170E-2;
out = out + genOh_abc(v,a,b);
return out
def leb350():
v=0.3006796749453936E-2;
out = genOh_a00(v);
v=0.3050627745650771E-2;
out = out + genOh_aaa(v);
a=0.7068965463912316E+0;
v=0.1621104600288991E-2;
out = out + genOh_aab(v,a);
a=0.4794682625712025E+0;
v=0.3005701484901752E-2;
out = out + genOh_aab(v,a);
a=0.1927533154878019E+0;
v=0.2990992529653774E-2;
out = out + genOh_aab(v,a);
a=0.6930357961327123E+0;
v=0.2982170644107595E-2;
out = out + genOh_aab(v,a);
a=0.3608302115520091E+0;
v=0.2721564237310992E-2;
out = out + genOh_aab(v,a);
a=0.6498486161496169E+0;
v=0.3033513795811141E-2;
out = out + genOh_aab(v,a);
a=0.1932945013230339E+0;
v=0.3007949555218533E-2;
out = out + genOh_ab0(v,a);
a=0.3800494919899303E+0;
v=0.2881964603055307E-2;
out = out + genOh_ab0(v,a);
a=0.2899558825499574E+0;
b=0.7934537856582316E+0;
v=0.2958357626535696E-2;
out = out + genOh_abc(v,a,b);
a=0.9684121455103957E-1;
b=0.8280801506686862E+0;
v=0.3036020026407088E-2;
out = out + genOh_abc(v,a,b);
a=0.1833434647041659E+0;
b=0.9074658265305127E+0;
v=0.2832187403926303E-2;
out = out + genOh_abc(v,a,b);
return out
def leb434():
v=0.5265897968224436E-3;
out = genOh_a00(v);
v=0.2548219972002607E-2;
out = out + genOh_aa0(v);
v=0.2512317418927307E-2;
out = out + genOh_aaa(v);
a=0.6909346307509111E+0;
v=0.2530403801186355E-2;
out = out + genOh_aab(v,a);
a=0.1774836054609158E+0;
v=0.2014279020918528E-2;
out = out + genOh_aab(v,a);
a=0.4914342637784746E+0;
v=0.2501725168402936E-2;
out = out + genOh_aab(v,a);
a=0.6456664707424256E+0;
v=0.2513267174597564E-2;
out = out + genOh_aab(v,a);
a=0.2861289010307638E+0;
v=0.2302694782227416E-2;
out = out + genOh_aab(v,a);
a=0.7568084367178018E-1;
v=0.1462495621594614E-2;
out = out + genOh_aab(v,a);
a=0.3927259763368002E+0;
v=0.2445373437312980E-2;
out = out + genOh_aab(v,a);
a=0.8818132877794288E+0;
v=0.2417442375638981E-2;
out = out + genOh_ab0(v,a);
a=0.9776428111182649E+0;
v=0.1910951282179532E-2;
out = out + genOh_ab0(v,a);
a=0.2054823696403044E+0;
b=0.8689460322872412E+0;
v=0.2416930044324775E-2;
out = out + genOh_abc(v,a,b);
a=0.5905157048925271E+0;
b=0.7999278543857286E+0;
v=0.2512236854563495E-2;
out = out + genOh_abc(v,a,b);
a=0.5550152361076807E+0;
b=0.7717462626915901E+0;
v=0.2496644054553086E-2;
out = out + genOh_abc(v,a,b);
a=0.9371809858553722E+0;
b=0.3344363145343455E+0;
v=0.2236607760437849E-2;
out = out + genOh_abc(v,a,b);
return out
def leb590():
v=0.3095121295306187E-3;
out = genOh_a00(v);
v=0.1852379698597489E-2;
out = out + genOh_aaa(v);
a=0.7040954938227469E+0;
v=0.1871790639277744E-2;
out = out + genOh_aab(v,a);
a=0.6807744066455243E+0;
v=0.1858812585438317E-2;
out = out + genOh_aab(v,a);
a=0.6372546939258752E+0;
v=0.1852028828296213E-2;
out = out + genOh_aab(v,a);
a=0.5044419707800358E+0;
v=0.1846715956151242E-2;
out = out + genOh_aab(v,a);
a=0.4215761784010967E+0;
v=0.1818471778162769E-2;
out = out + genOh_aab(v,a);
a=0.3317920736472123E+0;
v=0.1749564657281154E-2;
out = out + genOh_aab(v,a);
a=0.2384736701421887E+0;
v=0.1617210647254411E-2;
out = out + genOh_aab(v,a);
a=0.1459036449157763E+0;
v=0.1384737234851692E-2;
out = out + genOh_aab(v,a);
a=0.6095034115507196E-1;
v=0.9764331165051050E-3;
out = out + genOh_aab(v,a);
a=0.6116843442009876E+0;
v=0.1857161196774078E-2;
out = out + genOh_ab0(v,a);
a=0.3964755348199858E+0;
v=0.1705153996395864E-2;
out = out + genOh_ab0(v,a);
a=0.1724782009907724E+0;
v=0.1300321685886048E-2;
out = out + genOh_ab0(v,a);
a=0.5610263808622060E+0;
b=0.3518280927733519E+0;
v=0.1842866472905286E-2;
out = out + genOh_abc(v,a,b);
a=0.4742392842551980E+0;
b=0.2634716655937950E+0;
v=0.1802658934377451E-2;
out = out + genOh_abc(v,a,b);
a=0.5984126497885380E+0;
b=0.1816640840360209E+0;
v=0.1849830560443660E-2;
out = out + genOh_abc(v,a,b);
a=0.3791035407695563E+0;
b=0.1720795225656878E+0;
v=0.1713904507106709E-2;
out = out + genOh_abc(v,a,b);
a=0.2778673190586244E+0;
b=0.8213021581932511E-1;
v=0.1555213603396808E-2;
out = out + genOh_abc(v,a,b);
a=0.5033564271075117E+0;
b=0.8999205842074875E-1;
v=0.1802239128008525E-2;
out = out + genOh_abc(v,a,b);
return out
def leb770():
v=0.2192942088181184E-3;
out = genOh_a00(v);
v=0.1436433617319080E-2;
out = out + genOh_aa0(v);
v=0.1421940344335877E-2;
out = out + genOh_aaa(v);
a=0.5087204410502360E-1;
v=0.6798123511050502E-3;
out = out + genOh_aab(v,a);
a=0.1228198790178831E+0;
v=0.9913184235294912E-3;
out = out + genOh_aab(v,a);
a=0.2026890814408786E+0;
v=0.1180207833238949E-2;
out = out + genOh_aab(v,a);
a=0.2847745156464294E+0;
v=0.1296599602080921E-2;
out = out + genOh_aab(v,a);
a=0.3656719078978026E+0;
v=0.1365871427428316E-2;
out = out + genOh_aab(v,a);
a=0.4428264886713469E+0;
v=0.1402988604775325E-2;
out = out + genOh_aab(v,a);
a=0.5140619627249735E+0;
v=0.1418645563595609E-2;
out = out + genOh_aab(v,a);
a=0.6306401219166803E+0;
v=0.1421376741851662E-2;
out = out + genOh_aab(v,a);
a=0.6716883332022612E+0;
v=0.1423996475490962E-2;
out = out + genOh_aab(v,a);
a=0.6979792685336881E+0;
v=0.1431554042178567E-2;
out = out + genOh_aab(v,a);
a=0.1446865674195309E+0;
v=0.9254401499865368E-3;
out = out + genOh_ab0(v,a);
a=0.3390263475411216E+0;
v=0.1250239995053509E-2;
out = out + genOh_ab0(v,a);
a=0.5335804651263506E+0;
v=0.1394365843329230E-2;
out = out + genOh_ab0(v,a);
a=0.6944024393349413E-1;
b=0.2355187894242326E+0;
v=0.1127089094671749E-2;
out = out + genOh_abc(v,a,b);
a=0.2269004109529460E+0;
b=0.4102182474045730E+0;
v=0.1345753760910670E-2;
out = out + genOh_abc(v,a,b);
a=0.8025574607775339E-1;
b=0.6214302417481605E+0;
v=0.1424957283316783E-2;
out = out + genOh_abc(v,a,b);
a=0.1467999527896572E+0;
b=0.3245284345717394E+0;
v=0.1261523341237750E-2;
out = out + genOh_abc(v,a,b);
a=0.1571507769824727E+0;
b=0.5224482189696630E+0;
v=0.1392547106052696E-2;
out = out + genOh_abc(v,a,b);
a=0.2365702993157246E+0;
b=0.6017546634089558E+0;
v=0.1418761677877656E-2;
out = out + genOh_abc(v,a,b);
a=0.7714815866765732E-1;
b=0.4346575516141163E+0;
v=0.1338366684479554E-2;
out = out + genOh_abc(v,a,b);
a=0.3062936666210730E+0;
b=0.4908826589037616E+0;
v=0.1393700862676131E-2;
out = out + genOh_abc(v,a,b);
a=0.3822477379524787E+0;
b=0.5648768149099500E+0;
v=0.1415914757466932E-2;
out = out + genOh_abc(v,a,b);
return out
def leb974():
v=0.1438294190527431E-3;
out = genOh_a00(v);
v=0.1125772288287004E-2;
out = out + genOh_aaa(v);
a=0.4292963545341347E-1;
v=0.4948029341949241E-3;
out = out + genOh_aab(v,a);
a=0.1051426854086404E+0;
v=0.7357990109125470E-3;
out = out + genOh_aab(v,a);
a=0.1750024867623087E+0;
v=0.8889132771304384E-3;
out = out + genOh_aab(v,a);
a=0.2477653379650257E+0;
v=0.9888347838921435E-3;
out = out + genOh_aab(v,a);
a=0.3206567123955957E+0;
v=0.1053299681709471E-2;
out = out + genOh_aab(v,a);
a=0.3916520749849983E+0;
v=0.1092778807014578E-2;
out = out + genOh_aab(v,a);
a=0.4590825874187624E+0;
v=0.1114389394063227E-2;
out = out + genOh_aab(v,a);
a=0.5214563888415861E+0;
v=0.1123724788051555E-2;
out = out + genOh_aab(v,a);
a=0.6253170244654199E+0;
v=0.1125239325243814E-2;
out = out + genOh_aab(v,a);
a=0.6637926744523170E+0;
v=0.1126153271815905E-2;
out = out + genOh_aab(v,a);
a=0.6910410398498301E+0;
v=0.1130286931123841E-2;
out = out + genOh_aab(v,a);
a=0.7052907007457760E+0;
v=0.1134986534363955E-2;
out = out + genOh_aab(v,a);
a=0.1236686762657990E+0;
v=0.6823367927109931E-3;
out = out + genOh_ab0(v,a);
a=0.2940777114468387E+0;
v=0.9454158160447096E-3;
out = out + genOh_ab0(v,a);
a=0.4697753849207649E+0;
v=0.1074429975385679E-2;
out = out + genOh_ab0(v,a);
a=0.6334563241139567E+0;
v=0.1129300086569132E-2;
out = out + genOh_ab0(v,a);
a=0.5974048614181342E-1;
b=0.2029128752777523E+0;
v=0.8436884500901954E-3;
out = out + genOh_abc(v,a,b);
a=0.1375760408473636E+0;
b=0.4602621942484054E+0;
v=0.1075255720448885E-2;
out = out + genOh_abc(v,a,b);
a=0.3391016526336286E+0;
b=0.5030673999662036E+0;
v=0.1108577236864462E-2;
out = out + genOh_abc(v,a,b);
a=0.1271675191439820E+0;
b=0.2817606422442134E+0;
v=0.9566475323783357E-3;
out = out + genOh_abc(v,a,b);
a=0.2693120740413512E+0;
b=0.4331561291720157E+0;
v=0.1080663250717391E-2;
out = out + genOh_abc(v,a,b);
a=0.1419786452601918E+0;
b=0.6256167358580814E+0;
v=0.1126797131196295E-2;
out = out + genOh_abc(v,a,b);
a=0.6709284600738255E-1;
b=0.3798395216859157E+0;
v=0.1022568715358061E-2;
out = out + genOh_abc(v,a,b);
a=0.7057738183256172E-1;
b=0.5517505421423520E+0;
v=0.1108960267713108E-2;
out = out + genOh_abc(v,a,b);
a=0.2783888477882155E+0;
b=0.6029619156159187E+0;
v=0.1122790653435766E-2;
out = out + genOh_abc(v,a,b);
a=0.1979578938917407E+0;
b=0.3589606329589096E+0;
v=0.1032401847117460E-2;
out = out + genOh_abc(v,a,b);
a=0.2087307061103274E+0;
b=0.5348666438135476E+0;
v=0.1107249382283854E-2;
out = out + genOh_abc(v,a,b);
a=0.4055122137872836E+0;
b=0.5674997546074373E+0;
v=0.1121780048519972E-2;
out = out + genOh_abc(v,a,b);
return out
def leb1202():
v=0.1105189233267572E-3;
out = genOh_a00(v);
v=0.9205232738090741E-3;
out = out + genOh_aa0(v);
v=0.9133159786443561E-3;
out = out + genOh_aaa(v);
a=0.3712636449657089E-1;
v=0.3690421898017899E-3;
out = out + genOh_aab(v,a);
a=0.9140060412262223E-1;
v=0.5603990928680660E-3;
out = out + genOh_aab(v,a);
a=0.1531077852469906E+0;
v=0.6865297629282609E-3;
out = out + genOh_aab(v,a);
a=0.2180928891660612E+0;
v=0.7720338551145630E-3;
out = out + genOh_aab(v,a);
a=0.2839874532200175E+0;
v=0.8301545958894795E-3;
out = out + genOh_aab(v,a);
a=0.3491177600963764E+0;
v=0.8686692550179628E-3;
out = out + genOh_aab(v,a);
a=0.4121431461444309E+0;
v=0.8927076285846890E-3;
out = out + genOh_aab(v,a);
a=0.4718993627149127E+0;
v=0.9060820238568219E-3;
out = out + genOh_aab(v,a);
a=0.5273145452842337E+0;
v=0.9119777254940867E-3;
out = out + genOh_aab(v,a);
a=0.6209475332444019E+0;
v=0.9128720138604181E-3;
out = out + genOh_aab(v,a);
a=0.6569722711857291E+0;
v=0.9130714935691735E-3;
out = out + genOh_aab(v,a);
a=0.6841788309070143E+0;
v=0.9152873784554116E-3;
out = out + genOh_aab(v,a);
a=0.7012604330123631E+0;
v=0.9187436274321654E-3;
out = out + genOh_aab(v,a);
a=0.1072382215478166E+0;
v=0.5176977312965694E-3;
out = out + genOh_ab0(v,a);
a=0.2582068959496968E+0;
v=0.7331143682101417E-3;
out = out + genOh_ab0(v,a);
a=0.4172752955306717E+0;
v=0.8463232836379928E-3;
out = out + genOh_ab0(v,a);
a=0.5700366911792503E+0;
v=0.9031122694253992E-3;
out = out + genOh_ab0(v,a);
a=0.9827986018263947E+0;
b=0.1771774022615325E+0;
v=0.6485778453163257E-3;
out = out + genOh_abc(v,a,b);
a=0.9624249230326228E+0;
b=0.2475716463426288E+0;
v=0.7435030910982369E-3;
out = out + genOh_abc(v,a,b);
a=0.9402007994128811E+0;
b=0.3354616289066489E+0;
v=0.7998527891839054E-3;
out = out + genOh_abc(v,a,b);
a=0.9320822040143202E+0;
b=0.3173615246611977E+0;
v=0.8101731497468018E-3;
out = out + genOh_abc(v,a,b);
a=0.9043674199393299E+0;
b=0.4090268427085357E+0;
v=0.8483389574594331E-3;
out = out + genOh_abc(v,a,b);
a=0.8912407560074747E+0;
b=0.3854291150669224E+0;
v=0.8556299257311812E-3;
out = out + genOh_abc(v,a,b);
a=0.8676435628462708E+0;
b=0.4932221184851285E+0;
v=0.8803208679738260E-3;
out = out + genOh_abc(v,a,b);
a=0.8581979986041619E+0;
b=0.4785320675922435E+0;
v=0.8811048182425720E-3;
out = out + genOh_abc(v,a,b);
a=0.8396753624049856E+0;
b=0.4507422593157064E+0;
v=0.8850282341265444E-3;
out = out + genOh_abc(v,a,b);
a=0.8165288564022188E+0;
b=0.5632123020762100E+0;
v=0.9021342299040653E-3;
out = out + genOh_abc(v,a,b);
a=0.8015469370783529E+0;
b=0.5434303569693900E+0;
v=0.9010091677105086E-3;
out = out + genOh_abc(v,a,b);
a=0.7773563069070351E+0;
b=0.5123518486419871E+0;
v=0.9022692938426915E-3;
out = out + genOh_abc(v,a,b);
a=0.7661621213900394E+0;
b=0.6394279634749102E+0;
v=0.9158016174693465E-3;
out = out + genOh_abc(v,a,b);
a=0.7553584143533510E+0;
b=0.6269805509024392E+0;
v=0.9131578003189435E-3;
out = out + genOh_abc(v,a,b);
a=0.7344305757559503E+0;
b=0.6031161693096310E+0;
v=0.9107813579482705E-3;
out = out + genOh_abc(v,a,b);
a=0.7043837184021765E+0;
b=0.5693702498468441E+0;
v=0.9105760258970126E-3;
out = out + genOh_abc(v,a,b);
return out
def leb1454():
v=0.7777160743261247E-4;
out = genOh_a00(v);
v=0.7557646413004701E-3;
out = out + genOh_aaa(v);
a=0.3229290663413854E-1;
v=0.2841633806090617E-3;
out = out + genOh_aab(v,a);
a=0.8036733271462222E-1;
v=0.4374419127053555E-3;
out = out + genOh_aab(v,a);
a=0.1354289960531653E+0;
v=0.5417174740872172E-3;
out = out + genOh_aab(v,a);
a=0.1938963861114426E+0;
v=0.6148000891358593E-3;
out = out + genOh_aab(v,a);
a=0.2537343715011275E+0;
v=0.6664394485800705E-3;
out = out + genOh_aab(v,a);
a=0.3135251434752570E+0;
v=0.7025039356923220E-3;
out = out + genOh_aab(v,a);
a=0.3721558339375338E+0;
v=0.7268511789249627E-3;
out = out + genOh_aab(v,a);
a=0.4286809575195696E+0;
v=0.7422637534208629E-3;
out = out + genOh_aab(v,a);
a=0.4822510128282994E+0;
v=0.7509545035841214E-3;
out = out + genOh_aab(v,a);
a=0.5320679333566263E+0;
v=0.7548535057718401E-3;
out = out + genOh_aab(v,a);
a=0.6172998195394274E+0;
v=0.7554088969774001E-3;
out = out + genOh_aab(v,a);
a=0.6510679849127481E+0;
v=0.7553147174442808E-3;
out = out + genOh_aab(v,a);
a=0.6777315251687360E+0;
v=0.7564767653292297E-3;
out = out + genOh_aab(v,a);
a=0.6963109410648741E+0;
v=0.7587991808518730E-3;
out = out + genOh_aab(v,a);
a=0.7058935009831749E+0;
v=0.7608261832033027E-3;
out = out + genOh_aab(v,a);
a=0.9955546194091857E+0;
v=0.4021680447874916E-3;
out = out + genOh_ab0(v,a);
a=0.9734115901794209E+0;
v=0.5804871793945964E-3;
out = out + genOh_ab0(v,a);
a=0.9275693732388626E+0;
v=0.6792151955945159E-3;
out = out + genOh_ab0(v,a);
a=0.8568022422795103E+0;
v=0.7336741211286294E-3;
out = out + genOh_ab0(v,a);
a=0.7623495553719372E+0;
v=0.7581866300989608E-3;
out = out + genOh_ab0(v,a);
a=0.5707522908892223E+0;
b=0.4387028039889501E+0;
v=0.7538257859800743E-3;
out = out + genOh_abc(v,a,b);
a=0.5196463388403083E+0;
b=0.3858908414762617E+0;
v=0.7483517247053123E-3;
out = out + genOh_abc(v,a,b);
a=0.4646337531215351E+0;
b=0.3301937372343854E+0;
v=0.7371763661112059E-3;
out = out + genOh_abc(v,a,b);
a=0.4063901697557691E+0;
b=0.2725423573563777E+0;
v=0.7183448895756934E-3;
out = out + genOh_abc(v,a,b);
a=0.3456329466643087E+0;
b=0.2139510237495250E+0;
v=0.6895815529822191E-3;
out = out + genOh_abc(v,a,b);
a=0.2831395121050332E+0;
b=0.1555922309786647E+0;
v=0.6480105801792886E-3;
out = out + genOh_abc(v,a,b);
a=0.2197682022925330E+0;
b=0.9892878979686097E-1;
v=0.5897558896594636E-3;
out = out + genOh_abc(v,a,b);
a=0.1564696098650355E+0;
b=0.4598642910675510E-1;
v=0.5095708849247346E-3;
out = out + genOh_abc(v,a,b);
a=0.6027356673721295E+0;
b=0.3376625140173426E+0;
v=0.7536906428909755E-3;
out = out + genOh_abc(v,a,b);
a=0.5496032320255096E+0;
b=0.2822301309727988E+0;
v=0.7472505965575118E-3;
out = out + genOh_abc(v,a,b);
a=0.4921707755234567E+0;
b=0.2248632342592540E+0;
v=0.7343017132279698E-3;
out = out + genOh_abc(v,a,b);
a=0.4309422998598483E+0;
b=0.1666224723456479E+0;
v=0.7130871582177445E-3;
out = out + genOh_abc(v,a,b);
a=0.3664108182313672E+0;
b=0.1086964901822169E+0;
v=0.6817022032112776E-3;
out = out + genOh_abc(v,a,b);
a=0.2990189057758436E+0;
b=0.5251989784120085E-1;
v=0.6380941145604121E-3;
out = out + genOh_abc(v,a,b);
a=0.6268724013144998E+0;
b=0.2297523657550023E+0;
v=0.7550381377920310E-3;
out = out + genOh_abc(v,a,b);
a=0.5707324144834607E+0;
b=0.1723080607093800E+0;
v=0.7478646640144802E-3;
out = out + genOh_abc(v,a,b);
a=0.5096360901960365E+0;
b=0.1140238465390513E+0;
v=0.7335918720601220E-3;
out = out + genOh_abc(v,a,b);
a=0.4438729938312456E+0;
b=0.5611522095882537E-1;
v=0.7110120527658118E-3;
out = out + genOh_abc(v,a,b);
a=0.6419978471082389E+0;
b=0.1164174423140873E+0;
v=0.7571363978689501E-3;
out = out + genOh_abc(v,a,b);
a=0.5817218061802611E+0;
b=0.5797589531445219E-1;
v=0.7489908329079234E-3;
out = out + genOh_abc(v,a,b);
return out
def leb1730():
v=0.6309049437420976E-4;
out = genOh_a00(v);
v=0.6398287705571748E-3;
out = out + genOh_aa0(v);
v=0.6357185073530720E-3;
out = out + genOh_aaa(v);
a=0.2860923126194662E-1;
v=0.2221207162188168E-3;
out = out + genOh_aab(v,a);
a=0.7142556767711522E-1;
v=0.3475784022286848E-3;
out = out + genOh_aab(v,a);
a=0.1209199540995559E+0;
v=0.4350742443589804E-3;
out = out + genOh_aab(v,a);
a=0.1738673106594379E+0;
v=0.4978569136522127E-3;
out = out + genOh_aab(v,a);
a=0.2284645438467734E+0;
v=0.5435036221998053E-3;
out = out + genOh_aab(v,a);
a=0.2834807671701512E+0;
v=0.5765913388219542E-3;
out = out + genOh_aab(v,a);
a=0.3379680145467339E+0;
v=0.6001200359226003E-3;
out = out + genOh_aab(v,a);
a=0.3911355454819537E+0;
v=0.6162178172717512E-3;
out = out + genOh_aab(v,a);
a=0.4422860353001403E+0;
v=0.6265218152438485E-3;
out = out + genOh_aab(v,a);
a=0.4907781568726057E+0;
v=0.6323987160974212E-3;
out = out + genOh_aab(v,a);
a=0.5360006153211468E+0;
v=0.6350767851540569E-3;
out = out + genOh_aab(v,a);
a=0.6142105973596603E+0;
v=0.6354362775297107E-3;
out = out + genOh_aab(v,a);
a=0.6459300387977504E+0;
v=0.6352302462706235E-3;
out = out + genOh_aab(v,a);
a=0.6718056125089225E+0;
v=0.6358117881417972E-3;
out = out + genOh_aab(v,a);
a=0.6910888533186254E+0;
v=0.6373101590310117E-3;
out = out + genOh_aab(v,a);
a=0.7030467416823252E+0;
v=0.6390428961368665E-3;
out = out + genOh_aab(v,a);
a=0.8354951166354646E-1;
v=0.3186913449946576E-3;
out = out + genOh_ab0(v,a);
a=0.2050143009099486E+0;
v=0.4678028558591711E-3;
out = out + genOh_ab0(v,a);
a=0.3370208290706637E+0;
v=0.5538829697598626E-3;
out = out + genOh_ab0(v,a);
a=0.4689051484233963E+0;
v=0.6044475907190476E-3;
out = out + genOh_ab0(v,a);
a=0.5939400424557334E+0;
v=0.6313575103509012E-3;
out = out + genOh_ab0(v,a);
a=0.1394983311832261E+0;
b=0.4097581162050343E-1;
v=0.4078626431855630E-3;
out = out + genOh_abc(v,a,b);
a=0.1967999180485014E+0;
b=0.8851987391293348E-1;
v=0.4759933057812725E-3;