mirror of
https://github.com/QuantumPackage/qp2.git
synced 2024-11-12 08:23:39 +01:00
6952 lines
252 KiB
Fortran
6952 lines
252 KiB
Fortran
subroutine gen_oh(code, num, x, y, z, w, a, b, v)
|
|
implicit logical(a-z)
|
|
double precision x(*),y(*),z(*),w(*)
|
|
double precision a,b,v
|
|
integer code
|
|
integer num
|
|
double precision c
|
|
chvd
|
|
chvd This subroutine is part of a set of subroutines that generate
|
|
chvd Lebedev grids [1-6] for integration on a sphere. The original
|
|
chvd C-code [1] was kindly provided by Dr. Dmitri N. Laikov and
|
|
chvd translated into fortran by Dr. Christoph van Wuellen.
|
|
chvd This subroutine was translated from C to fortran77 by hand.
|
|
chvd
|
|
chvd Users of this code are asked to include reference [1] in their
|
|
chvd publications, and in the user- and programmers-manuals
|
|
chvd describing their codes.
|
|
chvd
|
|
chvd This code was distributed through CCL (http://www.ccl.net/).
|
|
chvd
|
|
chvd [1] V.I. Lebedev, and D.N. Laikov
|
|
chvd "A quadrature formula for the sphere of the 131st
|
|
chvd algebraic order of accuracy"
|
|
chvd Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
|
|
chvd
|
|
chvd [2] V.I. Lebedev
|
|
chvd "A quadrature formula for the sphere of 59th algebraic
|
|
chvd order of accuracy"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.
|
|
chvd
|
|
chvd [3] V.I. Lebedev, and A.L. Skorokhodov
|
|
chvd "Quadrature formulas of orders 41, 47, and 53 for the sphere"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.
|
|
chvd
|
|
chvd [4] V.I. Lebedev
|
|
chvd "Spherical quadrature formulas exact to orders 25-29"
|
|
chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.
|
|
chvd
|
|
chvd [5] V.I. Lebedev
|
|
chvd "Quadratures on a sphere"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 16,
|
|
chvd 1976, pp. 10-24.
|
|
chvd
|
|
chvd [6] V.I. Lebedev
|
|
chvd "Values of the nodes and weights of ninth to seventeenth
|
|
chvd order Gauss-Markov quadrature formulae invariant under the
|
|
chvd octahedron group with inversion"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 15,
|
|
chvd 1975, pp. 44-51.
|
|
chvd
|
|
cvw
|
|
cvw Given a point on a sphere (specified by a and b), generate all
|
|
cvw the equivalent points under Oh symmetry, making grid points with
|
|
cvw weight v.
|
|
cvw The variable num is increased by the number of different points
|
|
cvw generated.
|
|
cvw
|
|
cvw Depending on code, there are 6...48 different but equivalent
|
|
cvw points.
|
|
cvw
|
|
cvw code=1: (0,0,1) etc ( 6 points)
|
|
cvw code=2: (0,a,a) etc, a=1/sqrt(2) ( 12 points)
|
|
cvw code=3: (a,a,a) etc, a=1/sqrt(3) ( 8 points)
|
|
cvw code=4: (a,a,b) etc, b=sqrt(1-2 a^2) ( 24 points)
|
|
cvw code=5: (a,b,0) etc, b=sqrt(1-a^2), a input ( 24 points)
|
|
cvw code=6: (a,b,c) etc, c=sqrt(1-a^2-b^2), a/b input ( 48 points)
|
|
cvw
|
|
goto (1,2,3,4,5,6) code
|
|
write (6,*) 'Gen_Oh: Invalid Code'
|
|
stop
|
|
1 continue
|
|
a=1.0d0
|
|
x(1) = a
|
|
y(1) = 0.0d0
|
|
z(1) = 0.0d0
|
|
w(1) = v
|
|
x(2) = -a
|
|
y(2) = 0.0d0
|
|
z(2) = 0.0d0
|
|
w(2) = v
|
|
x(3) = 0.0d0
|
|
y(3) = a
|
|
z(3) = 0.0d0
|
|
w(3) = v
|
|
x(4) = 0.0d0
|
|
y(4) = -a
|
|
z(4) = 0.0d0
|
|
w(4) = v
|
|
x(5) = 0.0d0
|
|
y(5) = 0.0d0
|
|
z(5) = a
|
|
w(5) = v
|
|
x(6) = 0.0d0
|
|
y(6) = 0.0d0
|
|
z(6) = -a
|
|
w(6) = v
|
|
num=num+6
|
|
return
|
|
cvw
|
|
2 continue
|
|
a=sqrt(0.5d0)
|
|
x( 1) = 0d0
|
|
y( 1) = a
|
|
z( 1) = a
|
|
w( 1) = v
|
|
x( 2) = 0d0
|
|
y( 2) = -a
|
|
z( 2) = a
|
|
w( 2) = v
|
|
x( 3) = 0d0
|
|
y( 3) = a
|
|
z( 3) = -a
|
|
w( 3) = v
|
|
x( 4) = 0d0
|
|
y( 4) = -a
|
|
z( 4) = -a
|
|
w( 4) = v
|
|
x( 5) = a
|
|
y( 5) = 0d0
|
|
z( 5) = a
|
|
w( 5) = v
|
|
x( 6) = -a
|
|
y( 6) = 0d0
|
|
z( 6) = a
|
|
w( 6) = v
|
|
x( 7) = a
|
|
y( 7) = 0d0
|
|
z( 7) = -a
|
|
w( 7) = v
|
|
x( 8) = -a
|
|
y( 8) = 0d0
|
|
z( 8) = -a
|
|
w( 8) = v
|
|
x( 9) = a
|
|
y( 9) = a
|
|
z( 9) = 0d0
|
|
w( 9) = v
|
|
x(10) = -a
|
|
y(10) = a
|
|
z(10) = 0d0
|
|
w(10) = v
|
|
x(11) = a
|
|
y(11) = -a
|
|
z(11) = 0d0
|
|
w(11) = v
|
|
x(12) = -a
|
|
y(12) = -a
|
|
z(12) = 0d0
|
|
w(12) = v
|
|
num=num+12
|
|
return
|
|
cvw
|
|
3 continue
|
|
a = sqrt(1d0/3d0)
|
|
x(1) = a
|
|
y(1) = a
|
|
z(1) = a
|
|
w(1) = v
|
|
x(2) = -a
|
|
y(2) = a
|
|
z(2) = a
|
|
w(2) = v
|
|
x(3) = a
|
|
y(3) = -a
|
|
z(3) = a
|
|
w(3) = v
|
|
x(4) = -a
|
|
y(4) = -a
|
|
z(4) = a
|
|
w(4) = v
|
|
x(5) = a
|
|
y(5) = a
|
|
z(5) = -a
|
|
w(5) = v
|
|
x(6) = -a
|
|
y(6) = a
|
|
z(6) = -a
|
|
w(6) = v
|
|
x(7) = a
|
|
y(7) = -a
|
|
z(7) = -a
|
|
w(7) = v
|
|
x(8) = -a
|
|
y(8) = -a
|
|
z(8) = -a
|
|
w(8) = v
|
|
num=num+8
|
|
return
|
|
cvw
|
|
4 continue
|
|
b = sqrt(1d0 - 2d0*a*a)
|
|
x( 1) = a
|
|
y( 1) = a
|
|
z( 1) = b
|
|
w( 1) = v
|
|
x( 2) = -a
|
|
y( 2) = a
|
|
z( 2) = b
|
|
w( 2) = v
|
|
x( 3) = a
|
|
y( 3) = -a
|
|
z( 3) = b
|
|
w( 3) = v
|
|
x( 4) = -a
|
|
y( 4) = -a
|
|
z( 4) = b
|
|
w( 4) = v
|
|
x( 5) = a
|
|
y( 5) = a
|
|
z( 5) = -b
|
|
w( 5) = v
|
|
x( 6) = -a
|
|
y( 6) = a
|
|
z( 6) = -b
|
|
w( 6) = v
|
|
x( 7) = a
|
|
y( 7) = -a
|
|
z( 7) = -b
|
|
w( 7) = v
|
|
x( 8) = -a
|
|
y( 8) = -a
|
|
z( 8) = -b
|
|
w( 8) = v
|
|
x( 9) = a
|
|
y( 9) = b
|
|
z( 9) = a
|
|
w( 9) = v
|
|
x(10) = -a
|
|
y(10) = b
|
|
z(10) = a
|
|
w(10) = v
|
|
x(11) = a
|
|
y(11) = -b
|
|
z(11) = a
|
|
w(11) = v
|
|
x(12) = -a
|
|
y(12) = -b
|
|
z(12) = a
|
|
w(12) = v
|
|
x(13) = a
|
|
y(13) = b
|
|
z(13) = -a
|
|
w(13) = v
|
|
x(14) = -a
|
|
y(14) = b
|
|
z(14) = -a
|
|
w(14) = v
|
|
x(15) = a
|
|
y(15) = -b
|
|
z(15) = -a
|
|
w(15) = v
|
|
x(16) = -a
|
|
y(16) = -b
|
|
z(16) = -a
|
|
w(16) = v
|
|
x(17) = b
|
|
y(17) = a
|
|
z(17) = a
|
|
w(17) = v
|
|
x(18) = -b
|
|
y(18) = a
|
|
z(18) = a
|
|
w(18) = v
|
|
x(19) = b
|
|
y(19) = -a
|
|
z(19) = a
|
|
w(19) = v
|
|
x(20) = -b
|
|
y(20) = -a
|
|
z(20) = a
|
|
w(20) = v
|
|
x(21) = b
|
|
y(21) = a
|
|
z(21) = -a
|
|
w(21) = v
|
|
x(22) = -b
|
|
y(22) = a
|
|
z(22) = -a
|
|
w(22) = v
|
|
x(23) = b
|
|
y(23) = -a
|
|
z(23) = -a
|
|
w(23) = v
|
|
x(24) = -b
|
|
y(24) = -a
|
|
z(24) = -a
|
|
w(24) = v
|
|
num=num+24
|
|
return
|
|
cvw
|
|
5 continue
|
|
b=sqrt(1d0-a*a)
|
|
x( 1) = a
|
|
y( 1) = b
|
|
z( 1) = 0d0
|
|
w( 1) = v
|
|
x( 2) = -a
|
|
y( 2) = b
|
|
z( 2) = 0d0
|
|
w( 2) = v
|
|
x( 3) = a
|
|
y( 3) = -b
|
|
z( 3) = 0d0
|
|
w( 3) = v
|
|
x( 4) = -a
|
|
y( 4) = -b
|
|
z( 4) = 0d0
|
|
w( 4) = v
|
|
x( 5) = b
|
|
y( 5) = a
|
|
z( 5) = 0d0
|
|
w( 5) = v
|
|
x( 6) = -b
|
|
y( 6) = a
|
|
z( 6) = 0d0
|
|
w( 6) = v
|
|
x( 7) = b
|
|
y( 7) = -a
|
|
z( 7) = 0d0
|
|
w( 7) = v
|
|
x( 8) = -b
|
|
y( 8) = -a
|
|
z( 8) = 0d0
|
|
w( 8) = v
|
|
x( 9) = a
|
|
y( 9) = 0d0
|
|
z( 9) = b
|
|
w( 9) = v
|
|
x(10) = -a
|
|
y(10) = 0d0
|
|
z(10) = b
|
|
w(10) = v
|
|
x(11) = a
|
|
y(11) = 0d0
|
|
z(11) = -b
|
|
w(11) = v
|
|
x(12) = -a
|
|
y(12) = 0d0
|
|
z(12) = -b
|
|
w(12) = v
|
|
x(13) = b
|
|
y(13) = 0d0
|
|
z(13) = a
|
|
w(13) = v
|
|
x(14) = -b
|
|
y(14) = 0d0
|
|
z(14) = a
|
|
w(14) = v
|
|
x(15) = b
|
|
y(15) = 0d0
|
|
z(15) = -a
|
|
w(15) = v
|
|
x(16) = -b
|
|
y(16) = 0d0
|
|
z(16) = -a
|
|
w(16) = v
|
|
x(17) = 0d0
|
|
y(17) = a
|
|
z(17) = b
|
|
w(17) = v
|
|
x(18) = 0d0
|
|
y(18) = -a
|
|
z(18) = b
|
|
w(18) = v
|
|
x(19) = 0d0
|
|
y(19) = a
|
|
z(19) = -b
|
|
w(19) = v
|
|
x(20) = 0d0
|
|
y(20) = -a
|
|
z(20) = -b
|
|
w(20) = v
|
|
x(21) = 0d0
|
|
y(21) = b
|
|
z(21) = a
|
|
w(21) = v
|
|
x(22) = 0d0
|
|
y(22) = -b
|
|
z(22) = a
|
|
w(22) = v
|
|
x(23) = 0d0
|
|
y(23) = b
|
|
z(23) = -a
|
|
w(23) = v
|
|
x(24) = 0d0
|
|
y(24) = -b
|
|
z(24) = -a
|
|
w(24) = v
|
|
num=num+24
|
|
return
|
|
cvw
|
|
6 continue
|
|
c=sqrt(1d0 - a*a - b*b)
|
|
x( 1) = a
|
|
y( 1) = b
|
|
z( 1) = c
|
|
w( 1) = v
|
|
x( 2) = -a
|
|
y( 2) = b
|
|
z( 2) = c
|
|
w( 2) = v
|
|
x( 3) = a
|
|
y( 3) = -b
|
|
z( 3) = c
|
|
w( 3) = v
|
|
x( 4) = -a
|
|
y( 4) = -b
|
|
z( 4) = c
|
|
w( 4) = v
|
|
x( 5) = a
|
|
y( 5) = b
|
|
z( 5) = -c
|
|
w( 5) = v
|
|
x( 6) = -a
|
|
y( 6) = b
|
|
z( 6) = -c
|
|
w( 6) = v
|
|
x( 7) = a
|
|
y( 7) = -b
|
|
z( 7) = -c
|
|
w( 7) = v
|
|
x( 8) = -a
|
|
y( 8) = -b
|
|
z( 8) = -c
|
|
w( 8) = v
|
|
x( 9) = a
|
|
y( 9) = c
|
|
z( 9) = b
|
|
w( 9) = v
|
|
x(10) = -a
|
|
y(10) = c
|
|
z(10) = b
|
|
w(10) = v
|
|
x(11) = a
|
|
y(11) = -c
|
|
z(11) = b
|
|
w(11) = v
|
|
x(12) = -a
|
|
y(12) = -c
|
|
z(12) = b
|
|
w(12) = v
|
|
x(13) = a
|
|
y(13) = c
|
|
z(13) = -b
|
|
w(13) = v
|
|
x(14) = -a
|
|
y(14) = c
|
|
z(14) = -b
|
|
w(14) = v
|
|
x(15) = a
|
|
y(15) = -c
|
|
z(15) = -b
|
|
w(15) = v
|
|
x(16) = -a
|
|
y(16) = -c
|
|
z(16) = -b
|
|
w(16) = v
|
|
x(17) = b
|
|
y(17) = a
|
|
z(17) = c
|
|
w(17) = v
|
|
x(18) = -b
|
|
y(18) = a
|
|
z(18) = c
|
|
w(18) = v
|
|
x(19) = b
|
|
y(19) = -a
|
|
z(19) = c
|
|
w(19) = v
|
|
x(20) = -b
|
|
y(20) = -a
|
|
z(20) = c
|
|
w(20) = v
|
|
x(21) = b
|
|
y(21) = a
|
|
z(21) = -c
|
|
w(21) = v
|
|
x(22) = -b
|
|
y(22) = a
|
|
z(22) = -c
|
|
w(22) = v
|
|
x(23) = b
|
|
y(23) = -a
|
|
z(23) = -c
|
|
w(23) = v
|
|
x(24) = -b
|
|
y(24) = -a
|
|
z(24) = -c
|
|
w(24) = v
|
|
x(25) = b
|
|
y(25) = c
|
|
z(25) = a
|
|
w(25) = v
|
|
x(26) = -b
|
|
y(26) = c
|
|
z(26) = a
|
|
w(26) = v
|
|
x(27) = b
|
|
y(27) = -c
|
|
z(27) = a
|
|
w(27) = v
|
|
x(28) = -b
|
|
y(28) = -c
|
|
z(28) = a
|
|
w(28) = v
|
|
x(29) = b
|
|
y(29) = c
|
|
z(29) = -a
|
|
w(29) = v
|
|
x(30) = -b
|
|
y(30) = c
|
|
z(30) = -a
|
|
w(30) = v
|
|
x(31) = b
|
|
y(31) = -c
|
|
z(31) = -a
|
|
w(31) = v
|
|
x(32) = -b
|
|
y(32) = -c
|
|
z(32) = -a
|
|
w(32) = v
|
|
x(33) = c
|
|
y(33) = a
|
|
z(33) = b
|
|
w(33) = v
|
|
x(34) = -c
|
|
y(34) = a
|
|
z(34) = b
|
|
w(34) = v
|
|
x(35) = c
|
|
y(35) = -a
|
|
z(35) = b
|
|
w(35) = v
|
|
x(36) = -c
|
|
y(36) = -a
|
|
z(36) = b
|
|
w(36) = v
|
|
x(37) = c
|
|
y(37) = a
|
|
z(37) = -b
|
|
w(37) = v
|
|
x(38) = -c
|
|
y(38) = a
|
|
z(38) = -b
|
|
w(38) = v
|
|
x(39) = c
|
|
y(39) = -a
|
|
z(39) = -b
|
|
w(39) = v
|
|
x(40) = -c
|
|
y(40) = -a
|
|
z(40) = -b
|
|
w(40) = v
|
|
x(41) = c
|
|
y(41) = b
|
|
z(41) = a
|
|
w(41) = v
|
|
x(42) = -c
|
|
y(42) = b
|
|
z(42) = a
|
|
w(42) = v
|
|
x(43) = c
|
|
y(43) = -b
|
|
z(43) = a
|
|
w(43) = v
|
|
x(44) = -c
|
|
y(44) = -b
|
|
z(44) = a
|
|
w(44) = v
|
|
x(45) = c
|
|
y(45) = b
|
|
z(45) = -a
|
|
w(45) = v
|
|
x(46) = -c
|
|
y(46) = b
|
|
z(46) = -a
|
|
w(46) = v
|
|
x(47) = c
|
|
y(47) = -b
|
|
z(47) = -a
|
|
w(47) = v
|
|
x(48) = -c
|
|
y(48) = -b
|
|
z(48) = -a
|
|
w(48) = v
|
|
num=num+48
|
|
return
|
|
end
|
|
SUBROUTINE LD0006(X,Y,Z,W,N)
|
|
DOUBLE PRECISION X( 6)
|
|
DOUBLE PRECISION Y( 6)
|
|
DOUBLE PRECISION Z( 6)
|
|
DOUBLE PRECISION W( 6)
|
|
INTEGER N
|
|
DOUBLE PRECISION A,B,V
|
|
CVW
|
|
CVW LEBEDEV 6-POINT ANGULAR GRID
|
|
CVW
|
|
chvd
|
|
chvd This subroutine is part of a set of subroutines that generate
|
|
chvd Lebedev grids [1-6] for integration on a sphere. The original
|
|
chvd C-code [1] was kindly provided by Dr. Dmitri N. Laikov and
|
|
chvd translated into fortran by Dr. Christoph van Wuellen.
|
|
chvd This subroutine was translated using a C to fortran77 conversion
|
|
chvd tool written by Dr. Christoph van Wuellen.
|
|
chvd
|
|
chvd Users of this code are asked to include reference [1] in their
|
|
chvd publications, and in the user- and programmers-manuals
|
|
chvd describing their codes.
|
|
chvd
|
|
chvd This code was distributed through CCL (http://www.ccl.net/).
|
|
chvd
|
|
chvd [1] V.I. Lebedev, and D.N. Laikov
|
|
chvd "A quadrature formula for the sphere of the 131st
|
|
chvd algebraic order of accuracy"
|
|
chvd Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
|
|
chvd
|
|
chvd [2] V.I. Lebedev
|
|
chvd "A quadrature formula for the sphere of 59th algebraic
|
|
chvd order of accuracy"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.
|
|
chvd
|
|
chvd [3] V.I. Lebedev, and A.L. Skorokhodov
|
|
chvd "Quadrature formulas of orders 41, 47, and 53 for the sphere"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.
|
|
chvd
|
|
chvd [4] V.I. Lebedev
|
|
chvd "Spherical quadrature formulas exact to orders 25-29"
|
|
chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.
|
|
chvd
|
|
chvd [5] V.I. Lebedev
|
|
chvd "Quadratures on a sphere"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 16,
|
|
chvd 1976, pp. 10-24.
|
|
chvd
|
|
chvd [6] V.I. Lebedev
|
|
chvd "Values of the nodes and weights of ninth to seventeenth
|
|
chvd order Gauss-Markov quadrature formulae invariant under the
|
|
chvd octahedron group with inversion"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 15,
|
|
chvd 1975, pp. 44-51.
|
|
chvd
|
|
N=1
|
|
V=0.1666666666666667D+0
|
|
Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
N=N-1
|
|
RETURN
|
|
END
|
|
SUBROUTINE LD0014(X,Y,Z,W,N)
|
|
DOUBLE PRECISION X( 14)
|
|
DOUBLE PRECISION Y( 14)
|
|
DOUBLE PRECISION Z( 14)
|
|
DOUBLE PRECISION W( 14)
|
|
INTEGER N
|
|
DOUBLE PRECISION A,B,V
|
|
CVW
|
|
CVW LEBEDEV 14-POINT ANGULAR GRID
|
|
CVW
|
|
chvd
|
|
chvd This subroutine is part of a set of subroutines that generate
|
|
chvd Lebedev grids [1-6] for integration on a sphere. The original
|
|
chvd C-code [1] was kindly provided by Dr. Dmitri N. Laikov and
|
|
chvd translated into fortran by Dr. Christoph van Wuellen.
|
|
chvd This subroutine was translated using a C to fortran77 conversion
|
|
chvd tool written by Dr. Christoph van Wuellen.
|
|
chvd
|
|
chvd Users of this code are asked to include reference [1] in their
|
|
chvd publications, and in the user- and programmers-manuals
|
|
chvd describing their codes.
|
|
chvd
|
|
chvd This code was distributed through CCL (http://www.ccl.net/).
|
|
chvd
|
|
chvd [1] V.I. Lebedev, and D.N. Laikov
|
|
chvd "A quadrature formula for the sphere of the 131st
|
|
chvd algebraic order of accuracy"
|
|
chvd Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
|
|
chvd
|
|
chvd [2] V.I. Lebedev
|
|
chvd "A quadrature formula for the sphere of 59th algebraic
|
|
chvd order of accuracy"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.
|
|
chvd
|
|
chvd [3] V.I. Lebedev, and A.L. Skorokhodov
|
|
chvd "Quadrature formulas of orders 41, 47, and 53 for the sphere"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.
|
|
chvd
|
|
chvd [4] V.I. Lebedev
|
|
chvd "Spherical quadrature formulas exact to orders 25-29"
|
|
chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.
|
|
chvd
|
|
chvd [5] V.I. Lebedev
|
|
chvd "Quadratures on a sphere"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 16,
|
|
chvd 1976, pp. 10-24.
|
|
chvd
|
|
chvd [6] V.I. Lebedev
|
|
chvd "Values of the nodes and weights of ninth to seventeenth
|
|
chvd order Gauss-Markov quadrature formulae invariant under the
|
|
chvd octahedron group with inversion"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 15,
|
|
chvd 1975, pp. 44-51.
|
|
chvd
|
|
N=1
|
|
V=0.6666666666666667D-1
|
|
Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
V=0.7500000000000000D-1
|
|
Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
N=N-1
|
|
RETURN
|
|
END
|
|
SUBROUTINE LD0026(X,Y,Z,W,N)
|
|
DOUBLE PRECISION X( 26)
|
|
DOUBLE PRECISION Y( 26)
|
|
DOUBLE PRECISION Z( 26)
|
|
DOUBLE PRECISION W( 26)
|
|
INTEGER N
|
|
DOUBLE PRECISION A,B,V
|
|
CVW
|
|
CVW LEBEDEV 26-POINT ANGULAR GRID
|
|
CVW
|
|
chvd
|
|
chvd This subroutine is part of a set of subroutines that generate
|
|
chvd Lebedev grids [1-6] for integration on a sphere. The original
|
|
chvd C-code [1] was kindly provided by Dr. Dmitri N. Laikov and
|
|
chvd translated into fortran by Dr. Christoph van Wuellen.
|
|
chvd This subroutine was translated using a C to fortran77 conversion
|
|
chvd tool written by Dr. Christoph van Wuellen.
|
|
chvd
|
|
chvd Users of this code are asked to include reference [1] in their
|
|
chvd publications, and in the user- and programmers-manuals
|
|
chvd describing their codes.
|
|
chvd
|
|
chvd This code was distributed through CCL (http://www.ccl.net/).
|
|
chvd
|
|
chvd [1] V.I. Lebedev, and D.N. Laikov
|
|
chvd "A quadrature formula for the sphere of the 131st
|
|
chvd algebraic order of accuracy"
|
|
chvd Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
|
|
chvd
|
|
chvd [2] V.I. Lebedev
|
|
chvd "A quadrature formula for the sphere of 59th algebraic
|
|
chvd order of accuracy"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.
|
|
chvd
|
|
chvd [3] V.I. Lebedev, and A.L. Skorokhodov
|
|
chvd "Quadrature formulas of orders 41, 47, and 53 for the sphere"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.
|
|
chvd
|
|
chvd [4] V.I. Lebedev
|
|
chvd "Spherical quadrature formulas exact to orders 25-29"
|
|
chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.
|
|
chvd
|
|
chvd [5] V.I. Lebedev
|
|
chvd "Quadratures on a sphere"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 16,
|
|
chvd 1976, pp. 10-24.
|
|
chvd
|
|
chvd [6] V.I. Lebedev
|
|
chvd "Values of the nodes and weights of ninth to seventeenth
|
|
chvd order Gauss-Markov quadrature formulae invariant under the
|
|
chvd octahedron group with inversion"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 15,
|
|
chvd 1975, pp. 44-51.
|
|
chvd
|
|
N=1
|
|
V=0.4761904761904762D-1
|
|
Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
V=0.3809523809523810D-1
|
|
Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
V=0.3214285714285714D-1
|
|
Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
N=N-1
|
|
RETURN
|
|
END
|
|
SUBROUTINE LD0038(X,Y,Z,W,N)
|
|
DOUBLE PRECISION X( 38)
|
|
DOUBLE PRECISION Y( 38)
|
|
DOUBLE PRECISION Z( 38)
|
|
DOUBLE PRECISION W( 38)
|
|
INTEGER N
|
|
DOUBLE PRECISION A,B,V
|
|
CVW
|
|
CVW LEBEDEV 38-POINT ANGULAR GRID
|
|
CVW
|
|
chvd
|
|
chvd This subroutine is part of a set of subroutines that generate
|
|
chvd Lebedev grids [1-6] for integration on a sphere. The original
|
|
chvd C-code [1] was kindly provided by Dr. Dmitri N. Laikov and
|
|
chvd translated into fortran by Dr. Christoph van Wuellen.
|
|
chvd This subroutine was translated using a C to fortran77 conversion
|
|
chvd tool written by Dr. Christoph van Wuellen.
|
|
chvd
|
|
chvd Users of this code are asked to include reference [1] in their
|
|
chvd publications, and in the user- and programmers-manuals
|
|
chvd describing their codes.
|
|
chvd
|
|
chvd This code was distributed through CCL (http://www.ccl.net/).
|
|
chvd
|
|
chvd [1] V.I. Lebedev, and D.N. Laikov
|
|
chvd "A quadrature formula for the sphere of the 131st
|
|
chvd algebraic order of accuracy"
|
|
chvd Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
|
|
chvd
|
|
chvd [2] V.I. Lebedev
|
|
chvd "A quadrature formula for the sphere of 59th algebraic
|
|
chvd order of accuracy"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.
|
|
chvd
|
|
chvd [3] V.I. Lebedev, and A.L. Skorokhodov
|
|
chvd "Quadrature formulas of orders 41, 47, and 53 for the sphere"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.
|
|
chvd
|
|
chvd [4] V.I. Lebedev
|
|
chvd "Spherical quadrature formulas exact to orders 25-29"
|
|
chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.
|
|
chvd
|
|
chvd [5] V.I. Lebedev
|
|
chvd "Quadratures on a sphere"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 16,
|
|
chvd 1976, pp. 10-24.
|
|
chvd
|
|
chvd [6] V.I. Lebedev
|
|
chvd "Values of the nodes and weights of ninth to seventeenth
|
|
chvd order Gauss-Markov quadrature formulae invariant under the
|
|
chvd octahedron group with inversion"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 15,
|
|
chvd 1975, pp. 44-51.
|
|
chvd
|
|
N=1
|
|
V=0.9523809523809524D-2
|
|
Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
V=0.3214285714285714D-1
|
|
Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.4597008433809831D+0
|
|
V=0.2857142857142857D-1
|
|
Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
N=N-1
|
|
RETURN
|
|
END
|
|
SUBROUTINE LD0050(X,Y,Z,W,N)
|
|
DOUBLE PRECISION X( 50)
|
|
DOUBLE PRECISION Y( 50)
|
|
DOUBLE PRECISION Z( 50)
|
|
DOUBLE PRECISION W( 50)
|
|
INTEGER N
|
|
DOUBLE PRECISION A,B,V
|
|
CVW
|
|
CVW LEBEDEV 50-POINT ANGULAR GRID
|
|
CVW
|
|
chvd
|
|
chvd This subroutine is part of a set of subroutines that generate
|
|
chvd Lebedev grids [1-6] for integration on a sphere. The original
|
|
chvd C-code [1] was kindly provided by Dr. Dmitri N. Laikov and
|
|
chvd translated into fortran by Dr. Christoph van Wuellen.
|
|
chvd This subroutine was translated using a C to fortran77 conversion
|
|
chvd tool written by Dr. Christoph van Wuellen.
|
|
chvd
|
|
chvd Users of this code are asked to include reference [1] in their
|
|
chvd publications, and in the user- and programmers-manuals
|
|
chvd describing their codes.
|
|
chvd
|
|
chvd This code was distributed through CCL (http://www.ccl.net/).
|
|
chvd
|
|
chvd [1] V.I. Lebedev, and D.N. Laikov
|
|
chvd "A quadrature formula for the sphere of the 131st
|
|
chvd algebraic order of accuracy"
|
|
chvd Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
|
|
chvd
|
|
chvd [2] V.I. Lebedev
|
|
chvd "A quadrature formula for the sphere of 59th algebraic
|
|
chvd order of accuracy"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.
|
|
chvd
|
|
chvd [3] V.I. Lebedev, and A.L. Skorokhodov
|
|
chvd "Quadrature formulas of orders 41, 47, and 53 for the sphere"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.
|
|
chvd
|
|
chvd [4] V.I. Lebedev
|
|
chvd "Spherical quadrature formulas exact to orders 25-29"
|
|
chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.
|
|
chvd
|
|
chvd [5] V.I. Lebedev
|
|
chvd "Quadratures on a sphere"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 16,
|
|
chvd 1976, pp. 10-24.
|
|
chvd
|
|
chvd [6] V.I. Lebedev
|
|
chvd "Values of the nodes and weights of ninth to seventeenth
|
|
chvd order Gauss-Markov quadrature formulae invariant under the
|
|
chvd octahedron group with inversion"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 15,
|
|
chvd 1975, pp. 44-51.
|
|
chvd
|
|
N=1
|
|
V=0.1269841269841270D-1
|
|
Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
V=0.2257495590828924D-1
|
|
Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
V=0.2109375000000000D-1
|
|
Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.3015113445777636D+0
|
|
V=0.2017333553791887D-1
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
N=N-1
|
|
RETURN
|
|
END
|
|
SUBROUTINE LD0074(X,Y,Z,W,N)
|
|
DOUBLE PRECISION X( 74)
|
|
DOUBLE PRECISION Y( 74)
|
|
DOUBLE PRECISION Z( 74)
|
|
DOUBLE PRECISION W( 74)
|
|
INTEGER N
|
|
DOUBLE PRECISION A,B,V
|
|
CVW
|
|
CVW LEBEDEV 74-POINT ANGULAR GRID
|
|
CVW
|
|
chvd
|
|
chvd This subroutine is part of a set of subroutines that generate
|
|
chvd Lebedev grids [1-6] for integration on a sphere. The original
|
|
chvd C-code [1] was kindly provided by Dr. Dmitri N. Laikov and
|
|
chvd translated into fortran by Dr. Christoph van Wuellen.
|
|
chvd This subroutine was translated using a C to fortran77 conversion
|
|
chvd tool written by Dr. Christoph van Wuellen.
|
|
chvd
|
|
chvd Users of this code are asked to include reference [1] in their
|
|
chvd publications, and in the user- and programmers-manuals
|
|
chvd describing their codes.
|
|
chvd
|
|
chvd This code was distributed through CCL (http://www.ccl.net/).
|
|
chvd
|
|
chvd [1] V.I. Lebedev, and D.N. Laikov
|
|
chvd "A quadrature formula for the sphere of the 131st
|
|
chvd algebraic order of accuracy"
|
|
chvd Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
|
|
chvd
|
|
chvd [2] V.I. Lebedev
|
|
chvd "A quadrature formula for the sphere of 59th algebraic
|
|
chvd order of accuracy"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.
|
|
chvd
|
|
chvd [3] V.I. Lebedev, and A.L. Skorokhodov
|
|
chvd "Quadrature formulas of orders 41, 47, and 53 for the sphere"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.
|
|
chvd
|
|
chvd [4] V.I. Lebedev
|
|
chvd "Spherical quadrature formulas exact to orders 25-29"
|
|
chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.
|
|
chvd
|
|
chvd [5] V.I. Lebedev
|
|
chvd "Quadratures on a sphere"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 16,
|
|
chvd 1976, pp. 10-24.
|
|
chvd
|
|
chvd [6] V.I. Lebedev
|
|
chvd "Values of the nodes and weights of ninth to seventeenth
|
|
chvd order Gauss-Markov quadrature formulae invariant under the
|
|
chvd octahedron group with inversion"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 15,
|
|
chvd 1975, pp. 44-51.
|
|
chvd
|
|
N=1
|
|
V=0.5130671797338464D-3
|
|
Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
V=0.1660406956574204D-1
|
|
Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
V=-0.2958603896103896D-1
|
|
Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.4803844614152614D+0
|
|
V=0.2657620708215946D-1
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.3207726489807764D+0
|
|
V=0.1652217099371571D-1
|
|
Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
N=N-1
|
|
RETURN
|
|
END
|
|
SUBROUTINE LD0086(X,Y,Z,W,N)
|
|
DOUBLE PRECISION X( 86)
|
|
DOUBLE PRECISION Y( 86)
|
|
DOUBLE PRECISION Z( 86)
|
|
DOUBLE PRECISION W( 86)
|
|
INTEGER N
|
|
DOUBLE PRECISION A,B,V
|
|
CVW
|
|
CVW LEBEDEV 86-POINT ANGULAR GRID
|
|
CVW
|
|
chvd
|
|
chvd This subroutine is part of a set of subroutines that generate
|
|
chvd Lebedev grids [1-6] for integration on a sphere. The original
|
|
chvd C-code [1] was kindly provided by Dr. Dmitri N. Laikov and
|
|
chvd translated into fortran by Dr. Christoph van Wuellen.
|
|
chvd This subroutine was translated using a C to fortran77 conversion
|
|
chvd tool written by Dr. Christoph van Wuellen.
|
|
chvd
|
|
chvd Users of this code are asked to include reference [1] in their
|
|
chvd publications, and in the user- and programmers-manuals
|
|
chvd describing their codes.
|
|
chvd
|
|
chvd This code was distributed through CCL (http://www.ccl.net/).
|
|
chvd
|
|
chvd [1] V.I. Lebedev, and D.N. Laikov
|
|
chvd "A quadrature formula for the sphere of the 131st
|
|
chvd algebraic order of accuracy"
|
|
chvd Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
|
|
chvd
|
|
chvd [2] V.I. Lebedev
|
|
chvd "A quadrature formula for the sphere of 59th algebraic
|
|
chvd order of accuracy"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.
|
|
chvd
|
|
chvd [3] V.I. Lebedev, and A.L. Skorokhodov
|
|
chvd "Quadrature formulas of orders 41, 47, and 53 for the sphere"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.
|
|
chvd
|
|
chvd [4] V.I. Lebedev
|
|
chvd "Spherical quadrature formulas exact to orders 25-29"
|
|
chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.
|
|
chvd
|
|
chvd [5] V.I. Lebedev
|
|
chvd "Quadratures on a sphere"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 16,
|
|
chvd 1976, pp. 10-24.
|
|
chvd
|
|
chvd [6] V.I. Lebedev
|
|
chvd "Values of the nodes and weights of ninth to seventeenth
|
|
chvd order Gauss-Markov quadrature formulae invariant under the
|
|
chvd octahedron group with inversion"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 15,
|
|
chvd 1975, pp. 44-51.
|
|
chvd
|
|
N=1
|
|
V=0.1154401154401154D-1
|
|
Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
V=0.1194390908585628D-1
|
|
Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.3696028464541502D+0
|
|
V=0.1111055571060340D-1
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.6943540066026664D+0
|
|
V=0.1187650129453714D-1
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.3742430390903412D+0
|
|
V=0.1181230374690448D-1
|
|
Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
N=N-1
|
|
RETURN
|
|
END
|
|
SUBROUTINE LD0110(X,Y,Z,W,N)
|
|
DOUBLE PRECISION X( 110)
|
|
DOUBLE PRECISION Y( 110)
|
|
DOUBLE PRECISION Z( 110)
|
|
DOUBLE PRECISION W( 110)
|
|
INTEGER N
|
|
DOUBLE PRECISION A,B,V
|
|
CVW
|
|
CVW LEBEDEV 110-POINT ANGULAR GRID
|
|
CVW
|
|
chvd
|
|
chvd This subroutine is part of a set of subroutines that generate
|
|
chvd Lebedev grids [1-6] for integration on a sphere. The original
|
|
chvd C-code [1] was kindly provided by Dr. Dmitri N. Laikov and
|
|
chvd translated into fortran by Dr. Christoph van Wuellen.
|
|
chvd This subroutine was translated using a C to fortran77 conversion
|
|
chvd tool written by Dr. Christoph van Wuellen.
|
|
chvd
|
|
chvd Users of this code are asked to include reference [1] in their
|
|
chvd publications, and in the user- and programmers-manuals
|
|
chvd describing their codes.
|
|
chvd
|
|
chvd This code was distributed through CCL (http://www.ccl.net/).
|
|
chvd
|
|
chvd [1] V.I. Lebedev, and D.N. Laikov
|
|
chvd "A quadrature formula for the sphere of the 131st
|
|
chvd algebraic order of accuracy"
|
|
chvd Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
|
|
chvd
|
|
chvd [2] V.I. Lebedev
|
|
chvd "A quadrature formula for the sphere of 59th algebraic
|
|
chvd order of accuracy"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.
|
|
chvd
|
|
chvd [3] V.I. Lebedev, and A.L. Skorokhodov
|
|
chvd "Quadrature formulas of orders 41, 47, and 53 for the sphere"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.
|
|
chvd
|
|
chvd [4] V.I. Lebedev
|
|
chvd "Spherical quadrature formulas exact to orders 25-29"
|
|
chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.
|
|
chvd
|
|
chvd [5] V.I. Lebedev
|
|
chvd "Quadratures on a sphere"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 16,
|
|
chvd 1976, pp. 10-24.
|
|
chvd
|
|
chvd [6] V.I. Lebedev
|
|
chvd "Values of the nodes and weights of ninth to seventeenth
|
|
chvd order Gauss-Markov quadrature formulae invariant under the
|
|
chvd octahedron group with inversion"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 15,
|
|
chvd 1975, pp. 44-51.
|
|
chvd
|
|
N=1
|
|
V=0.3828270494937162D-2
|
|
Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
V=0.9793737512487512D-2
|
|
Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.1851156353447362D+0
|
|
V=0.8211737283191111D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.6904210483822922D+0
|
|
V=0.9942814891178103D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.3956894730559419D+0
|
|
V=0.9595471336070963D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.4783690288121502D+0
|
|
V=0.9694996361663028D-2
|
|
Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
N=N-1
|
|
RETURN
|
|
END
|
|
SUBROUTINE LD0146(X,Y,Z,W,N)
|
|
DOUBLE PRECISION X( 146)
|
|
DOUBLE PRECISION Y( 146)
|
|
DOUBLE PRECISION Z( 146)
|
|
DOUBLE PRECISION W( 146)
|
|
INTEGER N
|
|
DOUBLE PRECISION A,B,V
|
|
CVW
|
|
CVW LEBEDEV 146-POINT ANGULAR GRID
|
|
CVW
|
|
chvd
|
|
chvd This subroutine is part of a set of subroutines that generate
|
|
chvd Lebedev grids [1-6] for integration on a sphere. The original
|
|
chvd C-code [1] was kindly provided by Dr. Dmitri N. Laikov and
|
|
chvd translated into fortran by Dr. Christoph van Wuellen.
|
|
chvd This subroutine was translated using a C to fortran77 conversion
|
|
chvd tool written by Dr. Christoph van Wuellen.
|
|
chvd
|
|
chvd Users of this code are asked to include reference [1] in their
|
|
chvd publications, and in the user- and programmers-manuals
|
|
chvd describing their codes.
|
|
chvd
|
|
chvd This code was distributed through CCL (http://www.ccl.net/).
|
|
chvd
|
|
chvd [1] V.I. Lebedev, and D.N. Laikov
|
|
chvd "A quadrature formula for the sphere of the 131st
|
|
chvd algebraic order of accuracy"
|
|
chvd Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
|
|
chvd
|
|
chvd [2] V.I. Lebedev
|
|
chvd "A quadrature formula for the sphere of 59th algebraic
|
|
chvd order of accuracy"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.
|
|
chvd
|
|
chvd [3] V.I. Lebedev, and A.L. Skorokhodov
|
|
chvd "Quadrature formulas of orders 41, 47, and 53 for the sphere"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.
|
|
chvd
|
|
chvd [4] V.I. Lebedev
|
|
chvd "Spherical quadrature formulas exact to orders 25-29"
|
|
chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.
|
|
chvd
|
|
chvd [5] V.I. Lebedev
|
|
chvd "Quadratures on a sphere"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 16,
|
|
chvd 1976, pp. 10-24.
|
|
chvd
|
|
chvd [6] V.I. Lebedev
|
|
chvd "Values of the nodes and weights of ninth to seventeenth
|
|
chvd order Gauss-Markov quadrature formulae invariant under the
|
|
chvd octahedron group with inversion"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 15,
|
|
chvd 1975, pp. 44-51.
|
|
chvd
|
|
N=1
|
|
V=0.5996313688621381D-3
|
|
Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
V=0.7372999718620756D-2
|
|
Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
V=0.7210515360144488D-2
|
|
Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.6764410400114264D+0
|
|
V=0.7116355493117555D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.4174961227965453D+0
|
|
V=0.6753829486314477D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.1574676672039082D+0
|
|
V=0.7574394159054034D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.1403553811713183D+0
|
|
B=0.4493328323269557D+0
|
|
V=0.6991087353303262D-2
|
|
Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
N=N-1
|
|
RETURN
|
|
END
|
|
SUBROUTINE LD0170(X,Y,Z,W,N)
|
|
DOUBLE PRECISION X( 170)
|
|
DOUBLE PRECISION Y( 170)
|
|
DOUBLE PRECISION Z( 170)
|
|
DOUBLE PRECISION W( 170)
|
|
INTEGER N
|
|
DOUBLE PRECISION A,B,V
|
|
CVW
|
|
CVW LEBEDEV 170-POINT ANGULAR GRID
|
|
CVW
|
|
chvd
|
|
chvd This subroutine is part of a set of subroutines that generate
|
|
chvd Lebedev grids [1-6] for integration on a sphere. The original
|
|
chvd C-code [1] was kindly provided by Dr. Dmitri N. Laikov and
|
|
chvd translated into fortran by Dr. Christoph van Wuellen.
|
|
chvd This subroutine was translated using a C to fortran77 conversion
|
|
chvd tool written by Dr. Christoph van Wuellen.
|
|
chvd
|
|
chvd Users of this code are asked to include reference [1] in their
|
|
chvd publications, and in the user- and programmers-manuals
|
|
chvd describing their codes.
|
|
chvd
|
|
chvd This code was distributed through CCL (http://www.ccl.net/).
|
|
chvd
|
|
chvd [1] V.I. Lebedev, and D.N. Laikov
|
|
chvd "A quadrature formula for the sphere of the 131st
|
|
chvd algebraic order of accuracy"
|
|
chvd Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
|
|
chvd
|
|
chvd [2] V.I. Lebedev
|
|
chvd "A quadrature formula for the sphere of 59th algebraic
|
|
chvd order of accuracy"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.
|
|
chvd
|
|
chvd [3] V.I. Lebedev, and A.L. Skorokhodov
|
|
chvd "Quadrature formulas of orders 41, 47, and 53 for the sphere"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.
|
|
chvd
|
|
chvd [4] V.I. Lebedev
|
|
chvd "Spherical quadrature formulas exact to orders 25-29"
|
|
chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.
|
|
chvd
|
|
chvd [5] V.I. Lebedev
|
|
chvd "Quadratures on a sphere"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 16,
|
|
chvd 1976, pp. 10-24.
|
|
chvd
|
|
chvd [6] V.I. Lebedev
|
|
chvd "Values of the nodes and weights of ninth to seventeenth
|
|
chvd order Gauss-Markov quadrature formulae invariant under the
|
|
chvd octahedron group with inversion"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 15,
|
|
chvd 1975, pp. 44-51.
|
|
chvd
|
|
N=1
|
|
V=0.5544842902037365D-2
|
|
Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
V=0.6071332770670752D-2
|
|
Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
V=0.6383674773515093D-2
|
|
Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.2551252621114134D+0
|
|
V=0.5183387587747790D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.6743601460362766D+0
|
|
V=0.6317929009813725D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.4318910696719410D+0
|
|
V=0.6201670006589077D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.2613931360335988D+0
|
|
V=0.5477143385137348D-2
|
|
Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.4990453161796037D+0
|
|
B=0.1446630744325115D+0
|
|
V=0.5968383987681156D-2
|
|
Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
N=N-1
|
|
RETURN
|
|
END
|
|
SUBROUTINE LD0194(X,Y,Z,W,N)
|
|
DOUBLE PRECISION X( 194)
|
|
DOUBLE PRECISION Y( 194)
|
|
DOUBLE PRECISION Z( 194)
|
|
DOUBLE PRECISION W( 194)
|
|
INTEGER N
|
|
DOUBLE PRECISION A,B,V
|
|
CVW
|
|
CVW LEBEDEV 194-POINT ANGULAR GRID
|
|
CVW
|
|
chvd
|
|
chvd This subroutine is part of a set of subroutines that generate
|
|
chvd Lebedev grids [1-6] for integration on a sphere. The original
|
|
chvd C-code [1] was kindly provided by Dr. Dmitri N. Laikov and
|
|
chvd translated into fortran by Dr. Christoph van Wuellen.
|
|
chvd This subroutine was translated using a C to fortran77 conversion
|
|
chvd tool written by Dr. Christoph van Wuellen.
|
|
chvd
|
|
chvd Users of this code are asked to include reference [1] in their
|
|
chvd publications, and in the user- and programmers-manuals
|
|
chvd describing their codes.
|
|
chvd
|
|
chvd This code was distributed through CCL (http://www.ccl.net/).
|
|
chvd
|
|
chvd [1] V.I. Lebedev, and D.N. Laikov
|
|
chvd "A quadrature formula for the sphere of the 131st
|
|
chvd algebraic order of accuracy"
|
|
chvd Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
|
|
chvd
|
|
chvd [2] V.I. Lebedev
|
|
chvd "A quadrature formula for the sphere of 59th algebraic
|
|
chvd order of accuracy"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.
|
|
chvd
|
|
chvd [3] V.I. Lebedev, and A.L. Skorokhodov
|
|
chvd "Quadrature formulas of orders 41, 47, and 53 for the sphere"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.
|
|
chvd
|
|
chvd [4] V.I. Lebedev
|
|
chvd "Spherical quadrature formulas exact to orders 25-29"
|
|
chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.
|
|
chvd
|
|
chvd [5] V.I. Lebedev
|
|
chvd "Quadratures on a sphere"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 16,
|
|
chvd 1976, pp. 10-24.
|
|
chvd
|
|
chvd [6] V.I. Lebedev
|
|
chvd "Values of the nodes and weights of ninth to seventeenth
|
|
chvd order Gauss-Markov quadrature formulae invariant under the
|
|
chvd octahedron group with inversion"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 15,
|
|
chvd 1975, pp. 44-51.
|
|
chvd
|
|
N=1
|
|
V=0.1782340447244611D-2
|
|
Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
V=0.5716905949977102D-2
|
|
Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
V=0.5573383178848738D-2
|
|
Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.6712973442695226D+0
|
|
V=0.5608704082587997D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.2892465627575439D+0
|
|
V=0.5158237711805383D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.4446933178717437D+0
|
|
V=0.5518771467273614D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.1299335447650067D+0
|
|
V=0.4106777028169394D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.3457702197611283D+0
|
|
V=0.5051846064614808D-2
|
|
Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.1590417105383530D+0
|
|
B=0.8360360154824589D+0
|
|
V=0.5530248916233094D-2
|
|
Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
N=N-1
|
|
RETURN
|
|
END
|
|
SUBROUTINE LD0230(X,Y,Z,W,N)
|
|
DOUBLE PRECISION X( 230)
|
|
DOUBLE PRECISION Y( 230)
|
|
DOUBLE PRECISION Z( 230)
|
|
DOUBLE PRECISION W( 230)
|
|
INTEGER N
|
|
DOUBLE PRECISION A,B,V
|
|
CVW
|
|
CVW LEBEDEV 230-POINT ANGULAR GRID
|
|
CVW
|
|
chvd
|
|
chvd This subroutine is part of a set of subroutines that generate
|
|
chvd Lebedev grids [1-6] for integration on a sphere. The original
|
|
chvd C-code [1] was kindly provided by Dr. Dmitri N. Laikov and
|
|
chvd translated into fortran by Dr. Christoph van Wuellen.
|
|
chvd This subroutine was translated using a C to fortran77 conversion
|
|
chvd tool written by Dr. Christoph van Wuellen.
|
|
chvd
|
|
chvd Users of this code are asked to include reference [1] in their
|
|
chvd publications, and in the user- and programmers-manuals
|
|
chvd describing their codes.
|
|
chvd
|
|
chvd This code was distributed through CCL (http://www.ccl.net/).
|
|
chvd
|
|
chvd [1] V.I. Lebedev, and D.N. Laikov
|
|
chvd "A quadrature formula for the sphere of the 131st
|
|
chvd algebraic order of accuracy"
|
|
chvd Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
|
|
chvd
|
|
chvd [2] V.I. Lebedev
|
|
chvd "A quadrature formula for the sphere of 59th algebraic
|
|
chvd order of accuracy"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.
|
|
chvd
|
|
chvd [3] V.I. Lebedev, and A.L. Skorokhodov
|
|
chvd "Quadrature formulas of orders 41, 47, and 53 for the sphere"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.
|
|
chvd
|
|
chvd [4] V.I. Lebedev
|
|
chvd "Spherical quadrature formulas exact to orders 25-29"
|
|
chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.
|
|
chvd
|
|
chvd [5] V.I. Lebedev
|
|
chvd "Quadratures on a sphere"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 16,
|
|
chvd 1976, pp. 10-24.
|
|
chvd
|
|
chvd [6] V.I. Lebedev
|
|
chvd "Values of the nodes and weights of ninth to seventeenth
|
|
chvd order Gauss-Markov quadrature formulae invariant under the
|
|
chvd octahedron group with inversion"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 15,
|
|
chvd 1975, pp. 44-51.
|
|
chvd
|
|
N=1
|
|
V=-0.5522639919727325D-1
|
|
Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
V=0.4450274607445226D-2
|
|
Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.4492044687397611D+0
|
|
V=0.4496841067921404D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.2520419490210201D+0
|
|
V=0.5049153450478750D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.6981906658447242D+0
|
|
V=0.3976408018051883D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.6587405243460960D+0
|
|
V=0.4401400650381014D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.4038544050097660D-1
|
|
V=0.1724544350544401D-1
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.5823842309715585D+0
|
|
V=0.4231083095357343D-2
|
|
Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.3545877390518688D+0
|
|
V=0.5198069864064399D-2
|
|
Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.2272181808998187D+0
|
|
B=0.4864661535886647D+0
|
|
V=0.4695720972568883D-2
|
|
Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
N=N-1
|
|
RETURN
|
|
END
|
|
SUBROUTINE LD0266(X,Y,Z,W,N)
|
|
DOUBLE PRECISION X( 266)
|
|
DOUBLE PRECISION Y( 266)
|
|
DOUBLE PRECISION Z( 266)
|
|
DOUBLE PRECISION W( 266)
|
|
INTEGER N
|
|
DOUBLE PRECISION A,B,V
|
|
CVW
|
|
CVW LEBEDEV 266-POINT ANGULAR GRID
|
|
CVW
|
|
chvd
|
|
chvd This subroutine is part of a set of subroutines that generate
|
|
chvd Lebedev grids [1-6] for integration on a sphere. The original
|
|
chvd C-code [1] was kindly provided by Dr. Dmitri N. Laikov and
|
|
chvd translated into fortran by Dr. Christoph van Wuellen.
|
|
chvd This subroutine was translated using a C to fortran77 conversion
|
|
chvd tool written by Dr. Christoph van Wuellen.
|
|
chvd
|
|
chvd Users of this code are asked to include reference [1] in their
|
|
chvd publications, and in the user- and programmers-manuals
|
|
chvd describing their codes.
|
|
chvd
|
|
chvd This code was distributed through CCL (http://www.ccl.net/).
|
|
chvd
|
|
chvd [1] V.I. Lebedev, and D.N. Laikov
|
|
chvd "A quadrature formula for the sphere of the 131st
|
|
chvd algebraic order of accuracy"
|
|
chvd Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
|
|
chvd
|
|
chvd [2] V.I. Lebedev
|
|
chvd "A quadrature formula for the sphere of 59th algebraic
|
|
chvd order of accuracy"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.
|
|
chvd
|
|
chvd [3] V.I. Lebedev, and A.L. Skorokhodov
|
|
chvd "Quadrature formulas of orders 41, 47, and 53 for the sphere"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.
|
|
chvd
|
|
chvd [4] V.I. Lebedev
|
|
chvd "Spherical quadrature formulas exact to orders 25-29"
|
|
chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.
|
|
chvd
|
|
chvd [5] V.I. Lebedev
|
|
chvd "Quadratures on a sphere"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 16,
|
|
chvd 1976, pp. 10-24.
|
|
chvd
|
|
chvd [6] V.I. Lebedev
|
|
chvd "Values of the nodes and weights of ninth to seventeenth
|
|
chvd order Gauss-Markov quadrature formulae invariant under the
|
|
chvd octahedron group with inversion"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 15,
|
|
chvd 1975, pp. 44-51.
|
|
chvd
|
|
N=1
|
|
V=-0.1313769127326952D-2
|
|
Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
V=-0.2522728704859336D-2
|
|
Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
V=0.4186853881700583D-2
|
|
Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.7039373391585475D+0
|
|
V=0.5315167977810885D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.1012526248572414D+0
|
|
V=0.4047142377086219D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.4647448726420539D+0
|
|
V=0.4112482394406990D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.3277420654971629D+0
|
|
V=0.3595584899758782D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.6620338663699974D+0
|
|
V=0.4256131351428158D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.8506508083520399D+0
|
|
V=0.4229582700647240D-2
|
|
Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.3233484542692899D+0
|
|
B=0.1153112011009701D+0
|
|
V=0.4080914225780505D-2
|
|
Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.2314790158712601D+0
|
|
B=0.5244939240922365D+0
|
|
V=0.4071467593830964D-2
|
|
Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
N=N-1
|
|
RETURN
|
|
END
|
|
SUBROUTINE LD0302(X,Y,Z,W,N)
|
|
DOUBLE PRECISION X( 302)
|
|
DOUBLE PRECISION Y( 302)
|
|
DOUBLE PRECISION Z( 302)
|
|
DOUBLE PRECISION W( 302)
|
|
INTEGER N
|
|
DOUBLE PRECISION A,B,V
|
|
CVW
|
|
CVW LEBEDEV 302-POINT ANGULAR GRID
|
|
CVW
|
|
chvd
|
|
chvd This subroutine is part of a set of subroutines that generate
|
|
chvd Lebedev grids [1-6] for integration on a sphere. The original
|
|
chvd C-code [1] was kindly provided by Dr. Dmitri N. Laikov and
|
|
chvd translated into fortran by Dr. Christoph van Wuellen.
|
|
chvd This subroutine was translated using a C to fortran77 conversion
|
|
chvd tool written by Dr. Christoph van Wuellen.
|
|
chvd
|
|
chvd Users of this code are asked to include reference [1] in their
|
|
chvd publications, and in the user- and programmers-manuals
|
|
chvd describing their codes.
|
|
chvd
|
|
chvd This code was distributed through CCL (http://www.ccl.net/).
|
|
chvd
|
|
chvd [1] V.I. Lebedev, and D.N. Laikov
|
|
chvd "A quadrature formula for the sphere of the 131st
|
|
chvd algebraic order of accuracy"
|
|
chvd Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
|
|
chvd
|
|
chvd [2] V.I. Lebedev
|
|
chvd "A quadrature formula for the sphere of 59th algebraic
|
|
chvd order of accuracy"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.
|
|
chvd
|
|
chvd [3] V.I. Lebedev, and A.L. Skorokhodov
|
|
chvd "Quadrature formulas of orders 41, 47, and 53 for the sphere"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.
|
|
chvd
|
|
chvd [4] V.I. Lebedev
|
|
chvd "Spherical quadrature formulas exact to orders 25-29"
|
|
chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.
|
|
chvd
|
|
chvd [5] V.I. Lebedev
|
|
chvd "Quadratures on a sphere"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 16,
|
|
chvd 1976, pp. 10-24.
|
|
chvd
|
|
chvd [6] V.I. Lebedev
|
|
chvd "Values of the nodes and weights of ninth to seventeenth
|
|
chvd order Gauss-Markov quadrature formulae invariant under the
|
|
chvd octahedron group with inversion"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 15,
|
|
chvd 1975, pp. 44-51.
|
|
chvd
|
|
N=1
|
|
V=0.8545911725128148D-3
|
|
Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
V=0.3599119285025571D-2
|
|
Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.3515640345570105D+0
|
|
V=0.3449788424305883D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.6566329410219612D+0
|
|
V=0.3604822601419882D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.4729054132581005D+0
|
|
V=0.3576729661743367D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.9618308522614784D-1
|
|
V=0.2352101413689164D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.2219645236294178D+0
|
|
V=0.3108953122413675D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.7011766416089545D+0
|
|
V=0.3650045807677255D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.2644152887060663D+0
|
|
V=0.2982344963171804D-2
|
|
Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.5718955891878961D+0
|
|
V=0.3600820932216460D-2
|
|
Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.2510034751770465D+0
|
|
B=0.8000727494073952D+0
|
|
V=0.3571540554273387D-2
|
|
Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.1233548532583327D+0
|
|
B=0.4127724083168531D+0
|
|
V=0.3392312205006170D-2
|
|
Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
N=N-1
|
|
RETURN
|
|
END
|
|
SUBROUTINE LD0350(X,Y,Z,W,N)
|
|
DOUBLE PRECISION X( 350)
|
|
DOUBLE PRECISION Y( 350)
|
|
DOUBLE PRECISION Z( 350)
|
|
DOUBLE PRECISION W( 350)
|
|
INTEGER N
|
|
DOUBLE PRECISION A,B,V
|
|
CVW
|
|
CVW LEBEDEV 350-POINT ANGULAR GRID
|
|
CVW
|
|
chvd
|
|
chvd This subroutine is part of a set of subroutines that generate
|
|
chvd Lebedev grids [1-6] for integration on a sphere. The original
|
|
chvd C-code [1] was kindly provided by Dr. Dmitri N. Laikov and
|
|
chvd translated into fortran by Dr. Christoph van Wuellen.
|
|
chvd This subroutine was translated using a C to fortran77 conversion
|
|
chvd tool written by Dr. Christoph van Wuellen.
|
|
chvd
|
|
chvd Users of this code are asked to include reference [1] in their
|
|
chvd publications, and in the user- and programmers-manuals
|
|
chvd describing their codes.
|
|
chvd
|
|
chvd This code was distributed through CCL (http://www.ccl.net/).
|
|
chvd
|
|
chvd [1] V.I. Lebedev, and D.N. Laikov
|
|
chvd "A quadrature formula for the sphere of the 131st
|
|
chvd algebraic order of accuracy"
|
|
chvd Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
|
|
chvd
|
|
chvd [2] V.I. Lebedev
|
|
chvd "A quadrature formula for the sphere of 59th algebraic
|
|
chvd order of accuracy"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.
|
|
chvd
|
|
chvd [3] V.I. Lebedev, and A.L. Skorokhodov
|
|
chvd "Quadrature formulas of orders 41, 47, and 53 for the sphere"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.
|
|
chvd
|
|
chvd [4] V.I. Lebedev
|
|
chvd "Spherical quadrature formulas exact to orders 25-29"
|
|
chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.
|
|
chvd
|
|
chvd [5] V.I. Lebedev
|
|
chvd "Quadratures on a sphere"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 16,
|
|
chvd 1976, pp. 10-24.
|
|
chvd
|
|
chvd [6] V.I. Lebedev
|
|
chvd "Values of the nodes and weights of ninth to seventeenth
|
|
chvd order Gauss-Markov quadrature formulae invariant under the
|
|
chvd octahedron group with inversion"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 15,
|
|
chvd 1975, pp. 44-51.
|
|
chvd
|
|
N=1
|
|
V=0.3006796749453936D-2
|
|
Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
V=0.3050627745650771D-2
|
|
Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.7068965463912316D+0
|
|
V=0.1621104600288991D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.4794682625712025D+0
|
|
V=0.3005701484901752D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.1927533154878019D+0
|
|
V=0.2990992529653774D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.6930357961327123D+0
|
|
V=0.2982170644107595D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.3608302115520091D+0
|
|
V=0.2721564237310992D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.6498486161496169D+0
|
|
V=0.3033513795811141D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.1932945013230339D+0
|
|
V=0.3007949555218533D-2
|
|
Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.3800494919899303D+0
|
|
V=0.2881964603055307D-2
|
|
Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.2899558825499574D+0
|
|
B=0.7934537856582316D+0
|
|
V=0.2958357626535696D-2
|
|
Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.9684121455103957D-1
|
|
B=0.8280801506686862D+0
|
|
V=0.3036020026407088D-2
|
|
Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.1833434647041659D+0
|
|
B=0.9074658265305127D+0
|
|
V=0.2832187403926303D-2
|
|
Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
N=N-1
|
|
RETURN
|
|
END
|
|
SUBROUTINE LD0434(X,Y,Z,W,N)
|
|
DOUBLE PRECISION X( 434)
|
|
DOUBLE PRECISION Y( 434)
|
|
DOUBLE PRECISION Z( 434)
|
|
DOUBLE PRECISION W( 434)
|
|
INTEGER N
|
|
DOUBLE PRECISION A,B,V
|
|
CVW
|
|
CVW LEBEDEV 434-POINT ANGULAR GRID
|
|
CVW
|
|
chvd
|
|
chvd This subroutine is part of a set of subroutines that generate
|
|
chvd Lebedev grids [1-6] for integration on a sphere. The original
|
|
chvd C-code [1] was kindly provided by Dr. Dmitri N. Laikov and
|
|
chvd translated into fortran by Dr. Christoph van Wuellen.
|
|
chvd This subroutine was translated using a C to fortran77 conversion
|
|
chvd tool written by Dr. Christoph van Wuellen.
|
|
chvd
|
|
chvd Users of this code are asked to include reference [1] in their
|
|
chvd publications, and in the user- and programmers-manuals
|
|
chvd describing their codes.
|
|
chvd
|
|
chvd This code was distributed through CCL (http://www.ccl.net/).
|
|
chvd
|
|
chvd [1] V.I. Lebedev, and D.N. Laikov
|
|
chvd "A quadrature formula for the sphere of the 131st
|
|
chvd algebraic order of accuracy"
|
|
chvd Doklady Mathematics, Vol. 59, No. 3, 1999, pp. 477-481.
|
|
chvd
|
|
chvd [2] V.I. Lebedev
|
|
chvd "A quadrature formula for the sphere of 59th algebraic
|
|
chvd order of accuracy"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 50, 1995, pp. 283-286.
|
|
chvd
|
|
chvd [3] V.I. Lebedev, and A.L. Skorokhodov
|
|
chvd "Quadrature formulas of orders 41, 47, and 53 for the sphere"
|
|
chvd Russian Acad. Sci. Dokl. Math., Vol. 45, 1992, pp. 587-592.
|
|
chvd
|
|
chvd [4] V.I. Lebedev
|
|
chvd "Spherical quadrature formulas exact to orders 25-29"
|
|
chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99-107.
|
|
chvd
|
|
chvd [5] V.I. Lebedev
|
|
chvd "Quadratures on a sphere"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 16,
|
|
chvd 1976, pp. 10-24.
|
|
chvd
|
|
chvd [6] V.I. Lebedev
|
|
chvd "Values of the nodes and weights of ninth to seventeenth
|
|
chvd order Gauss-Markov quadrature formulae invariant under the
|
|
chvd octahedron group with inversion"
|
|
chvd Computational Mathematics and Mathematical Physics, Vol. 15,
|
|
chvd 1975, pp. 44-51.
|
|
chvd
|
|
N=1
|
|
V=0.5265897968224436D-3
|
|
Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
V=0.2548219972002607D-2
|
|
Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
V=0.2512317418927307D-2
|
|
Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.6909346307509111D+0
|
|
V=0.2530403801186355D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.1774836054609158D+0
|
|
V=0.2014279020918528D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.4914342637784746D+0
|
|
V=0.2501725168402936D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.6456664707424256D+0
|
|
V=0.2513267174597564D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.2861289010307638D+0
|
|
V=0.2302694782227416D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.7568084367178018D-1
|
|
V=0.1462495621594614D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.3927259763368002D+0
|
|
V=0.2445373437312980D-2
|
|
Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.8818132877794288D+0
|
|
V=0.2417442375638981D-2
|
|
Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.9776428111182649D+0
|
|
V=0.1910951282179532D-2
|
|
Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.2054823696403044D+0
|
|
B=0.8689460322872412D+0
|
|
V=0.2416930044324775D-2
|
|
Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.5905157048925271D+0
|
|
B=0.7999278543857286D+0
|
|
V=0.2512236854563495D-2
|
|
Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.5550152361076807D+0
|
|
B=0.7717462626915901D+0
|
|
V=0.2496644054553086D-2
|
|
Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
A=0.9371809858553722D+0
|
|
B=0.3344363145343455D+0
|
|
V=0.2236607760437849D-2
|
|
Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)
|
|
N=N-1
|
|
RETURN
|
|
END
|
|
SUBROUTINE LD0590(X,Y,Z,W,N)
|
|
DOUBLE PRECISION X( 590)
|
|
DOUBLE PRECISION Y( 590)
|
|
DOUBLE PRECISION Z( 590)
|
|
DOUBLE PRECISION W( 590)
|
|
INTEGER N
|
|
DOUBLE PRECISION A,B,V |