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qp2/src/becke_numerical_grid/angular.f
Anthony Scemama 24d9745056 Initial commit
2019-01-25 11:39:31 +01:00

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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