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6952 lines
252 KiB
Fortran
6952 lines
252 KiB
Fortran
subroutine gen_oh(code, num, x, y, z, w, a, b, v)


implicit logical(az)


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 [16] for integration on a sphere. The original


chvd Ccode [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 programmersmanuals


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. 477481.


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. 283286.


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. 587592.


chvd


chvd [4] V.I. Lebedev


chvd "Spherical quadrature formulas exact to orders 2529"


chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99107.


chvd


chvd [5] V.I. Lebedev


chvd "Quadratures on a sphere"


chvd Computational Mathematics and Mathematical Physics, Vol. 16,


chvd 1976, pp. 1024.


chvd


chvd [6] V.I. Lebedev


chvd "Values of the nodes and weights of ninth to seventeenth


chvd order GaussMarkov quadrature formulae invariant under the


chvd octahedron group with inversion"


chvd Computational Mathematics and Mathematical Physics, Vol. 15,


chvd 1975, pp. 4451.


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(12 a^2) ( 24 points)


cvw code=5: (a,b,0) etc, b=sqrt(1a^2), a input ( 24 points)


cvw code=6: (a,b,c) etc, c=sqrt(1a^2b^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(1d0a*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 6POINT ANGULAR GRID


CVW


chvd


chvd This subroutine is part of a set of subroutines that generate


chvd Lebedev grids [16] for integration on a sphere. The original


chvd Ccode [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 programmersmanuals


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. 477481.


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. 283286.


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. 587592.


chvd


chvd [4] V.I. Lebedev


chvd "Spherical quadrature formulas exact to orders 2529"


chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99107.


chvd


chvd [5] V.I. Lebedev


chvd "Quadratures on a sphere"


chvd Computational Mathematics and Mathematical Physics, Vol. 16,


chvd 1976, pp. 1024.


chvd


chvd [6] V.I. Lebedev


chvd "Values of the nodes and weights of ninth to seventeenth


chvd order GaussMarkov quadrature formulae invariant under the


chvd octahedron group with inversion"


chvd Computational Mathematics and Mathematical Physics, Vol. 15,


chvd 1975, pp. 4451.


chvd


N=1


V=0.1666666666666667D+0


Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)


N=N1


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 14POINT ANGULAR GRID


CVW


chvd


chvd This subroutine is part of a set of subroutines that generate


chvd Lebedev grids [16] for integration on a sphere. The original


chvd Ccode [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 programmersmanuals


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. 477481.


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. 283286.


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. 587592.


chvd


chvd [4] V.I. Lebedev


chvd "Spherical quadrature formulas exact to orders 2529"


chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99107.


chvd


chvd [5] V.I. Lebedev


chvd "Quadratures on a sphere"


chvd Computational Mathematics and Mathematical Physics, Vol. 16,


chvd 1976, pp. 1024.


chvd


chvd [6] V.I. Lebedev


chvd "Values of the nodes and weights of ninth to seventeenth


chvd order GaussMarkov quadrature formulae invariant under the


chvd octahedron group with inversion"


chvd Computational Mathematics and Mathematical Physics, Vol. 15,


chvd 1975, pp. 4451.


chvd


N=1


V=0.6666666666666667D1


Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)


V=0.7500000000000000D1


Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)


N=N1


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 26POINT ANGULAR GRID


CVW


chvd


chvd This subroutine is part of a set of subroutines that generate


chvd Lebedev grids [16] for integration on a sphere. The original


chvd Ccode [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 programmersmanuals


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. 477481.


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. 283286.


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. 587592.


chvd


chvd [4] V.I. Lebedev


chvd "Spherical quadrature formulas exact to orders 2529"


chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99107.


chvd


chvd [5] V.I. Lebedev


chvd "Quadratures on a sphere"


chvd Computational Mathematics and Mathematical Physics, Vol. 16,


chvd 1976, pp. 1024.


chvd


chvd [6] V.I. Lebedev


chvd "Values of the nodes and weights of ninth to seventeenth


chvd order GaussMarkov quadrature formulae invariant under the


chvd octahedron group with inversion"


chvd Computational Mathematics and Mathematical Physics, Vol. 15,


chvd 1975, pp. 4451.


chvd


N=1


V=0.4761904761904762D1


Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)


V=0.3809523809523810D1


Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V)


V=0.3214285714285714D1


Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)


N=N1


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 38POINT ANGULAR GRID


CVW


chvd


chvd This subroutine is part of a set of subroutines that generate


chvd Lebedev grids [16] for integration on a sphere. The original


chvd Ccode [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 programmersmanuals


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. 477481.


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. 283286.


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. 587592.


chvd


chvd [4] V.I. Lebedev


chvd "Spherical quadrature formulas exact to orders 2529"


chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99107.


chvd


chvd [5] V.I. Lebedev


chvd "Quadratures on a sphere"


chvd Computational Mathematics and Mathematical Physics, Vol. 16,


chvd 1976, pp. 1024.


chvd


chvd [6] V.I. Lebedev


chvd "Values of the nodes and weights of ninth to seventeenth


chvd order GaussMarkov quadrature formulae invariant under the


chvd octahedron group with inversion"


chvd Computational Mathematics and Mathematical Physics, Vol. 15,


chvd 1975, pp. 4451.


chvd


N=1


V=0.9523809523809524D2


Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)


V=0.3214285714285714D1


Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.4597008433809831D+0


V=0.2857142857142857D1


Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V)


N=N1


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 50POINT ANGULAR GRID


CVW


chvd


chvd This subroutine is part of a set of subroutines that generate


chvd Lebedev grids [16] for integration on a sphere. The original


chvd Ccode [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 programmersmanuals


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. 477481.


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. 283286.


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. 587592.


chvd


chvd [4] V.I. Lebedev


chvd "Spherical quadrature formulas exact to orders 2529"


chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99107.


chvd


chvd [5] V.I. Lebedev


chvd "Quadratures on a sphere"


chvd Computational Mathematics and Mathematical Physics, Vol. 16,


chvd 1976, pp. 1024.


chvd


chvd [6] V.I. Lebedev


chvd "Values of the nodes and weights of ninth to seventeenth


chvd order GaussMarkov quadrature formulae invariant under the


chvd octahedron group with inversion"


chvd Computational Mathematics and Mathematical Physics, Vol. 15,


chvd 1975, pp. 4451.


chvd


N=1


V=0.1269841269841270D1


Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)


V=0.2257495590828924D1


Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V)


V=0.2109375000000000D1


Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.3015113445777636D+0


V=0.2017333553791887D1


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


N=N1


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 74POINT ANGULAR GRID


CVW


chvd


chvd This subroutine is part of a set of subroutines that generate


chvd Lebedev grids [16] for integration on a sphere. The original


chvd Ccode [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 programmersmanuals


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. 477481.


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. 283286.


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. 587592.


chvd


chvd [4] V.I. Lebedev


chvd "Spherical quadrature formulas exact to orders 2529"


chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99107.


chvd


chvd [5] V.I. Lebedev


chvd "Quadratures on a sphere"


chvd Computational Mathematics and Mathematical Physics, Vol. 16,


chvd 1976, pp. 1024.


chvd


chvd [6] V.I. Lebedev


chvd "Values of the nodes and weights of ninth to seventeenth


chvd order GaussMarkov quadrature formulae invariant under the


chvd octahedron group with inversion"


chvd Computational Mathematics and Mathematical Physics, Vol. 15,


chvd 1975, pp. 4451.


chvd


N=1


V=0.5130671797338464D3


Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)


V=0.1660406956574204D1


Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V)


V=0.2958603896103896D1


Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.4803844614152614D+0


V=0.2657620708215946D1


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.3207726489807764D+0


V=0.1652217099371571D1


Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V)


N=N1


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 86POINT ANGULAR GRID


CVW


chvd


chvd This subroutine is part of a set of subroutines that generate


chvd Lebedev grids [16] for integration on a sphere. The original


chvd Ccode [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 programmersmanuals


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. 477481.


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. 283286.


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. 587592.


chvd


chvd [4] V.I. Lebedev


chvd "Spherical quadrature formulas exact to orders 2529"


chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99107.


chvd


chvd [5] V.I. Lebedev


chvd "Quadratures on a sphere"


chvd Computational Mathematics and Mathematical Physics, Vol. 16,


chvd 1976, pp. 1024.


chvd


chvd [6] V.I. Lebedev


chvd "Values of the nodes and weights of ninth to seventeenth


chvd order GaussMarkov quadrature formulae invariant under the


chvd octahedron group with inversion"


chvd Computational Mathematics and Mathematical Physics, Vol. 15,


chvd 1975, pp. 4451.


chvd


N=1


V=0.1154401154401154D1


Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)


V=0.1194390908585628D1


Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.3696028464541502D+0


V=0.1111055571060340D1


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.6943540066026664D+0


V=0.1187650129453714D1


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.3742430390903412D+0


V=0.1181230374690448D1


Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V)


N=N1


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 110POINT ANGULAR GRID


CVW


chvd


chvd This subroutine is part of a set of subroutines that generate


chvd Lebedev grids [16] for integration on a sphere. The original


chvd Ccode [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 programmersmanuals


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. 477481.


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. 283286.


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. 587592.


chvd


chvd [4] V.I. Lebedev


chvd "Spherical quadrature formulas exact to orders 2529"


chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99107.


chvd


chvd [5] V.I. Lebedev


chvd "Quadratures on a sphere"


chvd Computational Mathematics and Mathematical Physics, Vol. 16,


chvd 1976, pp. 1024.


chvd


chvd [6] V.I. Lebedev


chvd "Values of the nodes and weights of ninth to seventeenth


chvd order GaussMarkov quadrature formulae invariant under the


chvd octahedron group with inversion"


chvd Computational Mathematics and Mathematical Physics, Vol. 15,


chvd 1975, pp. 4451.


chvd


N=1


V=0.3828270494937162D2


Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)


V=0.9793737512487512D2


Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.1851156353447362D+0


V=0.8211737283191111D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.6904210483822922D+0


V=0.9942814891178103D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.3956894730559419D+0


V=0.9595471336070963D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.4783690288121502D+0


V=0.9694996361663028D2


Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V)


N=N1


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 146POINT ANGULAR GRID


CVW


chvd


chvd This subroutine is part of a set of subroutines that generate


chvd Lebedev grids [16] for integration on a sphere. The original


chvd Ccode [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 programmersmanuals


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. 477481.


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. 283286.


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. 587592.


chvd


chvd [4] V.I. Lebedev


chvd "Spherical quadrature formulas exact to orders 2529"


chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99107.


chvd


chvd [5] V.I. Lebedev


chvd "Quadratures on a sphere"


chvd Computational Mathematics and Mathematical Physics, Vol. 16,


chvd 1976, pp. 1024.


chvd


chvd [6] V.I. Lebedev


chvd "Values of the nodes and weights of ninth to seventeenth


chvd order GaussMarkov quadrature formulae invariant under the


chvd octahedron group with inversion"


chvd Computational Mathematics and Mathematical Physics, Vol. 15,


chvd 1975, pp. 4451.


chvd


N=1


V=0.5996313688621381D3


Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)


V=0.7372999718620756D2


Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V)


V=0.7210515360144488D2


Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.6764410400114264D+0


V=0.7116355493117555D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.4174961227965453D+0


V=0.6753829486314477D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.1574676672039082D+0


V=0.7574394159054034D2


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=0.6991087353303262D2


Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)


N=N1


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 170POINT ANGULAR GRID


CVW


chvd


chvd This subroutine is part of a set of subroutines that generate


chvd Lebedev grids [16] for integration on a sphere. The original


chvd Ccode [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 programmersmanuals


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. 477481.


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. 283286.


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. 587592.


chvd


chvd [4] V.I. Lebedev


chvd "Spherical quadrature formulas exact to orders 2529"


chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99107.


chvd


chvd [5] V.I. Lebedev


chvd "Quadratures on a sphere"


chvd Computational Mathematics and Mathematical Physics, Vol. 16,


chvd 1976, pp. 1024.


chvd


chvd [6] V.I. Lebedev


chvd "Values of the nodes and weights of ninth to seventeenth


chvd order GaussMarkov quadrature formulae invariant under the


chvd octahedron group with inversion"


chvd Computational Mathematics and Mathematical Physics, Vol. 15,


chvd 1975, pp. 4451.


chvd


N=1


V=0.5544842902037365D2


Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)


V=0.6071332770670752D2


Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V)


V=0.6383674773515093D2


Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.2551252621114134D+0


V=0.5183387587747790D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.6743601460362766D+0


V=0.6317929009813725D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.4318910696719410D+0


V=0.6201670006589077D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.2613931360335988D+0


V=0.5477143385137348D2


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=0.5968383987681156D2


Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)


N=N1


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 194POINT ANGULAR GRID


CVW


chvd


chvd This subroutine is part of a set of subroutines that generate


chvd Lebedev grids [16] for integration on a sphere. The original


chvd Ccode [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 programmersmanuals


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. 477481.


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. 283286.


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. 587592.


chvd


chvd [4] V.I. Lebedev


chvd "Spherical quadrature formulas exact to orders 2529"


chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99107.


chvd


chvd [5] V.I. Lebedev


chvd "Quadratures on a sphere"


chvd Computational Mathematics and Mathematical Physics, Vol. 16,


chvd 1976, pp. 1024.


chvd


chvd [6] V.I. Lebedev


chvd "Values of the nodes and weights of ninth to seventeenth


chvd order GaussMarkov quadrature formulae invariant under the


chvd octahedron group with inversion"


chvd Computational Mathematics and Mathematical Physics, Vol. 15,


chvd 1975, pp. 4451.


chvd


N=1


V=0.1782340447244611D2


Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)


V=0.5716905949977102D2


Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V)


V=0.5573383178848738D2


Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.6712973442695226D+0


V=0.5608704082587997D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.2892465627575439D+0


V=0.5158237711805383D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.4446933178717437D+0


V=0.5518771467273614D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.1299335447650067D+0


V=0.4106777028169394D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.3457702197611283D+0


V=0.5051846064614808D2


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=0.5530248916233094D2


Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)


N=N1


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 230POINT ANGULAR GRID


CVW


chvd


chvd This subroutine is part of a set of subroutines that generate


chvd Lebedev grids [16] for integration on a sphere. The original


chvd Ccode [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 programmersmanuals


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. 477481.


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. 283286.


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. 587592.


chvd


chvd [4] V.I. Lebedev


chvd "Spherical quadrature formulas exact to orders 2529"


chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99107.


chvd


chvd [5] V.I. Lebedev


chvd "Quadratures on a sphere"


chvd Computational Mathematics and Mathematical Physics, Vol. 16,


chvd 1976, pp. 1024.


chvd


chvd [6] V.I. Lebedev


chvd "Values of the nodes and weights of ninth to seventeenth


chvd order GaussMarkov quadrature formulae invariant under the


chvd octahedron group with inversion"


chvd Computational Mathematics and Mathematical Physics, Vol. 15,


chvd 1975, pp. 4451.


chvd


N=1


V=0.5522639919727325D1


Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)


V=0.4450274607445226D2


Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.4492044687397611D+0


V=0.4496841067921404D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.2520419490210201D+0


V=0.5049153450478750D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.6981906658447242D+0


V=0.3976408018051883D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.6587405243460960D+0


V=0.4401400650381014D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.4038544050097660D1


V=0.1724544350544401D1


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.5823842309715585D+0


V=0.4231083095357343D2


Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.3545877390518688D+0


V=0.5198069864064399D2


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=0.4695720972568883D2


Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)


N=N1


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 266POINT ANGULAR GRID


CVW


chvd


chvd This subroutine is part of a set of subroutines that generate


chvd Lebedev grids [16] for integration on a sphere. The original


chvd Ccode [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 programmersmanuals


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. 477481.


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. 283286.


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. 587592.


chvd


chvd [4] V.I. Lebedev


chvd "Spherical quadrature formulas exact to orders 2529"


chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99107.


chvd


chvd [5] V.I. Lebedev


chvd "Quadratures on a sphere"


chvd Computational Mathematics and Mathematical Physics, Vol. 16,


chvd 1976, pp. 1024.


chvd


chvd [6] V.I. Lebedev


chvd "Values of the nodes and weights of ninth to seventeenth


chvd order GaussMarkov quadrature formulae invariant under the


chvd octahedron group with inversion"


chvd Computational Mathematics and Mathematical Physics, Vol. 15,


chvd 1975, pp. 4451.


chvd


N=1


V=0.1313769127326952D2


Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)


V=0.2522728704859336D2


Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V)


V=0.4186853881700583D2


Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.7039373391585475D+0


V=0.5315167977810885D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.1012526248572414D+0


V=0.4047142377086219D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.4647448726420539D+0


V=0.4112482394406990D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.3277420654971629D+0


V=0.3595584899758782D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.6620338663699974D+0


V=0.4256131351428158D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.8506508083520399D+0


V=0.4229582700647240D2


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=0.4080914225780505D2


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=0.4071467593830964D2


Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)


N=N1


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 302POINT ANGULAR GRID


CVW


chvd


chvd This subroutine is part of a set of subroutines that generate


chvd Lebedev grids [16] for integration on a sphere. The original


chvd Ccode [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 programmersmanuals


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. 477481.


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. 283286.


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. 587592.


chvd


chvd [4] V.I. Lebedev


chvd "Spherical quadrature formulas exact to orders 2529"


chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99107.


chvd


chvd [5] V.I. Lebedev


chvd "Quadratures on a sphere"


chvd Computational Mathematics and Mathematical Physics, Vol. 16,


chvd 1976, pp. 1024.


chvd


chvd [6] V.I. Lebedev


chvd "Values of the nodes and weights of ninth to seventeenth


chvd order GaussMarkov quadrature formulae invariant under the


chvd octahedron group with inversion"


chvd Computational Mathematics and Mathematical Physics, Vol. 15,


chvd 1975, pp. 4451.


chvd


N=1


V=0.8545911725128148D3


Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)


V=0.3599119285025571D2


Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.3515640345570105D+0


V=0.3449788424305883D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.6566329410219612D+0


V=0.3604822601419882D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.4729054132581005D+0


V=0.3576729661743367D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.9618308522614784D1


V=0.2352101413689164D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.2219645236294178D+0


V=0.3108953122413675D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.7011766416089545D+0


V=0.3650045807677255D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.2644152887060663D+0


V=0.2982344963171804D2


Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.5718955891878961D+0


V=0.3600820932216460D2


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=0.3571540554273387D2


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=0.3392312205006170D2


Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)


N=N1


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 350POINT ANGULAR GRID


CVW


chvd


chvd This subroutine is part of a set of subroutines that generate


chvd Lebedev grids [16] for integration on a sphere. The original


chvd Ccode [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 programmersmanuals


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. 477481.


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. 283286.


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. 587592.


chvd


chvd [4] V.I. Lebedev


chvd "Spherical quadrature formulas exact to orders 2529"


chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99107.


chvd


chvd [5] V.I. Lebedev


chvd "Quadratures on a sphere"


chvd Computational Mathematics and Mathematical Physics, Vol. 16,


chvd 1976, pp. 1024.


chvd


chvd [6] V.I. Lebedev


chvd "Values of the nodes and weights of ninth to seventeenth


chvd order GaussMarkov quadrature formulae invariant under the


chvd octahedron group with inversion"


chvd Computational Mathematics and Mathematical Physics, Vol. 15,


chvd 1975, pp. 4451.


chvd


N=1


V=0.3006796749453936D2


Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)


V=0.3050627745650771D2


Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.7068965463912316D+0


V=0.1621104600288991D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.4794682625712025D+0


V=0.3005701484901752D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.1927533154878019D+0


V=0.2990992529653774D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.6930357961327123D+0


V=0.2982170644107595D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.3608302115520091D+0


V=0.2721564237310992D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.6498486161496169D+0


V=0.3033513795811141D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.1932945013230339D+0


V=0.3007949555218533D2


Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.3800494919899303D+0


V=0.2881964603055307D2


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=0.2958357626535696D2


Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.9684121455103957D1


B=0.8280801506686862D+0


V=0.3036020026407088D2


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=0.2832187403926303D2


Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)


N=N1


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 434POINT ANGULAR GRID


CVW


chvd


chvd This subroutine is part of a set of subroutines that generate


chvd Lebedev grids [16] for integration on a sphere. The original


chvd Ccode [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 programmersmanuals


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. 477481.


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. 283286.


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. 587592.


chvd


chvd [4] V.I. Lebedev


chvd "Spherical quadrature formulas exact to orders 2529"


chvd Siberian Mathematical Journal, Vol. 18, 1977, pp. 99107.


chvd


chvd [5] V.I. Lebedev


chvd "Quadratures on a sphere"


chvd Computational Mathematics and Mathematical Physics, Vol. 16,


chvd 1976, pp. 1024.


chvd


chvd [6] V.I. Lebedev


chvd "Values of the nodes and weights of ninth to seventeenth


chvd order GaussMarkov quadrature formulae invariant under the


chvd octahedron group with inversion"


chvd Computational Mathematics and Mathematical Physics, Vol. 15,


chvd 1975, pp. 4451.


chvd


N=1


V=0.5265897968224436D3


Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V)


V=0.2548219972002607D2


Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V)


V=0.2512317418927307D2


Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.6909346307509111D+0


V=0.2530403801186355D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.1774836054609158D+0


V=0.2014279020918528D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.4914342637784746D+0


V=0.2501725168402936D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.6456664707424256D+0


V=0.2513267174597564D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.2861289010307638D+0


V=0.2302694782227416D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.7568084367178018D1


V=0.1462495621594614D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.3927259763368002D+0


V=0.2445373437312980D2


Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.8818132877794288D+0


V=0.2417442375638981D2


Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V)


A=0.9776428111182649D+0


V=0.1910951282179532D2


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=0.2416930044324775D2


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=0.2512236854563495D2


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=0.2496644054553086D2


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=0.2236607760437849D2


Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V)


N=N1


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 