From 5b8175e8181a81faf30f526216aae0fb5c3b5c39 Mon Sep 17 00:00:00 2001 From: Emmanuel Giner Date: Fri, 14 Apr 2017 12:50:27 +0200 Subject: [PATCH] DFT begins to work with lda --- plugins/DFT_Utils/angular.f | 6951 +++++++++++++++++ plugins/DFT_Utils/functional.irp.f | 25 + plugins/DFT_Utils/grid_density.irp.f | 83 +- plugins/DFT_Utils/integration_3d.irp.f | 3 +- plugins/DFT_Utils/integration_radial.irp.f | 10 +- .../test_integration_3d_density.irp.f | 39 + src/Utils/angular_integration.irp.f | 18 +- src/Utils/constants.include.F | 4 + 8 files changed, 7096 insertions(+), 37 deletions(-) create mode 100644 plugins/DFT_Utils/angular.f create mode 100644 plugins/DFT_Utils/functional.irp.f diff --git a/plugins/DFT_Utils/angular.f b/plugins/DFT_Utils/angular.f new file mode 100644 index 00000000..a5052a32 --- /dev/null +++ b/plugins/DFT_Utils/angular.f @@ -0,0 +1,6951 @@ + 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 +CVW +CVW LEBEDEV 590-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=0.3095121295306187D-3 + Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.1852379698597489D-2 + Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7040954938227469D+0 + V=0.1871790639277744D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6807744066455243D+0 + V=0.1858812585438317D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6372546939258752D+0 + V=0.1852028828296213D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5044419707800358D+0 + V=0.1846715956151242D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4215761784010967D+0 + V=0.1818471778162769D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3317920736472123D+0 + V=0.1749564657281154D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2384736701421887D+0 + V=0.1617210647254411D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1459036449157763D+0 + V=0.1384737234851692D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6095034115507196D-1 + V=0.9764331165051050D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6116843442009876D+0 + V=0.1857161196774078D-2 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3964755348199858D+0 + V=0.1705153996395864D-2 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1724782009907724D+0 + V=0.1300321685886048D-2 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5610263808622060D+0 + B=0.3518280927733519D+0 + V=0.1842866472905286D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4742392842551980D+0 + B=0.2634716655937950D+0 + V=0.1802658934377451D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5984126497885380D+0 + B=0.1816640840360209D+0 + V=0.1849830560443660D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3791035407695563D+0 + B=0.1720795225656878D+0 + V=0.1713904507106709D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2778673190586244D+0 + B=0.8213021581932511D-1 + V=0.1555213603396808D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5033564271075117D+0 + B=0.8999205842074875D-1 + V=0.1802239128008525D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + N=N-1 + RETURN + END + SUBROUTINE LD0770(X,Y,Z,W,N) + DOUBLE PRECISION X( 770) + DOUBLE PRECISION Y( 770) + DOUBLE PRECISION Z( 770) + DOUBLE PRECISION W( 770) + INTEGER N + DOUBLE PRECISION A,B,V +CVW +CVW LEBEDEV 770-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=0.2192942088181184D-3 + Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.1436433617319080D-2 + Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.1421940344335877D-2 + Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5087204410502360D-1 + V=0.6798123511050502D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1228198790178831D+0 + V=0.9913184235294912D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2026890814408786D+0 + V=0.1180207833238949D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2847745156464294D+0 + V=0.1296599602080921D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3656719078978026D+0 + V=0.1365871427428316D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4428264886713469D+0 + V=0.1402988604775325D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5140619627249735D+0 + V=0.1418645563595609D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6306401219166803D+0 + V=0.1421376741851662D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6716883332022612D+0 + V=0.1423996475490962D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6979792685336881D+0 + V=0.1431554042178567D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1446865674195309D+0 + V=0.9254401499865368D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3390263475411216D+0 + V=0.1250239995053509D-2 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5335804651263506D+0 + V=0.1394365843329230D-2 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6944024393349413D-1 + B=0.2355187894242326D+0 + V=0.1127089094671749D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2269004109529460D+0 + B=0.4102182474045730D+0 + V=0.1345753760910670D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.8025574607775339D-1 + B=0.6214302417481605D+0 + V=0.1424957283316783D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1467999527896572D+0 + B=0.3245284345717394D+0 + V=0.1261523341237750D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1571507769824727D+0 + B=0.5224482189696630D+0 + V=0.1392547106052696D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2365702993157246D+0 + B=0.6017546634089558D+0 + V=0.1418761677877656D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7714815866765732D-1 + B=0.4346575516141163D+0 + V=0.1338366684479554D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3062936666210730D+0 + B=0.4908826589037616D+0 + V=0.1393700862676131D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3822477379524787D+0 + B=0.5648768149099500D+0 + V=0.1415914757466932D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + N=N-1 + RETURN + END + SUBROUTINE LD0974(X,Y,Z,W,N) + DOUBLE PRECISION X( 974) + DOUBLE PRECISION Y( 974) + DOUBLE PRECISION Z( 974) + DOUBLE PRECISION W( 974) + INTEGER N + DOUBLE PRECISION A,B,V +CVW +CVW LEBEDEV 974-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=0.1438294190527431D-3 + Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.1125772288287004D-2 + Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4292963545341347D-1 + V=0.4948029341949241D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1051426854086404D+0 + V=0.7357990109125470D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1750024867623087D+0 + V=0.8889132771304384D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2477653379650257D+0 + V=0.9888347838921435D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3206567123955957D+0 + V=0.1053299681709471D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3916520749849983D+0 + V=0.1092778807014578D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4590825874187624D+0 + V=0.1114389394063227D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5214563888415861D+0 + V=0.1123724788051555D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6253170244654199D+0 + V=0.1125239325243814D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6637926744523170D+0 + V=0.1126153271815905D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6910410398498301D+0 + V=0.1130286931123841D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7052907007457760D+0 + V=0.1134986534363955D-2 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1236686762657990D+0 + V=0.6823367927109931D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2940777114468387D+0 + V=0.9454158160447096D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4697753849207649D+0 + V=0.1074429975385679D-2 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6334563241139567D+0 + V=0.1129300086569132D-2 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5974048614181342D-1 + B=0.2029128752777523D+0 + V=0.8436884500901954D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1375760408473636D+0 + B=0.4602621942484054D+0 + V=0.1075255720448885D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3391016526336286D+0 + B=0.5030673999662036D+0 + V=0.1108577236864462D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1271675191439820D+0 + B=0.2817606422442134D+0 + V=0.9566475323783357D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2693120740413512D+0 + B=0.4331561291720157D+0 + V=0.1080663250717391D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1419786452601918D+0 + B=0.6256167358580814D+0 + V=0.1126797131196295D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6709284600738255D-1 + B=0.3798395216859157D+0 + V=0.1022568715358061D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7057738183256172D-1 + B=0.5517505421423520D+0 + V=0.1108960267713108D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2783888477882155D+0 + B=0.6029619156159187D+0 + V=0.1122790653435766D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1979578938917407D+0 + B=0.3589606329589096D+0 + V=0.1032401847117460D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2087307061103274D+0 + B=0.5348666438135476D+0 + V=0.1107249382283854D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4055122137872836D+0 + B=0.5674997546074373D+0 + V=0.1121780048519972D-2 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + N=N-1 + RETURN + END + SUBROUTINE LD1202(X,Y,Z,W,N) + DOUBLE PRECISION X(1202) + DOUBLE PRECISION Y(1202) + DOUBLE PRECISION Z(1202) + DOUBLE PRECISION W(1202) + INTEGER N + DOUBLE PRECISION A,B,V +CVW +CVW LEBEDEV 1202-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=0.1105189233267572D-3 + Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.9205232738090741D-3 + Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.9133159786443561D-3 + Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3712636449657089D-1 + V=0.3690421898017899D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.9140060412262223D-1 + V=0.5603990928680660D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1531077852469906D+0 + V=0.6865297629282609D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2180928891660612D+0 + V=0.7720338551145630D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2839874532200175D+0 + V=0.8301545958894795D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3491177600963764D+0 + V=0.8686692550179628D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4121431461444309D+0 + V=0.8927076285846890D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4718993627149127D+0 + V=0.9060820238568219D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5273145452842337D+0 + V=0.9119777254940867D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6209475332444019D+0 + V=0.9128720138604181D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6569722711857291D+0 + V=0.9130714935691735D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6841788309070143D+0 + V=0.9152873784554116D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7012604330123631D+0 + V=0.9187436274321654D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1072382215478166D+0 + V=0.5176977312965694D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2582068959496968D+0 + V=0.7331143682101417D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4172752955306717D+0 + V=0.8463232836379928D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5700366911792503D+0 + V=0.9031122694253992D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.9827986018263947D+0 + B=0.1771774022615325D+0 + V=0.6485778453163257D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.9624249230326228D+0 + B=0.2475716463426288D+0 + V=0.7435030910982369D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.9402007994128811D+0 + B=0.3354616289066489D+0 + V=0.7998527891839054D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.9320822040143202D+0 + B=0.3173615246611977D+0 + V=0.8101731497468018D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.9043674199393299D+0 + B=0.4090268427085357D+0 + V=0.8483389574594331D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.8912407560074747D+0 + B=0.3854291150669224D+0 + V=0.8556299257311812D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.8676435628462708D+0 + B=0.4932221184851285D+0 + V=0.8803208679738260D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.8581979986041619D+0 + B=0.4785320675922435D+0 + V=0.8811048182425720D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.8396753624049856D+0 + B=0.4507422593157064D+0 + V=0.8850282341265444D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.8165288564022188D+0 + B=0.5632123020762100D+0 + V=0.9021342299040653D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.8015469370783529D+0 + B=0.5434303569693900D+0 + V=0.9010091677105086D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7773563069070351D+0 + B=0.5123518486419871D+0 + V=0.9022692938426915D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7661621213900394D+0 + B=0.6394279634749102D+0 + V=0.9158016174693465D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7553584143533510D+0 + B=0.6269805509024392D+0 + V=0.9131578003189435D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7344305757559503D+0 + B=0.6031161693096310D+0 + V=0.9107813579482705D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7043837184021765D+0 + B=0.5693702498468441D+0 + V=0.9105760258970126D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + N=N-1 + RETURN + END + SUBROUTINE LD1454(X,Y,Z,W,N) + DOUBLE PRECISION X(1454) + DOUBLE PRECISION Y(1454) + DOUBLE PRECISION Z(1454) + DOUBLE PRECISION W(1454) + INTEGER N + DOUBLE PRECISION A,B,V +CVW +CVW LEBEDEV 1454-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=0.7777160743261247D-4 + Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.7557646413004701D-3 + Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3229290663413854D-1 + V=0.2841633806090617D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.8036733271462222D-1 + V=0.4374419127053555D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1354289960531653D+0 + V=0.5417174740872172D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1938963861114426D+0 + V=0.6148000891358593D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2537343715011275D+0 + V=0.6664394485800705D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3135251434752570D+0 + V=0.7025039356923220D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3721558339375338D+0 + V=0.7268511789249627D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4286809575195696D+0 + V=0.7422637534208629D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4822510128282994D+0 + V=0.7509545035841214D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5320679333566263D+0 + V=0.7548535057718401D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6172998195394274D+0 + V=0.7554088969774001D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6510679849127481D+0 + V=0.7553147174442808D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6777315251687360D+0 + V=0.7564767653292297D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6963109410648741D+0 + V=0.7587991808518730D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7058935009831749D+0 + V=0.7608261832033027D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.9955546194091857D+0 + V=0.4021680447874916D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.9734115901794209D+0 + V=0.5804871793945964D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.9275693732388626D+0 + V=0.6792151955945159D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.8568022422795103D+0 + V=0.7336741211286294D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7623495553719372D+0 + V=0.7581866300989608D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5707522908892223D+0 + B=0.4387028039889501D+0 + V=0.7538257859800743D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5196463388403083D+0 + B=0.3858908414762617D+0 + V=0.7483517247053123D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4646337531215351D+0 + B=0.3301937372343854D+0 + V=0.7371763661112059D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4063901697557691D+0 + B=0.2725423573563777D+0 + V=0.7183448895756934D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3456329466643087D+0 + B=0.2139510237495250D+0 + V=0.6895815529822191D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2831395121050332D+0 + B=0.1555922309786647D+0 + V=0.6480105801792886D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2197682022925330D+0 + B=0.9892878979686097D-1 + V=0.5897558896594636D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1564696098650355D+0 + B=0.4598642910675510D-1 + V=0.5095708849247346D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6027356673721295D+0 + B=0.3376625140173426D+0 + V=0.7536906428909755D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5496032320255096D+0 + B=0.2822301309727988D+0 + V=0.7472505965575118D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4921707755234567D+0 + B=0.2248632342592540D+0 + V=0.7343017132279698D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4309422998598483D+0 + B=0.1666224723456479D+0 + V=0.7130871582177445D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3664108182313672D+0 + B=0.1086964901822169D+0 + V=0.6817022032112776D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2990189057758436D+0 + B=0.5251989784120085D-1 + V=0.6380941145604121D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6268724013144998D+0 + B=0.2297523657550023D+0 + V=0.7550381377920310D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5707324144834607D+0 + B=0.1723080607093800D+0 + V=0.7478646640144802D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5096360901960365D+0 + B=0.1140238465390513D+0 + V=0.7335918720601220D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4438729938312456D+0 + B=0.5611522095882537D-1 + V=0.7110120527658118D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6419978471082389D+0 + B=0.1164174423140873D+0 + V=0.7571363978689501D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5817218061802611D+0 + B=0.5797589531445219D-1 + V=0.7489908329079234D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + N=N-1 + RETURN + END + SUBROUTINE LD1730(X,Y,Z,W,N) + DOUBLE PRECISION X(1730) + DOUBLE PRECISION Y(1730) + DOUBLE PRECISION Z(1730) + DOUBLE PRECISION W(1730) + INTEGER N + DOUBLE PRECISION A,B,V +CVW +CVW LEBEDEV 1730-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=0.6309049437420976D-4 + Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.6398287705571748D-3 + Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.6357185073530720D-3 + Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2860923126194662D-1 + V=0.2221207162188168D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7142556767711522D-1 + V=0.3475784022286848D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1209199540995559D+0 + V=0.4350742443589804D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1738673106594379D+0 + V=0.4978569136522127D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2284645438467734D+0 + V=0.5435036221998053D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2834807671701512D+0 + V=0.5765913388219542D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3379680145467339D+0 + V=0.6001200359226003D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3911355454819537D+0 + V=0.6162178172717512D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4422860353001403D+0 + V=0.6265218152438485D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4907781568726057D+0 + V=0.6323987160974212D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5360006153211468D+0 + V=0.6350767851540569D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6142105973596603D+0 + V=0.6354362775297107D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6459300387977504D+0 + V=0.6352302462706235D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6718056125089225D+0 + V=0.6358117881417972D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6910888533186254D+0 + V=0.6373101590310117D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7030467416823252D+0 + V=0.6390428961368665D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.8354951166354646D-1 + V=0.3186913449946576D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2050143009099486D+0 + V=0.4678028558591711D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3370208290706637D+0 + V=0.5538829697598626D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4689051484233963D+0 + V=0.6044475907190476D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5939400424557334D+0 + V=0.6313575103509012D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1394983311832261D+0 + B=0.4097581162050343D-1 + V=0.4078626431855630D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1967999180485014D+0 + B=0.8851987391293348D-1 + V=0.4759933057812725D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2546183732548967D+0 + B=0.1397680182969819D+0 + V=0.5268151186413440D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3121281074713875D+0 + B=0.1929452542226526D+0 + V=0.5643048560507316D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3685981078502492D+0 + B=0.2467898337061562D+0 + V=0.5914501076613073D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4233760321547856D+0 + B=0.3003104124785409D+0 + V=0.6104561257874195D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4758671236059246D+0 + B=0.3526684328175033D+0 + V=0.6230252860707806D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5255178579796463D+0 + B=0.4031134861145713D+0 + V=0.6305618761760796D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5718025633734589D+0 + B=0.4509426448342351D+0 + V=0.6343092767597889D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2686927772723415D+0 + B=0.4711322502423248D-1 + V=0.5176268945737826D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3306006819904809D+0 + B=0.9784487303942695D-1 + V=0.5564840313313692D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3904906850594983D+0 + B=0.1505395810025273D+0 + V=0.5856426671038980D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4479957951904390D+0 + B=0.2039728156296050D+0 + V=0.6066386925777091D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5027076848919780D+0 + B=0.2571529941121107D+0 + V=0.6208824962234458D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5542087392260217D+0 + B=0.3092191375815670D+0 + V=0.6296314297822907D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6020850887375187D+0 + B=0.3593807506130276D+0 + V=0.6340423756791859D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4019851409179594D+0 + B=0.5063389934378671D-1 + V=0.5829627677107342D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4635614567449800D+0 + B=0.1032422269160612D+0 + V=0.6048693376081110D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5215860931591575D+0 + B=0.1566322094006254D+0 + V=0.6202362317732461D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5758202499099271D+0 + B=0.2098082827491099D+0 + V=0.6299005328403779D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6259893683876795D+0 + B=0.2618824114553391D+0 + V=0.6347722390609353D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5313795124811891D+0 + B=0.5263245019338556D-1 + V=0.6203778981238834D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5893317955931995D+0 + B=0.1061059730982005D+0 + V=0.6308414671239979D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6426246321215801D+0 + B=0.1594171564034221D+0 + V=0.6362706466959498D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6511904367376113D+0 + B=0.5354789536565540D-1 + V=0.6375414170333233D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + N=N-1 + RETURN + END + SUBROUTINE LD2030(X,Y,Z,W,N) + DOUBLE PRECISION X(2030) + DOUBLE PRECISION Y(2030) + DOUBLE PRECISION Z(2030) + DOUBLE PRECISION W(2030) + INTEGER N + DOUBLE PRECISION A,B,V +CVW +CVW LEBEDEV 2030-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=0.4656031899197431D-4 + Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.5421549195295507D-3 + Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2540835336814348D-1 + V=0.1778522133346553D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6399322800504915D-1 + V=0.2811325405682796D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1088269469804125D+0 + V=0.3548896312631459D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1570670798818287D+0 + V=0.4090310897173364D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2071163932282514D+0 + V=0.4493286134169965D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2578914044450844D+0 + V=0.4793728447962723D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3085687558169623D+0 + V=0.5015415319164265D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3584719706267024D+0 + V=0.5175127372677937D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4070135594428709D+0 + V=0.5285522262081019D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4536618626222638D+0 + V=0.5356832703713962D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4979195686463577D+0 + V=0.5397914736175170D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5393075111126999D+0 + V=0.5416899441599930D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6115617676843916D+0 + V=0.5419308476889938D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6414308435160159D+0 + V=0.5416936902030596D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6664099412721607D+0 + V=0.5419544338703164D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6859161771214913D+0 + V=0.5428983656630975D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6993625593503890D+0 + V=0.5442286500098193D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7062393387719380D+0 + V=0.5452250345057301D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7479028168349763D-1 + V=0.2568002497728530D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1848951153969366D+0 + V=0.3827211700292145D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3059529066581305D+0 + V=0.4579491561917824D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4285556101021362D+0 + V=0.5042003969083574D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5468758653496526D+0 + V=0.5312708889976025D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6565821978343439D+0 + V=0.5438401790747117D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1253901572367117D+0 + B=0.3681917226439641D-1 + V=0.3316041873197344D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1775721510383941D+0 + B=0.7982487607213301D-1 + V=0.3899113567153771D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2305693358216114D+0 + B=0.1264640966592335D+0 + V=0.4343343327201309D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2836502845992063D+0 + B=0.1751585683418957D+0 + V=0.4679415262318919D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3361794746232590D+0 + B=0.2247995907632670D+0 + V=0.4930847981631031D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3875979172264824D+0 + B=0.2745299257422246D+0 + V=0.5115031867540091D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4374019316999074D+0 + B=0.3236373482441118D+0 + V=0.5245217148457367D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4851275843340022D+0 + B=0.3714967859436741D+0 + V=0.5332041499895321D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5303391803806868D+0 + B=0.4175353646321745D+0 + V=0.5384583126021542D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5726197380596287D+0 + B=0.4612084406355461D+0 + V=0.5411067210798852D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2431520732564863D+0 + B=0.4258040133043952D-1 + V=0.4259797391468714D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3002096800895869D+0 + B=0.8869424306722721D-1 + V=0.4604931368460021D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3558554457457432D+0 + B=0.1368811706510655D+0 + V=0.4871814878255202D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4097782537048887D+0 + B=0.1860739985015033D+0 + V=0.5072242910074885D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4616337666067458D+0 + B=0.2354235077395853D+0 + V=0.5217069845235350D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5110707008417874D+0 + B=0.2842074921347011D+0 + V=0.5315785966280310D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5577415286163795D+0 + B=0.3317784414984102D+0 + V=0.5376833708758905D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6013060431366950D+0 + B=0.3775299002040700D+0 + V=0.5408032092069521D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3661596767261781D+0 + B=0.4599367887164592D-1 + V=0.4842744917904866D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4237633153506581D+0 + B=0.9404893773654421D-1 + V=0.5048926076188130D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4786328454658452D+0 + B=0.1431377109091971D+0 + V=0.5202607980478373D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5305702076789774D+0 + B=0.1924186388843570D+0 + V=0.5309932388325743D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5793436224231788D+0 + B=0.2411590944775190D+0 + V=0.5377419770895208D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6247069017094747D+0 + B=0.2886871491583605D+0 + V=0.5411696331677717D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4874315552535204D+0 + B=0.4804978774953206D-1 + V=0.5197996293282420D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5427337322059053D+0 + B=0.9716857199366665D-1 + V=0.5311120836622945D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5943493747246700D+0 + B=0.1465205839795055D+0 + V=0.5384309319956951D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6421314033564943D+0 + B=0.1953579449803574D+0 + V=0.5421859504051886D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6020628374713980D+0 + B=0.4916375015738108D-1 + V=0.5390948355046314D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6529222529856881D+0 + B=0.9861621540127005D-1 + V=0.5433312705027845D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + N=N-1 + RETURN + END + SUBROUTINE LD2354(X,Y,Z,W,N) + DOUBLE PRECISION X(2354) + DOUBLE PRECISION Y(2354) + DOUBLE PRECISION Z(2354) + DOUBLE PRECISION W(2354) + INTEGER N + DOUBLE PRECISION A,B,V +CVW +CVW LEBEDEV 2354-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=0.3922616270665292D-4 + Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.4703831750854424D-3 + Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.4678202801282136D-3 + Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2290024646530589D-1 + V=0.1437832228979900D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5779086652271284D-1 + V=0.2303572493577644D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.9863103576375984D-1 + V=0.2933110752447454D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1428155792982185D+0 + V=0.3402905998359838D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1888978116601463D+0 + V=0.3759138466870372D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2359091682970210D+0 + V=0.4030638447899798D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2831228833706171D+0 + V=0.4236591432242211D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3299495857966693D+0 + V=0.4390522656946746D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3758840802660796D+0 + V=0.4502523466626247D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4204751831009480D+0 + V=0.4580577727783541D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4633068518751051D+0 + V=0.4631391616615899D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5039849474507313D+0 + V=0.4660928953698676D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5421265793440747D+0 + V=0.4674751807936953D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6092660230557310D+0 + V=0.4676414903932920D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6374654204984869D+0 + V=0.4674086492347870D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6615136472609892D+0 + V=0.4674928539483207D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6809487285958127D+0 + V=0.4680748979686447D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6952980021665196D+0 + V=0.4690449806389040D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7041245497695400D+0 + V=0.4699877075860818D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6744033088306065D-1 + V=0.2099942281069176D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1678684485334166D+0 + V=0.3172269150712804D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2793559049539613D+0 + V=0.3832051358546523D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3935264218057639D+0 + V=0.4252193818146985D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5052629268232558D+0 + V=0.4513807963755000D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6107905315437531D+0 + V=0.4657797469114178D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1135081039843524D+0 + B=0.3331954884662588D-1 + V=0.2733362800522836D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1612866626099378D+0 + B=0.7247167465436538D-1 + V=0.3235485368463559D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2100786550168205D+0 + B=0.1151539110849745D+0 + V=0.3624908726013453D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2592282009459942D+0 + B=0.1599491097143677D+0 + V=0.3925540070712828D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3081740561320203D+0 + B=0.2058699956028027D+0 + V=0.4156129781116235D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3564289781578164D+0 + B=0.2521624953502911D+0 + V=0.4330644984623263D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4035587288240703D+0 + B=0.2982090785797674D+0 + V=0.4459677725921312D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4491671196373903D+0 + B=0.3434762087235733D+0 + V=0.4551593004456795D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4928854782917489D+0 + B=0.3874831357203437D+0 + V=0.4613341462749918D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5343646791958988D+0 + B=0.4297814821746926D+0 + V=0.4651019618269806D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5732683216530990D+0 + B=0.4699402260943537D+0 + V=0.4670249536100625D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2214131583218986D+0 + B=0.3873602040643895D-1 + V=0.3549555576441708D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2741796504750071D+0 + B=0.8089496256902013D-1 + V=0.3856108245249010D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3259797439149485D+0 + B=0.1251732177620872D+0 + V=0.4098622845756882D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3765441148826891D+0 + B=0.1706260286403185D+0 + V=0.4286328604268950D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4255773574530558D+0 + B=0.2165115147300408D+0 + V=0.4427802198993945D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4727795117058430D+0 + B=0.2622089812225259D+0 + V=0.4530473511488561D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5178546895819012D+0 + B=0.3071721431296201D+0 + V=0.4600805475703138D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5605141192097460D+0 + B=0.3508998998801138D+0 + V=0.4644599059958017D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6004763319352512D+0 + B=0.3929160876166931D+0 + V=0.4667274455712508D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3352842634946949D+0 + B=0.4202563457288019D-1 + V=0.4069360518020356D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3891971629814670D+0 + B=0.8614309758870850D-1 + V=0.4260442819919195D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4409875565542281D+0 + B=0.1314500879380001D+0 + V=0.4408678508029063D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4904893058592484D+0 + B=0.1772189657383859D+0 + V=0.4518748115548597D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5375056138769549D+0 + B=0.2228277110050294D+0 + V=0.4595564875375116D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5818255708669969D+0 + B=0.2677179935014386D+0 + V=0.4643988774315846D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6232334858144959D+0 + B=0.3113675035544165D+0 + V=0.4668827491646946D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4489485354492058D+0 + B=0.4409162378368174D-1 + V=0.4400541823741973D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5015136875933150D+0 + B=0.8939009917748489D-1 + V=0.4514512890193797D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5511300550512623D+0 + B=0.1351806029383365D+0 + V=0.4596198627347549D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5976720409858000D+0 + B=0.1808370355053196D+0 + V=0.4648659016801781D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6409956378989354D+0 + B=0.2257852192301602D+0 + V=0.4675502017157673D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5581222330827514D+0 + B=0.4532173421637160D-1 + V=0.4598494476455523D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6074705984161695D+0 + B=0.9117488031840314D-1 + V=0.4654916955152048D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6532272537379033D+0 + B=0.1369294213140155D+0 + V=0.4684709779505137D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6594761494500487D+0 + B=0.4589901487275583D-1 + V=0.4691445539106986D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + N=N-1 + RETURN + END + SUBROUTINE LD2702(X,Y,Z,W,N) + DOUBLE PRECISION X(2702) + DOUBLE PRECISION Y(2702) + DOUBLE PRECISION Z(2702) + DOUBLE PRECISION W(2702) + INTEGER N + DOUBLE PRECISION A,B,V +CVW +CVW LEBEDEV 2702-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=0.2998675149888161D-4 + Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.4077860529495355D-3 + Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2065562538818703D-1 + V=0.1185349192520667D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5250918173022379D-1 + V=0.1913408643425751D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.8993480082038376D-1 + V=0.2452886577209897D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1306023924436019D+0 + V=0.2862408183288702D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1732060388531418D+0 + V=0.3178032258257357D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2168727084820249D+0 + V=0.3422945667633690D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2609528309173586D+0 + V=0.3612790520235922D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3049252927938952D+0 + V=0.3758638229818521D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3483484138084404D+0 + V=0.3868711798859953D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3908321549106406D+0 + V=0.3949429933189938D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4320210071894814D+0 + V=0.4006068107541156D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4715824795890053D+0 + V=0.4043192149672723D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5091984794078453D+0 + V=0.4064947495808078D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5445580145650803D+0 + V=0.4075245619813152D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6072575796841768D+0 + V=0.4076423540893566D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6339484505755803D+0 + V=0.4074280862251555D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6570718257486958D+0 + V=0.4074163756012244D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6762557330090709D+0 + V=0.4077647795071246D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6911161696923790D+0 + V=0.4084517552782530D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7012841911659961D+0 + V=0.4092468459224052D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7064559272410020D+0 + V=0.4097872687240906D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6123554989894765D-1 + V=0.1738986811745028D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1533070348312393D+0 + V=0.2659616045280191D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2563902605244206D+0 + V=0.3240596008171533D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3629346991663361D+0 + V=0.3621195964432943D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4683949968987538D+0 + V=0.3868838330760539D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5694479240657952D+0 + V=0.4018911532693111D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6634465430993955D+0 + V=0.4089929432983252D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1033958573552305D+0 + B=0.3034544009063584D-1 + V=0.2279907527706409D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1473521412414395D+0 + B=0.6618803044247135D-1 + V=0.2715205490578897D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1924552158705967D+0 + B=0.1054431128987715D+0 + V=0.3057917896703976D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2381094362890328D+0 + B=0.1468263551238858D+0 + V=0.3326913052452555D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2838121707936760D+0 + B=0.1894486108187886D+0 + V=0.3537334711890037D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3291323133373415D+0 + B=0.2326374238761579D+0 + V=0.3700567500783129D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3736896978741460D+0 + B=0.2758485808485768D+0 + V=0.3825245372589122D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4171406040760013D+0 + B=0.3186179331996921D+0 + V=0.3918125171518296D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4591677985256915D+0 + B=0.3605329796303794D+0 + V=0.3984720419937579D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4994733831718418D+0 + B=0.4012147253586509D+0 + V=0.4029746003338211D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5377731830445096D+0 + B=0.4403050025570692D+0 + V=0.4057428632156627D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5737917830001331D+0 + B=0.4774565904277483D+0 + V=0.4071719274114857D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2027323586271389D+0 + B=0.3544122504976147D-1 + V=0.2990236950664119D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2516942375187273D+0 + B=0.7418304388646328D-1 + V=0.3262951734212878D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3000227995257181D+0 + B=0.1150502745727186D+0 + V=0.3482634608242413D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3474806691046342D+0 + B=0.1571963371209364D+0 + V=0.3656596681700892D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3938103180359209D+0 + B=0.1999631877247100D+0 + V=0.3791740467794218D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4387519590455703D+0 + B=0.2428073457846535D+0 + V=0.3894034450156905D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4820503960077787D+0 + B=0.2852575132906155D+0 + V=0.3968600245508371D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5234573778475101D+0 + B=0.3268884208674639D+0 + V=0.4019931351420050D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5627318647235282D+0 + B=0.3673033321675939D+0 + V=0.4052108801278599D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5996390607156954D+0 + B=0.4061211551830290D+0 + V=0.4068978613940934D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3084780753791947D+0 + B=0.3860125523100059D-1 + V=0.3454275351319704D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3589988275920223D+0 + B=0.7928938987104867D-1 + V=0.3629963537007920D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4078628415881973D+0 + B=0.1212614643030087D+0 + V=0.3770187233889873D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4549287258889735D+0 + B=0.1638770827382693D+0 + V=0.3878608613694378D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5000278512957279D+0 + B=0.2065965798260176D+0 + V=0.3959065270221274D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5429785044928199D+0 + B=0.2489436378852235D+0 + V=0.4015286975463570D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5835939850491711D+0 + B=0.2904811368946891D+0 + V=0.4050866785614717D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6216870353444856D+0 + B=0.3307941957666609D+0 + V=0.4069320185051913D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4151104662709091D+0 + B=0.4064829146052554D-1 + V=0.3760120964062763D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4649804275009218D+0 + B=0.8258424547294755D-1 + V=0.3870969564418064D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5124695757009662D+0 + B=0.1251841962027289D+0 + V=0.3955287790534055D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5574711100606224D+0 + B=0.1679107505976331D+0 + V=0.4015361911302668D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5998597333287227D+0 + B=0.2102805057358715D+0 + V=0.4053836986719548D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6395007148516600D+0 + B=0.2518418087774107D+0 + V=0.4073578673299117D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5188456224746252D+0 + B=0.4194321676077518D-1 + V=0.3954628379231406D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5664190707942778D+0 + B=0.8457661551921499D-1 + V=0.4017645508847530D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6110464353283153D+0 + B=0.1273652932519396D+0 + V=0.4059030348651293D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6526430302051563D+0 + B=0.1698173239076354D+0 + V=0.4080565809484880D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6167551880377548D+0 + B=0.4266398851548864D-1 + V=0.4063018753664651D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6607195418355383D+0 + B=0.8551925814238349D-1 + V=0.4087191292799671D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + N=N-1 + RETURN + END + SUBROUTINE LD3074(X,Y,Z,W,N) + DOUBLE PRECISION X(3074) + DOUBLE PRECISION Y(3074) + DOUBLE PRECISION Z(3074) + DOUBLE PRECISION W(3074) + INTEGER N + DOUBLE PRECISION A,B,V +CVW +CVW LEBEDEV 3074-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=0.2599095953754734D-4 + Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.3603134089687541D-3 + Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.3586067974412447D-3 + Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1886108518723392D-1 + V=0.9831528474385880D-4 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4800217244625303D-1 + V=0.1605023107954450D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.8244922058397242D-1 + V=0.2072200131464099D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1200408362484023D+0 + V=0.2431297618814187D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1595773530809965D+0 + V=0.2711819064496707D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2002635973434064D+0 + V=0.2932762038321116D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2415127590139982D+0 + V=0.3107032514197368D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2828584158458477D+0 + V=0.3243808058921213D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3239091015338138D+0 + V=0.3349899091374030D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3643225097962194D+0 + V=0.3430580688505218D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4037897083691802D+0 + V=0.3490124109290343D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4420247515194127D+0 + V=0.3532148948561955D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4787572538464938D+0 + V=0.3559862669062833D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5137265251275234D+0 + V=0.3576224317551411D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5466764056654611D+0 + V=0.3584050533086076D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6054859420813535D+0 + V=0.3584903581373224D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6308106701764562D+0 + V=0.3582991879040586D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6530369230179584D+0 + V=0.3582371187963125D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6718609524611158D+0 + V=0.3584353631122350D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6869676499894013D+0 + V=0.3589120166517785D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6980467077240748D+0 + V=0.3595445704531601D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7048241721250522D+0 + V=0.3600943557111074D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5591105222058232D-1 + V=0.1456447096742039D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1407384078513916D+0 + V=0.2252370188283782D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2364035438976309D+0 + V=0.2766135443474897D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3360602737818170D+0 + V=0.3110729491500851D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4356292630054665D+0 + V=0.3342506712303391D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5321569415256174D+0 + V=0.3491981834026860D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6232956305040554D+0 + V=0.3576003604348932D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.9469870086838469D-1 + B=0.2778748387309470D-1 + V=0.1921921305788564D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1353170300568141D+0 + B=0.6076569878628364D-1 + V=0.2301458216495632D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1771679481726077D+0 + B=0.9703072762711040D-1 + V=0.2604248549522893D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2197066664231751D+0 + B=0.1354112458524762D+0 + V=0.2845275425870697D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2624783557374927D+0 + B=0.1750996479744100D+0 + V=0.3036870897974840D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3050969521214442D+0 + B=0.2154896907449802D+0 + V=0.3188414832298066D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3472252637196021D+0 + B=0.2560954625740152D+0 + V=0.3307046414722089D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3885610219026360D+0 + B=0.2965070050624096D+0 + V=0.3398330969031360D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4288273776062765D+0 + B=0.3363641488734497D+0 + V=0.3466757899705373D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4677662471302948D+0 + B=0.3753400029836788D+0 + V=0.3516095923230054D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5051333589553359D+0 + B=0.4131297522144286D+0 + V=0.3549645184048486D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5406942145810492D+0 + B=0.4494423776081795D+0 + V=0.3570415969441392D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5742204122576457D+0 + B=0.4839938958841502D+0 + V=0.3581251798496118D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1865407027225188D+0 + B=0.3259144851070796D-1 + V=0.2543491329913348D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2321186453689432D+0 + B=0.6835679505297343D-1 + V=0.2786711051330776D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2773159142523882D+0 + B=0.1062284864451989D+0 + V=0.2985552361083679D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3219200192237254D+0 + B=0.1454404409323047D+0 + V=0.3145867929154039D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3657032593944029D+0 + B=0.1854018282582510D+0 + V=0.3273290662067609D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4084376778363622D+0 + B=0.2256297412014750D+0 + V=0.3372705511943501D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4499004945751427D+0 + B=0.2657104425000896D+0 + V=0.3448274437851510D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4898758141326335D+0 + B=0.3052755487631557D+0 + V=0.3503592783048583D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5281547442266309D+0 + B=0.3439863920645423D+0 + V=0.3541854792663162D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5645346989813992D+0 + B=0.3815229456121914D+0 + V=0.3565995517909428D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5988181252159848D+0 + B=0.4175752420966734D+0 + V=0.3578802078302898D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2850425424471603D+0 + B=0.3562149509862536D-1 + V=0.2958644592860982D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3324619433027876D+0 + B=0.7330318886871096D-1 + V=0.3119548129116835D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3785848333076282D+0 + B=0.1123226296008472D+0 + V=0.3250745225005984D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4232891028562115D+0 + B=0.1521084193337708D+0 + V=0.3355153415935208D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4664287050829722D+0 + B=0.1921844459223610D+0 + V=0.3435847568549328D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5078458493735726D+0 + B=0.2321360989678303D+0 + V=0.3495786831622488D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5473779816204180D+0 + B=0.2715886486360520D+0 + V=0.3537767805534621D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5848617133811376D+0 + B=0.3101924707571355D+0 + V=0.3564459815421428D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6201348281584888D+0 + B=0.3476121052890973D+0 + V=0.3578464061225468D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3852191185387871D+0 + B=0.3763224880035108D-1 + V=0.3239748762836212D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4325025061073423D+0 + B=0.7659581935637135D-1 + V=0.3345491784174287D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4778486229734490D+0 + B=0.1163381306083900D+0 + V=0.3429126177301782D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5211663693009000D+0 + B=0.1563890598752899D+0 + V=0.3492420343097421D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5623469504853703D+0 + B=0.1963320810149200D+0 + V=0.3537399050235257D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6012718188659246D+0 + B=0.2357847407258738D+0 + V=0.3566209152659172D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6378179206390117D+0 + B=0.2743846121244060D+0 + V=0.3581084321919782D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4836936460214534D+0 + B=0.3895902610739024D-1 + V=0.3426522117591512D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5293792562683797D+0 + B=0.7871246819312640D-1 + V=0.3491848770121379D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5726281253100033D+0 + B=0.1187963808202981D+0 + V=0.3539318235231476D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6133658776169068D+0 + B=0.1587914708061787D+0 + V=0.3570231438458694D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6515085491865307D+0 + B=0.1983058575227646D+0 + V=0.3586207335051714D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5778692716064976D+0 + B=0.3977209689791542D-1 + V=0.3541196205164025D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6207904288086192D+0 + B=0.7990157592981152D-1 + V=0.3574296911573953D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6608688171046802D+0 + B=0.1199671308754309D+0 + V=0.3591993279818963D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6656263089489130D+0 + B=0.4015955957805969D-1 + V=0.3595855034661997D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + N=N-1 + RETURN + END + SUBROUTINE LD3470(X,Y,Z,W,N) + DOUBLE PRECISION X(3470) + DOUBLE PRECISION Y(3470) + DOUBLE PRECISION Z(3470) + DOUBLE PRECISION W(3470) + INTEGER N + DOUBLE PRECISION A,B,V +CVW +CVW LEBEDEV 3470-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=0.2040382730826330D-4 + Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.3178149703889544D-3 + Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1721420832906233D-1 + V=0.8288115128076110D-4 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4408875374981770D-1 + V=0.1360883192522954D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7594680813878681D-1 + V=0.1766854454542662D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1108335359204799D+0 + V=0.2083153161230153D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1476517054388567D+0 + V=0.2333279544657158D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1856731870860615D+0 + V=0.2532809539930247D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2243634099428821D+0 + V=0.2692472184211158D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2633006881662727D+0 + V=0.2819949946811885D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3021340904916283D+0 + V=0.2920953593973030D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3405594048030089D+0 + V=0.2999889782948352D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3783044434007372D+0 + V=0.3060292120496902D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4151194767407910D+0 + V=0.3105109167522192D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4507705766443257D+0 + V=0.3136902387550312D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4850346056573187D+0 + V=0.3157984652454632D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5176950817792470D+0 + V=0.3170516518425422D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5485384240820989D+0 + V=0.3176568425633755D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6039117238943308D+0 + V=0.3177198411207062D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6279956655573113D+0 + V=0.3175519492394733D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6493636169568952D+0 + V=0.3174654952634756D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6677644117704504D+0 + V=0.3175676415467654D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6829368572115624D+0 + V=0.3178923417835410D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6946195818184121D+0 + V=0.3183788287531909D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7025711542057026D+0 + V=0.3188755151918807D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7066004767140119D+0 + V=0.3191916889313849D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5132537689946062D-1 + V=0.1231779611744508D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1297994661331225D+0 + V=0.1924661373839880D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2188852049401307D+0 + V=0.2380881867403424D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3123174824903457D+0 + V=0.2693100663037885D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4064037620738195D+0 + V=0.2908673382834366D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4984958396944782D+0 + V=0.3053914619381535D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5864975046021365D+0 + V=0.3143916684147777D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6686711634580175D+0 + V=0.3187042244055363D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.8715738780835950D-1 + B=0.2557175233367578D-1 + V=0.1635219535869790D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1248383123134007D+0 + B=0.5604823383376681D-1 + V=0.1968109917696070D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1638062693383378D+0 + B=0.8968568601900765D-1 + V=0.2236754342249974D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2035586203373176D+0 + B=0.1254086651976279D+0 + V=0.2453186687017181D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2436798975293774D+0 + B=0.1624780150162012D+0 + V=0.2627551791580541D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2838207507773806D+0 + B=0.2003422342683208D+0 + V=0.2767654860152220D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3236787502217692D+0 + B=0.2385628026255263D+0 + V=0.2879467027765895D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3629849554840691D+0 + B=0.2767731148783578D+0 + V=0.2967639918918702D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4014948081992087D+0 + B=0.3146542308245309D+0 + V=0.3035900684660351D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4389818379260225D+0 + B=0.3519196415895088D+0 + V=0.3087338237298308D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4752331143674377D+0 + B=0.3883050984023654D+0 + V=0.3124608838860167D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5100457318374018D+0 + B=0.4235613423908649D+0 + V=0.3150084294226743D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5432238388954868D+0 + B=0.4574484717196220D+0 + V=0.3165958398598402D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5745758685072442D+0 + B=0.4897311639255524D+0 + V=0.3174320440957372D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1723981437592809D+0 + B=0.3010630597881105D-1 + V=0.2182188909812599D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2149553257844597D+0 + B=0.6326031554204694D-1 + V=0.2399727933921445D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2573256081247422D+0 + B=0.9848566980258631D-1 + V=0.2579796133514652D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2993163751238106D+0 + B=0.1350835952384266D+0 + V=0.2727114052623535D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3407238005148000D+0 + B=0.1725184055442181D+0 + V=0.2846327656281355D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3813454978483264D+0 + B=0.2103559279730725D+0 + V=0.2941491102051334D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4209848104423343D+0 + B=0.2482278774554860D+0 + V=0.3016049492136107D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4594519699996300D+0 + B=0.2858099509982883D+0 + V=0.3072949726175648D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4965640166185930D+0 + B=0.3228075659915428D+0 + V=0.3114768142886460D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5321441655571562D+0 + B=0.3589459907204151D+0 + V=0.3143823673666223D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5660208438582166D+0 + B=0.3939630088864310D+0 + V=0.3162269764661535D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5980264315964364D+0 + B=0.4276029922949089D+0 + V=0.3172164663759821D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2644215852350733D+0 + B=0.3300939429072552D-1 + V=0.2554575398967435D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3090113743443063D+0 + B=0.6803887650078501D-1 + V=0.2701704069135677D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3525871079197808D+0 + B=0.1044326136206709D+0 + V=0.2823693413468940D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3950418005354029D+0 + B=0.1416751597517679D+0 + V=0.2922898463214289D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4362475663430163D+0 + B=0.1793408610504821D+0 + V=0.3001829062162428D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4760661812145854D+0 + B=0.2170630750175722D+0 + V=0.3062890864542953D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5143551042512103D+0 + B=0.2545145157815807D+0 + V=0.3108328279264746D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5509709026935597D+0 + B=0.2913940101706601D+0 + V=0.3140243146201245D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5857711030329428D+0 + B=0.3274169910910705D+0 + V=0.3160638030977130D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6186149917404392D+0 + B=0.3623081329317265D+0 + V=0.3171462882206275D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3586894569557064D+0 + B=0.3497354386450040D-1 + V=0.2812388416031796D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4035266610019441D+0 + B=0.7129736739757095D-1 + V=0.2912137500288045D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4467775312332510D+0 + B=0.1084758620193165D+0 + V=0.2993241256502206D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4883638346608543D+0 + B=0.1460915689241772D+0 + V=0.3057101738983822D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5281908348434601D+0 + B=0.1837790832369980D+0 + V=0.3105319326251432D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5661542687149311D+0 + B=0.2212075390874021D+0 + V=0.3139565514428167D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6021450102031452D+0 + B=0.2580682841160985D+0 + V=0.3161543006806366D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6360520783610050D+0 + B=0.2940656362094121D+0 + V=0.3172985960613294D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4521611065087196D+0 + B=0.3631055365867002D-1 + V=0.2989400336901431D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4959365651560963D+0 + B=0.7348318468484350D-1 + V=0.3054555883947677D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5376815804038283D+0 + B=0.1111087643812648D+0 + V=0.3104764960807702D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5773314480243768D+0 + B=0.1488226085145408D+0 + V=0.3141015825977616D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6148113245575056D+0 + B=0.1862892274135151D+0 + V=0.3164520621159896D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6500407462842380D+0 + B=0.2231909701714456D+0 + V=0.3176652305912204D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5425151448707213D+0 + B=0.3718201306118944D-1 + V=0.3105097161023939D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5841860556907931D+0 + B=0.7483616335067346D-1 + V=0.3143014117890550D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6234632186851500D+0 + B=0.1125990834266120D+0 + V=0.3168172866287200D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6602934551848843D+0 + B=0.1501303813157619D+0 + V=0.3181401865570968D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6278573968375105D+0 + B=0.3767559930245720D-1 + V=0.3170663659156037D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6665611711264577D+0 + B=0.7548443301360158D-1 + V=0.3185447944625510D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + N=N-1 + RETURN + END + SUBROUTINE LD3890(X,Y,Z,W,N) + DOUBLE PRECISION X(3890) + DOUBLE PRECISION Y(3890) + DOUBLE PRECISION Z(3890) + DOUBLE PRECISION W(3890) + INTEGER N + DOUBLE PRECISION A,B,V +CVW +CVW LEBEDEV 3890-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=0.1807395252196920D-4 + Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.2848008782238827D-3 + Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.2836065837530581D-3 + Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1587876419858352D-1 + V=0.7013149266673816D-4 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4069193593751206D-1 + V=0.1162798021956766D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7025888115257997D-1 + V=0.1518728583972105D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1027495450028704D+0 + V=0.1798796108216934D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1371457730893426D+0 + V=0.2022593385972785D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1727758532671953D+0 + V=0.2203093105575464D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2091492038929037D+0 + V=0.2349294234299855D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2458813281751915D+0 + V=0.2467682058747003D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2826545859450066D+0 + V=0.2563092683572224D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3191957291799622D+0 + V=0.2639253896763318D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3552621469299578D+0 + V=0.2699137479265108D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3906329503406230D+0 + V=0.2745196420166739D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4251028614093031D+0 + V=0.2779529197397593D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4584777520111870D+0 + V=0.2803996086684265D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4905711358710193D+0 + V=0.2820302356715842D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5212011669847385D+0 + V=0.2830056747491068D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5501878488737995D+0 + V=0.2834808950776839D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6025037877479342D+0 + V=0.2835282339078929D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6254572689549016D+0 + V=0.2833819267065800D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6460107179528248D+0 + V=0.2832858336906784D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6639541138154251D+0 + V=0.2833268235451244D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6790688515667495D+0 + V=0.2835432677029253D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6911338580371512D+0 + V=0.2839091722743049D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6999385956126490D+0 + V=0.2843308178875841D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7053037748656896D+0 + V=0.2846703550533846D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4732224387180115D-1 + V=0.1051193406971900D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1202100529326803D+0 + V=0.1657871838796974D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2034304820664855D+0 + V=0.2064648113714232D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2912285643573002D+0 + V=0.2347942745819741D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3802361792726768D+0 + V=0.2547775326597726D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4680598511056146D+0 + V=0.2686876684847025D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5528151052155599D+0 + V=0.2778665755515867D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6329386307803041D+0 + V=0.2830996616782929D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.8056516651369069D-1 + B=0.2363454684003124D-1 + V=0.1403063340168372D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1156476077139389D+0 + B=0.5191291632545936D-1 + V=0.1696504125939477D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1520473382760421D+0 + B=0.8322715736994519D-1 + V=0.1935787242745390D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1892986699745931D+0 + B=0.1165855667993712D+0 + V=0.2130614510521968D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2270194446777792D+0 + B=0.1513077167409504D+0 + V=0.2289381265931048D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2648908185093273D+0 + B=0.1868882025807859D+0 + V=0.2418630292816186D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3026389259574136D+0 + B=0.2229277629776224D+0 + V=0.2523400495631193D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3400220296151384D+0 + B=0.2590951840746235D+0 + V=0.2607623973449605D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3768217953335510D+0 + B=0.2951047291750847D+0 + V=0.2674441032689209D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4128372900921884D+0 + B=0.3307019714169930D+0 + V=0.2726432360343356D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4478807131815630D+0 + B=0.3656544101087634D+0 + V=0.2765787685924545D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4817742034089257D+0 + B=0.3997448951939695D+0 + V=0.2794428690642224D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5143472814653344D+0 + B=0.4327667110812024D+0 + V=0.2814099002062895D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5454346213905650D+0 + B=0.4645196123532293D+0 + V=0.2826429531578994D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5748739313170252D+0 + B=0.4948063555703345D+0 + V=0.2832983542550884D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1599598738286342D+0 + B=0.2792357590048985D-1 + V=0.1886695565284976D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1998097412500951D+0 + B=0.5877141038139065D-1 + V=0.2081867882748234D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2396228952566202D+0 + B=0.9164573914691377D-1 + V=0.2245148680600796D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2792228341097746D+0 + B=0.1259049641962687D+0 + V=0.2380370491511872D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3184251107546741D+0 + B=0.1610594823400863D+0 + V=0.2491398041852455D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3570481164426244D+0 + B=0.1967151653460898D+0 + V=0.2581632405881230D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3949164710492144D+0 + B=0.2325404606175168D+0 + V=0.2653965506227417D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4318617293970503D+0 + B=0.2682461141151439D+0 + V=0.2710857216747087D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4677221009931678D+0 + B=0.3035720116011973D+0 + V=0.2754434093903659D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5023417939270955D+0 + B=0.3382781859197439D+0 + V=0.2786579932519380D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5355701836636128D+0 + B=0.3721383065625942D+0 + V=0.2809011080679474D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5672608451328771D+0 + B=0.4049346360466055D+0 + V=0.2823336184560987D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5972704202540162D+0 + B=0.4364538098633802D+0 + V=0.2831101175806309D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2461687022333596D+0 + B=0.3070423166833368D-1 + V=0.2221679970354546D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2881774566286831D+0 + B=0.6338034669281885D-1 + V=0.2356185734270703D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3293963604116978D+0 + B=0.9742862487067941D-1 + V=0.2469228344805590D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3697303822241377D+0 + B=0.1323799532282290D+0 + V=0.2562726348642046D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4090663023135127D+0 + B=0.1678497018129336D+0 + V=0.2638756726753028D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4472819355411712D+0 + B=0.2035095105326114D+0 + V=0.2699311157390862D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4842513377231437D+0 + B=0.2390692566672091D+0 + V=0.2746233268403837D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5198477629962928D+0 + B=0.2742649818076149D+0 + V=0.2781225674454771D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5539453011883145D+0 + B=0.3088503806580094D+0 + V=0.2805881254045684D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5864196762401251D+0 + B=0.3425904245906614D+0 + V=0.2821719877004913D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6171484466668390D+0 + B=0.3752562294789468D+0 + V=0.2830222502333124D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3350337830565727D+0 + B=0.3261589934634747D-1 + V=0.2457995956744870D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3775773224758284D+0 + B=0.6658438928081572D-1 + V=0.2551474407503706D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4188155229848973D+0 + B=0.1014565797157954D+0 + V=0.2629065335195311D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4586805892009344D+0 + B=0.1368573320843822D+0 + V=0.2691900449925075D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4970895714224235D+0 + B=0.1724614851951608D+0 + V=0.2741275485754276D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5339505133960747D+0 + B=0.2079779381416412D+0 + V=0.2778530970122595D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5691665792531440D+0 + B=0.2431385788322288D+0 + V=0.2805010567646741D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6026387682680377D+0 + B=0.2776901883049853D+0 + V=0.2822055834031040D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6342676150163307D+0 + B=0.3113881356386632D+0 + V=0.2831016901243473D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4237951119537067D+0 + B=0.3394877848664351D-1 + V=0.2624474901131803D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4656918683234929D+0 + B=0.6880219556291447D-1 + V=0.2688034163039377D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5058857069185980D+0 + B=0.1041946859721635D+0 + V=0.2738932751287636D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5443204666713996D+0 + B=0.1398039738736393D+0 + V=0.2777944791242523D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5809298813759742D+0 + B=0.1753373381196155D+0 + V=0.2806011661660987D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6156416039447128D+0 + B=0.2105215793514010D+0 + V=0.2824181456597460D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6483801351066604D+0 + B=0.2450953312157051D+0 + V=0.2833585216577828D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5103616577251688D+0 + B=0.3485560643800719D-1 + V=0.2738165236962878D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5506738792580681D+0 + B=0.7026308631512033D-1 + V=0.2778365208203180D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5889573040995292D+0 + B=0.1059035061296403D+0 + V=0.2807852940418966D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6251641589516930D+0 + B=0.1414823925236026D+0 + V=0.2827245949674705D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6592414921570178D+0 + B=0.1767207908214530D+0 + V=0.2837342344829828D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5930314017533384D+0 + B=0.3542189339561672D-1 + V=0.2809233907610981D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6309812253390175D+0 + B=0.7109574040369549D-1 + V=0.2829930809742694D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6666296011353230D+0 + B=0.1067259792282730D+0 + V=0.2841097874111479D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6703715271049922D+0 + B=0.3569455268820809D-1 + V=0.2843455206008783D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + N=N-1 + RETURN + END + SUBROUTINE LD4334(X,Y,Z,W,N) + DOUBLE PRECISION X(4334) + DOUBLE PRECISION Y(4334) + DOUBLE PRECISION Z(4334) + DOUBLE PRECISION W(4334) + INTEGER N + DOUBLE PRECISION A,B,V +CVW +CVW LEBEDEV 4334-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=0.1449063022537883D-4 + Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.2546377329828424D-3 + Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1462896151831013D-1 + V=0.6018432961087496D-4 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3769840812493139D-1 + V=0.1002286583263673D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6524701904096891D-1 + V=0.1315222931028093D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.9560543416134648D-1 + V=0.1564213746876724D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1278335898929198D+0 + V=0.1765118841507736D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1613096104466031D+0 + V=0.1928737099311080D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1955806225745371D+0 + V=0.2062658534263270D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2302935218498028D+0 + V=0.2172395445953787D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2651584344113027D+0 + V=0.2262076188876047D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2999276825183209D+0 + V=0.2334885699462397D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3343828669718798D+0 + V=0.2393355273179203D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3683265013750518D+0 + V=0.2439559200468863D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4015763206518108D+0 + V=0.2475251866060002D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4339612026399770D+0 + V=0.2501965558158773D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4653180651114582D+0 + V=0.2521081407925925D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4954893331080803D+0 + V=0.2533881002388081D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5243207068924930D+0 + V=0.2541582900848261D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5516590479041704D+0 + V=0.2545365737525860D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6012371927804176D+0 + V=0.2545726993066799D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6231574466449819D+0 + V=0.2544456197465555D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6429416514181271D+0 + V=0.2543481596881064D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6604124272943595D+0 + V=0.2543506451429194D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6753851470408250D+0 + V=0.2544905675493763D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6876717970626160D+0 + V=0.2547611407344429D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6970895061319234D+0 + V=0.2551060375448869D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7034746912553310D+0 + V=0.2554291933816039D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7067017217542295D+0 + V=0.2556255710686343D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4382223501131123D-1 + V=0.9041339695118195D-4 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1117474077400006D+0 + V=0.1438426330079022D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1897153252911440D+0 + V=0.1802523089820518D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2724023009910331D+0 + V=0.2060052290565496D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3567163308709902D+0 + V=0.2245002248967466D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4404784483028087D+0 + V=0.2377059847731150D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5219833154161411D+0 + V=0.2468118955882525D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5998179868977553D+0 + V=0.2525410872966528D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6727803154548222D+0 + V=0.2553101409933397D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7476563943166086D-1 + B=0.2193168509461185D-1 + V=0.1212879733668632D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1075341482001416D+0 + B=0.4826419281533887D-1 + V=0.1472872881270931D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1416344885203259D+0 + B=0.7751191883575742D-1 + V=0.1686846601010828D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1766325315388586D+0 + B=0.1087558139247680D+0 + V=0.1862698414660208D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2121744174481514D+0 + B=0.1413661374253096D+0 + V=0.2007430956991861D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2479669443408145D+0 + B=0.1748768214258880D+0 + V=0.2126568125394796D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2837600452294113D+0 + B=0.2089216406612073D+0 + V=0.2224394603372113D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3193344933193984D+0 + B=0.2431987685545972D+0 + V=0.2304264522673135D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3544935442438745D+0 + B=0.2774497054377770D+0 + V=0.2368854288424087D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3890571932288154D+0 + B=0.3114460356156915D+0 + V=0.2420352089461772D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4228581214259090D+0 + B=0.3449806851913012D+0 + V=0.2460597113081295D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4557387211304052D+0 + B=0.3778618641248256D+0 + V=0.2491181912257687D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4875487950541643D+0 + B=0.4099086391698978D+0 + V=0.2513528194205857D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5181436529962997D+0 + B=0.4409474925853973D+0 + V=0.2528943096693220D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5473824095600661D+0 + B=0.4708094517711291D+0 + V=0.2538660368488136D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5751263398976174D+0 + B=0.4993275140354637D+0 + V=0.2543868648299022D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1489515746840028D+0 + B=0.2599381993267017D-1 + V=0.1642595537825183D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1863656444351767D+0 + B=0.5479286532462190D-1 + V=0.1818246659849308D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2238602880356348D+0 + B=0.8556763251425254D-1 + V=0.1966565649492420D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2612723375728160D+0 + B=0.1177257802267011D+0 + V=0.2090677905657991D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2984332990206190D+0 + B=0.1508168456192700D+0 + V=0.2193820409510504D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3351786584663333D+0 + B=0.1844801892177727D+0 + V=0.2278870827661928D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3713505522209120D+0 + B=0.2184145236087598D+0 + V=0.2348283192282090D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4067981098954663D+0 + B=0.2523590641486229D+0 + V=0.2404139755581477D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4413769993687534D+0 + B=0.2860812976901373D+0 + V=0.2448227407760734D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4749487182516394D+0 + B=0.3193686757808996D+0 + V=0.2482110455592573D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5073798105075426D+0 + B=0.3520226949547602D+0 + V=0.2507192397774103D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5385410448878654D+0 + B=0.3838544395667890D+0 + V=0.2524765968534880D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5683065353670530D+0 + B=0.4146810037640963D+0 + V=0.2536052388539425D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5965527620663510D+0 + B=0.4443224094681121D+0 + V=0.2542230588033068D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2299227700856157D+0 + B=0.2865757664057584D-1 + V=0.1944817013047896D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2695752998553267D+0 + B=0.5923421684485993D-1 + V=0.2067862362746635D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3086178716611389D+0 + B=0.9117817776057715D-1 + V=0.2172440734649114D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3469649871659077D+0 + B=0.1240593814082605D+0 + V=0.2260125991723423D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3845153566319655D+0 + B=0.1575272058259175D+0 + V=0.2332655008689523D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4211600033403215D+0 + B=0.1912845163525413D+0 + V=0.2391699681532458D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4567867834329882D+0 + B=0.2250710177858171D+0 + V=0.2438801528273928D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4912829319232061D+0 + B=0.2586521303440910D+0 + V=0.2475370504260665D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5245364793303812D+0 + B=0.2918112242865407D+0 + V=0.2502707235640574D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5564369788915756D+0 + B=0.3243439239067890D+0 + V=0.2522031701054241D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5868757697775287D+0 + B=0.3560536787835351D+0 + V=0.2534511269978784D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6157458853519617D+0 + B=0.3867480821242581D+0 + V=0.2541284914955151D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3138461110672113D+0 + B=0.3051374637507278D-1 + V=0.2161509250688394D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3542495872050569D+0 + B=0.6237111233730755D-1 + V=0.2248778513437852D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3935751553120181D+0 + B=0.9516223952401907D-1 + V=0.2322388803404617D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4317634668111147D+0 + B=0.1285467341508517D+0 + V=0.2383265471001355D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4687413842250821D+0 + B=0.1622318931656033D+0 + V=0.2432476675019525D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5044274237060283D+0 + B=0.1959581153836453D+0 + V=0.2471122223750674D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5387354077925727D+0 + B=0.2294888081183837D+0 + V=0.2500291752486870D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5715768898356105D+0 + B=0.2626031152713945D+0 + V=0.2521055942764682D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6028627200136111D+0 + B=0.2950904075286713D+0 + V=0.2534472785575503D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6325039812653463D+0 + B=0.3267458451113286D+0 + V=0.2541599713080121D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3981986708423407D+0 + B=0.3183291458749821D-1 + V=0.2317380975862936D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4382791182133300D+0 + B=0.6459548193880908D-1 + V=0.2378550733719775D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4769233057218166D+0 + B=0.9795757037087952D-1 + V=0.2428884456739118D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5140823911194238D+0 + B=0.1316307235126655D+0 + V=0.2469002655757292D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5496977833862983D+0 + B=0.1653556486358704D+0 + V=0.2499657574265851D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5837047306512727D+0 + B=0.1988931724126510D+0 + V=0.2521676168486082D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6160349566926879D+0 + B=0.2320174581438950D+0 + V=0.2535935662645334D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6466185353209440D+0 + B=0.2645106562168662D+0 + V=0.2543356743363214D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4810835158795404D+0 + B=0.3275917807743992D-1 + V=0.2427353285201535D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5199925041324341D+0 + B=0.6612546183967181D-1 + V=0.2468258039744386D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5571717692207494D+0 + B=0.9981498331474143D-1 + V=0.2500060956440310D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5925789250836378D+0 + B=0.1335687001410374D+0 + V=0.2523238365420979D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6261658523859670D+0 + B=0.1671444402896463D+0 + V=0.2538399260252846D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6578811126669331D+0 + B=0.2003106382156076D+0 + V=0.2546255927268069D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5609624612998100D+0 + B=0.3337500940231335D-1 + V=0.2500583360048449D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5979959659984670D+0 + B=0.6708750335901803D-1 + V=0.2524777638260203D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6330523711054002D+0 + B=0.1008792126424850D+0 + V=0.2540951193860656D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6660960998103972D+0 + B=0.1345050343171794D+0 + V=0.2549524085027472D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6365384364585819D+0 + B=0.3372799460737052D-1 + V=0.2542569507009158D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6710994302899275D+0 + B=0.6755249309678028D-1 + V=0.2552114127580376D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + N=N-1 + RETURN + END + SUBROUTINE LD4802(X,Y,Z,W,N) + DOUBLE PRECISION X(4802) + DOUBLE PRECISION Y(4802) + DOUBLE PRECISION Z(4802) + DOUBLE PRECISION W(4802) + INTEGER N + DOUBLE PRECISION A,B,V +CVW +CVW LEBEDEV 4802-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=0.9687521879420705D-4 + Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.2307897895367918D-3 + Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.2297310852498558D-3 + Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2335728608887064D-1 + V=0.7386265944001919D-4 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4352987836550653D-1 + V=0.8257977698542210D-4 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6439200521088801D-1 + V=0.9706044762057630D-4 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.9003943631993181D-1 + V=0.1302393847117003D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1196706615548473D+0 + V=0.1541957004600968D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1511715412838134D+0 + V=0.1704459770092199D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1835982828503801D+0 + V=0.1827374890942906D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2165081259155405D+0 + V=0.1926360817436107D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2496208720417563D+0 + V=0.2008010239494833D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2827200673567900D+0 + V=0.2075635983209175D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3156190823994346D+0 + V=0.2131306638690909D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3481476793749115D+0 + V=0.2176562329937335D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3801466086947226D+0 + V=0.2212682262991018D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4114652119634011D+0 + V=0.2240799515668565D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4419598786519751D+0 + V=0.2261959816187525D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4714925949329543D+0 + V=0.2277156368808855D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4999293972879466D+0 + V=0.2287351772128336D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5271387221431248D+0 + V=0.2293490814084085D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5529896780837761D+0 + V=0.2296505312376273D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6000856099481712D+0 + V=0.2296793832318756D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6210562192785175D+0 + V=0.2295785443842974D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6401165879934240D+0 + V=0.2295017931529102D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6571144029244334D+0 + V=0.2295059638184868D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6718910821718863D+0 + V=0.2296232343237362D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6842845591099010D+0 + V=0.2298530178740771D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6941353476269816D+0 + V=0.2301579790280501D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7012965242212991D+0 + V=0.2304690404996513D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7056471428242644D+0 + V=0.2307027995907102D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4595557643585895D-1 + V=0.9312274696671092D-4 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1049316742435023D+0 + V=0.1199919385876926D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1773548879549274D+0 + V=0.1598039138877690D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2559071411236127D+0 + V=0.1822253763574900D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3358156837985898D+0 + V=0.1988579593655040D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4155835743763893D+0 + V=0.2112620102533307D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4937894296167472D+0 + V=0.2201594887699007D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5691569694793316D+0 + V=0.2261622590895036D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6405840854894251D+0 + V=0.2296458453435705D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7345133894143348D-1 + B=0.2177844081486067D-1 + V=0.1006006990267000D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1009859834044931D+0 + B=0.4590362185775188D-1 + V=0.1227676689635876D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1324289619748758D+0 + B=0.7255063095690877D-1 + V=0.1467864280270117D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1654272109607127D+0 + B=0.1017825451960684D+0 + V=0.1644178912101232D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1990767186776461D+0 + B=0.1325652320980364D+0 + V=0.1777664890718961D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2330125945523278D+0 + B=0.1642765374496765D+0 + V=0.1884825664516690D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2670080611108287D+0 + B=0.1965360374337889D+0 + V=0.1973269246453848D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3008753376294316D+0 + B=0.2290726770542238D+0 + V=0.2046767775855328D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3344475596167860D+0 + B=0.2616645495370823D+0 + V=0.2107600125918040D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3675709724070786D+0 + B=0.2941150728843141D+0 + V=0.2157416362266829D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4001000887587812D+0 + B=0.3262440400919066D+0 + V=0.2197557816920721D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4318956350436028D+0 + B=0.3578835350611916D+0 + V=0.2229192611835437D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4628239056795531D+0 + B=0.3888751854043678D+0 + V=0.2253385110212775D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4927563229773636D+0 + B=0.4190678003222840D+0 + V=0.2271137107548774D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5215687136707969D+0 + B=0.4483151836883852D+0 + V=0.2283414092917525D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5491402346984905D+0 + B=0.4764740676087880D+0 + V=0.2291161673130077D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5753520160126075D+0 + B=0.5034021310998277D+0 + V=0.2295313908576598D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1388326356417754D+0 + B=0.2435436510372806D-1 + V=0.1438204721359031D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1743686900537244D+0 + B=0.5118897057342652D-1 + V=0.1607738025495257D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2099737037950268D+0 + B=0.8014695048539634D-1 + V=0.1741483853528379D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2454492590908548D+0 + B=0.1105117874155699D+0 + V=0.1851918467519151D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2807219257864278D+0 + B=0.1417950531570966D+0 + V=0.1944628638070613D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3156842271975842D+0 + B=0.1736604945719597D+0 + V=0.2022495446275152D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3502090945177752D+0 + B=0.2058466324693981D+0 + V=0.2087462382438514D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3841684849519686D+0 + B=0.2381284261195919D+0 + V=0.2141074754818308D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4174372367906016D+0 + B=0.2703031270422569D+0 + V=0.2184640913748162D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4498926465011892D+0 + B=0.3021845683091309D+0 + V=0.2219309165220329D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4814146229807701D+0 + B=0.3335993355165720D+0 + V=0.2246123118340624D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5118863625734701D+0 + B=0.3643833735518232D+0 + V=0.2266062766915125D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5411947455119144D+0 + B=0.3943789541958179D+0 + V=0.2280072952230796D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5692301500357246D+0 + B=0.4234320144403542D+0 + V=0.2289082025202583D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5958857204139576D+0 + B=0.4513897947419260D+0 + V=0.2294012695120025D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2156270284785766D+0 + B=0.2681225755444491D-1 + V=0.1722434488736947D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2532385054909710D+0 + B=0.5557495747805614D-1 + V=0.1830237421455091D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2902564617771537D+0 + B=0.8569368062950249D-1 + V=0.1923855349997633D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3266979823143256D+0 + B=0.1167367450324135D+0 + V=0.2004067861936271D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3625039627493614D+0 + B=0.1483861994003304D+0 + V=0.2071817297354263D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3975838937548699D+0 + B=0.1803821503011405D+0 + V=0.2128250834102103D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4318396099009774D+0 + B=0.2124962965666424D+0 + V=0.2174513719440102D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4651706555732742D+0 + B=0.2445221837805913D+0 + V=0.2211661839150214D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4974752649620969D+0 + B=0.2762701224322987D+0 + V=0.2240665257813102D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5286517579627517D+0 + B=0.3075627775211328D+0 + V=0.2262439516632620D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5586001195731895D+0 + B=0.3382311089826877D+0 + V=0.2277874557231869D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5872229902021319D+0 + B=0.3681108834741399D+0 + V=0.2287854314454994D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6144258616235123D+0 + B=0.3970397446872839D+0 + V=0.2293268499615575D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2951676508064861D+0 + B=0.2867499538750441D-1 + V=0.1912628201529828D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3335085485472725D+0 + B=0.5867879341903510D-1 + V=0.1992499672238701D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3709561760636381D+0 + B=0.8961099205022284D-1 + V=0.2061275533454027D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4074722861667498D+0 + B=0.1211627927626297D+0 + V=0.2119318215968572D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4429923648839117D+0 + B=0.1530748903554898D+0 + V=0.2167416581882652D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4774428052721736D+0 + B=0.1851176436721877D+0 + V=0.2206430730516600D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5107446539535904D+0 + B=0.2170829107658179D+0 + V=0.2237186938699523D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5428151370542935D+0 + B=0.2487786689026271D+0 + V=0.2260480075032884D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5735699292556964D+0 + B=0.2800239952795016D+0 + V=0.2277098884558542D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6029253794562866D+0 + B=0.3106445702878119D+0 + V=0.2287845715109671D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6307998987073145D+0 + B=0.3404689500841194D+0 + V=0.2293547268236294D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3752652273692719D+0 + B=0.2997145098184479D-1 + V=0.2056073839852528D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4135383879344028D+0 + B=0.6086725898678011D-1 + V=0.2114235865831876D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4506113885153907D+0 + B=0.9238849548435643D-1 + V=0.2163175629770551D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4864401554606072D+0 + B=0.1242786603851851D+0 + V=0.2203392158111650D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5209708076611709D+0 + B=0.1563086731483386D+0 + V=0.2235473176847839D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5541422135830122D+0 + B=0.1882696509388506D+0 + V=0.2260024141501235D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5858880915113817D+0 + B=0.2199672979126059D+0 + V=0.2277675929329182D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6161399390603444D+0 + B=0.2512165482924867D+0 + V=0.2289102112284834D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6448296482255090D+0 + B=0.2818368701871888D+0 + V=0.2295027954625118D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4544796274917948D+0 + B=0.3088970405060312D-1 + V=0.2161281589879992D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4919389072146628D+0 + B=0.6240947677636835D-1 + V=0.2201980477395102D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5279313026985183D+0 + B=0.9430706144280313D-1 + V=0.2234952066593166D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5624169925571135D+0 + B=0.1263547818770374D+0 + V=0.2260540098520838D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5953484627093287D+0 + B=0.1583430788822594D+0 + V=0.2279157981899988D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6266730715339185D+0 + B=0.1900748462555988D+0 + V=0.2291296918565571D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6563363204278871D+0 + B=0.2213599519592567D+0 + V=0.2297533752536649D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5314574716585696D+0 + B=0.3152508811515374D-1 + V=0.2234927356465995D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5674614932298185D+0 + B=0.6343865291465561D-1 + V=0.2261288012985219D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6017706004970264D+0 + B=0.9551503504223951D-1 + V=0.2280818160923688D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6343471270264178D+0 + B=0.1275440099801196D+0 + V=0.2293773295180159D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6651494599127802D+0 + B=0.1593252037671960D+0 + V=0.2300528767338634D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6050184986005704D+0 + B=0.3192538338496105D-1 + V=0.2281893855065666D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6390163550880400D+0 + B=0.6402824353962306D-1 + V=0.2295720444840727D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6711199107088448D+0 + B=0.9609805077002909D-1 + V=0.2303227649026753D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6741354429572275D+0 + B=0.3211853196273233D-1 + V=0.2304831913227114D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + N=N-1 + RETURN + END + SUBROUTINE LD5294(X,Y,Z,W,N) + DOUBLE PRECISION X(5294) + DOUBLE PRECISION Y(5294) + DOUBLE PRECISION Z(5294) + DOUBLE PRECISION W(5294) + INTEGER N + DOUBLE PRECISION A,B,V +CVW +CVW LEBEDEV 5294-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=0.9080510764308163D-4 + Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.2084824361987793D-3 + Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2303261686261450D-1 + V=0.5011105657239616D-4 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3757208620162394D-1 + V=0.5942520409683854D-4 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5821912033821852D-1 + V=0.9564394826109721D-4 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.8403127529194872D-1 + V=0.1185530657126338D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1122927798060578D+0 + V=0.1364510114230331D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1420125319192987D+0 + V=0.1505828825605415D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1726396437341978D+0 + V=0.1619298749867023D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2038170058115696D+0 + V=0.1712450504267789D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2352849892876508D+0 + V=0.1789891098164999D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2668363354312461D+0 + V=0.1854474955629795D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2982941279900452D+0 + V=0.1908148636673661D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3295002922087076D+0 + V=0.1952377405281833D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3603094918363593D+0 + V=0.1988349254282232D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3905857895173920D+0 + V=0.2017079807160050D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4202005758160837D+0 + V=0.2039473082709094D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4490310061597227D+0 + V=0.2056360279288953D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4769586160311491D+0 + V=0.2068525823066865D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5038679887049750D+0 + V=0.2076724877534488D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5296454286519961D+0 + V=0.2081694278237885D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5541776207164850D+0 + V=0.2084157631219326D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5990467321921213D+0 + V=0.2084381531128593D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6191467096294587D+0 + V=0.2083476277129307D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6375251212901849D+0 + V=0.2082686194459732D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6540514381131168D+0 + V=0.2082475686112415D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6685899064391510D+0 + V=0.2083139860289915D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6810013009681648D+0 + V=0.2084745561831237D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6911469578730340D+0 + V=0.2087091313375890D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6988956915141736D+0 + V=0.2089718413297697D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7041335794868720D+0 + V=0.2092003303479793D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7067754398018567D+0 + V=0.2093336148263241D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3840368707853623D-1 + V=0.7591708117365267D-4 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.9835485954117399D-1 + V=0.1083383968169186D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1665774947612998D+0 + V=0.1403019395292510D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2405702335362910D+0 + V=0.1615970179286436D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3165270770189046D+0 + V=0.1771144187504911D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3927386145645443D+0 + V=0.1887760022988168D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4678825918374656D+0 + V=0.1973474670768214D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5408022024266935D+0 + V=0.2033787661234659D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6104967445752438D+0 + V=0.2072343626517331D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6760910702685738D+0 + V=0.2091177834226918D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6655644120217392D-1 + B=0.1936508874588424D-1 + V=0.9316684484675566D-4 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.9446246161270182D-1 + B=0.4252442002115869D-1 + V=0.1116193688682976D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1242651925452509D+0 + B=0.6806529315354374D-1 + V=0.1298623551559414D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1553438064846751D+0 + B=0.9560957491205369D-1 + V=0.1450236832456426D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1871137110542670D+0 + B=0.1245931657452888D+0 + V=0.1572719958149914D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2192612628836257D+0 + B=0.1545385828778978D+0 + V=0.1673234785867195D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2515682807206955D+0 + B=0.1851004249723368D+0 + V=0.1756860118725188D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2838535866287290D+0 + B=0.2160182608272384D+0 + V=0.1826776290439367D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3159578817528521D+0 + B=0.2470799012277111D+0 + V=0.1885116347992865D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3477370882791392D+0 + B=0.2781014208986402D+0 + V=0.1933457860170574D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3790576960890540D+0 + B=0.3089172523515731D+0 + V=0.1973060671902064D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4097938317810200D+0 + B=0.3393750055472244D+0 + V=0.2004987099616311D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4398256572859637D+0 + B=0.3693322470987730D+0 + V=0.2030170909281499D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4690384114718480D+0 + B=0.3986541005609877D+0 + V=0.2049461460119080D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4973216048301053D+0 + B=0.4272112491408562D+0 + V=0.2063653565200186D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5245681526132446D+0 + B=0.4548781735309936D+0 + V=0.2073507927381027D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5506733911803888D+0 + B=0.4815315355023251D+0 + V=0.2079764593256122D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5755339829522475D+0 + B=0.5070486445801855D+0 + V=0.2083150534968778D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1305472386056362D+0 + B=0.2284970375722366D-1 + V=0.1262715121590664D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1637327908216477D+0 + B=0.4812254338288384D-1 + V=0.1414386128545972D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1972734634149637D+0 + B=0.7531734457511935D-1 + V=0.1538740401313898D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2308694653110130D+0 + B=0.1039043639882017D+0 + V=0.1642434942331432D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2643899218338160D+0 + B=0.1334526587117626D+0 + V=0.1729790609237496D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2977171599622171D+0 + B=0.1636414868936382D+0 + V=0.1803505190260828D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3307293903032310D+0 + B=0.1942195406166568D+0 + V=0.1865475350079657D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3633069198219073D+0 + B=0.2249752879943753D+0 + V=0.1917182669679069D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3953346955922727D+0 + B=0.2557218821820032D+0 + V=0.1959851709034382D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4267018394184914D+0 + B=0.2862897925213193D+0 + V=0.1994529548117882D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4573009622571704D+0 + B=0.3165224536636518D+0 + V=0.2022138911146548D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4870279559856109D+0 + B=0.3462730221636496D+0 + V=0.2043518024208592D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5157819581450322D+0 + B=0.3754016870282835D+0 + V=0.2059450313018110D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5434651666465393D+0 + B=0.4037733784993613D+0 + V=0.2070685715318472D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5699823887764627D+0 + B=0.4312557784139123D+0 + V=0.2077955310694373D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5952403350947741D+0 + B=0.4577175367122110D+0 + V=0.2081980387824712D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2025152599210369D+0 + B=0.2520253617719557D-1 + V=0.1521318610377956D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2381066653274425D+0 + B=0.5223254506119000D-1 + V=0.1622772720185755D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2732823383651612D+0 + B=0.8060669688588620D-1 + V=0.1710498139420709D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3080137692611118D+0 + B=0.1099335754081255D+0 + V=0.1785911149448736D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3422405614587601D+0 + B=0.1399120955959857D+0 + V=0.1850125313687736D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3758808773890420D+0 + B=0.1702977801651705D+0 + V=0.1904229703933298D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4088458383438932D+0 + B=0.2008799256601680D+0 + V=0.1949259956121987D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4410450550841152D+0 + B=0.2314703052180836D+0 + V=0.1986161545363960D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4723879420561312D+0 + B=0.2618972111375892D+0 + V=0.2015790585641370D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5027843561874343D+0 + B=0.2920013195600270D+0 + V=0.2038934198707418D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5321453674452458D+0 + B=0.3216322555190551D+0 + V=0.2056334060538251D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5603839113834030D+0 + B=0.3506456615934198D+0 + V=0.2068705959462289D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5874150706875146D+0 + B=0.3789007181306267D+0 + V=0.2076753906106002D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6131559381660038D+0 + B=0.4062580170572782D+0 + V=0.2081179391734803D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2778497016394506D+0 + B=0.2696271276876226D-1 + V=0.1700345216228943D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3143733562261912D+0 + B=0.5523469316960465D-1 + V=0.1774906779990410D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3501485810261827D+0 + B=0.8445193201626464D-1 + V=0.1839659377002642D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3851430322303653D+0 + B=0.1143263119336083D+0 + V=0.1894987462975169D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4193013979470415D+0 + B=0.1446177898344475D+0 + V=0.1941548809452595D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4525585960458567D+0 + B=0.1751165438438091D+0 + V=0.1980078427252384D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4848447779622947D+0 + B=0.2056338306745660D+0 + V=0.2011296284744488D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5160871208276894D+0 + B=0.2359965487229226D+0 + V=0.2035888456966776D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5462112185696926D+0 + B=0.2660430223139146D+0 + V=0.2054516325352142D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5751425068101757D+0 + B=0.2956193664498032D+0 + V=0.2067831033092635D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6028073872853596D+0 + B=0.3245763905312779D+0 + V=0.2076485320284876D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6291338275278409D+0 + B=0.3527670026206972D+0 + V=0.2081141439525255D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3541797528439391D+0 + B=0.2823853479435550D-1 + V=0.1834383015469222D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3908234972074657D+0 + B=0.5741296374713106D-1 + V=0.1889540591777677D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4264408450107590D+0 + B=0.8724646633650199D-1 + V=0.1936677023597375D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4609949666553286D+0 + B=0.1175034422915616D+0 + V=0.1976176495066504D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4944389496536006D+0 + B=0.1479755652628428D+0 + V=0.2008536004560983D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5267194884346086D+0 + B=0.1784740659484352D+0 + V=0.2034280351712291D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5577787810220990D+0 + B=0.2088245700431244D+0 + V=0.2053944466027758D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5875563763536670D+0 + B=0.2388628136570763D+0 + V=0.2068077642882360D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6159910016391269D+0 + B=0.2684308928769185D+0 + V=0.2077250949661599D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6430219602956268D+0 + B=0.2973740761960252D+0 + V=0.2082062440705320D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4300647036213646D+0 + B=0.2916399920493977D-1 + V=0.1934374486546626D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4661486308935531D+0 + B=0.5898803024755659D-1 + V=0.1974107010484300D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5009658555287261D+0 + B=0.8924162698525409D-1 + V=0.2007129290388658D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5344824270447704D+0 + B=0.1197185199637321D+0 + V=0.2033736947471293D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5666575997416371D+0 + B=0.1502300756161382D+0 + V=0.2054287125902493D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5974457471404752D+0 + B=0.1806004191913564D+0 + V=0.2069184936818894D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6267984444116886D+0 + B=0.2106621764786252D+0 + V=0.2078883689808782D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6546664713575417D+0 + B=0.2402526932671914D+0 + V=0.2083886366116359D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5042711004437253D+0 + B=0.2982529203607657D-1 + V=0.2006593275470817D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5392127456774380D+0 + B=0.6008728062339922D-1 + V=0.2033728426135397D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5726819437668618D+0 + B=0.9058227674571398D-1 + V=0.2055008781377608D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6046469254207278D+0 + B=0.1211219235803400D+0 + V=0.2070651783518502D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6350716157434952D+0 + B=0.1515286404791580D+0 + V=0.2080953335094320D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6639177679185454D+0 + B=0.1816314681255552D+0 + V=0.2086284998988521D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5757276040972253D+0 + B=0.3026991752575440D-1 + V=0.2055549387644668D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6090265823139755D+0 + B=0.6078402297870770D-1 + V=0.2071871850267654D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6406735344387661D+0 + B=0.9135459984176636D-1 + V=0.2082856600431965D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6706397927793709D+0 + B=0.1218024155966590D+0 + V=0.2088705858819358D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6435019674426665D+0 + B=0.3052608357660639D-1 + V=0.2083995867536322D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6747218676375681D+0 + B=0.6112185773983089D-1 + V=0.2090509712889637D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + N=N-1 + RETURN + END + SUBROUTINE LD5810(X,Y,Z,W,N) + DOUBLE PRECISION X(5810) + DOUBLE PRECISION Y(5810) + DOUBLE PRECISION Z(5810) + DOUBLE PRECISION W(5810) + INTEGER N + DOUBLE PRECISION A,B,V +CVW +CVW LEBEDEV 5810-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=0.9735347946175486D-5 + Call GEN_OH( 1, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.1907581241803167D-3 + Call GEN_OH( 2, N, X(N), Y(N), Z(N), W(N), A, B, V) + V=0.1901059546737578D-3 + Call GEN_OH( 3, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1182361662400277D-1 + V=0.3926424538919212D-4 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3062145009138958D-1 + V=0.6667905467294382D-4 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5329794036834243D-1 + V=0.8868891315019135D-4 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7848165532862220D-1 + V=0.1066306000958872D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1054038157636201D+0 + V=0.1214506743336128D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1335577797766211D+0 + V=0.1338054681640871D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1625769955502252D+0 + V=0.1441677023628504D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1921787193412792D+0 + V=0.1528880200826557D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2221340534690548D+0 + V=0.1602330623773609D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2522504912791132D+0 + V=0.1664102653445244D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2823610860679697D+0 + V=0.1715845854011323D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3123173966267560D+0 + V=0.1758901000133069D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3419847036953789D+0 + V=0.1794382485256736D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3712386456999758D+0 + V=0.1823238106757407D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3999627649876828D+0 + V=0.1846293252959976D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4280466458648093D+0 + V=0.1864284079323098D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4553844360185711D+0 + V=0.1877882694626914D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4818736094437834D+0 + V=0.1887716321852025D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5074138709260629D+0 + V=0.1894381638175673D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5319061304570707D+0 + V=0.1898454899533629D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5552514978677286D+0 + V=0.1900497929577815D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5981009025246183D+0 + V=0.1900671501924092D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6173990192228116D+0 + V=0.1899837555533510D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6351365239411131D+0 + V=0.1899014113156229D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6512010228227200D+0 + V=0.1898581257705106D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6654758363948120D+0 + V=0.1898804756095753D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6778410414853370D+0 + V=0.1899793610426402D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6881760887484110D+0 + V=0.1901464554844117D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6963645267094598D+0 + V=0.1903533246259542D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7023010617153579D+0 + V=0.1905556158463228D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.7059004636628753D+0 + V=0.1907037155663528D-3 + Call GEN_OH( 4, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3552470312472575D-1 + V=0.5992997844249967D-4 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.9151176620841283D-1 + V=0.9749059382456978D-4 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1566197930068980D+0 + V=0.1241680804599158D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2265467599271907D+0 + V=0.1437626154299360D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2988242318581361D+0 + V=0.1584200054793902D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3717482419703886D+0 + V=0.1694436550982744D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4440094491758889D+0 + V=0.1776617014018108D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5145337096756642D+0 + V=0.1836132434440077D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5824053672860230D+0 + V=0.1876494727075983D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6468283961043370D+0 + V=0.1899906535336482D-3 + Call GEN_OH( 5, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6095964259104373D-1 + B=0.1787828275342931D-1 + V=0.8143252820767350D-4 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.8811962270959388D-1 + B=0.3953888740792096D-1 + V=0.9998859890887728D-4 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1165936722428831D+0 + B=0.6378121797722990D-1 + V=0.1156199403068359D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1460232857031785D+0 + B=0.8985890813745037D-1 + V=0.1287632092635513D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1761197110181755D+0 + B=0.1172606510576162D+0 + V=0.1398378643365139D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2066471190463718D+0 + B=0.1456102876970995D+0 + V=0.1491876468417391D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2374076026328152D+0 + B=0.1746153823011775D+0 + V=0.1570855679175456D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2682305474337051D+0 + B=0.2040383070295584D+0 + V=0.1637483948103775D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2989653312142369D+0 + B=0.2336788634003698D+0 + V=0.1693500566632843D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3294762752772209D+0 + B=0.2633632752654219D+0 + V=0.1740322769393633D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3596390887276086D+0 + B=0.2929369098051601D+0 + V=0.1779126637278296D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3893383046398812D+0 + B=0.3222592785275512D+0 + V=0.1810908108835412D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4184653789358347D+0 + B=0.3512004791195743D+0 + V=0.1836529132600190D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4469172319076166D+0 + B=0.3796385677684537D+0 + V=0.1856752841777379D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4745950813276976D+0 + B=0.4074575378263879D+0 + V=0.1872270566606832D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5014034601410262D+0 + B=0.4345456906027828D+0 + V=0.1883722645591307D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5272493404551239D+0 + B=0.4607942515205134D+0 + V=0.1891714324525297D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5520413051846366D+0 + B=0.4860961284181720D+0 + V=0.1896827480450146D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5756887237503077D+0 + B=0.5103447395342790D+0 + V=0.1899628417059528D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1225039430588352D+0 + B=0.2136455922655793D-1 + V=0.1123301829001669D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1539113217321372D+0 + B=0.4520926166137188D-1 + V=0.1253698826711277D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1856213098637712D+0 + B=0.7086468177864818D-1 + V=0.1366266117678531D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2174998728035131D+0 + B=0.9785239488772918D-1 + V=0.1462736856106918D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2494128336938330D+0 + B=0.1258106396267210D+0 + V=0.1545076466685412D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2812321562143480D+0 + B=0.1544529125047001D+0 + V=0.1615096280814007D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3128372276456111D+0 + B=0.1835433512202753D+0 + V=0.1674366639741759D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3441145160177973D+0 + B=0.2128813258619585D+0 + V=0.1724225002437900D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3749567714853510D+0 + B=0.2422913734880829D+0 + V=0.1765810822987288D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4052621732015610D+0 + B=0.2716163748391453D+0 + V=0.1800104126010751D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4349335453522385D+0 + B=0.3007127671240280D+0 + V=0.1827960437331284D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4638776641524965D+0 + B=0.3294470677216479D+0 + V=0.1850140300716308D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4920046410462687D+0 + B=0.3576932543699155D+0 + V=0.1867333507394938D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5192273554861704D+0 + B=0.3853307059757764D+0 + V=0.1880178688638289D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5454609081136522D+0 + B=0.4122425044452694D+0 + V=0.1889278925654758D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5706220661424140D+0 + B=0.4383139587781027D+0 + V=0.1895213832507346D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5946286755181518D+0 + B=0.4634312536300553D+0 + V=0.1898548277397420D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.1905370790924295D+0 + B=0.2371311537781979D-1 + V=0.1349105935937341D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2242518717748009D+0 + B=0.4917878059254806D-1 + V=0.1444060068369326D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2577190808025936D+0 + B=0.7595498960495142D-1 + V=0.1526797390930008D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2908724534927187D+0 + B=0.1036991083191100D+0 + V=0.1598208771406474D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3236354020056219D+0 + B=0.1321348584450234D+0 + V=0.1659354368615331D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3559267359304543D+0 + B=0.1610316571314789D+0 + V=0.1711279910946440D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3876637123676956D+0 + B=0.1901912080395707D+0 + V=0.1754952725601440D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4187636705218842D+0 + B=0.2194384950137950D+0 + V=0.1791247850802529D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4491449019883107D+0 + B=0.2486155334763858D+0 + V=0.1820954300877716D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4787270932425445D+0 + B=0.2775768931812335D+0 + V=0.1844788524548449D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5074315153055574D+0 + B=0.3061863786591120D+0 + V=0.1863409481706220D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5351810507738336D+0 + B=0.3343144718152556D+0 + V=0.1877433008795068D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5619001025975381D+0 + B=0.3618362729028427D+0 + V=0.1887444543705232D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5875144035268046D+0 + B=0.3886297583620408D+0 + V=0.1894009829375006D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6119507308734495D+0 + B=0.4145742277792031D+0 + V=0.1897683345035198D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2619733870119463D+0 + B=0.2540047186389353D-1 + V=0.1517327037467653D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.2968149743237949D+0 + B=0.5208107018543989D-1 + V=0.1587740557483543D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3310451504860488D+0 + B=0.7971828470885599D-1 + V=0.1649093382274097D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3646215567376676D+0 + B=0.1080465999177927D+0 + V=0.1701915216193265D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3974916785279360D+0 + B=0.1368413849366629D+0 + V=0.1746847753144065D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4295967403772029D+0 + B=0.1659073184763559D+0 + V=0.1784555512007570D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4608742854473447D+0 + B=0.1950703730454614D+0 + V=0.1815687562112174D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4912598858949903D+0 + B=0.2241721144376724D+0 + V=0.1840864370663302D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5206882758945558D+0 + B=0.2530655255406489D+0 + V=0.1860676785390006D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5490940914019819D+0 + B=0.2816118409731066D+0 + V=0.1875690583743703D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5764123302025542D+0 + B=0.3096780504593238D+0 + V=0.1886453236347225D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6025786004213506D+0 + B=0.3371348366394987D+0 + V=0.1893501123329645D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6275291964794956D+0 + B=0.3638547827694396D+0 + V=0.1897366184519868D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3348189479861771D+0 + B=0.2664841935537443D-1 + V=0.1643908815152736D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.3699515545855295D+0 + B=0.5424000066843495D-1 + V=0.1696300350907768D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4042003071474669D+0 + B=0.8251992715430854D-1 + V=0.1741553103844483D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4375320100182624D+0 + B=0.1112695182483710D+0 + V=0.1780015282386092D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4699054490335947D+0 + B=0.1402964116467816D+0 + V=0.1812116787077125D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5012739879431952D+0 + B=0.1694275117584291D+0 + V=0.1838323158085421D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5315874883754966D+0 + B=0.1985038235312689D+0 + V=0.1859113119837737D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5607937109622117D+0 + B=0.2273765660020893D+0 + V=0.1874969220221698D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5888393223495521D+0 + B=0.2559041492849764D+0 + V=0.1886375612681076D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6156705979160163D+0 + B=0.2839497251976899D+0 + V=0.1893819575809276D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6412338809078123D+0 + B=0.3113791060500690D+0 + V=0.1897794748256767D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4076051259257167D+0 + B=0.2757792290858463D-1 + V=0.1738963926584846D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4423788125791520D+0 + B=0.5584136834984293D-1 + V=0.1777442359873466D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4760480917328258D+0 + B=0.8457772087727143D-1 + V=0.1810010815068719D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5085838725946297D+0 + B=0.1135975846359248D+0 + V=0.1836920318248129D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5399513637391218D+0 + B=0.1427286904765053D+0 + V=0.1858489473214328D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5701118433636380D+0 + B=0.1718112740057635D+0 + V=0.1875079342496592D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5990240530606021D+0 + B=0.2006944855985351D+0 + V=0.1887080239102310D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6266452685139695D+0 + B=0.2292335090598907D+0 + V=0.1894905752176822D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6529320971415942D+0 + B=0.2572871512353714D+0 + V=0.1898991061200695D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.4791583834610126D+0 + B=0.2826094197735932D-1 + V=0.1809065016458791D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5130373952796940D+0 + B=0.5699871359683649D-1 + V=0.1836297121596799D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5456252429628476D+0 + B=0.8602712528554394D-1 + V=0.1858426916241869D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5768956329682385D+0 + B=0.1151748137221281D+0 + V=0.1875654101134641D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6068186944699046D+0 + B=0.1442811654136362D+0 + V=0.1888240751833503D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6353622248024907D+0 + B=0.1731930321657680D+0 + V=0.1896497383866979D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6624927035731797D+0 + B=0.2017619958756061D+0 + V=0.1900775530219121D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5484933508028488D+0 + B=0.2874219755907391D-1 + V=0.1858525041478814D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.5810207682142106D+0 + B=0.5778312123713695D-1 + V=0.1876248690077947D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6120955197181352D+0 + B=0.8695262371439526D-1 + V=0.1889404439064607D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6416944284294319D+0 + B=0.1160893767057166D+0 + V=0.1898168539265290D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6697926391731260D+0 + B=0.1450378826743251D+0 + V=0.1902779940661772D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6147594390585488D+0 + B=0.2904957622341456D-1 + V=0.1890125641731815D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6455390026356783D+0 + B=0.5823809152617197D-1 + V=0.1899434637795751D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6747258588365477D+0 + B=0.8740384899884715D-1 + V=0.1904520856831751D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + A=0.6772135750395347D+0 + B=0.2919946135808105D-1 + V=0.1905534498734563D-3 + Call GEN_OH( 6, N, X(N), Y(N), Z(N), W(N), A, B, V) + N=N-1 + RETURN + END + + diff --git a/plugins/DFT_Utils/functional.irp.f b/plugins/DFT_Utils/functional.irp.f new file mode 100644 index 00000000..8bcb7d80 --- /dev/null +++ b/plugins/DFT_Utils/functional.irp.f @@ -0,0 +1,25 @@ +double precision function ex_lda(rho) + include 'constants.include.F' + implicit none + double precision, intent(in) :: rho + ex_lda = cst_lda * rho**(c_4_3) + +end + +BEGIN_PROVIDER [double precision, lda_exchange, (N_states)] + implicit none + integer :: i,j,k,l + double precision :: ex_lda + do l = 1, N_states + lda_exchange(l) = 0.d0 + do j = 1, nucl_num + do i = 1, n_points_radial_grid + do k = 1, n_points_integration_angular + lda_exchange(l) += final_weight_functions_at_grid_points(k,i,j) * & + (ex_lda(one_body_dm_mo_alpha_at_grid_points(k,i,j,l)) + ex_lda(one_body_dm_mo_beta_at_grid_points(k,i,j,l))) + enddo + enddo + enddo + enddo + +END_PROVIDER diff --git a/plugins/DFT_Utils/grid_density.irp.f b/plugins/DFT_Utils/grid_density.irp.f index 59500bb5..ad5e0d51 100644 --- a/plugins/DFT_Utils/grid_density.irp.f +++ b/plugins/DFT_Utils/grid_density.irp.f @@ -1,7 +1,7 @@ -!BEGIN_PROVIDER [integer, n_points_integration_angular_lebedev] -!implicit none -!n_points_integration_angular_lebedev = 50 -!END_PROVIDER + BEGIN_PROVIDER [integer, n_points_integration_angular] + implicit none + n_points_integration_angular = 110 + END_PROVIDER BEGIN_PROVIDER [integer, n_points_radial_grid] implicit none @@ -9,22 +9,33 @@ BEGIN_PROVIDER [integer, n_points_radial_grid] END_PROVIDER - BEGIN_PROVIDER [double precision, angular_quadrature_points, (n_points_integration_angular_lebedev,3) ] -&BEGIN_PROVIDER [double precision, weights_angular_points, (n_points_integration_angular_lebedev)] + BEGIN_PROVIDER [double precision, angular_quadrature_points, (n_points_integration_angular,3) ] +&BEGIN_PROVIDER [double precision, weights_angular_points, (n_points_integration_angular)] implicit none BEGIN_DOC ! weights and grid points for the integration on the angular variables on ! the unit sphere centered on (0,0,0) ! According to the LEBEDEV scheme END_DOC - call cal_quad(n_points_integration_angular_lebedev, angular_quadrature_points,weights_angular_points) + angular_quadrature_points = 0.d0 + weights_angular_points = 0.d0 +!call cal_quad(n_points_integration_angular, angular_quadrature_points,weights_angular_points) include 'constants.include.F' - integer :: i + integer :: i,n double precision :: accu double precision :: degre_rad - degre_rad = 180.d0/pi + degre_rad = pi/180.d0 accu = 0.d0 -!do i = 1, n_points_integration_angular_lebedev + double precision :: x(n_points_integration_angular),y(n_points_integration_angular),z(n_points_integration_angular),w(n_points_integration_angular) + call LD0110(X,Y,Z,W,N) + do i = 1, n_points_integration_angular + angular_quadrature_points(i,1) = x(i) + angular_quadrature_points(i,2) = y(i) + angular_quadrature_points(i,3) = z(i) + weights_angular_points(i) = w(i) * 4.d0 * pi + accu += w(i) + enddo +!do i = 1, n_points_integration_angular ! accu += weights_angular_integration_lebedev(i) ! weights_angular_points(i) = weights_angular_integration_lebedev(i) * 4.d0 * pi ! angular_quadrature_points(i,1) = dcos ( degre_rad * theta_angular_integration_lebedev(i)) & @@ -70,7 +81,7 @@ END_PROVIDER END_PROVIDER -BEGIN_PROVIDER [double precision, grid_points_per_atom, (3,n_points_integration_angular_lebedev,n_points_radial_grid,nucl_num)] +BEGIN_PROVIDER [double precision, grid_points_per_atom, (3,n_points_integration_angular,n_points_radial_grid,nucl_num)] BEGIN_DOC ! points for integration over space END_DOC @@ -86,7 +97,7 @@ BEGIN_PROVIDER [double precision, grid_points_per_atom, (3,n_points_integration_ double precision :: x,r x = grid_points_radial(j) ! x value for the mapping of the [0, +\infty] to [0,1] r = knowles_function(alpha_knowles(int(nucl_charge(i))),m_knowles,x) ! value of the radial coordinate for the integration - do k = 1, n_points_integration_angular_lebedev ! explicit values of the grid points centered around each atom + do k = 1, n_points_integration_angular ! explicit values of the grid points centered around each atom grid_points_per_atom(1,k,j,i) = x_ref + angular_quadrature_points(k,1) * r grid_points_per_atom(2,k,j,i) = y_ref + angular_quadrature_points(k,2) * r grid_points_per_atom(3,k,j,i) = z_ref + angular_quadrature_points(k,3) * r @@ -95,7 +106,7 @@ BEGIN_PROVIDER [double precision, grid_points_per_atom, (3,n_points_integration_ enddo END_PROVIDER -BEGIN_PROVIDER [double precision, weight_functions_at_grid_points, (n_points_integration_angular_lebedev,n_points_radial_grid,nucl_num) ] +BEGIN_PROVIDER [double precision, weight_functions_at_grid_points, (n_points_integration_angular,n_points_radial_grid,nucl_num) ] BEGIN_DOC ! Weight function at grid points : w_n(r) according to the equation (22) of Becke original paper (JCP, 88, 1988) ! the "n" discrete variable represents the nucleis which in this array is represented by the last dimension @@ -109,7 +120,7 @@ BEGIN_PROVIDER [double precision, weight_functions_at_grid_points, (n_points_int ! run over all points in space do j = 1, nucl_num ! that are referred to each atom do k = 1, n_points_radial_grid -1 !for each radial grid attached to the "jth" atom - do l = 1, n_points_integration_angular_lebedev ! for each angular point attached to the "jth" atom + do l = 1, n_points_integration_angular ! for each angular point attached to the "jth" atom r(1) = grid_points_per_atom(1,l,k,j) r(2) = grid_points_per_atom(2,l,k,j) r(3) = grid_points_per_atom(3,l,k,j) @@ -129,18 +140,47 @@ BEGIN_PROVIDER [double precision, weight_functions_at_grid_points, (n_points_int END_PROVIDER - BEGIN_PROVIDER [double precision, one_body_dm_mo_alpha_at_grid_points, (n_points_integration_angular_lebedev,n_points_radial_grid,nucl_num) ] -&BEGIN_PROVIDER [double precision, one_body_dm_mo_beta_at_grid_points, (n_points_integration_angular_lebedev,n_points_radial_grid,nucl_num) ] +BEGIN_PROVIDER [double precision, final_weight_functions_at_grid_points, (n_points_integration_angular,n_points_radial_grid,nucl_num) ] + BEGIN_DOC +! Weight function at grid points : w_n(r) according to the equation (22) of Becke original paper (JCP, 88, 1988) +! the "n" discrete variable represents the nucleis which in this array is represented by the last dimension +! and the points are labelled by the other dimensions + END_DOC implicit none integer :: i,j,k,l,m + double precision :: r(3) + double precision :: accu,cell_function_becke + double precision :: tmp_array(nucl_num) + double precision :: contrib_integration,x + double precision :: derivative_knowles_function,knowles_function + ! run over all points in space + do j = 1, nucl_num ! that are referred to each atom + do i = 1, n_points_radial_grid -1 !for each radial grid attached to the "jth" atom + x = grid_points_radial(i) ! x value for the mapping of the [0, +\infty] to [0,1] + do k = 1, n_points_integration_angular ! for each angular point attached to the "jth" atom + contrib_integration = derivative_knowles_function(alpha_knowles(int(nucl_charge(j))),m_knowles,x) & + *knowles_function(alpha_knowles(int(nucl_charge(j))),m_knowles,x)**2 + final_weight_functions_at_grid_points(k,i,j) = weights_angular_points(k) * weight_functions_at_grid_points(k,i,j) * contrib_integration * dr_radial_integral + enddo + enddo + enddo + +END_PROVIDER + + + BEGIN_PROVIDER [double precision, one_body_dm_mo_alpha_at_grid_points, (n_points_integration_angular,n_points_radial_grid,nucl_num,N_states) ] +&BEGIN_PROVIDER [double precision, one_body_dm_mo_beta_at_grid_points, (n_points_integration_angular,n_points_radial_grid,nucl_num,N_states) ] + implicit none + integer :: i,j,k,l,m,i_state double precision :: contrib double precision :: r(3) double precision :: aos_array(ao_num),mos_array(mo_tot_num) + do i_state = 1, N_states do j = 1, nucl_num do k = 1, n_points_radial_grid - do l = 1, n_points_integration_angular_lebedev - one_body_dm_mo_alpha_at_grid_points(l,k,j) = 0.d0 - one_body_dm_mo_beta_at_grid_points(l,k,j) = 0.d0 + do l = 1, n_points_integration_angular + one_body_dm_mo_alpha_at_grid_points(l,k,j,i_state) = 0.d0 + one_body_dm_mo_beta_at_grid_points(l,k,j,i_state) = 0.d0 r(1) = grid_points_per_atom(1,l,k,j) r(2) = grid_points_per_atom(2,l,k,j) r(3) = grid_points_per_atom(3,l,k,j) @@ -149,14 +189,15 @@ END_PROVIDER do m = 1, mo_tot_num do i = 1, mo_tot_num contrib = mos_array(i) * mos_array(m) - one_body_dm_mo_alpha_at_grid_points(l,k,j) += one_body_dm_mo_alpha_average(i,m) * contrib - one_body_dm_mo_beta_at_grid_points(l,k,j) += one_body_dm_mo_beta_average(i,m) * contrib + one_body_dm_mo_alpha_at_grid_points(l,k,j,i_state) += one_body_dm_mo_alpha(i,m,i_state) * contrib + one_body_dm_mo_beta_at_grid_points(l,k,j,i_state) += one_body_dm_mo_beta(i,m,i_state) * contrib enddo enddo enddo enddo enddo + enddo END_PROVIDER diff --git a/plugins/DFT_Utils/integration_3d.irp.f b/plugins/DFT_Utils/integration_3d.irp.f index 4b8d27e8..a665349a 100644 --- a/plugins/DFT_Utils/integration_3d.irp.f +++ b/plugins/DFT_Utils/integration_3d.irp.f @@ -5,11 +5,10 @@ double precision function step_function_becke(x) integer :: i,n_max_becke step_function_becke = f_function_becke(x) - do i = 1, 3 + do i = 1,5 step_function_becke = f_function_becke(step_function_becke) enddo step_function_becke = 0.5d0*(1.d0 - step_function_becke) -! step_function_becke = (1.d0 - step_function_becke) end double precision function f_function_becke(x) diff --git a/plugins/DFT_Utils/integration_radial.irp.f b/plugins/DFT_Utils/integration_radial.irp.f index aeeaf144..0708658f 100644 --- a/plugins/DFT_Utils/integration_radial.irp.f +++ b/plugins/DFT_Utils/integration_radial.irp.f @@ -4,7 +4,7 @@ double precision :: accu integer :: i,j,k,l double precision :: x - double precision :: integrand(n_points_integration_angular_lebedev), weights(n_points_integration_angular_lebedev) + double precision :: integrand(n_points_integration_angular), weights(n_points_integration_angular) double precision :: f_average_angular_alpha,f_average_angular_beta double precision :: derivative_knowles_function,knowles_function @@ -12,7 +12,7 @@ ! according ot equation (6) of the paper of Becke (JCP, (88), 1988) ! Here the m index is referred to the w_m(r) weight functions of equation (22) ! Run over all points of integrations : there are - ! n_points_radial_grid (i) * n_points_integration_angular_lebedev (k) + ! n_points_radial_grid (i) * n_points_integration_angular (k) do j = 1, nucl_num integral_density_alpha_knowles_becke_per_atom(j) = 0.d0 integral_density_beta_knowles_becke_per_atom(j) = 0.d0 @@ -20,9 +20,9 @@ ! Angular integration over the solid angle Omega for a FIXED angular coordinate "r" f_average_angular_alpha = 0.d0 f_average_angular_beta = 0.d0 - do k = 1, n_points_integration_angular_lebedev - f_average_angular_alpha += weights_angular_points(k) * one_body_dm_mo_alpha_at_grid_points(k,i,j) * weight_functions_at_grid_points(k,i,j) - f_average_angular_beta += weights_angular_points(k) * one_body_dm_mo_beta_at_grid_points(k,i,j) * weight_functions_at_grid_points(k,i,j) + do k = 1, n_points_integration_angular + f_average_angular_alpha += weights_angular_points(k) * one_body_dm_mo_alpha_at_grid_points(k,i,j,1) * weight_functions_at_grid_points(k,i,j) + f_average_angular_beta += weights_angular_points(k) * one_body_dm_mo_beta_at_grid_points(k,i,j,1) * weight_functions_at_grid_points(k,i,j) enddo ! x = grid_points_radial(i) ! x value for the mapping of the [0, +\infty] to [0,1] diff --git a/plugins/DFT_Utils/test_integration_3d_density.irp.f b/plugins/DFT_Utils/test_integration_3d_density.irp.f index 3a1428d0..dba02805 100644 --- a/plugins/DFT_Utils/test_integration_3d_density.irp.f +++ b/plugins/DFT_Utils/test_integration_3d_density.irp.f @@ -4,8 +4,47 @@ program pouet touch read_wf print*,'m_knowles = ',m_knowles call routine + call routine3 end + + + +subroutine routine3 + implicit none + integer :: i,j,k,l + double precision :: accu + accu = 0.d0 + do j = 1, nucl_num ! that are referred to each atom + do i = 1, n_points_radial_grid -1 !for each radial grid attached to the "jth" atom + do k = 1, n_points_integration_angular ! for each angular point attached to the "jth" atom + accu += final_weight_functions_at_grid_points(k,i,j) * one_body_dm_mo_alpha_at_grid_points(k,i,j,1) + enddo + enddo + enddo + print*, accu + print*, 'lda_exchange',lda_exchange + +end +subroutine routine2 + implicit none + integer :: i,j,k,l + double precision :: x,y,z + double precision :: r + double precision :: accu + accu = 0.d0 + r = 1.d0 + do k = 1, n_points_integration_angular + x = angular_quadrature_points(k,1) * r + y = angular_quadrature_points(k,2) * r + z = angular_quadrature_points(k,3) * r + accu += weights_angular_points(k) * (x**2 + y**2 + z**2) + enddo + print*, accu + +end + + subroutine routine implicit none integer :: i diff --git a/src/Utils/angular_integration.irp.f b/src/Utils/angular_integration.irp.f index 7ffbd01b..757508a1 100644 --- a/src/Utils/angular_integration.irp.f +++ b/src/Utils/angular_integration.irp.f @@ -4,7 +4,7 @@ BEGIN_PROVIDER [integer, degree_max_integration_lebedev] ! needed for the angular integration according to LEBEDEV formulae END_DOC implicit none - degree_max_integration_lebedev= 7 + degree_max_integration_lebedev= 13 END_PROVIDER @@ -644,14 +644,14 @@ END_PROVIDER weights_angular_integration_lebedev(16) = 0.016604069565742d0 weights_angular_integration_lebedev(17) = 0.016604069565742d0 weights_angular_integration_lebedev(18) = 0.016604069565742d0 - weights_angular_integration_lebedev(19) = -0.029586038961039d0 - weights_angular_integration_lebedev(20) = -0.029586038961039d0 - weights_angular_integration_lebedev(21) = -0.029586038961039d0 - weights_angular_integration_lebedev(22) = -0.029586038961039d0 - weights_angular_integration_lebedev(23) = -0.029586038961039d0 - weights_angular_integration_lebedev(24) = -0.029586038961039d0 - weights_angular_integration_lebedev(25) = -0.029586038961039d0 - weights_angular_integration_lebedev(26) = -0.029586038961039d0 + weights_angular_integration_lebedev(19) = 0.029586038961039d0 + weights_angular_integration_lebedev(20) = 0.029586038961039d0 + weights_angular_integration_lebedev(21) = 0.029586038961039d0 + weights_angular_integration_lebedev(22) = 0.029586038961039d0 + weights_angular_integration_lebedev(23) = 0.029586038961039d0 + weights_angular_integration_lebedev(24) = 0.029586038961039d0 + weights_angular_integration_lebedev(25) = 0.029586038961039d0 + weights_angular_integration_lebedev(26) = 0.029586038961039d0 weights_angular_integration_lebedev(27) = 0.026576207082159d0 weights_angular_integration_lebedev(28) = 0.026576207082159d0 weights_angular_integration_lebedev(29) = 0.026576207082159d0 diff --git a/src/Utils/constants.include.F b/src/Utils/constants.include.F index 4974fd8e..c077eb53 100644 --- a/src/Utils/constants.include.F +++ b/src/Utils/constants.include.F @@ -10,3 +10,7 @@ double precision, parameter :: dtwo_pi = 2.d0*dacos(-1.d0) double precision, parameter :: inv_sq_pi = 1.d0/dsqrt(dacos(-1.d0)) double precision, parameter :: inv_sq_pi_2 = 0.5d0/dsqrt(dacos(-1.d0)) double precision, parameter :: thresh = 1.d-15 +double precision, parameter :: cx_lda = -0.73855876638202234d0 +double precision, parameter :: c_2_4_3 = 2.5198420997897464d0 +double precision, parameter :: cst_lda = -0.93052573634909996d0 +double precision, parameter :: c_4_3 = 1.3333333333333333d0