4 April 2023 7:44:18.905 PM sparse_grid_hw_test(): FORTRAN90 version Test sparse_grid_hw(). CCL_TEST: CCL_ORDER + CC 1D quadrature: Clenshaw Curtis Linear (CCL) quadrature over [0,1]: Level Nodes Estimate Error 1 1 0.193334 0.977527E-02 2 3 0.191473 0.568167E-04 3 5 0.191462 0.395965E-07 4 7 0.191462 0.117826E-10 5 9 0.191462 0.652348E-14 CCL_SPARSE_TEST: CCL_ORDER + CC sparse grid: Sparse Clenshaw Curtis Linear quadrature over [0,1]. D Level Nodes SG error MC error 10 8 584665 .94032E-11 .15257E-03 CCS_TEST: CCS_ORDER + CC 1D quadrature: Clenshaw Curtis Slow (CCS) quadrature over [0,1]: Level Nodes Estimate Error 1 1 0.193334 0.977527E-02 2 3 0.191473 0.568167E-04 3 5 0.191462 0.395965E-07 4 9 0.191462 0.652348E-14 5 9 0.191462 0.652348E-14 CCS_SPARSE_TEST: CCS_ORDER + CC sparse grid: Sparse Clenshaw Curtis Slow quadrature over [0,1]. D Level Nodes SG error MC error 10 2 21 .39099E-02 .25878E-01 10 3 221 .64537E-04 .78998E-02 10 4 1581 .12369E-06 .28176E-02 10 5 8721 .10089E-07 .12552E-02 10 6 39665 .88636E-10 .57553E-03 10 7 155105 .11030E-11 .29732E-03 CCE_TEST: CCE_ORDER + CC 1D quadrature: Clenshaw Curtis Exponential (CCE) quadrature over [0,1]: Level Nodes Estimate Error 1 1 0.193334 0.977527E-02 2 3 0.191473 0.568167E-04 3 5 0.191462 0.395965E-07 4 9 0.191462 0.652348E-14 5 17 0.191462 0.289932E-15 CCE_SPARSE_TEST: CCE_ORDER + CC sparse grid: Sparse Gaussian unweighted quadrature over [0,1]. D Level Nodes SG error MC error 10 2 21 .39099E-02 .25878E-01 10 3 221 .64537E-04 .78998E-02 10 4 1581 .12369E-06 .28176E-02 10 5 8801 .10089E-07 .12216E-02 10 6 41265 .88715E-10 .56375E-03 10 7 171425 .28594E-11 .27978E-03 GET_SEQ_TEST GET_SEQ returns D-dimensional vectors summing to NORM. D = 3 NORM = 6 The compositions Col 1 2 3 Row 1: 4 1 1 2: 3 2 1 3: 3 1 2 4: 2 3 1 5: 2 2 2 6: 2 1 3 7: 1 4 1 8: 1 3 2 9: 1 2 3 10: 1 1 4 GQN_TEST: Gauss-Hermite quadrature over (-oo,+oo): Level Nodes Estimate Error 1 1 0.00000 1.00000 2 2 1.00000 0.933333 3 3 9.00000 0.400000 4 4 15.0000 0.473695E-15 5 5 15.0000 0.236848E-15 gqn_sparse_test: Sparse Gaussian quadrature with Hermite weight over (-oo,+oo). Use GQN_ORDER: the growth rule N = L. D Level Nodes SG error MC error 10 2 21 .93333 1.2367 10 3 221 .40000 .49856 10 4 1581 .58265E-13 .16722 10 5 8761 .14613E-12 .75489E-01 10 6 40405 .23597E-11 .34419E-01 10 7 162025 .16110E-10 .16991E-01 GQN2_SPARSE_TEST: GQN sparse grid: Gauss-Hermite sparse grids over (-oo,+oo). Use GQN2_ORDER, the growth rule N = 2 * L - 1. Estimate weighted integral of 1/(1+x^2+y^2). J W X Y 1 0.166667 -1.73205 0.00000 2 0.166667 0.00000 -1.73205 3 0.333333 0.00000 0.00000 4 0.166667 0.00000 1.73205 5 0.166667 1.73205 0.00000 Integral estimate = 0.500000 J W X Y 1 0.112574E-01 -2.85697 0.00000 2 0.277778E-01 -1.73205 -1.73205 3 -0.555556E-01 -1.73205 0.00000 4 0.277778E-01 -1.73205 1.73205 5 0.222076 -1.35563 0.00000 6 0.112574E-01 0.00000 -2.85697 7 -0.555556E-01 0.00000 -1.73205 8 0.222076 0.00000 -1.35563 9 0.177778 0.00000 0.00000 10 0.222076 0.00000 1.35563 11 -0.555556E-01 0.00000 1.73205 12 0.112574E-01 0.00000 2.85697 13 0.222076 1.35563 0.00000 14 0.277778E-01 1.73205 -1.73205 15 -0.555556E-01 1.73205 0.00000 16 0.277778E-01 1.73205 1.73205 17 0.112574E-01 2.85697 0.00000 Integral estimate = 0.456044 J W X Y 1 0.548269E-03 -3.75044 0.00000 2 0.187624E-02 -2.85697 -1.73205 3 -0.375247E-02 -2.85697 0.00000 4 0.187624E-02 -2.85697 1.73205 5 0.307571E-01 -2.36676 0.00000 6 0.187624E-02 -1.73205 -2.85697 7 -0.277778E-01 -1.73205 -1.73205 8 0.370127E-01 -1.73205 -1.35563 9 -0.222222E-01 -1.73205 0.00000 10 0.370127E-01 -1.73205 1.35563 11 -0.277778E-01 -1.73205 1.73205 12 0.187624E-02 -1.73205 2.85697 13 0.370127E-01 -1.35563 -1.73205 14 -0.740253E-01 -1.35563 0.00000 15 0.370127E-01 -1.35563 1.73205 16 0.240123 -1.15441 0.00000 17 0.548269E-03 0.00000 -3.75044 18 -0.375247E-02 0.00000 -2.85697 19 0.307571E-01 0.00000 -2.36676 20 -0.222222E-01 0.00000 -1.73205 21 -0.740253E-01 0.00000 -1.35563 22 0.240123 0.00000 -1.15441 23 0.114286 0.00000 0.00000 24 0.240123 0.00000 1.15441 25 -0.740253E-01 0.00000 1.35563 26 -0.222222E-01 0.00000 1.73205 27 0.307571E-01 0.00000 2.36676 28 -0.375247E-02 0.00000 2.85697 29 0.548269E-03 0.00000 3.75044 30 0.240123 1.15441 0.00000 31 0.370127E-01 1.35563 -1.73205 32 -0.740253E-01 1.35563 0.00000 33 0.370127E-01 1.35563 1.73205 34 0.187624E-02 1.73205 -2.85697 35 -0.277778E-01 1.73205 -1.73205 36 0.370127E-01 1.73205 -1.35563 37 -0.222222E-01 1.73205 0.00000 38 0.370127E-01 1.73205 1.35563 39 -0.277778E-01 1.73205 1.73205 40 0.187624E-02 1.73205 2.85697 41 0.307571E-01 2.36676 0.00000 42 0.187624E-02 2.85697 -1.73205 43 -0.375247E-02 2.85697 0.00000 44 0.187624E-02 2.85697 1.73205 45 0.548269E-03 3.75044 0.00000 Integral estimate = 0.452706 J W X Y 1 0.223458E-04 -4.51275 0.00000 2 0.913781E-04 -3.75044 -1.73205 3 -0.182756E-03 -3.75044 0.00000 4 0.913781E-04 -3.75044 1.73205 5 0.278914E-02 -3.20543 0.00000 6 0.126729E-03 -2.85697 -2.85697 7 -0.187624E-02 -2.85697 -1.73205 8 0.250000E-02 -2.85697 -1.35563 9 -0.150099E-02 -2.85697 0.00000 10 0.250000E-02 -2.85697 1.35563 11 -0.187624E-02 -2.85697 1.73205 12 0.126729E-03 -2.85697 2.85697 13 0.512619E-02 -2.36676 -1.73205 14 -0.102524E-01 -2.36676 0.00000 15 0.512619E-02 -2.36676 1.73205 16 0.499164E-01 -2.07685 0.00000 17 0.913781E-04 -1.73205 -3.75044 18 -0.187624E-02 -1.73205 -2.85697 19 0.512619E-02 -1.73205 -2.36676 20 -0.370127E-01 -1.73205 -1.35563 21 0.400205E-01 -1.73205 -1.15441 22 -0.126984E-01 -1.73205 0.00000 23 0.400205E-01 -1.73205 1.15441 24 -0.370127E-01 -1.73205 1.35563 25 0.512619E-02 -1.73205 2.36676 26 -0.187624E-02 -1.73205 2.85697 27 0.913781E-04 -1.73205 3.75044 28 0.250000E-02 -1.35563 -2.85697 29 -0.370127E-01 -1.35563 -1.73205 30 0.493177E-01 -1.35563 -1.35563 31 -0.296101E-01 -1.35563 0.00000 32 0.493177E-01 -1.35563 1.35563 33 -0.370127E-01 -1.35563 1.73205 34 0.250000E-02 -1.35563 2.85697 35 0.400205E-01 -1.15441 -1.73205 36 -0.800411E-01 -1.15441 0.00000 37 0.400205E-01 -1.15441 1.73205 38 0.244098 -1.02326 0.00000 39 0.223458E-04 0.00000 -4.51275 40 -0.182756E-03 0.00000 -3.75044 41 0.278914E-02 0.00000 -3.20543 42 -0.150099E-02 0.00000 -2.85697 43 -0.102524E-01 0.00000 -2.36676 44 0.499164E-01 0.00000 -2.07685 45 -0.126984E-01 0.00000 -1.73205 46 -0.296101E-01 0.00000 -1.35563 47 -0.800411E-01 0.00000 -1.15441 48 0.244098 0.00000 -1.02326 49 0.812698E-01 0.00000 0.00000 50 0.244098 0.00000 1.02326 51 -0.800411E-01 0.00000 1.15441 52 -0.296101E-01 0.00000 1.35563 53 -0.126984E-01 0.00000 1.73205 54 0.499164E-01 0.00000 2.07685 55 -0.102524E-01 0.00000 2.36676 56 -0.150099E-02 0.00000 2.85697 57 0.278914E-02 0.00000 3.20543 58 -0.182756E-03 0.00000 3.75044 59 0.223458E-04 0.00000 4.51275 60 0.244098 1.02326 0.00000 61 0.400205E-01 1.15441 -1.73205 62 -0.800411E-01 1.15441 0.00000 63 0.400205E-01 1.15441 1.73205 64 0.250000E-02 1.35563 -2.85697 65 -0.370127E-01 1.35563 -1.73205 66 0.493177E-01 1.35563 -1.35563 67 -0.296101E-01 1.35563 0.00000 68 0.493177E-01 1.35563 1.35563 69 -0.370127E-01 1.35563 1.73205 70 0.250000E-02 1.35563 2.85697 71 0.913781E-04 1.73205 -3.75044 72 -0.187624E-02 1.73205 -2.85697 73 0.512619E-02 1.73205 -2.36676 74 -0.370127E-01 1.73205 -1.35563 75 0.400205E-01 1.73205 -1.15441 76 -0.126984E-01 1.73205 0.00000 77 0.400205E-01 1.73205 1.15441 78 -0.370127E-01 1.73205 1.35563 79 0.512619E-02 1.73205 2.36676 80 -0.187624E-02 1.73205 2.85697 81 0.913781E-04 1.73205 3.75044 82 0.499164E-01 2.07685 0.00000 83 0.512619E-02 2.36676 -1.73205 84 -0.102524E-01 2.36676 0.00000 85 0.512619E-02 2.36676 1.73205 86 0.126729E-03 2.85697 -2.85697 87 -0.187624E-02 2.85697 -1.73205 88 0.250000E-02 2.85697 -1.35563 89 -0.150099E-02 2.85697 0.00000 90 0.250000E-02 2.85697 1.35563 91 -0.187624E-02 2.85697 1.73205 92 0.126729E-03 2.85697 2.85697 93 0.278914E-02 3.20543 0.00000 94 0.913781E-04 3.75044 -1.73205 95 -0.182756E-03 3.75044 0.00000 96 0.913781E-04 3.75044 1.73205 97 0.223458E-04 4.51275 0.00000 Integral estimate = 0.454644 GQU_TEST: Gauss-Legendre quadrature over [0,1]: Level Nodes Estimate Error 1 1 0.193334 0.977527E-02 2 2 0.191455 0.379650E-04 3 3 0.191462 0.946584E-07 4 4 0.191462 0.174249E-09 5 5 0.191462 0.254416E-12 GQU_SPARSE_TEST: GQU sparse grid: Sparse Gauss-Legendre quadrature with unit weight over [0,1]. D Level Nodes SG error MC error 10 2 21 .49444E-02 .25878E-01 10 3 221 .15519E-03 .78998E-02 10 4 1581 .35752E-05 .28176E-02 10 5 8761 .64664E-07 .12298E-02 10 6 40405 .95702E-09 .58170E-03 10 7 162025 .17590E-10 .28711E-03 KPN_TEST: Kronrod-Patterson-Hermite quadrature over (-oo,+oo): Level Nodes Estimate Error 1 1 0.00000 1.00000 2 3 9.00000 0.400000 3 3 9.00000 0.400000 4 7 15.0000 0.473695E-15 5 9 15.0000 0.236848E-15 KPN_SPARSE_TEST: KPN sparse grid: Sparse Kronrod quadrature with Hermite weight over (-oo,+oo). D Level Nodes SG error MC error 10 2 21 .40000 1.2367 10 3 201 .40000 .53710 10 4 1201 .29606E-14 .20018 10 5 5301 .70758E-12 .96658E-01 10 6 19485 .72291E-11 .50696E-01 10 7 63405 .87123E-10 .26963E-01 KPU_TEST: Kronrod-Patterson quadrature over [0,1]: Level Nodes Estimate Error 1 1 0.193334 0.977527E-02 2 3 0.191462 0.946584E-07 3 3 0.191462 0.946584E-07 4 7 0.191462 0.434898E-15 5 7 0.191462 0.434898E-15 KPU_SPARSE_TEST: KPU sparse grid: Sparse Kronrod quadrature with unit weight over [0,1]. D Level Nodes SG error MC error 10 2 21 .45290E-02 .25878E-01 10 3 201 .11892E-03 .84054E-02 10 4 1201 .20959E-05 .32769E-02 10 5 5281 .26831E-07 .16055E-02 10 6 19105 .26775E-09 .82166E-03 10 7 60225 .64250E-11 .47571E-03 NWSPGR_SIZE_TEST: NWSPGR_SIZE returns the size of a sparse grid, based on either: one of the built-in 1D rules, or a family of 1D rules supplied by the user. Kronrod-Patterson, [0,1], Dim 2, Level 3, Symmetric Full 21 Kronrod-Patterson, (-oo,+oo), Dim 2, Level 3, Symmetric Full 21 Gauss-Legendre, [0,1], Dim 2, Level 3, Symmetric Full 14 Gauss Hermite, (-oo,+oo), [0,1], Dim 2, Level 3, Symmetric Full 14 Clenshaw Curtis Exponential, [-1,+1], [0,1], Dim 2, Level 3, Unsymmetric Full 25 Dimension / Level table for Clenshaw Curtis Exponential Dim: 1 2 3 4 5 6 7 8 9 10 Level 1 1 1 1 1 1 1 1 1 1 1 2 3 7 10 13 16 19 22 25 28 31 3 5 25 52 87 131 184 246 317 397 486 4 9 67 195 411 746 1228 1884 2741 3826 5166 5 17 161 609 1573 3376 6430 11222 18319 28369 42101 NWSPGR_TIME_TEST: This function measures the time in seconds required by NWSPGR to compute a sparse grid, based on either: one of the built-in 1D rules, or a family of 1D rules supplied by the user. Kronrod-Patterson, [0,1], Dim 20, Level 5, Symmetric Full 2.19020 Kronrod-Patterson, (-oo,+oo), Dim 20, Level 5, Symmetric Full 2.19214 Gauss-Legendre, [0,1], Dim 20, Level 5, Symmetric Full 0.423477 Gauss Hermite, (-oo,+oo), [0,1], Dim 20, Level 5, Symmetric Full 0.420642 Clenshaw Curtis Exponential, [-1,+1], [0,1], Dim 20, Level 5, Unsymmetric Full 2.50329 Dimension / Level table for Clenshaw Curtis Exponential Dim: 1 2 3 4 5 6 7 8 9 10 Level 1 0.12E-04 0.40E-05 0.40E-05 0.30E-05 0.20E-05 0.30E-05 0.30E-05 0.30E-05 0.30E-05 0.40E-05 2 0.60E-05 0.70E-05 0.10E-04 0.12E-04 0.16E-04 0.21E-04 0.26E-04 0.30E-04 0.37E-04 0.41E-04 3 0.60E-05 0.15E-04 0.36E-04 0.64E-04 0.11E-03 0.16E-03 0.24E-03 0.34E-03 0.47E-03 0.63E-03 4 0.90E-05 0.37E-04 0.12E-03 0.30E-03 0.60E-03 0.11E-02 0.19E-02 0.32E-02 0.50E-02 0.74E-02 5 0.17E-04 0.83E-04 0.37E-03 0.12E-02 0.29E-02 0.65E-02 0.13E-01 0.24E-01 0.42E-01 0.71E-01 Dim: 11 12 13 14 15 16 17 18 19 20 Level 1 0.60E-05 0.50E-05 0.40E-05 0.40E-05 0.50E-05 0.50E-05 0.40E-05 0.40E-05 0.40E-05 0.50E-05 2 0.54E-04 0.59E-04 0.65E-04 0.72E-04 0.81E-04 0.90E-04 0.10E-03 0.11E-03 0.12E-03 0.14E-03 3 0.81E-03 0.10E-02 0.13E-02 0.16E-02 0.19E-02 0.23E-02 0.27E-02 0.33E-02 0.37E-02 0.44E-02 4 0.11E-01 0.15E-01 0.20E-01 0.27E-01 0.35E-01 0.44E-01 0.56E-01 0.72E-01 0.90E-01 0.11 5 0.11 0.17 0.26 0.37 0.53 0.74 1.1 1.4 1.9 2.5 NWSPGR_TEST: NWSPGR generates a sparse grid, based on either: one of the built-in 1D rules, or a family of 1D rules supplied by the user. Kronrod-Patterson, [0,1], Dim 2, Level 3 1 0.077160 * f ( 0.112702, 0.112702 ) 2 0.123457 * f ( 0.112702, 0.500000 ) 3 0.077160 * f ( 0.112702, 0.887298 ) 4 0.123457 * f ( 0.500000, 0.112702 ) 5 0.197531 * f ( 0.500000, 0.500000 ) 6 0.123457 * f ( 0.500000, 0.887298 ) 7 0.077160 * f ( 0.887298, 0.112702 ) 8 0.123457 * f ( 0.887298, 0.500000 ) 9 0.077160 * f ( 0.887298, 0.887298 ) Kronrod-Patterson, (-oo,+oo), Dim 2, Level 3 1 0.027778 * f ( -1.732051, -1.732051 ) 2 0.111111 * f ( -1.732051, 0.000000 ) 3 0.027778 * f ( -1.732051, 1.732051 ) 4 0.111111 * f ( 0.000000, -1.732051 ) 5 0.444444 * f ( 0.000000, 0.000000 ) 6 0.111111 * f ( 0.000000, 1.732051 ) 7 0.027778 * f ( 1.732051, -1.732051 ) 8 0.111111 * f ( 1.732051, 0.000000 ) 9 0.027778 * f ( 1.732051, 1.732051 ) Gauss-Legendre, [0,1], Dim 2, Level 3 1 0.277778 * f ( 0.112702, 0.500000 ) 2 0.250000 * f ( 0.211325, 0.211325 ) 3 -0.500000 * f ( 0.211325, 0.500000 ) 4 0.250000 * f ( 0.211325, 0.788675 ) 5 0.277778 * f ( 0.500000, 0.112702 ) 6 -0.500000 * f ( 0.500000, 0.211325 ) 7 0.888889 * f ( 0.500000, 0.500000 ) 8 -0.500000 * f ( 0.500000, 0.788675 ) 9 0.277778 * f ( 0.500000, 0.887298 ) 10 0.250000 * f ( 0.788675, 0.211325 ) 11 -0.500000 * f ( 0.788675, 0.500000 ) 12 0.250000 * f ( 0.788675, 0.788675 ) 13 0.277778 * f ( 0.887298, 0.500000 ) Gauss Hermite, (-oo,+oo), Dim 2, Level 3 1 0.166667 * f ( -1.732051, 0.000000 ) 2 0.250000 * f ( -1.000000, -1.000000 ) 3 -0.500000 * f ( -1.000000, 0.000000 ) 4 0.250000 * f ( -1.000000, 1.000000 ) 5 0.166667 * f ( 0.000000, -1.732051 ) 6 -0.500000 * f ( 0.000000, -1.000000 ) 7 1.333333 * f ( 0.000000, 0.000000 ) 8 -0.500000 * f ( 0.000000, 1.000000 ) 9 0.166667 * f ( 0.000000, 1.732051 ) 10 0.250000 * f ( 1.000000, -1.000000 ) 11 -0.500000 * f ( 1.000000, 0.000000 ) 12 0.250000 * f ( 1.000000, 1.000000 ) 13 0.166667 * f ( 1.732051, 0.000000 ) Clenshaw Curtis Exponential, [-1,+1], Dim 2, Level 3 1 0.027778 * f ( 0.000000, 0.000000 ) 2 -0.022222 * f ( 0.000000, 0.500000 ) 3 0.027778 * f ( 0.000000, 1.000000 ) 4 0.266667 * f ( 0.146447, 0.500000 ) 5 -0.022222 * f ( 0.500000, 0.000000 ) 6 0.266667 * f ( 0.500000, 0.146447 ) 7 -0.088889 * f ( 0.500000, 0.500000 ) 8 0.266667 * f ( 0.500000, 0.853553 ) 9 -0.022222 * f ( 0.500000, 1.000000 ) 10 0.266667 * f ( 0.853553, 0.500000 ) 11 0.027778 * f ( 1.000000, 0.000000 ) 12 -0.022222 * f ( 1.000000, 0.500000 ) 13 0.027778 * f ( 1.000000, 1.000000 ) ORDER_REPORT For each family of rules, report: L, the level index, RP, the required polynomial precision, AP, the actual polynomial precision, O, the rule order (number of points). GQN family Gauss quadrature, exponential weight, (-oo,+oo) L RP AP O 1 1 1 1 2 3 3 2 3 5 5 3 4 7 7 4 5 9 9 5 6 11 11 6 7 13 13 7 8 15 15 8 9 17 17 9 10 19 19 10 11 21 21 11 12 23 23 12 13 25 25 13 14 27 27 14 15 29 29 15 16 31 31 16 17 33 33 17 18 35 35 18 19 37 37 19 20 39 39 20 21 41 41 21 22 43 43 22 23 45 45 23 24 47 47 24 25 49 49 25 GQU family Gauss quadrature, unit weight, [0,1] L RP AP O 1 1 1 1 2 3 3 2 3 5 5 3 4 7 7 4 5 9 9 5 6 11 11 6 7 13 13 7 8 15 15 8 9 17 17 9 10 19 19 10 11 21 21 11 12 23 23 12 13 25 25 13 14 27 27 14 15 29 29 15 16 31 31 16 17 33 33 17 18 35 35 18 19 37 37 19 20 39 39 20 21 41 41 21 22 43 43 22 23 45 45 23 24 47 47 24 25 49 49 25 KPN family Gauss-Kronrod-Patterson quadrature, exponential weight, (-oo,+oo) L RP AP O 1 1 1 1 2 3 5 3 3 5 5 3 4 7 7 7 5 9 15 9 6 11 15 9 7 13 15 9 8 15 15 9 9 17 17 17 10 19 29 19 11 21 29 19 12 23 29 19 13 25 29 19 14 27 29 19 15 29 29 19 16 31 31 31 17 33 33 33 18 35 51 35 19 37 51 35 20 39 51 35 21 41 51 35 22 43 51 35 23 45 51 35 24 47 51 35 25 49 51 35 KPU family Gauss-Kronrod-Patterson quadrature, unit weight, [0,1] L RP AP O 1 1 1 1 2 3 5 3 3 5 5 3 4 7 11 7 5 9 11 7 6 11 11 7 7 13 23 15 8 15 23 15 9 17 23 15 10 19 23 15 11 21 23 15 12 23 23 15 13 25 47 31 14 27 47 31 15 29 47 31 16 31 47 31 17 33 47 31 18 35 47 31 19 37 47 31 20 39 47 31 21 41 47 31 22 43 47 31 23 45 47 31 24 47 47 31 25 49 95 63 SYMMETRIC_SPARSE_SIZE_TEST Given a symmetric sparse grid rule represented only by the points with positive values, determine the total number of points in the grid. For dimension DIM, we report R, the number of points in the positive orthant, and R2, the total number of points. DIM R R2 5 6 11 5 21 61 3 23 69 TENSOR_PRODUCT_TEST: Given a sequence of 1D quadrature rules, construct the tensor product rule. A 1D rule over [-1,+1]: 1 1.000000 * f ( -1.000000 ) 2 1.000000 * f ( 1.000000 ) A 2D rule over [-1,+1] x [2.0,3.0]: 1 0.250000 * f ( -1.000000, 2.000000 ) 2 0.250000 * f ( 1.000000, 2.000000 ) 3 0.500000 * f ( -1.000000, 2.500000 ) 4 0.500000 * f ( 1.000000, 2.500000 ) 5 0.250000 * f ( -1.000000, 3.000000 ) 6 0.250000 * f ( 1.000000, 3.000000 ) A 3D rule over [-1,+1] x [2.0,3.0] x [10.0,15.0]: 1 0.625000 * f ( -1.000000, 2.000000, 10.000000 ) 2 0.625000 * f ( 1.000000, 2.000000, 10.000000 ) 3 1.250000 * f ( -1.000000, 2.500000, 10.000000 ) 4 1.250000 * f ( 1.000000, 2.500000, 10.000000 ) 5 0.625000 * f ( -1.000000, 3.000000, 10.000000 ) 6 0.625000 * f ( 1.000000, 3.000000, 10.000000 ) 7 0.625000 * f ( -1.000000, 2.000000, 15.000000 ) 8 0.625000 * f ( 1.000000, 2.000000, 15.000000 ) 9 1.250000 * f ( -1.000000, 2.500000, 15.000000 ) 10 1.250000 * f ( 1.000000, 2.500000, 15.000000 ) 11 0.625000 * f ( -1.000000, 3.000000, 15.000000 ) 12 0.625000 * f ( 1.000000, 3.000000, 15.000000 ) TENSOR_PRODUCT_TEST_CELL: Given a set of 1D quadrature rules stored in a cell array, construct the tensor product rule. A 1D rule over [-1,+1]: 1 1.000000 * f ( -1.000000 ) 2 1.000000 * f ( 1.000000 ) A 1D rule over [-1,+1]: 1 0.250000 * f ( -1.000000, 2.000000 ) 2 0.250000 * f ( 1.000000, 2.000000 ) 3 0.500000 * f ( -1.000000, 2.500000 ) 4 0.500000 * f ( 1.000000, 2.500000 ) 5 0.250000 * f ( -1.000000, 3.000000 ) 6 0.250000 * f ( 1.000000, 3.000000 ) A 1D rule over [-1,+1]: 1 0.625000 * f ( -1.000000, 2.000000, 10.000000 ) 2 0.625000 * f ( 1.000000, 2.000000, 10.000000 ) 3 1.250000 * f ( -1.000000, 2.500000, 10.000000 ) 4 1.250000 * f ( 1.000000, 2.500000, 10.000000 ) 5 0.625000 * f ( -1.000000, 3.000000, 10.000000 ) 6 0.625000 * f ( 1.000000, 3.000000, 10.000000 ) 7 0.625000 * f ( -1.000000, 2.000000, 15.000000 ) 8 0.625000 * f ( 1.000000, 2.000000, 15.000000 ) 9 1.250000 * f ( -1.000000, 2.500000, 15.000000 ) 10 1.250000 * f ( 1.000000, 2.500000, 15.000000 ) 11 0.625000 * f ( -1.000000, 3.000000, 15.000000 ) 12 0.625000 * f ( 1.000000, 3.000000, 15.000000 ) sparse_grid_hw_test Normal end of execution. 4 April 2023 7:52:37.442 PM