02-Apr-2024 14:30:43 truncated_normal_sparse_grid_test(): MATLAB/Octave version 6.4.0 Test truncated_normal_sparse_grid(). tno_order_test(): tno_order() is given a level L, and returns the order N of a Truncated Normal Odd (TNO) quadrature rule. Level Order 1 1 2 3 3 3 4 5 5 5 6 7 7 7 8 9 9 9 10 11 11 11 12 13 13 13 14 15 15 15 16 17 17 17 18 19 19 19 20 21 tno_test(): tno() is given a level L, and returns points and weights of a Truncated Normal Odd (TNO) quadrature rule. Level L = 5 Order N = 5 TN - Generating TN rule of order 5. Points and weights: 1: -0.89845 0.0987714 2: -0.521317 0.242237 3: 3.12687e-18 0.317984 4: 0.521317 0.242237 5: 0.89845 0.0987714 tno_persistence_test(): tno() is given a level L, and returns points and weights of a Truncated Normal Odd (TNO) quadrature rule. The first time TNO is called for a particular order N it must compute the corresponding rule. It prints a message, and saves the data in persistent arrays. To verify this, compute a sequence of levels L for which the values of N repeat. The message should only show up once for each value of N. L = 1, N = 1 TN - Generating TN rule of order 1. L = 2, N = 3 TN - Generating TN rule of order 3. L = 3, N = 3 L = 4, N = 5 L = 5, N = 5 L = 6, N = 7 TN - Generating TN rule of order 7. tno_sparse_grid_test(): nwspgr() generates a sparse grid in 2D based on the Truncated Normal Odd (TNO) family. TNO sparse grid, Dim 2, Level 1 1 1 0 0 TNO sparse grid, Dim 2, Level 2 1 0.2576098038951921 -0.751698407412144 0 2 0.4847803922096159 -1.084202172485504e-16 0 3 0.2576098038951921 0 -0.751698407412144 4 0.4847803922096159 0 -1.084202172485504e-16 5 -0.9999999999999996 0 0 6 0.2576098038951918 0 0.751698407412144 7 0.2576098038951918 0.751698407412144 0 TNO sparse grid, Dim 2, Level 3 1 0.06636281106291934 -0.751698407412144 -0.751698407412144 2 0.1248841817693535 -0.751698407412144 -1.084202172485504e-16 3 0 -0.751698407412144 0 4 0.06636281106291927 -0.751698407412144 0.751698407412144 5 0.1248841817693535 -1.084202172485504e-16 -0.751698407412144 6 0.2350120286709092 -1.084202172485504e-16 -1.084202172485504e-16 7 0 -1.084202172485504e-16 0 8 0.1248841817693534 -1.084202172485504e-16 0.751698407412144 9 0 0 -0.751698407412144 10 0 0 -1.084202172485504e-16 11 0 0 0.751698407412144 12 0.06636281106291927 0.751698407412144 -0.751698407412144 13 0.1248841817693534 0.751698407412144 -1.084202172485504e-16 14 0 0.751698407412144 0 15 0.06636281106291922 0.751698407412144 0.751698407412144 TNO sparse grid, Dim 2, Level 4 1 0.09877141338753173 -0.8984499284579617 0 2 0.06636281106291932 -0.751698407412144 -0.751698407412144 3 0.1248841817693535 -0.751698407412144 -1.084202172485504e-16 4 -0.2576098038951919 -0.751698407412144 0 5 0.06636281106291925 -0.751698407412144 0.751698407412144 6 0.2422365795893658 -0.5213172863125559 0 7 0.1248841817693535 -1.084202172485504e-16 -0.751698407412144 8 0.2350120286709091 -1.084202172485504e-16 -1.084202172485504e-16 9 -0.4847803922096157 -1.084202172485504e-16 0 10 0.1248841817693533 -1.084202172485504e-16 0.751698407412144 11 0.09877141338753173 0 -0.8984499284579617 12 -0.2576098038951919 0 -0.751698407412144 13 0.2422365795893658 0 -0.5213172863125559 14 -0.4847803922096157 0 -1.084202172485504e-16 15 0.3179840140462045 0 3.126872543830576e-18 16 0.2422365795893659 0 0.5213172863125557 17 -0.2576098038951917 0 0.751698407412144 18 0.09877141338753169 0 0.8984499284579619 19 0.3179840140462045 3.126872543830576e-18 0 20 0.2422365795893659 0.5213172863125557 0 21 0.06636281106291925 0.751698407412144 -0.751698407412144 22 0.1248841817693533 0.751698407412144 -1.084202172485504e-16 23 -0.2576098038951917 0.751698407412144 0 24 0.06636281106291919 0.751698407412144 0.751698407412144 25 0.09877141338753169 0.8984499284579619 0 TNO sparse grid, Dim 2, Level 5 1 0.025444484433213 -0.8984499284579617 -0.751698407412144 2 0.04788244452110577 -0.8984499284579617 -1.084202172485504e-16 3 0 -0.8984499284579617 0 4 0.02544448443321298 -0.8984499284579617 0.751698407412144 5 0.025444484433213 -0.751698407412144 -0.8984499284579617 6 -0.06636281106291932 -0.751698407412144 -0.751698407412144 7 0.06240251776425863 -0.751698407412144 -0.5213172863125559 8 -0.1248841817693535 -0.751698407412144 -1.084202172485504e-16 9 0.08191579950024877 -0.751698407412144 3.126872543830576e-18 10 0.06240251776425867 -0.751698407412144 0.5213172863125557 11 -0.06636281106291925 -0.751698407412144 0.751698407412144 12 0.02544448443321299 -0.751698407412144 0.8984499284579619 13 0.06240251776425863 -0.5213172863125559 -0.751698407412144 14 0.1174315440608486 -0.5213172863125559 -1.084202172485504e-16 15 0 -0.5213172863125559 0 16 0.06240251776425857 -0.5213172863125559 0.751698407412144 17 0.04788244452110577 -1.084202172485504e-16 -0.8984499284579617 18 -0.1248841817693535 -1.084202172485504e-16 -0.751698407412144 19 0.1174315440608486 -1.084202172485504e-16 -0.5213172863125559 20 -0.2350120286709091 -1.084202172485504e-16 -1.084202172485504e-16 21 0.1541524150457071 -1.084202172485504e-16 3.126872543830576e-18 22 0.1174315440608487 -1.084202172485504e-16 0.5213172863125557 23 -0.1248841817693533 -1.084202172485504e-16 0.751698407412144 24 0.04788244452110575 -1.084202172485504e-16 0.8984499284579619 25 0 0 -0.8984499284579617 26 0 0 -0.5213172863125559 27 0 0 3.126872543830576e-18 28 0 0 0.5213172863125557 29 0 0 0.8984499284579619 30 0.08191579950024877 3.126872543830576e-18 -0.751698407412144 31 0.1541524150457071 3.126872543830576e-18 -1.084202172485504e-16 32 0 3.126872543830576e-18 0 33 0.0819157995002487 3.126872543830576e-18 0.751698407412144 34 0.06240251776425867 0.5213172863125557 -0.751698407412144 35 0.1174315440608487 0.5213172863125557 -1.084202172485504e-16 36 0 0.5213172863125557 0 37 0.06240251776425861 0.5213172863125557 0.751698407412144 38 0.02544448443321298 0.751698407412144 -0.8984499284579617 39 -0.06636281106291925 0.751698407412144 -0.751698407412144 40 0.06240251776425857 0.751698407412144 -0.5213172863125559 41 -0.1248841817693533 0.751698407412144 -1.084202172485504e-16 42 0.0819157995002487 0.751698407412144 3.126872543830576e-18 43 0.06240251776425861 0.751698407412144 0.5213172863125557 44 -0.06636281106291919 0.751698407412144 0.751698407412144 45 0.02544448443321297 0.751698407412144 0.8984499284579619 46 0.02544448443321299 0.8984499284579619 -0.751698407412144 47 0.04788244452110575 0.8984499284579619 -1.084202172485504e-16 48 0 0.8984499284579619 0 49 0.02544448443321297 0.8984499284579619 0.751698407412144 TNO sparse grid, Dim 2, Level 6 1 0.05120922616144839 -0.9458406558947008 0 2 0.02544448443321304 -0.8984499284579617 -0.751698407412144 3 0.04788244452110583 -0.8984499284579617 -1.084202172485504e-16 4 -0.09877141338753186 -0.8984499284579617 0 5 0.02544448443321302 -0.8984499284579617 0.751698407412144 6 0.02544448443321304 -0.751698407412144 -0.8984499284579617 7 -0.0663628110629194 -0.751698407412144 -0.751698407412144 8 0.06240251776425871 -0.751698407412144 -0.5213172863125559 9 -0.1248841817693536 -0.751698407412144 -1.084202172485504e-16 10 0.08191579950024888 -0.751698407412144 3.126872543830576e-18 11 0.06240251776425875 -0.751698407412144 0.5213172863125557 12 -0.06636281106291933 -0.751698407412144 0.751698407412144 13 0.02544448443321303 -0.751698407412144 0.8984499284579619 14 0.1277556497685094 -0.7302915927779311 0 15 0.06240251776425871 -0.5213172863125559 -0.751698407412144 16 0.1174315440608488 -0.5213172863125559 -1.084202172485504e-16 17 -0.2422365795893661 -0.5213172863125559 0 18 0.06240251776425865 -0.5213172863125559 0.751698407412144 19 0.2028471683540219 -0.3947841138633845 0 20 0.04788244452110583 -1.084202172485504e-16 -0.8984499284579617 21 -0.1248841817693536 -1.084202172485504e-16 -0.751698407412144 22 0.1174315440608488 -1.084202172485504e-16 -0.5213172863125559 23 -0.2350120286709094 -1.084202172485504e-16 -1.084202172485504e-16 24 0.1541524150457073 -1.084202172485504e-16 3.126872543830576e-18 25 0.1174315440608489 -1.084202172485504e-16 0.5213172863125557 26 -0.1248841817693535 -1.084202172485504e-16 0.751698407412144 27 0.04788244452110581 -1.084202172485504e-16 0.8984499284579619 28 0.05120922616144839 0 -0.9458406558947008 29 -0.09877141338753186 0 -0.8984499284579617 30 0.1277556497685094 0 -0.7302915927779311 31 -0.2422365795893661 0 -0.5213172863125559 32 0.2028471683540219 0 -0.3947841138633845 33 -0.3179840140462049 0 3.126872543830576e-18 34 0.2363759114320405 0 5.527527213390232e-17 35 0.2028471683540225 0 0.3947841138633847 36 -0.2422365795893663 0 0.5213172863125557 37 0.127755649768509 0 0.730291592777931 38 -0.09877141338753181 0 0.8984499284579619 39 0.05120922616144857 0 0.9458406558947008 40 0.08191579950024888 3.126872543830576e-18 -0.751698407412144 41 0.1541524150457073 3.126872543830576e-18 -1.084202172485504e-16 42 -0.3179840140462049 3.126872543830576e-18 0 43 0.08191579950024881 3.126872543830576e-18 0.751698407412144 44 0.2363759114320405 5.527527213390232e-17 0 45 0.2028471683540225 0.3947841138633847 0 46 0.06240251776425875 0.5213172863125557 -0.751698407412144 47 0.1174315440608489 0.5213172863125557 -1.084202172485504e-16 48 -0.2422365795893663 0.5213172863125557 0 49 0.0624025177642587 0.5213172863125557 0.751698407412144 50 0.127755649768509 0.730291592777931 0 51 0.02544448443321302 0.751698407412144 -0.8984499284579617 52 -0.06636281106291933 0.751698407412144 -0.751698407412144 53 0.06240251776425865 0.751698407412144 -0.5213172863125559 54 -0.1248841817693535 0.751698407412144 -1.084202172485504e-16 55 0.08191579950024881 0.751698407412144 3.126872543830576e-18 56 0.0624025177642587 0.751698407412144 0.5213172863125557 57 -0.06636281106291927 0.751698407412144 0.751698407412144 58 0.02544448443321301 0.751698407412144 0.8984499284579619 59 0.02544448443321303 0.8984499284579619 -0.751698407412144 60 0.04788244452110581 0.8984499284579619 -1.084202172485504e-16 61 -0.09877141338753181 0.8984499284579619 0 62 0.02544448443321301 0.8984499284579619 0.751698407412144 63 0.05120922616144857 0.9458406558947008 0 TNO sparse grid, Dim 2, Level 7 1 0.01319199870907527 -0.9458406558947008 -0.751698407412144 2 0.02482522874329789 -0.9458406558947008 -1.084202172485504e-16 3 0 -0.9458406558947008 0 4 0.01319199870907526 -0.9458406558947008 0.751698407412144 5 0.009755792102570705 -0.8984499284579617 -0.8984499284579617 6 -0.02544448443321304 -0.8984499284579617 -0.751698407412144 7 0.02392604934020303 -0.8984499284579617 -0.5213172863125559 8 -0.04788244452110584 -0.8984499284579617 -1.084202172485504e-16 9 0.03140773050198443 -0.8984499284579617 3.126872543830576e-18 10 0.02392604934020305 -0.8984499284579617 0.5213172863125557 11 -0.02544448443321302 -0.8984499284579617 0.751698407412144 12 0.009755792102570699 -0.8984499284579617 0.8984499284579619 13 0.01319199870907527 -0.751698407412144 -0.9458406558947008 14 -0.02544448443321304 -0.751698407412144 -0.8984499284579617 15 0.03291110788336855 -0.751698407412144 -0.7302915927779311 16 -0.06240251776425872 -0.751698407412144 -0.5213172863125559 17 0.05225541926037463 -0.751698407412144 -0.3947841138633845 18 -0.08191579950024888 -0.751698407412144 3.126872543830576e-18 19 0.06089275218955528 -0.751698407412144 5.527527213390232e-17 20 0.05225541926037477 -0.751698407412144 0.3947841138633847 21 -0.06240251776425876 -0.751698407412144 0.5213172863125557 22 0.03291110788336847 -0.751698407412144 0.730291592777931 23 -0.02544448443321303 -0.751698407412144 0.8984499284579619 24 0.01319199870907531 -0.751698407412144 0.9458406558947008 25 0.03291110788336855 -0.7302915927779311 -0.751698407412144 26 0.06193343400177233 -0.7302915927779311 -1.084202172485504e-16 27 0 -0.7302915927779311 0 28 0.03291110788336853 -0.7302915927779311 0.751698407412144 29 0.02392604934020303 -0.5213172863125559 -0.8984499284579617 30 -0.06240251776425872 -0.5213172863125559 -0.751698407412144 31 0.05867856049115527 -0.5213172863125559 -0.5213172863125559 32 -0.1174315440608488 -0.5213172863125559 -1.084202172485504e-16 33 0.07702735992664958 -0.5213172863125559 3.126872543830576e-18 34 0.05867856049115532 -0.5213172863125559 0.5213172863125557 35 -0.06240251776425866 -0.5213172863125559 0.751698407412144 36 0.02392604934020302 -0.5213172863125559 0.8984499284579619 37 0.05225541926037463 -0.3947841138633845 -0.751698407412144 38 0.09833632983327281 -0.3947841138633845 -1.084202172485504e-16 39 0 -0.3947841138633845 0 40 0.05225541926037459 -0.3947841138633845 0.751698407412144 41 0.02482522874329789 -1.084202172485504e-16 -0.9458406558947008 42 -0.04788244452110584 -1.084202172485504e-16 -0.8984499284579617 43 0.06193343400177233 -1.084202172485504e-16 -0.7302915927779311 44 -0.1174315440608488 -1.084202172485504e-16 -0.5213172863125559 45 0.09833632983327281 -1.084202172485504e-16 -0.3947841138633845 46 -0.1541524150457073 -1.084202172485504e-16 3.126872543830576e-18 47 0.1145904070529301 -1.084202172485504e-16 5.527527213390232e-17 48 0.09833632983327308 -1.084202172485504e-16 0.3947841138633847 49 -0.1174315440608489 -1.084202172485504e-16 0.5213172863125557 50 0.06193343400177218 -1.084202172485504e-16 0.730291592777931 51 -0.04788244452110581 -1.084202172485504e-16 0.8984499284579619 52 0.02482522874329798 -1.084202172485504e-16 0.9458406558947008 53 0 0 -0.9458406558947008 54 0 0 -0.7302915927779311 55 0 0 -0.3947841138633845 56 0 0 5.527527213390232e-17 57 0 0 0.3947841138633847 58 0 0 0.730291592777931 59 0 0 0.9458406558947008 60 0.03140773050198443 3.126872543830576e-18 -0.8984499284579617 61 -0.08191579950024888 3.126872543830576e-18 -0.751698407412144 62 0.07702735992664958 3.126872543830576e-18 -0.5213172863125559 63 -0.1541524150457073 3.126872543830576e-18 -1.084202172485504e-16 64 0.101113833188937 3.126872543830576e-18 3.126872543830576e-18 65 0.07702735992664964 3.126872543830576e-18 0.5213172863125557 66 -0.08191579950024881 3.126872543830576e-18 0.751698407412144 67 0.03140773050198442 3.126872543830576e-18 0.8984499284579619 68 0.06089275218955528 5.527527213390232e-17 -0.751698407412144 69 0.1145904070529301 5.527527213390232e-17 -1.084202172485504e-16 70 0 5.527527213390232e-17 0 71 0.06089275218955523 5.527527213390232e-17 0.751698407412144 72 0.05225541926037477 0.3947841138633847 -0.751698407412144 73 0.09833632983327308 0.3947841138633847 -1.084202172485504e-16 74 0 0.3947841138633847 0 75 0.05225541926037473 0.3947841138633847 0.751698407412144 76 0.02392604934020305 0.5213172863125557 -0.8984499284579617 77 -0.06240251776425876 0.5213172863125557 -0.751698407412144 78 0.05867856049115532 0.5213172863125557 -0.5213172863125559 79 -0.1174315440608489 0.5213172863125557 -1.084202172485504e-16 80 0.07702735992664964 0.5213172863125557 3.126872543830576e-18 81 0.05867856049115536 0.5213172863125557 0.5213172863125557 82 -0.0624025177642587 0.5213172863125557 0.751698407412144 83 0.02392604934020304 0.5213172863125557 0.8984499284579619 84 0.03291110788336847 0.730291592777931 -0.751698407412144 85 0.06193343400177218 0.730291592777931 -1.084202172485504e-16 86 0 0.730291592777931 0 87 0.03291110788336844 0.730291592777931 0.751698407412144 88 0.01319199870907526 0.751698407412144 -0.9458406558947008 89 -0.02544448443321302 0.751698407412144 -0.8984499284579617 90 0.03291110788336853 0.751698407412144 -0.7302915927779311 91 -0.06240251776425866 0.751698407412144 -0.5213172863125559 92 0.05225541926037459 0.751698407412144 -0.3947841138633845 93 -0.08191579950024881 0.751698407412144 3.126872543830576e-18 94 0.06089275218955523 0.751698407412144 5.527527213390232e-17 95 0.05225541926037473 0.751698407412144 0.3947841138633847 96 -0.0624025177642587 0.751698407412144 0.5213172863125557 97 0.03291110788336844 0.751698407412144 0.730291592777931 98 -0.02544448443321301 0.751698407412144 0.8984499284579619 99 0.0131919987090753 0.751698407412144 0.9458406558947008 100 0.009755792102570699 0.8984499284579619 -0.8984499284579617 101 -0.02544448443321303 0.8984499284579619 -0.751698407412144 102 0.02392604934020302 0.8984499284579619 -0.5213172863125559 103 -0.04788244452110581 0.8984499284579619 -1.084202172485504e-16 104 0.03140773050198442 0.8984499284579619 3.126872543830576e-18 105 0.02392604934020304 0.8984499284579619 0.5213172863125557 106 -0.02544448443321301 0.8984499284579619 0.751698407412144 107 0.009755792102570696 0.8984499284579619 0.8984499284579619 108 0.01319199870907531 0.9458406558947008 -0.751698407412144 109 0.02482522874329798 0.9458406558947008 -1.084202172485504e-16 110 0 0.9458406558947008 0 111 0.0131919987090753 0.9458406558947008 0.751698407412144 tno_sparse_grid_size_test(): nwspgr_size() returns the size of a sparse grid formed from 1D quadrature rules. Our 1D rules will be the Truncated Normal Odd (TNO) family. Dimension / Level table for TNO Family 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: 3 15 37 67 106 154 211 277 352 436 4: 5 25 78 195 401 724 1191 1829 2665 3726 5: 5 49 168 455 1106 2389 4656 8339 13951 22086 6: 7 63 315 1023 2733 6589 14533 29563 55972 99592 tno_sparse_grid_test(): nwspgr() generates a sparse grid in 2D based on the Truncated Normal Odd (TNO) family. TNO sparse grid, Dim 2, Level 1 1 1 0 0 TNO sparse grid, Dim 2, Level 2 1 0.2576098038951921 -0.751698407412144 0 2 0.4847803922096159 -1.084202172485504e-16 0 3 0.2576098038951921 0 -0.751698407412144 4 0.4847803922096159 0 -1.084202172485504e-16 5 -0.9999999999999996 0 0 6 0.2576098038951918 0 0.751698407412144 7 0.2576098038951918 0.751698407412144 0 TNO sparse grid, Dim 2, Level 3 1 0.06636281106291934 -0.751698407412144 -0.751698407412144 2 0.1248841817693535 -0.751698407412144 -1.084202172485504e-16 3 0 -0.751698407412144 0 4 0.06636281106291927 -0.751698407412144 0.751698407412144 5 0.1248841817693535 -1.084202172485504e-16 -0.751698407412144 6 0.2350120286709092 -1.084202172485504e-16 -1.084202172485504e-16 7 0 -1.084202172485504e-16 0 8 0.1248841817693534 -1.084202172485504e-16 0.751698407412144 9 0 0 -0.751698407412144 10 0 0 -1.084202172485504e-16 11 0 0 0.751698407412144 12 0.06636281106291927 0.751698407412144 -0.751698407412144 13 0.1248841817693534 0.751698407412144 -1.084202172485504e-16 14 0 0.751698407412144 0 15 0.06636281106291922 0.751698407412144 0.751698407412144 TNO sparse grid, Dim 2, Level 4 1 0.09877141338753173 -0.8984499284579617 0 2 0.06636281106291932 -0.751698407412144 -0.751698407412144 3 0.1248841817693535 -0.751698407412144 -1.084202172485504e-16 4 -0.2576098038951919 -0.751698407412144 0 5 0.06636281106291925 -0.751698407412144 0.751698407412144 6 0.2422365795893658 -0.5213172863125559 0 7 0.1248841817693535 -1.084202172485504e-16 -0.751698407412144 8 0.2350120286709091 -1.084202172485504e-16 -1.084202172485504e-16 9 -0.4847803922096157 -1.084202172485504e-16 0 10 0.1248841817693533 -1.084202172485504e-16 0.751698407412144 11 0.09877141338753173 0 -0.8984499284579617 12 -0.2576098038951919 0 -0.751698407412144 13 0.2422365795893658 0 -0.5213172863125559 14 -0.4847803922096157 0 -1.084202172485504e-16 15 0.3179840140462045 0 3.126872543830576e-18 16 0.2422365795893659 0 0.5213172863125557 17 -0.2576098038951917 0 0.751698407412144 18 0.09877141338753169 0 0.8984499284579619 19 0.3179840140462045 3.126872543830576e-18 0 20 0.2422365795893659 0.5213172863125557 0 21 0.06636281106291925 0.751698407412144 -0.751698407412144 22 0.1248841817693533 0.751698407412144 -1.084202172485504e-16 23 -0.2576098038951917 0.751698407412144 0 24 0.06636281106291919 0.751698407412144 0.751698407412144 25 0.09877141338753169 0.8984499284579619 0 TNO sparse grid, Dim 2, Level 5 1 0.025444484433213 -0.8984499284579617 -0.751698407412144 2 0.04788244452110577 -0.8984499284579617 -1.084202172485504e-16 3 0 -0.8984499284579617 0 4 0.02544448443321298 -0.8984499284579617 0.751698407412144 5 0.025444484433213 -0.751698407412144 -0.8984499284579617 6 -0.06636281106291932 -0.751698407412144 -0.751698407412144 7 0.06240251776425863 -0.751698407412144 -0.5213172863125559 8 -0.1248841817693535 -0.751698407412144 -1.084202172485504e-16 9 0.08191579950024877 -0.751698407412144 3.126872543830576e-18 10 0.06240251776425867 -0.751698407412144 0.5213172863125557 11 -0.06636281106291925 -0.751698407412144 0.751698407412144 12 0.02544448443321299 -0.751698407412144 0.8984499284579619 13 0.06240251776425863 -0.5213172863125559 -0.751698407412144 14 0.1174315440608486 -0.5213172863125559 -1.084202172485504e-16 15 0 -0.5213172863125559 0 16 0.06240251776425857 -0.5213172863125559 0.751698407412144 17 0.04788244452110577 -1.084202172485504e-16 -0.8984499284579617 18 -0.1248841817693535 -1.084202172485504e-16 -0.751698407412144 19 0.1174315440608486 -1.084202172485504e-16 -0.5213172863125559 20 -0.2350120286709091 -1.084202172485504e-16 -1.084202172485504e-16 21 0.1541524150457071 -1.084202172485504e-16 3.126872543830576e-18 22 0.1174315440608487 -1.084202172485504e-16 0.5213172863125557 23 -0.1248841817693533 -1.084202172485504e-16 0.751698407412144 24 0.04788244452110575 -1.084202172485504e-16 0.8984499284579619 25 0 0 -0.8984499284579617 26 0 0 -0.5213172863125559 27 0 0 3.126872543830576e-18 28 0 0 0.5213172863125557 29 0 0 0.8984499284579619 30 0.08191579950024877 3.126872543830576e-18 -0.751698407412144 31 0.1541524150457071 3.126872543830576e-18 -1.084202172485504e-16 32 0 3.126872543830576e-18 0 33 0.0819157995002487 3.126872543830576e-18 0.751698407412144 34 0.06240251776425867 0.5213172863125557 -0.751698407412144 35 0.1174315440608487 0.5213172863125557 -1.084202172485504e-16 36 0 0.5213172863125557 0 37 0.06240251776425861 0.5213172863125557 0.751698407412144 38 0.02544448443321298 0.751698407412144 -0.8984499284579617 39 -0.06636281106291925 0.751698407412144 -0.751698407412144 40 0.06240251776425857 0.751698407412144 -0.5213172863125559 41 -0.1248841817693533 0.751698407412144 -1.084202172485504e-16 42 0.0819157995002487 0.751698407412144 3.126872543830576e-18 43 0.06240251776425861 0.751698407412144 0.5213172863125557 44 -0.06636281106291919 0.751698407412144 0.751698407412144 45 0.02544448443321297 0.751698407412144 0.8984499284579619 46 0.02544448443321299 0.8984499284579619 -0.751698407412144 47 0.04788244452110575 0.8984499284579619 -1.084202172485504e-16 48 0 0.8984499284579619 0 49 0.02544448443321297 0.8984499284579619 0.751698407412144 TNO sparse grid, Dim 2, Level 6 1 0.05120922616144839 -0.9458406558947008 0 2 0.02544448443321304 -0.8984499284579617 -0.751698407412144 3 0.04788244452110583 -0.8984499284579617 -1.084202172485504e-16 4 -0.09877141338753186 -0.8984499284579617 0 5 0.02544448443321302 -0.8984499284579617 0.751698407412144 6 0.02544448443321304 -0.751698407412144 -0.8984499284579617 7 -0.0663628110629194 -0.751698407412144 -0.751698407412144 8 0.06240251776425871 -0.751698407412144 -0.5213172863125559 9 -0.1248841817693536 -0.751698407412144 -1.084202172485504e-16 10 0.08191579950024888 -0.751698407412144 3.126872543830576e-18 11 0.06240251776425875 -0.751698407412144 0.5213172863125557 12 -0.06636281106291933 -0.751698407412144 0.751698407412144 13 0.02544448443321303 -0.751698407412144 0.8984499284579619 14 0.1277556497685094 -0.7302915927779311 0 15 0.06240251776425871 -0.5213172863125559 -0.751698407412144 16 0.1174315440608488 -0.5213172863125559 -1.084202172485504e-16 17 -0.2422365795893661 -0.5213172863125559 0 18 0.06240251776425865 -0.5213172863125559 0.751698407412144 19 0.2028471683540219 -0.3947841138633845 0 20 0.04788244452110583 -1.084202172485504e-16 -0.8984499284579617 21 -0.1248841817693536 -1.084202172485504e-16 -0.751698407412144 22 0.1174315440608488 -1.084202172485504e-16 -0.5213172863125559 23 -0.2350120286709094 -1.084202172485504e-16 -1.084202172485504e-16 24 0.1541524150457073 -1.084202172485504e-16 3.126872543830576e-18 25 0.1174315440608489 -1.084202172485504e-16 0.5213172863125557 26 -0.1248841817693535 -1.084202172485504e-16 0.751698407412144 27 0.04788244452110581 -1.084202172485504e-16 0.8984499284579619 28 0.05120922616144839 0 -0.9458406558947008 29 -0.09877141338753186 0 -0.8984499284579617 30 0.1277556497685094 0 -0.7302915927779311 31 -0.2422365795893661 0 -0.5213172863125559 32 0.2028471683540219 0 -0.3947841138633845 33 -0.3179840140462049 0 3.126872543830576e-18 34 0.2363759114320405 0 5.527527213390232e-17 35 0.2028471683540225 0 0.3947841138633847 36 -0.2422365795893663 0 0.5213172863125557 37 0.127755649768509 0 0.730291592777931 38 -0.09877141338753181 0 0.8984499284579619 39 0.05120922616144857 0 0.9458406558947008 40 0.08191579950024888 3.126872543830576e-18 -0.751698407412144 41 0.1541524150457073 3.126872543830576e-18 -1.084202172485504e-16 42 -0.3179840140462049 3.126872543830576e-18 0 43 0.08191579950024881 3.126872543830576e-18 0.751698407412144 44 0.2363759114320405 5.527527213390232e-17 0 45 0.2028471683540225 0.3947841138633847 0 46 0.06240251776425875 0.5213172863125557 -0.751698407412144 47 0.1174315440608489 0.5213172863125557 -1.084202172485504e-16 48 -0.2422365795893663 0.5213172863125557 0 49 0.0624025177642587 0.5213172863125557 0.751698407412144 50 0.127755649768509 0.730291592777931 0 51 0.02544448443321302 0.751698407412144 -0.8984499284579617 52 -0.06636281106291933 0.751698407412144 -0.751698407412144 53 0.06240251776425865 0.751698407412144 -0.5213172863125559 54 -0.1248841817693535 0.751698407412144 -1.084202172485504e-16 55 0.08191579950024881 0.751698407412144 3.126872543830576e-18 56 0.0624025177642587 0.751698407412144 0.5213172863125557 57 -0.06636281106291927 0.751698407412144 0.751698407412144 58 0.02544448443321301 0.751698407412144 0.8984499284579619 59 0.02544448443321303 0.8984499284579619 -0.751698407412144 60 0.04788244452110581 0.8984499284579619 -1.084202172485504e-16 61 -0.09877141338753181 0.8984499284579619 0 62 0.02544448443321301 0.8984499284579619 0.751698407412144 63 0.05120922616144857 0.9458406558947008 0 TNO sparse grid, Dim 2, Level 7 1 0.01319199870907527 -0.9458406558947008 -0.751698407412144 2 0.02482522874329789 -0.9458406558947008 -1.084202172485504e-16 3 0 -0.9458406558947008 0 4 0.01319199870907526 -0.9458406558947008 0.751698407412144 5 0.009755792102570705 -0.8984499284579617 -0.8984499284579617 6 -0.02544448443321304 -0.8984499284579617 -0.751698407412144 7 0.02392604934020303 -0.8984499284579617 -0.5213172863125559 8 -0.04788244452110584 -0.8984499284579617 -1.084202172485504e-16 9 0.03140773050198443 -0.8984499284579617 3.126872543830576e-18 10 0.02392604934020305 -0.8984499284579617 0.5213172863125557 11 -0.02544448443321302 -0.8984499284579617 0.751698407412144 12 0.009755792102570699 -0.8984499284579617 0.8984499284579619 13 0.01319199870907527 -0.751698407412144 -0.9458406558947008 14 -0.02544448443321304 -0.751698407412144 -0.8984499284579617 15 0.03291110788336855 -0.751698407412144 -0.7302915927779311 16 -0.06240251776425872 -0.751698407412144 -0.5213172863125559 17 0.05225541926037463 -0.751698407412144 -0.3947841138633845 18 -0.08191579950024888 -0.751698407412144 3.126872543830576e-18 19 0.06089275218955528 -0.751698407412144 5.527527213390232e-17 20 0.05225541926037477 -0.751698407412144 0.3947841138633847 21 -0.06240251776425876 -0.751698407412144 0.5213172863125557 22 0.03291110788336847 -0.751698407412144 0.730291592777931 23 -0.02544448443321303 -0.751698407412144 0.8984499284579619 24 0.01319199870907531 -0.751698407412144 0.9458406558947008 25 0.03291110788336855 -0.7302915927779311 -0.751698407412144 26 0.06193343400177233 -0.7302915927779311 -1.084202172485504e-16 27 0 -0.7302915927779311 0 28 0.03291110788336853 -0.7302915927779311 0.751698407412144 29 0.02392604934020303 -0.5213172863125559 -0.8984499284579617 30 -0.06240251776425872 -0.5213172863125559 -0.751698407412144 31 0.05867856049115527 -0.5213172863125559 -0.5213172863125559 32 -0.1174315440608488 -0.5213172863125559 -1.084202172485504e-16 33 0.07702735992664958 -0.5213172863125559 3.126872543830576e-18 34 0.05867856049115532 -0.5213172863125559 0.5213172863125557 35 -0.06240251776425866 -0.5213172863125559 0.751698407412144 36 0.02392604934020302 -0.5213172863125559 0.8984499284579619 37 0.05225541926037463 -0.3947841138633845 -0.751698407412144 38 0.09833632983327281 -0.3947841138633845 -1.084202172485504e-16 39 0 -0.3947841138633845 0 40 0.05225541926037459 -0.3947841138633845 0.751698407412144 41 0.02482522874329789 -1.084202172485504e-16 -0.9458406558947008 42 -0.04788244452110584 -1.084202172485504e-16 -0.8984499284579617 43 0.06193343400177233 -1.084202172485504e-16 -0.7302915927779311 44 -0.1174315440608488 -1.084202172485504e-16 -0.5213172863125559 45 0.09833632983327281 -1.084202172485504e-16 -0.3947841138633845 46 -0.1541524150457073 -1.084202172485504e-16 3.126872543830576e-18 47 0.1145904070529301 -1.084202172485504e-16 5.527527213390232e-17 48 0.09833632983327308 -1.084202172485504e-16 0.3947841138633847 49 -0.1174315440608489 -1.084202172485504e-16 0.5213172863125557 50 0.06193343400177218 -1.084202172485504e-16 0.730291592777931 51 -0.04788244452110581 -1.084202172485504e-16 0.8984499284579619 52 0.02482522874329798 -1.084202172485504e-16 0.9458406558947008 53 0 0 -0.9458406558947008 54 0 0 -0.7302915927779311 55 0 0 -0.3947841138633845 56 0 0 5.527527213390232e-17 57 0 0 0.3947841138633847 58 0 0 0.730291592777931 59 0 0 0.9458406558947008 60 0.03140773050198443 3.126872543830576e-18 -0.8984499284579617 61 -0.08191579950024888 3.126872543830576e-18 -0.751698407412144 62 0.07702735992664958 3.126872543830576e-18 -0.5213172863125559 63 -0.1541524150457073 3.126872543830576e-18 -1.084202172485504e-16 64 0.101113833188937 3.126872543830576e-18 3.126872543830576e-18 65 0.07702735992664964 3.126872543830576e-18 0.5213172863125557 66 -0.08191579950024881 3.126872543830576e-18 0.751698407412144 67 0.03140773050198442 3.126872543830576e-18 0.8984499284579619 68 0.06089275218955528 5.527527213390232e-17 -0.751698407412144 69 0.1145904070529301 5.527527213390232e-17 -1.084202172485504e-16 70 0 5.527527213390232e-17 0 71 0.06089275218955523 5.527527213390232e-17 0.751698407412144 72 0.05225541926037477 0.3947841138633847 -0.751698407412144 73 0.09833632983327308 0.3947841138633847 -1.084202172485504e-16 74 0 0.3947841138633847 0 75 0.05225541926037473 0.3947841138633847 0.751698407412144 76 0.02392604934020305 0.5213172863125557 -0.8984499284579617 77 -0.06240251776425876 0.5213172863125557 -0.751698407412144 78 0.05867856049115532 0.5213172863125557 -0.5213172863125559 79 -0.1174315440608489 0.5213172863125557 -1.084202172485504e-16 80 0.07702735992664964 0.5213172863125557 3.126872543830576e-18 81 0.05867856049115536 0.5213172863125557 0.5213172863125557 82 -0.0624025177642587 0.5213172863125557 0.751698407412144 83 0.02392604934020304 0.5213172863125557 0.8984499284579619 84 0.03291110788336847 0.730291592777931 -0.751698407412144 85 0.06193343400177218 0.730291592777931 -1.084202172485504e-16 86 0 0.730291592777931 0 87 0.03291110788336844 0.730291592777931 0.751698407412144 88 0.01319199870907526 0.751698407412144 -0.9458406558947008 89 -0.02544448443321302 0.751698407412144 -0.8984499284579617 90 0.03291110788336853 0.751698407412144 -0.7302915927779311 91 -0.06240251776425866 0.751698407412144 -0.5213172863125559 92 0.05225541926037459 0.751698407412144 -0.3947841138633845 93 -0.08191579950024881 0.751698407412144 3.126872543830576e-18 94 0.06089275218955523 0.751698407412144 5.527527213390232e-17 95 0.05225541926037473 0.751698407412144 0.3947841138633847 96 -0.0624025177642587 0.751698407412144 0.5213172863125557 97 0.03291110788336844 0.751698407412144 0.730291592777931 98 -0.02544448443321301 0.751698407412144 0.8984499284579619 99 0.0131919987090753 0.751698407412144 0.9458406558947008 100 0.009755792102570699 0.8984499284579619 -0.8984499284579617 101 -0.02544448443321303 0.8984499284579619 -0.751698407412144 102 0.02392604934020302 0.8984499284579619 -0.5213172863125559 103 -0.04788244452110581 0.8984499284579619 -1.084202172485504e-16 104 0.03140773050198442 0.8984499284579619 3.126872543830576e-18 105 0.02392604934020304 0.8984499284579619 0.5213172863125557 106 -0.02544448443321301 0.8984499284579619 0.751698407412144 107 0.009755792102570696 0.8984499284579619 0.8984499284579619 108 0.01319199870907531 0.9458406558947008 -0.751698407412144 109 0.02482522874329798 0.9458406558947008 -1.084202172485504e-16 110 0 0.9458406558947008 0 111 0.0131919987090753 0.9458406558947008 0.751698407412144 tno_sparse_grid_write_test(): Write a TNO sparse grid to a file. W data written to "tno_d2_level1_w.txt". X data written to "tno_d2_level1_x.txt", W data written to "tno_d2_level2_w.txt". X data written to "tno_d2_level2_x.txt", W data written to "tno_d2_level3_w.txt". X data written to "tno_d2_level3_x.txt", W data written to "tno_d2_level4_w.txt". X data written to "tno_d2_level4_x.txt", W data written to "tno_d2_level5_w.txt". X data written to "tno_d2_level5_x.txt", W data written to "tno_d2_level6_w.txt". X data written to "tno_d2_level6_x.txt", W data written to "tno_d2_level7_w.txt". X data written to "tno_d2_level7_x.txt", truncated_normal_sparse_grid_test(): Normal end of execution. 02-Apr-2024 14:30:56