5 April 2023 9:55:24.054 AM SOBOL_TEST(): FORTRAN90 version Test SOBOL(). TEST01 IEOR is a FORTRAN90 function which returns the bitwise exclusive OR of two integers. I J IEOR(I,J) 22 96 118 83 56 107 41 6 47 26 11 17 4 64 68 6 45 43 40 76 100 80 0 80 90 35 121 9 1 8 TEST02 I4_BIT_HI1 returns the location of the high 1 bit. I I4_BIT_HI1(I) 22 5 96 7 83 7 56 6 41 6 6 3 26 5 11 4 4 3 64 7 TEST03 I4_BIT_LO0 returns the location of the lowest 0 bit. I I4_BIT_LO0(I) 22 1 96 1 83 3 56 1 41 2 6 1 26 1 11 3 4 1 64 1 TEST04 I4_SOBOL computes the next element of a Sobol sequence. In this test, we call I4_SOBOL repeatedly. Using dimension DIM_NUM = 2 Seed Seed I4_SOBOL In Out 0 1 0.000000 0.000000 1 2 0.500000 0.500000 2 3 0.750000 0.250000 3 4 0.250000 0.750000 4 5 0.375000 0.375000 5 6 0.875000 0.875000 6 7 0.625000 0.125000 7 8 0.125000 0.625000 8 9 0.187500 0.312500 9 10 0.687500 0.812500 10 11 0.937500 0.062500 11 12 0.437500 0.562500 ...................... 95 96 0.054688 0.929688 96 97 0.039062 0.132812 97 98 0.539062 0.632812 98 99 0.789062 0.382812 99 100 0.289062 0.882812 100 101 0.414062 0.257812 101 102 0.914062 0.757812 102 103 0.664062 0.007812 103 104 0.164062 0.507812 104 105 0.226562 0.445312 105 106 0.726562 0.945312 106 107 0.976562 0.195312 107 108 0.476562 0.695312 108 109 0.351562 0.070312 109 110 0.851562 0.570312 110 111 0.601562 0.320312 Using dimension DIM_NUM = 3 Seed Seed I4_SOBOL In Out 0 1 0.000000 0.000000 0.000000 1 2 0.500000 0.500000 0.500000 2 3 0.750000 0.250000 0.750000 3 4 0.250000 0.750000 0.250000 4 5 0.375000 0.375000 0.625000 5 6 0.875000 0.875000 0.125000 6 7 0.625000 0.125000 0.375000 7 8 0.125000 0.625000 0.875000 8 9 0.187500 0.312500 0.312500 9 10 0.687500 0.812500 0.812500 10 11 0.937500 0.062500 0.562500 11 12 0.437500 0.562500 0.062500 ...................... 95 96 0.054688 0.929688 0.101562 96 97 0.039062 0.132812 0.929688 97 98 0.539062 0.632812 0.429688 98 99 0.789062 0.382812 0.179688 99 100 0.289062 0.882812 0.679688 100 101 0.414062 0.257812 0.304688 101 102 0.914062 0.757812 0.804688 102 103 0.664062 0.007812 0.554688 103 104 0.164062 0.507812 0.054688 104 105 0.226562 0.445312 0.742188 105 106 0.726562 0.945312 0.242188 106 107 0.976562 0.195312 0.492188 107 108 0.476562 0.695312 0.992188 108 109 0.351562 0.070312 0.117188 109 110 0.851562 0.570312 0.617188 110 111 0.601562 0.320312 0.867188 Using dimension DIM_NUM = 4 Seed Seed I4_SOBOL In Out 0 1 0.000000 0.000000 0.000000 0.000000 1 2 0.500000 0.500000 0.500000 0.500000 2 3 0.750000 0.250000 0.750000 0.250000 3 4 0.250000 0.750000 0.250000 0.750000 4 5 0.375000 0.375000 0.625000 0.125000 5 6 0.875000 0.875000 0.125000 0.625000 6 7 0.625000 0.125000 0.375000 0.375000 7 8 0.125000 0.625000 0.875000 0.875000 8 9 0.187500 0.312500 0.312500 0.687500 9 10 0.687500 0.812500 0.812500 0.187500 10 11 0.937500 0.062500 0.562500 0.937500 11 12 0.437500 0.562500 0.062500 0.437500 ...................... 95 96 0.054688 0.929688 0.101562 0.960938 96 97 0.039062 0.132812 0.929688 0.351562 97 98 0.539062 0.632812 0.429688 0.851562 98 99 0.789062 0.382812 0.179688 0.101562 99 100 0.289062 0.882812 0.679688 0.601562 100 101 0.414062 0.257812 0.304688 0.476562 101 102 0.914062 0.757812 0.804688 0.976562 102 103 0.664062 0.007812 0.554688 0.226562 103 104 0.164062 0.507812 0.054688 0.726562 104 105 0.226562 0.445312 0.742188 0.914062 105 106 0.726562 0.945312 0.242188 0.414062 106 107 0.976562 0.195312 0.492188 0.664062 107 108 0.476562 0.695312 0.992188 0.164062 108 109 0.351562 0.070312 0.117188 0.789062 109 110 0.851562 0.570312 0.617188 0.289062 110 111 0.601562 0.320312 0.867188 0.539062 Repeat the 2D calculation, but start with different seeds. Using dimension DIM_NUM = 2 Seed Seed I4_SOBOL In Out 0 1 0.000000 0.000000 1 2 0.500000 0.500000 2 3 0.750000 0.250000 3 4 0.250000 0.750000 4 5 0.375000 0.375000 5 6 0.875000 0.875000 6 7 0.625000 0.125000 7 8 0.125000 0.625000 8 9 0.187500 0.312500 9 10 0.687500 0.812500 10 11 0.937500 0.062500 11 12 0.437500 0.562500 ...................... 95 96 0.054688 0.929688 96 97 0.039062 0.132812 97 98 0.539062 0.632812 98 99 0.789062 0.382812 99 100 0.289062 0.882812 100 101 0.414062 0.257812 101 102 0.914062 0.757812 102 103 0.664062 0.007812 103 104 0.164062 0.507812 104 105 0.226562 0.445312 105 106 0.726562 0.945312 106 107 0.976562 0.195312 107 108 0.476562 0.695312 108 109 0.351562 0.070312 109 110 0.851562 0.570312 110 111 0.601562 0.320312 Seed Seed I4_SOBOL In Out 1 2 0.500000 0.500000 2 3 0.750000 0.250000 3 4 0.250000 0.750000 4 5 0.375000 0.375000 5 6 0.875000 0.875000 6 7 0.625000 0.125000 7 8 0.125000 0.625000 8 9 0.187500 0.312500 9 10 0.687500 0.812500 10 11 0.937500 0.062500 11 12 0.437500 0.562500 12 13 0.312500 0.187500 ...................... 96 97 0.039062 0.132812 97 98 0.539062 0.632812 98 99 0.789062 0.382812 99 100 0.289062 0.882812 100 101 0.414062 0.257812 101 102 0.914062 0.757812 102 103 0.664062 0.007812 103 104 0.164062 0.507812 104 105 0.226562 0.445312 105 106 0.726562 0.945312 106 107 0.976562 0.195312 107 108 0.476562 0.695312 108 109 0.351562 0.070312 109 110 0.851562 0.570312 110 111 0.601562 0.320312 111 112 0.101562 0.820312 Seed Seed I4_SOBOL In Out 2 3 0.750000 0.250000 3 4 0.250000 0.750000 4 5 0.375000 0.375000 5 6 0.875000 0.875000 6 7 0.625000 0.125000 7 8 0.125000 0.625000 8 9 0.187500 0.312500 9 10 0.687500 0.812500 10 11 0.937500 0.062500 11 12 0.437500 0.562500 12 13 0.312500 0.187500 13 14 0.812500 0.687500 ...................... 97 98 0.539062 0.632812 98 99 0.789062 0.382812 99 100 0.289062 0.882812 100 101 0.414062 0.257812 101 102 0.914062 0.757812 102 103 0.664062 0.007812 103 104 0.164062 0.507812 104 105 0.226562 0.445312 105 106 0.726562 0.945312 106 107 0.976562 0.195312 107 108 0.476562 0.695312 108 109 0.351562 0.070312 109 110 0.851562 0.570312 110 111 0.601562 0.320312 111 112 0.101562 0.820312 112 113 0.070312 0.351562 Seed Seed I4_SOBOL In Out 3 4 0.250000 0.750000 4 5 0.375000 0.375000 5 6 0.875000 0.875000 6 7 0.625000 0.125000 7 8 0.125000 0.625000 8 9 0.187500 0.312500 9 10 0.687500 0.812500 10 11 0.937500 0.062500 11 12 0.437500 0.562500 12 13 0.312500 0.187500 13 14 0.812500 0.687500 14 15 0.562500 0.437500 ...................... 98 99 0.789062 0.382812 99 100 0.289062 0.882812 100 101 0.414062 0.257812 101 102 0.914062 0.757812 102 103 0.664062 0.007812 103 104 0.164062 0.507812 104 105 0.226562 0.445312 105 106 0.726562 0.945312 106 107 0.976562 0.195312 107 108 0.476562 0.695312 108 109 0.351562 0.070312 109 110 0.851562 0.570312 110 111 0.601562 0.320312 111 112 0.101562 0.820312 112 113 0.070312 0.351562 113 114 0.570312 0.851562 Seed Seed I4_SOBOL In Out 4 5 0.375000 0.375000 5 6 0.875000 0.875000 6 7 0.625000 0.125000 7 8 0.125000 0.625000 8 9 0.187500 0.312500 9 10 0.687500 0.812500 10 11 0.937500 0.062500 11 12 0.437500 0.562500 12 13 0.312500 0.187500 13 14 0.812500 0.687500 14 15 0.562500 0.437500 15 16 0.062500 0.937500 ...................... 99 100 0.289062 0.882812 100 101 0.414062 0.257812 101 102 0.914062 0.757812 102 103 0.664062 0.007812 103 104 0.164062 0.507812 104 105 0.226562 0.445312 105 106 0.726562 0.945312 106 107 0.976562 0.195312 107 108 0.476562 0.695312 108 109 0.351562 0.070312 109 110 0.851562 0.570312 110 111 0.601562 0.320312 111 112 0.101562 0.820312 112 113 0.070312 0.351562 113 114 0.570312 0.851562 114 115 0.820312 0.101562 Seed Seed I4_SOBOL In Out 5 6 0.875000 0.875000 6 7 0.625000 0.125000 7 8 0.125000 0.625000 8 9 0.187500 0.312500 9 10 0.687500 0.812500 10 11 0.937500 0.062500 11 12 0.437500 0.562500 12 13 0.312500 0.187500 13 14 0.812500 0.687500 14 15 0.562500 0.437500 15 16 0.062500 0.937500 16 17 0.093750 0.468750 ...................... 100 101 0.414062 0.257812 101 102 0.914062 0.757812 102 103 0.664062 0.007812 103 104 0.164062 0.507812 104 105 0.226562 0.445312 105 106 0.726562 0.945312 106 107 0.976562 0.195312 107 108 0.476562 0.695312 108 109 0.351562 0.070312 109 110 0.851562 0.570312 110 111 0.601562 0.320312 111 112 0.101562 0.820312 112 113 0.070312 0.351562 113 114 0.570312 0.851562 114 115 0.820312 0.101562 115 116 0.320312 0.601562 Seed Seed I4_SOBOL In Out 6 7 0.625000 0.125000 7 8 0.125000 0.625000 8 9 0.187500 0.312500 9 10 0.687500 0.812500 10 11 0.937500 0.062500 11 12 0.437500 0.562500 12 13 0.312500 0.187500 13 14 0.812500 0.687500 14 15 0.562500 0.437500 15 16 0.062500 0.937500 16 17 0.093750 0.468750 17 18 0.593750 0.968750 ...................... 101 102 0.914062 0.757812 102 103 0.664062 0.007812 103 104 0.164062 0.507812 104 105 0.226562 0.445312 105 106 0.726562 0.945312 106 107 0.976562 0.195312 107 108 0.476562 0.695312 108 109 0.351562 0.070312 109 110 0.851562 0.570312 110 111 0.601562 0.320312 111 112 0.101562 0.820312 112 113 0.070312 0.351562 113 114 0.570312 0.851562 114 115 0.820312 0.101562 115 116 0.320312 0.601562 116 117 0.445312 0.226562 Seed Seed I4_SOBOL In Out 7 8 0.125000 0.625000 8 9 0.187500 0.312500 9 10 0.687500 0.812500 10 11 0.937500 0.062500 11 12 0.437500 0.562500 12 13 0.312500 0.187500 13 14 0.812500 0.687500 14 15 0.562500 0.437500 15 16 0.062500 0.937500 16 17 0.093750 0.468750 17 18 0.593750 0.968750 18 19 0.843750 0.218750 ...................... 102 103 0.664062 0.007812 103 104 0.164062 0.507812 104 105 0.226562 0.445312 105 106 0.726562 0.945312 106 107 0.976562 0.195312 107 108 0.476562 0.695312 108 109 0.351562 0.070312 109 110 0.851562 0.570312 110 111 0.601562 0.320312 111 112 0.101562 0.820312 112 113 0.070312 0.351562 113 114 0.570312 0.851562 114 115 0.820312 0.101562 115 116 0.320312 0.601562 116 117 0.445312 0.226562 117 118 0.945312 0.726562 Seed Seed I4_SOBOL In Out 8 9 0.187500 0.312500 9 10 0.687500 0.812500 10 11 0.937500 0.062500 11 12 0.437500 0.562500 12 13 0.312500 0.187500 13 14 0.812500 0.687500 14 15 0.562500 0.437500 15 16 0.062500 0.937500 16 17 0.093750 0.468750 17 18 0.593750 0.968750 18 19 0.843750 0.218750 19 20 0.343750 0.718750 ...................... 103 104 0.164062 0.507812 104 105 0.226562 0.445312 105 106 0.726562 0.945312 106 107 0.976562 0.195312 107 108 0.476562 0.695312 108 109 0.351562 0.070312 109 110 0.851562 0.570312 110 111 0.601562 0.320312 111 112 0.101562 0.820312 112 113 0.070312 0.351562 113 114 0.570312 0.851562 114 115 0.820312 0.101562 115 116 0.320312 0.601562 116 117 0.445312 0.226562 117 118 0.945312 0.726562 118 119 0.695312 0.476562 Seed Seed I4_SOBOL In Out 9 10 0.687500 0.812500 10 11 0.937500 0.062500 11 12 0.437500 0.562500 12 13 0.312500 0.187500 13 14 0.812500 0.687500 14 15 0.562500 0.437500 15 16 0.062500 0.937500 16 17 0.093750 0.468750 17 18 0.593750 0.968750 18 19 0.843750 0.218750 19 20 0.343750 0.718750 20 21 0.468750 0.093750 ...................... 104 105 0.226562 0.445312 105 106 0.726562 0.945312 106 107 0.976562 0.195312 107 108 0.476562 0.695312 108 109 0.351562 0.070312 109 110 0.851562 0.570312 110 111 0.601562 0.320312 111 112 0.101562 0.820312 112 113 0.070312 0.351562 113 114 0.570312 0.851562 114 115 0.820312 0.101562 115 116 0.320312 0.601562 116 117 0.445312 0.226562 117 118 0.945312 0.726562 118 119 0.695312 0.476562 119 120 0.195312 0.976562 Seed Seed I4_SOBOL In Out 10 11 0.937500 0.062500 11 12 0.437500 0.562500 12 13 0.312500 0.187500 13 14 0.812500 0.687500 14 15 0.562500 0.437500 15 16 0.062500 0.937500 16 17 0.093750 0.468750 17 18 0.593750 0.968750 18 19 0.843750 0.218750 19 20 0.343750 0.718750 20 21 0.468750 0.093750 21 22 0.968750 0.593750 ...................... 105 106 0.726562 0.945312 106 107 0.976562 0.195312 107 108 0.476562 0.695312 108 109 0.351562 0.070312 109 110 0.851562 0.570312 110 111 0.601562 0.320312 111 112 0.101562 0.820312 112 113 0.070312 0.351562 113 114 0.570312 0.851562 114 115 0.820312 0.101562 115 116 0.320312 0.601562 116 117 0.445312 0.226562 117 118 0.945312 0.726562 118 119 0.695312 0.476562 119 120 0.195312 0.976562 120 121 0.132812 0.039062 TEST05 I4_SOBOL computes the next element of a Sobol sequence. In this test, we demonstrate how the SEED can be manipulated to skip ahead in the sequence, or to come back to any part of the sequence. Using dimension DIM_NUM = 3 Seed Seed I4_SOBOL In Out 0 1 0.000000 0.000000 0.000000 1 2 0.500000 0.500000 0.500000 2 3 0.750000 0.250000 0.750000 3 4 0.250000 0.750000 0.250000 4 5 0.375000 0.375000 0.625000 5 6 0.875000 0.875000 0.125000 6 7 0.625000 0.125000 0.375000 7 8 0.125000 0.625000 0.875000 8 9 0.187500 0.312500 0.312500 9 10 0.687500 0.812500 0.812500 10 11 0.937500 0.062500 0.562500 Jump ahead by increasing SEED: Seed Seed I4_SOBOL In Out 100 101 0.414062 0.257812 0.304688 101 102 0.914062 0.757812 0.804688 102 103 0.664062 0.007812 0.554688 103 104 0.164062 0.507812 0.054688 104 105 0.226562 0.445312 0.742188 Jump back by decreasing SEED: Seed Seed I4_SOBOL In Out 3 4 0.250000 0.750000 0.250000 4 5 0.375000 0.375000 0.625000 5 6 0.875000 0.875000 0.125000 6 7 0.625000 0.125000 0.375000 7 8 0.125000 0.625000 0.875000 8 9 0.187500 0.312500 0.312500 9 10 0.687500 0.812500 0.812500 10 11 0.937500 0.062500 0.562500 11 12 0.437500 0.562500 0.062500 12 13 0.312500 0.187500 0.937500 13 14 0.812500 0.687500 0.437500 Jump ahead by increasing SEED: Seed Seed I4_SOBOL In Out 98 99 0.789062 0.382812 0.179688 99 100 0.289062 0.882812 0.679688 100 101 0.414062 0.257812 0.304688 101 102 0.914062 0.757812 0.804688 102 103 0.664062 0.007812 0.554688 TEST06 I4_SOBOL computes the next element of a Sobol sequence. In this test, we get a few samples at high dimension. We only print the first and last 2 entries of each sample. Using dimension DIM_NUM = 100 Seed Seed I4_SOBOL In Out (First 2, Last 2) 0 1 0.000000 0.000000 0.000000 0.000000 1 2 0.500000 0.500000 0.500000 0.500000 2 3 0.750000 0.250000 0.250000 0.750000 3 4 0.250000 0.750000 0.750000 0.250000 4 5 0.375000 0.375000 0.125000 0.125000 5 6 0.875000 0.875000 0.625000 0.625000 6 7 0.625000 0.125000 0.375000 0.875000 7 8 0.125000 0.625000 0.875000 0.375000 8 9 0.187500 0.312500 0.312500 0.687500 9 10 0.687500 0.812500 0.812500 0.187500 10 11 0.937500 0.062500 0.062500 0.437500 100000 100001 0.061073 0.107582 0.155632 0.230919 100001 100002 0.561073 0.607582 0.655632 0.730919 100002 100003 0.811073 0.357582 0.405632 0.980919 100003 100004 0.311073 0.857582 0.905632 0.480919 100004 100005 0.436073 0.482582 0.030632 0.105919 Using dimension DIM_NUM = 500 Seed Seed I4_SOBOL In Out (First 2, Last 2) 0 1 0.000000 0.000000 0.000000 0.000000 1 2 0.500000 0.500000 0.500000 0.500000 2 3 0.750000 0.250000 0.250000 0.750000 3 4 0.250000 0.750000 0.750000 0.250000 4 5 0.375000 0.375000 0.625000 0.875000 5 6 0.875000 0.875000 0.125000 0.375000 6 7 0.625000 0.125000 0.875000 0.125000 7 8 0.125000 0.625000 0.375000 0.625000 8 9 0.187500 0.312500 0.187500 0.937500 9 10 0.687500 0.812500 0.687500 0.437500 10 11 0.937500 0.062500 0.437500 0.187500 100000 100001 0.061073 0.107582 0.967598 0.142342 100001 100002 0.561073 0.607582 0.467598 0.642342 100002 100003 0.811073 0.357582 0.717598 0.892342 100003 100004 0.311073 0.857582 0.217598 0.392342 100004 100005 0.436073 0.482582 0.342598 0.767342 Using dimension DIM_NUM = 1000 Seed Seed I4_SOBOL In Out (First 2, Last 2) 0 1 0.000000 0.000000 0.000000 0.000000 1 2 0.500000 0.500000 0.500000 0.500000 2 3 0.750000 0.250000 0.750000 0.750000 3 4 0.250000 0.750000 0.250000 0.250000 4 5 0.375000 0.375000 0.875000 0.875000 5 6 0.875000 0.875000 0.375000 0.375000 6 7 0.625000 0.125000 0.125000 0.125000 7 8 0.125000 0.625000 0.625000 0.625000 8 9 0.187500 0.312500 0.187500 0.687500 9 10 0.687500 0.812500 0.687500 0.187500 10 11 0.937500 0.062500 0.937500 0.437500 100000 100001 0.061073 0.107582 0.155571 0.018913 100001 100002 0.561073 0.607582 0.655571 0.518913 100002 100003 0.811073 0.357582 0.905571 0.768913 100003 100004 0.311073 0.857582 0.405571 0.268913 100004 100005 0.436073 0.482582 0.780571 0.893913 TEST08 IEOR is a FORTRAN90 function which returns the bitwise exclusive OR of two integers. I J IEOR(I,J) 22 96 118 83 56 107 41 6 47 26 11 17 4 64 68 6 45 43 40 76 100 80 0 80 90 35 121 9 1 8 TEST09 I8_BIT_HI1 returns the location of the high 1 bit. I I8_BIT_HI1(I) 22 5 96 7 83 7 56 6 41 6 6 3 26 5 11 4 4 3 64 7 TEST10 I8_BIT_LO0 returns the location of the lowest 0 bit. I I8_BIT_LO0(I) 22 1 96 1 83 3 56 1 41 2 6 1 26 1 11 3 4 1 64 1 TEST11 I8_SOBOL computes the next element of a Sobol sequence. In this test, we call I8_SOBOL repeatedly. Using dimension DIM_NUM = 2 Seed Seed I8_SOBOL In Out 0 1 0.000000 0.000000 1 2 0.500000 0.500000 2 3 0.750000 0.250000 3 4 0.250000 0.750000 4 5 0.375000 0.375000 5 6 0.875000 0.875000 6 7 0.625000 0.125000 7 8 0.125000 0.625000 8 9 0.187500 0.312500 9 10 0.687500 0.812500 10 11 0.937500 0.062500 11 12 0.437500 0.562500 ...................... 95 96 0.054688 0.929688 96 97 0.039062 0.132812 97 98 0.539062 0.632812 98 99 0.789062 0.382812 99 100 0.289062 0.882812 100 101 0.414062 0.257812 101 102 0.914062 0.757812 102 103 0.664062 0.007812 103 104 0.164062 0.507812 104 105 0.226562 0.445312 105 106 0.726562 0.945312 106 107 0.976562 0.195312 107 108 0.476562 0.695312 108 109 0.351562 0.070312 109 110 0.851562 0.570312 110 111 0.601562 0.320312 Using dimension DIM_NUM = 3 Seed Seed I8_SOBOL In Out 0 1 0.000000 0.000000 0.000000 1 2 0.500000 0.500000 0.500000 2 3 0.750000 0.250000 0.750000 3 4 0.250000 0.750000 0.250000 4 5 0.375000 0.375000 0.625000 5 6 0.875000 0.875000 0.125000 6 7 0.625000 0.125000 0.375000 7 8 0.125000 0.625000 0.875000 8 9 0.187500 0.312500 0.312500 9 10 0.687500 0.812500 0.812500 10 11 0.937500 0.062500 0.562500 11 12 0.437500 0.562500 0.062500 ...................... 95 96 0.054688 0.929688 0.101562 96 97 0.039062 0.132812 0.929688 97 98 0.539062 0.632812 0.429688 98 99 0.789062 0.382812 0.179688 99 100 0.289062 0.882812 0.679688 100 101 0.414062 0.257812 0.304688 101 102 0.914062 0.757812 0.804688 102 103 0.664062 0.007812 0.554688 103 104 0.164062 0.507812 0.054688 104 105 0.226562 0.445312 0.742188 105 106 0.726562 0.945312 0.242188 106 107 0.976562 0.195312 0.492188 107 108 0.476562 0.695312 0.992188 108 109 0.351562 0.070312 0.117188 109 110 0.851562 0.570312 0.617188 110 111 0.601562 0.320312 0.867188 Using dimension DIM_NUM = 4 Seed Seed I8_SOBOL In Out 0 1 0.000000 0.000000 0.000000 0.000000 1 2 0.500000 0.500000 0.500000 0.500000 2 3 0.750000 0.250000 0.750000 0.250000 3 4 0.250000 0.750000 0.250000 0.750000 4 5 0.375000 0.375000 0.625000 0.125000 5 6 0.875000 0.875000 0.125000 0.625000 6 7 0.625000 0.125000 0.375000 0.375000 7 8 0.125000 0.625000 0.875000 0.875000 8 9 0.187500 0.312500 0.312500 0.687500 9 10 0.687500 0.812500 0.812500 0.187500 10 11 0.937500 0.062500 0.562500 0.937500 11 12 0.437500 0.562500 0.062500 0.437500 ...................... 95 96 0.054688 0.929688 0.101562 0.960938 96 97 0.039062 0.132812 0.929688 0.351562 97 98 0.539062 0.632812 0.429688 0.851562 98 99 0.789062 0.382812 0.179688 0.101562 99 100 0.289062 0.882812 0.679688 0.601562 100 101 0.414062 0.257812 0.304688 0.476562 101 102 0.914062 0.757812 0.804688 0.976562 102 103 0.664062 0.007812 0.554688 0.226562 103 104 0.164062 0.507812 0.054688 0.726562 104 105 0.226562 0.445312 0.742188 0.914062 105 106 0.726562 0.945312 0.242188 0.414062 106 107 0.976562 0.195312 0.492188 0.664062 107 108 0.476562 0.695312 0.992188 0.164062 108 109 0.351562 0.070312 0.117188 0.789062 109 110 0.851562 0.570312 0.617188 0.289062 110 111 0.601562 0.320312 0.867188 0.539062 TEST12 I8_SOBOL computes the next element of a Sobol sequence. In this test, we demonstrate how the SEED can be manipulated to skip ahead in the sequence, or to come back to any part of the sequence. Using dimension DIM_NUM = 3 Seed Seed I8_SOBOL In Out 0 1 0.000000 0.000000 0.000000 1 2 0.500000 0.500000 0.500000 2 3 0.750000 0.250000 0.750000 3 4 0.250000 0.750000 0.250000 4 5 0.375000 0.375000 0.625000 5 6 0.875000 0.875000 0.125000 6 7 0.625000 0.125000 0.375000 7 8 0.125000 0.625000 0.875000 8 9 0.187500 0.312500 0.312500 9 10 0.687500 0.812500 0.812500 10 11 0.937500 0.062500 0.562500 Jump ahead by increasing SEED: Seed Seed I8_SOBOL In Out 100 101 0.414062 0.257812 0.304688 101 102 0.914062 0.757812 0.804688 102 103 0.664062 0.007812 0.554688 103 104 0.164062 0.507812 0.054688 104 105 0.226562 0.445312 0.742188 Jump back by decreasing SEED: Seed Seed I8_SOBOL In Out 3 4 0.250000 0.750000 0.250000 4 5 0.375000 0.375000 0.625000 5 6 0.875000 0.875000 0.125000 6 7 0.625000 0.125000 0.375000 7 8 0.125000 0.625000 0.875000 8 9 0.187500 0.312500 0.312500 9 10 0.687500 0.812500 0.812500 10 11 0.937500 0.062500 0.562500 11 12 0.437500 0.562500 0.062500 12 13 0.312500 0.187500 0.937500 13 14 0.812500 0.687500 0.437500 Jump ahead by increasing SEED: Seed Seed I8_SOBOL In Out 98 99 0.789062 0.382812 0.179688 99 100 0.289062 0.882812 0.679688 100 101 0.414062 0.257812 0.304688 101 102 0.914062 0.757812 0.804688 102 103 0.664062 0.007812 0.554688 TEST13 I8_SOBOL computes the next element of a Sobol sequence. In this test, we get a few samples at high dimension. We only print the first and last 2 entries of each sample. Using dimension DIM_NUM = 100 Seed Seed I8_SOBOL In Out (First 2, Last 2) 0 1 0.000000 0.000000 0.000000 0.000000 1 2 0.500000 0.500000 0.500000 0.500000 2 3 0.750000 0.250000 0.250000 0.750000 3 4 0.250000 0.750000 0.750000 0.250000 4 5 0.375000 0.375000 0.125000 0.125000 5 6 0.875000 0.875000 0.625000 0.625000 6 7 0.625000 0.125000 0.375000 0.875000 7 8 0.125000 0.625000 0.875000 0.375000 8 9 0.187500 0.312500 0.312500 0.687500 9 10 0.687500 0.812500 0.812500 0.187500 10 11 0.937500 0.062500 0.062500 0.437500 100000 100001 0.061073 0.107582 0.155632 0.230919 100001 100002 0.561073 0.607582 0.655632 0.730919 100002 100003 0.811073 0.357582 0.405632 0.980919 100003 100004 0.311073 0.857582 0.905632 0.480919 100004 100005 0.436073 0.482582 0.030632 0.105919 Using dimension DIM_NUM = 500 Seed Seed I8_SOBOL In Out (First 2, Last 2) 0 1 0.000000 0.000000 0.000000 0.000000 1 2 0.500000 0.500000 0.500000 0.500000 2 3 0.750000 0.250000 0.250000 0.750000 3 4 0.250000 0.750000 0.750000 0.250000 4 5 0.375000 0.375000 0.625000 0.875000 5 6 0.875000 0.875000 0.125000 0.375000 6 7 0.625000 0.125000 0.875000 0.125000 7 8 0.125000 0.625000 0.375000 0.625000 8 9 0.187500 0.312500 0.187500 0.937500 9 10 0.687500 0.812500 0.687500 0.437500 10 11 0.937500 0.062500 0.437500 0.187500 100000 100001 0.061073 0.107582 0.967598 0.142342 100001 100002 0.561073 0.607582 0.467598 0.642342 100002 100003 0.811073 0.357582 0.717598 0.892342 100003 100004 0.311073 0.857582 0.217598 0.392342 100004 100005 0.436073 0.482582 0.342598 0.767342 Using dimension DIM_NUM = 1000 Seed Seed I8_SOBOL In Out (First 2, Last 2) 0 1 0.000000 0.000000 0.000000 0.000000 1 2 0.500000 0.500000 0.500000 0.500000 2 3 0.750000 0.250000 0.750000 0.750000 3 4 0.250000 0.750000 0.250000 0.250000 4 5 0.375000 0.375000 0.875000 0.875000 5 6 0.875000 0.875000 0.375000 0.375000 6 7 0.625000 0.125000 0.125000 0.125000 7 8 0.125000 0.625000 0.625000 0.625000 8 9 0.187500 0.312500 0.187500 0.687500 9 10 0.687500 0.812500 0.687500 0.187500 10 11 0.937500 0.062500 0.937500 0.437500 100000 100001 0.061073 0.107582 0.155571 0.018913 100001 100002 0.561073 0.607582 0.655571 0.518913 100002 100003 0.811073 0.357582 0.905571 0.768913 100003 100004 0.311073 0.857582 0.405571 0.268913 100004 100005 0.436073 0.482582 0.780571 0.893913 SOBOL_TEST Normal end of execution. 5 April 2023 9:55:24.504 AM