halton_test 29-Jan-2005 08:42:09 HALTON_TEST Test the MATLAB HALTON routines. HALTON_TEST01 HALTON returns the next element of a Halton sequence. HALTON_STEP_SET sets the step. In this test, we try several values of STEP. We repeat the test for several dimensions. We assume defaults for SEED, LEAP and BASE. NDIM = 1 N = 11 STEP = 0 SEED = 0 BASE = 2 STEP Halton 0 0.000000 1 0.500000 2 0.250000 3 0.750000 4 0.125000 5 0.625000 6 0.375000 7 0.875000 8 0.062500 9 0.562500 10 0.312500 NDIM = 1 N = 11 STEP = 5 SEED = 0 BASE = 2 STEP Halton 5 0.625000 6 0.375000 7 0.875000 8 0.062500 9 0.562500 10 0.312500 11 0.812500 12 0.187500 13 0.687500 14 0.437500 15 0.937500 NDIM = 1 N = 11 STEP = 1000 SEED = 0 BASE = 2 STEP Halton 1000 0.092773 1001 0.592773 1002 0.342773 1003 0.842773 1004 0.217773 1005 0.717773 1006 0.467773 1007 0.967773 1008 0.061523 1009 0.561523 1010 0.311523 NDIM = 1 N = 11 STEP = 1000000 SEED = 0 BASE = 2 STEP Halton 1000000 0.008834 1000001 0.508834 1000002 0.258834 1000003 0.758834 1000004 0.133834 1000005 0.633834 1000006 0.383834 1000007 0.883834 1000008 0.071334 1000009 0.571334 1000010 0.321334 NDIM = 2 N = 11 STEP = 0 SEED = 0 0 BASE = 2 3 STEP Halton 0 0.000000 0.000000 1 0.500000 0.333333 2 0.250000 0.666667 3 0.750000 0.111111 4 0.125000 0.444444 5 0.625000 0.777778 6 0.375000 0.222222 7 0.875000 0.555556 8 0.062500 0.888889 9 0.562500 0.037037 10 0.312500 0.370370 NDIM = 2 N = 11 STEP = 5 SEED = 0 0 BASE = 2 3 STEP Halton 5 0.625000 0.777778 6 0.375000 0.222222 7 0.875000 0.555556 8 0.062500 0.888889 9 0.562500 0.037037 10 0.312500 0.370370 11 0.812500 0.703704 12 0.187500 0.148148 13 0.687500 0.481481 14 0.437500 0.814815 15 0.937500 0.259259 NDIM = 2 N = 11 STEP = 1000 SEED = 0 0 BASE = 2 3 STEP Halton 1000 0.092773 0.347508 1001 0.592773 0.680841 1002 0.342773 0.125286 1003 0.842773 0.458619 1004 0.217773 0.791952 1005 0.717773 0.236397 1006 0.467773 0.569730 1007 0.967773 0.903064 1008 0.061523 0.051212 1009 0.561523 0.384545 1010 0.311523 0.717878 NDIM = 2 N = 11 STEP = 1000000 SEED = 0 0 BASE = 2 3 STEP Halton 1000000 0.008834 0.361066 1000001 0.508834 0.694399 1000002 0.258834 0.138844 1000003 0.758834 0.472177 1000004 0.133834 0.805511 1000005 0.633834 0.249955 1000006 0.383834 0.583288 1000007 0.883834 0.916622 1000008 0.071334 0.064770 1000009 0.571334 0.398103 1000010 0.321334 0.731436 NDIM = 3 N = 11 STEP = 0 SEED = 0 0 0 BASE = 2 3 5 STEP Halton 0 0.000000 0.000000 0.000000 1 0.500000 0.333333 0.200000 2 0.250000 0.666667 0.400000 3 0.750000 0.111111 0.600000 4 0.125000 0.444444 0.800000 5 0.625000 0.777778 0.040000 6 0.375000 0.222222 0.240000 7 0.875000 0.555556 0.440000 8 0.062500 0.888889 0.640000 9 0.562500 0.037037 0.840000 10 0.312500 0.370370 0.080000 NDIM = 3 N = 11 STEP = 5 SEED = 0 0 0 BASE = 2 3 5 STEP Halton 5 0.625000 0.777778 0.040000 6 0.375000 0.222222 0.240000 7 0.875000 0.555556 0.440000 8 0.062500 0.888889 0.640000 9 0.562500 0.037037 0.840000 10 0.312500 0.370370 0.080000 11 0.812500 0.703704 0.280000 12 0.187500 0.148148 0.480000 13 0.687500 0.481481 0.680000 14 0.437500 0.814815 0.880000 15 0.937500 0.259259 0.120000 NDIM = 3 N = 11 STEP = 1000 SEED = 0 0 0 BASE = 2 3 5 STEP Halton 1000 0.092773 0.347508 0.005120 1001 0.592773 0.680841 0.205120 1002 0.342773 0.125286 0.405120 1003 0.842773 0.458619 0.605120 1004 0.217773 0.791952 0.805120 1005 0.717773 0.236397 0.045120 1006 0.467773 0.569730 0.245120 1007 0.967773 0.903064 0.445120 1008 0.061523 0.051212 0.645120 1009 0.561523 0.384545 0.845120 1010 0.311523 0.717878 0.085120 NDIM = 3 N = 11 STEP = 1000000 SEED = 0 0 0 BASE = 2 3 5 STEP Halton 1000000 0.008834 0.361066 0.000057 1000001 0.508834 0.694399 0.200057 1000002 0.258834 0.138844 0.400057 1000003 0.758834 0.472177 0.600057 1000004 0.133834 0.805511 0.800057 1000005 0.633834 0.249955 0.040057 1000006 0.383834 0.583288 0.240057 1000007 0.883834 0.916622 0.440057 1000008 0.071334 0.064770 0.640057 1000009 0.571334 0.398103 0.840057 1000010 0.321334 0.731436 0.080057 TEST0125 I_TO_HALTON computes a Halton sequence. The user specifies all data explicitly. In this test, we call I_TO_HALTON repeatedly. We use distinct primes as bases. NDIM = 1 N = 11 STEP = 0 SEED = 0 LEAP = 1 BASE = 2 STEP Halton 0 0.000000 1 0.500000 2 0.250000 3 0.750000 4 0.125000 5 0.625000 6 0.375000 7 0.875000 8 0.062500 9 0.562500 10 0.312500 NDIM = 2 N = 11 STEP = 0 SEED = 0 0 LEAP = 1 1 BASE = 2 3 STEP Halton 0 0.000000 0.000000 1 0.500000 0.333333 2 0.250000 0.666667 3 0.750000 0.111111 4 0.125000 0.444444 5 0.625000 0.777778 6 0.375000 0.222222 7 0.875000 0.555556 8 0.062500 0.888889 9 0.562500 0.037037 10 0.312500 0.370370 NDIM = 3 N = 11 STEP = 0 SEED = 0 0 0 LEAP = 1 1 1 BASE = 2 3 5 STEP Halton 0 0.000000 0.000000 0.000000 1 0.500000 0.333333 0.200000 2 0.250000 0.666667 0.400000 3 0.750000 0.111111 0.600000 4 0.125000 0.444444 0.800000 5 0.625000 0.777778 0.040000 6 0.375000 0.222222 0.240000 7 0.875000 0.555556 0.440000 8 0.062500 0.888889 0.640000 9 0.562500 0.037037 0.840000 10 0.312500 0.370370 0.080000 TEST0126 I_TO_HALTON computes a Halton sequence. The user gives the seed and bases as explicit input. In this test, we call I_TO_HALTON repeatedly. We use the same value for all bases. NDIM = 3 N = 11 SEED = 0 0 0 LEAP = 1 1 1 BASE = 2 2 2 STEP Halton 0 0.000000 0.000000 0.000000 1 0.500000 0.500000 0.500000 2 0.250000 0.250000 0.250000 3 0.750000 0.750000 0.750000 4 0.125000 0.125000 0.125000 5 0.625000 0.625000 0.625000 6 0.375000 0.375000 0.375000 7 0.875000 0.875000 0.875000 8 0.062500 0.062500 0.062500 9 0.562500 0.562500 0.562500 10 0.312500 0.312500 0.312500 TEST02 HALTON_SEQUENCE computes N elements of a Halton sequence on a single call. NDIM = 3 N = 10 STEP = 0 SEED = 0 0 0 STEP Halton 0 0.000000 0.000000 0.000000 1 0.500000 0.333333 0.200000 2 0.250000 0.666667 0.400000 3 0.750000 0.111111 0.600000 4 0.125000 0.444444 0.800000 5 0.625000 0.777778 0.040000 6 0.375000 0.222222 0.240000 7 0.875000 0.555556 0.440000 8 0.062500 0.888889 0.640000 9 0.562500 0.037037 0.840000 TEST025 I_TO_HALTON_SEQUENCE computes N elements of a Halton sequence on a single call. All arguments are specified explicitly. NDIM = 3 N = 10 STEP = 0 SEED = 0 0 0 LEAP = 1 1 1 BASE = 2 3 5 STEP Halton 0 0.000000 0.000000 0.000000 1 0.500000 0.333333 0.200000 2 0.250000 0.666667 0.400000 3 0.750000 0.111111 0.600000 4 0.125000 0.444444 0.800000 5 0.625000 0.777778 0.040000 6 0.375000 0.222222 0.240000 7 0.875000 0.555556 0.440000 8 0.062500 0.888889 0.640000 9 0.562500 0.037037 0.840000 NDIM = 3 N = 10 STEP = 0 SEED = 1 2 3 LEAP = 1 1 1 BASE = 2 3 5 STEP Halton 0 0.500000 0.666667 0.600000 1 0.250000 0.111111 0.800000 2 0.750000 0.444444 0.040000 3 0.125000 0.777778 0.240000 4 0.625000 0.222222 0.440000 5 0.375000 0.555556 0.640000 6 0.875000 0.888889 0.840000 7 0.062500 0.037037 0.080000 8 0.562500 0.370370 0.280000 9 0.312500 0.703704 0.480000 NDIM = 3 N = 10 STEP = 0 SEED = 1 1 1 LEAP = 3 3 3 BASE = 2 3 5 STEP Halton 0 0.500000 0.333333 0.200000 1 0.125000 0.444444 0.800000 2 0.875000 0.555556 0.440000 3 0.312500 0.370370 0.080000 4 0.687500 0.481481 0.680000 5 0.031250 0.592593 0.320000 6 0.781250 0.407407 0.920000 7 0.406250 0.518519 0.560000 8 0.593750 0.629630 0.008000 9 0.218750 0.345679 0.608000 NDIM = 3 N = 10 STEP = 0 SEED = 1 2 3 LEAP = 1 1 1 BASE = 2 2 2 STEP Halton 0 0.500000 0.250000 0.750000 1 0.250000 0.750000 0.125000 2 0.750000 0.125000 0.625000 3 0.125000 0.625000 0.375000 4 0.625000 0.375000 0.875000 5 0.375000 0.875000 0.062500 6 0.875000 0.062500 0.562500 7 0.062500 0.562500 0.312500 8 0.562500 0.312500 0.812500 9 0.312500 0.812500 0.187500 TEST03 HALTON_STEP_SET specifies the next element of the Halton subsequence to compute. In this test, we demonstrate how resetting STEP determines the next element computed. NDIM = 1 N = 11 STEP = 0 SEED = 0 STEP Halton 0 0.000000 1 0.500000 2 0.250000 3 0.750000 4 0.125000 5 0.625000 6 0.375000 7 0.875000 8 0.062500 9 0.562500 10 0.312500 N = 11 STEP = 6 STEP Halton 6 0.375000 7 0.875000 8 0.062500 9 0.562500 10 0.312500 11 0.812500 12 0.187500 13 0.687500 14 0.437500 15 0.937500 16 0.031250 N = 6 STEP = 0 STEP Halton 0 0.000000 1 0.500000 2 0.250000 3 0.750000 4 0.125000 5 0.625000 N = 5 STEP = 100 STEP Halton 100 0.148438 101 0.648438 102 0.398438 103 0.898438 104 0.085938 TEST04 HALTON_BASE_GET gets the current Halton base. HALTON_BASE_SET sets the current Halton base. In this test, we compute a Halton sequence with the default base, then change the base, reset the seed, and recompute the sequence. NDIM = 1 N = 10 STEP = 0 SEED = 0 BASE = 2 STEP Halton 0 0.000000 1 0.500000 2 0.250000 3 0.750000 4 0.125000 5 0.625000 6 0.375000 7 0.875000 8 0.062500 9 0.562500 N = 10 STEP = 0 BASE = 3 STEP Halton 0 0.000000 1 0.333333 2 0.666667 3 0.111111 4 0.444444 5 0.777778 6 0.222222 7 0.555556 8 0.888889 9 0.037037 N = 10 STEP = 0 BASE = 4 STEP Halton 0 0.000000 1 0.250000 2 0.500000 3 0.750000 4 0.062500 5 0.312500 6 0.562500 7 0.812500 8 0.125000 9 0.375000 TEST045 HALTON_SEQUENCE computes N elements of a Halton sequence on a single call. NDIM = 2 N = 101 STEP = 0 SEED = 0 0 BASE = 2 3 STEP Halton 0 0.000000 0.000000 1 0.500000 0.333333 2 0.250000 0.666667 3 0.750000 0.111111 4 0.125000 0.444444 5 0.625000 0.777778 6 0.375000 0.222222 7 0.875000 0.555556 8 0.062500 0.888889 9 0.562500 0.037037 10 0.312500 0.370370 11 0.812500 0.703704 12 0.187500 0.148148 13 0.687500 0.481481 14 0.437500 0.814815 15 0.937500 0.259259 16 0.031250 0.592593 17 0.531250 0.925926 18 0.281250 0.074074 19 0.781250 0.407407 20 0.156250 0.740741 21 0.656250 0.185185 22 0.406250 0.518519 23 0.906250 0.851852 24 0.093750 0.296296 25 0.593750 0.629630 26 0.343750 0.962963 27 0.843750 0.012346 28 0.218750 0.345679 29 0.718750 0.679012 30 0.468750 0.123457 31 0.968750 0.456790 32 0.015625 0.790123 33 0.515625 0.234568 34 0.265625 0.567901 35 0.765625 0.901235 36 0.140625 0.049383 37 0.640625 0.382716 38 0.390625 0.716049 39 0.890625 0.160494 40 0.078125 0.493827 41 0.578125 0.827160 42 0.328125 0.271605 43 0.828125 0.604938 44 0.203125 0.938272 45 0.703125 0.086420 46 0.453125 0.419753 47 0.953125 0.753086 48 0.046875 0.197531 49 0.546875 0.530864 50 0.296875 0.864198 51 0.796875 0.308642 52 0.171875 0.641975 53 0.671875 0.975309 54 0.421875 0.024691 55 0.921875 0.358025 56 0.109375 0.691358 57 0.609375 0.135802 58 0.359375 0.469136 59 0.859375 0.802469 60 0.234375 0.246914 61 0.734375 0.580247 62 0.484375 0.913580 63 0.984375 0.061728 64 0.007813 0.395062 65 0.507813 0.728395 66 0.257813 0.172840 67 0.757813 0.506173 68 0.132813 0.839506 69 0.632813 0.283951 70 0.382813 0.617284 71 0.882813 0.950617 72 0.070313 0.098765 73 0.570313 0.432099 74 0.320313 0.765432 75 0.820313 0.209877 76 0.195313 0.543210 77 0.695313 0.876543 78 0.445313 0.320988 79 0.945313 0.654321 80 0.039063 0.987654 81 0.539063 0.004115 82 0.289063 0.337449 83 0.789063 0.670782 84 0.164063 0.115226 85 0.664063 0.448560 86 0.414063 0.781893 87 0.914063 0.226337 88 0.101563 0.559671 89 0.601563 0.893004 90 0.351563 0.041152 91 0.851563 0.374486 92 0.226563 0.707819 93 0.726563 0.152263 94 0.476563 0.485597 95 0.976563 0.818930 96 0.023438 0.263374 97 0.523438 0.596708 98 0.273438 0.930041 99 0.773438 0.078189 100 0.148438 0.411523 TEST05 HALTON computes the elements of a vector Halton sequence. Each call produces the next value. By default, the bases are the first NDIM primes. In this test, we call HALTON several times, with the default bases. NDIM = 4 N = 11 STEP = 0 SEED = 0 0 0 0 BASE = 2 3 5 7 STEP Halton 0 0.000000 0.000000 0.000000 0.000000 1 0.500000 0.333333 0.200000 0.142857 2 0.250000 0.666667 0.400000 0.285714 3 0.750000 0.111111 0.600000 0.428571 4 0.125000 0.444444 0.800000 0.571429 5 0.625000 0.777778 0.040000 0.714286 6 0.375000 0.222222 0.240000 0.857143 7 0.875000 0.555556 0.440000 0.020408 8 0.062500 0.888889 0.640000 0.163265 9 0.562500 0.037037 0.840000 0.306122 10 0.312500 0.370370 0.080000 0.448980 TEST06 HALTON_SEQUENCE computes the next N elements of a vector Halton sequence. Each call produces the next value. By default, the bases are the first NDIM primes. In this test, we demonstrate how one call can compute many successive vector elements of the sequence. NDIM = 4 N = 11 STEP = 0 SEED = 0 0 0 0 STEP Halton 0 0.000000 0.000000 0.000000 0.000000 1 0.500000 0.333333 0.200000 0.142857 2 0.250000 0.666667 0.400000 0.285714 3 0.750000 0.111111 0.600000 0.428571 4 0.125000 0.444444 0.800000 0.571429 5 0.625000 0.777778 0.040000 0.714286 6 0.375000 0.222222 0.240000 0.857143 7 0.875000 0.555556 0.440000 0.020408 8 0.062500 0.888889 0.640000 0.163265 9 0.562500 0.037037 0.840000 0.306122 10 0.312500 0.370370 0.080000 0.448980 TEST07 HALTON_STEP_SET specifies which element of the Halton subsequence to compute. Here we show how STEP chooses the next element. NDIM = 4 N = 10 STEP = 0 SEED = 0 0 0 0 STEP Halton 0 0.000000 0.000000 0.000000 0.000000 1 0.500000 0.333333 0.200000 0.142857 2 0.250000 0.666667 0.400000 0.285714 3 0.750000 0.111111 0.600000 0.428571 4 0.125000 0.444444 0.800000 0.571429 5 0.625000 0.777778 0.040000 0.714286 6 0.375000 0.222222 0.240000 0.857143 7 0.875000 0.555556 0.440000 0.020408 8 0.062500 0.888889 0.640000 0.163265 9 0.562500 0.037037 0.840000 0.306122 N = 10 STEP = 6 STEP Halton 6 0.375000 0.222222 0.240000 0.857143 7 0.875000 0.555556 0.440000 0.020408 8 0.062500 0.888889 0.640000 0.163265 9 0.562500 0.037037 0.840000 0.306122 10 0.312500 0.370370 0.080000 0.448980 11 0.812500 0.703704 0.280000 0.591837 12 0.187500 0.148148 0.480000 0.734694 13 0.687500 0.481481 0.680000 0.877551 14 0.437500 0.814815 0.880000 0.040816 15 0.937500 0.259259 0.120000 0.183673 N = 6 STEP = 0 STEP Halton 0 0.000000 0.000000 0.000000 0.000000 1 0.500000 0.333333 0.200000 0.142857 2 0.250000 0.666667 0.400000 0.285714 3 0.750000 0.111111 0.600000 0.428571 4 0.125000 0.444444 0.800000 0.571429 5 0.625000 0.777778 0.040000 0.714286 N = 5 STEP = 100 STEP Halton 100 0.148438 0.411523 0.032000 0.291545 101 0.648438 0.744856 0.232000 0.434402 102 0.398438 0.189300 0.432000 0.577259 103 0.898438 0.522634 0.632000 0.720117 104 0.085938 0.855967 0.832000 0.862974 TEST08 HALTON_BASE_GET gets the current bases. HALTON_BASE_SET sets the current bases. HALTON_SEQUENCE computes the next N elements of a vector Halton sequence. In this test, we compute the first 10 elements of the default sequence, then change bases, reset the seed and recompute the first 10 elements. NDIM = 4 N = 10 STEP = 0 SEED = 0 0 0 0 BASE = 2 3 5 7 STEP Halton 0 0.000000 0.000000 0.000000 0.000000 1 0.500000 0.333333 0.200000 0.142857 2 0.250000 0.666667 0.400000 0.285714 3 0.750000 0.111111 0.600000 0.428571 4 0.125000 0.444444 0.800000 0.571429 5 0.625000 0.777778 0.040000 0.714286 6 0.375000 0.222222 0.240000 0.857143 7 0.875000 0.555556 0.440000 0.020408 8 0.062500 0.888889 0.640000 0.163265 9 0.562500 0.037037 0.840000 0.306122 N = 10 STEP = 0 BASE = 3 7 13 19 STEP Halton 0 0.000000 0.000000 0.000000 0.000000 1 0.333333 0.142857 0.076923 0.052632 2 0.666667 0.285714 0.153846 0.105263 3 0.111111 0.428571 0.230769 0.157895 4 0.444444 0.571429 0.307692 0.210526 5 0.777778 0.714286 0.384615 0.263158 6 0.222222 0.857143 0.461538 0.315789 7 0.555556 0.020408 0.538462 0.368421 8 0.888889 0.163265 0.615385 0.421053 9 0.037037 0.306122 0.692308 0.473684 TEST09 For the unit sphere in 2 dimensions (the circle): HALTON generates "U1" points, U1_TO_SPHERE_UNIT_2D samples the circle; NDIM = 1 N = 5 STEP = 0 A few sample values: 1.000000 0.000000 -1.000000 0.000000 0.000000 1.000000 -0.000000 -1.000000 0.707107 0.707107 N = 1000 STEP = 0 Average the points, which should get a value close to zero, and closer as N increases. Average: -0.000000 0.000000 Now choose a random direction, sample the same number of points, and compute the dot product with the direction. Take the absolute value of each dot product and sum and average. We expect a value near 2 / PI = 0.6366... Random V: -0.397913 -0.917423 Average |(XdotV)| = 0.636688 Random V: 0.986980 0.160842 Average |(XdotV)| = 0.636428 Random V: 0.498065 0.867140 Average |(XdotV)| = 0.636461 Random V: -0.428245 0.903663 Average |(XdotV)| = 0.636686 Random V: 0.996790 -0.080059 Average |(XdotV)| = 0.636686 TEST10 For the unit ball in 2 dimensions (the disk): U2_TO_BALL_UNIT_2D samples; NDIM = 2 N = 5 STEP = 0 A few sample values: 0.000000 0.000000 -0.353553 0.612372 -0.250000 -0.433013 0.663414 0.556670 -0.332232 0.120922 N = 1000 STEP = 0 Average the points, which should get a value close to zero, and closer as N increases. Average: 0.000588 0.000106 Average the distance of the points from the center, which should be NDIM/(NDIM+1) = 0.666667 Average: 0.665496 Average the angle THETA, which should approach PI. Average: 3.130124 TEST11 For the unit sphere in 3 dimensions: U2_TO_SPHERE_UNIT_3D samples; NDIM = 2 N = 5 STEP = 123456789 A few sample values: 0.745567 0.585674 0.317989 -0.912665 0.365944 -0.182011 0.081559 -0.569423 0.817989 0.121255 0.577953 -0.807011 -0.932375 -0.305668 0.192989 N = 1000 STEP = 0 Average the points, which should get a value close to zero, and closer as N increases. Average: 7.581004e-004 -2.604710e-005 -2.453125e-003 Now choose a random direction, sample the same number of points, and compute the dot product with the direction. Take the absolute value of each dot product and sum and average. Random V: 0.210689 0.965330 -0.154104 Average |(XdotV)| 0.499763 Random V: 0.452432 0.845178 -0.284567 Average |(XdotV)| 0.499811 Random V: 0.203803 0.249710 -0.946631 Average |(XdotV)| 0.499625 Random V: 0.234771 0.952537 -0.193793 Average |(XdotV)| 0.499484 Random V: 0.475379 0.666334 -0.574469 Average |(XdotV)| 0.499895 TEST12 For the unit ball in 3 dimensions: U3_TO_BALL_UNIT_3D samples; NDIM = 3 N = 5 STEP = 0 A few sample values: 0.000000 0.000000 0.000000 -0.292402 0.506455 0.000000 -0.319046 -0.552605 -0.368403 0.559545 0.469514 0.421716 -0.576994 0.210009 -0.696238 N = 1000 STEP = 0 Average the points, which should get a value close to zero, and closer as N increases. Average: 0.000438 0.000567 -0.001714 Average the distance of the points from the center, which should be NDIM/(NDIM+1) = 0.750000 Average: 0.748738 Average the angle THETA, which should approach PI. Average: 3.130124 Average the angle PHI, which should approach PI/2. Average: 1.571363 TEST13 HALHAM_WRITE writes a Halton or Hammersley dataset to a file NDIM = 3 N = 10 STEP = 0 SEED = 0 0 0 LEAP = 1 1 1 BASE = 2 3 5 STEP Halton 0 0.000000 0.000000 0.000000 1 0.500000 0.333333 0.200000 2 0.250000 0.666667 0.400000 3 0.750000 0.111111 0.600000 4 0.125000 0.444444 0.800000 5 0.625000 0.777778 0.040000 6 0.375000 0.222222 0.240000 7 0.875000 0.555556 0.440000 8 0.062500 0.888889 0.640000 9 0.562500 0.037037 0.840000 The data was written to "halton_03_00010.txt". HALTON_TEST Normal end of execution. 29-Jan-2005 08:42:41