August 26 2003 2:57:03.508 PM INTEGRAL_TEST Test a file of sample points for use in equally weighted quadrature. The point data will be read from "halton_02_00010.txt". The weight data will be read from "halton_02_00010_weight_b.txt". The spatial dimension is 2 The number of points is 10 # halton_02_00010.txt # created by HALTON_DATASET. # # File generated on March 16 2003 9:25:10.385 AM # # Spatial dimension M = 2 # Number of points N = 10 # Bases: 2 3 # Initial values skipped = 0 # The input data file has been read. # halton_02_00010_weight_b.txt # created by VORONOI_WEIGHT_WRITE # at June 3 2003 8:33:41.953 AM # # Spatial dimension M = 2 # Number of points N = 10 # EPSILON (unit roundoff) = 0.119209E-06 # # Initial SEED = 123456789 # # The generator points were read from the file: "/home/r1/src-samples/datasets/halton/halton_02_00010.txt". # Sampling by UNIFORM. # Number of sample points = 1000000 # The file of weights was successfully read. INTEGRAL_TEST_01 Using a set of points in [0,1]^N, approximate integrals from the TESTNINT set. Problem Region Correct Estimated Absolute Relative Index Volume Integral Integral Error Error (%) 1 1.00000 1.16667 1.05541 0.111256 9.53622 2 1.00000 1.06667 0.932538 0.134129 12.5746 4 1.00000 2.28571 2.84748 0.561769 24.5774 6 1.00000 1.00000 0.866684 0.133316 13.3316 8 1.00000 0.500000 0.475253 0.247472E-01 4.94943 9 1.00000 1.68336 1.64106 0.422968E-01 2.51264 10 1.00000 0.500000 0.473746 0.262541E-01 5.25081 11 1.00000 2.95249 2.79647 0.156024 5.28448 14 1.00000 -0.250000 -0.255039 0.503924E-02 2.01570 15 1.00000 0.399576 0.413118 0.135414E-01 3.38894 16 1.00000 0.500000 0.473746 0.262541E-01 5.25081 17 1.00000 0.166667 0.151714 0.149529E-01 8.97172 18 1.00000 0.785398 0.885805 0.100407 12.7842 19 1.00000 0.241265 0.243685 0.242023E-02 1.00314 24 1.00000 1.00000 0.866684 0.133316 13.3316 25 1.00000 1.08030 1.07120 0.909340E-02 0.841752 26 1.00000 0.154818 0.157816 0.299807E-02 1.93651 28 1.00000 0.859876 0.871294 0.114177E-01 1.32783 30 1.00000 0.959521 0.963117 0.359535E-02 0.374703 31 1.00000 0.841679 0.788644 0.530340E-01 6.30098 INTEGRAL_TEST_01: Normal conclusion. INTEGRAL_TEST_02 Using a set of points in [0,1]^N, approximate integrals from the TESTNINT set. The integrands depend on a base point. We randomly vary the base point repeatedly, and look at the average behavior. Because the base point moves, the value of the exact integral changes on each repetition! Number of repetitions = 100 Average Maximum Average Maximum Integral Absolute Absolute Relative Relative Error Error Error % Error % 15 0.012320 0.027760 3.793515 9.247782 16 0.019047 0.038925 2.972238 6.433490 17 0.018737 0.053233 5.879105 13.070591 19 0.010557 0.033541 3.791360 14.581955 INTEGRAL_TEST_02: Normal conclusion. INTEGRAL_TEST_03 Using a set of points in [0,1]^N, approximate integrals from the TESTNINT set. Integrand J has the form: product ( 1 <= I <= J ) X(mod(I,N)+1) Problem Region Correct Estimated Absolute Relative Index Volume Integral Integral Error Error (%) 1 1.00000 1.00000 0.958382 0.416180E-01 4.16180 2 1.00000 0.500000 0.478863 0.211374E-01 4.22748 3 1.00000 0.250000 0.223823 0.261767E-01 10.4707 4 1.00000 0.166667 0.142169 0.244978E-01 14.6987 5 1.00000 0.111111 0.860530E-01 0.250581E-01 22.5523 6 1.00000 0.833333E-01 0.602972E-01 0.230361E-01 27.6433 7 1.00000 0.625000E-01 0.391068E-01 0.233932E-01 37.4292 8 1.00000 0.500000E-01 0.282463E-01 0.217537E-01 43.5074 9 1.00000 0.400000E-01 0.186290E-01 0.213710E-01 53.4276 10 1.00000 0.333333E-01 0.135838E-01 0.197496E-01 59.2487 INTEGRAL_TEST_03: Normal conclusion. INTEGRAL_TEST: Averaged relative error: 6.33255 INTEGRAL_TEST: Normal end of execution. August 26 2003 2:57:03.548 PM