August 26 2003 2:57:03.911 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_g.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_g.txt # created by VORONOI_WEIGHT_WRITE # at June 3 2003 8:34:33.470 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 = 100000000 # 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 1.05562 0.111045 9.51818 2 1.00000 1.06667 0.932827 0.133840 12.5475 4 1.00000 2.28571 2.84948 0.563769 24.6649 6 1.00000 1.00000 0.868389 0.131611 13.1611 8 1.00000 0.500000 0.475362 0.246375E-01 4.92750 9 1.00000 1.68336 1.64116 0.421972E-01 2.50673 10 1.00000 0.500000 0.474020 0.259798E-01 5.19595 11 1.00000 2.95249 2.79845 0.154047 5.21751 14 1.00000 -0.250000 -0.254542 0.454229E-02 1.81692 15 1.00000 0.399576 0.412946 0.133696E-01 3.34595 16 1.00000 0.500000 0.474020 0.259798E-01 5.19595 17 1.00000 0.166667 0.151837 0.148294E-01 8.89761 18 1.00000 0.785398 0.885048 0.996498E-01 12.6878 19 1.00000 0.241265 0.243829 0.256363E-02 1.06258 24 1.00000 1.00000 0.868389 0.131611 13.1611 25 1.00000 1.08030 1.07119 0.910163E-02 0.842513 26 1.00000 0.154818 0.157805 0.298655E-02 1.92907 28 1.00000 0.859876 0.871204 0.113274E-01 1.31733 30 1.00000 0.959521 0.963088 0.356632E-02 0.371677 31 1.00000 0.841679 0.787884 0.537949E-01 6.39138 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 0.012272 0.027610 3.781056 9.060965 16 0.018883 0.038680 2.945742 6.376776 17 0.018571 0.052841 5.826835 12.977988 19 0.010515 0.033354 3.778263 14.500731 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 0.958348 0.416520E-01 4.16520 2 1.00000 0.500000 0.478341 0.216595E-01 4.33189 3 1.00000 0.250000 0.223798 0.262017E-01 10.4807 4 1.00000 0.166667 0.142089 0.245775E-01 14.7465 5 1.00000 0.111111 0.860394E-01 0.250717E-01 22.5645 6 1.00000 0.833333E-01 0.602689E-01 0.230645E-01 27.6773 7 1.00000 0.625000E-01 0.391005E-01 0.233995E-01 37.4391 8 1.00000 0.500000E-01 0.282336E-01 0.217664E-01 43.5329 9 1.00000 0.400000E-01 0.186260E-01 0.213740E-01 53.4349 10 1.00000 0.333333E-01 0.135777E-01 0.197556E-01 59.2669 INTEGRAL_TEST_03: Normal conclusion. INTEGRAL_TEST: Averaged relative error: 6.29546 INTEGRAL_TEST: Normal end of execution. August 26 2003 2:57:03.936 PM