August 26 2003 2:57:03.594 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_c.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_c.txt # created by VORONOI_WEIGHT_WRITE # at June 3 2003 8:33:42.469 AM # # Spatial dimension M = 2 # Number of points N = 10 # EPSILON (unit roundoff) = 0.119209E-06 # # Initial SEED = 987654321 # # 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 1.05506 0.111602 9.56588 2 1.00000 1.06667 0.933858 0.132809 12.4509 4 1.00000 2.28571 2.85423 0.568513 24.8724 6 1.00000 1.00000 0.868618 0.131382 13.1382 8 1.00000 0.500000 0.475170 0.248296E-01 4.96593 9 1.00000 1.68336 1.64092 0.424322E-01 2.52069 10 1.00000 0.500000 0.474022 0.259778E-01 5.19556 11 1.00000 2.95249 2.79866 0.153830 5.21017 14 1.00000 -0.250000 -0.254537 0.453705E-02 1.81482 15 1.00000 0.399576 0.412971 0.133941E-01 3.35208 16 1.00000 0.500000 0.474022 0.259778E-01 5.19556 17 1.00000 0.166667 0.151845 0.148216E-01 8.89299 18 1.00000 0.785398 0.885022 0.996238E-01 12.6845 19 1.00000 0.241265 0.243735 0.246961E-02 1.02361 24 1.00000 1.00000 0.868618 0.131382 13.1382 25 1.00000 1.08030 1.07115 0.914788E-02 0.846795 26 1.00000 0.154818 0.157827 0.300863E-02 1.94333 28 1.00000 0.859876 0.871201 0.113248E-01 1.31702 30 1.00000 0.959521 0.963086 0.356483E-02 0.371522 31 1.00000 0.841679 0.788381 0.532972E-01 6.33225 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 0.012283 0.027510 3.785125 9.072921 16 0.018925 0.038949 2.950798 6.353068 17 0.018639 0.053078 5.845085 13.009146 19 0.010510 0.033274 3.774730 14.465761 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 0.958272 0.417280E-01 4.17280 2 1.00000 0.500000 0.478195 0.218049E-01 4.36098 3 1.00000 0.250000 0.223658 0.263419E-01 10.5367 4 1.00000 0.166667 0.141976 0.246908E-01 14.8145 5 1.00000 0.111111 0.859523E-01 0.251588E-01 22.6429 6 1.00000 0.833333E-01 0.602049E-01 0.231284E-01 27.7541 7 1.00000 0.625000E-01 0.390554E-01 0.234446E-01 37.5114 8 1.00000 0.500000E-01 0.282012E-01 0.217988E-01 43.5976 9 1.00000 0.400000E-01 0.186036E-01 0.213964E-01 53.4909 10 1.00000 0.333333E-01 0.135618E-01 0.197716E-01 59.3147 INTEGRAL_TEST_03: Normal conclusion. INTEGRAL_TEST: Averaged relative error: 6.29951 INTEGRAL_TEST: Normal end of execution. August 26 2003 2:57:03.631 PM