August 26 2003 2:57:08.566 PM INTEGRAL_TEST Test a file of sample points for use in equally weighted quadrature. The point data will be read from "halton_02_00100.txt". The weight data will be read from "halton_02_00100_weight_b.txt". The spatial dimension is 2 The number of points is 100 # halton_02_00100.txt # created by HALTON_DATASET. # # File generated on March 16 2003 9:39:34.875 AM # # Spatial dimension M = 2 # Number of points N = 100 # Bases: 2 3 # Initial values skipped = 0 # The input data file has been read. # halton_02_00100_weight_b.txt # created by VORONOI_WEIGHT_WRITE # at May 30 2003 10:39:12.004 AM # # Spatial dimension M = 2 # Number of points N = 100 # 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_00100.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 1.16076 0.590658E-02 0.506278 2 1.00000 1.06667 1.02887 0.377917E-01 3.54297 4 1.00000 2.28571 2.12944 0.156278 6.83718 6 1.00000 1.00000 0.992658 0.734180E-02 0.734180 8 1.00000 0.500000 0.499231 0.768989E-03 0.153798 9 1.00000 1.68336 1.68127 0.208545E-02 0.123886 10 1.00000 0.500000 0.497926 0.207424E-02 0.414848 11 1.00000 2.95249 2.93644 0.160537E-01 0.543733 14 1.00000 -0.250000 -0.250695 0.694752E-03 0.277901 15 1.00000 0.399576 0.400981 0.140435E-02 0.351458 16 1.00000 0.500000 0.497926 0.207424E-02 0.414848 17 1.00000 0.166667 0.164997 0.166988E-02 1.00193 18 1.00000 0.785398 0.798191 0.127928E-01 1.62883 19 1.00000 0.241265 0.240491 0.773877E-03 0.320758 24 1.00000 1.00000 0.992658 0.734180E-02 0.734180 25 1.00000 1.08030 1.07985 0.445008E-03 0.411932E-01 26 1.00000 0.154818 0.154926 0.107959E-03 0.697327E-01 28 1.00000 0.859876 0.860945 0.106865E-02 0.124280 30 1.00000 0.959521 0.959910 0.388265E-03 0.404644E-01 31 1.00000 0.841679 0.808202 0.334764E-01 3.97733 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 0.000917 0.002303 0.281716 0.671873 16 0.001766 0.003261 0.276417 0.537436 17 0.001707 0.003406 0.566114 1.091388 19 0.000976 0.003060 0.352264 1.046372 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 0.996399 0.360101E-02 0.360101 2 1.00000 0.500000 0.499512 0.487596E-03 0.975192E-01 3 1.00000 0.250000 0.248818 0.118227E-02 0.472909 4 1.00000 0.166667 0.165181 0.148612E-02 0.891674 5 1.00000 0.111111 0.109326 0.178535E-02 1.60681 6 1.00000 0.833333E-01 0.813745E-01 0.195886E-02 2.35063 7 1.00000 0.625000E-01 0.604246E-01 0.207543E-02 3.32069 8 1.00000 0.500000E-01 0.478096E-01 0.219041E-02 4.38081 9 1.00000 0.400000E-01 0.377371E-01 0.226291E-02 5.65726 10 1.00000 0.333333E-01 0.309885E-01 0.234488E-02 7.03463 INTEGRAL_TEST_03: Normal conclusion. INTEGRAL_TEST: Averaged relative error: 0.971512 INTEGRAL_TEST: Normal end of execution. August 26 2003 2:57:08.625 PM