August 26 2003 2:57:08.758 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_d.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_d.txt # created by VORONOI_WEIGHT_WRITE # at May 30 2003 10:39:16.868 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 RANDOM_NUMBER (Fortran90 intrinsic). # 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 1.16150 0.516284E-02 0.442529 2 1.00000 1.06667 1.03061 0.360574E-01 3.38038 4 1.00000 2.28571 2.13450 0.151210 6.61544 6 1.00000 1.00000 0.994946 0.505376E-02 0.505376 8 1.00000 0.500000 0.499457 0.543386E-03 0.108677 9 1.00000 1.68336 1.68155 0.180614E-02 0.107294 10 1.00000 0.500000 0.498311 0.168911E-02 0.337821 11 1.00000 2.95249 2.93940 0.130959E-01 0.443553 14 1.00000 -0.250000 -0.249913 0.867546E-04 0.347018E-01 15 1.00000 0.399576 0.400756 0.117996E-02 0.295304 16 1.00000 0.500000 0.498311 0.168911E-02 0.337821 17 1.00000 0.166667 0.165210 0.145714E-02 0.874284 18 1.00000 0.785398 0.797291 0.118930E-01 1.51426 19 1.00000 0.241265 0.240790 0.474617E-03 0.196720 24 1.00000 1.00000 0.994946 0.505376E-02 0.505376 25 1.00000 1.08030 1.07989 0.405073E-03 0.374965E-01 26 1.00000 0.154818 0.154906 0.876337E-04 0.566043E-01 28 1.00000 0.859876 0.860796 0.919402E-03 0.106923 30 1.00000 0.959521 0.959860 0.338614E-03 0.352899E-01 31 1.00000 0.841679 0.807068 0.346107E-01 4.11211 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 0.000791 0.002201 0.244917 0.688863 16 0.001479 0.002359 0.231287 0.395325 17 0.001433 0.002851 0.478922 0.957825 19 0.000893 0.002493 0.318729 0.878262 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 0.996365 0.363487E-02 0.363487 2 1.00000 0.500000 0.498845 0.115463E-02 0.230926 3 1.00000 0.250000 0.248932 0.106773E-02 0.427091 4 1.00000 0.166667 0.165212 0.145423E-02 0.872540 5 1.00000 0.111111 0.109447 0.166442E-02 1.49798 6 1.00000 0.833333E-01 0.814434E-01 0.188991E-02 2.26789 7 1.00000 0.625000E-01 0.605105E-01 0.198953E-02 3.18325 8 1.00000 0.500000E-01 0.478602E-01 0.213975E-02 4.27951 9 1.00000 0.400000E-01 0.377922E-01 0.220780E-02 5.51951 10 1.00000 0.333333E-01 0.310199E-01 0.231344E-02 6.94032 INTEGRAL_TEST_03: Normal conclusion. INTEGRAL_TEST: Averaged relative error: 0.888409 INTEGRAL_TEST: Normal end of execution. August 26 2003 2:57:08.832 PM