August 26 2003 2:57:03.751 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_e.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_e.txt # created by VORONOI_WEIGHT_WRITE # at June 3 2003 8:33:47.764 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 HALTON. # 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 1.05561 0.111054 9.51890 2 1.00000 1.06667 0.932342 0.134324 12.5929 4 1.00000 2.28571 2.84735 0.561637 24.5716 6 1.00000 1.00000 0.868218 0.131782 13.1782 8 1.00000 0.500000 0.475357 0.246427E-01 4.92854 9 1.00000 1.68336 1.64116 0.421970E-01 2.50672 10 1.00000 0.500000 0.474000 0.259996E-01 5.19991 11 1.00000 2.95249 2.79826 0.154234 5.22386 14 1.00000 -0.250000 -0.254546 0.454575E-02 1.81830 15 1.00000 0.399576 0.412954 0.133774E-01 3.34789 16 1.00000 0.500000 0.474000 0.259996E-01 5.19991 17 1.00000 0.166667 0.151828 0.148390E-01 8.90338 18 1.00000 0.785398 0.885085 0.996869E-01 12.6925 19 1.00000 0.241265 0.243821 0.255597E-02 1.05940 24 1.00000 1.00000 0.868218 0.131782 13.1782 25 1.00000 1.08030 1.07119 0.910199E-02 0.842546 26 1.00000 0.154818 0.157804 0.298594E-02 1.92868 28 1.00000 0.859876 0.871210 0.113335E-01 1.31803 30 1.00000 0.959521 0.963090 0.356865E-02 0.371920 31 1.00000 0.841679 0.787925 0.537537E-01 6.38649 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 0.012275 0.027613 3.781727 9.058126 16 0.018890 0.038686 2.946952 6.379391 17 0.018575 0.052848 5.828454 12.982538 19 0.010515 0.033366 3.778388 14.505783 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 0.416179E-01 4.16179 2 1.00000 0.500000 0.478343 0.216569E-01 4.33137 3 1.00000 0.250000 0.223797 0.262026E-01 10.4810 4 1.00000 0.166667 0.142092 0.245745E-01 14.7447 5 1.00000 0.111111 0.860402E-01 0.250710E-01 22.5639 6 1.00000 0.833333E-01 0.602714E-01 0.230620E-01 27.6744 7 1.00000 0.625000E-01 0.391012E-01 0.233988E-01 37.4380 8 1.00000 0.500000E-01 0.282349E-01 0.217651E-01 43.5301 9 1.00000 0.400000E-01 0.186264E-01 0.213736E-01 53.4339 10 1.00000 0.333333E-01 0.135784E-01 0.197549E-01 59.2648 INTEGRAL_TEST_03: Normal conclusion. INTEGRAL_TEST: Averaged relative error: 6.29597 INTEGRAL_TEST: Normal end of execution. August 26 2003 2:57:03.780 PM