August 26 2003 2:57:03.315 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 "". 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. 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 0.823604 0.343063 29.4054 2 1.00000 1.06667 1.83725 0.770587 72.2426 4 1.00000 2.28571 6.56278 4.27706 187.121 6 1.00000 1.00000 1.11852 0.118519 11.8519 8 1.00000 0.500000 0.386478 0.113522 22.7044 9 1.00000 1.68336 1.53338 0.149976 8.90935 10 1.00000 0.500000 0.524074 0.240743E-01 4.81486 11 1.00000 2.95249 3.19635 0.243860 8.25948 14 1.00000 -0.250000 -0.252083 0.208330E-02 0.833321 15 1.00000 0.399576 0.384531 0.150451E-01 3.76527 16 1.00000 0.500000 0.524074 0.240743E-01 4.81486 17 1.00000 0.166667 0.186567 0.199000E-01 11.9400 18 1.00000 0.785398 0.800000 0.146019E-01 1.85917 19 1.00000 0.241265 0.238018 0.324696E-02 1.34581 24 1.00000 1.00000 1.11852 0.118519 11.8519 25 1.00000 1.08030 1.05071 0.295892E-01 2.73899 26 1.00000 0.154818 0.169580 0.147617E-01 9.53486 28 1.00000 0.859876 0.847182 0.126944E-01 1.47630 30 1.00000 0.959521 0.954960 0.456160E-02 0.475404 31 1.00000 0.841679 0.926393 0.847147E-01 10.0650 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 0.035188 0.072025 11.439149 28.877447 16 0.066386 0.166472 9.829843 20.382874 17 0.063170 0.169830 19.203245 38.376984 19 0.029581 0.097819 10.081674 26.846428 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 0.900000 0.999999E-01 9.99999 2 1.00000 0.500000 0.412500 0.875000E-01 17.5000 3 1.00000 0.250000 0.160417 0.895833E-01 35.8333 4 1.00000 0.166667 0.970052E-01 0.696614E-01 41.7969 5 1.00000 0.111111 0.548660E-01 0.562451E-01 50.6206 6 1.00000 0.833333E-01 0.383925E-01 0.449408E-01 53.9290 7 1.00000 0.625000E-01 0.240509E-01 0.384491E-01 61.5186 8 1.00000 0.500000E-01 0.176466E-01 0.323534E-01 64.7068 9 1.00000 0.400000E-01 0.113338E-01 0.286662E-01 71.6654 10 1.00000 0.333333E-01 0.843944E-02 0.248939E-01 74.6817 INTEGRAL_TEST_03: Normal conclusion. INTEGRAL_TEST: Averaged relative error: 19.0235 INTEGRAL_TEST: Normal end of execution. August 26 2003 2:57:03.361 PM