August 26 2003 2:44:49.703 PM INTEGRAL_TEST Test a file of sample points for use in equally weighted quadrature. The point data will be read from "cvt_02_01000.txt". The weight data will be read from "". The spatial dimension is 2 The number of points is 1000 # cvt_02_01000.txt # created by CVT_DATASET # at April 11 2003 12:32:28.499 PM # # Spatial dimension M = 2 # Number of points N = 1000 # # Initial SEED = 123456789 # Initialization by UNIFORM. # Sampling by UNIFORM. # Number of sample points = 500000 # Number of sampling iterations = 100 # L2 norm of dataset change on last step = 0.020973 # 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 1.15083 0.158415E-01 1.35784 2 1.00000 1.06667 1.03169 0.349737E-01 3.27879 4 1.00000 2.28571 2.19178 0.939367E-01 4.10973 6 1.00000 1.00000 0.990916 0.908428E-02 0.908428 8 1.00000 0.500000 0.495808 0.419152E-02 0.838304 9 1.00000 1.68336 1.67737 0.598681E-02 0.355647 10 1.00000 0.500000 0.499254 0.746369E-03 0.149274 11 1.00000 2.95249 2.94389 0.859809E-02 0.291215 14 1.00000 -0.250000 -0.253554 0.355387E-02 1.42155 15 1.00000 0.399576 0.399528 0.480413E-04 0.120231E-01 16 1.00000 0.500000 0.499254 0.746369E-03 0.149274 17 1.00000 0.166667 0.166275 0.391722E-03 0.235033 18 1.00000 0.785398 0.791993 0.659519E-02 0.839726 19 1.00000 0.241265 0.238876 0.238931E-02 0.990326 24 1.00000 1.00000 0.990916 0.908428E-02 0.908428 25 1.00000 1.08030 1.07875 0.154555E-02 0.143067 26 1.00000 0.154818 0.155249 0.430390E-03 0.277997 28 1.00000 0.859876 0.860111 0.234604E-03 0.272834E-01 30 1.00000 0.959521 0.959609 0.880957E-04 0.918121E-02 31 1.00000 0.841679 0.843002 0.132400E-02 0.157304 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 0.002152 0.004232 0.689200 1.678928 16 0.003679 0.006470 0.543101 0.937624 17 0.002763 0.006454 0.809021 1.456199 19 0.001823 0.004357 0.630023 1.159711 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 0.999991 0.929832E-05 0.929832E-03 2 1.00000 0.500000 0.499007 0.993043E-03 0.198609 3 1.00000 0.250000 0.245453 0.454663E-02 1.81865 4 1.00000 0.166667 0.162713 0.395317E-02 2.37190 5 1.00000 0.111111 0.107374 0.373679E-02 3.36311 6 1.00000 0.833333E-01 0.799995E-01 0.333381E-02 4.00057 7 1.00000 0.625000E-01 0.596043E-01 0.289568E-02 4.63309 8 1.00000 0.500000E-01 0.473509E-01 0.264909E-02 5.29817 9 1.00000 0.400000E-01 0.377213E-01 0.227873E-02 5.69682 10 1.00000 0.333333E-01 0.312176E-01 0.211573E-02 6.34718 INTEGRAL_TEST_03: Normal conclusion. INTEGRAL_TEST: Averaged relative error: 0.797157 INTEGRAL_TEST: Normal end of execution. August 26 2003 2:44:49.931 PM