August 26 2003 2:44:44.591 PM INTEGRAL_TEST Test a file of sample points for use in equally weighted quadrature. The point data will be read from "cvt_02_00100.txt". The weight data will be read from "". The spatial dimension is 2 The number of points is 100 # cvt_02_00100.txt # created by CVT_DATASET # at April 11 2003 12:10:57.078 PM # # Spatial dimension M = 2 # Number of points N = 100 # # 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 = 0.007545 # 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 1.14423 0.224323E-01 1.92277 2 1.00000 1.06667 1.03381 0.328591E-01 3.08054 4 1.00000 2.28571 2.17444 0.111278 4.86843 6 1.00000 1.00000 0.983741 0.162588E-01 1.62588 8 1.00000 0.500000 0.493569 0.643092E-02 1.28618 9 1.00000 1.68336 1.67450 0.886178E-02 0.526435 10 1.00000 0.500000 0.496815 0.318512E-02 0.637025 11 1.00000 2.95249 2.92759 0.248973E-01 0.843265 14 1.00000 -0.250000 -0.245964 0.403613E-02 1.61445 15 1.00000 0.399576 0.401538 0.196168E-02 0.490939 16 1.00000 0.500000 0.496815 0.318512E-02 0.637025 17 1.00000 0.166667 0.164625 0.204198E-02 1.22519 18 1.00000 0.785398 0.790000 0.460136E-02 0.585863 19 1.00000 0.241265 0.238733 0.253202E-02 1.04948 24 1.00000 1.00000 0.983741 0.162588E-01 1.62588 25 1.00000 1.08030 1.07851 0.178850E-02 0.165556 26 1.00000 0.154818 0.155531 0.712752E-03 0.460380 28 1.00000 0.859876 0.861153 0.127703E-02 0.148513 30 1.00000 0.959521 0.959993 0.471711E-03 0.491611E-01 31 1.00000 0.841679 0.922318 0.806397E-01 9.58081 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 0.002653 0.006769 0.870796 2.790257 16 0.005154 0.011805 0.758959 1.610304 17 0.004500 0.011129 1.356534 2.964830 19 0.002640 0.008784 0.899430 2.310019 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 0.999999 0.655651E-06 0.655651E-04 2 1.00000 0.500000 0.490713 0.928727E-02 1.85745 3 1.00000 0.250000 0.244749 0.525132E-02 2.10053 4 1.00000 0.166667 0.161258 0.540820E-02 3.24492 5 1.00000 0.111111 0.106745 0.436594E-02 3.92935 6 1.00000 0.833333E-01 0.793229E-01 0.401048E-02 4.81258 7 1.00000 0.625000E-01 0.590904E-01 0.340959E-02 5.45535 8 1.00000 0.500000E-01 0.468581E-01 0.314187E-02 6.28374 9 1.00000 0.400000E-01 0.372165E-01 0.278346E-02 6.95865 10 1.00000 0.333333E-01 0.307381E-01 0.259527E-02 7.78582 INTEGRAL_TEST_03: Normal conclusion. INTEGRAL_TEST: Averaged relative error: 1.51290 INTEGRAL_TEST: Normal end of execution. August 26 2003 2:44:44.655 PM