August 26 2003 2:44:39.194 PM INTEGRAL_TEST Test a file of sample points for use in equally weighted quadrature. The point data will be read from "cvt_02_00010.txt". The weight data will be read from "". The spatial dimension is 2 The number of points is 10 # cvt_02_00010.txt # created by CVT_DATASET # at April 11 2003 12:04:56.303 PM # # Spatial dimension M = 2 # Number of points N = 10 # # 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 = 0.001501 # 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 1.10078 0.658904E-01 5.64775 2 1.00000 1.06667 0.847671 0.218996 20.5309 4 1.00000 2.28571 1.45130 0.834414 36.5056 6 1.00000 1.00000 0.893923 0.106077 10.6077 8 1.00000 0.500000 0.482976 0.170236E-01 3.40472 9 1.00000 1.68336 1.65864 0.247173E-01 1.46834 10 1.00000 0.500000 0.469219 0.307808E-01 6.15616 11 1.00000 2.95249 2.77307 0.179426 6.07710 14 1.00000 -0.250000 -0.237260 0.127398E-01 5.09591 15 1.00000 0.399576 0.430326 0.307500E-01 7.69565 16 1.00000 0.500000 0.469219 0.307808E-01 6.15616 17 1.00000 0.166667 0.152906 0.137604E-01 8.25624 18 1.00000 0.785398 0.800000 0.146019E-01 1.85917 19 1.00000 0.241265 0.249689 0.842397E-02 3.49158 24 1.00000 1.00000 0.893923 0.106077 10.6077 25 1.00000 1.08030 1.07569 0.460958E-02 0.426697 26 1.00000 0.154818 0.156550 0.173196E-02 1.11871 28 1.00000 0.859876 0.867506 0.762987E-02 0.887322 30 1.00000 0.959521 0.962675 0.315404E-02 0.328710 31 1.00000 0.841679 0.814388 0.272907E-01 3.24241 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 0.013240 0.054394 4.266160 18.227938 16 0.019300 0.071706 2.868603 9.892999 17 0.015531 0.038664 4.976158 11.441217 19 0.014301 0.082013 4.990864 26.770554 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 1.00000 0.119209E-06 0.119209E-04 2 1.00000 0.500000 0.474170 0.258303E-01 5.16605 3 1.00000 0.250000 0.236909 0.130905E-01 5.23621 4 1.00000 0.166667 0.150213 0.164538E-01 9.87230 5 1.00000 0.111111 0.971611E-01 0.139500E-01 12.5550 6 1.00000 0.833333E-01 0.703889E-01 0.129445E-01 15.5334 7 1.00000 0.625000E-01 0.511152E-01 0.113848E-01 18.2157 8 1.00000 0.500000E-01 0.393401E-01 0.106599E-01 21.3197 9 1.00000 0.400000E-01 0.302023E-01 0.979766E-02 24.4942 10 1.00000 0.333333E-01 0.239967E-01 0.933660E-02 28.0098 INTEGRAL_TEST_03: Normal conclusion. INTEGRAL_TEST: Averaged relative error: 6.52777 INTEGRAL_TEST: Normal end of execution. August 26 2003 2:44:39.228 PM