August 26 2003 2:44:39.281 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 "cvt_02_00010_weight_a.txt". 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. # cvt_02_00010_weight_a.txt # created by VORONOI_WEIGHT_WRITE # at May 30 2003 1:11:06.666 PM # # 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/cvt/cvt_02_00010.txt". # Sampling by UNIFORM. # Number of sample points = 10000 # 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 1.13684 0.298222E-01 2.55619 2 1.00000 1.06667 0.822631 0.244036 22.8784 4 1.00000 2.28571 1.39530 0.890416 38.9557 6 1.00000 1.00000 0.844836 0.155164 15.5164 8 1.00000 0.500000 0.495759 0.424150E-02 0.848299 9 1.00000 1.68336 1.67409 0.927043E-02 0.550711 10 1.00000 0.500000 0.458459 0.415411E-01 8.30823 11 1.00000 2.95249 2.71693 0.235561 7.97837 14 1.00000 -0.250000 -0.251788 0.178757E-02 0.715029 15 1.00000 0.399576 0.439550 0.399735E-01 10.0040 16 1.00000 0.500000 0.458459 0.415411E-01 8.30823 17 1.00000 0.166667 0.149293 0.173735E-01 10.4241 18 1.00000 0.785398 0.831600 0.462019E-01 5.88261 19 1.00000 0.241265 0.252451 0.111860E-01 4.63640 24 1.00000 1.00000 0.844836 0.155164 15.5164 25 1.00000 1.08030 1.07909 0.120509E-02 0.111552 26 1.00000 0.154818 0.155063 0.244722E-03 0.158071 28 1.00000 0.859876 0.870415 0.105390E-01 1.22564 30 1.00000 0.959521 0.963542 0.402093E-02 0.419056 31 1.00000 0.841679 0.802994 0.386841E-01 4.59607 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 0.010680 0.043330 3.369933 12.670118 16 0.017251 0.047620 2.655899 7.692806 17 0.017583 0.024148 5.875767 10.339285 19 0.012423 0.065010 4.380560 21.220617 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 0.596046E-07 0.596046E-05 2 1.00000 0.500000 0.499090 0.910223E-03 0.182045 3 1.00000 0.250000 0.247302 0.269781E-02 1.07912 4 1.00000 0.166667 0.160527 0.613938E-02 3.68363 5 1.00000 0.111111 0.103183 0.792848E-02 7.13563 6 1.00000 0.833333E-01 0.753411E-01 0.799227E-02 9.59072 7 1.00000 0.625000E-01 0.544443E-01 0.805566E-02 12.8891 8 1.00000 0.500000E-01 0.420019E-01 0.799806E-02 15.9961 9 1.00000 0.400000E-01 0.321268E-01 0.787323E-02 19.6831 10 1.00000 0.333333E-01 0.255443E-01 0.778908E-02 23.3672 INTEGRAL_TEST_03: Normal conclusion. INTEGRAL_TEST: Averaged relative error: 7.32798 INTEGRAL_TEST: Normal end of execution. August 26 2003 2:44:39.305 PM