24 December 2011 11:55:19 AM TEST_NINT_PRB C++ version Test the TEST_NINT library. TEST01 GET_PROBLEM_NUM returns the number of problems. P00_NAME(#) returns the name for problem #. We use these two routines to print a directory of all the problems. The number of problems available is 32 1 "SquareSum". 2 "QuadSum". 3 "QuintSum". 4 "HexSum". 5 "ST04". 6 "DR4061". 7 "DR4062". 8 "RC01". 9 "Patterson #7". 10 "Patterson #4". 11 "Patterson #2, exp(sum(abs(X)))". 12 "BFN02". 13 "BFN03". 14 "BFN04". 15 "Partial product ( X(1:N) )". 16 "L1(X-Z)". 17 "L2(X-Z)^2". 18 "Disk". 19 "Sqrt-Prod". 20 "Sum^P". 21 "SphereMonomial". 22 "BallMonomial". 23 "SimplexMonomial". 24 "(|4X-2|+c)/(1+c)". 25 "Patterson #3, exp(c*X)". 26 "Patterson #1". 27 "Genz #1 / Patterson #5, Oscillatory". 28 "Genz #2 / Patterson #6, Product Peak". 29 "Genz #3 / Patterson #8, Corner Peak". 30 "Genz #4 / Patterson #9, Gaussian". 31 "Genz #5, C0 Pseudo-Gaussian". 32 "Genz #6, Discontinuous". TEST02 GET_PROBLEM_NUM returns the number of problems. P00_TITLE(#) prints the title for problem #. We use these two routines to print a directory of all the problems. The number of problems available is 32 Problem 01 Name: SquareSum Region: 0 <= X(i) <= 1 Integrand: F(X) = ( sum ( X(i) ) )^2 Problem 02 Name: QuadSum Davis, Rabinowitz, page 370, #1. Region: 0 <= X(i) <= 1 Integrand: F(X) = ( sum ( 2 * X(i) - 1 ) )^4 Problem 03 Name: QuintSum Davis, Rabinowitz, page 370, #3. Region: 0 <= X(i) <= 1 Integrand: F(X) = ( sum ( X(i) ) )^5 Problem 04 Name: HexSum Davis, Rabinowitz, page 370, #2. Region: 0 <= X(i) <= 1 Integrand: F(X) = ( sum ( 2 * X(i) - 1 ) )^6 Problem 05 Name: ST04 Stroud #4, page 26. Region: 0 <= X(i) <= 1 Integrand: F(X) = 1 / ( 1 + sum ( 2 * X(i) ) ) Problem 07 Name: DR4061 Davis, Rabinowitz, page 406, #1. Region: 0 <= X(i) <= 1 Integrand: F(X) = product ( abs ( 4 * X(i) - 2 ) ) Problem 07 Name: DR4062 Davis, Rabinowitz, page 406, #2. Region: 0 <= X(i) <= 1 Integrand: F(X) = product ( pi * sin ( pi * X(i) ) / 2 ) Problem 08 Name: RC01 Crandall, page 49, #1 Region: 0 <= X(i) <= 1 Integrand: F(X) = sin^2 ( pi/4 * sum ( X(i) ) ) Problem 09 Name: Patterson #7 Region: 0 <= X(i) <= 1 Integrand: F(X) = exp ( sum ( C(i) * X(i) ) ) Parameters: C(1:DIM_NUM) defaults to 1/DIM_NUM. Problem 10 Name: Patterson #4 Stroud, page ? Region: 0 <= X(i) <= 1 Integrand: F(X) = sum ( abs ( X(i) - 0.5 ) ) Problem 11 Name: Patterson #2, exp(sum(abs(X))) Region: 0 <= X(i) <= 1 Integrand: F(X) = exp ( sum ( abs ( X(i) ))) Problem 12 Name: BFN02 Bratley, Fox, Niederreiter, #2 Region: 0 <= X(i) <= 1 Integrand: F(X) = product ( i * cos ( X(i) ) ) Problem 13 Name: BFN03 Bratley, Fox, Niederreiter, #3 Region: 0 <= X(i) <= 1 Integrand: F(X) = product ( low order Chebyshevs ) Problem 14 Name: BFN04 Bratley, Fox, Niederreiter, #4 Region: 0 <= X(i) <= 1 Integrand: F(X) = sum ( -1^I * product(X(1:I)) ) Problem 15 Name: Partial product ( X(1:N) ) Region: 0 <= X(i) <= 1 Integrand: F(X) = product ( X(1:N) ) Parameters: N, defaults to 1 Problem 16 Name: L1(X-Z) Lipschitz continuous. Region: 0 <= X(i) <= 1 Integrand: F(X) = sum ( | X(i) - Z(i) | ) Parameters: Z(1:DIM_NUM) defaults to (0.5,0.5,...) Problem 17 Name: L2(X-Z)^2 Zero at point Z. Radially symmetric. Region: 0 <= X(i) <= 1 Integrand: F(X) = sum ( ( X(i) - Z(i) )^2 ) Parameters: Z(1:DIM_NUM) defaults to (0.5,0.5,...) Problem 18 Name: Disk Disk of radius R centered at Z. Region: 0 <= X(i) <= 1 Integrand: F(X) = sphere interior characteristic Parameters: R, defaults to 0.5 Z(1:DIM_NUM) defaults to (0.5,0.5,...0.5) Problem 19 Name: Sqrt-Prod Region: 0 <= X(i) <= 1 Integrand: F(X) = prod ( sqrt ( | X(i) - Z(i) | ) ) Parameters: Z(1:DIM_NUM) defaults to (1/3,1/3,...,1/3) Problem 20 Name: Sum^P Region: A <= X(i) <= B Integrand: F(X) = ( sum ( X(i) ) )^p Parameters: A, defaults to 0.0, B, defaults to 1.0, P, defaults to 2.0, Problem 21 Name: SphereMonomial Region: Sphere surface, radius 1, center 0 Integrand: F(X) = C * product ( X(i)^E(i) ) Parameters: C, defaults to 1.0 E(1:DIM_NUM) defaults to 2. Problem 22 Name: BallMonomial Region: Sphere interior, radius R, center 0 Integrand: F(X) = C * product ( X(i)^E(i) ) Parameters: C, defaults to 1.0; R, defaults to 1.0; E(1:DIM_NUM) defaults to 2; Problem 23 Name: SimplexMonomial Region: Interior of unit simplex Integrand: F(X) = C * product ( X(i)^E(i) ) Parameters: C, defaults to 1.0; E(1:DIM_NUM) defaults to 2; Problem 24 Name: (|4X-2|+c)/(1+c) Region: 0 <= X(i) <= 1, Integrand: F(X) = product ( ( |4*X(i)-2| + C(i) ) / (1 + C(i) ) Parameters: C(1:DIM_NUM) defaults to 0.0; Problem 25 Name: Patterson #3, exp(c*X)) Region: 0 <= X(i) <= 1 Integrand: F(X) = exp ( C * product ( X(i) ) ) Parameters: C, defaults to 0.3 Problem 26 Name: Patterson #1 Region: 0 <= X(i) <= 1 Integrand: F(X) = product ( C(i) * exp ( - C(i) * X(i) ) ) Parameters: C(1:DIM_NUM) defaults to 1/DIM_NUM. Problem 27 Name: Genz #1 / Patterson #5, Oscillatory Region: 0 <= X(i) <= 1 Integrand: F(X) = cos ( 2 * pi * R + sum ( C(i) * X(i) ) ) Parameters: R, defaults to 0.3 C(1:DIM_NUM) defaults to 1/DIM_NUM Problem 28 Name: Genz #2 / Patterson #6, Product Peak Region: 0 <= X(i) <= 1 Integrand: F(X) = 1 / product ( C(i)^2 + ( X(i) - Z(i) )^2 ) Parameters: C(1:DIM_NUM) defaults to DIM_NUM^(9/4)/sqrt(170) Z(1:DIM_NUM) defaults to 0.5. Problem 29 Name: Genz #3 / Patterson #8, Corner Peak Region: 0 <= X(i) <= 1 Integrand: F(X) = 1 / ( 1 + sum ( C(i) * X(i) ) )^R Parameters: R, defaults to 0.3 C(1:DIM_NUM) defaults to 1/DIM_NUM. Problem 30 Name: Genz #4 / Patterson #9, Gaussian Region: 0 <= X(i) <= 1 Integrand: F(X) = exp ( sum ( C(i)^2 * ( X(i) - Z(i) )^2 ) Parameters: C(1:DIM_NUM) defaults to 1/DIM_NUM. Z(1:DIM_NUM) defaults to 0.5. Problem 31 Name: Genz #5, C0 Pseudo-Gaussian Nondifferentiable peak at point Z. Region: 0 <= X(i) <= 1 Integrand: F(X) = exp ( -sum ( C(i) * | X(i) - Z(i) | ) ) Parameters: C(1:DIM_NUM) defaults to 2.0; Z(1:DIM_NUM) defaults to 0.5; Problem 32 Name: Genz #6, Discontinuous Region: 0 <= X(i) <= 1 Integrand: F(X) = exp ( C(i) * X(i) ) if X <= Z, 0 otherwise. Parameters: C(1:DIM_NUM) defaults to 1/DIM_NUM. Z(1:DIM_NUM) defaults to 0.5. TEST03 Use a simple product rule on box regions. Use a fixed spatial dimension. Prob Dim Subs Approx Exact Error 1 3 1 2.5 2.5 4.44089e-16 1 3 3 2.5 2.5 7.54952e-15 1 3 5 2.5 2.5 1.33227e-15 2 3 1 2.6 2.6 4.44089e-16 2 3 3 2.6 2.6 2.26485e-14 2 3 5 2.6 2.6 1.42553e-13 3 3 1 -2.41474e-15 0 2.41474e-15 3 3 3 -9.22513e-15 0 9.22513e-15 3 3 5 -3.48654e-15 0 3.48654e-15 4 3 1 9.7619 9.7619 8.88178e-15 4 3 3 9.7619 9.7619 4.61853e-14 4 3 5 9.7619 9.7619 1.1191e-13 5 3 1 2.15214 2.15214 3.1588e-07 5 3 3 2.15214 2.15214 4.78373e-11 5 3 5 2.15214 2.15214 4.53415e-13 6 3 1 0.843508 1 0.156492 6 3 3 0.981729 1 0.0182708 6 3 5 0.993397 1 0.00660336 7 3 1 1 1 1.65427e-07 7 3 3 1 1 1.94289e-12 7 3 5 1 1 2.66454e-14 8 3 1 0.758012 0.758012 3.06247e-11 8 3 3 0.758012 0.758012 4.77396e-15 8 3 5 0.758012 0.758012 1.77636e-14 9 3 1 1.67176 1.67176 4.44089e-16 9 3 3 1.67176 1.67176 1.33227e-15 9 3 5 1.67176 1.67176 4.79616e-14 10 3 1 0.708638 0.75 0.0413622 10 3 3 0.745404 0.75 0.0045958 10 3 5 0.748346 0.75 0.00165449 11 3 1 4.83433 5.07321 0.238888 11 3 3 5.04614 5.07321 0.0270711 11 3 5 5.06345 5.07321 0.00976102 12 3 1 0.107978 0.107978 3.66118e-09 12 3 3 0.107978 0.107978 4.51167e-14 12 3 5 0.107978 0.107978 1.22125e-15 13 3 1 7.69784e-17 0 7.69784e-17 13 3 3 -1.02397e-16 0 1.02397e-16 13 3 5 7.21824e-16 0 7.21824e-16 14 3 1 -0.375 -0.375 1.11022e-16 14 3 3 -0.375 -0.375 4.996e-16 14 3 5 -0.375 -0.375 4.32987e-15 15 3 1 0.0555556 0.0833333 0.0277778 15 3 3 0.0555556 0.0833333 0.0277778 15 3 5 0.0555556 0.0833333 0.0277778 16 3 1 0.708638 0.75 0.0413622 16 3 3 0.745404 0.75 0.0045958 16 3 5 0.748346 0.75 0.00165449 17 3 1 0.25 0.25 0 17 3 3 0.25 0.25 3.33067e-16 17 3 5 0.25 0.25 4.4964e-15 18 3 1 0.501831 0.523599 0.0217678 18 3 3 0.538509 0.523599 0.01491 18 3 5 0.531268 0.523599 0.00766915 19 3 1 0.130655 0.118506 0.0121487 19 3 3 0.118682 0.118506 0.000175632 19 3 5 0.119561 0.118506 0.00105459 20 3 1 2.5 2.5 4.44089e-16 20 3 3 2.5 2.5 7.54952e-15 20 3 5 2.5 2.5 1.33227e-15 24 3 1 0.843508 1 0.156492 24 3 3 0.981729 1 0.0182708 24 3 5 0.993397 1 0.00660336 25 3 1 1.03924 1.03924 0 25 3 3 1.03924 1.03924 1.33227e-15 25 3 5 1.03924 1.03924 3.33067e-15 26 3 1 0.022778 0.022778 1.04083e-17 26 3 3 0.022778 0.022778 1.04083e-17 26 3 5 0.022778 0.022778 4.57967e-16 27 3 1 -0.71711 -0.71711 0 27 3 3 -0.71711 -0.71711 4.44089e-16 27 3 5 -0.71711 -0.71711 3.44169e-15 28 3 1 0.797361 0.797359 1.97503e-06 28 3 3 0.797359 0.797359 1.37912e-12 28 3 5 0.797359 0.797359 1.85407e-14 29 3 1 0.287607 0.287607 8.22067e-11 29 3 3 0.287607 0.287607 7.43849e-15 29 3 5 0.287607 0.287607 6.60583e-15 30 3 1 0.972704 0.972704 5.89084e-13 30 3 3 0.972704 0.972704 3.88578e-15 30 3 5 0.972704 0.972704 5.55112e-16 31 3 1 0.286876 0.25258 0.034296 31 3 3 0.256268 0.25258 0.00368801 31 3 5 0.253905 0.25258 0.00132417 32 3 1 2.0681 1.35153 0.716572 32 3 3 1.29697 1.35153 0.0545545 32 3 5 1.39548 1.35153 0.0439507 TEST04 Use a Monte Carlo rule on box regions. Use a fixed spatial dimension. Repeatedly multiply the number of points by 16. Prob Dim Points Approx Exact Error 1 3 1 4.017 2.5 1.517 1 3 16 1.98069 2.5 0.519314 1 3 256 2.51538 2.5 0.0153838 1 3 4096 2.46408 2.5 0.0359208 1 3 65536 2.48823 2.5 0.0117677 2 3 1 1.0344 2.6 1.5656 2 3 16 1.97205 2.6 0.627951 2 3 256 2.19528 2.6 0.404718 2 3 4096 2.52913 2.6 0.0708695 2 3 65536 2.6071 2.6 0.00710206 3 3 1 1.04318 0 1.04318 3 3 16 -2.99187 0 2.99187 3 3 256 -0.7862 0 0.7862 3 3 4096 -0.441875 0 0.441875 3 3 65536 -0.0880609 0 0.0880609 4 3 1 1.05203 9.7619 8.70987 4 3 16 7.26339 9.7619 2.49851 4 3 256 7.52632 9.7619 2.23559 4 3 4096 9.11323 9.7619 0.648678 4 3 65536 9.83619 9.7619 0.0742864 5 3 1 1.59729 2.15214 0.554855 5 3 16 2.32895 2.15214 0.176805 5 3 256 2.12889 2.15214 0.0232496 5 3 4096 2.16561 2.15214 0.0134657 5 3 65536 2.15723 2.15214 0.00509 6 3 1 2.70969 1 1.70969 6 3 16 1.39964 1 0.399639 6 3 256 0.927314 1 0.0726859 6 3 4096 1.01947 1 0.0194699 6 3 65536 0.988955 1 0.0110454 7 3 1 0.171452 1 0.828548 7 3 16 0.84167 1 0.15833 7 3 256 1.04765 1 0.0476485 7 3 4096 1.00357 1 0.00356759 7 3 65536 1.00419 1 0.0041861 8 3 1 0.999989 0.758012 0.241977 8 3 16 0.689194 0.758012 0.0688182 8 3 256 0.773012 0.758012 0.0149998 8 3 4096 0.754223 0.758012 0.0037896 8 3 65536 0.756453 0.758012 0.00155909 9 3 1 1.95049 1.67176 0.278734 9 3 16 1.57779 1.67176 0.0939654 9 3 256 1.67642 1.67176 0.0046567 9 3 4096 1.66522 1.67176 0.00653733 9 3 65536 1.66957 1.67176 0.00219179 10 3 1 1.06741 0.75 0.317409 10 3 16 0.810449 0.75 0.0604495 10 3 256 0.736137 0.75 0.0138628 10 3 4096 0.752979 0.75 0.00297908 10 3 65536 0.747869 0.75 0.00213106 11 3 1 8.4555 5.07321 3.38229 11 3 16 5.7675 5.07321 0.69429 11 3 256 4.93312 5.07321 0.140091 11 3 4096 5.11274 5.07321 0.0395218 11 3 65536 5.05083 5.07321 0.0223889 12 3 1 1.55949 0.107978 1.45151 12 3 16 0.833615 0.107978 0.725638 12 3 256 0.137672 0.107978 0.0296946 12 3 4096 0.118813 0.107978 0.0108351 12 3 65536 0.11386 0.107978 0.00588253 13 3 1 0.111466 0 0.111466 13 3 16 -0.65298 0 0.65298 13 3 256 -0.178717 0 0.178717 13 3 4096 -0.0365333 0 0.0365333 13 3 65536 0.0173751 0 0.0173751 14 3 1 -0.182807 -0.375 0.192193 14 3 16 -0.310928 -0.375 0.064072 14 3 256 -0.37366 -0.375 0.00133984 14 3 4096 -0.37087 -0.375 0.00412971 14 3 65536 -0.372828 -0.375 0.00217178 15 3 1 0.0361912 0.0833333 0.0471421 15 3 16 0.025008 0.0833333 0.0583253 15 3 256 0.0538751 0.0833333 0.0294582 15 3 4096 0.0528793 0.0833333 0.030454 15 3 65536 0.0549606 0.0833333 0.0283727 16 3 1 1.06741 0.75 0.317409 16 3 16 0.810449 0.75 0.0604495 16 3 256 0.736137 0.75 0.0138628 16 3 4096 0.752979 0.75 0.00297908 16 3 65536 0.747869 0.75 0.00213106 17 3 1 0.39609 0.25 0.14609 17 3 16 0.275293 0.25 0.0252929 17 3 256 0.244171 0.25 0.00582935 17 3 4096 0.251083 0.25 0.00108302 17 3 65536 0.249087 0.25 0.000912782 18 3 1 0 0.523599 0.523599 18 3 16 0.625 0.523599 0.101401 18 3 256 0.527344 0.523599 0.00374497 18 3 4096 0.522949 0.523599 0.000649557 18 3 65536 0.525803 0.523599 0.00220384 19 3 1 0.188471 0.118506 0.0699647 19 3 16 0.101971 0.118506 0.0165355 19 3 256 0.114447 0.118506 0.0040589 19 3 4096 0.117241 0.118506 0.0012655 19 3 65536 0.11768 0.118506 0.00082618 20 3 1 4.017 2.5 1.517 20 3 16 1.98069 2.5 0.519314 20 3 256 2.51538 2.5 0.0153838 20 3 4096 2.46408 2.5 0.0359208 20 3 65536 2.48823 2.5 0.0117677 24 3 1 2.70969 1 1.70969 24 3 16 1.39964 1 0.399639 24 3 256 0.927314 1 0.0726859 24 3 4096 1.01947 1 0.0194699 24 3 65536 0.988955 1 0.0110454 25 3 1 1.05335 1.03924 0.0141146 25 3 16 1.0253 1.03924 0.0139381 25 3 256 1.03907 1.03924 0.000170837 25 3 4096 1.03816 1.03924 0.0010826 25 3 65536 1.03896 1.03924 0.00028111 26 3 1 0.0189886 0.022778 0.00378942 26 3 16 0.0240013 0.022778 0.00122333 26 3 256 0.0226612 0.022778 0.000116791 26 3 4096 0.0228626 0.022778 8.46653e-05 26 3 65536 0.022808 0.022778 3.00166e-05 27 3 1 -0.831744 -0.71711 0.114634 27 3 16 -0.680456 -0.71711 0.036654 27 3 256 -0.72077 -0.71711 0.00366041 27 3 4096 -0.714615 -0.71711 0.00249475 27 3 65536 -0.716219 -0.71711 0.000891248 28 3 1 0.69175 0.797359 0.10561 28 3 16 0.779424 0.797359 0.0179354 28 3 256 0.801944 0.797359 0.004585 28 3 4096 0.796695 0.797359 0.000664494 28 3 65536 0.798027 0.797359 0.000667379 29 3 1 0.184792 0.287607 0.102815 29 3 16 0.320299 0.287607 0.0326922 29 3 256 0.283335 0.287607 0.0042717 29 3 4096 0.290027 0.287607 0.00241961 29 3 65536 0.2885 0.287607 0.00089336 30 3 1 0.956944 0.972704 0.01576 30 3 16 0.969986 0.972704 0.00271879 30 3 256 0.973337 0.972704 0.000632361 30 3 4096 0.97259 0.972704 0.000114316 30 3 65536 0.972803 0.972704 9.84143e-05 31 3 1 0.118266 0.25258 0.134314 31 3 16 0.221384 0.25258 0.0311968 31 3 256 0.259995 0.25258 0.00741418 31 3 4096 0.251361 0.25258 0.00121901 31 3 65536 0.25344 0.25258 0.00085948 32 3 1 0 1.35153 1.35153 32 3 16 1.0341 1.35153 0.317429 32 3 256 1.36951 1.35153 0.0179842 32 3 4096 1.35156 1.35153 3.08634e-05 32 3 65536 1.36334 1.35153 0.0118134 TEST05 Demonstrate problems that use a base point by moving the base point around. Use a Monte Carlo rule on box regions. Use a fixed spatial dimension. Problem number = 16 Run number 1 Basis point Z = 0.218418 0.956318 Prob Dim Points Approx Exact Error 16 2 10 0.840784 0.787514 0.0532697 16 2 1000 0.793654 0.787514 0.00613983 16 2 100000 0.787792 0.787514 0.000277882 Run number 2 Basis point Z = 0.829509 0.561695 Prob Dim Points Approx Exact Error 16 2 10 0.745229 0.612383 0.132847 16 2 1000 0.614758 0.612383 0.0023755 16 2 100000 0.612616 0.612383 0.000233775 Run number 3 Basis point Z = 0.415307 0.0661187 Prob Dim Points Approx Exact Error 16 2 10 0.616367 0.695426 0.0790589 16 2 1000 0.689503 0.695426 0.00592292 16 2 100000 0.69359 0.695426 0.00183558 Problem number = 17 Run number 1 Basis point Z = 0.257578 0.109957 Prob Dim Points Approx Exact Error 17 2 10 0.299242 0.377569 0.0783266 17 2 1000 0.372033 0.377569 0.00553584 17 2 100000 0.375314 0.377569 0.00225471 Run number 2 Basis point Z = 0.043829 0.633966 Prob Dim Points Approx Exact Error 17 2 10 0.387798 0.392705 0.00490725 17 2 1000 0.392704 0.392705 1.89028e-06 17 2 100000 0.39118 0.392705 0.00152562 Run number 3 Basis point Z = 0.0617272 0.449539 Prob Dim Points Approx Exact Error 17 2 10 0.319277 0.361296 0.0420187 17 2 1000 0.359104 0.361296 0.00219181 17 2 100000 0.359354 0.361296 0.0019422 Problem number = 18 Run number 1 Basis point Z = 0.401306 0.754673 Prob Dim Points Approx Exact Error 18 2 10 0.5 0.785398 0.285398 18 2 1000 0.587 0.785398 0.198398 18 2 100000 0.58835 0.785398 0.197048 Run number 2 Basis point Z = 0.797287 0.00183837 Prob Dim Points Approx Exact Error 18 2 10 0.3 0.785398 0.485398 18 2 1000 0.324 0.785398 0.461398 18 2 100000 0.29785 0.785398 0.487548 Run number 3 Basis point Z = 0.897504 0.350752 Prob Dim Points Approx Exact Error 18 2 10 0.3 0.785398 0.485398 18 2 1000 0.444 0.785398 0.341398 18 2 100000 0.44269 0.785398 0.342708 Problem number = 19 Run number 1 Basis point Z = 0.0945448 0.0136169 Prob Dim Points Approx Exact Error 19 2 10 0.261655 0.38842 0.126766 19 2 1000 0.381927 0.38842 0.00649348 19 2 100000 0.387221 0.38842 0.00119932 Run number 2 Basis point Z = 0.859097 0.840847 Prob Dim Points Approx Exact Error 19 2 10 0.394038 0.314958 0.0790801 19 2 1000 0.317779 0.314958 0.00282142 19 2 100000 0.316299 0.314958 0.00134091 Run number 3 Basis point Z = 0.123104 0.00751236 Prob Dim Points Approx Exact Error 19 2 10 0.260874 0.380081 0.119208 19 2 1000 0.374378 0.380081 0.00570331 19 2 100000 0.379008 0.380081 0.00107332 Problem number = 31 Run number 1 Basis point Z = 0.260303 0.912484 Prob Dim Points Approx Exact Error 31 2 10 0.278917 0.294324 0.0154068 31 2 1000 0.293259 0.294324 0.00106485 31 2 100000 0.293668 0.294324 0.000655911 Run number 2 Basis point Z = 0.113664 0.351629 Prob Dim Points Approx Exact Error 31 2 10 0.348145 0.318205 0.02994 31 2 1000 0.318928 0.318205 0.000722404 31 2 100000 0.319552 0.318205 0.00134675 Run number 3 Basis point Z = 0.822887 0.267132 Prob Dim Points Approx Exact Error 31 2 10 0.29974 0.326926 0.0271858 31 2 1000 0.332656 0.326926 0.00573047 31 2 100000 0.326865 0.326926 6.06648e-05 TEST06 Use a simple product rule on a box region. Use a fixed problem; Let the spatial dimension increase. Prob Dim Subs Approx Exact Error Calls 6 1 1 0.94485 1 0.0551496 5 6 1 3 0.993872 1 0.00612773 15 6 1 5 0.997794 1 0.00220598 25 6 2 1 0.892742 1 0.107258 25 6 2 3 0.987782 1 0.0122179 225 6 2 5 0.995593 1 0.0044071 625 6 3 1 0.843508 1 0.156492 125 6 3 3 0.981729 1 0.0182708 3375 6 3 5 0.993397 1 0.00660336 15625 6 4 1 0.796989 1 0.203011 625 6 4 3 0.975713 1 0.0242865 50625 6 4 5 0.991205 1 0.00879477 390625 6 5 1 0.753035 1 0.246965 3125 6 5 3 0.969735 1 0.0302654 759375 6 5 5 0.989019 1 0.0109814 9765625 6 6 1 0.711506 1 0.288494 15625 6 6 3 0.963792 1 0.0362077 11390625 6 6 5 0.986837 1 0.0131631 244140625 TEST_NINT_PRB Normal end of execution. 24 December 2011 11:56:19 AM