17 September 2021 11:53:59.964 PM TEST_NINT_TEST FORTRAN90 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 33 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, Continuous". 32 "Genz #6, Discontinuous". 33 "Ball R^2". 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 33 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) = prod ( 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, Continuous 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. Problem 33 Name: Ball R^2 Region: Sphere interior, radius 1, center 0 Integrand: F(X) = sum ( X(1:N)^2 ) TEST03 Use a simple product rule on box regions. Use a fixed spatial dimension. Prob Dim Subs Approx Exact Error 1 3 1 2.50000 2.50000 0.444089E-15 1 3 3 2.50000 2.50000 0.754952E-14 1 3 5 2.50000 2.50000 0.133227E-14 2 3 1 2.60000 2.60000 0.444089E-15 2 3 3 2.60000 2.60000 0.226485E-13 2 3 5 2.60000 2.60000 0.142553E-12 3 3 1 -0.241474E-14 0.00000 0.241474E-14 3 3 3 -0.922513E-14 0.00000 0.922513E-14 3 3 5 -0.348654E-14 0.00000 0.348654E-14 4 3 1 9.76190 9.76190 0.888178E-14 4 3 3 9.76190 9.76190 0.461853E-13 4 3 5 9.76190 9.76190 0.111910E-12 5 3 1 2.15214 2.15214 0.315880E-06 5 3 3 2.15214 2.15214 0.478373E-10 5 3 5 2.15214 2.15214 0.453415E-12 6 3 1 0.843508 1.00000 0.156492 6 3 3 0.981729 1.00000 0.182708E-01 6 3 5 0.993397 1.00000 0.660336E-02 7 3 1 1.00000 1.00000 0.165427E-06 7 3 3 1.00000 1.00000 0.194289E-11 7 3 5 1.00000 1.00000 0.266454E-13 8 3 1 0.758012 0.758012 0.306247E-10 8 3 3 0.758012 0.758012 0.477396E-14 8 3 5 0.758012 0.758012 0.177636E-13 9 3 1 1.67176 1.67176 0.444089E-15 9 3 3 1.67176 1.67176 0.133227E-14 9 3 5 1.67176 1.67176 0.479616E-13 10 3 1 0.708638 0.750000 0.413622E-01 10 3 3 0.745404 0.750000 0.459580E-02 10 3 5 0.748346 0.750000 0.165449E-02 11 3 1 4.83433 5.07321 0.238888 11 3 3 5.04614 5.07321 0.270711E-01 11 3 5 5.06345 5.07321 0.976102E-02 12 3 1 0.107978 0.107978 0.366118E-08 12 3 3 0.107978 0.107978 0.451861E-13 12 3 5 0.107978 0.107978 0.115186E-14 13 3 1 0.769784E-16 0.00000 0.769784E-16 13 3 3 -0.102397E-15 0.00000 0.102397E-15 13 3 5 0.721824E-15 0.00000 0.721824E-15 14 3 1 -0.375000 -0.375000 0.111022E-15 14 3 3 -0.375000 -0.375000 0.499600E-15 14 3 5 -0.375000 -0.375000 0.432987E-14 15 3 1 0.833333E-01 0.833333E-01 0.277556E-16 15 3 3 0.833333E-01 0.833333E-01 0.416334E-16 15 3 5 0.833333E-01 0.833333E-01 0.111022E-15 16 3 1 0.708638 0.750000 0.413622E-01 16 3 3 0.745404 0.750000 0.459580E-02 16 3 5 0.748346 0.750000 0.165449E-02 17 3 1 0.250000 0.250000 0.00000 17 3 3 0.250000 0.250000 0.333067E-15 17 3 5 0.250000 0.250000 0.449640E-14 18 3 1 0.501831 0.523599 0.217678E-01 18 3 3 0.538509 0.523599 0.149100E-01 18 3 5 0.531268 0.523599 0.766915E-02 19 3 1 0.130655 0.118506 0.121487E-01 19 3 3 0.118682 0.118506 0.175632E-03 19 3 5 0.119561 0.118506 0.105459E-02 20 3 1 2.50000 2.50000 0.444089E-15 20 3 3 2.50000 2.50000 0.754952E-14 20 3 5 2.50000 2.50000 0.133227E-14 24 3 1 0.843508 1.00000 0.156492 24 3 3 0.981729 1.00000 0.182708E-01 24 3 5 0.993397 1.00000 0.660336E-02 25 3 1 1.03924 1.03924 0.00000 25 3 3 1.03924 1.03924 0.133227E-14 25 3 5 1.03924 1.03924 0.333067E-14 26 3 1 0.227780E-01 0.227780E-01 0.104083E-16 26 3 3 0.227780E-01 0.227780E-01 0.104083E-16 26 3 5 0.227780E-01 0.227780E-01 0.457967E-15 27 3 1 -0.717110 -0.717110 0.111022E-15 27 3 3 -0.717110 -0.717110 0.333067E-15 27 3 5 -0.717110 -0.717110 0.355271E-14 28 3 1 0.797361 0.797359 0.197503E-05 28 3 3 0.797359 0.797359 0.137879E-11 28 3 5 0.797359 0.797359 0.182077E-13 29 3 1 0.287607 0.287607 0.822067E-10 29 3 3 0.287607 0.287607 0.743849E-14 29 3 5 0.287607 0.287607 0.660583E-14 30 3 1 0.972704 0.972704 0.589084E-12 30 3 3 0.972704 0.972704 0.388578E-14 30 3 5 0.972704 0.972704 0.555112E-15 31 3 1 0.286876 0.252580 0.342960E-01 31 3 3 0.256268 0.252580 0.368801E-02 31 3 5 0.253905 0.252580 0.132417E-02 32 3 1 2.06810 1.35153 0.716572 32 3 3 1.29697 1.35153 0.545545E-01 32 3 5 1.39548 1.35153 0.439507E-01 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 2.59449 2.50000 0.944870E-01 1 3 16 2.66593 2.50000 0.165932 1 3 256 2.57484 2.50000 0.748423E-01 1 3 4096 2.51341 2.50000 0.134143E-01 1 3 65536 2.49950 2.50000 0.497387E-03 2 3 1 0.240633E-02 2.60000 2.59759 2 3 16 2.46669 2.60000 0.133307 2 3 256 2.46265 2.60000 0.137349 2 3 4096 2.60261 2.60000 0.261446E-02 2 3 65536 2.59121 2.60000 0.879101E-02 3 3 1 0.532961E-03 0.00000 0.532961E-03 3 3 16 -0.671079 0.00000 0.671079 3 3 256 0.336427 0.00000 0.336427 3 3 4096 0.352657 0.00000 0.352657 3 3 65536 -0.293605E-01 0.00000 0.293605E-01 4 3 1 0.118041E-03 9.76190 9.76179 4 3 16 8.70905 9.76190 1.05286 4 3 256 8.75682 9.76190 1.00509 4 3 4096 9.82452 9.76190 0.626194E-01 4 3 65536 9.72310 9.76190 0.388074E-01 5 3 1 1.89507 2.15214 0.257074 5 3 16 2.07500 2.15214 0.771392E-01 5 3 256 2.11594 2.15214 0.362020E-01 5 3 4096 2.14256 2.15214 0.958108E-02 5 3 65536 2.15177 2.15214 0.373831E-03 6 3 1 0.478799E-01 1.00000 0.952120 6 3 16 1.15313 1.00000 0.153128 6 3 256 0.983169 1.00000 0.168313E-01 6 3 4096 0.979727 1.00000 0.202734E-01 6 3 65536 0.997592 1.00000 0.240786E-02 7 3 1 1.67424 1.00000 0.674240 7 3 16 1.38117 1.00000 0.381167 7 3 256 1.09887 1.00000 0.988717E-01 7 3 4096 1.03181 1.00000 0.318076E-01 7 3 65536 1.00265 1.00000 0.265278E-02 8 3 1 0.909409 0.758012 0.151397 8 3 16 0.797807 0.758012 0.397949E-01 8 3 256 0.771138 0.758012 0.131258E-01 8 3 4096 0.760133 0.758012 0.212076E-02 8 3 65536 0.758375 0.758012 0.362442E-03 9 3 1 1.71072 1.67176 0.389605E-01 9 3 16 1.70431 1.67176 0.325499E-01 9 3 256 1.68611 1.67176 0.143529E-01 9 3 4096 1.67451 1.67176 0.275105E-02 9 3 65536 1.67173 1.67176 0.300309E-04 10 3 1 0.538860 0.750000 0.211140 10 3 16 0.705612 0.750000 0.443878E-01 10 3 256 0.731610 0.750000 0.183903E-01 10 3 4096 0.743418 0.750000 0.658191E-02 10 3 65536 0.749535 0.750000 0.465274E-03 11 3 1 2.93797 5.07321 2.13524 11 3 16 4.93815 5.07321 0.135069 11 3 256 4.98033 5.07321 0.928879E-01 11 3 4096 5.01594 5.07321 0.572694E-01 11 3 65536 5.06890 5.07321 0.431148E-02 12 3 1 -0.193359 0.107978 0.301337 12 3 16 0.807789E-01 0.107978 0.271987E-01 12 3 256 0.145392 0.107978 0.374141E-01 12 3 4096 0.906724E-01 0.107978 0.173052E-01 12 3 65536 0.107316 0.107978 0.661184E-03 13 3 1 0.114483E-01 0.00000 0.114483E-01 13 3 16 0.200319 0.00000 0.200319 13 3 256 0.744157E-02 0.00000 0.744157E-02 13 3 4096 -0.369485E-01 0.00000 0.369485E-01 13 3 65536 -0.604267E-03 0.00000 0.604267E-03 14 3 1 -0.214169 -0.375000 0.160831 14 3 16 -0.391304 -0.375000 0.163040E-01 14 3 256 -0.374377 -0.375000 0.623260E-03 14 3 4096 -0.382289 -0.375000 0.728900E-02 14 3 65536 -0.375590 -0.375000 0.590025E-03 15 3 1 0.607857E-01 0.833333E-01 0.225476E-01 15 3 16 0.948958E-01 0.833333E-01 0.115624E-01 15 3 256 0.892396E-01 0.833333E-01 0.590629E-02 15 3 4096 0.865538E-01 0.833333E-01 0.322046E-02 15 3 65536 0.831634E-01 0.833333E-01 0.169954E-03 16 3 1 0.538860 0.750000 0.211140 16 3 16 0.705612 0.750000 0.443878E-01 16 3 256 0.731610 0.750000 0.183903E-01 16 3 4096 0.743418 0.750000 0.658191E-02 16 3 65536 0.749535 0.750000 0.465274E-03 17 3 1 0.144327 0.250000 0.105673 17 3 16 0.220938 0.250000 0.290621E-01 17 3 256 0.242691 0.250000 0.730896E-02 17 3 4096 0.246655 0.250000 0.334538E-02 17 3 65536 0.249788 0.250000 0.211984E-03 18 3 1 1.00000 0.523599 0.476401 18 3 16 0.687500 0.523599 0.163901 18 3 256 0.554688 0.523599 0.310887E-01 18 3 4096 0.534180 0.523599 0.105809E-01 18 3 65536 0.523361 0.523599 0.237570E-03 19 3 1 0.636210E-01 0.118506 0.548854E-01 19 3 16 0.117856 0.118506 0.650313E-03 19 3 256 0.119084 0.118506 0.577417E-03 19 3 4096 0.118084 0.118506 0.422206E-03 19 3 65536 0.118244 0.118506 0.262735E-03 20 3 1 2.59449 2.50000 0.944870E-01 20 3 16 2.66593 2.50000 0.165932 20 3 256 2.57484 2.50000 0.748423E-01 20 3 4096 2.51341 2.50000 0.134143E-01 20 3 65536 2.49950 2.50000 0.497387E-03 24 3 1 0.478799E-01 1.00000 0.952120 24 3 16 1.15313 1.00000 0.153128 24 3 256 0.983169 1.00000 0.168313E-01 24 3 4096 0.979727 1.00000 0.202734E-01 24 3 65536 0.997592 1.00000 0.240786E-02 25 3 1 1.03632 1.03924 0.291934E-02 25 3 16 1.04459 1.03924 0.535479E-02 25 3 256 1.04200 1.03924 0.275912E-02 25 3 4096 1.03997 1.03924 0.731383E-03 25 3 65536 1.03918 1.03924 0.621580E-04 26 3 1 0.216500E-01 0.227780E-01 0.112800E-02 26 3 16 0.222795E-01 0.227780E-01 0.498452E-03 26 3 256 0.225690E-01 0.227780E-01 0.209020E-03 26 3 4096 0.227350E-01 0.227780E-01 0.429964E-04 26 3 65536 0.227766E-01 0.227780E-01 0.138106E-05 27 3 1 -0.751988 -0.717110 0.348781E-01 27 3 16 -0.732260 -0.717110 0.151497E-01 27 3 256 -0.723368 -0.717110 0.625779E-02 27 3 4096 -0.718354 -0.717110 0.124371E-02 27 3 65536 -0.717156 -0.717110 0.464293E-04 28 3 1 0.870433 0.797359 0.730738E-01 28 3 16 0.819808 0.797359 0.224488E-01 28 3 256 0.803391 0.797359 0.603159E-02 28 3 4096 0.799862 0.797359 0.250306E-02 28 3 65536 0.797523 0.797359 0.163923E-03 29 3 1 0.242135 0.287607 0.454724E-01 29 3 16 0.272979 0.287607 0.146282E-01 29 3 256 0.281223 0.287607 0.638381E-02 29 3 4096 0.286033 0.287607 0.157425E-02 29 3 65536 0.287537 0.287607 0.700483E-04 30 3 1 0.984092 0.972704 0.113872E-01 30 3 16 0.975882 0.972704 0.317776E-02 30 3 256 0.973506 0.972704 0.801316E-03 30 3 4096 0.973067 0.972704 0.362517E-03 30 3 65536 0.972727 0.972704 0.230644E-04 31 3 1 0.340371 0.252580 0.877902E-01 31 3 16 0.289314 0.252580 0.367338E-01 31 3 256 0.267557 0.252580 0.149769E-01 31 3 4096 0.256798 0.252580 0.421711E-02 31 3 65536 0.252874 0.252580 0.293829E-03 32 3 1 0.00000 1.35153 1.35153 32 3 16 1.21242 1.35153 0.139113 32 3 256 1.43134 1.35153 0.798138E-01 32 3 4096 1.38939 1.35153 0.378638E-01 32 3 65536 1.35249 1.35153 0.962786E-03 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 = 0.7034 0.8141 Prob Dim Points Approx Exact Error 16 2 10 0.767946 0.640054 0.127892 16 2 1000 0.630412 0.640054 0.964199E-02 16 2 100000 0.640782 0.640054 0.727919E-03 Run number 2 Basis point Z = 0.1212 0.5164 Prob Dim Points Approx Exact Error 16 2 10 0.658607 0.643736 0.148710E-01 16 2 1000 0.647820 0.643736 0.408374E-02 16 2 100000 0.644882 0.643736 0.114548E-02 Run number 3 Basis point Z = 0.7322 0.6402 Prob Dim Points Approx Exact Error 16 2 10 0.813742 0.573582 0.240159 16 2 1000 0.566529 0.573582 0.705331E-02 16 2 100000 0.574628 0.573582 0.104554E-02 Problem number = 17 Run number 1 Basis point Z = 0.9081 0.8318 Prob Dim Points Approx Exact Error 17 2 10 0.674302 0.443256 0.231047 17 2 1000 0.446587 0.443256 0.333100E-02 17 2 100000 0.443486 0.443256 0.230876E-03 Run number 2 Basis point Z = 0.8785 0.7310 Prob Dim Points Approx Exact Error 17 2 10 0.263522 0.363289 0.997673E-01 17 2 1000 0.359591 0.363289 0.369864E-02 17 2 100000 0.363777 0.363289 0.488251E-03 Run number 3 Basis point Z = 0.3730 0.6649 Prob Dim Points Approx Exact Error 17 2 10 0.201970 0.210007 0.803714E-02 17 2 1000 0.208837 0.210007 0.116986E-02 17 2 100000 0.209844 0.210007 0.162239E-03 Problem number = 18 Run number 1 Basis point Z = 0.9780 0.8824 Prob Dim Points Approx Exact Error 18 2 10 0.100000 0.785398 0.685398 18 2 1000 0.250000 0.785398 0.535398 18 2 100000 0.270440 0.785398 0.514958 Run number 2 Basis point Z = 0.0836 0.7511 Prob Dim Points Approx Exact Error 18 2 10 0.500000 0.785398 0.285398 18 2 1000 0.386000 0.785398 0.399398 18 2 100000 0.381570 0.785398 0.403828 Run number 3 Basis point Z = 0.0908 0.2545 Prob Dim Points Approx Exact Error 18 2 10 0.200000 0.785398 0.585398 18 2 1000 0.368000 0.785398 0.417398 18 2 100000 0.384260 0.785398 0.401138 Problem number = 19 Run number 1 Basis point Z = 0.5906 0.9783 Prob Dim Points Approx Exact Error 19 2 10 0.331652 0.308873 0.227788E-01 19 2 1000 0.315819 0.308873 0.694604E-02 19 2 100000 0.308420 0.308873 0.452817E-03 Run number 2 Basis point Z = 0.9248 0.8867 Prob Dim Points Approx Exact Error 19 2 10 0.361379 0.353098 0.828133E-02 19 2 1000 0.344751 0.353098 0.834705E-02 19 2 100000 0.354475 0.353098 0.137680E-02 Run number 3 Basis point Z = 0.5154 0.2088 Prob Dim Points Approx Exact Error 19 2 10 0.271862 0.251237 0.206250E-01 19 2 1000 0.249525 0.251237 0.171227E-02 19 2 100000 0.251242 0.251237 0.483572E-05 Problem number = 31 Run number 1 Basis point Z = 0.9425 0.4391 Prob Dim Points Approx Exact Error 31 2 10 0.260599 0.301114 0.405142E-01 31 2 1000 0.300698 0.301114 0.415307E-03 31 2 100000 0.301525 0.301114 0.411723E-03 Run number 2 Basis point Z = 0.0384 0.2604 Prob Dim Points Approx Exact Error 31 2 10 0.274052 0.273266 0.786690E-03 31 2 1000 0.271380 0.273266 0.188552E-02 31 2 100000 0.272401 0.273266 0.864787E-03 Run number 3 Basis point Z = 0.3294 0.0727 Prob Dim Points Approx Exact Error 31 2 10 0.418129 0.298771 0.119358 31 2 1000 0.301441 0.298771 0.267057E-02 31 2 100000 0.299376 0.298771 0.604925E-03 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 0.944850 1.00000 0.055150 5 6 1 3 0.993872 1.00000 0.006128 15 6 1 5 0.997794 1.00000 0.002206 25 6 2 1 0.892742 1.00000 0.107258 25 6 2 3 0.987782 1.00000 0.012218 225 6 2 5 0.995593 1.00000 0.004407 625 6 3 1 0.843508 1.00000 0.156492 125 6 3 3 0.981729 1.00000 0.018271 3375 6 3 5 0.993397 1.00000 0.006603 15625 6 4 1 0.796989 1.00000 0.203011 625 6 4 3 0.975713 1.00000 0.024287 50625 6 4 5 0.991205 1.00000 0.008795 390625 6 5 1 0.753035 1.00000 0.246965 3125 6 5 3 0.969735 1.00000 0.030265 759375 6 5 5 0.989019 1.00000 0.010981 9765625 6 6 1 0.711506 1.00000 0.288494 15625 6 6 3 0.963792 1.00000 0.036208 11390625 6 6 5 0.986837 1.00000 0.013163 244140625 TEST_NINT_TEST Normal end of execution. 17 September 2021 11:54:16.183 PM