27 June 2025 11:35:00.472 AM test_int_nd_test(): Fortran90 version Test test_int_nd(). 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 5.37241 2.50000 2.87241 1 3 16 2.56511 2.50000 0.651095E-01 1 3 256 2.50131 2.50000 0.131031E-02 1 3 4096 2.51089 2.50000 0.108947E-01 1 3 65536 2.50040 2.50000 0.399724E-03 2 3 1 7.15826 2.60000 4.55826 2 3 16 4.47830 2.60000 1.87830 2 3 256 2.53824 2.60000 0.617565E-01 2 3 4096 2.65071 2.60000 0.507062E-01 2 3 65536 2.55668 2.60000 0.433201E-01 3 3 1 11.7087 0.00000 11.7087 3 3 16 -3.47956 0.00000 3.47956 3 3 256 -1.46839 0.00000 1.46839 3 3 4096 -0.351149 0.00000 0.351149 3 3 65536 -0.612624E-01 0.00000 0.612624E-01 4 3 1 19.1519 9.76190 9.38996 4 3 16 18.1390 9.76190 8.37714 4 3 256 9.47690 9.76190 0.285004 4 3 4096 9.93169 9.76190 0.169782 4 3 65536 9.50603 9.76190 0.255879 5 3 1 1.41952 2.15214 0.732619 5 3 16 2.27289 2.15214 0.120742 5 3 256 2.15910 2.15214 0.695612E-02 5 3 4096 2.15343 2.15214 0.128484E-02 5 3 65536 2.15022 2.15214 0.192414E-02 6 3 1 0.166477 1.00000 0.833523 6 3 16 0.963024 1.00000 0.369765E-01 6 3 256 0.994584 1.00000 0.541557E-02 6 3 4096 1.01967 1.00000 0.196745E-01 6 3 65536 0.994175 1.00000 0.582511E-02 7 3 1 0.363701 1.00000 0.636299 7 3 16 1.07503 1.00000 0.750275E-01 7 3 256 0.986280 1.00000 0.137196E-01 7 3 4096 0.999941 1.00000 0.590870E-04 7 3 65536 1.00964 1.00000 0.963851E-02 8 3 1 0.938966 0.758012 0.180953 8 3 16 0.719978 0.758012 0.380346E-01 8 3 256 0.763906 0.758012 0.589346E-02 8 3 4096 0.759772 0.758012 0.176004E-02 8 3 65536 0.759240 0.758012 0.122789E-02 9 3 1 2.16542 1.67176 0.493664 9 3 16 1.67267 1.67176 0.913613E-03 9 3 256 1.67202 1.67176 0.266354E-03 9 3 4096 1.67348 1.67176 0.172223E-02 9 3 65536 1.67200 1.67176 0.242015E-03 10 3 1 0.817847 0.750000 0.678466E-01 10 3 16 0.716895 0.750000 0.331050E-01 10 3 256 0.751646 0.750000 0.164645E-02 10 3 4096 0.751905 0.750000 0.190526E-02 10 3 65536 0.747709 0.750000 0.229142E-02 11 3 1 5.13302 5.07321 0.598011E-01 11 3 16 4.96763 5.07321 0.105580 11 3 256 5.09673 5.07321 0.235131E-01 11 3 4096 5.10334 5.07321 0.301213E-01 11 3 65536 5.05354 5.07321 0.196789E-01 12 3 1 -0.191009E-01 0.107978 0.127078 12 3 16 0.515123 0.107978 0.407146 12 3 256 -0.148786E-01 0.107978 0.122856 12 3 4096 0.107506 0.107978 0.471458E-03 12 3 65536 0.108307 0.107978 0.329708E-03 13 3 1 -0.451102E-01 0.00000 0.451102E-01 13 3 16 -0.108527 0.00000 0.108527 13 3 256 0.597571E-01 0.00000 0.597571E-01 13 3 4096 0.176935E-01 0.00000 0.176935E-01 13 3 65536 -0.105901E-02 0.00000 0.105901E-02 14 3 1 -0.507382 -0.375000 0.132382 14 3 16 -0.410507 -0.375000 0.355066E-01 14 3 256 -0.383536 -0.375000 0.853611E-02 14 3 4096 -0.379945 -0.375000 0.494513E-02 14 3 65536 -0.374382 -0.375000 0.617576E-03 15 3 1 0.376990 0.833333E-01 0.293657 15 3 16 0.104617 0.833333E-01 0.212834E-01 15 3 256 0.788576E-01 0.833333E-01 0.447576E-02 15 3 4096 0.835257E-01 0.833333E-01 0.192389E-03 15 3 65536 0.830032E-01 0.833333E-01 0.330091E-03 16 3 1 0.817847 0.750000 0.678466E-01 16 3 16 0.716895 0.750000 0.331050E-01 16 3 256 0.751646 0.750000 0.164645E-02 16 3 4096 0.751905 0.750000 0.190526E-02 16 3 65536 0.747709 0.750000 0.229142E-02 17 3 1 0.321590 0.250000 0.715898E-01 17 3 16 0.247185 0.250000 0.281546E-02 17 3 256 0.252933 0.250000 0.293299E-02 17 3 4096 0.250903 0.250000 0.902842E-03 17 3 65536 0.248787 0.250000 0.121268E-02 18 3 1 0.00000 0.523599 0.523599 18 3 16 0.500000 0.523599 0.235988E-01 18 3 256 0.511719 0.523599 0.118800E-01 18 3 4096 0.508301 0.523599 0.152980E-01 18 3 65536 0.527924 0.523599 0.432481E-02 19 3 1 0.242671 0.118506 0.124164 19 3 16 0.127070 0.118506 0.856369E-02 19 3 256 0.117018 0.118506 0.148852E-02 19 3 4096 0.117988 0.118506 0.518264E-03 19 3 65536 0.117923 0.118506 0.583447E-03 20 3 1 5.37241 2.50000 2.87241 20 3 16 2.56511 2.50000 0.651095E-01 20 3 256 2.50131 2.50000 0.131031E-02 20 3 4096 2.51089 2.50000 0.108947E-01 20 3 65536 2.50040 2.50000 0.399724E-03 24 3 1 0.166477 1.00000 0.833523 24 3 16 0.963024 1.00000 0.369765E-01 24 3 256 0.994584 1.00000 0.541557E-02 24 3 4096 1.01967 1.00000 0.196745E-01 24 3 65536 0.994175 1.00000 0.582511E-02 25 3 1 1.13390 1.03924 0.946626E-01 25 3 16 1.04695 1.03924 0.770721E-02 25 3 256 1.03857 1.03924 0.666370E-03 25 3 4096 1.03949 1.03924 0.249157E-03 25 3 65536 1.03919 1.03924 0.504724E-04 26 3 1 0.171038E-01 0.227780E-01 0.567415E-02 26 3 16 0.230538E-01 0.227780E-01 0.275772E-03 26 3 256 0.227669E-01 0.227780E-01 0.110540E-04 26 3 4096 0.227606E-01 0.227780E-01 0.174019E-04 26 3 65536 0.227697E-01 0.227780E-01 0.826588E-05 27 3 1 -0.885131 -0.717110 0.168021 27 3 16 -0.709035 -0.717110 0.807496E-02 27 3 256 -0.717649 -0.717110 0.538979E-03 27 3 4096 -0.717685 -0.717110 0.575162E-03 27 3 65536 -0.717372 -0.717110 0.262405E-03 28 3 1 0.742119 0.797359 0.552405E-01 28 3 16 0.802073 0.797359 0.471368E-02 28 3 256 0.795409 0.797359 0.195030E-02 28 3 4096 0.796811 0.797359 0.548403E-03 28 3 65536 0.798250 0.797359 0.890576E-03 29 3 1 0.151207 0.287607 0.136400 29 3 16 0.305703 0.287607 0.180957E-01 29 3 256 0.288069 0.287607 0.461707E-03 29 3 4096 0.287576 0.287607 0.310106E-04 29 3 65536 0.287275 0.287607 0.332115E-03 30 3 1 0.964899 0.972704 0.780571E-02 30 3 16 0.973036 0.972704 0.331509E-03 30 3 256 0.972388 0.972704 0.315916E-03 30 3 4096 0.972608 0.972704 0.959965E-04 30 3 65536 0.972836 0.972704 0.131316E-03 31 3 1 0.194817 0.252580 0.577632E-01 31 3 16 0.280766 0.252580 0.281852E-01 31 3 256 0.252835 0.252580 0.254079E-03 31 3 4096 0.252355 0.252580 0.225725E-03 31 3 65536 0.253845 0.252580 0.126485E-02 32 3 1 0.00000 1.35153 1.35153 32 3 16 1.50247 1.35153 0.150941 32 3 256 1.31403 1.35153 0.374966E-01 32 3 4096 1.32529 1.35153 0.262397E-01 32 3 65536 1.35449 1.35153 0.296367E-02 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 = 0.1014 0.6563 Prob Dim Points Approx Exact Error 16 2 10 0.739744 0.683285 0.564587E-01 16 2 1000 0.681438 0.683285 0.184667E-02 16 2 100000 0.683604 0.683285 0.319621E-03 Run number 2 Basis point Z = 0.5458 0.4503 Prob Dim Points Approx Exact Error 16 2 10 0.562919 0.504566 0.583528E-01 16 2 1000 0.508099 0.504566 0.353291E-02 16 2 100000 0.504666 0.504566 0.994943E-04 Run number 3 Basis point Z = 0.0236 0.4092 Prob Dim Points Approx Exact Error 16 2 10 0.844970 0.735234 0.109735 16 2 1000 0.731601 0.735234 0.363302E-02 16 2 100000 0.734967 0.735234 0.267836E-03 Problem number = 17 Run number 1 Basis point Z = 0.0773 0.2983 Prob Dim Points Approx Exact Error 17 2 10 0.407879 0.385978 0.219004E-01 17 2 1000 0.385496 0.385978 0.481926E-03 17 2 100000 0.385593 0.385978 0.385211E-03 Run number 2 Basis point Z = 0.9407 0.8114 Prob Dim Points Approx Exact Error 17 2 10 0.257484 0.457850 0.200365 17 2 1000 0.454638 0.457850 0.321210E-02 17 2 100000 0.457183 0.457850 0.666411E-03 Run number 3 Basis point Z = 0.7128 0.0805 Prob Dim Points Approx Exact Error 17 2 10 0.254605 0.387907 0.133302 17 2 1000 0.380215 0.387907 0.769216E-02 17 2 100000 0.388408 0.387907 0.500792E-03 Problem number = 18 Run number 1 Basis point Z = 0.7271 0.6271 Prob Dim Points Approx Exact Error 18 2 10 0.600000 0.785398 0.185398 18 2 1000 0.584000 0.785398 0.201398 18 2 100000 0.596260 0.785398 0.189138 Run number 2 Basis point Z = 0.2347 0.8732 Prob Dim Points Approx Exact Error 18 2 10 0.500000 0.785398 0.285398 18 2 1000 0.423000 0.785398 0.362398 18 2 100000 0.403200 0.785398 0.382198 Run number 3 Basis point Z = 0.1738 0.3619 Prob Dim Points Approx Exact Error 18 2 10 0.300000 0.785398 0.485398 18 2 1000 0.491000 0.785398 0.294398 18 2 100000 0.508100 0.785398 0.277298 Problem number = 19 Run number 1 Basis point Z = 0.3779 0.3881 Prob Dim Points Approx Exact Error 19 2 10 0.202453 0.231488 0.290352E-01 19 2 1000 0.238516 0.231488 0.702808E-02 19 2 100000 0.231549 0.231488 0.603259E-04 Run number 2 Basis point Z = 0.4886 0.5721 Prob Dim Points Approx Exact Error 19 2 10 0.276336 0.224002 0.523347E-01 19 2 1000 0.225376 0.224002 0.137400E-02 19 2 100000 0.223481 0.224002 0.520916E-03 Run number 3 Basis point Z = 0.9932 0.0522 Prob Dim Points Approx Exact Error 19 2 10 0.267110 0.411380 0.144270 19 2 1000 0.411465 0.411380 0.845038E-04 19 2 100000 0.412011 0.411380 0.630860E-03 Problem number = 31 Run number 1 Basis point Z = 0.8878 0.4535 Prob Dim Points Approx Exact Error 31 2 10 0.316631 0.325247 0.861622E-02 31 2 1000 0.330716 0.325247 0.546856E-02 31 2 100000 0.326916 0.325247 0.166880E-02 Run number 2 Basis point Z = 0.5854 0.9379 Prob Dim Points Approx Exact Error 31 2 10 0.248057 0.301953 0.538962E-01 31 2 1000 0.298407 0.301953 0.354657E-02 31 2 100000 0.301655 0.301953 0.298485E-03 Run number 3 Basis point Z = 0.5684 0.7787 Prob Dim Points Approx Exact Error 31 2 10 0.319566 0.360529 0.409628E-01 31 2 1000 0.359721 0.360529 0.807874E-03 31 2 100000 0.360045 0.360529 0.484145E-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_int_nd_test(): Normal end of execution. 27 June 2025 11:35:19.661 AM