>> cd test_nint >> test_nint_test 13-Aug-2008 11:57:59 TEST_NINT_TEST MATLAB version Test the routines in 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) = 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) = prod ( (|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 2.500000 2.500000 0.000000 1 3 3 2.500000 2.500000 0.000000 1 3 5 2.500000 2.500000 0.000000 2 3 1 2.600000 2.600000 0.000000 2 3 3 2.600000 2.600000 0.000000 2 3 5 2.600000 2.600000 0.000000 3 3 1 -0.000000 0.000000 0.000000 3 3 3 -0.000000 0.000000 0.000000 3 3 5 -0.000000 0.000000 0.000000 4 3 1 9.761905 9.761905 0.000000 4 3 3 9.761905 9.761905 0.000000 4 3 5 9.761905 9.761905 0.000000 5 3 1 2.152143 2.152143 0.000000 5 3 3 2.152143 2.152143 0.000000 5 3 5 2.152143 2.152143 0.000000 6 3 1 0.843508 1.000000 0.156492 6 3 3 0.981729 1.000000 0.018271 6 3 5 0.993397 1.000000 0.006603 7 3 1 1.000000 1.000000 0.000000 7 3 3 1.000000 1.000000 0.000000 7 3 5 1.000000 1.000000 0.000000 8 3 1 0.758012 0.758012 0.000000 8 3 3 0.758012 0.758012 0.000000 8 3 5 0.758012 0.758012 0.000000 9 3 1 1.671758 1.671758 0.000000 9 3 3 1.671758 1.671758 0.000000 9 3 5 1.671758 1.671758 0.000000 10 3 1 0.708638 0.750000 0.041362 10 3 3 0.745404 0.750000 0.004596 10 3 5 0.748346 0.750000 0.001654 11 3 1 4.834326 5.073214 0.238888 11 3 3 5.046143 5.073214 0.027071 11 3 5 5.063453 5.073214 0.009761 12 3 1 0.107978 0.107978 0.000000 12 3 3 0.107978 0.107978 0.000000 12 3 5 0.107978 0.107978 0.000000 13 3 1 0.000000 0.000000 0.000000 13 3 3 -0.000000 0.000000 0.000000 13 3 5 0.000000 0.000000 0.000000 14 3 1 -0.375000 -0.375000 0.000000 14 3 3 -0.375000 -0.375000 0.000000 14 3 5 -0.375000 -0.375000 0.000000 15 3 1 0.083333 0.083333 0.000000 15 3 3 0.083333 0.083333 0.000000 15 3 5 0.083333 0.083333 0.000000 16 3 1 0.708638 0.750000 0.041362 16 3 3 0.745404 0.750000 0.004596 16 3 5 0.748346 0.750000 0.001654 17 3 1 0.250000 0.250000 0.000000 17 3 3 0.250000 0.250000 0.000000 17 3 5 0.250000 0.250000 0.000000 18 3 1 0.501831 0.523599 0.021768 18 3 3 0.538509 0.523599 0.014910 18 3 5 0.531268 0.523599 0.007669 19 3 1 0.130655 0.118506 0.012149 19 3 3 0.118682 0.118506 0.000176 19 3 5 0.119561 0.118506 0.001055 20 3 1 2.500000 2.500000 0.000000 20 3 3 2.500000 2.500000 0.000000 20 3 5 2.500000 2.500000 0.000000 24 3 1 0.843508 1.000000 0.156492 24 3 3 0.981729 1.000000 0.018271 24 3 5 0.993397 1.000000 0.006603 25 3 1 1.039240 1.039240 0.000000 25 3 3 1.039240 1.039240 0.000000 25 3 5 1.039240 1.039240 0.000000 26 3 1 0.022778 0.022778 0.000000 26 3 3 0.022778 0.022778 0.000000 26 3 5 0.022778 0.022778 0.000000 27 3 1 -0.717110 -0.717110 0.000000 27 3 3 -0.717110 -0.717110 0.000000 27 3 5 -0.717110 -0.717110 0.000000 28 3 1 0.797361 0.797359 0.000002 28 3 3 0.797359 0.797359 0.000000 28 3 5 0.797359 0.797359 0.000000 29 3 1 0.287607 0.287607 0.000000 29 3 3 0.287607 0.287607 0.000000 29 3 5 0.287607 0.287607 0.000000 30 3 1 0.972704 0.972704 0.000000 30 3 3 0.972704 0.972704 0.000000 30 3 5 0.972704 0.972704 0.000000 31 3 1 0.286876 0.252580 0.034296 31 3 3 0.256268 0.252580 0.003688 31 3 5 0.253905 0.252580 0.001324 32 3 1 2.068101 1.351529 0.716572 32 3 3 1.296975 1.351529 0.054555 32 3 5 1.395480 1.351529 0.043951 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 2.548762 2.500000 0.048762 1 3 16 2.261578 2.500000 0.238422 1 3 256 2.510141 2.500000 0.010141 1 3 4096 2.549767 2.500000 0.049767 1 3 65536 2.501972 2.500000 0.001972 2 3 1 0.001387 2.600000 2.598613 2 3 16 2.242493 2.600000 0.357507 2 3 256 1.977388 2.600000 0.622612 2 3 4096 2.505521 2.600000 0.094479 2 3 65536 2.599704 2.600000 0.000296 3 3 1 0.000268 0.000000 0.000268 3 3 16 -0.478674 0.000000 0.478674 3 3 256 0.589828 0.000000 0.589828 3 3 4096 0.484442 0.000000 0.484442 3 3 65536 0.078407 0.000000 0.078407 4 3 1 0.000052 9.761905 9.761853 4 3 16 5.660965 9.761905 4.100940 4 3 256 6.173681 9.761905 3.588223 4 3 4096 9.197223 9.761905 0.564682 4 3 65536 9.754091 9.761905 0.007814 5 3 1 1.907956 2.152143 0.244187 5 3 16 2.251569 2.152143 0.099426 5 3 256 2.113108 2.152143 0.039035 5 3 4096 2.126194 2.152143 0.025949 5 3 65536 2.150585 2.152143 0.001558 6 3 1 0.050377 1.000000 0.949623 6 3 16 0.474929 1.000000 0.525071 6 3 256 0.918899 1.000000 0.081101 6 3 4096 0.980927 1.000000 0.019073 6 3 65536 1.000031 1.000000 0.000031 7 3 1 2.990067 1.000000 1.990067 7 3 16 1.180898 1.000000 0.180898 7 3 256 1.028511 1.000000 0.028511 7 3 4096 0.995086 1.000000 0.004914 7 3 65536 1.000844 1.000000 0.000844 8 3 1 0.902879 0.758012 0.144867 8 3 16 0.704209 0.758012 0.053804 8 3 256 0.770367 0.758012 0.012354 8 3 4096 0.766239 0.758012 0.008227 8 3 65536 0.758285 0.758012 0.000273 9 3 1 1.702608 1.671758 0.030850 9 3 16 1.625767 1.671758 0.045992 9 3 256 1.676198 1.671758 0.004439 9 3 4096 1.681361 1.671758 0.009602 9 3 65536 1.672163 1.671758 0.000404 10 3 1 0.341490 0.750000 0.408510 10 3 16 0.674809 0.750000 0.075191 10 3 256 0.737474 0.750000 0.012526 10 3 4096 0.748917 0.750000 0.001083 10 3 65536 0.750198 0.750000 0.000198 11 3 1 1.979769 5.073214 3.093445 11 3 16 4.070189 5.073214 1.003025 11 3 256 4.903825 5.073214 0.169389 11 3 4096 5.039679 5.073214 0.033536 11 3 65536 5.075403 5.073214 0.002189 12 3 1 -1.740787 0.107978 1.848765 12 3 16 0.390636 0.107978 0.282659 12 3 256 -0.016248 0.107978 0.124225 12 3 4096 0.042390 0.107978 0.065588 12 3 65536 0.102027 0.107978 0.005951 13 3 1 0.058492 0.000000 0.058492 13 3 16 0.036134 0.000000 0.036134 13 3 256 -0.050539 0.000000 0.050539 13 3 4096 -0.031813 0.000000 0.031813 13 3 65536 -0.000961 0.000000 0.000961 14 3 1 -0.471114 -0.375000 0.096114 14 3 16 -0.423240 -0.375000 0.048240 14 3 256 -0.365144 -0.375000 0.009856 14 3 4096 -0.380909 -0.375000 0.005909 14 3 65536 -0.375426 -0.375000 0.000426 15 3 1 0.073888 0.083333 0.009445 15 3 16 0.085039 0.083333 0.001706 15 3 256 0.082275 0.083333 0.001058 15 3 4096 0.086020 0.083333 0.002687 15 3 65536 0.083566 0.083333 0.000233 16 3 1 0.341490 0.750000 0.408510 16 3 16 0.674809 0.750000 0.075191 16 3 256 0.737474 0.750000 0.012526 16 3 4096 0.748917 0.750000 0.001083 16 3 65536 0.750198 0.750000 0.000198 17 3 1 0.050111 0.250000 0.199889 17 3 16 0.209143 0.250000 0.040857 17 3 256 0.242481 0.250000 0.007519 17 3 4096 0.249140 0.250000 0.000860 17 3 65536 0.250088 0.250000 0.000088 18 3 1 1.000000 0.523599 0.476401 18 3 16 0.812500 0.523599 0.288901 18 3 256 0.542969 0.523599 0.019370 18 3 4096 0.515625 0.523599 0.007974 18 3 65536 0.522781 0.523599 0.000817 19 3 1 0.055879 0.118506 0.062628 19 3 16 0.093760 0.118506 0.024747 19 3 256 0.116591 0.118506 0.001916 19 3 4096 0.119509 0.118506 0.001002 19 3 65536 0.118479 0.118506 0.000028 20 3 1 2.548762 2.500000 0.048762 20 3 16 2.261578 2.500000 0.238422 20 3 256 2.510141 2.500000 0.010141 20 3 4096 2.549767 2.500000 0.049767 20 3 65536 2.501972 2.500000 0.001972 24 3 1 0.050377 1.000000 0.949623 24 3 16 0.474929 1.000000 0.525071 24 3 256 0.918899 1.000000 0.081101 24 3 4096 0.980927 1.000000 0.019073 24 3 65536 1.000031 1.000000 0.000031 25 3 1 1.042311 1.039240 0.003071 25 3 16 1.037799 1.039240 0.001441 25 3 256 1.038774 1.039240 0.000466 25 3 4096 1.040443 1.039240 0.001203 25 3 65536 1.039282 1.039240 0.000042 26 3 1 0.021753 0.022778 0.001025 26 3 16 0.023459 0.022778 0.000681 26 3 256 0.022650 0.022778 0.000128 26 3 4096 0.022638 0.022778 0.000140 26 3 65536 0.022772 0.022778 0.000006 27 3 1 -0.748847 -0.717110 0.031737 27 3 16 -0.696448 -0.717110 0.020662 27 3 256 -0.720931 -0.717110 0.003821 27 3 4096 -0.721283 -0.717110 0.004173 27 3 65536 -0.717289 -0.717110 0.000179 28 3 1 0.951764 0.797359 0.154405 28 3 16 0.825174 0.797359 0.027815 28 3 256 0.802283 0.797359 0.004924 28 3 4096 0.797800 0.797359 0.000440 28 3 65536 0.797311 0.797359 0.000048 29 3 1 0.244622 0.287607 0.042985 29 3 16 0.306993 0.287607 0.019386 29 3 256 0.281554 0.287607 0.006053 29 3 4096 0.283156 0.287607 0.004451 29 3 65536 0.287367 0.287607 0.000240 30 3 1 0.994448 0.972704 0.021743 30 3 16 0.977089 0.972704 0.004385 30 3 256 0.973509 0.972704 0.000805 30 3 4096 0.972794 0.972704 0.000089 30 3 65536 0.972695 0.972704 0.000009 31 3 1 0.505110 0.252580 0.252529 31 3 16 0.272154 0.252580 0.019573 31 3 256 0.256535 0.252580 0.003955 31 3 4096 0.252583 0.252580 0.000003 31 3 65536 0.252549 0.252580 0.000031 32 3 1 3.550649 1.351529 2.199119 32 3 16 1.538406 1.351529 0.186876 32 3 256 1.301632 1.351529 0.049897 32 3 4096 1.329304 1.351529 0.022226 32 3 65536 1.349049 1.351529 0.002480 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 = ( 0.628832, 0.168501 ) Prob Dim Points Approx Exact Error 16 2 10 0.549823 0.626489 0.076666 16 2 1000 0.623861 0.626489 0.002628 16 2 100000 0.625110 0.626489 0.001380 Run number 2 Basis point Z = ( 0.017329, 0.972843 ) Prob Dim Points Approx Exact Error 16 2 10 0.746513 0.956551 0.210039 16 2 1000 0.945204 0.956551 0.011347 16 2 100000 0.956607 0.956551 0.000056 Run number 3 Basis point Z = ( 0.656158, 0.518006 ) Prob Dim Points Approx Exact Error 16 2 10 0.607324 0.524710 0.082614 16 2 1000 0.527564 0.524710 0.002854 16 2 100000 0.523386 0.524710 0.001324 Problem number = 17 Run number 1 Basis point Z = ( 0.139408, 0.321705 ) Prob Dim Points Approx Exact Error 17 2 10 0.348326 0.328483 0.019843 17 2 1000 0.333570 0.328483 0.005088 17 2 100000 0.329753 0.328483 0.001270 Run number 2 Basis point Z = ( 0.899115, 0.204426 ) Prob Dim Points Approx Exact Error 17 2 10 0.553725 0.413323 0.140402 17 2 1000 0.412068 0.413323 0.001254 17 2 100000 0.412996 0.413323 0.000327 Run number 3 Basis point Z = ( 0.142828, 0.398927 ) Prob Dim Points Approx Exact Error 17 2 10 0.217359 0.304454 0.087096 17 2 1000 0.302146 0.304454 0.002309 17 2 100000 0.303510 0.304454 0.000945 Problem number = 18 Run number 1 Basis point Z = ( 0.823610, 0.061574 ) Prob Dim Points Approx Exact Error 18 2 10 0.300000 0.785398 0.485398 18 2 1000 0.330000 0.785398 0.455398 18 2 100000 0.322120 0.785398 0.463278 Run number 2 Basis point Z = ( 0.671038, 0.539344 ) Prob Dim Points Approx Exact Error 18 2 10 0.700000 0.785398 0.085398 18 2 1000 0.693000 0.785398 0.092398 18 2 100000 0.687160 0.785398 0.098238 Run number 3 Basis point Z = ( 0.780677, 0.520424 ) Prob Dim Points Approx Exact Error 18 2 10 0.600000 0.785398 0.185398 18 2 1000 0.571000 0.785398 0.214398 18 2 100000 0.601570 0.785398 0.183828 Problem number = 19 Run number 1 Basis point Z = ( 0.908416, 0.650436 ) Prob Dim Points Approx Exact Error 19 2 10 0.332231 0.290399 0.041833 19 2 1000 0.291624 0.290399 0.001225 19 2 100000 0.289838 0.290399 0.000561 Run number 2 Basis point Z = ( 0.688979, 0.951461 ) Prob Dim Points Approx Exact Error 19 2 10 0.270316 0.310981 0.040665 19 2 1000 0.312100 0.310981 0.001119 19 2 100000 0.311377 0.310981 0.000395 Run number 3 Basis point Z = ( 0.205334, 0.502405 ) Prob Dim Points Approx Exact Error 19 2 10 0.174806 0.251871 0.077065 19 2 1000 0.260266 0.251871 0.008395 19 2 100000 0.251876 0.251871 0.000005 Problem number = 31 Run number 1 Basis point Z = ( 0.992767, 0.910087 ) Prob Dim Points Approx Exact Error 31 2 10 0.216778 0.219831 0.003053 31 2 1000 0.222826 0.219831 0.002995 31 2 100000 0.220110 0.219831 0.000279 Run number 2 Basis point Z = ( 0.939637, 0.830024 ) Prob Dim Points Approx Exact Error 31 2 10 0.257219 0.263817 0.006598 31 2 1000 0.260604 0.263817 0.003213 31 2 100000 0.264005 0.263817 0.000189 Run number 3 Basis point Z = ( 0.348532, 0.951278 ) Prob Dim Points Approx Exact Error 31 2 10 0.314374 0.290228 0.024146 31 2 1000 0.291512 0.290228 0.001284 31 2 100000 0.290592 0.290228 0.000364 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 1.000000 0.055150 5 6 1 3 0.993872 1.000000 0.006128 15 6 1 5 0.997794 1.000000 0.002206 25 6 2 1 0.892742 1.000000 0.107258 25 6 2 3 0.987782 1.000000 0.012218 225 6 2 5 0.995593 1.000000 0.004407 625 6 3 1 0.843508 1.000000 0.156492 125 6 3 3 0.981729 1.000000 0.018271 3375 6 3 5 0.993397 1.000000 0.006603 15625 6 4 1 0.796989 1.000000 0.203011 625 6 4 3 0.975713 1.000000 0.024287 50625 6 4 5 0.991205 1.000000 0.008795 390625 6 5 1 0.753035 1.000000 0.246965 3125 6 5 3 0.969735 1.000000 0.030265 759375 ??? Operation terminated by user during ==> p06_i4 at 36 In ==> p06_f at 63 p06_i4 ( 'I', '#', point_num ); In ==> p00_f at 40 value = p06_f ( dim_num, point_num, x ); In ==> p00_box_gl05 at 101 value = p00_f ( problem, dim_num, point_num, x ); In ==> test_nint_test06 at 37 result = p00_box_gl05 ( problem, dim_num, sub_num ); In ==> test_nint_test at 30 test_nint_test06 ( ); >> test_nint_test 13-Aug-2008 12:24:21 TEST_NINT_TEST MATLAB version Test the routines in 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) = 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) = prod ( (|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 2.500000 2.500000 0.000000 1 3 3 2.500000 2.500000 0.000000 1 3 5 2.500000 2.500000 0.000000 2 3 1 2.600000 2.600000 0.000000 2 3 3 2.600000 2.600000 0.000000 2 3 5 2.600000 2.600000 0.000000 3 3 1 -0.000000 0.000000 0.000000 3 3 3 -0.000000 0.000000 0.000000 3 3 5 -0.000000 0.000000 0.000000 4 3 1 9.761905 9.761905 0.000000 4 3 3 9.761905 9.761905 0.000000 4 3 5 9.761905 9.761905 0.000000 5 3 1 2.152143 2.152143 0.000000 5 3 3 2.152143 2.152143 0.000000 5 3 5 2.152143 2.152143 0.000000 6 3 1 0.843508 1.000000 0.156492 6 3 3 0.981729 1.000000 0.018271 6 3 5 0.993397 1.000000 0.006603 7 3 1 1.000000 1.000000 0.000000 7 3 3 1.000000 1.000000 0.000000 7 3 5 1.000000 1.000000 0.000000 8 3 1 0.758012 0.758012 0.000000 8 3 3 0.758012 0.758012 0.000000 8 3 5 0.758012 0.758012 0.000000 9 3 1 1.671758 1.671758 0.000000 9 3 3 1.671758 1.671758 0.000000 9 3 5 1.671758 1.671758 0.000000 10 3 1 0.708638 0.750000 0.041362 10 3 3 0.745404 0.750000 0.004596 10 3 5 0.748346 0.750000 0.001654 11 3 1 4.834326 5.073214 0.238888 11 3 3 5.046143 5.073214 0.027071 11 3 5 5.063453 5.073214 0.009761 12 3 1 0.107978 0.107978 0.000000 12 3 3 0.107978 0.107978 0.000000 12 3 5 0.107978 0.107978 0.000000 13 3 1 0.000000 0.000000 0.000000 13 3 3 -0.000000 0.000000 0.000000 13 3 5 0.000000 0.000000 0.000000 14 3 1 -0.375000 -0.375000 0.000000 14 3 3 -0.375000 -0.375000 0.000000 14 3 5 -0.375000 -0.375000 0.000000 15 3 1 0.083333 0.083333 0.000000 15 3 3 0.083333 0.083333 0.000000 15 3 5 0.083333 0.083333 0.000000 16 3 1 0.708638 0.750000 0.041362 16 3 3 0.745404 0.750000 0.004596 16 3 5 0.748346 0.750000 0.001654 17 3 1 0.250000 0.250000 0.000000 17 3 3 0.250000 0.250000 0.000000 17 3 5 0.250000 0.250000 0.000000 18 3 1 0.501831 0.523599 0.021768 18 3 3 0.538509 0.523599 0.014910 18 3 5 0.531268 0.523599 0.007669 19 3 1 0.130655 0.118506 0.012149 19 3 3 0.118682 0.118506 0.000176 19 3 5 0.119561 0.118506 0.001055 20 3 1 2.500000 2.500000 0.000000 20 3 3 2.500000 2.500000 0.000000 20 3 5 2.500000 2.500000 0.000000 24 3 1 0.843508 1.000000 0.156492 24 3 3 0.981729 1.000000 0.018271 24 3 5 0.993397 1.000000 0.006603 25 3 1 1.039240 1.039240 0.000000 25 3 3 1.039240 1.039240 0.000000 25 3 5 1.039240 1.039240 0.000000 26 3 1 0.022778 0.022778 0.000000 26 3 3 0.022778 0.022778 0.000000 26 3 5 0.022778 0.022778 0.000000 27 3 1 -0.717110 -0.717110 0.000000 27 3 3 -0.717110 -0.717110 0.000000 27 3 5 -0.717110 -0.717110 0.000000 28 3 1 0.797361 0.797359 0.000002 28 3 3 0.797359 0.797359 0.000000 28 3 5 0.797359 0.797359 0.000000 29 3 1 0.287607 0.287607 0.000000 29 3 3 0.287607 0.287607 0.000000 29 3 5 0.287607 0.287607 0.000000 30 3 1 0.972704 0.972704 0.000000 30 3 3 0.972704 0.972704 0.000000 30 3 5 0.972704 0.972704 0.000000 31 3 1 0.286876 0.252580 0.034296 31 3 3 0.256268 0.252580 0.003688 31 3 5 0.253905 0.252580 0.001324 32 3 1 2.068101 1.351529 0.716572 32 3 3 1.296975 1.351529 0.054555 32 3 5 1.395480 1.351529 0.043951 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 2.548762 2.500000 0.048762 1 3 16 2.261578 2.500000 0.238422 1 3 256 2.510141 2.500000 0.010141 1 3 4096 2.549767 2.500000 0.049767 1 3 65536 2.501972 2.500000 0.001972 2 3 1 0.001387 2.600000 2.598613 2 3 16 2.242493 2.600000 0.357507 2 3 256 1.977388 2.600000 0.622612 2 3 4096 2.505521 2.600000 0.094479 2 3 65536 2.599704 2.600000 0.000296 3 3 1 0.000268 0.000000 0.000268 3 3 16 -0.478674 0.000000 0.478674 3 3 256 0.589828 0.000000 0.589828 3 3 4096 0.484442 0.000000 0.484442 3 3 65536 0.078407 0.000000 0.078407 4 3 1 0.000052 9.761905 9.761853 4 3 16 5.660965 9.761905 4.100940 4 3 256 6.173681 9.761905 3.588223 4 3 4096 9.197223 9.761905 0.564682 4 3 65536 9.754091 9.761905 0.007814 5 3 1 1.907956 2.152143 0.244187 5 3 16 2.251569 2.152143 0.099426 5 3 256 2.113108 2.152143 0.039035 5 3 4096 2.126194 2.152143 0.025949 5 3 65536 2.150585 2.152143 0.001558 6 3 1 0.050377 1.000000 0.949623 6 3 16 0.474929 1.000000 0.525071 6 3 256 0.918899 1.000000 0.081101 6 3 4096 0.980927 1.000000 0.019073 6 3 65536 1.000031 1.000000 0.000031 7 3 1 2.990067 1.000000 1.990067 7 3 16 1.180898 1.000000 0.180898 7 3 256 1.028511 1.000000 0.028511 7 3 4096 0.995086 1.000000 0.004914 7 3 65536 1.000844 1.000000 0.000844 8 3 1 0.902879 0.758012 0.144867 8 3 16 0.704209 0.758012 0.053804 8 3 256 0.770367 0.758012 0.012354 8 3 4096 0.766239 0.758012 0.008227 8 3 65536 0.758285 0.758012 0.000273 9 3 1 1.702608 1.671758 0.030850 9 3 16 1.625767 1.671758 0.045992 9 3 256 1.676198 1.671758 0.004439 9 3 4096 1.681361 1.671758 0.009602 9 3 65536 1.672163 1.671758 0.000404 10 3 1 0.341490 0.750000 0.408510 10 3 16 0.674809 0.750000 0.075191 10 3 256 0.737474 0.750000 0.012526 10 3 4096 0.748917 0.750000 0.001083 10 3 65536 0.750198 0.750000 0.000198 11 3 1 1.979769 5.073214 3.093445 11 3 16 4.070189 5.073214 1.003025 11 3 256 4.903825 5.073214 0.169389 11 3 4096 5.039679 5.073214 0.033536 11 3 65536 5.075403 5.073214 0.002189 12 3 1 -1.740787 0.107978 1.848765 12 3 16 0.390636 0.107978 0.282659 12 3 256 -0.016248 0.107978 0.124225 12 3 4096 0.042390 0.107978 0.065588 12 3 65536 0.102027 0.107978 0.005951 13 3 1 0.058492 0.000000 0.058492 13 3 16 0.036134 0.000000 0.036134 13 3 256 -0.050539 0.000000 0.050539 13 3 4096 -0.031813 0.000000 0.031813 13 3 65536 -0.000961 0.000000 0.000961 14 3 1 -0.471114 -0.375000 0.096114 14 3 16 -0.423240 -0.375000 0.048240 14 3 256 -0.365144 -0.375000 0.009856 14 3 4096 -0.380909 -0.375000 0.005909 14 3 65536 -0.375426 -0.375000 0.000426 15 3 1 0.073888 0.083333 0.009445 15 3 16 0.085039 0.083333 0.001706 15 3 256 0.082275 0.083333 0.001058 15 3 4096 0.086020 0.083333 0.002687 15 3 65536 0.083566 0.083333 0.000233 16 3 1 0.341490 0.750000 0.408510 16 3 16 0.674809 0.750000 0.075191 16 3 256 0.737474 0.750000 0.012526 16 3 4096 0.748917 0.750000 0.001083 16 3 65536 0.750198 0.750000 0.000198 17 3 1 0.050111 0.250000 0.199889 17 3 16 0.209143 0.250000 0.040857 17 3 256 0.242481 0.250000 0.007519 17 3 4096 0.249140 0.250000 0.000860 17 3 65536 0.250088 0.250000 0.000088 18 3 1 1.000000 0.523599 0.476401 18 3 16 0.812500 0.523599 0.288901 18 3 256 0.542969 0.523599 0.019370 18 3 4096 0.515625 0.523599 0.007974 18 3 65536 0.522781 0.523599 0.000817 19 3 1 0.055879 0.118506 0.062628 19 3 16 0.093760 0.118506 0.024747 19 3 256 0.116591 0.118506 0.001916 19 3 4096 0.119509 0.118506 0.001002 19 3 65536 0.118479 0.118506 0.000028 20 3 1 2.548762 2.500000 0.048762 20 3 16 2.261578 2.500000 0.238422 20 3 256 2.510141 2.500000 0.010141 20 3 4096 2.549767 2.500000 0.049767 20 3 65536 2.501972 2.500000 0.001972 24 3 1 0.050377 1.000000 0.949623 24 3 16 0.474929 1.000000 0.525071 24 3 256 0.918899 1.000000 0.081101 24 3 4096 0.980927 1.000000 0.019073 24 3 65536 1.000031 1.000000 0.000031 25 3 1 1.042311 1.039240 0.003071 25 3 16 1.037799 1.039240 0.001441 25 3 256 1.038774 1.039240 0.000466 25 3 4096 1.040443 1.039240 0.001203 25 3 65536 1.039282 1.039240 0.000042 26 3 1 0.021753 0.022778 0.001025 26 3 16 0.023459 0.022778 0.000681 26 3 256 0.022650 0.022778 0.000128 26 3 4096 0.022638 0.022778 0.000140 26 3 65536 0.022772 0.022778 0.000006 27 3 1 -0.748847 -0.717110 0.031737 27 3 16 -0.696448 -0.717110 0.020662 27 3 256 -0.720931 -0.717110 0.003821 27 3 4096 -0.721283 -0.717110 0.004173 27 3 65536 -0.717289 -0.717110 0.000179 28 3 1 0.951764 0.797359 0.154405 28 3 16 0.825174 0.797359 0.027815 28 3 256 0.802283 0.797359 0.004924 28 3 4096 0.797800 0.797359 0.000440 28 3 65536 0.797311 0.797359 0.000048 29 3 1 0.244622 0.287607 0.042985 29 3 16 0.306993 0.287607 0.019386 29 3 256 0.281554 0.287607 0.006053 29 3 4096 0.283156 0.287607 0.004451 29 3 65536 0.287367 0.287607 0.000240 30 3 1 0.994448 0.972704 0.021743 30 3 16 0.977089 0.972704 0.004385 30 3 256 0.973509 0.972704 0.000805 30 3 4096 0.972794 0.972704 0.000089 30 3 65536 0.972695 0.972704 0.000009 31 3 1 0.505110 0.252580 0.252529 31 3 16 0.272154 0.252580 0.019573 31 3 256 0.256535 0.252580 0.003955 31 3 4096 0.252583 0.252580 0.000003 31 3 65536 0.252549 0.252580 0.000031 32 3 1 3.550649 1.351529 2.199119 32 3 16 1.538406 1.351529 0.186876 32 3 256 1.301632 1.351529 0.049897 32 3 4096 1.329304 1.351529 0.022226 32 3 65536 1.349049 1.351529 0.002480 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 = ( 0.628832, 0.168501 ) Prob Dim Points Approx Exact Error 16 2 10 0.549823 0.626489 0.076666 16 2 1000 0.623861 0.626489 0.002628 16 2 100000 0.625110 0.626489 0.001380 Run number 2 Basis point Z = ( 0.017329, 0.972843 ) Prob Dim Points Approx Exact Error 16 2 10 0.746513 0.956551 0.210039 16 2 1000 0.945204 0.956551 0.011347 16 2 100000 0.956607 0.956551 0.000056 Run number 3 Basis point Z = ( 0.656158, 0.518006 ) Prob Dim Points Approx Exact Error 16 2 10 0.607324 0.524710 0.082614 16 2 1000 0.527564 0.524710 0.002854 16 2 100000 0.523386 0.524710 0.001324 Problem number = 17 Run number 1 Basis point Z = ( 0.139408, 0.321705 ) Prob Dim Points Approx Exact Error 17 2 10 0.348326 0.328483 0.019843 17 2 1000 0.333570 0.328483 0.005088 17 2 100000 0.329753 0.328483 0.001270 Run number 2 Basis point Z = ( 0.899115, 0.204426 ) Prob Dim Points Approx Exact Error 17 2 10 0.553725 0.413323 0.140402 17 2 1000 0.412068 0.413323 0.001254 17 2 100000 0.412996 0.413323 0.000327 Run number 3 Basis point Z = ( 0.142828, 0.398927 ) Prob Dim Points Approx Exact Error 17 2 10 0.217359 0.304454 0.087096 17 2 1000 0.302146 0.304454 0.002309 17 2 100000 0.303510 0.304454 0.000945 Problem number = 18 Run number 1 Basis point Z = ( 0.823610, 0.061574 ) Prob Dim Points Approx Exact Error 18 2 10 0.300000 0.785398 0.485398 18 2 1000 0.330000 0.785398 0.455398 18 2 100000 0.322120 0.785398 0.463278 Run number 2 Basis point Z = ( 0.671038, 0.539344 ) Prob Dim Points Approx Exact Error 18 2 10 0.700000 0.785398 0.085398 18 2 1000 0.693000 0.785398 0.092398 18 2 100000 0.687160 0.785398 0.098238 Run number 3 Basis point Z = ( 0.780677, 0.520424 ) Prob Dim Points Approx Exact Error 18 2 10 0.600000 0.785398 0.185398 18 2 1000 0.571000 0.785398 0.214398 18 2 100000 0.601570 0.785398 0.183828 Problem number = 19 Run number 1 Basis point Z = ( 0.908416, 0.650436 ) Prob Dim Points Approx Exact Error 19 2 10 0.332231 0.290399 0.041833 19 2 1000 0.291624 0.290399 0.001225 19 2 100000 0.289838 0.290399 0.000561 Run number 2 Basis point Z = ( 0.688979, 0.951461 ) Prob Dim Points Approx Exact Error 19 2 10 0.270316 0.310981 0.040665 19 2 1000 0.312100 0.310981 0.001119 19 2 100000 0.311377 0.310981 0.000395 Run number 3 Basis point Z = ( 0.205334, 0.502405 ) Prob Dim Points Approx Exact Error 19 2 10 0.174806 0.251871 0.077065 19 2 1000 0.260266 0.251871 0.008395 19 2 100000 0.251876 0.251871 0.000005 Problem number = 31 Run number 1 Basis point Z = ( 0.992767, 0.910087 ) Prob Dim Points Approx Exact Error 31 2 10 0.216778 0.219831 0.003053 31 2 1000 0.222826 0.219831 0.002995 31 2 100000 0.220110 0.219831 0.000279 Run number 2 Basis point Z = ( 0.939637, 0.830024 ) Prob Dim Points Approx Exact Error 31 2 10 0.257219 0.263817 0.006598 31 2 1000 0.260604 0.263817 0.003213 31 2 100000 0.264005 0.263817 0.000189 Run number 3 Basis point Z = ( 0.348532, 0.951278 ) Prob Dim Points Approx Exact Error 31 2 10 0.314374 0.290228 0.024146 31 2 1000 0.291512 0.290228 0.001284 31 2 100000 0.290592 0.290228 0.000364 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 1.000000 0.055150 5 6 1 3 0.993872 1.000000 0.006128 15 6 1 5 0.997794 1.000000 0.002206 25 6 2 1 0.892742 1.000000 0.107258 25 6 2 3 0.987782 1.000000 0.012218 225 6 2 5 0.995593 1.000000 0.004407 625 6 3 1 0.843508 1.000000 0.156492 125 6 3 3 0.981729 1.000000 0.018271 3375 6 3 5 0.993397 1.000000 0.006603 15625 6 4 1 0.796989 1.000000 0.203011 625 6 4 3 0.975713 1.000000 0.024287 50625 6 4 5 0.991205 1.000000 0.008795 390625 TEST_NINT_TEST Normal end of execution. 13-Aug-2008 12:32:41 >>