26 February 2014 1:21:12.274 PM SPARSE_GRID_HW_PRB FORTRAN77 version Test the SPARSE_GRID_HW library. CCL_TEST: Use CCL_ORDER + CC. Clenshaw Curtis Linear (CCL) quadrature over [0,1]: Level Nodes Estimate Error 1 1 0.193334 0.977527E-02 2 3 0.191473 0.568167E-04 3 5 0.191462 0.395965E-07 4 7 0.191462 0.117826E-10 5 9 0.191462 0.652348E-14 CCS_TEST: Use CCS_ORDER + CC. Clenshaw Curtis Slow quadrature over [0,1]: Level Nodes Estimate Error 1 1 0.193334 0.977527E-02 2 3 0.191473 0.568167E-04 3 5 0.191462 0.395965E-07 4 9 0.191462 0.652348E-14 5 9 0.191462 0.652348E-14 CCE_TEST: Use CCE_ORDER + CC. Clenshaw Curtis Exponential 1D quadrature: Level Nodes Estimate Error 1 1 0.193334 0.977527E-02 2 3 0.191473 0.568167E-04 3 5 0.191462 0.395965E-07 4 9 0.191462 0.652348E-14 5 17 0.191462 0.289932E-15 GET_SEQ_TEST GET_SEQ returns all D-dimensional vectors that sum to NORM. D = 3 NORM = 6 The compositions Col 1 2 3 Row 1: 4 1 1 2: 3 2 1 3: 3 1 2 4: 2 3 1 5: 2 2 2 6: 2 1 3 7: 1 4 1 8: 1 3 2 9: 1 2 3 10: 1 1 4 GQN_TEST: Gauss-Hermite quadrature over (-oo,+oo): Level Nodes Estimate Error 1 1 0.00000 1.00000 2 2 1.00000 0.933333 3 3 9.00000 0.400000 4 4 15.0000 0.473695E-15 5 5 15.0000 0.00000 GQU_TEST: Gauss-Legendre quadrature over [0,1]: Level Nodes Estimate Error 1 1 0.193334 0.977527E-02 2 2 0.191455 0.379650E-04 3 3 0.191462 0.946584E-07 4 4 0.191462 0.174249E-09 5 5 0.191462 0.254416E-12 KPN_TEST: Kronrod-Patterson-Hermite quadrature over (-oo,+oo): Level Nodes Estimate Error 1 1 0.00000 1.00000 2 3 9.00000 0.400000 3 3 9.00000 0.400000 4 7 15.0000 0.473695E-15 5 9 15.0000 0.118424E-15 KPU_TEST: Kronrod-Patterson quadrature over [0,1]: Level Nodes Estimate Error 1 1 0.193334 0.977527E-02 2 3 0.191462 0.956087E-07 3 3 0.191462 0.956087E-07 4 7 0.191462 0.210222E-08 5 7 0.191462 0.210222E-08 NWSPGR_SIZE_TEST: NWSPGR_SIZE: size of a sparse grid, based on either: one of the built-in 1D rules, or a family of 1D rules supplied by the user. Kronrod-Patterson, [0,1], Dim 2, Level 3, Symmetric Full 10 Kronrod-Patterson, (-oo,+oo), Dim 2, Level 3, Symmetric Full 10 Gauss-Legendre, [0,1], Dim 2, Level 3, Symmetric Full 7 Gauss Hermite, (-oo,+oo), [0,1], Dim 2, Level 3, Symmetric Full 7 Clenshaw Curtis Exponential, [-1,+1], [0,1], Dim 2, Level 3, Unsymmetric Full 10 Dimension / Level table for Clenshaw Curtis Exponential Dim: 1 2 3 4 5 6 7 8 9 10 Level 1 1 1 1 1 1 1 1 1 1 1 2 3 7 10 13 16 19 22 25 28 31 3 5 25 52 87 131 184 246 317 397 486 4 9 67 195 411 746 1228 1884 2741 3826 5166 5 17 161 609 1573 3376 6430 11222 18319 28369 42101 ORDER_REPORT For each family of rules, report: L, the level index, RP, the required polynomial precision, AP, the actual polynomial precision, O, the rule order (number of points). GQN family Gauss quadrature, exponential weight, (-oo,+oo) L RP AP O 1 1 1 1 2 3 3 2 3 5 5 3 4 7 7 4 5 9 9 5 6 11 11 6 7 13 13 7 8 15 15 8 9 17 17 9 10 19 19 10 11 21 21 11 12 23 23 12 13 25 25 13 14 27 27 14 15 29 29 15 16 31 31 16 17 33 33 17 18 35 35 18 19 37 37 19 20 39 39 20 21 41 41 21 22 43 43 22 23 45 45 23 24 47 47 24 25 49 49 25 GQU family Gauss quadrature, unit weight, [0,1] L RP AP O 1 1 1 1 2 3 3 2 3 5 5 3 4 7 7 4 5 9 9 5 6 11 11 6 7 13 13 7 8 15 15 8 9 17 17 9 10 19 19 10 11 21 21 11 12 23 23 12 13 25 25 13 14 27 27 14 15 29 29 15 16 31 31 16 17 33 33 17 18 35 35 18 19 37 37 19 20 39 39 20 21 41 41 21 22 43 43 22 23 45 45 23 24 47 47 24 25 49 49 25 KPN family Gauss-Kronrod-Patterson quadrature, exponential weight, (-oo,+oo) L RP AP O 1 1 1 1 2 3 5 3 3 5 5 3 4 7 7 7 5 9 15 9 6 11 15 9 7 13 15 9 8 15 15 9 9 17 17 17 10 19 29 19 11 21 29 19 12 23 29 19 13 25 29 19 14 27 29 19 15 29 29 19 16 31 31 31 17 33 33 33 18 35 51 35 19 37 51 35 20 39 51 35 21 41 51 35 22 43 51 35 23 45 51 35 24 47 51 35 25 49 51 35 KPU family Gauss-Kronrod-Patterson quadrature, unit weight, [0,1] L RP AP O 1 1 1 1 2 3 5 3 3 5 5 3 4 7 11 7 5 9 11 7 6 11 11 7 7 13 23 15 8 15 23 15 9 17 23 15 10 19 23 15 11 21 23 15 12 23 23 15 13 25 47 31 14 27 47 31 15 29 47 31 16 31 47 31 17 33 47 31 18 35 47 31 19 37 47 31 20 39 47 31 21 41 47 31 22 43 47 31 23 45 47 31 24 47 47 31 25 49 95 63 SYMMETRIC_SPARSE_SIZE_TEST Given a symmetric sparse grid rule represented only by the points with positive values, determine the total number of points in the grid. For dimension DIM, we report R, the number of points in the positive orthant, and R2, the total number of points. DIM R R2 5 6 11 5 21 61 3 23 69 SPARSE_GRID_HW_PRB Normal end of execution. 26 February 2014 1:21:12.276 PM