16-Jan-2023 22:27:53 sparse_grid_mixed_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test sparse_grid_mixed(). COMP_NEXT_TESTS MATLAB version Call COMP_NEXT_TEST with various arguments. COMP_NEXT_TEST COMP_NEXT generates, one at a time, vectors LEVEL_1D(1:DIM_NUM) whose components add up to LEVEL. We call with: DIM_NUM = 2 0 = LEVEL_MIN <= LEVEL <= LEVEL_MAX = 0 LEVEL INDEX LEVEL_1D Vector 0 1 0 0 COMP_NEXT_TEST COMP_NEXT generates, one at a time, vectors LEVEL_1D(1:DIM_NUM) whose components add up to LEVEL. We call with: DIM_NUM = 2 0 = LEVEL_MIN <= LEVEL <= LEVEL_MAX = 1 LEVEL INDEX LEVEL_1D Vector 0 1 0 0 1 1 1 0 1 2 0 1 COMP_NEXT_TEST COMP_NEXT generates, one at a time, vectors LEVEL_1D(1:DIM_NUM) whose components add up to LEVEL. We call with: DIM_NUM = 2 1 = LEVEL_MIN <= LEVEL <= LEVEL_MAX = 2 LEVEL INDEX LEVEL_1D Vector 1 1 1 0 1 2 0 1 2 1 2 0 2 2 1 1 2 3 0 2 COMP_NEXT_TEST COMP_NEXT generates, one at a time, vectors LEVEL_1D(1:DIM_NUM) whose components add up to LEVEL. We call with: DIM_NUM = 2 2 = LEVEL_MIN <= LEVEL <= LEVEL_MAX = 3 LEVEL INDEX LEVEL_1D Vector 2 1 2 0 2 2 1 1 2 3 0 2 3 1 3 0 3 2 2 1 3 3 1 2 3 4 0 3 COMP_NEXT_TEST COMP_NEXT generates, one at a time, vectors LEVEL_1D(1:DIM_NUM) whose components add up to LEVEL. We call with: DIM_NUM = 2 3 = LEVEL_MIN <= LEVEL <= LEVEL_MAX = 4 LEVEL INDEX LEVEL_1D Vector 3 1 3 0 3 2 2 1 3 3 1 2 3 4 0 3 4 1 4 0 4 2 3 1 4 3 2 2 4 4 1 3 4 5 0 4 COMP_NEXT_TEST COMP_NEXT generates, one at a time, vectors LEVEL_1D(1:DIM_NUM) whose components add up to LEVEL. We call with: DIM_NUM = 3 0 = LEVEL_MIN <= LEVEL <= LEVEL_MAX = 0 LEVEL INDEX LEVEL_1D Vector 0 1 0 0 0 COMP_NEXT_TEST COMP_NEXT generates, one at a time, vectors LEVEL_1D(1:DIM_NUM) whose components add up to LEVEL. We call with: DIM_NUM = 3 0 = LEVEL_MIN <= LEVEL <= LEVEL_MAX = 1 LEVEL INDEX LEVEL_1D Vector 0 1 0 0 0 1 1 1 0 0 1 2 0 1 0 1 3 0 0 1 COMP_NEXT_TEST COMP_NEXT generates, one at a time, vectors LEVEL_1D(1:DIM_NUM) whose components add up to LEVEL. We call with: DIM_NUM = 3 0 = LEVEL_MIN <= LEVEL <= LEVEL_MAX = 2 LEVEL INDEX LEVEL_1D Vector 0 1 0 0 0 1 1 1 0 0 1 2 0 1 0 1 3 0 0 1 2 1 2 0 0 2 2 1 1 0 2 3 0 2 0 2 4 1 0 1 2 5 0 1 1 2 6 0 0 2 COMP_NEXT_TEST COMP_NEXT generates, one at a time, vectors LEVEL_1D(1:DIM_NUM) whose components add up to LEVEL. We call with: DIM_NUM = 3 1 = LEVEL_MIN <= LEVEL <= LEVEL_MAX = 3 LEVEL INDEX LEVEL_1D Vector 1 1 1 0 0 1 2 0 1 0 1 3 0 0 1 2 1 2 0 0 2 2 1 1 0 2 3 0 2 0 2 4 1 0 1 2 5 0 1 1 2 6 0 0 2 3 1 3 0 0 3 2 2 1 0 3 3 1 2 0 3 4 0 3 0 3 5 2 0 1 3 6 1 1 1 3 7 0 2 1 3 8 1 0 2 3 9 0 1 2 3 10 0 0 3 COMP_NEXT_TEST COMP_NEXT generates, one at a time, vectors LEVEL_1D(1:DIM_NUM) whose components add up to LEVEL. We call with: DIM_NUM = 3 2 = LEVEL_MIN <= LEVEL <= LEVEL_MAX = 4 LEVEL INDEX LEVEL_1D Vector 2 1 2 0 0 2 2 1 1 0 2 3 0 2 0 2 4 1 0 1 2 5 0 1 1 2 6 0 0 2 3 1 3 0 0 3 2 2 1 0 3 3 1 2 0 3 4 0 3 0 3 5 2 0 1 3 6 1 1 1 3 7 0 2 1 3 8 1 0 2 3 9 0 1 2 3 10 0 0 3 4 1 4 0 0 4 2 3 1 0 4 3 2 2 0 4 4 1 3 0 4 5 0 4 0 4 6 3 0 1 4 7 2 1 1 4 8 1 2 1 4 9 0 3 1 4 10 2 0 2 4 11 1 1 2 4 12 0 2 2 4 13 1 0 3 4 14 0 1 3 4 15 0 0 4 COMP_NEXT_TEST COMP_NEXT generates, one at a time, vectors LEVEL_1D(1:DIM_NUM) whose components add up to LEVEL. We call with: DIM_NUM = 4 0 = LEVEL_MIN <= LEVEL <= LEVEL_MAX = 2 LEVEL INDEX LEVEL_1D Vector 0 1 0 0 0 0 1 1 1 0 0 0 1 2 0 1 0 0 1 3 0 0 1 0 1 4 0 0 0 1 2 1 2 0 0 0 2 2 1 1 0 0 2 3 0 2 0 0 2 4 1 0 1 0 2 5 0 1 1 0 2 6 0 0 2 0 2 7 1 0 0 1 2 8 0 1 0 1 2 9 0 0 1 1 2 10 0 0 0 2 COMP_NEXT_TEST COMP_NEXT generates, one at a time, vectors LEVEL_1D(1:DIM_NUM) whose components add up to LEVEL. We call with: DIM_NUM = 4 0 = LEVEL_MIN <= LEVEL <= LEVEL_MAX = 3 LEVEL INDEX LEVEL_1D Vector 0 1 0 0 0 0 1 1 1 0 0 0 1 2 0 1 0 0 1 3 0 0 1 0 1 4 0 0 0 1 2 1 2 0 0 0 2 2 1 1 0 0 2 3 0 2 0 0 2 4 1 0 1 0 2 5 0 1 1 0 2 6 0 0 2 0 2 7 1 0 0 1 2 8 0 1 0 1 2 9 0 0 1 1 2 10 0 0 0 2 3 1 3 0 0 0 3 2 2 1 0 0 3 3 1 2 0 0 3 4 0 3 0 0 3 5 2 0 1 0 3 6 1 1 1 0 3 7 0 2 1 0 3 8 1 0 2 0 3 9 0 1 2 0 3 10 0 0 3 0 3 11 2 0 0 1 3 12 1 1 0 1 3 13 0 2 0 1 3 14 1 0 1 1 3 15 0 1 1 1 3 16 0 0 2 1 3 17 1 0 0 2 3 18 0 1 0 2 3 19 0 0 1 2 3 20 0 0 0 3 COMP_NEXT_TESTS Normal end of execution. PRODUCT_MIXED_WEIGHT_TESTS MATLAB version Call PRODUCT_MIXED_WEIGHT_TEST with various arguments. PRODUCT_MIXED_WEIGHT_TEST: Compute the weights of a mixed factor product grid. As a simple test, sum these weights. They should sum to exactly 4.000000 Spatial dimension DIM_NUM = 2 Dimension Rule Order Alpha Beta 1 1 3 2 1 5 Weight sum Expected sum Difference 4.000000e+00 4.000000e+00 8.881784e-16 PRODUCT_MIXED_WEIGHT_TEST: Compute the weights of a mixed factor product grid. As a simple test, sum these weights. They should sum to exactly 3.544908 Spatial dimension DIM_NUM = 2 Dimension Rule Order Alpha Beta 1 1 3 2 5 7 Weight sum Expected sum Difference 3.544908e+00 3.544908e+00 2.664535e-15 PRODUCT_MIXED_WEIGHT_TEST: Compute the weights of a mixed factor product grid. As a simple test, sum these weights. They should sum to exactly 2.000000 Spatial dimension DIM_NUM = 2 Dimension Rule Order Alpha Beta 1 3 3 2 7 3 Weight sum Expected sum Difference 2.000000e+00 2.000000e+00 0.000000e+00 PRODUCT_MIXED_WEIGHT_TEST: Compute the weights of a mixed factor product grid. As a simple test, sum these weights. They should sum to exactly 2.658681 Spatial dimension DIM_NUM = 2 Dimension Rule Order Alpha Beta 1 1 5 2 8 5 1.500000e+00 Weight sum Expected sum Difference 2.658681e+00 2.658681e+00 4.440892e-16 PRODUCT_MIXED_WEIGHT_TEST: Compute the weights of a mixed factor product grid. As a simple test, sum these weights. They should sum to exactly 3.141593 Spatial dimension DIM_NUM = 2 Dimension Rule Order Alpha Beta 1 2 5 2 9 5 5.000000e-01 1.500000e+00 Weight sum Expected sum Difference 3.141593e+00 3.141593e+00 3.108624e-15 PRODUCT_MIXED_WEIGHT_TEST: Compute the weights of a mixed factor product grid. As a simple test, sum these weights. They should sum to exactly 1.772454 Spatial dimension DIM_NUM = 2 Dimension Rule Order Alpha Beta 1 6 7 2.000000e+00 2 4 7 Weight sum Expected sum Difference 1.772454e+00 1.772454e+00 1.554312e-15 PRODUCT_MIXED_WEIGHT_TEST: Compute the weights of a mixed factor product grid. As a simple test, sum these weights. They should sum to exactly 7.089815 Spatial dimension DIM_NUM = 3 Dimension Rule Order Alpha Beta 1 1 2 2 3 3 3 5 3 Weight sum Expected sum Difference 7.089815e+00 7.089815e+00 8.881784e-16 PRODUCT_MIXED_WEIGHT_TEST: Compute the weights of a mixed factor product grid. As a simple test, sum these weights. They should sum to exactly 4.000000 Spatial dimension DIM_NUM = 2 Dimension Rule Order Alpha Beta 1 13 15 2 13 15 Weight sum Expected sum Difference 4.000000e+00 4.000000e+00 3.552714e-15 PRODUCT_MIXED_WEIGHT_TEST: Compute the weights of a mixed factor product grid. As a simple test, sum these weights. They should sum to exactly 4.000000 Spatial dimension DIM_NUM = 2 Dimension Rule Order Alpha Beta 1 16 15 2 16 15 Weight sum Expected sum Difference 4.000000e+00 4.000000e+00 3.552714e-15 PRODUCT_MIXED_WEIGHT_TEST: Compute the weights of a mixed factor product grid. As a simple test, sum these weights. They should sum to exactly 4.000000 Spatial dimension DIM_NUM = 2 Dimension Rule Order Alpha Beta 1 17 15 2 17 15 Weight sum Expected sum Difference 4.000000e+00 4.000000e+00 2.570388e-12 PRODUCT_MIXED_WEIGHT_TESTS Normal end of execution. SPARSE_GRID_MIXED_INDEX_TESTS MATLAB version Call SPARSE_GRID_MIXED_INDEX_TEST with various arguments. All tests will use a point equality tolerance of 1.490116e-08 SPARSE_GRID_MIXED_INDEX_TEST SPARSE_GRID_MIXED_INDEX returns index and order vectors that identify each point in a multidimensional sparse grid with mixed factors. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 1 For LEVEL_MAX = 0 1: 1 / 1, 1 / 1, For LEVEL_MAX = 1 1: 1 / 3, 1 / 1, 2: 1 / 1, 1 / 3, 3: 1 / 1, 2 / 3, 4: 1 / 1, 3 / 3, 5: 3 / 3, 1 / 1, For LEVEL_MAX = 2 1: 1 / 3, 1 / 3, 2: 1 / 3, 2 / 3, 3: 1 / 3, 3 / 3, 4: 2 / 5, 1 / 1, 5: 1 / 1, 1 / 5, 6: 1 / 1, 2 / 5, 7: 1 / 1, 3 / 5, 8: 1 / 1, 4 / 5, 9: 1 / 1, 5 / 5, 10: 4 / 5, 1 / 1, 11: 3 / 3, 1 / 3, 12: 3 / 3, 2 / 3, 13: 3 / 3, 3 / 3, SPARSE_GRID_MIXED_INDEX_TEST SPARSE_GRID_MIXED_INDEX returns index and order vectors that identify each point in a multidimensional sparse grid with mixed factors. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 3 For LEVEL_MAX = 0 1: 1 / 1, 1 / 1, For LEVEL_MAX = 1 1: 1 / 3, 1 / 1, 2: 1 / 1, 1 / 3, 3: 1 / 1, 2 / 3, 4: 1 / 1, 3 / 3, 5: 3 / 3, 1 / 1, For LEVEL_MAX = 2 1: 1 / 3, 1 / 3, 2: 1 / 3, 2 / 3, 3: 1 / 3, 3 / 3, 4: 2 / 5, 1 / 1, 5: 1 / 1, 1 / 7, 6: 1 / 1, 2 / 7, 7: 1 / 1, 3 / 7, 8: 1 / 1, 4 / 7, 9: 1 / 1, 5 / 7, 10: 1 / 1, 6 / 7, 11: 1 / 1, 7 / 7, 12: 4 / 5, 1 / 1, 13: 3 / 3, 1 / 3, 14: 3 / 3, 2 / 3, 15: 3 / 3, 3 / 3, SPARSE_GRID_MIXED_INDEX_TEST SPARSE_GRID_MIXED_INDEX returns index and order vectors that identify each point in a multidimensional sparse grid with mixed factors. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 4 For LEVEL_MAX = 0 1: 1 / 1, 1 / 1, For LEVEL_MAX = 1 1: 1 / 3, 1 / 1, 2: 1 / 1, 1 / 3, 3: 1 / 1, 2 / 3, 4: 1 / 1, 3 / 3, 5: 3 / 3, 1 / 1, For LEVEL_MAX = 2 1: 1 / 3, 1 / 3, 2: 1 / 3, 2 / 3, 3: 1 / 3, 3 / 3, 4: 2 / 5, 1 / 1, 5: 1 / 1, 1 / 5, 6: 2 / 3, 1 / 3, 7: 1 / 1, 2 / 5, 8: 1 / 1, 3 / 5, 9: 1 / 1, 4 / 5, 10: 2 / 3, 3 / 3, 11: 1 / 1, 5 / 5, 12: 4 / 5, 1 / 1, 13: 3 / 3, 1 / 3, 14: 3 / 3, 2 / 3, 15: 3 / 3, 3 / 3, SPARSE_GRID_MIXED_INDEX_TEST SPARSE_GRID_MIXED_INDEX returns index and order vectors that identify each point in a multidimensional sparse grid with mixed factors. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 7 For LEVEL_MAX = 0 1: 1 / 1, 1 / 1, For LEVEL_MAX = 1 1: 1 / 3, 1 / 1, 2: 1 / 1, 1 / 3, 3: 2 / 3, 1 / 1, 4: 1 / 1, 2 / 3, 5: 1 / 1, 3 / 3, 6: 3 / 3, 1 / 1, For LEVEL_MAX = 2 1: 1 / 3, 1 / 3, 2: 1 / 5, 1 / 1, 3: 1 / 3, 2 / 3, 4: 1 / 3, 3 / 3, 5: 2 / 5, 1 / 1, 6: 1 / 1, 1 / 5, 7: 2 / 3, 1 / 3, 8: 3 / 5, 1 / 1, 9: 1 / 1, 2 / 5, 10: 2 / 3, 2 / 3, 11: 1 / 1, 3 / 5, 12: 2 / 3, 3 / 3, 13: 1 / 1, 4 / 5, 14: 1 / 1, 5 / 5, 15: 4 / 5, 1 / 1, 16: 3 / 3, 1 / 3, 17: 5 / 5, 1 / 1, 18: 3 / 3, 2 / 3, 19: 3 / 3, 3 / 3, SPARSE_GRID_MIXED_INDEX_TEST SPARSE_GRID_MIXED_INDEX returns index and order vectors that identify each point in a multidimensional sparse grid with mixed factors. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 8 1.500000e+00 For LEVEL_MAX = 0 1: 1 / 1, 1 / 1, For LEVEL_MAX = 1 1: 1 / 3, 1 / 1, 2: 1 / 1, 1 / 3, 3: 2 / 3, 1 / 1, 4: 1 / 1, 2 / 3, 5: 1 / 1, 3 / 3, 6: 3 / 3, 1 / 1, For LEVEL_MAX = 2 1: 1 / 3, 1 / 3, 2: 1 / 5, 1 / 1, 3: 1 / 3, 2 / 3, 4: 1 / 3, 3 / 3, 5: 2 / 5, 1 / 1, 6: 1 / 1, 1 / 5, 7: 2 / 3, 1 / 3, 8: 1 / 1, 2 / 5, 9: 3 / 5, 1 / 1, 10: 2 / 3, 2 / 3, 11: 1 / 1, 3 / 5, 12: 2 / 3, 3 / 3, 13: 1 / 1, 4 / 5, 14: 1 / 1, 5 / 5, 15: 4 / 5, 1 / 1, 16: 3 / 3, 1 / 3, 17: 5 / 5, 1 / 1, 18: 3 / 3, 2 / 3, 19: 3 / 3, 3 / 3, SPARSE_GRID_MIXED_INDEX_TEST SPARSE_GRID_MIXED_INDEX returns index and order vectors that identify each point in a multidimensional sparse grid with mixed factors. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 2 2 9 5.000000e-01 1.500000e+00 For LEVEL_MAX = 0 1: 1 / 1, 1 / 1, For LEVEL_MAX = 1 1: 1 / 3, 1 / 1, 2: 1 / 1, 1 / 3, 3: 1 / 1, 2 / 3, 4: 2 / 3, 1 / 1, 5: 1 / 1, 3 / 3, 6: 3 / 3, 1 / 1, For LEVEL_MAX = 2 1: 1 / 7, 1 / 1, 2: 1 / 3, 1 / 3, 3: 1 / 3, 2 / 3, 4: 2 / 7, 1 / 1, 5: 1 / 3, 3 / 3, 6: 3 / 7, 1 / 1, 7: 1 / 1, 1 / 5, 8: 2 / 3, 1 / 3, 9: 1 / 1, 2 / 5, 10: 1 / 1, 3 / 5, 11: 2 / 3, 2 / 3, 12: 4 / 7, 1 / 1, 13: 1 / 1, 4 / 5, 14: 2 / 3, 3 / 3, 15: 1 / 1, 5 / 5, 16: 5 / 7, 1 / 1, 17: 3 / 3, 1 / 3, 18: 3 / 3, 2 / 3, 19: 6 / 7, 1 / 1, 20: 3 / 3, 3 / 3, 21: 7 / 7, 1 / 1, SPARSE_GRID_MIXED_INDEX_TEST SPARSE_GRID_MIXED_INDEX returns index and order vectors that identify each point in a multidimensional sparse grid with mixed factors. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 6 2.000000e+00 2 4 For LEVEL_MAX = 0 1: 1 / 1, 1 / 1, For LEVEL_MAX = 1 1: 1 / 3, 1 / 1, 2: 1 / 1, 1 / 3, 3: 1 / 1, 2 / 3, 4: 1 / 1, 3 / 3, 5: 2 / 3, 1 / 1, 6: 3 / 3, 1 / 1, For LEVEL_MAX = 2 1: 1 / 5, 1 / 1, 2: 1 / 3, 1 / 3, 3: 1 / 3, 2 / 3, 4: 1 / 3, 3 / 3, 5: 2 / 5, 1 / 1, 6: 1 / 1, 1 / 5, 7: 1 / 1, 1 / 3, 8: 1 / 1, 2 / 5, 9: 1 / 1, 3 / 5, 10: 1 / 1, 4 / 5, 11: 1 / 1, 3 / 3, 12: 1 / 1, 5 / 5, 13: 2 / 3, 1 / 3, 14: 2 / 3, 2 / 3, 15: 2 / 3, 3 / 3, 16: 3 / 5, 1 / 1, 17: 4 / 5, 1 / 1, 18: 3 / 3, 1 / 3, 19: 3 / 3, 2 / 3, 20: 3 / 3, 3 / 3, 21: 5 / 5, 1 / 1, SPARSE_GRID_MIXED_INDEX_TEST SPARSE_GRID_MIXED_INDEX returns index and order vectors that identify each point in a multidimensional sparse grid with mixed factors. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 2 3 5 For LEVEL_MAX = 0 1: 1 / 1, 1 / 1, 1 / 1, For LEVEL_MAX = 1 1: 1 / 3, 1 / 1, 1 / 1, 2: 1 / 1, 1 / 3, 1 / 1, 3: 1 / 1, 1 / 1, 1 / 3, 4: 1 / 1, 1 / 1, 2 / 3, 5: 1 / 1, 1 / 1, 3 / 3, 6: 1 / 1, 3 / 3, 1 / 1, 7: 3 / 3, 1 / 1, 1 / 1, For LEVEL_MAX = 2 1: 1 / 3, 1 / 3, 1 / 1, 2: 1 / 3, 1 / 1, 1 / 3, 3: 1 / 3, 1 / 1, 2 / 3, 4: 1 / 3, 1 / 1, 3 / 3, 5: 1 / 3, 3 / 3, 1 / 1, 6: 2 / 5, 1 / 1, 1 / 1, 7: 1 / 1, 1 / 7, 1 / 1, 8: 1 / 1, 1 / 3, 1 / 3, 9: 1 / 1, 1 / 3, 2 / 3, 10: 1 / 1, 1 / 3, 3 / 3, 11: 1 / 1, 3 / 7, 1 / 1, 12: 1 / 1, 1 / 1, 1 / 5, 13: 1 / 1, 2 / 3, 1 / 3, 14: 1 / 1, 1 / 1, 2 / 5, 15: 1 / 1, 1 / 1, 3 / 5, 16: 1 / 1, 1 / 1, 4 / 5, 17: 1 / 1, 2 / 3, 3 / 3, 18: 1 / 1, 1 / 1, 5 / 5, 19: 1 / 1, 5 / 7, 1 / 1, 20: 1 / 1, 3 / 3, 1 / 3, 21: 1 / 1, 3 / 3, 2 / 3, 22: 1 / 1, 3 / 3, 3 / 3, 23: 1 / 1, 7 / 7, 1 / 1, 24: 4 / 5, 1 / 1, 1 / 1, 25: 3 / 3, 1 / 3, 1 / 1, 26: 3 / 3, 1 / 1, 1 / 3, 27: 3 / 3, 1 / 1, 2 / 3, 28: 3 / 3, 1 / 1, 3 / 3, 29: 3 / 3, 3 / 3, 1 / 1, SPARSE_GRID_MIXED_INDEX_TEST SPARSE_GRID_MIXED_INDEX returns index and order vectors that identify each point in a multidimensional sparse grid with mixed factors. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 13 2 13 For LEVEL_MAX = 3 1: 1 / 7, 1 / 1, 2: 1 / 3, 1 / 3, 3: 1 / 3, 2 / 3, 4: 1 / 3, 3 / 3, 5: 3 / 7, 1 / 1, 6: 1 / 1, 1 / 7, 7: 1 / 1, 2 / 7, 8: 1 / 1, 3 / 7, 9: 1 / 1, 4 / 7, 10: 1 / 1, 5 / 7, 11: 1 / 1, 6 / 7, 12: 1 / 1, 7 / 7, 13: 5 / 7, 1 / 1, 14: 3 / 3, 1 / 3, 15: 3 / 3, 2 / 3, 16: 3 / 3, 3 / 3, 17: 7 / 7, 1 / 1, SPARSE_GRID_MIXED_INDEX_TEST SPARSE_GRID_MIXED_INDEX returns index and order vectors that identify each point in a multidimensional sparse grid with mixed factors. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 16 2 16 For LEVEL_MAX = 3 1: 1 / 15, 1 / 1, 2: 1 / 7, 1 / 3, 3: 1 / 7, 2 / 3, 4: 1 / 7, 3 / 3, 5: 3 / 15, 1 / 1, 6: 1 / 3, 1 / 7, 7: 1 / 3, 2 / 7, 8: 1 / 3, 3 / 7, 9: 1 / 3, 4 / 7, 10: 1 / 3, 5 / 7, 11: 1 / 3, 6 / 7, 12: 1 / 3, 7 / 7, 13: 5 / 15, 1 / 1, 14: 3 / 7, 1 / 3, 15: 3 / 7, 2 / 3, 16: 3 / 7, 3 / 3, 17: 7 / 15, 1 / 1, 18: 1 / 1, 1 / 15, 19: 1 / 1, 2 / 15, 20: 1 / 1, 3 / 15, 21: 1 / 1, 4 / 15, 22: 1 / 1, 5 / 15, 23: 1 / 1, 6 / 15, 24: 1 / 1, 7 / 15, 25: 1 / 1, 8 / 15, 26: 1 / 1, 9 / 15, 27: 1 / 1, 10 / 15, 28: 1 / 1, 11 / 15, 29: 1 / 1, 12 / 15, 30: 1 / 1, 13 / 15, 31: 1 / 1, 14 / 15, 32: 1 / 1, 15 / 15, 33: 9 / 15, 1 / 1, 34: 5 / 7, 1 / 3, 35: 5 / 7, 2 / 3, 36: 5 / 7, 3 / 3, 37: 11 / 15, 1 / 1, 38: 3 / 3, 1 / 7, 39: 3 / 3, 2 / 7, 40: 3 / 3, 3 / 7, 41: 3 / 3, 4 / 7, 42: 3 / 3, 5 / 7, 43: 3 / 3, 6 / 7, 44: 3 / 3, 7 / 7, 45: 13 / 15, 1 / 1, 46: 7 / 7, 1 / 3, 47: 7 / 7, 2 / 3, 48: 7 / 7, 3 / 3, 49: 15 / 15, 1 / 1, SPARSE_GRID_MIXED_INDEX_TEST SPARSE_GRID_MIXED_INDEX returns index and order vectors that identify each point in a multidimensional sparse grid with mixed factors. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 17 2 17 For LEVEL_MAX = 4 1: 2 / 3, 2 / 7, 2: 2 / 3, 4 / 7, 3: 2 / 3, 6 / 7, 4: 2 / 3, 1 / 7, 5: 2 / 3, 7 / 7, 6: 2 / 3, 5 / 7, 7: 2 / 3, 3 / 7, 8: 8 / 9, 1 / 1, 9: 4 / 5, 2 / 5, 10: 4 / 5, 4 / 5, 11: 4 / 5, 1 / 5, 12: 4 / 5, 5 / 5, 13: 4 / 5, 3 / 5, 14: 6 / 7, 2 / 3, 15: 6 / 7, 1 / 3, 16: 6 / 7, 3 / 3, 17: 1 / 1, 2 / 9, 18: 1 / 1, 8 / 9, 19: 1 / 1, 4 / 9, 20: 1 / 1, 6 / 9, 21: 1 / 1, 1 / 9, 22: 1 / 1, 7 / 9, 23: 1 / 1, 5 / 9, 24: 1 / 1, 9 / 9, 25: 1 / 1, 3 / 9, 26: 7 / 7, 2 / 3, 27: 7 / 7, 1 / 3, 28: 7 / 7, 3 / 3, 29: 5 / 5, 2 / 5, 30: 5 / 5, 4 / 5, 31: 5 / 5, 1 / 5, 32: 5 / 5, 5 / 5, 33: 5 / 5, 3 / 5, 34: 9 / 9, 1 / 1, 35: 3 / 3, 2 / 7, 36: 3 / 3, 4 / 7, 37: 3 / 3, 6 / 7, 38: 3 / 3, 1 / 7, 39: 3 / 3, 7 / 7, 40: 3 / 3, 5 / 7, 41: 3 / 3, 3 / 7, SPARSE_GRID_MIXED_INDEX_TESTS Normal end of execution. SPARSE_GRID_MIXED_POINT_TESTS MATLAB version Call SPARSE_GRID_MIXED_POINT_TEST with various arguments. All tests will use a point equality tolerance of 1.490116e-08 SPARSE_GRID_MIXED_POINT_TEST SPARSE_GRID_MIXED_POINT returns an array containing the points that form a multidimensional sparse grid of mixed factors. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 1 For LEVEL_MAX = 0 1: 0.000000e+00, 0.000000e+00, For LEVEL_MAX = 1 1: -1.000000e+00, 0.000000e+00, 2: 0.000000e+00, -1.000000e+00, 3: 0.000000e+00, 0.000000e+00, 4: 0.000000e+00, 1.000000e+00, 5: 1.000000e+00, 0.000000e+00, For LEVEL_MAX = 2 1: -1.000000e+00, -1.000000e+00, 2: -1.000000e+00, 0.000000e+00, 3: -1.000000e+00, 1.000000e+00, 4: -7.071068e-01, 0.000000e+00, 5: 0.000000e+00, -1.000000e+00, 6: 0.000000e+00, -7.071068e-01, 7: 0.000000e+00, 0.000000e+00, 8: 0.000000e+00, 7.071068e-01, 9: 0.000000e+00, 1.000000e+00, 10: 7.071068e-01, 0.000000e+00, 11: 1.000000e+00, -1.000000e+00, 12: 1.000000e+00, 0.000000e+00, 13: 1.000000e+00, 1.000000e+00, SPARSE_GRID_MIXED_POINT_TEST SPARSE_GRID_MIXED_POINT returns an array containing the points that form a multidimensional sparse grid of mixed factors. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 3 For LEVEL_MAX = 0 1: 0.000000e+00, 0.000000e+00, For LEVEL_MAX = 1 1: -1.000000e+00, 0.000000e+00, 2: 0.000000e+00, -7.745967e-01, 3: 0.000000e+00, 0.000000e+00, 4: 0.000000e+00, 7.745967e-01, 5: 1.000000e+00, 0.000000e+00, For LEVEL_MAX = 2 1: -1.000000e+00, -7.745967e-01, 2: -1.000000e+00, 0.000000e+00, 3: -1.000000e+00, 7.745967e-01, 4: -7.071068e-01, 0.000000e+00, 5: 0.000000e+00, -9.604913e-01, 6: 0.000000e+00, -7.745967e-01, 7: 0.000000e+00, -4.342437e-01, 8: 0.000000e+00, 0.000000e+00, 9: 0.000000e+00, 4.342437e-01, 10: 0.000000e+00, 7.745967e-01, 11: 0.000000e+00, 9.604913e-01, 12: 7.071068e-01, 0.000000e+00, 13: 1.000000e+00, -7.745967e-01, 14: 1.000000e+00, 0.000000e+00, 15: 1.000000e+00, 7.745967e-01, SPARSE_GRID_MIXED_POINT_TEST SPARSE_GRID_MIXED_POINT returns an array containing the points that form a multidimensional sparse grid of mixed factors. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 4 For LEVEL_MAX = 0 1: 0.000000e+00, 0.000000e+00, For LEVEL_MAX = 1 1: -1.000000e+00, 0.000000e+00, 2: 0.000000e+00, -7.745967e-01, 3: 0.000000e+00, 1.994932e-17, 4: 0.000000e+00, 7.745967e-01, 5: 1.000000e+00, 0.000000e+00, For LEVEL_MAX = 2 1: -1.000000e+00, -7.745967e-01, 2: -1.000000e+00, 1.994932e-17, 3: -1.000000e+00, 7.745967e-01, 4: -7.071068e-01, 0.000000e+00, 5: 0.000000e+00, -9.061798e-01, 6: 0.000000e+00, -7.745967e-01, 7: 0.000000e+00, -5.384693e-01, 8: 0.000000e+00, -1.081854e-16, 9: 0.000000e+00, 5.384693e-01, 10: 0.000000e+00, 7.745967e-01, 11: 0.000000e+00, 9.061798e-01, 12: 7.071068e-01, 0.000000e+00, 13: 1.000000e+00, -7.745967e-01, 14: 1.000000e+00, 1.994932e-17, 15: 1.000000e+00, 7.745967e-01, SPARSE_GRID_MIXED_POINT_TEST SPARSE_GRID_MIXED_POINT returns an array containing the points that form a multidimensional sparse grid of mixed factors. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 7 For LEVEL_MAX = 0 1: 0.000000e+00, 1.000000e+00, For LEVEL_MAX = 1 1: -1.000000e+00, 1.000000e+00, 2: 0.000000e+00, 4.157746e-01, 3: 0.000000e+00, 1.000000e+00, 4: 0.000000e+00, 2.294280e+00, 5: 0.000000e+00, 6.289945e+00, 6: 1.000000e+00, 1.000000e+00, For LEVEL_MAX = 2 1: -1.000000e+00, 4.157746e-01, 2: -1.000000e+00, 1.000000e+00, 3: -1.000000e+00, 2.294280e+00, 4: -1.000000e+00, 6.289945e+00, 5: -7.071068e-01, 1.000000e+00, 6: 0.000000e+00, 2.635603e-01, 7: 0.000000e+00, 4.157746e-01, 8: 0.000000e+00, 1.000000e+00, 9: 0.000000e+00, 1.413403e+00, 10: 0.000000e+00, 2.294280e+00, 11: 0.000000e+00, 3.596426e+00, 12: 0.000000e+00, 6.289945e+00, 13: 0.000000e+00, 7.085810e+00, 14: 0.000000e+00, 1.264080e+01, 15: 7.071068e-01, 1.000000e+00, 16: 1.000000e+00, 4.157746e-01, 17: 1.000000e+00, 1.000000e+00, 18: 1.000000e+00, 2.294280e+00, 19: 1.000000e+00, 6.289945e+00, SPARSE_GRID_MIXED_POINT_TEST SPARSE_GRID_MIXED_POINT returns an array containing the points that form a multidimensional sparse grid of mixed factors. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 8 1.500000e+00 For LEVEL_MAX = 0 1: 0.000000e+00, 2.500000e+00, For LEVEL_MAX = 1 1: -1.000000e+00, 2.500000e+00, 2: 0.000000e+00, 1.220402e+00, 3: 0.000000e+00, 2.500000e+00, 4: 0.000000e+00, 3.808881e+00, 5: 0.000000e+00, 8.470717e+00, 6: 1.000000e+00, 2.500000e+00, For LEVEL_MAX = 2 1: -1.000000e+00, 1.220402e+00, 2: -1.000000e+00, 2.500000e+00, 3: -1.000000e+00, 3.808881e+00, 4: -1.000000e+00, 8.470717e+00, 5: -7.071068e-01, 2.500000e+00, 6: 0.000000e+00, 8.176318e-01, 7: 0.000000e+00, 1.220402e+00, 8: 0.000000e+00, 2.472334e+00, 9: 0.000000e+00, 2.500000e+00, 10: 0.000000e+00, 3.808881e+00, 11: 0.000000e+00, 5.116006e+00, 12: 0.000000e+00, 8.470717e+00, 13: 0.000000e+00, 9.044147e+00, 14: 0.000000e+00, 1.504988e+01, 15: 7.071068e-01, 2.500000e+00, 16: 1.000000e+00, 1.220402e+00, 17: 1.000000e+00, 2.500000e+00, 18: 1.000000e+00, 3.808881e+00, 19: 1.000000e+00, 8.470717e+00, SPARSE_GRID_MIXED_POINT_TEST SPARSE_GRID_MIXED_POINT returns an array containing the points that form a multidimensional sparse grid of mixed factors. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 17 For LEVEL_MAX = 0 1: 0.000000e+00, 0.000000e+00, For LEVEL_MAX = 1 1: -1.000000e+00, 0.000000e+00, 2: 0.000000e+00, -1.000000e+00, 3: 0.000000e+00, 0.000000e+00, 4: 0.000000e+00, 1.000000e+00, 5: 1.000000e+00, 0.000000e+00, For LEVEL_MAX = 2 1: -1.000000e+00, -1.000000e+00, 2: -1.000000e+00, 0.000000e+00, 3: -1.000000e+00, 1.000000e+00, 4: -7.071068e-01, 0.000000e+00, 5: 0.000000e+00, -1.000000e+00, 6: 0.000000e+00, -7.071068e-01, 7: 0.000000e+00, 0.000000e+00, 8: 0.000000e+00, 7.071068e-01, 9: 0.000000e+00, 1.000000e+00, 10: 7.071068e-01, 0.000000e+00, 11: 1.000000e+00, -1.000000e+00, 12: 1.000000e+00, 0.000000e+00, 13: 1.000000e+00, 1.000000e+00, SPARSE_GRID_MIXED_POINT_TEST SPARSE_GRID_MIXED_POINT returns an array containing the points that form a multidimensional sparse grid of mixed factors. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 2 2 9 5.000000e-01 1.500000e+00 For LEVEL_MAX = 0 1: 0.000000e+00, 2.500000e-01, For LEVEL_MAX = 1 1: -7.071068e-01, 2.500000e-01, 2: 0.000000e+00, -5.379862e-01, 3: 0.000000e+00, 1.528289e-01, 4: 0.000000e+00, 2.500000e-01, 5: 0.000000e+00, 7.601573e-01, 6: 7.071068e-01, 2.500000e-01, For LEVEL_MAX = 2 1: -9.238795e-01, 2.500000e-01, 2: -7.071068e-01, -5.379862e-01, 3: -7.071068e-01, 1.528289e-01, 4: -7.071068e-01, 2.500000e-01, 5: -7.071068e-01, 7.601573e-01, 6: -3.826834e-01, 2.500000e-01, 7: 0.000000e+00, -7.695413e-01, 8: 0.000000e+00, -5.379862e-01, 9: 0.000000e+00, -3.708136e-01, 10: 0.000000e+00, 1.100274e-01, 11: 0.000000e+00, 1.528289e-01, 12: 0.000000e+00, 2.500000e-01, 13: 0.000000e+00, 5.629059e-01, 14: 0.000000e+00, 7.601573e-01, 15: 0.000000e+00, 8.840883e-01, 16: 3.826834e-01, 2.500000e-01, 17: 7.071068e-01, -5.379862e-01, 18: 7.071068e-01, 1.528289e-01, 19: 7.071068e-01, 2.500000e-01, 20: 7.071068e-01, 7.601573e-01, 21: 9.238795e-01, 2.500000e-01, SPARSE_GRID_MIXED_POINT_TEST SPARSE_GRID_MIXED_POINT returns an array containing the points that form a multidimensional sparse grid of mixed factors. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 6 2.000000e+00 2 4 For LEVEL_MAX = 0 1: 0.000000e+00, 0.000000e+00, For LEVEL_MAX = 1 1: -1.581139e+00, 0.000000e+00, 2: 0.000000e+00, -7.745967e-01, 3: 0.000000e+00, 1.994932e-17, 4: 0.000000e+00, 7.745967e-01, 5: 1.370432e-16, 0.000000e+00, 6: 1.581139e+00, 0.000000e+00, For LEVEL_MAX = 2 1: -2.317505e+00, 0.000000e+00, 2: -1.581139e+00, -7.745967e-01, 3: -1.581139e+00, 1.994932e-17, 4: -1.581139e+00, 7.745967e-01, 5: -1.276390e+00, 0.000000e+00, 6: 0.000000e+00, -9.061798e-01, 7: 0.000000e+00, -7.745967e-01, 8: 0.000000e+00, -5.384693e-01, 9: 0.000000e+00, -1.081854e-16, 10: 0.000000e+00, 5.384693e-01, 11: 0.000000e+00, 7.745967e-01, 12: 0.000000e+00, 9.061798e-01, 13: 1.370432e-16, -7.745967e-01, 14: 1.370432e-16, 1.994932e-17, 15: 1.370432e-16, 7.745967e-01, 16: 5.112030e-16, 0.000000e+00, 17: 1.276390e+00, 0.000000e+00, 18: 1.581139e+00, -7.745967e-01, 19: 1.581139e+00, 1.994932e-17, 20: 1.581139e+00, 7.745967e-01, 21: 2.317505e+00, 0.000000e+00, SPARSE_GRID_MIXED_POINT_TEST SPARSE_GRID_MIXED_POINT returns an array containing the points that form a multidimensional sparse grid of mixed factors. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 2 3 5 For LEVEL_MAX = 0 1: 0.000000e+00, 0.000000e+00, 0.000000e+00, For LEVEL_MAX = 1 1: -1.000000e+00, 0.000000e+00, 0.000000e+00, 2: 0.000000e+00, -7.071068e-01, 0.000000e+00, 3: 0.000000e+00, 0.000000e+00, -1.224745e+00, 4: 0.000000e+00, 0.000000e+00, 0.000000e+00, 5: 0.000000e+00, 0.000000e+00, 1.224745e+00, 6: 0.000000e+00, 7.071068e-01, 0.000000e+00, 7: 1.000000e+00, 0.000000e+00, 0.000000e+00, For LEVEL_MAX = 2 1: -1.000000e+00, -7.071068e-01, 0.000000e+00, 2: -1.000000e+00, 0.000000e+00, -1.224745e+00, 3: -1.000000e+00, 0.000000e+00, 0.000000e+00, 4: -1.000000e+00, 0.000000e+00, 1.224745e+00, 5: -1.000000e+00, 7.071068e-01, 0.000000e+00, 6: -7.071068e-01, 0.000000e+00, 0.000000e+00, 7: 0.000000e+00, -9.238795e-01, 0.000000e+00, 8: 0.000000e+00, -7.071068e-01, -1.224745e+00, 9: 0.000000e+00, -7.071068e-01, 0.000000e+00, 10: 0.000000e+00, -7.071068e-01, 1.224745e+00, 11: 0.000000e+00, -3.826834e-01, 0.000000e+00, 12: 0.000000e+00, 0.000000e+00, -2.020183e+00, 13: 0.000000e+00, 0.000000e+00, -1.224745e+00, 14: 0.000000e+00, 0.000000e+00, -9.585725e-01, 15: 0.000000e+00, 0.000000e+00, 0.000000e+00, 16: 0.000000e+00, 0.000000e+00, 9.585725e-01, 17: 0.000000e+00, 0.000000e+00, 1.224745e+00, 18: 0.000000e+00, 0.000000e+00, 2.020183e+00, 19: 0.000000e+00, 3.826834e-01, 0.000000e+00, 20: 0.000000e+00, 7.071068e-01, -1.224745e+00, 21: 0.000000e+00, 7.071068e-01, 0.000000e+00, 22: 0.000000e+00, 7.071068e-01, 1.224745e+00, 23: 0.000000e+00, 9.238795e-01, 0.000000e+00, 24: 7.071068e-01, 0.000000e+00, 0.000000e+00, 25: 1.000000e+00, -7.071068e-01, 0.000000e+00, 26: 1.000000e+00, 0.000000e+00, -1.224745e+00, 27: 1.000000e+00, 0.000000e+00, 0.000000e+00, 28: 1.000000e+00, 0.000000e+00, 1.224745e+00, 29: 1.000000e+00, 7.071068e-01, 0.000000e+00, SPARSE_GRID_MIXED_POINT_TEST SPARSE_GRID_MIXED_POINT returns an array containing the points that form a multidimensional sparse grid of mixed factors. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 13 2 13 For LEVEL_MAX = 4 1: -9.604913e-01, -7.745967e-01, 2: -9.604913e-01, 0.000000e+00, 3: -9.604913e-01, 7.745967e-01, 4: -7.745967e-01, -9.604913e-01, 5: -7.745967e-01, -7.745967e-01, 6: -7.745967e-01, -4.342437e-01, 7: -7.745967e-01, 0.000000e+00, 8: -7.745967e-01, 4.342437e-01, 9: -7.745967e-01, 7.745967e-01, 10: -7.745967e-01, 9.604913e-01, 11: -4.342437e-01, -7.745967e-01, 12: -4.342437e-01, 0.000000e+00, 13: -4.342437e-01, 7.745967e-01, 14: 0.000000e+00, -9.604913e-01, 15: 0.000000e+00, -7.745967e-01, 16: 0.000000e+00, -4.342437e-01, 17: 0.000000e+00, 0.000000e+00, 18: 0.000000e+00, 4.342437e-01, 19: 0.000000e+00, 7.745967e-01, 20: 0.000000e+00, 9.604913e-01, 21: 4.342437e-01, -7.745967e-01, 22: 4.342437e-01, 0.000000e+00, 23: 4.342437e-01, 7.745967e-01, 24: 7.745967e-01, -9.604913e-01, 25: 7.745967e-01, -7.745967e-01, 26: 7.745967e-01, -4.342437e-01, 27: 7.745967e-01, 0.000000e+00, 28: 7.745967e-01, 4.342437e-01, 29: 7.745967e-01, 7.745967e-01, 30: 7.745967e-01, 9.604913e-01, 31: 9.604913e-01, -7.745967e-01, 32: 9.604913e-01, 0.000000e+00, 33: 9.604913e-01, 7.745967e-01, SPARSE_GRID_MIXED_POINT_TEST SPARSE_GRID_MIXED_POINT returns an array containing the points that form a multidimensional sparse grid of mixed factors. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 16 2 16 For LEVEL_MAX = 4 1: -9.938320e-01, -7.745967e-01, 2: -9.938320e-01, 0.000000e+00, 3: -9.938320e-01, 7.745967e-01, 4: -9.604913e-01, -9.604913e-01, 5: -9.604913e-01, -7.745967e-01, 6: -9.604913e-01, -4.342437e-01, 7: -9.604913e-01, 0.000000e+00, 8: -9.604913e-01, 4.342437e-01, 9: -9.604913e-01, 7.745967e-01, 10: -9.604913e-01, 9.604913e-01, 11: -8.884592e-01, -7.745967e-01, 12: -8.884592e-01, 0.000000e+00, 13: -8.884592e-01, 7.745967e-01, 14: -7.745967e-01, -9.938320e-01, 15: -7.745967e-01, -9.604913e-01, 16: -7.745967e-01, -8.884592e-01, 17: -7.745967e-01, -7.745967e-01, 18: -7.745967e-01, -6.211029e-01, 19: -7.745967e-01, -4.342437e-01, 20: -7.745967e-01, -2.233867e-01, 21: -7.745967e-01, 0.000000e+00, 22: -7.745967e-01, 2.233867e-01, 23: -7.745967e-01, 4.342437e-01, 24: -7.745967e-01, 6.211029e-01, 25: -7.745967e-01, 7.745967e-01, 26: -7.745967e-01, 8.884592e-01, 27: -7.745967e-01, 9.604913e-01, 28: -7.745967e-01, 9.938320e-01, 29: -6.211029e-01, -7.745967e-01, 30: -6.211029e-01, 0.000000e+00, 31: -6.211029e-01, 7.745967e-01, 32: -4.342437e-01, -9.604913e-01, 33: -4.342437e-01, -7.745967e-01, 34: -4.342437e-01, -4.342437e-01, 35: -4.342437e-01, 0.000000e+00, 36: -4.342437e-01, 4.342437e-01, 37: -4.342437e-01, 7.745967e-01, 38: -4.342437e-01, 9.604913e-01, 39: -2.233867e-01, -7.745967e-01, 40: -2.233867e-01, 0.000000e+00, 41: -2.233867e-01, 7.745967e-01, 42: 0.000000e+00, -9.938320e-01, 43: 0.000000e+00, -9.604913e-01, 44: 0.000000e+00, -8.884592e-01, 45: 0.000000e+00, -7.745967e-01, 46: 0.000000e+00, -6.211029e-01, 47: 0.000000e+00, -4.342437e-01, 48: 0.000000e+00, -2.233867e-01, 49: 0.000000e+00, 0.000000e+00, 50: 0.000000e+00, 2.233867e-01, 51: 0.000000e+00, 4.342437e-01, 52: 0.000000e+00, 6.211029e-01, 53: 0.000000e+00, 7.745967e-01, 54: 0.000000e+00, 8.884592e-01, 55: 0.000000e+00, 9.604913e-01, 56: 0.000000e+00, 9.938320e-01, 57: 2.233867e-01, -7.745967e-01, 58: 2.233867e-01, 0.000000e+00, 59: 2.233867e-01, 7.745967e-01, 60: 4.342437e-01, -9.604913e-01, 61: 4.342437e-01, -7.745967e-01, 62: 4.342437e-01, -4.342437e-01, 63: 4.342437e-01, 0.000000e+00, 64: 4.342437e-01, 4.342437e-01, 65: 4.342437e-01, 7.745967e-01, 66: 4.342437e-01, 9.604913e-01, 67: 6.211029e-01, -7.745967e-01, 68: 6.211029e-01, 0.000000e+00, 69: 6.211029e-01, 7.745967e-01, 70: 7.745967e-01, -9.938320e-01, 71: 7.745967e-01, -9.604913e-01, 72: 7.745967e-01, -8.884592e-01, 73: 7.745967e-01, -7.745967e-01, 74: 7.745967e-01, -6.211029e-01, 75: 7.745967e-01, -4.342437e-01, 76: 7.745967e-01, -2.233867e-01, 77: 7.745967e-01, 0.000000e+00, 78: 7.745967e-01, 2.233867e-01, 79: 7.745967e-01, 4.342437e-01, 80: 7.745967e-01, 6.211029e-01, 81: 7.745967e-01, 7.745967e-01, 82: 7.745967e-01, 8.884592e-01, 83: 7.745967e-01, 9.604913e-01, 84: 7.745967e-01, 9.938320e-01, 85: 8.884592e-01, -7.745967e-01, 86: 8.884592e-01, 0.000000e+00, 87: 8.884592e-01, 7.745967e-01, 88: 9.604913e-01, -9.604913e-01, 89: 9.604913e-01, -7.745967e-01, 90: 9.604913e-01, -4.342437e-01, 91: 9.604913e-01, 0.000000e+00, 92: 9.604913e-01, 4.342437e-01, 93: 9.604913e-01, 7.745967e-01, 94: 9.604913e-01, 9.604913e-01, 95: 9.938320e-01, -7.745967e-01, 96: 9.938320e-01, 0.000000e+00, 97: 9.938320e-01, 7.745967e-01, SPARSE_GRID_MIXED_POINT_TEST SPARSE_GRID_MIXED_POINT returns an array containing the points that form a multidimensional sparse grid of mixed factors. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 17 2 17 For LEVEL_MAX = 4 1: -1.000000e+00, -1.000000e+00, 2: -1.000000e+00, -7.071068e-01, 3: -1.000000e+00, -3.826834e-01, 4: -1.000000e+00, 0.000000e+00, 5: -1.000000e+00, 3.826834e-01, 6: -1.000000e+00, 7.071068e-01, 7: -1.000000e+00, 1.000000e+00, 8: -9.238795e-01, 0.000000e+00, 9: -7.071068e-01, -1.000000e+00, 10: -7.071068e-01, -7.071068e-01, 11: -7.071068e-01, 0.000000e+00, 12: -7.071068e-01, 7.071068e-01, 13: -7.071068e-01, 1.000000e+00, 14: -3.826834e-01, -1.000000e+00, 15: -3.826834e-01, 0.000000e+00, 16: -3.826834e-01, 1.000000e+00, 17: 0.000000e+00, -1.000000e+00, 18: 0.000000e+00, -9.238795e-01, 19: 0.000000e+00, -7.071068e-01, 20: 0.000000e+00, -3.826834e-01, 21: 0.000000e+00, 0.000000e+00, 22: 0.000000e+00, 3.826834e-01, 23: 0.000000e+00, 7.071068e-01, 24: 0.000000e+00, 9.238795e-01, 25: 0.000000e+00, 1.000000e+00, 26: 3.826834e-01, -1.000000e+00, 27: 3.826834e-01, 0.000000e+00, 28: 3.826834e-01, 1.000000e+00, 29: 7.071068e-01, -1.000000e+00, 30: 7.071068e-01, -7.071068e-01, 31: 7.071068e-01, 0.000000e+00, 32: 7.071068e-01, 7.071068e-01, 33: 7.071068e-01, 1.000000e+00, 34: 9.238795e-01, 0.000000e+00, 35: 1.000000e+00, -1.000000e+00, 36: 1.000000e+00, -7.071068e-01, 37: 1.000000e+00, -3.826834e-01, 38: 1.000000e+00, 0.000000e+00, 39: 1.000000e+00, 3.826834e-01, 40: 1.000000e+00, 7.071068e-01, 41: 1.000000e+00, 1.000000e+00, SPARSE_GRID_MIXED_POINT_TESTS Normal end of execution. SPARSE_GRID_MIXED_SIZE_TESTS MATLAB version Call SPARSE_GRID_MIXED_SIZE_TEST with various arguments. All tests will use a point equality tolerance of 1.490116e-08 SPARSE_GRID_MIXED_SIZE_TEST SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a multidimensional sparse grid with mixed factors. SPARSE_GRID_MIXED_SIZE_TOTAL returns the number of points in a multidimensional sparse grid with mixed factors without checking for duplication. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 1 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 0 1 1 0 1 5 7 1 2 13 25 SPARSE_GRID_MIXED_SIZE_TEST SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a multidimensional sparse grid with mixed factors. SPARSE_GRID_MIXED_SIZE_TOTAL returns the number of points in a multidimensional sparse grid with mixed factors without checking for duplication. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 3 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 0 1 1 0 1 5 7 1 2 15 27 SPARSE_GRID_MIXED_SIZE_TEST SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a multidimensional sparse grid with mixed factors. SPARSE_GRID_MIXED_SIZE_TOTAL returns the number of points in a multidimensional sparse grid with mixed factors without checking for duplication. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 4 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 0 1 1 0 1 5 7 1 2 15 25 SPARSE_GRID_MIXED_SIZE_TEST SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a multidimensional sparse grid with mixed factors. SPARSE_GRID_MIXED_SIZE_TOTAL returns the number of points in a multidimensional sparse grid with mixed factors without checking for duplication. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 7 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 0 1 1 0 1 6 7 1 2 19 25 SPARSE_GRID_MIXED_SIZE_TEST SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a multidimensional sparse grid with mixed factors. SPARSE_GRID_MIXED_SIZE_TOTAL returns the number of points in a multidimensional sparse grid with mixed factors without checking for duplication. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 8 1.500000e+00 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 0 1 1 0 1 6 7 1 2 19 25 SPARSE_GRID_MIXED_SIZE_TEST SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a multidimensional sparse grid with mixed factors. SPARSE_GRID_MIXED_SIZE_TOTAL returns the number of points in a multidimensional sparse grid with mixed factors without checking for duplication. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 2 2 9 5.000000e-01 1.500000e+00 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 0 1 1 0 1 6 7 1 2 21 27 SPARSE_GRID_MIXED_SIZE_TEST SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a multidimensional sparse grid with mixed factors. SPARSE_GRID_MIXED_SIZE_TOTAL returns the number of points in a multidimensional sparse grid with mixed factors without checking for duplication. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 6 2.000000e+00 2 4 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 0 1 1 0 1 6 7 1 2 21 25 SPARSE_GRID_MIXED_SIZE_TEST SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a multidimensional sparse grid with mixed factors. SPARSE_GRID_MIXED_SIZE_TOTAL returns the number of points in a multidimensional sparse grid with mixed factors without checking for duplication. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 2 3 5 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 0 1 1 0 1 7 10 0 2 29 54 SPARSE_GRID_MIXED_SIZE_TEST SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a multidimensional sparse grid with mixed factors. SPARSE_GRID_MIXED_SIZE_TOTAL returns the number of points in a multidimensional sparse grid with mixed factors without checking for duplication. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 13 2 13 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 0 1 1 0 1 5 7 1 2 9 21 SPARSE_GRID_MIXED_SIZE_TEST SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a multidimensional sparse grid with mixed factors. SPARSE_GRID_MIXED_SIZE_TOTAL returns the number of points in a multidimensional sparse grid with mixed factors without checking for duplication. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 16 2 16 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 0 1 1 0 1 5 7 1 2 17 29 SPARSE_GRID_MIXED_SIZE_TEST SPARSE_GRID_MIXED_SIZE returns the number of distinct points in a multidimensional sparse grid with mixed factors. SPARSE_GRID_MIXED_SIZE_TOTAL returns the number of points in a multidimensional sparse grid with mixed factors without checking for duplication. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 17 2 17 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 0 1 1 0 1 5 7 1 2 13 25 2 3 25 63 3 4 41 129 SPARSE_GRID_MIXED_SIZE_TESTS Normal end of execution. SPARSE_GRID_MIXED_UNIQUE_INDEX_TESTS MATLAB version Call SPARSE_GRID_MIXED_UNIQUE_INDEX_TEST with various arguments. All tests will use a point equality tolerance of 1.490116e-08 SPARSE_GRID_MIXED_UNIQUE_INDEX_TEST SPARSE_GRID_MIXED_UNIQUE_INDEX returns a mapping between the nonunique and unique points in a sparse grid. Dimension Rule Alpha Beta 1 1 2 1 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 0 1 1 POINT UNIQUE 1 1 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 1 5 7 POINT UNIQUE 1 3 2 1 3 3 4 5 5 2 6 3 7 4 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 1 2 13 25 POINT UNIQUE 1 2 2 7 3 12 4 5 5 7 6 9 7 2 8 4 9 7 10 10 11 12 12 1 13 5 14 11 15 2 16 7 17 12 18 3 19 9 20 13 21 5 22 6 23 7 24 8 25 9 SPARSE_GRID_MIXED_UNIQUE_INDEX_TEST SPARSE_GRID_MIXED_UNIQUE_INDEX returns a mapping between the nonunique and unique points in a sparse grid. Dimension Rule Alpha Beta 1 1 2 3 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 0 1 1 POINT UNIQUE 1 1 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 1 5 7 POINT UNIQUE 1 3 2 1 3 3 4 5 5 2 6 3 7 4 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 1 2 15 27 POINT UNIQUE 1 2 2 8 3 14 4 6 5 8 6 10 7 2 8 4 9 8 10 12 11 14 12 1 13 6 14 13 15 2 16 8 17 14 18 3 19 10 20 15 21 5 22 6 23 7 24 8 25 9 26 10 27 11 SPARSE_GRID_MIXED_UNIQUE_INDEX_TEST SPARSE_GRID_MIXED_UNIQUE_INDEX returns a mapping between the nonunique and unique points in a sparse grid. Dimension Rule Alpha Beta 1 1 2 4 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 0 1 1 POINT UNIQUE 1 1 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 1 5 7 POINT UNIQUE 1 3 2 1 3 3 4 5 5 2 6 3 7 4 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 1 2 15 25 POINT UNIQUE 1 2 2 8 3 14 4 6 5 8 6 10 7 2 8 4 9 8 10 12 11 14 12 1 13 6 14 13 15 2 16 8 17 14 18 3 19 10 20 15 21 5 22 7 23 8 24 9 25 11 SPARSE_GRID_MIXED_UNIQUE_INDEX_TEST SPARSE_GRID_MIXED_UNIQUE_INDEX returns a mapping between the nonunique and unique points in a sparse grid. Dimension Rule Alpha Beta 1 1 2 7 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 0 1 1 POINT UNIQUE 1 1 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 1 6 7 POINT UNIQUE 1 3 2 1 3 3 4 6 5 2 6 4 7 5 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 1 2 19 25 POINT UNIQUE 1 2 2 8 3 17 4 7 5 10 6 12 7 2 8 5 9 8 10 15 11 17 12 1 13 7 14 16 15 3 16 10 17 18 18 4 19 12 20 19 21 6 22 9 23 11 24 13 25 14 SPARSE_GRID_MIXED_UNIQUE_INDEX_TEST SPARSE_GRID_MIXED_UNIQUE_INDEX returns a mapping between the nonunique and unique points in a sparse grid. Dimension Rule Alpha Beta 1 1 2 8 1.500000e+00 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 0 1 1 POINT UNIQUE 1 1 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 1 6 7 POINT UNIQUE 1 3 2 1 3 3 4 6 5 2 6 4 7 5 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 1 2 19 25 POINT UNIQUE 1 2 2 9 3 17 4 7 5 10 6 12 7 2 8 5 9 9 10 15 11 17 12 1 13 7 14 16 15 3 16 10 17 18 18 4 19 12 20 19 21 6 22 8 23 11 24 13 25 14 SPARSE_GRID_MIXED_UNIQUE_INDEX_TEST SPARSE_GRID_MIXED_UNIQUE_INDEX returns a mapping between the nonunique and unique points in a sparse grid. Dimension Rule Alpha Beta 1 2 2 9 5.000000e-01 1.500000e+00 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 0 1 1 POINT UNIQUE 1 1 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 1 6 7 POINT UNIQUE 1 4 2 1 3 4 4 6 5 2 6 3 7 5 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 1 2 21 27 POINT UNIQUE 1 4 2 12 3 19 4 8 5 11 6 14 7 1 8 4 9 6 10 12 11 16 12 19 13 21 14 2 15 8 16 17 17 3 18 11 19 18 20 5 21 14 22 20 23 7 24 9 25 10 26 13 27 15 SPARSE_GRID_MIXED_UNIQUE_INDEX_TEST SPARSE_GRID_MIXED_UNIQUE_INDEX returns a mapping between the nonunique and unique points in a sparse grid. Dimension Rule Alpha Beta 1 6 2.000000e+00 2 4 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 0 1 1 POINT UNIQUE 1 1 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 1 6 7 POINT UNIQUE 1 3 2 1 3 5 4 6 5 2 6 3 7 4 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 1 2 21 25 POINT UNIQUE 1 3 2 14 3 19 4 7 5 9 6 11 7 1 8 5 9 16 10 17 11 21 12 2 13 13 14 18 15 3 16 14 17 19 18 4 19 15 20 20 21 6 22 8 23 9 24 10 25 12 SPARSE_GRID_MIXED_UNIQUE_INDEX_TEST SPARSE_GRID_MIXED_UNIQUE_INDEX returns a mapping between the nonunique and unique points in a sparse grid. Dimension Rule Alpha Beta 1 1 2 2 3 5 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 0 1 1 POINT UNIQUE 1 1 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 1 7 10 POINT UNIQUE 1 4 2 1 3 4 4 7 5 2 6 4 7 6 8 3 9 4 10 5 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 0 2 29 54 POINT UNIQUE 1 15 2 3 3 15 4 27 5 9 6 15 7 21 8 13 9 15 10 17 11 3 12 6 13 15 14 24 15 27 16 1 17 9 18 25 19 3 20 15 21 27 22 5 23 21 24 29 25 7 26 9 27 11 28 15 29 19 30 21 31 23 32 2 33 13 34 26 35 3 36 15 37 27 38 4 39 17 40 28 41 8 42 13 43 20 44 9 45 15 46 21 47 10 48 17 49 22 50 12 51 14 52 15 53 16 54 18 SPARSE_GRID_MIXED_UNIQUE_INDEX_TEST SPARSE_GRID_MIXED_UNIQUE_INDEX returns a mapping between the nonunique and unique points in a sparse grid. Dimension Rule Alpha Beta 1 3 2 3 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 3 4 129 273 POINT UNIQUE 1 3 2 9 3 15 4 25 5 35 6 41 7 47 8 65 9 83 10 89 11 95 12 105 13 115 14 121 15 127 16 7 17 21 18 39 19 57 20 87 21 101 22 119 23 9 24 25 25 41 26 65 27 89 28 105 29 121 30 11 31 29 32 43 33 73 34 91 35 109 36 123 37 19 38 53 39 99 40 21 41 57 42 101 43 23 44 61 45 103 46 25 47 65 48 105 49 27 50 69 51 107 52 29 53 73 54 109 55 31 56 77 57 111 58 51 59 53 60 55 61 57 62 59 63 61 64 63 65 65 66 67 67 69 68 71 69 73 70 75 71 77 72 79 73 1 74 3 75 5 76 9 77 13 78 15 79 17 80 25 81 33 82 35 83 37 84 41 85 45 86 47 87 49 88 65 89 81 90 83 91 85 92 89 93 93 94 95 95 97 96 105 97 113 98 115 99 117 100 121 101 125 102 127 103 129 104 2 105 7 106 14 107 21 108 34 109 39 110 46 111 57 112 82 113 87 114 94 115 101 116 114 117 119 118 126 119 3 120 9 121 15 122 25 123 35 124 41 125 47 126 65 127 83 128 89 129 95 130 105 131 115 132 121 133 127 134 4 135 11 136 16 137 29 138 36 139 43 140 48 141 73 142 84 143 91 144 96 145 109 146 116 147 123 148 128 149 6 150 19 151 38 152 53 153 86 154 99 155 118 156 7 157 21 158 39 159 57 160 87 161 101 162 119 163 8 164 23 165 40 166 61 167 88 168 103 169 120 170 9 171 25 172 41 173 65 174 89 175 105 176 121 177 10 178 27 179 42 180 69 181 90 182 107 183 122 184 11 185 29 186 43 187 73 188 91 189 109 190 123 191 12 192 31 193 44 194 77 195 92 196 111 197 124 198 18 199 51 200 98 201 19 202 53 203 99 204 20 205 55 206 100 207 21 208 57 209 101 210 22 211 59 212 102 213 23 214 61 215 103 216 24 217 63 218 104 219 25 220 65 221 105 222 26 223 67 224 106 225 27 226 69 227 107 228 28 229 71 230 108 231 29 232 73 233 109 234 30 235 75 236 110 237 31 238 77 239 111 240 32 241 79 242 112 243 50 244 51 245 52 246 53 247 54 248 55 249 56 250 57 251 58 252 59 253 60 254 61 255 62 256 63 257 64 258 65 259 66 260 67 261 68 262 69 263 70 264 71 265 72 266 73 267 74 268 75 269 76 270 77 271 78 272 79 273 80 SPARSE_GRID_MIXED_UNIQUE_INDEX_TEST SPARSE_GRID_MIXED_UNIQUE_INDEX returns a mapping between the nonunique and unique points in a sparse grid. Dimension Rule Alpha Beta 1 13 2 13 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 3 4 33 97 POINT UNIQUE 1 2 2 7 3 12 4 17 5 22 6 27 7 32 8 5 9 15 10 25 11 7 12 17 13 27 14 9 15 19 16 29 17 5 18 15 19 25 20 7 21 17 22 27 23 9 24 19 25 29 26 14 27 15 28 16 29 17 30 18 31 19 32 20 33 2 34 7 35 12 36 17 37 22 38 27 39 32 40 1 41 5 42 11 43 15 44 21 45 25 46 31 47 2 48 7 49 12 50 17 51 22 52 27 53 32 54 3 55 9 56 13 57 19 58 23 59 29 60 33 61 5 62 15 63 25 64 7 65 17 66 27 67 9 68 19 69 29 70 4 71 14 72 24 73 5 74 15 75 25 76 6 77 16 78 26 79 7 80 17 81 27 82 8 83 18 84 28 85 9 86 19 87 29 88 10 89 20 90 30 91 14 92 15 93 16 94 17 95 18 96 19 97 20 SPARSE_GRID_MIXED_UNIQUE_INDEX_TEST SPARSE_GRID_MIXED_UNIQUE_INDEX returns a mapping between the nonunique and unique points in a sparse grid. Dimension Rule Alpha Beta 1 16 2 16 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 3 4 97 241 POINT UNIQUE 1 2 2 7 3 12 4 21 5 30 6 35 7 40 8 49 9 58 10 63 11 68 12 77 13 86 14 91 15 96 16 5 17 17 18 33 19 45 20 61 21 73 22 89 23 7 24 21 25 35 26 49 27 63 28 77 29 91 30 9 31 25 32 37 33 53 34 65 35 81 36 93 37 15 38 43 39 71 40 17 41 45 42 73 43 19 44 47 45 75 46 21 47 49 48 77 49 23 50 51 51 79 52 25 53 53 54 81 55 27 56 55 57 83 58 42 59 43 60 44 61 45 62 46 63 47 64 48 65 49 66 50 67 51 68 52 69 53 70 54 71 55 72 56 73 2 74 7 75 12 76 21 77 30 78 35 79 40 80 49 81 58 82 63 83 68 84 77 85 86 86 91 87 96 88 1 89 5 90 11 91 17 92 29 93 33 94 39 95 45 96 57 97 61 98 67 99 73 100 85 101 89 102 95 103 2 104 7 105 12 106 21 107 30 108 35 109 40 110 49 111 58 112 63 113 68 114 77 115 86 116 91 117 96 118 3 119 9 120 13 121 25 122 31 123 37 124 41 125 53 126 59 127 65 128 69 129 81 130 87 131 93 132 97 133 4 134 15 135 32 136 43 137 60 138 71 139 88 140 5 141 17 142 33 143 45 144 61 145 73 146 89 147 6 148 19 149 34 150 47 151 62 152 75 153 90 154 7 155 21 156 35 157 49 158 63 159 77 160 91 161 8 162 23 163 36 164 51 165 64 166 79 167 92 168 9 169 25 170 37 171 53 172 65 173 81 174 93 175 10 176 27 177 38 178 55 179 66 180 83 181 94 182 14 183 42 184 70 185 15 186 43 187 71 188 16 189 44 190 72 191 17 192 45 193 73 194 18 195 46 196 74 197 19 198 47 199 75 200 20 201 48 202 76 203 21 204 49 205 77 206 22 207 50 208 78 209 23 210 51 211 79 212 24 213 52 214 80 215 25 216 53 217 81 218 26 219 54 220 82 221 27 222 55 223 83 224 28 225 56 226 84 227 42 228 43 229 44 230 45 231 46 232 47 233 48 234 49 235 50 236 51 237 52 238 53 239 54 240 55 241 56 SPARSE_GRID_MIXED_UNIQUE_INDEX_TEST SPARSE_GRID_MIXED_UNIQUE_INDEX returns a mapping between the nonunique and unique points in a sparse grid. Dimension Rule Alpha Beta 1 17 2 17 LEVEL_MIN LEVEL_MAX POINT_NUM POINT_NUM Unique Total 3 4 41 129 POINT UNIQUE 1 21 2 4 3 38 4 11 5 31 6 15 7 27 8 21 9 4 10 38 11 11 12 31 13 17 14 1 15 35 16 9 17 29 18 25 19 7 20 41 21 13 22 33 23 21 24 4 25 38 26 17 27 1 28 35 29 25 30 7 31 41 32 19 33 2 34 36 35 23 36 6 37 40 38 21 39 17 40 25 41 19 42 23 43 20 44 22 45 21 46 4 47 38 48 11 49 31 50 15 51 27 52 8 53 34 54 21 55 4 56 38 57 11 58 31 59 15 60 27 61 17 62 1 63 35 64 9 65 29 66 14 67 26 68 25 69 7 70 41 71 13 72 33 73 16 74 28 75 21 76 4 77 38 78 11 79 31 80 17 81 1 82 35 83 9 84 29 85 25 86 7 87 41 88 13 89 33 90 19 91 2 92 36 93 10 94 30 95 23 96 6 97 40 98 12 99 32 100 21 101 4 102 38 103 17 104 1 105 35 106 25 107 7 108 41 109 19 110 2 111 36 112 23 113 6 114 40 115 20 116 3 117 37 118 22 119 5 120 39 121 21 122 17 123 25 124 19 125 23 126 20 127 22 128 18 129 24 SPARSE_GRID_MIXED_UNIQUE_INDEX_TESTS Normal end of execution. SPARSE_GRID_MIXED_WEIGHT_TESTS MATLAB version Call SPARSE_GRID_MIXED_WEIGHT with various arguments. All tests will use a point equality tolerance of 1.490116e-08 SPARSE_GRID_MIXED_WEIGHT_TEST: Compute the weights of a sparse grid. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 1 As a simple test, sum these weights. They should sum to exactly 4.000000 Level Weight sum Expected sum Difference 0 4.000000e+00 4.000000e+00 0.000000e+00 1 4.000000e+00 4.000000e+00 0.000000e+00 2 4.000000e+00 4.000000e+00 0.000000e+00 SPARSE_GRID_MIXED_WEIGHT_TEST: Compute the weights of a sparse grid. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 3 As a simple test, sum these weights. They should sum to exactly 4.000000 Level Weight sum Expected sum Difference 0 4.000000e+00 4.000000e+00 0.000000e+00 1 4.000000e+00 4.000000e+00 0.000000e+00 2 4.000000e+00 4.000000e+00 4.440892e-16 SPARSE_GRID_MIXED_WEIGHT_TEST: Compute the weights of a sparse grid. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 4 As a simple test, sum these weights. They should sum to exactly 4.000000 Level Weight sum Expected sum Difference 0 4.000000e+00 4.000000e+00 8.881784e-16 1 4.000000e+00 4.000000e+00 8.881784e-16 2 4.000000e+00 4.000000e+00 3.552714e-15 SPARSE_GRID_MIXED_WEIGHT_TEST: Compute the weights of a sparse grid. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 7 As a simple test, sum these weights. They should sum to exactly 2.000000 Level Weight sum Expected sum Difference 0 2.000000e+00 2.000000e+00 0.000000e+00 1 2.000000e+00 2.000000e+00 0.000000e+00 2 2.000000e+00 2.000000e+00 4.440892e-16 SPARSE_GRID_MIXED_WEIGHT_TEST: Compute the weights of a sparse grid. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 8 1.500000e+00 As a simple test, sum these weights. They should sum to exactly 2.658681 Level Weight sum Expected sum Difference 0 2.658681e+00 2.658681e+00 4.440892e-16 1 2.658681e+00 2.658681e+00 4.440892e-16 2 2.658681e+00 2.658681e+00 4.440892e-16 SPARSE_GRID_MIXED_WEIGHT_TEST: Compute the weights of a sparse grid. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 2 2 9 5.000000e-01 1.500000e+00 As a simple test, sum these weights. They should sum to exactly 3.141593 Level Weight sum Expected sum Difference 0 3.141593e+00 3.141593e+00 4.440892e-16 1 3.141593e+00 3.141593e+00 0.000000e+00 2 3.141593e+00 3.141593e+00 4.440892e-15 SPARSE_GRID_MIXED_WEIGHT_TEST: Compute the weights of a sparse grid. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 6 2.000000e+00 2 4 As a simple test, sum these weights. They should sum to exactly 1.772454 Level Weight sum Expected sum Difference 0 1.772454e+00 1.772454e+00 4.440892e-16 1 1.772454e+00 1.772454e+00 8.881784e-16 2 1.772454e+00 1.772454e+00 1.110223e-15 SPARSE_GRID_MIXED_WEIGHT_TEST: Compute the weights of a sparse grid. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 1 2 2 3 5 As a simple test, sum these weights. They should sum to exactly 7.089815 Level Weight sum Expected sum Difference 0 7.089815e+00 7.089815e+00 8.881784e-16 1 7.089815e+00 7.089815e+00 1.776357e-15 2 7.089815e+00 7.089815e+00 1.776357e-15 SPARSE_GRID_MIXED_WEIGHT_TEST: Compute the weights of a sparse grid. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 3 2 3 As a simple test, sum these weights. They should sum to exactly 4.000000 Level Weight sum Expected sum Difference 0 4.000000e+00 4.000000e+00 0.000000e+00 1 4.000000e+00 4.000000e+00 0.000000e+00 2 4.000000e+00 4.000000e+00 0.000000e+00 3 4.000000e+00 4.000000e+00 0.000000e+00 4 4.000000e+00 4.000000e+00 8.881784e-16 SPARSE_GRID_MIXED_WEIGHT_TEST: Compute the weights of a sparse grid. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 13 2 13 As a simple test, sum these weights. They should sum to exactly 4.000000 Level Weight sum Expected sum Difference 0 4.000000e+00 4.000000e+00 0.000000e+00 1 4.000000e+00 4.000000e+00 0.000000e+00 2 4.000000e+00 4.000000e+00 0.000000e+00 3 4.000000e+00 4.000000e+00 8.881784e-16 4 4.000000e+00 4.000000e+00 8.881784e-16 SPARSE_GRID_MIXED_WEIGHT_TEST: Compute the weights of a sparse grid. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 16 2 16 As a simple test, sum these weights. They should sum to exactly 4.000000 Level Weight sum Expected sum Difference 0 4.000000e+00 4.000000e+00 0.000000e+00 1 4.000000e+00 4.000000e+00 0.000000e+00 2 4.000000e+00 4.000000e+00 0.000000e+00 3 4.000000e+00 4.000000e+00 0.000000e+00 4 4.000000e+00 4.000000e+00 8.881784e-16 SPARSE_GRID_MIXED_WEIGHT_TEST: Compute the weights of a sparse grid. Each sparse grid is of spatial dimension DIM_NUM, and is made up of product grids of levels up to LEVEL_MAX. Dimension Rule Alpha Beta 1 17 2 17 As a simple test, sum these weights. They should sum to exactly 4.000000 Level Weight sum Expected sum Difference 0 4.000000e+00 4.000000e+00 0.000000e+00 1 4.000000e+00 4.000000e+00 0.000000e+00 2 4.000000e+00 4.000000e+00 8.881784e-16 3 4.000000e+00 4.000000e+00 3.996803e-15 4 4.000000e+00 4.000000e+00 1.154632e-14 SPARSE_GRID_MIXED_WEIGHT_TESTS Normal end of execution. SPARSE_GRID_MIXED_WRITE_TESTS MATLAB version Call SPARSE_GRID_MIXED_WRITE_TEST with various arguments. All tests will use a point equality tolerance of 1.490116e-08 SPARSE_GRID_MIXED_WRITE_TEST SPARSE_GRID_MIXED_WRITE writes a sparse grid rule to A, B, R, W and X files. SPARSE_GRID_MIXED_WRITE: Wrote the A file = "sparse_grid_mixed_d2_l2_ccxcc_a.txt". Wrote the B file = "sparse_grid_mixed_d2_l2_ccxcc_b.txt". Wrote the R file = "sparse_grid_mixed_d2_l2_ccxcc_r.txt". Wrote the W file = "sparse_grid_mixed_d2_l2_ccxcc_w.txt". Wrote the X file = "sparse_grid_mixed_d2_l2_ccxcc_x.txt". SPARSE_GRID_MIXED_WRITE_TEST SPARSE_GRID_MIXED_WRITE writes a sparse grid rule to A, B, R, W and X files. SPARSE_GRID_MIXED_WRITE: Wrote the A file = "sparse_grid_mixed_d2_l3_ccxgp_a.txt". Wrote the B file = "sparse_grid_mixed_d2_l3_ccxgp_b.txt". Wrote the R file = "sparse_grid_mixed_d2_l3_ccxgp_r.txt". Wrote the W file = "sparse_grid_mixed_d2_l3_ccxgp_w.txt". Wrote the X file = "sparse_grid_mixed_d2_l3_ccxgp_x.txt". SPARSE_GRID_MIXED_WRITE_TEST SPARSE_GRID_MIXED_WRITE writes a sparse grid rule to A, B, R, W and X files. SPARSE_GRID_MIXED_WRITE: Wrote the A file = "sparse_grid_mixed_d2_l2_ccxgl_a.txt". Wrote the B file = "sparse_grid_mixed_d2_l2_ccxgl_b.txt". Wrote the R file = "sparse_grid_mixed_d2_l2_ccxgl_r.txt". Wrote the W file = "sparse_grid_mixed_d2_l2_ccxgl_w.txt". Wrote the X file = "sparse_grid_mixed_d2_l2_ccxgl_x.txt". SPARSE_GRID_MIXED_WRITE_TEST SPARSE_GRID_MIXED_WRITE writes a sparse grid rule to A, B, R, W and X files. SPARSE_GRID_MIXED_WRITE: Wrote the A file = "sparse_grid_mixed_d2_l2_ccxlg_a.txt". Wrote the B file = "sparse_grid_mixed_d2_l2_ccxlg_b.txt". Wrote the R file = "sparse_grid_mixed_d2_l2_ccxlg_r.txt". Wrote the W file = "sparse_grid_mixed_d2_l2_ccxlg_w.txt". Wrote the X file = "sparse_grid_mixed_d2_l2_ccxlg_x.txt". SPARSE_GRID_MIXED_WRITE_TEST SPARSE_GRID_MIXED_WRITE writes a sparse grid rule to A, B, R, W and X files. SPARSE_GRID_MIXED_WRITE: Wrote the A file = "sparse_grid_mixed_d2_l2_ccxglg_a.txt". Wrote the B file = "sparse_grid_mixed_d2_l2_ccxglg_b.txt". Wrote the R file = "sparse_grid_mixed_d2_l2_ccxglg_r.txt". Wrote the W file = "sparse_grid_mixed_d2_l2_ccxglg_w.txt". Wrote the X file = "sparse_grid_mixed_d2_l2_ccxglg_x.txt". SPARSE_GRID_MIXED_WRITE_TEST SPARSE_GRID_MIXED_WRITE writes a sparse grid rule to A, B, R, W and X files. SPARSE_GRID_MIXED_WRITE: Wrote the A file = "sparse_grid_mixed_d2_l2_f2xgj_a.txt". Wrote the B file = "sparse_grid_mixed_d2_l2_f2xgj_b.txt". Wrote the R file = "sparse_grid_mixed_d2_l2_f2xgj_r.txt". Wrote the W file = "sparse_grid_mixed_d2_l2_f2xgj_w.txt". Wrote the X file = "sparse_grid_mixed_d2_l2_f2xgj_x.txt". SPARSE_GRID_MIXED_WRITE_TEST SPARSE_GRID_MIXED_WRITE writes a sparse grid rule to A, B, R, W and X files. SPARSE_GRID_MIXED_WRITE: Wrote the A file = "sparse_grid_mixed_d2_l2_gghxgl_a.txt". Wrote the B file = "sparse_grid_mixed_d2_l2_gghxgl_b.txt". Wrote the R file = "sparse_grid_mixed_d2_l2_gghxgl_r.txt". Wrote the W file = "sparse_grid_mixed_d2_l2_gghxgl_w.txt". Wrote the X file = "sparse_grid_mixed_d2_l2_gghxgl_x.txt". SPARSE_GRID_MIXED_WRITE_TEST SPARSE_GRID_MIXED_WRITE writes a sparse grid rule to A, B, R, W and X files. SPARSE_GRID_MIXED_WRITE: Wrote the A file = "sparse_grid_mixed_d3_l2_ccxf2xgh_a.txt". Wrote the B file = "sparse_grid_mixed_d3_l2_ccxf2xgh_b.txt". Wrote the R file = "sparse_grid_mixed_d3_l2_ccxf2xgh_r.txt". Wrote the W file = "sparse_grid_mixed_d3_l2_ccxf2xgh_w.txt". Wrote the X file = "sparse_grid_mixed_d3_l2_ccxf2xgh_x.txt". SPARSE_GRID_MIXED_WRITE_TEST SPARSE_GRID_MIXED_WRITE writes a sparse grid rule to A, B, R, W and X files. SPARSE_GRID_MIXED_WRITE: Wrote the A file = "sparse_grid_mixed_d2_l4_gpxgp_a.txt". Wrote the B file = "sparse_grid_mixed_d2_l4_gpxgp_b.txt". Wrote the R file = "sparse_grid_mixed_d2_l4_gpxgp_r.txt". Wrote the W file = "sparse_grid_mixed_d2_l4_gpxgp_w.txt". Wrote the X file = "sparse_grid_mixed_d2_l4_gpxgp_x.txt". SPARSE_GRID_MIXED_WRITE_TEST SPARSE_GRID_MIXED_WRITE writes a sparse grid rule to A, B, R, W and X files. SPARSE_GRID_MIXED_WRITE: Wrote the A file = "sparse_grid_mixed_d2_l4_gpsexgpse_a.txt". Wrote the B file = "sparse_grid_mixed_d2_l4_gpsexgpse_b.txt". Wrote the R file = "sparse_grid_mixed_d2_l4_gpsexgpse_r.txt". Wrote the W file = "sparse_grid_mixed_d2_l4_gpsexgpse_w.txt". Wrote the X file = "sparse_grid_mixed_d2_l4_gpsexgpse_x.txt". SPARSE_GRID_MIXED_WRITE_TEST SPARSE_GRID_MIXED_WRITE writes a sparse grid rule to A, B, R, W and X files. SPARSE_GRID_MIXED_WRITE: Wrote the A file = "sparse_grid_mixed_d2_l4_gpmexgpme_a.txt". Wrote the B file = "sparse_grid_mixed_d2_l4_gpmexgpme_b.txt". Wrote the R file = "sparse_grid_mixed_d2_l4_gpmexgpme_r.txt". Wrote the W file = "sparse_grid_mixed_d2_l4_gpmexgpme_w.txt". Wrote the X file = "sparse_grid_mixed_d2_l4_gpmexgpme_x.txt". SPARSE_GRID_MIXED_WRITE_TEST SPARSE_GRID_MIXED_WRITE writes a sparse grid rule to A, B, R, W and X files. SPARSE_GRID_MIXED_WRITE: Wrote the A file = "sparse_grid_mixed_d2_l4_ccnxccn_a.txt". Wrote the B file = "sparse_grid_mixed_d2_l4_ccnxccn_b.txt". Wrote the R file = "sparse_grid_mixed_d2_l4_ccnxccn_r.txt". Wrote the W file = "sparse_grid_mixed_d2_l4_ccnxccn_w.txt". Wrote the X file = "sparse_grid_mixed_d2_l4_ccnxccn_x.txt". SPARSE_GRID_MIXED_WRITE_TESTS Normal end of execution. sparse_grid_mixed_test(): Normal end of execution. 16-Jan-2023 22:27:54